Upload
others
View
3
Download
0
Embed Size (px)
Citation preview
t(JJ ~ h
x Ashy~ A
tj Q ~ QyJ Pt- hf1rs =(b()~
~u l f0f C) ~ ( AU 6) ( (fj C) i ~ (Mb S I) 6k ac
~ f (b Uc) ~ (~(fj) LJ (A 0()
ft ul Cjn c)~ (A Uf)) ( lA-U C)
XE- Pt u(6(1( ) C~h iA i E A f J x c=Gn C
( t A- yEO ~j XE (fi
~ ~ X G- n lAfG~ A I f- ur~
r(C-~UC
1 ) J n ( fJ c Pr U ( ftn c
J
i S (WJ QI l (MLJC ) j
J
i [i~
c -
cent~ =- iJ
f Fe-Alprl 1lt
(PTJ~)( ~_ f C n~(
(r- n traquo1 A( lJ eshy
~nlt PiAu _
X9 Ch) Qj ( f(l6) = (A6)u t6fr) ~ ~ f (A-V6) (P-(lfb)
I
E t
2 x~ 0 X yenp ) Y ~ (f) h )A
e(bfU(P )
2 x ~ (~b) ~J (f~f)
X t frt) LA j lAX E- l~~ P1 )
( I ~ l il- ) ( )1 - l ~ I u )
xPh-r
---b-irbj- fi I~~(-l--- _I~~~ - _ J
1- shy
M~
- -~ f---(J~~] ~ Y--(~~~(J-=~~--
y f- -~ V lt --~tfS IA x Eh Y --r( - - -I-
( t ) ( igt 0) r-b I 1
- ~ ~
V X ~ IX
V E CA(C
I - i (
1 r 1
tI6 r rcA (Qi)b) U C -- -
u l-AtQ)
x H (-) (fJu (t i rh- 0 -- -r~ I H)J shy
r-
x e (rmr~ IU I fi -j shy
I tlt f- l~f J E
x- c - P l
I D X F
evr- -J
~rAP)~L~_CK0 I
b~fl-
(
lt - I j
t
f T f
t r _ Cbjl
Y i vX E (G)
x (~) rl 51 (~J 1- ~ J (t~ nY((~)
Or ~ kf ltmiddot t Ji v I e- J )~
I
X ( )1 J f~ l D
9 ( ) Co I r- gt ) f l 0 n~- rth J rd b ) (-1 0 i
)(0
C-Y(r~~ j ~
I -
~
I I
C_ (i ri fdEJ lt r v
t l~ 0
Ih~ Y
~ f J ~) o JJ~~ cp ~0_
1 ~J HI I--(t1-~ 1 0 0-
-~eV_J~~Ob f)~IA~l1 l i h Q
h ~S~
~Q e ~ (c d)
l
t~d
( I I) Fgt l
shy shy ~ _i
j
lrf fl r
I - I f-
l~UC) J
__ ~_2lt71j --A~ ~ t A
~~__ ~_0
i-Ax-gshy
_(~-ij
R~
J~ ~
_-middot1
E
I y~l
I _--u r
1- y
( 4 e- (1 Ie --I
u
DAmiddotmiddotmiddot ~ middotfIc+ft ~u rrgtJ JQLl~
ldegfJ5 o-yenf~ h~1~t
(3 -=~f1~6 bullA~0~S-A~~~~ftA~jb~j laquo
]If~middot oj v ~
--- -0 ~
tr
- - middot-ft- -shyLmiddot ~(~ ampJ~ ff)rh-~Iltx__6p-uJ~ 1)__ _ p(~middot~r (IJ D] 1-shy
)
-- l ~ ~q(~ J
n vYl shy
I
i 1-I
r
( f-_c l VI
OIKcf _t (1 IJ -~ ~IQ) ~)v~JJ
~ fc ~A
ft (GiG) rfVlt ~-1Qpe4gt~elLu6~
2 lAM~rUUA- shy
J1 shy
A~~ CAl e-) C j
(
j I
(S)
j -
(~) I
~ c hA-
( [l ~ J
-
j
J
l
e I
Iermiddot1 I-v
1
( c c-) --
0) B I e~~ r
I
C ( Y~ 1-~ J j ~
I
~ l 0 b) (-- ---
rlt
i~(1) I _1 0 li~ ) 7 - tshy-l
)j)t 17-f1~ t
-i
klt txt
)( 1~~ ) t-~
19-~Ilt~~ (-gtSlx-t) J - i lsj lYJ)
( Y - t) X) t~
t ~
~-~ l~l ~) c-J I
I I I Y l IX ) (~
n
l~ ~ (XI))
lX(
1
J
J
I )~iI ~gt ~-- c ~i ~ treg J I W~ 01 ltxj - -I~
J J
l fL~ ir~ ) jet ) r~ 0R
Grr) Ir ~ 0 ) - ~ eli DIgt
r~f~ A ) lttl (J ~_)
1 ( I J c
-j
( ~
- ) C- ()70 7( gtJ ~ I
i~lt I -- - r I
I j
- ] -w - ) -- j r
I 1 I t fI t __ J
~(
4 1 ~ -- J
- - ~~- ---
v~ middotmiddotmiddot~t
- _I
~
~ ~~-- ~--
- j- shy
)0 ~r tTl
--t
t -j lr0 (i
~i -Y -1 ~~0 +
(0 ~~ r - It Itmiddot- lshy I I ~
~bull k~L lt~ I
v )t~ltl $ l J lt1
~~ ) r j shy
I t i ~ - 1 f
shy -- lt Ashy~ 2 1 -
J
l
1 v
t1
-
I 0 --Ch it ~~
0~ - J shy I -
j 0-
-- I t 7I J 1 J
t ~ 1
r
( r 11 11shyl
i
I I
)
-~ ~) jr- r~ A 5tTgt - ~-- 1] _shy -
I - r
t ~ A l~_- p-
C~ t7 f~)-- _ ~jiX)- -
~A=JS- J = Y-
i i I
c -t E- ( t r- f)~ y ( (11 )J t - ( (JJ)
~E ((0J
X G- f- Ii )lt c D ~ C ~ -1 e D J
lf)j)E A-x( (~j) amp- GxCgt
t PyL
t- (-ty Craquo (
l L
i I 0~)~ ) y )-7shy
t ~ lY~)
Clt - l t Cmiddot
I Ii_ bull-lt F V tI 1 Ii (I )
V Y ( ( I~ c i~-4 J- (-b
l~- t ~) y J
imiddotJ
f lQ)
~ I
1 ( ~ laquo~J V J J J
1 t J
OC06
~
0 7I r c) JGlt lmiddot -r
) )
r) gt ( - --~
)
shy
(
(
~ilt Z - LA
-) J I( j ( -
~i- _y~~f~ ~j~ ~ ~ A~~A
~~ (~ ls) Ci_fshy~~~J- t]~(t)~~
r--c- f ~ ~~
- - - ~-- bull -shy
Cflt(V ~([~e~~- f K JO-~
V
-Ij--XtAshy
))_ jtt_~ _~~
X-y
v CJ lt feshy
___ _ _ __r~middot _ ___ _~_
helfBbAh c~Jn
shy
L~v-1 - l
~ ~ ~y-
t - ~I
1 E C~
- - vJ - )j I
J
I A ~ ~ - ~
(rvjl
~C C1
( l
)( T
j
~ v -- 11 lt-J ~
(~ lu ~ 00 n f-~J~ J
f ~ 12 cent1 D~-gtl (
l
[
8 ~-=-~~i
( nfl2bc[r6 ~1vl kC
t ~ ex (x~c) - -
-~ kJ)1~iKlftYKlA (~l(-J~_C~Jr~tgt~x lLJi fr(t ~i1cent 1)) e biyI--r) lt2
rshy1
shy
~
lt)-
~(Almiddot Pc~
rJ- -~p~tA - - shy
I
shy (-j) -r---
I
r T I
1 ~_
0 1 1t b( 1 tlt E 1 ~E Z
K J ~ -- ~ ~
reg (jj P
r-~A~
( -oJ -J 11
D r )J ] ~~-~
(i) A Y =1-
+ (
~ J
~+11
+1 -t ~ 7 )
I
)J
j
tlJ + b1 t bf i (
~ ( ~ ~l t t bc
l rr y) +Sc
+- I gtlt0 = xfc I ~LX ~J E-t L~ JOx 1 )eA ) +( 1+ b~~~ shy
( J J ) - -p
I-- -h_ e ytbX - J It( I -shy-I It ~t-M I
J
Ie E - ~ -1 f 1+ 1 l IAI f ~r t - b X )
j
- =r~ - GX cft I ~ s -t) shy
~ r
t-t1 01 J
11 I-=~ I jh v - 1 - shy
I 1 ~ ~ I
o Aj
A~ J Q
(l- E2J lltJ eL~ I)
_)1(K~
Jlt- j X y ~ t
4-shy
sA i ~6 t
f
C
yS -~7
t )l - ~tL ~l X J ~f
1
J ~ n f t-~ - I - fmiddot~) ~ J J
j ~ J shy
middot1
---_
_r
--
-
~ - - ~l ~5 ~ )~-~ ~
1
l __-l
~ )
I
~ ~ A 2~ l ~ ~ l =IV
A-- fC ~1Jfn
(x D
) ~
0 -
i - )
4middot
~
~
_ IJ I f -~-
i -) ~
--- -
i
( ~
-~ r- t
~-- ~lS c f j VI t
~ A ~ J
- --~~-
I A _1 L
~ Y -)lt-2 A + shy
(shy
_J -L
--Ii
~
- l~
1 r
_)
11VV
0
-
~1
___t
1
-~
) 1))
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
cent~ =- iJ
f Fe-Alprl 1lt
(PTJ~)( ~_ f C n~(
(r- n traquo1 A( lJ eshy
~nlt PiAu _
X9 Ch) Qj ( f(l6) = (A6)u t6fr) ~ ~ f (A-V6) (P-(lfb)
I
E t
2 x~ 0 X yenp ) Y ~ (f) h )A
e(bfU(P )
2 x ~ (~b) ~J (f~f)
X t frt) LA j lAX E- l~~ P1 )
( I ~ l il- ) ( )1 - l ~ I u )
xPh-r
---b-irbj- fi I~~(-l--- _I~~~ - _ J
1- shy
M~
- -~ f---(J~~] ~ Y--(~~~(J-=~~--
y f- -~ V lt --~tfS IA x Eh Y --r( - - -I-
( t ) ( igt 0) r-b I 1
- ~ ~
V X ~ IX
V E CA(C
I - i (
1 r 1
tI6 r rcA (Qi)b) U C -- -
u l-AtQ)
x H (-) (fJu (t i rh- 0 -- -r~ I H)J shy
r-
x e (rmr~ IU I fi -j shy
I tlt f- l~f J E
x- c - P l
I D X F
evr- -J
~rAP)~L~_CK0 I
b~fl-
(
lt - I j
t
f T f
t r _ Cbjl
Y i vX E (G)
x (~) rl 51 (~J 1- ~ J (t~ nY((~)
Or ~ kf ltmiddot t Ji v I e- J )~
I
X ( )1 J f~ l D
9 ( ) Co I r- gt ) f l 0 n~- rth J rd b ) (-1 0 i
)(0
C-Y(r~~ j ~
I -
~
I I
C_ (i ri fdEJ lt r v
t l~ 0
Ih~ Y
~ f J ~) o JJ~~ cp ~0_
1 ~J HI I--(t1-~ 1 0 0-
-~eV_J~~Ob f)~IA~l1 l i h Q
h ~S~
~Q e ~ (c d)
l
t~d
( I I) Fgt l
shy shy ~ _i
j
lrf fl r
I - I f-
l~UC) J
__ ~_2lt71j --A~ ~ t A
~~__ ~_0
i-Ax-gshy
_(~-ij
R~
J~ ~
_-middot1
E
I y~l
I _--u r
1- y
( 4 e- (1 Ie --I
u
DAmiddotmiddotmiddot ~ middotfIc+ft ~u rrgtJ JQLl~
ldegfJ5 o-yenf~ h~1~t
(3 -=~f1~6 bullA~0~S-A~~~~ftA~jb~j laquo
]If~middot oj v ~
--- -0 ~
tr
- - middot-ft- -shyLmiddot ~(~ ampJ~ ff)rh-~Iltx__6p-uJ~ 1)__ _ p(~middot~r (IJ D] 1-shy
)
-- l ~ ~q(~ J
n vYl shy
I
i 1-I
r
( f-_c l VI
OIKcf _t (1 IJ -~ ~IQ) ~)v~JJ
~ fc ~A
ft (GiG) rfVlt ~-1Qpe4gt~elLu6~
2 lAM~rUUA- shy
J1 shy
A~~ CAl e-) C j
(
j I
(S)
j -
(~) I
~ c hA-
( [l ~ J
-
j
J
l
e I
Iermiddot1 I-v
1
( c c-) --
0) B I e~~ r
I
C ( Y~ 1-~ J j ~
I
~ l 0 b) (-- ---
rlt
i~(1) I _1 0 li~ ) 7 - tshy-l
)j)t 17-f1~ t
-i
klt txt
)( 1~~ ) t-~
19-~Ilt~~ (-gtSlx-t) J - i lsj lYJ)
( Y - t) X) t~
t ~
~-~ l~l ~) c-J I
I I I Y l IX ) (~
n
l~ ~ (XI))
lX(
1
J
J
I )~iI ~gt ~-- c ~i ~ treg J I W~ 01 ltxj - -I~
J J
l fL~ ir~ ) jet ) r~ 0R
Grr) Ir ~ 0 ) - ~ eli DIgt
r~f~ A ) lttl (J ~_)
1 ( I J c
-j
( ~
- ) C- ()70 7( gtJ ~ I
i~lt I -- - r I
I j
- ] -w - ) -- j r
I 1 I t fI t __ J
~(
4 1 ~ -- J
- - ~~- ---
v~ middotmiddotmiddot~t
- _I
~
~ ~~-- ~--
- j- shy
)0 ~r tTl
--t
t -j lr0 (i
~i -Y -1 ~~0 +
(0 ~~ r - It Itmiddot- lshy I I ~
~bull k~L lt~ I
v )t~ltl $ l J lt1
~~ ) r j shy
I t i ~ - 1 f
shy -- lt Ashy~ 2 1 -
J
l
1 v
t1
-
I 0 --Ch it ~~
0~ - J shy I -
j 0-
-- I t 7I J 1 J
t ~ 1
r
( r 11 11shyl
i
I I
)
-~ ~) jr- r~ A 5tTgt - ~-- 1] _shy -
I - r
t ~ A l~_- p-
C~ t7 f~)-- _ ~jiX)- -
~A=JS- J = Y-
i i I
c -t E- ( t r- f)~ y ( (11 )J t - ( (JJ)
~E ((0J
X G- f- Ii )lt c D ~ C ~ -1 e D J
lf)j)E A-x( (~j) amp- GxCgt
t PyL
t- (-ty Craquo (
l L
i I 0~)~ ) y )-7shy
t ~ lY~)
Clt - l t Cmiddot
I Ii_ bull-lt F V tI 1 Ii (I )
V Y ( ( I~ c i~-4 J- (-b
l~- t ~) y J
imiddotJ
f lQ)
~ I
1 ( ~ laquo~J V J J J
1 t J
OC06
~
0 7I r c) JGlt lmiddot -r
) )
r) gt ( - --~
)
shy
(
(
~ilt Z - LA
-) J I( j ( -
~i- _y~~f~ ~j~ ~ ~ A~~A
~~ (~ ls) Ci_fshy~~~J- t]~(t)~~
r--c- f ~ ~~
- - - ~-- bull -shy
Cflt(V ~([~e~~- f K JO-~
V
-Ij--XtAshy
))_ jtt_~ _~~
X-y
v CJ lt feshy
___ _ _ __r~middot _ ___ _~_
helfBbAh c~Jn
shy
L~v-1 - l
~ ~ ~y-
t - ~I
1 E C~
- - vJ - )j I
J
I A ~ ~ - ~
(rvjl
~C C1
( l
)( T
j
~ v -- 11 lt-J ~
(~ lu ~ 00 n f-~J~ J
f ~ 12 cent1 D~-gtl (
l
[
8 ~-=-~~i
( nfl2bc[r6 ~1vl kC
t ~ ex (x~c) - -
-~ kJ)1~iKlftYKlA (~l(-J~_C~Jr~tgt~x lLJi fr(t ~i1cent 1)) e biyI--r) lt2
rshy1
shy
~
lt)-
~(Almiddot Pc~
rJ- -~p~tA - - shy
I
shy (-j) -r---
I
r T I
1 ~_
0 1 1t b( 1 tlt E 1 ~E Z
K J ~ -- ~ ~
reg (jj P
r-~A~
( -oJ -J 11
D r )J ] ~~-~
(i) A Y =1-
+ (
~ J
~+11
+1 -t ~ 7 )
I
)J
j
tlJ + b1 t bf i (
~ ( ~ ~l t t bc
l rr y) +Sc
+- I gtlt0 = xfc I ~LX ~J E-t L~ JOx 1 )eA ) +( 1+ b~~~ shy
( J J ) - -p
I-- -h_ e ytbX - J It( I -shy-I It ~t-M I
J
Ie E - ~ -1 f 1+ 1 l IAI f ~r t - b X )
j
- =r~ - GX cft I ~ s -t) shy
~ r
t-t1 01 J
11 I-=~ I jh v - 1 - shy
I 1 ~ ~ I
o Aj
A~ J Q
(l- E2J lltJ eL~ I)
_)1(K~
Jlt- j X y ~ t
4-shy
sA i ~6 t
f
C
yS -~7
t )l - ~tL ~l X J ~f
1
J ~ n f t-~ - I - fmiddot~) ~ J J
j ~ J shy
middot1
---_
_r
--
-
~ - - ~l ~5 ~ )~-~ ~
1
l __-l
~ )
I
~ ~ A 2~ l ~ ~ l =IV
A-- fC ~1Jfn
(x D
) ~
0 -
i - )
4middot
~
~
_ IJ I f -~-
i -) ~
--- -
i
( ~
-~ r- t
~-- ~lS c f j VI t
~ A ~ J
- --~~-
I A _1 L
~ Y -)lt-2 A + shy
(shy
_J -L
--Ii
~
- l~
1 r
_)
11VV
0
-
~1
___t
1
-~
) 1))
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
( I ~ l il- ) ( )1 - l ~ I u )
xPh-r
---b-irbj- fi I~~(-l--- _I~~~ - _ J
1- shy
M~
- -~ f---(J~~] ~ Y--(~~~(J-=~~--
y f- -~ V lt --~tfS IA x Eh Y --r( - - -I-
( t ) ( igt 0) r-b I 1
- ~ ~
V X ~ IX
V E CA(C
I - i (
1 r 1
tI6 r rcA (Qi)b) U C -- -
u l-AtQ)
x H (-) (fJu (t i rh- 0 -- -r~ I H)J shy
r-
x e (rmr~ IU I fi -j shy
I tlt f- l~f J E
x- c - P l
I D X F
evr- -J
~rAP)~L~_CK0 I
b~fl-
(
lt - I j
t
f T f
t r _ Cbjl
Y i vX E (G)
x (~) rl 51 (~J 1- ~ J (t~ nY((~)
Or ~ kf ltmiddot t Ji v I e- J )~
I
X ( )1 J f~ l D
9 ( ) Co I r- gt ) f l 0 n~- rth J rd b ) (-1 0 i
)(0
C-Y(r~~ j ~
I -
~
I I
C_ (i ri fdEJ lt r v
t l~ 0
Ih~ Y
~ f J ~) o JJ~~ cp ~0_
1 ~J HI I--(t1-~ 1 0 0-
-~eV_J~~Ob f)~IA~l1 l i h Q
h ~S~
~Q e ~ (c d)
l
t~d
( I I) Fgt l
shy shy ~ _i
j
lrf fl r
I - I f-
l~UC) J
__ ~_2lt71j --A~ ~ t A
~~__ ~_0
i-Ax-gshy
_(~-ij
R~
J~ ~
_-middot1
E
I y~l
I _--u r
1- y
( 4 e- (1 Ie --I
u
DAmiddotmiddotmiddot ~ middotfIc+ft ~u rrgtJ JQLl~
ldegfJ5 o-yenf~ h~1~t
(3 -=~f1~6 bullA~0~S-A~~~~ftA~jb~j laquo
]If~middot oj v ~
--- -0 ~
tr
- - middot-ft- -shyLmiddot ~(~ ampJ~ ff)rh-~Iltx__6p-uJ~ 1)__ _ p(~middot~r (IJ D] 1-shy
)
-- l ~ ~q(~ J
n vYl shy
I
i 1-I
r
( f-_c l VI
OIKcf _t (1 IJ -~ ~IQ) ~)v~JJ
~ fc ~A
ft (GiG) rfVlt ~-1Qpe4gt~elLu6~
2 lAM~rUUA- shy
J1 shy
A~~ CAl e-) C j
(
j I
(S)
j -
(~) I
~ c hA-
( [l ~ J
-
j
J
l
e I
Iermiddot1 I-v
1
( c c-) --
0) B I e~~ r
I
C ( Y~ 1-~ J j ~
I
~ l 0 b) (-- ---
rlt
i~(1) I _1 0 li~ ) 7 - tshy-l
)j)t 17-f1~ t
-i
klt txt
)( 1~~ ) t-~
19-~Ilt~~ (-gtSlx-t) J - i lsj lYJ)
( Y - t) X) t~
t ~
~-~ l~l ~) c-J I
I I I Y l IX ) (~
n
l~ ~ (XI))
lX(
1
J
J
I )~iI ~gt ~-- c ~i ~ treg J I W~ 01 ltxj - -I~
J J
l fL~ ir~ ) jet ) r~ 0R
Grr) Ir ~ 0 ) - ~ eli DIgt
r~f~ A ) lttl (J ~_)
1 ( I J c
-j
( ~
- ) C- ()70 7( gtJ ~ I
i~lt I -- - r I
I j
- ] -w - ) -- j r
I 1 I t fI t __ J
~(
4 1 ~ -- J
- - ~~- ---
v~ middotmiddotmiddot~t
- _I
~
~ ~~-- ~--
- j- shy
)0 ~r tTl
--t
t -j lr0 (i
~i -Y -1 ~~0 +
(0 ~~ r - It Itmiddot- lshy I I ~
~bull k~L lt~ I
v )t~ltl $ l J lt1
~~ ) r j shy
I t i ~ - 1 f
shy -- lt Ashy~ 2 1 -
J
l
1 v
t1
-
I 0 --Ch it ~~
0~ - J shy I -
j 0-
-- I t 7I J 1 J
t ~ 1
r
( r 11 11shyl
i
I I
)
-~ ~) jr- r~ A 5tTgt - ~-- 1] _shy -
I - r
t ~ A l~_- p-
C~ t7 f~)-- _ ~jiX)- -
~A=JS- J = Y-
i i I
c -t E- ( t r- f)~ y ( (11 )J t - ( (JJ)
~E ((0J
X G- f- Ii )lt c D ~ C ~ -1 e D J
lf)j)E A-x( (~j) amp- GxCgt
t PyL
t- (-ty Craquo (
l L
i I 0~)~ ) y )-7shy
t ~ lY~)
Clt - l t Cmiddot
I Ii_ bull-lt F V tI 1 Ii (I )
V Y ( ( I~ c i~-4 J- (-b
l~- t ~) y J
imiddotJ
f lQ)
~ I
1 ( ~ laquo~J V J J J
1 t J
OC06
~
0 7I r c) JGlt lmiddot -r
) )
r) gt ( - --~
)
shy
(
(
~ilt Z - LA
-) J I( j ( -
~i- _y~~f~ ~j~ ~ ~ A~~A
~~ (~ ls) Ci_fshy~~~J- t]~(t)~~
r--c- f ~ ~~
- - - ~-- bull -shy
Cflt(V ~([~e~~- f K JO-~
V
-Ij--XtAshy
))_ jtt_~ _~~
X-y
v CJ lt feshy
___ _ _ __r~middot _ ___ _~_
helfBbAh c~Jn
shy
L~v-1 - l
~ ~ ~y-
t - ~I
1 E C~
- - vJ - )j I
J
I A ~ ~ - ~
(rvjl
~C C1
( l
)( T
j
~ v -- 11 lt-J ~
(~ lu ~ 00 n f-~J~ J
f ~ 12 cent1 D~-gtl (
l
[
8 ~-=-~~i
( nfl2bc[r6 ~1vl kC
t ~ ex (x~c) - -
-~ kJ)1~iKlftYKlA (~l(-J~_C~Jr~tgt~x lLJi fr(t ~i1cent 1)) e biyI--r) lt2
rshy1
shy
~
lt)-
~(Almiddot Pc~
rJ- -~p~tA - - shy
I
shy (-j) -r---
I
r T I
1 ~_
0 1 1t b( 1 tlt E 1 ~E Z
K J ~ -- ~ ~
reg (jj P
r-~A~
( -oJ -J 11
D r )J ] ~~-~
(i) A Y =1-
+ (
~ J
~+11
+1 -t ~ 7 )
I
)J
j
tlJ + b1 t bf i (
~ ( ~ ~l t t bc
l rr y) +Sc
+- I gtlt0 = xfc I ~LX ~J E-t L~ JOx 1 )eA ) +( 1+ b~~~ shy
( J J ) - -p
I-- -h_ e ytbX - J It( I -shy-I It ~t-M I
J
Ie E - ~ -1 f 1+ 1 l IAI f ~r t - b X )
j
- =r~ - GX cft I ~ s -t) shy
~ r
t-t1 01 J
11 I-=~ I jh v - 1 - shy
I 1 ~ ~ I
o Aj
A~ J Q
(l- E2J lltJ eL~ I)
_)1(K~
Jlt- j X y ~ t
4-shy
sA i ~6 t
f
C
yS -~7
t )l - ~tL ~l X J ~f
1
J ~ n f t-~ - I - fmiddot~) ~ J J
j ~ J shy
middot1
---_
_r
--
-
~ - - ~l ~5 ~ )~-~ ~
1
l __-l
~ )
I
~ ~ A 2~ l ~ ~ l =IV
A-- fC ~1Jfn
(x D
) ~
0 -
i - )
4middot
~
~
_ IJ I f -~-
i -) ~
--- -
i
( ~
-~ r- t
~-- ~lS c f j VI t
~ A ~ J
- --~~-
I A _1 L
~ Y -)lt-2 A + shy
(shy
_J -L
--Ii
~
- l~
1 r
_)
11VV
0
-
~1
___t
1
-~
) 1))
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
I - i (
1 r 1
tI6 r rcA (Qi)b) U C -- -
u l-AtQ)
x H (-) (fJu (t i rh- 0 -- -r~ I H)J shy
r-
x e (rmr~ IU I fi -j shy
I tlt f- l~f J E
x- c - P l
I D X F
evr- -J
~rAP)~L~_CK0 I
b~fl-
(
lt - I j
t
f T f
t r _ Cbjl
Y i vX E (G)
x (~) rl 51 (~J 1- ~ J (t~ nY((~)
Or ~ kf ltmiddot t Ji v I e- J )~
I
X ( )1 J f~ l D
9 ( ) Co I r- gt ) f l 0 n~- rth J rd b ) (-1 0 i
)(0
C-Y(r~~ j ~
I -
~
I I
C_ (i ri fdEJ lt r v
t l~ 0
Ih~ Y
~ f J ~) o JJ~~ cp ~0_
1 ~J HI I--(t1-~ 1 0 0-
-~eV_J~~Ob f)~IA~l1 l i h Q
h ~S~
~Q e ~ (c d)
l
t~d
( I I) Fgt l
shy shy ~ _i
j
lrf fl r
I - I f-
l~UC) J
__ ~_2lt71j --A~ ~ t A
~~__ ~_0
i-Ax-gshy
_(~-ij
R~
J~ ~
_-middot1
E
I y~l
I _--u r
1- y
( 4 e- (1 Ie --I
u
DAmiddotmiddotmiddot ~ middotfIc+ft ~u rrgtJ JQLl~
ldegfJ5 o-yenf~ h~1~t
(3 -=~f1~6 bullA~0~S-A~~~~ftA~jb~j laquo
]If~middot oj v ~
--- -0 ~
tr
- - middot-ft- -shyLmiddot ~(~ ampJ~ ff)rh-~Iltx__6p-uJ~ 1)__ _ p(~middot~r (IJ D] 1-shy
)
-- l ~ ~q(~ J
n vYl shy
I
i 1-I
r
( f-_c l VI
OIKcf _t (1 IJ -~ ~IQ) ~)v~JJ
~ fc ~A
ft (GiG) rfVlt ~-1Qpe4gt~elLu6~
2 lAM~rUUA- shy
J1 shy
A~~ CAl e-) C j
(
j I
(S)
j -
(~) I
~ c hA-
( [l ~ J
-
j
J
l
e I
Iermiddot1 I-v
1
( c c-) --
0) B I e~~ r
I
C ( Y~ 1-~ J j ~
I
~ l 0 b) (-- ---
rlt
i~(1) I _1 0 li~ ) 7 - tshy-l
)j)t 17-f1~ t
-i
klt txt
)( 1~~ ) t-~
19-~Ilt~~ (-gtSlx-t) J - i lsj lYJ)
( Y - t) X) t~
t ~
~-~ l~l ~) c-J I
I I I Y l IX ) (~
n
l~ ~ (XI))
lX(
1
J
J
I )~iI ~gt ~-- c ~i ~ treg J I W~ 01 ltxj - -I~
J J
l fL~ ir~ ) jet ) r~ 0R
Grr) Ir ~ 0 ) - ~ eli DIgt
r~f~ A ) lttl (J ~_)
1 ( I J c
-j
( ~
- ) C- ()70 7( gtJ ~ I
i~lt I -- - r I
I j
- ] -w - ) -- j r
I 1 I t fI t __ J
~(
4 1 ~ -- J
- - ~~- ---
v~ middotmiddotmiddot~t
- _I
~
~ ~~-- ~--
- j- shy
)0 ~r tTl
--t
t -j lr0 (i
~i -Y -1 ~~0 +
(0 ~~ r - It Itmiddot- lshy I I ~
~bull k~L lt~ I
v )t~ltl $ l J lt1
~~ ) r j shy
I t i ~ - 1 f
shy -- lt Ashy~ 2 1 -
J
l
1 v
t1
-
I 0 --Ch it ~~
0~ - J shy I -
j 0-
-- I t 7I J 1 J
t ~ 1
r
( r 11 11shyl
i
I I
)
-~ ~) jr- r~ A 5tTgt - ~-- 1] _shy -
I - r
t ~ A l~_- p-
C~ t7 f~)-- _ ~jiX)- -
~A=JS- J = Y-
i i I
c -t E- ( t r- f)~ y ( (11 )J t - ( (JJ)
~E ((0J
X G- f- Ii )lt c D ~ C ~ -1 e D J
lf)j)E A-x( (~j) amp- GxCgt
t PyL
t- (-ty Craquo (
l L
i I 0~)~ ) y )-7shy
t ~ lY~)
Clt - l t Cmiddot
I Ii_ bull-lt F V tI 1 Ii (I )
V Y ( ( I~ c i~-4 J- (-b
l~- t ~) y J
imiddotJ
f lQ)
~ I
1 ( ~ laquo~J V J J J
1 t J
OC06
~
0 7I r c) JGlt lmiddot -r
) )
r) gt ( - --~
)
shy
(
(
~ilt Z - LA
-) J I( j ( -
~i- _y~~f~ ~j~ ~ ~ A~~A
~~ (~ ls) Ci_fshy~~~J- t]~(t)~~
r--c- f ~ ~~
- - - ~-- bull -shy
Cflt(V ~([~e~~- f K JO-~
V
-Ij--XtAshy
))_ jtt_~ _~~
X-y
v CJ lt feshy
___ _ _ __r~middot _ ___ _~_
helfBbAh c~Jn
shy
L~v-1 - l
~ ~ ~y-
t - ~I
1 E C~
- - vJ - )j I
J
I A ~ ~ - ~
(rvjl
~C C1
( l
)( T
j
~ v -- 11 lt-J ~
(~ lu ~ 00 n f-~J~ J
f ~ 12 cent1 D~-gtl (
l
[
8 ~-=-~~i
( nfl2bc[r6 ~1vl kC
t ~ ex (x~c) - -
-~ kJ)1~iKlftYKlA (~l(-J~_C~Jr~tgt~x lLJi fr(t ~i1cent 1)) e biyI--r) lt2
rshy1
shy
~
lt)-
~(Almiddot Pc~
rJ- -~p~tA - - shy
I
shy (-j) -r---
I
r T I
1 ~_
0 1 1t b( 1 tlt E 1 ~E Z
K J ~ -- ~ ~
reg (jj P
r-~A~
( -oJ -J 11
D r )J ] ~~-~
(i) A Y =1-
+ (
~ J
~+11
+1 -t ~ 7 )
I
)J
j
tlJ + b1 t bf i (
~ ( ~ ~l t t bc
l rr y) +Sc
+- I gtlt0 = xfc I ~LX ~J E-t L~ JOx 1 )eA ) +( 1+ b~~~ shy
( J J ) - -p
I-- -h_ e ytbX - J It( I -shy-I It ~t-M I
J
Ie E - ~ -1 f 1+ 1 l IAI f ~r t - b X )
j
- =r~ - GX cft I ~ s -t) shy
~ r
t-t1 01 J
11 I-=~ I jh v - 1 - shy
I 1 ~ ~ I
o Aj
A~ J Q
(l- E2J lltJ eL~ I)
_)1(K~
Jlt- j X y ~ t
4-shy
sA i ~6 t
f
C
yS -~7
t )l - ~tL ~l X J ~f
1
J ~ n f t-~ - I - fmiddot~) ~ J J
j ~ J shy
middot1
---_
_r
--
-
~ - - ~l ~5 ~ )~-~ ~
1
l __-l
~ )
I
~ ~ A 2~ l ~ ~ l =IV
A-- fC ~1Jfn
(x D
) ~
0 -
i - )
4middot
~
~
_ IJ I f -~-
i -) ~
--- -
i
( ~
-~ r- t
~-- ~lS c f j VI t
~ A ~ J
- --~~-
I A _1 L
~ Y -)lt-2 A + shy
(shy
_J -L
--Ii
~
- l~
1 r
_)
11VV
0
-
~1
___t
1
-~
) 1))
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
t r _ Cbjl
Y i vX E (G)
x (~) rl 51 (~J 1- ~ J (t~ nY((~)
Or ~ kf ltmiddot t Ji v I e- J )~
I
X ( )1 J f~ l D
9 ( ) Co I r- gt ) f l 0 n~- rth J rd b ) (-1 0 i
)(0
C-Y(r~~ j ~
I -
~
I I
C_ (i ri fdEJ lt r v
t l~ 0
Ih~ Y
~ f J ~) o JJ~~ cp ~0_
1 ~J HI I--(t1-~ 1 0 0-
-~eV_J~~Ob f)~IA~l1 l i h Q
h ~S~
~Q e ~ (c d)
l
t~d
( I I) Fgt l
shy shy ~ _i
j
lrf fl r
I - I f-
l~UC) J
__ ~_2lt71j --A~ ~ t A
~~__ ~_0
i-Ax-gshy
_(~-ij
R~
J~ ~
_-middot1
E
I y~l
I _--u r
1- y
( 4 e- (1 Ie --I
u
DAmiddotmiddotmiddot ~ middotfIc+ft ~u rrgtJ JQLl~
ldegfJ5 o-yenf~ h~1~t
(3 -=~f1~6 bullA~0~S-A~~~~ftA~jb~j laquo
]If~middot oj v ~
--- -0 ~
tr
- - middot-ft- -shyLmiddot ~(~ ampJ~ ff)rh-~Iltx__6p-uJ~ 1)__ _ p(~middot~r (IJ D] 1-shy
)
-- l ~ ~q(~ J
n vYl shy
I
i 1-I
r
( f-_c l VI
OIKcf _t (1 IJ -~ ~IQ) ~)v~JJ
~ fc ~A
ft (GiG) rfVlt ~-1Qpe4gt~elLu6~
2 lAM~rUUA- shy
J1 shy
A~~ CAl e-) C j
(
j I
(S)
j -
(~) I
~ c hA-
( [l ~ J
-
j
J
l
e I
Iermiddot1 I-v
1
( c c-) --
0) B I e~~ r
I
C ( Y~ 1-~ J j ~
I
~ l 0 b) (-- ---
rlt
i~(1) I _1 0 li~ ) 7 - tshy-l
)j)t 17-f1~ t
-i
klt txt
)( 1~~ ) t-~
19-~Ilt~~ (-gtSlx-t) J - i lsj lYJ)
( Y - t) X) t~
t ~
~-~ l~l ~) c-J I
I I I Y l IX ) (~
n
l~ ~ (XI))
lX(
1
J
J
I )~iI ~gt ~-- c ~i ~ treg J I W~ 01 ltxj - -I~
J J
l fL~ ir~ ) jet ) r~ 0R
Grr) Ir ~ 0 ) - ~ eli DIgt
r~f~ A ) lttl (J ~_)
1 ( I J c
-j
( ~
- ) C- ()70 7( gtJ ~ I
i~lt I -- - r I
I j
- ] -w - ) -- j r
I 1 I t fI t __ J
~(
4 1 ~ -- J
- - ~~- ---
v~ middotmiddotmiddot~t
- _I
~
~ ~~-- ~--
- j- shy
)0 ~r tTl
--t
t -j lr0 (i
~i -Y -1 ~~0 +
(0 ~~ r - It Itmiddot- lshy I I ~
~bull k~L lt~ I
v )t~ltl $ l J lt1
~~ ) r j shy
I t i ~ - 1 f
shy -- lt Ashy~ 2 1 -
J
l
1 v
t1
-
I 0 --Ch it ~~
0~ - J shy I -
j 0-
-- I t 7I J 1 J
t ~ 1
r
( r 11 11shyl
i
I I
)
-~ ~) jr- r~ A 5tTgt - ~-- 1] _shy -
I - r
t ~ A l~_- p-
C~ t7 f~)-- _ ~jiX)- -
~A=JS- J = Y-
i i I
c -t E- ( t r- f)~ y ( (11 )J t - ( (JJ)
~E ((0J
X G- f- Ii )lt c D ~ C ~ -1 e D J
lf)j)E A-x( (~j) amp- GxCgt
t PyL
t- (-ty Craquo (
l L
i I 0~)~ ) y )-7shy
t ~ lY~)
Clt - l t Cmiddot
I Ii_ bull-lt F V tI 1 Ii (I )
V Y ( ( I~ c i~-4 J- (-b
l~- t ~) y J
imiddotJ
f lQ)
~ I
1 ( ~ laquo~J V J J J
1 t J
OC06
~
0 7I r c) JGlt lmiddot -r
) )
r) gt ( - --~
)
shy
(
(
~ilt Z - LA
-) J I( j ( -
~i- _y~~f~ ~j~ ~ ~ A~~A
~~ (~ ls) Ci_fshy~~~J- t]~(t)~~
r--c- f ~ ~~
- - - ~-- bull -shy
Cflt(V ~([~e~~- f K JO-~
V
-Ij--XtAshy
))_ jtt_~ _~~
X-y
v CJ lt feshy
___ _ _ __r~middot _ ___ _~_
helfBbAh c~Jn
shy
L~v-1 - l
~ ~ ~y-
t - ~I
1 E C~
- - vJ - )j I
J
I A ~ ~ - ~
(rvjl
~C C1
( l
)( T
j
~ v -- 11 lt-J ~
(~ lu ~ 00 n f-~J~ J
f ~ 12 cent1 D~-gtl (
l
[
8 ~-=-~~i
( nfl2bc[r6 ~1vl kC
t ~ ex (x~c) - -
-~ kJ)1~iKlftYKlA (~l(-J~_C~Jr~tgt~x lLJi fr(t ~i1cent 1)) e biyI--r) lt2
rshy1
shy
~
lt)-
~(Almiddot Pc~
rJ- -~p~tA - - shy
I
shy (-j) -r---
I
r T I
1 ~_
0 1 1t b( 1 tlt E 1 ~E Z
K J ~ -- ~ ~
reg (jj P
r-~A~
( -oJ -J 11
D r )J ] ~~-~
(i) A Y =1-
+ (
~ J
~+11
+1 -t ~ 7 )
I
)J
j
tlJ + b1 t bf i (
~ ( ~ ~l t t bc
l rr y) +Sc
+- I gtlt0 = xfc I ~LX ~J E-t L~ JOx 1 )eA ) +( 1+ b~~~ shy
( J J ) - -p
I-- -h_ e ytbX - J It( I -shy-I It ~t-M I
J
Ie E - ~ -1 f 1+ 1 l IAI f ~r t - b X )
j
- =r~ - GX cft I ~ s -t) shy
~ r
t-t1 01 J
11 I-=~ I jh v - 1 - shy
I 1 ~ ~ I
o Aj
A~ J Q
(l- E2J lltJ eL~ I)
_)1(K~
Jlt- j X y ~ t
4-shy
sA i ~6 t
f
C
yS -~7
t )l - ~tL ~l X J ~f
1
J ~ n f t-~ - I - fmiddot~) ~ J J
j ~ J shy
middot1
---_
_r
--
-
~ - - ~l ~5 ~ )~-~ ~
1
l __-l
~ )
I
~ ~ A 2~ l ~ ~ l =IV
A-- fC ~1Jfn
(x D
) ~
0 -
i - )
4middot
~
~
_ IJ I f -~-
i -) ~
--- -
i
( ~
-~ r- t
~-- ~lS c f j VI t
~ A ~ J
- --~~-
I A _1 L
~ Y -)lt-2 A + shy
(shy
_J -L
--Ii
~
- l~
1 r
_)
11VV
0
-
~1
___t
1
-~
) 1))
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
~
I I
C_ (i ri fdEJ lt r v
t l~ 0
Ih~ Y
~ f J ~) o JJ~~ cp ~0_
1 ~J HI I--(t1-~ 1 0 0-
-~eV_J~~Ob f)~IA~l1 l i h Q
h ~S~
~Q e ~ (c d)
l
t~d
( I I) Fgt l
shy shy ~ _i
j
lrf fl r
I - I f-
l~UC) J
__ ~_2lt71j --A~ ~ t A
~~__ ~_0
i-Ax-gshy
_(~-ij
R~
J~ ~
_-middot1
E
I y~l
I _--u r
1- y
( 4 e- (1 Ie --I
u
DAmiddotmiddotmiddot ~ middotfIc+ft ~u rrgtJ JQLl~
ldegfJ5 o-yenf~ h~1~t
(3 -=~f1~6 bullA~0~S-A~~~~ftA~jb~j laquo
]If~middot oj v ~
--- -0 ~
tr
- - middot-ft- -shyLmiddot ~(~ ampJ~ ff)rh-~Iltx__6p-uJ~ 1)__ _ p(~middot~r (IJ D] 1-shy
)
-- l ~ ~q(~ J
n vYl shy
I
i 1-I
r
( f-_c l VI
OIKcf _t (1 IJ -~ ~IQ) ~)v~JJ
~ fc ~A
ft (GiG) rfVlt ~-1Qpe4gt~elLu6~
2 lAM~rUUA- shy
J1 shy
A~~ CAl e-) C j
(
j I
(S)
j -
(~) I
~ c hA-
( [l ~ J
-
j
J
l
e I
Iermiddot1 I-v
1
( c c-) --
0) B I e~~ r
I
C ( Y~ 1-~ J j ~
I
~ l 0 b) (-- ---
rlt
i~(1) I _1 0 li~ ) 7 - tshy-l
)j)t 17-f1~ t
-i
klt txt
)( 1~~ ) t-~
19-~Ilt~~ (-gtSlx-t) J - i lsj lYJ)
( Y - t) X) t~
t ~
~-~ l~l ~) c-J I
I I I Y l IX ) (~
n
l~ ~ (XI))
lX(
1
J
J
I )~iI ~gt ~-- c ~i ~ treg J I W~ 01 ltxj - -I~
J J
l fL~ ir~ ) jet ) r~ 0R
Grr) Ir ~ 0 ) - ~ eli DIgt
r~f~ A ) lttl (J ~_)
1 ( I J c
-j
( ~
- ) C- ()70 7( gtJ ~ I
i~lt I -- - r I
I j
- ] -w - ) -- j r
I 1 I t fI t __ J
~(
4 1 ~ -- J
- - ~~- ---
v~ middotmiddotmiddot~t
- _I
~
~ ~~-- ~--
- j- shy
)0 ~r tTl
--t
t -j lr0 (i
~i -Y -1 ~~0 +
(0 ~~ r - It Itmiddot- lshy I I ~
~bull k~L lt~ I
v )t~ltl $ l J lt1
~~ ) r j shy
I t i ~ - 1 f
shy -- lt Ashy~ 2 1 -
J
l
1 v
t1
-
I 0 --Ch it ~~
0~ - J shy I -
j 0-
-- I t 7I J 1 J
t ~ 1
r
( r 11 11shyl
i
I I
)
-~ ~) jr- r~ A 5tTgt - ~-- 1] _shy -
I - r
t ~ A l~_- p-
C~ t7 f~)-- _ ~jiX)- -
~A=JS- J = Y-
i i I
c -t E- ( t r- f)~ y ( (11 )J t - ( (JJ)
~E ((0J
X G- f- Ii )lt c D ~ C ~ -1 e D J
lf)j)E A-x( (~j) amp- GxCgt
t PyL
t- (-ty Craquo (
l L
i I 0~)~ ) y )-7shy
t ~ lY~)
Clt - l t Cmiddot
I Ii_ bull-lt F V tI 1 Ii (I )
V Y ( ( I~ c i~-4 J- (-b
l~- t ~) y J
imiddotJ
f lQ)
~ I
1 ( ~ laquo~J V J J J
1 t J
OC06
~
0 7I r c) JGlt lmiddot -r
) )
r) gt ( - --~
)
shy
(
(
~ilt Z - LA
-) J I( j ( -
~i- _y~~f~ ~j~ ~ ~ A~~A
~~ (~ ls) Ci_fshy~~~J- t]~(t)~~
r--c- f ~ ~~
- - - ~-- bull -shy
Cflt(V ~([~e~~- f K JO-~
V
-Ij--XtAshy
))_ jtt_~ _~~
X-y
v CJ lt feshy
___ _ _ __r~middot _ ___ _~_
helfBbAh c~Jn
shy
L~v-1 - l
~ ~ ~y-
t - ~I
1 E C~
- - vJ - )j I
J
I A ~ ~ - ~
(rvjl
~C C1
( l
)( T
j
~ v -- 11 lt-J ~
(~ lu ~ 00 n f-~J~ J
f ~ 12 cent1 D~-gtl (
l
[
8 ~-=-~~i
( nfl2bc[r6 ~1vl kC
t ~ ex (x~c) - -
-~ kJ)1~iKlftYKlA (~l(-J~_C~Jr~tgt~x lLJi fr(t ~i1cent 1)) e biyI--r) lt2
rshy1
shy
~
lt)-
~(Almiddot Pc~
rJ- -~p~tA - - shy
I
shy (-j) -r---
I
r T I
1 ~_
0 1 1t b( 1 tlt E 1 ~E Z
K J ~ -- ~ ~
reg (jj P
r-~A~
( -oJ -J 11
D r )J ] ~~-~
(i) A Y =1-
+ (
~ J
~+11
+1 -t ~ 7 )
I
)J
j
tlJ + b1 t bf i (
~ ( ~ ~l t t bc
l rr y) +Sc
+- I gtlt0 = xfc I ~LX ~J E-t L~ JOx 1 )eA ) +( 1+ b~~~ shy
( J J ) - -p
I-- -h_ e ytbX - J It( I -shy-I It ~t-M I
J
Ie E - ~ -1 f 1+ 1 l IAI f ~r t - b X )
j
- =r~ - GX cft I ~ s -t) shy
~ r
t-t1 01 J
11 I-=~ I jh v - 1 - shy
I 1 ~ ~ I
o Aj
A~ J Q
(l- E2J lltJ eL~ I)
_)1(K~
Jlt- j X y ~ t
4-shy
sA i ~6 t
f
C
yS -~7
t )l - ~tL ~l X J ~f
1
J ~ n f t-~ - I - fmiddot~) ~ J J
j ~ J shy
middot1
---_
_r
--
-
~ - - ~l ~5 ~ )~-~ ~
1
l __-l
~ )
I
~ ~ A 2~ l ~ ~ l =IV
A-- fC ~1Jfn
(x D
) ~
0 -
i - )
4middot
~
~
_ IJ I f -~-
i -) ~
--- -
i
( ~
-~ r- t
~-- ~lS c f j VI t
~ A ~ J
- --~~-
I A _1 L
~ Y -)lt-2 A + shy
(shy
_J -L
--Ii
~
- l~
1 r
_)
11VV
0
-
~1
___t
1
-~
) 1))
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
I - I f-
l~UC) J
__ ~_2lt71j --A~ ~ t A
~~__ ~_0
i-Ax-gshy
_(~-ij
R~
J~ ~
_-middot1
E
I y~l
I _--u r
1- y
( 4 e- (1 Ie --I
u
DAmiddotmiddotmiddot ~ middotfIc+ft ~u rrgtJ JQLl~
ldegfJ5 o-yenf~ h~1~t
(3 -=~f1~6 bullA~0~S-A~~~~ftA~jb~j laquo
]If~middot oj v ~
--- -0 ~
tr
- - middot-ft- -shyLmiddot ~(~ ampJ~ ff)rh-~Iltx__6p-uJ~ 1)__ _ p(~middot~r (IJ D] 1-shy
)
-- l ~ ~q(~ J
n vYl shy
I
i 1-I
r
( f-_c l VI
OIKcf _t (1 IJ -~ ~IQ) ~)v~JJ
~ fc ~A
ft (GiG) rfVlt ~-1Qpe4gt~elLu6~
2 lAM~rUUA- shy
J1 shy
A~~ CAl e-) C j
(
j I
(S)
j -
(~) I
~ c hA-
( [l ~ J
-
j
J
l
e I
Iermiddot1 I-v
1
( c c-) --
0) B I e~~ r
I
C ( Y~ 1-~ J j ~
I
~ l 0 b) (-- ---
rlt
i~(1) I _1 0 li~ ) 7 - tshy-l
)j)t 17-f1~ t
-i
klt txt
)( 1~~ ) t-~
19-~Ilt~~ (-gtSlx-t) J - i lsj lYJ)
( Y - t) X) t~
t ~
~-~ l~l ~) c-J I
I I I Y l IX ) (~
n
l~ ~ (XI))
lX(
1
J
J
I )~iI ~gt ~-- c ~i ~ treg J I W~ 01 ltxj - -I~
J J
l fL~ ir~ ) jet ) r~ 0R
Grr) Ir ~ 0 ) - ~ eli DIgt
r~f~ A ) lttl (J ~_)
1 ( I J c
-j
( ~
- ) C- ()70 7( gtJ ~ I
i~lt I -- - r I
I j
- ] -w - ) -- j r
I 1 I t fI t __ J
~(
4 1 ~ -- J
- - ~~- ---
v~ middotmiddotmiddot~t
- _I
~
~ ~~-- ~--
- j- shy
)0 ~r tTl
--t
t -j lr0 (i
~i -Y -1 ~~0 +
(0 ~~ r - It Itmiddot- lshy I I ~
~bull k~L lt~ I
v )t~ltl $ l J lt1
~~ ) r j shy
I t i ~ - 1 f
shy -- lt Ashy~ 2 1 -
J
l
1 v
t1
-
I 0 --Ch it ~~
0~ - J shy I -
j 0-
-- I t 7I J 1 J
t ~ 1
r
( r 11 11shyl
i
I I
)
-~ ~) jr- r~ A 5tTgt - ~-- 1] _shy -
I - r
t ~ A l~_- p-
C~ t7 f~)-- _ ~jiX)- -
~A=JS- J = Y-
i i I
c -t E- ( t r- f)~ y ( (11 )J t - ( (JJ)
~E ((0J
X G- f- Ii )lt c D ~ C ~ -1 e D J
lf)j)E A-x( (~j) amp- GxCgt
t PyL
t- (-ty Craquo (
l L
i I 0~)~ ) y )-7shy
t ~ lY~)
Clt - l t Cmiddot
I Ii_ bull-lt F V tI 1 Ii (I )
V Y ( ( I~ c i~-4 J- (-b
l~- t ~) y J
imiddotJ
f lQ)
~ I
1 ( ~ laquo~J V J J J
1 t J
OC06
~
0 7I r c) JGlt lmiddot -r
) )
r) gt ( - --~
)
shy
(
(
~ilt Z - LA
-) J I( j ( -
~i- _y~~f~ ~j~ ~ ~ A~~A
~~ (~ ls) Ci_fshy~~~J- t]~(t)~~
r--c- f ~ ~~
- - - ~-- bull -shy
Cflt(V ~([~e~~- f K JO-~
V
-Ij--XtAshy
))_ jtt_~ _~~
X-y
v CJ lt feshy
___ _ _ __r~middot _ ___ _~_
helfBbAh c~Jn
shy
L~v-1 - l
~ ~ ~y-
t - ~I
1 E C~
- - vJ - )j I
J
I A ~ ~ - ~
(rvjl
~C C1
( l
)( T
j
~ v -- 11 lt-J ~
(~ lu ~ 00 n f-~J~ J
f ~ 12 cent1 D~-gtl (
l
[
8 ~-=-~~i
( nfl2bc[r6 ~1vl kC
t ~ ex (x~c) - -
-~ kJ)1~iKlftYKlA (~l(-J~_C~Jr~tgt~x lLJi fr(t ~i1cent 1)) e biyI--r) lt2
rshy1
shy
~
lt)-
~(Almiddot Pc~
rJ- -~p~tA - - shy
I
shy (-j) -r---
I
r T I
1 ~_
0 1 1t b( 1 tlt E 1 ~E Z
K J ~ -- ~ ~
reg (jj P
r-~A~
( -oJ -J 11
D r )J ] ~~-~
(i) A Y =1-
+ (
~ J
~+11
+1 -t ~ 7 )
I
)J
j
tlJ + b1 t bf i (
~ ( ~ ~l t t bc
l rr y) +Sc
+- I gtlt0 = xfc I ~LX ~J E-t L~ JOx 1 )eA ) +( 1+ b~~~ shy
( J J ) - -p
I-- -h_ e ytbX - J It( I -shy-I It ~t-M I
J
Ie E - ~ -1 f 1+ 1 l IAI f ~r t - b X )
j
- =r~ - GX cft I ~ s -t) shy
~ r
t-t1 01 J
11 I-=~ I jh v - 1 - shy
I 1 ~ ~ I
o Aj
A~ J Q
(l- E2J lltJ eL~ I)
_)1(K~
Jlt- j X y ~ t
4-shy
sA i ~6 t
f
C
yS -~7
t )l - ~tL ~l X J ~f
1
J ~ n f t-~ - I - fmiddot~) ~ J J
j ~ J shy
middot1
---_
_r
--
-
~ - - ~l ~5 ~ )~-~ ~
1
l __-l
~ )
I
~ ~ A 2~ l ~ ~ l =IV
A-- fC ~1Jfn
(x D
) ~
0 -
i - )
4middot
~
~
_ IJ I f -~-
i -) ~
--- -
i
( ~
-~ r- t
~-- ~lS c f j VI t
~ A ~ J
- --~~-
I A _1 L
~ Y -)lt-2 A + shy
(shy
_J -L
--Ii
~
- l~
1 r
_)
11VV
0
-
~1
___t
1
-~
) 1))
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
u
DAmiddotmiddotmiddot ~ middotfIc+ft ~u rrgtJ JQLl~
ldegfJ5 o-yenf~ h~1~t
(3 -=~f1~6 bullA~0~S-A~~~~ftA~jb~j laquo
]If~middot oj v ~
--- -0 ~
tr
- - middot-ft- -shyLmiddot ~(~ ampJ~ ff)rh-~Iltx__6p-uJ~ 1)__ _ p(~middot~r (IJ D] 1-shy
)
-- l ~ ~q(~ J
n vYl shy
I
i 1-I
r
( f-_c l VI
OIKcf _t (1 IJ -~ ~IQ) ~)v~JJ
~ fc ~A
ft (GiG) rfVlt ~-1Qpe4gt~elLu6~
2 lAM~rUUA- shy
J1 shy
A~~ CAl e-) C j
(
j I
(S)
j -
(~) I
~ c hA-
( [l ~ J
-
j
J
l
e I
Iermiddot1 I-v
1
( c c-) --
0) B I e~~ r
I
C ( Y~ 1-~ J j ~
I
~ l 0 b) (-- ---
rlt
i~(1) I _1 0 li~ ) 7 - tshy-l
)j)t 17-f1~ t
-i
klt txt
)( 1~~ ) t-~
19-~Ilt~~ (-gtSlx-t) J - i lsj lYJ)
( Y - t) X) t~
t ~
~-~ l~l ~) c-J I
I I I Y l IX ) (~
n
l~ ~ (XI))
lX(
1
J
J
I )~iI ~gt ~-- c ~i ~ treg J I W~ 01 ltxj - -I~
J J
l fL~ ir~ ) jet ) r~ 0R
Grr) Ir ~ 0 ) - ~ eli DIgt
r~f~ A ) lttl (J ~_)
1 ( I J c
-j
( ~
- ) C- ()70 7( gtJ ~ I
i~lt I -- - r I
I j
- ] -w - ) -- j r
I 1 I t fI t __ J
~(
4 1 ~ -- J
- - ~~- ---
v~ middotmiddotmiddot~t
- _I
~
~ ~~-- ~--
- j- shy
)0 ~r tTl
--t
t -j lr0 (i
~i -Y -1 ~~0 +
(0 ~~ r - It Itmiddot- lshy I I ~
~bull k~L lt~ I
v )t~ltl $ l J lt1
~~ ) r j shy
I t i ~ - 1 f
shy -- lt Ashy~ 2 1 -
J
l
1 v
t1
-
I 0 --Ch it ~~
0~ - J shy I -
j 0-
-- I t 7I J 1 J
t ~ 1
r
( r 11 11shyl
i
I I
)
-~ ~) jr- r~ A 5tTgt - ~-- 1] _shy -
I - r
t ~ A l~_- p-
C~ t7 f~)-- _ ~jiX)- -
~A=JS- J = Y-
i i I
c -t E- ( t r- f)~ y ( (11 )J t - ( (JJ)
~E ((0J
X G- f- Ii )lt c D ~ C ~ -1 e D J
lf)j)E A-x( (~j) amp- GxCgt
t PyL
t- (-ty Craquo (
l L
i I 0~)~ ) y )-7shy
t ~ lY~)
Clt - l t Cmiddot
I Ii_ bull-lt F V tI 1 Ii (I )
V Y ( ( I~ c i~-4 J- (-b
l~- t ~) y J
imiddotJ
f lQ)
~ I
1 ( ~ laquo~J V J J J
1 t J
OC06
~
0 7I r c) JGlt lmiddot -r
) )
r) gt ( - --~
)
shy
(
(
~ilt Z - LA
-) J I( j ( -
~i- _y~~f~ ~j~ ~ ~ A~~A
~~ (~ ls) Ci_fshy~~~J- t]~(t)~~
r--c- f ~ ~~
- - - ~-- bull -shy
Cflt(V ~([~e~~- f K JO-~
V
-Ij--XtAshy
))_ jtt_~ _~~
X-y
v CJ lt feshy
___ _ _ __r~middot _ ___ _~_
helfBbAh c~Jn
shy
L~v-1 - l
~ ~ ~y-
t - ~I
1 E C~
- - vJ - )j I
J
I A ~ ~ - ~
(rvjl
~C C1
( l
)( T
j
~ v -- 11 lt-J ~
(~ lu ~ 00 n f-~J~ J
f ~ 12 cent1 D~-gtl (
l
[
8 ~-=-~~i
( nfl2bc[r6 ~1vl kC
t ~ ex (x~c) - -
-~ kJ)1~iKlftYKlA (~l(-J~_C~Jr~tgt~x lLJi fr(t ~i1cent 1)) e biyI--r) lt2
rshy1
shy
~
lt)-
~(Almiddot Pc~
rJ- -~p~tA - - shy
I
shy (-j) -r---
I
r T I
1 ~_
0 1 1t b( 1 tlt E 1 ~E Z
K J ~ -- ~ ~
reg (jj P
r-~A~
( -oJ -J 11
D r )J ] ~~-~
(i) A Y =1-
+ (
~ J
~+11
+1 -t ~ 7 )
I
)J
j
tlJ + b1 t bf i (
~ ( ~ ~l t t bc
l rr y) +Sc
+- I gtlt0 = xfc I ~LX ~J E-t L~ JOx 1 )eA ) +( 1+ b~~~ shy
( J J ) - -p
I-- -h_ e ytbX - J It( I -shy-I It ~t-M I
J
Ie E - ~ -1 f 1+ 1 l IAI f ~r t - b X )
j
- =r~ - GX cft I ~ s -t) shy
~ r
t-t1 01 J
11 I-=~ I jh v - 1 - shy
I 1 ~ ~ I
o Aj
A~ J Q
(l- E2J lltJ eL~ I)
_)1(K~
Jlt- j X y ~ t
4-shy
sA i ~6 t
f
C
yS -~7
t )l - ~tL ~l X J ~f
1
J ~ n f t-~ - I - fmiddot~) ~ J J
j ~ J shy
middot1
---_
_r
--
-
~ - - ~l ~5 ~ )~-~ ~
1
l __-l
~ )
I
~ ~ A 2~ l ~ ~ l =IV
A-- fC ~1Jfn
(x D
) ~
0 -
i - )
4middot
~
~
_ IJ I f -~-
i -) ~
--- -
i
( ~
-~ r- t
~-- ~lS c f j VI t
~ A ~ J
- --~~-
I A _1 L
~ Y -)lt-2 A + shy
(shy
_J -L
--Ii
~
- l~
1 r
_)
11VV
0
-
~1
___t
1
-~
) 1))
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
OIKcf _t (1 IJ -~ ~IQ) ~)v~JJ
~ fc ~A
ft (GiG) rfVlt ~-1Qpe4gt~elLu6~
2 lAM~rUUA- shy
J1 shy
A~~ CAl e-) C j
(
j I
(S)
j -
(~) I
~ c hA-
( [l ~ J
-
j
J
l
e I
Iermiddot1 I-v
1
( c c-) --
0) B I e~~ r
I
C ( Y~ 1-~ J j ~
I
~ l 0 b) (-- ---
rlt
i~(1) I _1 0 li~ ) 7 - tshy-l
)j)t 17-f1~ t
-i
klt txt
)( 1~~ ) t-~
19-~Ilt~~ (-gtSlx-t) J - i lsj lYJ)
( Y - t) X) t~
t ~
~-~ l~l ~) c-J I
I I I Y l IX ) (~
n
l~ ~ (XI))
lX(
1
J
J
I )~iI ~gt ~-- c ~i ~ treg J I W~ 01 ltxj - -I~
J J
l fL~ ir~ ) jet ) r~ 0R
Grr) Ir ~ 0 ) - ~ eli DIgt
r~f~ A ) lttl (J ~_)
1 ( I J c
-j
( ~
- ) C- ()70 7( gtJ ~ I
i~lt I -- - r I
I j
- ] -w - ) -- j r
I 1 I t fI t __ J
~(
4 1 ~ -- J
- - ~~- ---
v~ middotmiddotmiddot~t
- _I
~
~ ~~-- ~--
- j- shy
)0 ~r tTl
--t
t -j lr0 (i
~i -Y -1 ~~0 +
(0 ~~ r - It Itmiddot- lshy I I ~
~bull k~L lt~ I
v )t~ltl $ l J lt1
~~ ) r j shy
I t i ~ - 1 f
shy -- lt Ashy~ 2 1 -
J
l
1 v
t1
-
I 0 --Ch it ~~
0~ - J shy I -
j 0-
-- I t 7I J 1 J
t ~ 1
r
( r 11 11shyl
i
I I
)
-~ ~) jr- r~ A 5tTgt - ~-- 1] _shy -
I - r
t ~ A l~_- p-
C~ t7 f~)-- _ ~jiX)- -
~A=JS- J = Y-
i i I
c -t E- ( t r- f)~ y ( (11 )J t - ( (JJ)
~E ((0J
X G- f- Ii )lt c D ~ C ~ -1 e D J
lf)j)E A-x( (~j) amp- GxCgt
t PyL
t- (-ty Craquo (
l L
i I 0~)~ ) y )-7shy
t ~ lY~)
Clt - l t Cmiddot
I Ii_ bull-lt F V tI 1 Ii (I )
V Y ( ( I~ c i~-4 J- (-b
l~- t ~) y J
imiddotJ
f lQ)
~ I
1 ( ~ laquo~J V J J J
1 t J
OC06
~
0 7I r c) JGlt lmiddot -r
) )
r) gt ( - --~
)
shy
(
(
~ilt Z - LA
-) J I( j ( -
~i- _y~~f~ ~j~ ~ ~ A~~A
~~ (~ ls) Ci_fshy~~~J- t]~(t)~~
r--c- f ~ ~~
- - - ~-- bull -shy
Cflt(V ~([~e~~- f K JO-~
V
-Ij--XtAshy
))_ jtt_~ _~~
X-y
v CJ lt feshy
___ _ _ __r~middot _ ___ _~_
helfBbAh c~Jn
shy
L~v-1 - l
~ ~ ~y-
t - ~I
1 E C~
- - vJ - )j I
J
I A ~ ~ - ~
(rvjl
~C C1
( l
)( T
j
~ v -- 11 lt-J ~
(~ lu ~ 00 n f-~J~ J
f ~ 12 cent1 D~-gtl (
l
[
8 ~-=-~~i
( nfl2bc[r6 ~1vl kC
t ~ ex (x~c) - -
-~ kJ)1~iKlftYKlA (~l(-J~_C~Jr~tgt~x lLJi fr(t ~i1cent 1)) e biyI--r) lt2
rshy1
shy
~
lt)-
~(Almiddot Pc~
rJ- -~p~tA - - shy
I
shy (-j) -r---
I
r T I
1 ~_
0 1 1t b( 1 tlt E 1 ~E Z
K J ~ -- ~ ~
reg (jj P
r-~A~
( -oJ -J 11
D r )J ] ~~-~
(i) A Y =1-
+ (
~ J
~+11
+1 -t ~ 7 )
I
)J
j
tlJ + b1 t bf i (
~ ( ~ ~l t t bc
l rr y) +Sc
+- I gtlt0 = xfc I ~LX ~J E-t L~ JOx 1 )eA ) +( 1+ b~~~ shy
( J J ) - -p
I-- -h_ e ytbX - J It( I -shy-I It ~t-M I
J
Ie E - ~ -1 f 1+ 1 l IAI f ~r t - b X )
j
- =r~ - GX cft I ~ s -t) shy
~ r
t-t1 01 J
11 I-=~ I jh v - 1 - shy
I 1 ~ ~ I
o Aj
A~ J Q
(l- E2J lltJ eL~ I)
_)1(K~
Jlt- j X y ~ t
4-shy
sA i ~6 t
f
C
yS -~7
t )l - ~tL ~l X J ~f
1
J ~ n f t-~ - I - fmiddot~) ~ J J
j ~ J shy
middot1
---_
_r
--
-
~ - - ~l ~5 ~ )~-~ ~
1
l __-l
~ )
I
~ ~ A 2~ l ~ ~ l =IV
A-- fC ~1Jfn
(x D
) ~
0 -
i - )
4middot
~
~
_ IJ I f -~-
i -) ~
--- -
i
( ~
-~ r- t
~-- ~lS c f j VI t
~ A ~ J
- --~~-
I A _1 L
~ Y -)lt-2 A + shy
(shy
_J -L
--Ii
~
- l~
1 r
_)
11VV
0
-
~1
___t
1
-~
) 1))
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
i~(1) I _1 0 li~ ) 7 - tshy-l
)j)t 17-f1~ t
-i
klt txt
)( 1~~ ) t-~
19-~Ilt~~ (-gtSlx-t) J - i lsj lYJ)
( Y - t) X) t~
t ~
~-~ l~l ~) c-J I
I I I Y l IX ) (~
n
l~ ~ (XI))
lX(
1
J
J
I )~iI ~gt ~-- c ~i ~ treg J I W~ 01 ltxj - -I~
J J
l fL~ ir~ ) jet ) r~ 0R
Grr) Ir ~ 0 ) - ~ eli DIgt
r~f~ A ) lttl (J ~_)
1 ( I J c
-j
( ~
- ) C- ()70 7( gtJ ~ I
i~lt I -- - r I
I j
- ] -w - ) -- j r
I 1 I t fI t __ J
~(
4 1 ~ -- J
- - ~~- ---
v~ middotmiddotmiddot~t
- _I
~
~ ~~-- ~--
- j- shy
)0 ~r tTl
--t
t -j lr0 (i
~i -Y -1 ~~0 +
(0 ~~ r - It Itmiddot- lshy I I ~
~bull k~L lt~ I
v )t~ltl $ l J lt1
~~ ) r j shy
I t i ~ - 1 f
shy -- lt Ashy~ 2 1 -
J
l
1 v
t1
-
I 0 --Ch it ~~
0~ - J shy I -
j 0-
-- I t 7I J 1 J
t ~ 1
r
( r 11 11shyl
i
I I
)
-~ ~) jr- r~ A 5tTgt - ~-- 1] _shy -
I - r
t ~ A l~_- p-
C~ t7 f~)-- _ ~jiX)- -
~A=JS- J = Y-
i i I
c -t E- ( t r- f)~ y ( (11 )J t - ( (JJ)
~E ((0J
X G- f- Ii )lt c D ~ C ~ -1 e D J
lf)j)E A-x( (~j) amp- GxCgt
t PyL
t- (-ty Craquo (
l L
i I 0~)~ ) y )-7shy
t ~ lY~)
Clt - l t Cmiddot
I Ii_ bull-lt F V tI 1 Ii (I )
V Y ( ( I~ c i~-4 J- (-b
l~- t ~) y J
imiddotJ
f lQ)
~ I
1 ( ~ laquo~J V J J J
1 t J
OC06
~
0 7I r c) JGlt lmiddot -r
) )
r) gt ( - --~
)
shy
(
(
~ilt Z - LA
-) J I( j ( -
~i- _y~~f~ ~j~ ~ ~ A~~A
~~ (~ ls) Ci_fshy~~~J- t]~(t)~~
r--c- f ~ ~~
- - - ~-- bull -shy
Cflt(V ~([~e~~- f K JO-~
V
-Ij--XtAshy
))_ jtt_~ _~~
X-y
v CJ lt feshy
___ _ _ __r~middot _ ___ _~_
helfBbAh c~Jn
shy
L~v-1 - l
~ ~ ~y-
t - ~I
1 E C~
- - vJ - )j I
J
I A ~ ~ - ~
(rvjl
~C C1
( l
)( T
j
~ v -- 11 lt-J ~
(~ lu ~ 00 n f-~J~ J
f ~ 12 cent1 D~-gtl (
l
[
8 ~-=-~~i
( nfl2bc[r6 ~1vl kC
t ~ ex (x~c) - -
-~ kJ)1~iKlftYKlA (~l(-J~_C~Jr~tgt~x lLJi fr(t ~i1cent 1)) e biyI--r) lt2
rshy1
shy
~
lt)-
~(Almiddot Pc~
rJ- -~p~tA - - shy
I
shy (-j) -r---
I
r T I
1 ~_
0 1 1t b( 1 tlt E 1 ~E Z
K J ~ -- ~ ~
reg (jj P
r-~A~
( -oJ -J 11
D r )J ] ~~-~
(i) A Y =1-
+ (
~ J
~+11
+1 -t ~ 7 )
I
)J
j
tlJ + b1 t bf i (
~ ( ~ ~l t t bc
l rr y) +Sc
+- I gtlt0 = xfc I ~LX ~J E-t L~ JOx 1 )eA ) +( 1+ b~~~ shy
( J J ) - -p
I-- -h_ e ytbX - J It( I -shy-I It ~t-M I
J
Ie E - ~ -1 f 1+ 1 l IAI f ~r t - b X )
j
- =r~ - GX cft I ~ s -t) shy
~ r
t-t1 01 J
11 I-=~ I jh v - 1 - shy
I 1 ~ ~ I
o Aj
A~ J Q
(l- E2J lltJ eL~ I)
_)1(K~
Jlt- j X y ~ t
4-shy
sA i ~6 t
f
C
yS -~7
t )l - ~tL ~l X J ~f
1
J ~ n f t-~ - I - fmiddot~) ~ J J
j ~ J shy
middot1
---_
_r
--
-
~ - - ~l ~5 ~ )~-~ ~
1
l __-l
~ )
I
~ ~ A 2~ l ~ ~ l =IV
A-- fC ~1Jfn
(x D
) ~
0 -
i - )
4middot
~
~
_ IJ I f -~-
i -) ~
--- -
i
( ~
-~ r- t
~-- ~lS c f j VI t
~ A ~ J
- --~~-
I A _1 L
~ Y -)lt-2 A + shy
(shy
_J -L
--Ii
~
- l~
1 r
_)
11VV
0
-
~1
___t
1
-~
) 1))
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
~(
4 1 ~ -- J
- - ~~- ---
v~ middotmiddotmiddot~t
- _I
~
~ ~~-- ~--
- j- shy
)0 ~r tTl
--t
t -j lr0 (i
~i -Y -1 ~~0 +
(0 ~~ r - It Itmiddot- lshy I I ~
~bull k~L lt~ I
v )t~ltl $ l J lt1
~~ ) r j shy
I t i ~ - 1 f
shy -- lt Ashy~ 2 1 -
J
l
1 v
t1
-
I 0 --Ch it ~~
0~ - J shy I -
j 0-
-- I t 7I J 1 J
t ~ 1
r
( r 11 11shyl
i
I I
)
-~ ~) jr- r~ A 5tTgt - ~-- 1] _shy -
I - r
t ~ A l~_- p-
C~ t7 f~)-- _ ~jiX)- -
~A=JS- J = Y-
i i I
c -t E- ( t r- f)~ y ( (11 )J t - ( (JJ)
~E ((0J
X G- f- Ii )lt c D ~ C ~ -1 e D J
lf)j)E A-x( (~j) amp- GxCgt
t PyL
t- (-ty Craquo (
l L
i I 0~)~ ) y )-7shy
t ~ lY~)
Clt - l t Cmiddot
I Ii_ bull-lt F V tI 1 Ii (I )
V Y ( ( I~ c i~-4 J- (-b
l~- t ~) y J
imiddotJ
f lQ)
~ I
1 ( ~ laquo~J V J J J
1 t J
OC06
~
0 7I r c) JGlt lmiddot -r
) )
r) gt ( - --~
)
shy
(
(
~ilt Z - LA
-) J I( j ( -
~i- _y~~f~ ~j~ ~ ~ A~~A
~~ (~ ls) Ci_fshy~~~J- t]~(t)~~
r--c- f ~ ~~
- - - ~-- bull -shy
Cflt(V ~([~e~~- f K JO-~
V
-Ij--XtAshy
))_ jtt_~ _~~
X-y
v CJ lt feshy
___ _ _ __r~middot _ ___ _~_
helfBbAh c~Jn
shy
L~v-1 - l
~ ~ ~y-
t - ~I
1 E C~
- - vJ - )j I
J
I A ~ ~ - ~
(rvjl
~C C1
( l
)( T
j
~ v -- 11 lt-J ~
(~ lu ~ 00 n f-~J~ J
f ~ 12 cent1 D~-gtl (
l
[
8 ~-=-~~i
( nfl2bc[r6 ~1vl kC
t ~ ex (x~c) - -
-~ kJ)1~iKlftYKlA (~l(-J~_C~Jr~tgt~x lLJi fr(t ~i1cent 1)) e biyI--r) lt2
rshy1
shy
~
lt)-
~(Almiddot Pc~
rJ- -~p~tA - - shy
I
shy (-j) -r---
I
r T I
1 ~_
0 1 1t b( 1 tlt E 1 ~E Z
K J ~ -- ~ ~
reg (jj P
r-~A~
( -oJ -J 11
D r )J ] ~~-~
(i) A Y =1-
+ (
~ J
~+11
+1 -t ~ 7 )
I
)J
j
tlJ + b1 t bf i (
~ ( ~ ~l t t bc
l rr y) +Sc
+- I gtlt0 = xfc I ~LX ~J E-t L~ JOx 1 )eA ) +( 1+ b~~~ shy
( J J ) - -p
I-- -h_ e ytbX - J It( I -shy-I It ~t-M I
J
Ie E - ~ -1 f 1+ 1 l IAI f ~r t - b X )
j
- =r~ - GX cft I ~ s -t) shy
~ r
t-t1 01 J
11 I-=~ I jh v - 1 - shy
I 1 ~ ~ I
o Aj
A~ J Q
(l- E2J lltJ eL~ I)
_)1(K~
Jlt- j X y ~ t
4-shy
sA i ~6 t
f
C
yS -~7
t )l - ~tL ~l X J ~f
1
J ~ n f t-~ - I - fmiddot~) ~ J J
j ~ J shy
middot1
---_
_r
--
-
~ - - ~l ~5 ~ )~-~ ~
1
l __-l
~ )
I
~ ~ A 2~ l ~ ~ l =IV
A-- fC ~1Jfn
(x D
) ~
0 -
i - )
4middot
~
~
_ IJ I f -~-
i -) ~
--- -
i
( ~
-~ r- t
~-- ~lS c f j VI t
~ A ~ J
- --~~-
I A _1 L
~ Y -)lt-2 A + shy
(shy
_J -L
--Ii
~
- l~
1 r
_)
11VV
0
-
~1
___t
1
-~
) 1))
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
i
I I
)
-~ ~) jr- r~ A 5tTgt - ~-- 1] _shy -
I - r
t ~ A l~_- p-
C~ t7 f~)-- _ ~jiX)- -
~A=JS- J = Y-
i i I
c -t E- ( t r- f)~ y ( (11 )J t - ( (JJ)
~E ((0J
X G- f- Ii )lt c D ~ C ~ -1 e D J
lf)j)E A-x( (~j) amp- GxCgt
t PyL
t- (-ty Craquo (
l L
i I 0~)~ ) y )-7shy
t ~ lY~)
Clt - l t Cmiddot
I Ii_ bull-lt F V tI 1 Ii (I )
V Y ( ( I~ c i~-4 J- (-b
l~- t ~) y J
imiddotJ
f lQ)
~ I
1 ( ~ laquo~J V J J J
1 t J
OC06
~
0 7I r c) JGlt lmiddot -r
) )
r) gt ( - --~
)
shy
(
(
~ilt Z - LA
-) J I( j ( -
~i- _y~~f~ ~j~ ~ ~ A~~A
~~ (~ ls) Ci_fshy~~~J- t]~(t)~~
r--c- f ~ ~~
- - - ~-- bull -shy
Cflt(V ~([~e~~- f K JO-~
V
-Ij--XtAshy
))_ jtt_~ _~~
X-y
v CJ lt feshy
___ _ _ __r~middot _ ___ _~_
helfBbAh c~Jn
shy
L~v-1 - l
~ ~ ~y-
t - ~I
1 E C~
- - vJ - )j I
J
I A ~ ~ - ~
(rvjl
~C C1
( l
)( T
j
~ v -- 11 lt-J ~
(~ lu ~ 00 n f-~J~ J
f ~ 12 cent1 D~-gtl (
l
[
8 ~-=-~~i
( nfl2bc[r6 ~1vl kC
t ~ ex (x~c) - -
-~ kJ)1~iKlftYKlA (~l(-J~_C~Jr~tgt~x lLJi fr(t ~i1cent 1)) e biyI--r) lt2
rshy1
shy
~
lt)-
~(Almiddot Pc~
rJ- -~p~tA - - shy
I
shy (-j) -r---
I
r T I
1 ~_
0 1 1t b( 1 tlt E 1 ~E Z
K J ~ -- ~ ~
reg (jj P
r-~A~
( -oJ -J 11
D r )J ] ~~-~
(i) A Y =1-
+ (
~ J
~+11
+1 -t ~ 7 )
I
)J
j
tlJ + b1 t bf i (
~ ( ~ ~l t t bc
l rr y) +Sc
+- I gtlt0 = xfc I ~LX ~J E-t L~ JOx 1 )eA ) +( 1+ b~~~ shy
( J J ) - -p
I-- -h_ e ytbX - J It( I -shy-I It ~t-M I
J
Ie E - ~ -1 f 1+ 1 l IAI f ~r t - b X )
j
- =r~ - GX cft I ~ s -t) shy
~ r
t-t1 01 J
11 I-=~ I jh v - 1 - shy
I 1 ~ ~ I
o Aj
A~ J Q
(l- E2J lltJ eL~ I)
_)1(K~
Jlt- j X y ~ t
4-shy
sA i ~6 t
f
C
yS -~7
t )l - ~tL ~l X J ~f
1
J ~ n f t-~ - I - fmiddot~) ~ J J
j ~ J shy
middot1
---_
_r
--
-
~ - - ~l ~5 ~ )~-~ ~
1
l __-l
~ )
I
~ ~ A 2~ l ~ ~ l =IV
A-- fC ~1Jfn
(x D
) ~
0 -
i - )
4middot
~
~
_ IJ I f -~-
i -) ~
--- -
i
( ~
-~ r- t
~-- ~lS c f j VI t
~ A ~ J
- --~~-
I A _1 L
~ Y -)lt-2 A + shy
(shy
_J -L
--Ii
~
- l~
1 r
_)
11VV
0
-
~1
___t
1
-~
) 1))
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
c -t E- ( t r- f)~ y ( (11 )J t - ( (JJ)
~E ((0J
X G- f- Ii )lt c D ~ C ~ -1 e D J
lf)j)E A-x( (~j) amp- GxCgt
t PyL
t- (-ty Craquo (
l L
i I 0~)~ ) y )-7shy
t ~ lY~)
Clt - l t Cmiddot
I Ii_ bull-lt F V tI 1 Ii (I )
V Y ( ( I~ c i~-4 J- (-b
l~- t ~) y J
imiddotJ
f lQ)
~ I
1 ( ~ laquo~J V J J J
1 t J
OC06
~
0 7I r c) JGlt lmiddot -r
) )
r) gt ( - --~
)
shy
(
(
~ilt Z - LA
-) J I( j ( -
~i- _y~~f~ ~j~ ~ ~ A~~A
~~ (~ ls) Ci_fshy~~~J- t]~(t)~~
r--c- f ~ ~~
- - - ~-- bull -shy
Cflt(V ~([~e~~- f K JO-~
V
-Ij--XtAshy
))_ jtt_~ _~~
X-y
v CJ lt feshy
___ _ _ __r~middot _ ___ _~_
helfBbAh c~Jn
shy
L~v-1 - l
~ ~ ~y-
t - ~I
1 E C~
- - vJ - )j I
J
I A ~ ~ - ~
(rvjl
~C C1
( l
)( T
j
~ v -- 11 lt-J ~
(~ lu ~ 00 n f-~J~ J
f ~ 12 cent1 D~-gtl (
l
[
8 ~-=-~~i
( nfl2bc[r6 ~1vl kC
t ~ ex (x~c) - -
-~ kJ)1~iKlftYKlA (~l(-J~_C~Jr~tgt~x lLJi fr(t ~i1cent 1)) e biyI--r) lt2
rshy1
shy
~
lt)-
~(Almiddot Pc~
rJ- -~p~tA - - shy
I
shy (-j) -r---
I
r T I
1 ~_
0 1 1t b( 1 tlt E 1 ~E Z
K J ~ -- ~ ~
reg (jj P
r-~A~
( -oJ -J 11
D r )J ] ~~-~
(i) A Y =1-
+ (
~ J
~+11
+1 -t ~ 7 )
I
)J
j
tlJ + b1 t bf i (
~ ( ~ ~l t t bc
l rr y) +Sc
+- I gtlt0 = xfc I ~LX ~J E-t L~ JOx 1 )eA ) +( 1+ b~~~ shy
( J J ) - -p
I-- -h_ e ytbX - J It( I -shy-I It ~t-M I
J
Ie E - ~ -1 f 1+ 1 l IAI f ~r t - b X )
j
- =r~ - GX cft I ~ s -t) shy
~ r
t-t1 01 J
11 I-=~ I jh v - 1 - shy
I 1 ~ ~ I
o Aj
A~ J Q
(l- E2J lltJ eL~ I)
_)1(K~
Jlt- j X y ~ t
4-shy
sA i ~6 t
f
C
yS -~7
t )l - ~tL ~l X J ~f
1
J ~ n f t-~ - I - fmiddot~) ~ J J
j ~ J shy
middot1
---_
_r
--
-
~ - - ~l ~5 ~ )~-~ ~
1
l __-l
~ )
I
~ ~ A 2~ l ~ ~ l =IV
A-- fC ~1Jfn
(x D
) ~
0 -
i - )
4middot
~
~
_ IJ I f -~-
i -) ~
--- -
i
( ~
-~ r- t
~-- ~lS c f j VI t
~ A ~ J
- --~~-
I A _1 L
~ Y -)lt-2 A + shy
(shy
_J -L
--Ii
~
- l~
1 r
_)
11VV
0
-
~1
___t
1
-~
) 1))
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
1 ( ~ laquo~J V J J J
1 t J
OC06
~
0 7I r c) JGlt lmiddot -r
) )
r) gt ( - --~
)
shy
(
(
~ilt Z - LA
-) J I( j ( -
~i- _y~~f~ ~j~ ~ ~ A~~A
~~ (~ ls) Ci_fshy~~~J- t]~(t)~~
r--c- f ~ ~~
- - - ~-- bull -shy
Cflt(V ~([~e~~- f K JO-~
V
-Ij--XtAshy
))_ jtt_~ _~~
X-y
v CJ lt feshy
___ _ _ __r~middot _ ___ _~_
helfBbAh c~Jn
shy
L~v-1 - l
~ ~ ~y-
t - ~I
1 E C~
- - vJ - )j I
J
I A ~ ~ - ~
(rvjl
~C C1
( l
)( T
j
~ v -- 11 lt-J ~
(~ lu ~ 00 n f-~J~ J
f ~ 12 cent1 D~-gtl (
l
[
8 ~-=-~~i
( nfl2bc[r6 ~1vl kC
t ~ ex (x~c) - -
-~ kJ)1~iKlftYKlA (~l(-J~_C~Jr~tgt~x lLJi fr(t ~i1cent 1)) e biyI--r) lt2
rshy1
shy
~
lt)-
~(Almiddot Pc~
rJ- -~p~tA - - shy
I
shy (-j) -r---
I
r T I
1 ~_
0 1 1t b( 1 tlt E 1 ~E Z
K J ~ -- ~ ~
reg (jj P
r-~A~
( -oJ -J 11
D r )J ] ~~-~
(i) A Y =1-
+ (
~ J
~+11
+1 -t ~ 7 )
I
)J
j
tlJ + b1 t bf i (
~ ( ~ ~l t t bc
l rr y) +Sc
+- I gtlt0 = xfc I ~LX ~J E-t L~ JOx 1 )eA ) +( 1+ b~~~ shy
( J J ) - -p
I-- -h_ e ytbX - J It( I -shy-I It ~t-M I
J
Ie E - ~ -1 f 1+ 1 l IAI f ~r t - b X )
j
- =r~ - GX cft I ~ s -t) shy
~ r
t-t1 01 J
11 I-=~ I jh v - 1 - shy
I 1 ~ ~ I
o Aj
A~ J Q
(l- E2J lltJ eL~ I)
_)1(K~
Jlt- j X y ~ t
4-shy
sA i ~6 t
f
C
yS -~7
t )l - ~tL ~l X J ~f
1
J ~ n f t-~ - I - fmiddot~) ~ J J
j ~ J shy
middot1
---_
_r
--
-
~ - - ~l ~5 ~ )~-~ ~
1
l __-l
~ )
I
~ ~ A 2~ l ~ ~ l =IV
A-- fC ~1Jfn
(x D
) ~
0 -
i - )
4middot
~
~
_ IJ I f -~-
i -) ~
--- -
i
( ~
-~ r- t
~-- ~lS c f j VI t
~ A ~ J
- --~~-
I A _1 L
~ Y -)lt-2 A + shy
(shy
_J -L
--Ii
~
- l~
1 r
_)
11VV
0
-
~1
___t
1
-~
) 1))
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
~i- _y~~f~ ~j~ ~ ~ A~~A
~~ (~ ls) Ci_fshy~~~J- t]~(t)~~
r--c- f ~ ~~
- - - ~-- bull -shy
Cflt(V ~([~e~~- f K JO-~
V
-Ij--XtAshy
))_ jtt_~ _~~
X-y
v CJ lt feshy
___ _ _ __r~middot _ ___ _~_
helfBbAh c~Jn
shy
L~v-1 - l
~ ~ ~y-
t - ~I
1 E C~
- - vJ - )j I
J
I A ~ ~ - ~
(rvjl
~C C1
( l
)( T
j
~ v -- 11 lt-J ~
(~ lu ~ 00 n f-~J~ J
f ~ 12 cent1 D~-gtl (
l
[
8 ~-=-~~i
( nfl2bc[r6 ~1vl kC
t ~ ex (x~c) - -
-~ kJ)1~iKlftYKlA (~l(-J~_C~Jr~tgt~x lLJi fr(t ~i1cent 1)) e biyI--r) lt2
rshy1
shy
~
lt)-
~(Almiddot Pc~
rJ- -~p~tA - - shy
I
shy (-j) -r---
I
r T I
1 ~_
0 1 1t b( 1 tlt E 1 ~E Z
K J ~ -- ~ ~
reg (jj P
r-~A~
( -oJ -J 11
D r )J ] ~~-~
(i) A Y =1-
+ (
~ J
~+11
+1 -t ~ 7 )
I
)J
j
tlJ + b1 t bf i (
~ ( ~ ~l t t bc
l rr y) +Sc
+- I gtlt0 = xfc I ~LX ~J E-t L~ JOx 1 )eA ) +( 1+ b~~~ shy
( J J ) - -p
I-- -h_ e ytbX - J It( I -shy-I It ~t-M I
J
Ie E - ~ -1 f 1+ 1 l IAI f ~r t - b X )
j
- =r~ - GX cft I ~ s -t) shy
~ r
t-t1 01 J
11 I-=~ I jh v - 1 - shy
I 1 ~ ~ I
o Aj
A~ J Q
(l- E2J lltJ eL~ I)
_)1(K~
Jlt- j X y ~ t
4-shy
sA i ~6 t
f
C
yS -~7
t )l - ~tL ~l X J ~f
1
J ~ n f t-~ - I - fmiddot~) ~ J J
j ~ J shy
middot1
---_
_r
--
-
~ - - ~l ~5 ~ )~-~ ~
1
l __-l
~ )
I
~ ~ A 2~ l ~ ~ l =IV
A-- fC ~1Jfn
(x D
) ~
0 -
i - )
4middot
~
~
_ IJ I f -~-
i -) ~
--- -
i
( ~
-~ r- t
~-- ~lS c f j VI t
~ A ~ J
- --~~-
I A _1 L
~ Y -)lt-2 A + shy
(shy
_J -L
--Ii
~
- l~
1 r
_)
11VV
0
-
~1
___t
1
-~
) 1))
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
l
[
8 ~-=-~~i
( nfl2bc[r6 ~1vl kC
t ~ ex (x~c) - -
-~ kJ)1~iKlftYKlA (~l(-J~_C~Jr~tgt~x lLJi fr(t ~i1cent 1)) e biyI--r) lt2
rshy1
shy
~
lt)-
~(Almiddot Pc~
rJ- -~p~tA - - shy
I
shy (-j) -r---
I
r T I
1 ~_
0 1 1t b( 1 tlt E 1 ~E Z
K J ~ -- ~ ~
reg (jj P
r-~A~
( -oJ -J 11
D r )J ] ~~-~
(i) A Y =1-
+ (
~ J
~+11
+1 -t ~ 7 )
I
)J
j
tlJ + b1 t bf i (
~ ( ~ ~l t t bc
l rr y) +Sc
+- I gtlt0 = xfc I ~LX ~J E-t L~ JOx 1 )eA ) +( 1+ b~~~ shy
( J J ) - -p
I-- -h_ e ytbX - J It( I -shy-I It ~t-M I
J
Ie E - ~ -1 f 1+ 1 l IAI f ~r t - b X )
j
- =r~ - GX cft I ~ s -t) shy
~ r
t-t1 01 J
11 I-=~ I jh v - 1 - shy
I 1 ~ ~ I
o Aj
A~ J Q
(l- E2J lltJ eL~ I)
_)1(K~
Jlt- j X y ~ t
4-shy
sA i ~6 t
f
C
yS -~7
t )l - ~tL ~l X J ~f
1
J ~ n f t-~ - I - fmiddot~) ~ J J
j ~ J shy
middot1
---_
_r
--
-
~ - - ~l ~5 ~ )~-~ ~
1
l __-l
~ )
I
~ ~ A 2~ l ~ ~ l =IV
A-- fC ~1Jfn
(x D
) ~
0 -
i - )
4middot
~
~
_ IJ I f -~-
i -) ~
--- -
i
( ~
-~ r- t
~-- ~lS c f j VI t
~ A ~ J
- --~~-
I A _1 L
~ Y -)lt-2 A + shy
(shy
_J -L
--Ii
~
- l~
1 r
_)
11VV
0
-
~1
___t
1
-~
) 1))
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
r T I
1 ~_
0 1 1t b( 1 tlt E 1 ~E Z
K J ~ -- ~ ~
reg (jj P
r-~A~
( -oJ -J 11
D r )J ] ~~-~
(i) A Y =1-
+ (
~ J
~+11
+1 -t ~ 7 )
I
)J
j
tlJ + b1 t bf i (
~ ( ~ ~l t t bc
l rr y) +Sc
+- I gtlt0 = xfc I ~LX ~J E-t L~ JOx 1 )eA ) +( 1+ b~~~ shy
( J J ) - -p
I-- -h_ e ytbX - J It( I -shy-I It ~t-M I
J
Ie E - ~ -1 f 1+ 1 l IAI f ~r t - b X )
j
- =r~ - GX cft I ~ s -t) shy
~ r
t-t1 01 J
11 I-=~ I jh v - 1 - shy
I 1 ~ ~ I
o Aj
A~ J Q
(l- E2J lltJ eL~ I)
_)1(K~
Jlt- j X y ~ t
4-shy
sA i ~6 t
f
C
yS -~7
t )l - ~tL ~l X J ~f
1
J ~ n f t-~ - I - fmiddot~) ~ J J
j ~ J shy
middot1
---_
_r
--
-
~ - - ~l ~5 ~ )~-~ ~
1
l __-l
~ )
I
~ ~ A 2~ l ~ ~ l =IV
A-- fC ~1Jfn
(x D
) ~
0 -
i - )
4middot
~
~
_ IJ I f -~-
i -) ~
--- -
i
( ~
-~ r- t
~-- ~lS c f j VI t
~ A ~ J
- --~~-
I A _1 L
~ Y -)lt-2 A + shy
(shy
_J -L
--Ii
~
- l~
1 r
_)
11VV
0
-
~1
___t
1
-~
) 1))
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
)J
j
tlJ + b1 t bf i (
~ ( ~ ~l t t bc
l rr y) +Sc
+- I gtlt0 = xfc I ~LX ~J E-t L~ JOx 1 )eA ) +( 1+ b~~~ shy
( J J ) - -p
I-- -h_ e ytbX - J It( I -shy-I It ~t-M I
J
Ie E - ~ -1 f 1+ 1 l IAI f ~r t - b X )
j
- =r~ - GX cft I ~ s -t) shy
~ r
t-t1 01 J
11 I-=~ I jh v - 1 - shy
I 1 ~ ~ I
o Aj
A~ J Q
(l- E2J lltJ eL~ I)
_)1(K~
Jlt- j X y ~ t
4-shy
sA i ~6 t
f
C
yS -~7
t )l - ~tL ~l X J ~f
1
J ~ n f t-~ - I - fmiddot~) ~ J J
j ~ J shy
middot1
---_
_r
--
-
~ - - ~l ~5 ~ )~-~ ~
1
l __-l
~ )
I
~ ~ A 2~ l ~ ~ l =IV
A-- fC ~1Jfn
(x D
) ~
0 -
i - )
4middot
~
~
_ IJ I f -~-
i -) ~
--- -
i
( ~
-~ r- t
~-- ~lS c f j VI t
~ A ~ J
- --~~-
I A _1 L
~ Y -)lt-2 A + shy
(shy
_J -L
--Ii
~
- l~
1 r
_)
11VV
0
-
~1
___t
1
-~
) 1))
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
1
J ~ n f t-~ - I - fmiddot~) ~ J J
j ~ J shy
middot1
---_
_r
--
-
~ - - ~l ~5 ~ )~-~ ~
1
l __-l
~ )
I
~ ~ A 2~ l ~ ~ l =IV
A-- fC ~1Jfn
(x D
) ~
0 -
i - )
4middot
~
~
_ IJ I f -~-
i -) ~
--- -
i
( ~
-~ r- t
~-- ~lS c f j VI t
~ A ~ J
- --~~-
I A _1 L
~ Y -)lt-2 A + shy
(shy
_J -L
--Ii
~
- l~
1 r
_)
11VV
0
-
~1
___t
1
-~
) 1))
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
--- -
i
( ~
-~ r- t
~-- ~lS c f j VI t
~ A ~ J
- --~~-
I A _1 L
~ Y -)lt-2 A + shy
(shy
_J -L
--Ii
~
- l~
1 r
_)
11VV
0
-
~1
___t
1
-~
) 1))
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
C
45 1 ~ ~-~
II~ 1 - ) j
I
(JJ)t J ~ J )
(
- ~ (f)lr ~ r r _xC I ~
(Alc) l t
~I ~ r ~ t i J ~ C
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
_ y y
t -- --J C ~ - 1 J ( ltqshy I
(J 7 1- y) gt y 1 TQ
1 Oy hC) V 9 IJ rl -1 1 r (
JYr~ 11 (v Cl H ~j dC VII) V jj dl-(G~ j J r ~
1 f fshyj v l j -
~ y--- 1~~ 1 G t r IV~ ~
shy
~ y
c- ~
0- ( r f
~
tf (
( l )
( r
lt ( ~ ~lt
( - ~ C r j I l
-A ~ J 7 I- l r1 t ) t
j
c ~~J )
r
JATYi (V y vJ
1 111-d1J ~-jrt ty lCl y lt
cyen)l LoJOv CNVdd ~ ( ~
r- I
j i)~ cnD Ir-7 X
~~Sv91C1~1 ~ ~ tq - v lb
~-~x e~ x 7 0 vli4-j(~ W x C)t19) --gtf v (- ~ ---II -shy~ )
( C- W i~ d -J ~i JT L~1dc0JO V~ li-1 r VIy() c~ shy
D X rfdq f -gt X~middot C) icil It l~i- ~ )0(l 7 J
_ r ( J-aSIdW j 10 -V JC) -JC ltriO I -LYI(3y(dVlt) gt1 H IJVl Wnll V ~ i
X ye (1tl~ j X OyfVl -Qlt 11 ~~ 1 middotlt1ClYQ0 Y~~~l ~0 Y Ih~ tf - gt C)ljCJJ -hc 1 j CJ )dlt(cIC ~~If~~i
V
7 (rU l 1 J I I ~ ~ LJ shy f I
v j r_cflJ f2J y )(1 soJ ~0~CJ ~
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
11 L 1+
Vk t A
ty E FtMLA~-
VY~A
I
l 0 J X -j x ~o
cO -X-=-7 raquolt =- ~O
ct) f1=~ I~J X~ J
A f AxA ~A--
~ rJf-J~IJ A- (IQfe(
)--~jM~~cv -10- 0C~lA JVV APICJ
~ ) ~t- (p ~I gt- c )lt~2 X I ~
LPr~ )lt J v 1 ) gt1ij ~ ~
J ~j
_ 7-
j
( 0I ---- shy
If X
-
- ~
rlaquo-= r~ )
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
--
t r
1 - V j~ i
-) shy
-1shy
fvmiddotA
~~1 - -
_~)A- y -A I -shy
~ iJ-e-~ V 5
J _ -lt 1
JJ
r (
U
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
_l j
~ I
1 1 I l II
i
I 1
l V )
~
c
t C~x -ltj i
-
_If-mAul Pc -J
~z
X LJ2
~Q~
H~S~ ff~A-~
--- shy -- Q--I ~ J __ ___
- It A I f_n ~ I ~
- I J
-x ~ -fr ~
-J I
C lC ~
l ~
J
V) xI -x
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
q-f( ~ ~-7j
~
()~ 1 -) t (
j ~
v ()Q
--
J ~~
)IL
lt
- ( lt) -gt Xmiddotlaquo r
) -i
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
J
rr I (i) ~ J
1o i U -
1lt A~middot it J
+ ( (
=-A i gt1 -J - -I
(0 Jr) e -=) v -1 =x 2 -i
-J
--UJ~I )lt-11 0 -
CJ Ji-lte ( j LA - Hk )4- ()Oktf12 - ~e r~ VI V 0
1 ) J J J c_ Qltshy
j
~
a- ~
e-X-shy -1J-
v J
~)~ L) - er( ~l- r- c_ CTr ( l -J U -v)
i - v
J t -) C
~
UTo o
shyAXC)( T poundc- t
i
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
I~
p
l r ~
5 r~~K~-j ----~ ---__
)
~ r t-p J
-=
_J -rA
3 jr- C~Ack~ ishy
n -gt
I ~ 7) ) j v_
- i
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
l--shy
-~
~=_c_ -c- Gj_~(~J (Oci5V1
r
(p) )
( f I ( ( r J ~ I)
yC fUf~ (X)~j
11 ~ c-r
q~ lX) )
~j~ ~(k) lAS l J ~(6)
I r I
(ri ) ~( I II i - J
)) l
1 r
r ( Ar Ir~~ -J~
u ( c()) ~ l l
j Ji-middot r~) ~
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
2deg r ~ Imiddot ( I ~gt i shyL f )- J -
~
r J (
)
(
J(- r - t~ --- r- v --
- 1 J
I
l ~) ) -~r j I r bull I jVp lf ( r~(rl S1t - 11 i -=r
J - -l
ly j
~I ( ( r r f r
-~ ff ) r ) II ( eA )-
~ t--
(- - (~ f6)1
) r ) H ( rI
f I
-- I
)
K -~
shyx 1-
( r I 1 r (
~f Imiddot e 1 1) )
I ~
-~
r middotr X t_ (
-Cshy I- f
J
(
pK
l
t t -
I I
~
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
--
~
J
~)
CD ~ ~l j
( n l lt imiddotlp~ (~-A ( r
r (~ J I C I i+ (1febA ~o 1shy
rs~ (J CJ V1 (b() 10 Ir 11
V
C~)) 6J -~ -~- -shy Sf C -~( B)) Cfr ~ (0 Clj_h
~~(5) )
-6
k~6
( -1jf c i( u- ~ J __ _
fl-
r-nib r UtA-I --
~ (0) f~(tr~)~ (gtlt) ~- J
_
) ~- - r
r( ~ l r ~ r I ___ i _ ~ ~ I l - shy
J shy J I
t shyr- -lt
2 J L~ ~j- It- 0v
J
r Ii
- -j
-
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
-1 C
-L
J
tj~~(~)) middot~f-L
e AshyJ
f~~~ middotf-JKrScentflA~h~P f C~ty~~
plusmn~=~~~(5fC~) J 1- iv)sect ~t ~~
r -shy
-~ ( - )
p
J (
) J
r r ( (fmiddotmiddot ~ J-- ~~ 1-~J j ~) J v
( - middotmiddot1)
-1lt-
r -j
- f f[)6 [ 0 (i
( 1 ~ ( ) shy
( I
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
r I ~t -i1 j I C J l j
- ~ --~ f (
~ I 1 J -- ( 2-_ r -0 Jj
c- r l
1
J-
reg 1(--J e- n pOVJ +shy+ ~ I
middotmiddotmiddotmiddotmiddotmiddotmiddotD
middot1-middot~tbYsmiddotomiddot-shy~r~ Joj ~S ()
- 1
21 Cb~v-
~ (p--I) v-) rr
1- 1
(b)~A
i
i
11-( 0
7
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
I 1 I L~1-jJfJO Ifr=-lA I J
v t I I f bull ~ ~~-- i ~ y_ lu- y
Jl ~ lt Qt- (0(- V ~q I I J 1(~ L~ -tv i i ( -V ~ r- J -71
J )~
1- ~- )
of ~~~~f~jlV~_N~
~ hl ~gt ~~ Crlt) gt fl
KJ-~l (e (A j
( ~ J
shyI shy
( ~) ~ ~ (nj J
j
_f A - ~ 7- frt- ~
(i( (
t-
I f
l Vn j ()
t -+- f
(rJ ~-_ bull [) n - I
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
-
1 I
1 A- 0fE6fb1 ~G ~j
j tlJ ~ frJ -
~Crt) 2Vf
s (rn II
J
()h - 2hz
r r
L~_l ~ (r A ~ f (nt ~
- ( b f)IJ I C- J
j J
0 _gt ~
~---1j
l-) c v -
t( 0- -shyshy
shyJ
IN iV t ( p~-f)01 ~ )
lt- ~~ h -J
r M7-CgtlVr ~ ~
y )1 i
~- ---gt lY WI lt-0
i
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
~ =- Qshy
fsJO 1) o-~ t~l-
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
~hoe - -~ --~~()- f
~~~X--~o--middot~- ---~--~---r~----
lA-t~~~6~ ~Z-A -- ~ --~
~~-~-~~
f r shyA -I -Jj 1 ) 1 r r
~J I -=)
-shy
iJ (
shy
j -
tJlt
lt
t3
r
1 (6A( )
r (+ r6e()
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
-z --_------- ( -(V- L I-t-- ~ 1-11(v k V ~v) lJ+V) ( -- I ~k-V)
v I
~
J )
f = V+-) )+- vH- -t- C ~ Y
u ~ L
---------~------IVi J + 7 r V
(1 V+I) H~ f
u ~~--- LiV) Cvh)di- ) tJ yen 1l-It--i0 I IQ ra-(j1
L iJ+ ) ( +- ~ A) 7 drmiddot ~ ~ 0 )1 IICif~ L Q)j~J JJ2r()J (v- v) ~1
tV-d L OUlltJv - L 1-- gt v or J1 YIl j[i- (~) ~IO
( r ~ ~ O) 1111 ~ gt-dv VI 1shyif CZV9J (~~)1(VkV)~ V ~
- v J ~If~ g v CHln --i - -= + -r G+V
(v+Vt ) U r
VILJsxrY 0 f V(C t L(J~ I (I IG IlVu_u rid1--1 rJ CD
~1 1 1 N+ V oyiamp0j ~J ( c 11k)Jl
f
1 v tmiddot J ~~) OJ--v ~1 0
lfrltJr r L
r4J- l-+171110 ~V) C~1hVl j -tld I Ij Cdg V1~YcLJv V~~~ ~ 0
(f) s1)r)Yi i ~TyenV~t k _L- I
if c-J7J if JoJ- LIO1hl oIr(O ~ ~ l1JJ 1 ( 1 I
fi ~d9 4j 11 c JlAdtI 1 tFi1) -1 b 1) 1 ~fgti) )Ij d ( i ~1j
~ fYb~h~~v gt1 hY1L--d~L~W Ny~vJ lbshy
y tvt It - - l0
r--c___________________~___ __ --- ~ ~L Jt 11-~~ 6 -) 1S-1 I CIt it -1 _ bulln -yenII - 1JA11 4- ~
~r--~_ -- - I___ ~ V-iJ - CVVd A f _ ) U -tj --t cUOV = ( VfJ) q t)u I]Vlt
1- I -
J J -=)v i))J Jll 7 Jlfl A - - J I
- ) ---( CIIII )) -4 bull Ci _i) -1 )7i - 11 J -1 xtmiddot i- ) I~ ) ~ -- CII~
~
Ii
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
c~ J- v -~
(~) _T (1A 1 ==-1l
t (It) fe --r flY t1Q
(~) n~-r() AA- le -rfrVl-1ol(r1) ~ -t-~ r -t-fZfl - ~ (l shy
P-tO K fb j jcito l yenvr~ 0 aT LA ULr A- 1--0tf) il -r-t- +2Vl~A r (flH) -1-==(1l-r12
~ r) r~) i euro --rt4~J ~ CA1rlt If ( t~ I
J
) (f V ( 11 J-+ 5 ) l~ 1) -O~
-~
CIlJ
k (~) I) rmiddotmiddot --shyJ
(---t
i - (fltj II
I ~ ( I
_ i
bull y J
ff-)1 60I ~ ~ gt nolA Jo rIL q (7r f
C (vJ-1 Ai j f- )
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
~ ~ICO 1_ ~ J
L)--~ 2rr~
-r2
2V~ll-r middotmiddot-1 t~ 411 1
r-l- i
1- 1
l f J -
I I(1+ - 1 -f)
_ r1- - ~ I~ ~ J
-
-)shy ~
J ~~~ ~~--lt ~- --shy
~ I
1
j
I
= -(n
J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v
r - r
L (~1 r(jI(~ 2 --
tV f- Il~e ~
-- --shyd (~) L - if I 11) 0
~tr
- I
--~-------r-~~--~~ middotmiddot~ -shy
I
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
i Vltj
1-J) V )30 JeLl l dCJ 1 i o
- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU
-~- yl- v - i - ) Jshy
[
t ~ ifshy _i 1~gtft- iJ 3(--1 le J
-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy
~ ( V) ~ ~ i
-I
) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)
J I -
j) -VI J53 Q(t~I ) I
~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-
( -I 0 ~ lt~ V-- J-- 11-
1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d
Vi I l l
J -~ ---J ~ ) ~ J c)0)shy
c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v
)- I- I c- l- shyc
I __ __ Jgt- ~--v~T(v-t~~- 2____ L
-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy
- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~
C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I
C -Zshy I
shy1- -VI-J
L----v J 2- -T1-- FV shy
C -_ ))- L _( ~~ V_ l vshy
- ~ GvJ gtJ~_) _-- __ 1 v
-11 I
- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J
~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4
---- -(------~----- - - shy
---y
~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy
-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -
1 ~ gtf J hj J itcmiddot -I~ ~ _gt l
tr-l t -~~~ J L
~
J I-j 0
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
- ~f V ~ - J-- IJ-j - )
J J J r1~ 0- v ~ j -~-
~ J w~j_1_ ) ( v c
I~G V
i y_l Ii ) T V V
I -~ v L=shy v- -U t) lv l7
j J C r
I ~V-~7 J I I-L) -- vt
v V-rV I -
OIv 01h~L (vi) T (
r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1
)
r vi d L J ~ i c L j U) v]~l - (
j ~J J U
J Ji f - L t I-~ ~- l J l_J
y-v-
v~~~O~ (0) I ~
W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ
j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)
c L t
I~~~ a deg1 H twog VI d)
~ shy
----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I
Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0
v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c
H- Ir~ V J
~-vQ ~ ~ 0
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
--
1J h+ A
- ( --A 1) I( - ) r 1-
Ii ~
-~
-~ i) jt PrihoC ~r
~ )__ -i( rr 0 r 0
~- J
1r
20
J i I
i J
t 1
Jishy
~
l-iA)
I CI -- V I
1-(
2 ~-r
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t
(Alt fl 00shyi) (xl ey - It
J 6 ~
et~ I
6) ~ (A or I - I
j
~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy
q= ej + ( q r C c v v I
r lt- fr
b(IJI ( M eshyI J
r~
-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~
H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J
(
crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(
(~Ie)
0- e62KA~hW9A-k)e S ( t1J i~ fl
(A V Ir o (0 ceCr _ _ t s
f-~~ ~ttVgVl
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
o~ Y ~ ~~ J~r~ ~ JO flr~TA
fPttl cp0 P0 A J~fJ
h i i
5tTh A~ LA_i
cg C(56f1~~
1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i
1rfl~c4gt lJ tlVTHh _I-Ai-Ayen
J(
o 1- t (l j- rt-toJ~e (1 ~_
1- f t ~ J
J n(~l
r nmiddot e-J--~ Of7 beibE ~~IA
f) -+1
np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16
1ltamp ~
flpQ~5r~)(
bull I
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA
rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM
) v
fA= ~ ~L f1 no(1oj1 0ff ~ fA
Pc ICA
D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v
regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It
1gt vHA-- 1 (0 h1f1 1-10 tH-of 0
O~-i p~ j f- ~ ~ I
nI ~ ~ (G iA I~ lbt2~ 5J k
iF l-
I
~ l
( v 2 ~ = it il Ii
iyen rshy
-gt
ic
A p r Rin () iL ~ 1i
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY
oJ1A ) J~D fA 0 [ JHA (It Gt +5
r I)
0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5
~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH
t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r
-rJ 1061 VlKA
(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA
r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c
1
t2L~~ (1 PI f m + 0
5
I
r~ amp 6 I ( je 1
I 1 I
Ie C jJ
poundPJlitshy
F~ ~ c
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
NidCtA~)
Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)
cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA
dIV v d er d L tA d ~ - Q- L1
(l~ ~ d( -7 d)[ d (A
c)~~ r
v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_
~ rJ Ned ( t~
(~ - ir 1 ~ -tC~
e~ ~1 I 1 rj if l lt2-
1 ~f1~ ()
(L r~ J -+ rt O Igt
cO
C-2 -- rl l -Ii r~ o
r v---fI ~ ~ I
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
--
IlVll elf~ ~(bIJ 611~ fhAl~ IA
J (T(0 TI~ J
r
tJ
bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ
8~D=- 2513 +1CL
LS 2 = A62~ JO ~ t_ 50 l + ~2
o - 2- ~ 1 fJl (3pound5 I -==- ~8
n3~ -- 0
13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2
JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L
~A
33) 3 1iY1 [5 v J1It~J A
r t I I reg 0 117t Vshy
I t
6 Aft
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
( 0
N20( A( ~) -~ - pound0 ~Pt-
lL0 shyJ
0 -
gt-n lt-~) J
h
2
L 0 itl
I
f
I
i I
I
I
J7j i --=gt 0 ~
~q I f
~~ ~ ~1
IG A
Sj -[ V2 - t ~5
~---~-
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
~~~(l0~lt
p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)
~m I~j
l we~O
Q ~amp ~~~
u --~f 6 k()
rC~T AOkftN~o)
OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0
fA~ ~ Lj = ~ t 1- r-dj I X I J e i-
Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d
111-1
C -~d
S~ --+ ) 9A ~S--==0
CL = Me O-KZo M la-tr
CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J
bull 30 I2 -~3
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
() - 2L -~~
rf 2 _ ~ ~1~ 112
16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~
1= ~ 3 c
1~ --A~
reg 21=M
C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j
c~ -~ rn lt~ -- t
)
iv- ~
f1 I
~ Vvtz-t t G
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
) J U-IQ
tt
J1Jh A r=A It k)
OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1
b X -= SA-=gt
X=7J~
(h J) ~ A r~---~---(
L~ )~ 1j ~ J
A- -~
reg ut(Vk-
(A I rli )= 1
nOUlJV o -iVV I 0 ~ A
~ 100 i11 1 1 0
~ i ~Iv - yYI
JA 2~b ~l=
l~c)J I
10 SAyoshy t~ b (0 ~i
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )
-= - f5 - 2 )~~-
0 =tI f
~_O~L
m ~y-- (~l1J -J - ~ ~
(~3~A
) Y =c s h
-I ) (~ ([~~
~J)en_pound nOJ ~jlle C J
reg Gf~fr~ d~- J L1 (0 (1)
I t A
j )A (~)~ ~WC-~2~l)
I
1=M ~
b~-=~ U ~ ~ (A ~J I 1
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
1)(~
8f I) __
J ( lJ L(-I2 8 8raquo ~ 7
~I ~L
21 f t1shy
1 = c i
JI (Q~- 2_ lt-Gl VI v J
Q_ ~ -1 i) J 1 rebk hA i
JIJ ~ ) ~
CUC10 rP0e~-u---vj A
y - f l- L ~ =- rv b r3
J (111f)pound~)~ f1 I t1
)J =- ~l~ ~ VV _ L I
A
M hA _ _
IV_ tt
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
~~ ~ A A 3~ LA -== II 5- -4 f
olt0
I f- ~ c ~ ~ II
( 1-7 I
x =+ 1
C-Oj ~ j~ ~ - ~S
(NY
(25 j JshyM1 - ~ fAshy
~- G~
k ~--= (~ )~1 J = ~ 51 ~S-
j5K~ ~ ~ 8~ ~~ S - 3
I _
t
bJ v -= _~ ( shyf 5 ~ A )3- l
10 ~ ~S S~ ~
~~k L S c
I
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
( - G(~ (~ vr c 111
~-J 0~C -~I
S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V
I f Ii c
y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J
I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~
Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull
( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij
d J OJ
( r )
( J I ~~ ~ 0
ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~
c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J
v)J (~J J - (V U) ch
j-A J ~)d l)cJJ ia d
1(t cZ I j
_ i I
I ~Jlt+~ L1JJrl-h~ Ii i
i
(IA) ~--~ ~ 53 VI
) -lQn~crto-
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
)e GflJ~ ~~tt14 tt
( ~l ~~l ~ L ~l~ 1
~
r ftX
k~
(lV1fD- G fOI D --I
J
2oo~
t r(M bull ~) ~ ( ~) j If (~)
~CC ~) ~ ~(L~r =~~~~~
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
1 i) ( ~-
(~ (X)) A
~ (~GO A
1(00 I
~ 2shy
100 - 2
~ (V) ) V) ( i ~ ~J
CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc
13~ L Co
~J ~~ -5 _j -==
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
AJlj 2- ~~_tL1f 312shy k ~N~~j -
v I1-
---shy1
t9~J -- 1shy
cf y ( ~ i-J ~~
~(1-) (-~-1 ) ~ - ~t
3~2 - Lmiddot (
1 bull
)
- ljx S
L X I - --
I - jtv ty- ~ rfl 2 a lr1 -iJ
~-v~ ---~ - l r A
- (Ml -shy-
I f
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
~ k -tampJ -= LA t CG t reg
fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1
_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J
d~c0
dl) d(
j e6 If ~ P-t 0 ao rft~rop ATamp A HI
d
-I 0
-t t) ) ~ 6--e~~~~ J~ oj
middot~middotLAi~V(
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
d
~ t t2~~ l)
~ =0 -tL bull
c ~ )--ti
l ( ()
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
C0Q]) IAVI jEth f ~
2d (3 L I I-t S) - ~
~ )
I 0
( ~ -1 ( )
reg L9A oj1 =-LO CA L C
u 1 ~ )
0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11
I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy
l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ
+- lt fV-II f-shy -
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k
(JY61 i Jil~y 40
T -BQNlQ ~ 1J) ---J
ImiddotGS ~ 0
1 ~ --z11
0 -
~ B ) ~~ ~ ~ ) I A (
J J
j (J ~ky ~ -3 G
0~ ~ G ~~~t
J -= - V Z-~~) - t ( tc-1)
JJrOl(ff-1 v A~ 1 ~f1
nbull bull -= tCshyv VI_
W1 d
bltf L 1
-=r
(1~lmiddot1l-t- 4 L - =
-
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
- t
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
tmiddot
( I t
) J C ~
-y ygt 1 f
) ~j v ~
1-- i
ff
11
N2-d( I
I)]
~ ( 1
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
(1 - It) middot -- 1~to
I X 10 cO xV A - i
Jlfr~~06V ~f-knA
(j f~) f- j J e
J
( Y j J I ~- X fltj
I
I~ l
i V
f
i j l f
Y f 1 Z )l
~ll+r Ul)4~~f)~4-~~QC_~[Atil11
f ~ V
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_
-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA
et~ pound~O~Amiddot M rfkip1middot MA- Tf1
amp0 ~ AvA -II middot0
Y~7 ~(() Xl=X
~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~
- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -
Jz ~ - ~
CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J
11 ~~Lr)1 j~ = )lt K J
~0 )iV Y Kj) ~
-
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
middotrv~(R) ~middot1
C c-C
11 -no rV-tv~e -D he))N~re
S~ p 2 I f i LK~- ~A CJ)064
lt VI 1 f
~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~
~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~
1 (1-) fT I6 b f ~ e) A-t___ I I _
s
IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU
~o r~ J11 flt
r)r
~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -
UiJ)i = f
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
lAY (( f ~) lw (A-) ~ j~lr C~)e
I tr ( tJ )) =IT (Ai V 111 (6)
r~ fh~
10u If) ~ T
1Ci lJ) ~ 1
Iv- (Q ) 1shy t
lt~ ~gt ~r- ~
-T (=7 T 1- ~gtl
Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd
(vI() p- f j~Pi
- Jli- (f) L= J-L
__i
l~ If~) ~ T
23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT
bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j
(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J
rb~SJ p()j~ ~n- ~0j (~~1 Hill
I I
rgt 1 bull (f~ ) ~() V (A I =_- ---
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
(p) 1shy
reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J
(1~ c no GCJ A PAaljrt tA~A 1 flczv A~
r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T
~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~
Jv C F) v Ir-( F( ~) ~ T
~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P
(lIJ tIt- (f) l Jf(fJ
lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~
t lID gt6 n-II~
X PtU () - I
( 1 t x B
- b( 1i f(i Imiddot l n i
r 1Y x (pYG) t C~ () c) I
it gt(~~ ~hC (t~ L )( C h n c
1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
-iFt((~bC) (0dlCJ) b (~ nC)- --
PfC~ VJ tf1-) VlF0)
v r) ( [) ~ a r)_V --- I ok) ( P shyshy
1 plusmn T 1 T T ~
1- -j-T1shy I
IT 1 T T T T ~T) l 1-
T~I1 T T T L T T T)
1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy
-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l
- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-
L-JL-J --_---1
J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1
~ ) Cshy
_~ i1G f-CeVG ~c (A fJ)
J~ J~(- ~ ~
middotif ~ (J V f I
k
AQ~Jtt~ iA Jtf Je - i -
i
EE ihJ10~Q~-~X~ 1b~~~h~ ~~
ltJl
1~ b ~bU ( )) ~-=gt 1J ~ D 11
- ( fc (5 i
~ r
_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D
shy ~
fk
1 1
- L~-=-J-
L~0UC0 ~(~i
- - I
I) 1~1QJofL JA lt)
( Cv D) ~L
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
llt v ~ e fit ill
tr n
lJ
trU ~~) I
~~middotmiddotJ~~C6)- 1 bull
1~ A- J~)
t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)
A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj
JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A
t1 rf CF vl_ vr) (f J ~f) (
( AH0J)DtA L j j tk8HcrM AD HI
~ ft V f+l j V rt 11 I
blf J hUyjJ Pjf IJl L-1 1v CA)
-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~
lt2bJe ~ A-ltjTDJlOrlnj A
UVlU2ampO ft 15
M ~ t~JC~) bull p~~ cp (6)middot i i
~n(Orl~~ rsf~--Jb B~~ iI
0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j
I I i A~~rs r ~)~) iT~5~)~)
D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0
jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S
1 (Av rst~ liN ~~
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)
( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)
~(~~ k V (b r c) =-~ vE) ( (F+ If c)
l2J c)v ~ (0( rt) ~ (Cr Aj
rt f ~ K hf v h H~
lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1
-( I -7 pVJ ( prf) f f -1 ~~
-=It Fr ~ 1 r )
h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f
1 ~ rt-= 1+ ( I ~ t
-r~=
f lr (ct -lp~) ~ ( ~ ~l)~) f) ~
( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2
II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)
k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j
ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)
I I
i i i
l~l~~~~~ ~~ ~pMJI
I I I
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
(
-sJIt HlJ~
7 Iv- (PrJ) V Pn )
Fi L4-Cr) ~c r 7f 1(() - T
1 r ~ i Cf () ~Q
0K Hrp LA ~ n IIqtn r~ I hlf
v J
w ( ~ V jI
J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l
I -L i ti
l l-r T 1 l[ 1 ldJ 1 T [I
I
J r 1- T T j i- T i
I
I Tr I
I
T -- shy
J_ 1 11-I I
I I 1I
bull If V ~ (
Y1~ (f 0
~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)
~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )
-I -
TT -i 1 T
-I
r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1
I _t _ shy
1 1 T T 1- 1shyT 1shyT iT T2- 1
i _I I
1 1 1 IJ- l- T
-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--
~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)
j (--1 f 1 ~l ~ l ()
reg
crJk)ttll tAUlll
i ~rl_
TVIHttmiddot~ H ~
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
~ TC~) ~)
X( G ~)J
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
~~ i
i16~i~(f)(L) ~
( tJ(~) ii
pF~~h) ~ F[PvfJI3) 1 (~) C~)
~o tiC f~(8) 11 rJ(p (1) J
h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)
)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)
1+r-LJJ eft ~) 11 IFl vr) ell )
X(r~+) x ( f-1d j]
le - fr0JbCA f
~ gtJ
6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ
~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl
I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I
P-V(f1tieM j b~ orJ4 ()
iJjampt~J f~ ~Or L1 Ute
3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z
i
=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
1~ F1b) 1~ T( ~J b)
xC 5 i~)
(hP(~)( B) 1 TUJ (0)
~ (fl)A b) x CA~lAltO)
2AtItJ 3 l~ TCs)(J) 2l1 Tht)(
y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)
i
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
middotlaquo(~1 e) V1 R(Y-I e)
VXj~J tltl Kj) -- ~fMl~J A
X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~
-i~0pMPlr-r-ePk
L
eYOfy~Ptltj~JI f
i(fL It~)I bull
h~PJfeuro1)~1~~ 1
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
Ii i ii J
[
b _~ 1tf c Ci pj C1(11J ~ shy
~yS J- middotmiddotv 1
VI
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe
CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY
jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1
HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))
(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je
OHO Cn060lJHO HnI1 Be3aHO
V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)
(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c
I1HTeprrpeTalmja Ha Z
RZ =~ (ypeljeIbe ueJIHX 6pojeBa)
SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)
GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O
I1HTepnpeTaUHja Ha N
RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)
SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)
GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N
eN = 1
I1l-nepnpeTaQHja Ha peN)
RP(N) =~ (nonCKyn)
SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)
GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii
= N x) eP(Ii) = 0
I1HTepnpeTaQHja Ha X
RX = (a c) (bc)(cc)(ab) SX acl~
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
2
= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM
b ~ ~ b b be c ebb ~
GX = e npH qeMY je eX -+ X J]aTO ca
a be) e ( a a a
(a) OrrpellJUM BpellHOCTH TepMa
F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y
X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (
N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )
- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3
a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (
(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))
y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1
X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1
) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3
X y ) ( a b
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe
3
bull S(G(e)))
bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))
bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N
- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj
- CBaKU upocia 6poj 6ehu oq 2je HeilapaH
Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType
P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil
- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU
- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH
(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap
jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY
HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa
bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i
bull VxR(x x) V VxR(x x) v(lfFI I
I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))
bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe
bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))
bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe