32
Cko.rtef' -, CtIOr4rt... tt. 1 (I TfS' rHO) u.t A,8,C, D Jisf."c{ por..f,s 011\" ';f\f. I i .. DY.(U; c,."t'CiO$ ... el ... , •• efefS .4c IA""- &1> ; .. te "Sect. At Ke-J. Y. L&i Xl n Be .. t . Let P I.e II\. xy wi14. P:I: Z. L;,at cp r...te,..,-t, C&"'de ...ef .... AC II. t C ..,..( M. BP i..tincct c :tt.l e wr'((, .t ...... ..,. ... 8 t> At 8 " .... c M. (; ..es AM, 'I Are .[ $j.... ""c-t:l , ... YbIe$1 - - A-D, C-a, . . .. '" t Z -t- -FJ't. "'- Aoo4 'lC-,cts .'" (11\8 - ltt e 10, i£... artlf . ... -4. left . C t ... It \. ....... ,. .. t \ ""'"" ,t...&. "",... r. I. ,_ . ...J... Urdc. lUi"" .J- •• c...e.t e't.. "'< T'\I,. . -;J -.-,.,. "-1. 0) .... na.(' (': 1#.e" A': ('lC ("t; ,0 ), c... ('It 1''< tj 0) I..et p= (0-:) Q $r ..<A. AM J. CP ,,"" "'- ..P Ct> -u. /r.. .L; )J " ' -.,. Ill-I'" , , "f AM IS ('Xt,+fi)X - )- '= kt AM.{\"/. "I. Q., Q. ': (0, §cc+ \.. (I f f APMO) ut A Be. f,e ..f""'*ff. GMcL 1) -tle1-t .... A. Let E J F(,e ""'-Q (, .....e. 1> iII,.-.t A E .L SE I AF J. CF..J. E, F'" b. ltt M,1.1 I.. 4!eJ-t 8C, E F A'" .i. N M. s :...- ________-., 8 A 'If \,Ie set d ]) A--d 'X-a,cl5 CI'\ ,-t!-e", .t&$?r e If ",,;\1 '" E D F -t. A let dry I ..... C W Sf-"-Y\'zG,,:t .. l. $01,,1(14", Lc.t A =(0,0) A..G. e .&,... F I.e =b let .. ( ... ,,,, I E- e.b), F .. (,f, "'l4 "&(l '''Gels to 1> = , w k..-..c.. 15 IWf: A/lolol"(. S'o *0. ">:'IIcc, BEJ. Ae Aood. ,L-.I AG is b/e So '=t J we .. -'- se \S. elC-t by s 6) . Ii - '\" .. <S'{h\i( ....l)lJ er-c4 .... /lf c F 1'$ = f \- ® e-" I . -;: <I(. 'f>C 1\ J-.c-tl.r c{4"t. (j) ;>0 VI..., 1.!J ....... t1:/ w-e fi...( _ .:ie '$;_ .",..1 I . B - (.,(ote, 4, - "'t;"). SC w..(@, 'Vf F-.J. C:=Ut.f, A-t>. , S't""l..il Y1 I.t 'ON (\)('1 = I -Ke" .. M = I N= b). V,'MIl';l. Vi. "- Z X"= ":'"'7< ... Q of M N i"s - (ew sf"". -I AN 24 _ 1\ 1. " .1. \I 1. " 1. ..J I - eti! . 0, '( 0(( 0..)( ll\tCr ts - f. :. J. N"'. r

(I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

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Page 1: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

~ Ckortef - CtIOr4rttt G~Ps

~~~1 (ITfS rHO) ut A8CD ~ Jisfc porfs

011 ff I i ~i DY(U ~ ctCiO$ ~1 elbullbullefefS 4c IA- amp1gt te Sect At Ke-J Y Lampi Xl n Be t

Let P Ie II ~t xy wi14 PI Z Lat cp rte-t Campde t~ ~~ef AC IIt C( M Itt~ BP itincct cttle wr(( t 8 tgt At 8 c M ~ (es AM ~Nt( I Are ClYGNI~e~1 [ ~tamp $jc-tl YbIe$1

~ - shyA-D C-a M~N

~ t ~on~Iot Z -t- ~- -FJt - ~ Aoo4 lC-cts (118 ~1gt

- ltt e 10 ipoundartlf -4 left Ct ~ It w~ ~ t ~o

tamp r I _ J

Urdc ~~t lUi ~A J- v(~ bullbull cet et lt TI -J -- -1 JC~ 0) na( (

1e A (lC (t 0) c (It1lt tj 0) Iet p= (0-) ~ Q

$rltA AM J CP - P Ctgt i~ -u r L )J bull

~ - ~ Ill-I t~ f AM IS (Xt+fi)X - )-~ = ~-=-r~ kt AM I Q ~Q (0 (I-~~)4)

sectcc+ (If f~ APMO) ut ABe fe fff GMcL 1) -tle1-t 4-H~~~A Let EJ F(e -Q (e~I1gt ~JiII-t AE L SE I AFJ CFJ E Fb ltt M11 I J~I-f$ 4eJ-t 8C EF ~JVt~ ~-e~t A i N M s

-________- 8 A ~rts If Ie set O~Id ])

A--d X-acl5 CI ~C -t-e ~ ~ CoO~Ibulltamp$reIf 1 1oItSS~

E D F -t Alet dry seflt11pounde~I C W Sf--YzGtl

$011(14 Lct A=(00) AG e amp euroF Ie =b let ~ ( I E- eb) F (f ~) l4 QI~ amp(l

Gels to 1gt =euro wk-c 15 IWf Alolol( So ~0 gtIIcc BEJ Ae Aood L-I AG is be So~ =t J

we~~ -- ~4 se S elC-t by s e~fo 6) Ii -

ltShi(l)lJ er-c4lf cF 1$ Pt-t~~ =f - ~ reg e- I - ~ ltI( fgtC 1 J-c-tlr c4t (j) gt0 VI 1Jt1 w-e fi( _ ie $_ 1 I bull B - ((ote 4 - t)

~~ SC vl~e~ w( Vf F-J C=Utf A-tgt StlilY1 It ON ()(1 =~ I -Ke ~= lO((-lI~Yy)e M=~t ~ I b-~(lf) N= (~ b)

VMIll Vi-X~ ZX=7lt~ Q~~ S(~ ofMN is - (ew ~OJ sf -IAN ~ 24_ 1 1 1 I 1 1 J I - eti

0( 0(( 0)( ~~ lltCr 1~d ts - f A~ J N r

~

~o~ 1 (2000 1MO) a~u r r1 tJe~t ~)(4IMfI( 1 (20ooAPMo) Lampt ASC ~4-t~le LdJ MJ N 1 S ( -- fcSt 044 r T ~~ M 14 1e1l2 iIe ~lts 11 UoeIItJd~ tIt -~CI+OsIdI

Ms dsc -to 1 iIIn N 5 Iampt f of r 4t A ~ ~t A~~de ~c~~y lampt Q P~ fa fi~ r1 t S let -ilo Ae -tI~ M p-Ile( -t1 ~ (0 oIk iIe ferrrc ot AI fImiddotJA ttf ~A BA r 8Ic)-t c J r1A~d 1) Iampt CAnpeeo At ( Clgt p 8N() CI) Q sit fut EP= EQmiddot

r _ 1~1~wt~ lC-4lCu-k - trt ~-tIa ce~J t~ t~4A6 ~11 c~Wcl

~=CI~ kt~-try~tlaquo~ X~I$IOt-~ ~t- seto 1 At AtpoJ f-)t~ II- RA6 ~t 6 (0) I ( t)J 0 (01) o~(fa) e~ c-= (-gtt) 1)= (-ab-St)

SICL C ) UA6 bull ( CJ) 210 2M I we ~ A EAte middot

trt~ ~ Ceuro ~eIy So E (s-t) fi~ LCD ~M ffftbJoJTo IS ePEQ tt sces -to 4w 11 i$ )(po-f

Q Sce O(4 IfAIaJ J~ OA IS ( r VE J So

~~ c( e 14111 ~ bx-+ (r~-rl)~ s~ (rl- r )t (-) ~1Ct (hfo r t -1 OMs Wt et1

(b-s)+ (t1--it rrt bull ( s(rmiddotmiddotd= fit

Stllo-tltt~-tlesfJ - 3~ b~ bs+ (n-r)ts i pl~ (bA2o) Samptf~$ (t) $0 fe MAlhllects AB Siloce MU PQI ~II rfetts P~middot 14~MQ ~P=EQ I

7cfNe(1 let 0 be -t( POlt t eJt -tIo pe~t-c(r

P to A Ute ANfYIc frw~ QOL Be

8 ~~ se1lt~ ~U~50W AtJ wl( Si ~y~t~M~ -f4Aj(~

A 0 1o5Ic-f0V AAJ of ~ BAc rte A~ c ~~s~s-frttrI(~t

~CI(~ Set No 00)-L1It X-41(s 0 tlt Ani let -f- ~ ~ Aa lilt ~=cD~ eO A=-(-otIt1 o) P=-(ob)

- tltstl ~of Ac is OJ ~-AX-b -( $ril el11 of Po is j - tx b CM-)

111 )=-o ~ qt 0- ~ )t ltIto) r - 0

~ -~~8C ~ i~cox -The gtolbullbull~c)-( 1oIe~J amp (ti c~~ ) So(vl CD -c6) Wlaquo

tl C ( -c~ - c~)~ -del( 1= ( tt b_ -c E~ cot AM ts J ~(X+ b ctqtmiddot c~t) ~ ~o ~ et C e ) S( c4- t Q =(0I ~) bull

ope C c ~( 0( amp0 5 -i - Q 0 L ~c

~~

- bull

(~y ra JMO) l fft (01 ~WfiWItll A~Ie Se~~ - LtktU~4

Liacs

er wtIfo~ Ae J 61gt Ad A8t-l)C S~rfamp ~-( 1la r-t P lAJer~middot C 2

f~ 1~-

c Itgt C71 ilt ~(re~tW ~seto1S ~AR~ ~c eet s istt(e A8Ct) gt(oVt ~ AaCD S A C1cJ~cZ~r(~bull

ipound1 ~ tfgtoly L AA8P MJ ACOP Iv~~ ef(Clt~ llpse

( Ictide) I -tc e s

$olt- Set-t- ~~ilt PbullL C) rV] ( X X ~ltgtJc ~~ rallI Ibullbull Ac fl lt4Ei-AlC$

J) lttiM~ middotAe~~)=r OIX~I~kSampbpound etI~J-f(eL __ _ ~ ~ t~ ~~ Itgt ~-l I -J1 0 1D

LetAP=6Pr~CPlgtp Sde - 51=AX~bnitt~t41+ej-tf=o CiE-)

A(-Jt~ft p) ~=(IJfJi)C=(Iti pb)=4-~) ~ eft 1l1C~cle~ Et W (4egt 4=000) bull f ~ A+O I~We ~J at ~ 4l +0

A(cL1A8(gtN-AcOP 6O1~1 JrljtI_11 -fsl-tt ( ASSue ci Icj 5 foitlts yen~ ~c cf 2 ~ ~1 -2 tr- P Wt CI4 ~-s1-t~~ to Cyenc)-to def~n- b c c( e 41 Srt p r- ( -~ I I TI I ~i(~f+tr~fiJ ~)=Jl i i Cieler ~ to ~c~ tSeltt 4t + foifts

IJ -r 2lop ls-f Jsrz )qp ~ ~ ~ y-=s 0_ rL_) tT-if t ~ JU ZlrP+lt~~fi) ~ ABc D IS ~~cf1I1~ ~( X~lp( 11 ~ CAse ~3eoocll ill( t~fc fOit is c~-fWIIWt-e

1$ (cft tik~ bull ~ol(A ~ IgI f~ 11 G ~c~~ Co fts$eS -tl~bullu -ht~ ytgt~ ~ -tao oftet ~~t- c ocl lt1ffI ~ St(~)()_S~II1 ~10ft bull 1k1u~ef-COl s of -fle -fo(1V SI6c~) $AS~~~) SOfWe ~e (( bull

G~sD 6)(Affe 6 Let 0 he -f(f -ftrtf~ crrtuW~middotJ QfAAec W It A) t tI~-fu utff~el At 1gt f~ -t-e tAftcccmiddotdt fettect iIlaquo Be -f P let Ie 1gt0 i+tfTect k~s AC1 AB t H~AI reft~ frot -tit4t 0~=aN

obeJSet ~or~ i t 0 f

p -fa

~h ~ ~ X-4lt 0 L MN

f Let plJe1fa pect~~p i~ ~sct +0 o

A Lampt p=( t))~ p~ (-po)

-rtte~ c(~a~~ ~~-t- ~to~~r-Vgtqkt ~~ I AP Ie A( -fle sI-pe t( (4Lc

8C~ n ~~of4 ~ll~~s AP~(

~~~ II( ltf4 r )tes A6 middotoflie -s of ~~ I( t_ r amp= l(1-6ctpl1l-fI amp_ ~ ~t So~ AE ~1iiiO--------___-=---__

St~ ]=0 to Jet tkX-c-Jwfts 4~N ~e Wt k~rt= I6c~ 2) (~O

So M= (coJ 0) tV (-0)0) -f SotMe ~oeuro tR ~-tt~-ht~ () bull OM ON

ec s r(1j_~(~P))(_rt~_P))=O ~~ ~ -vs

~ reApi r-Lk~ ~

(frsl) ste-~~1~~ Ceo Us ~ FotrAAOC J let Dbe O~ ~ff U - -- A Let Dbe 0- Sce ac Let p= ADU - 81gt I)l W -= cD e 1) C 2+ eln= a( )

tiV+lG PM tW yen~-~ t-=- (10deg- middot ~o

(os tCos(llodeg-l)_ -CO$~ jlell byeose I 1

~ ~ t 1 I I l tf fJo= Cos 1-+ Cos t - Wotf - C + t~p- ~4 ~t zWp + set

Aeelok-s A (0 Let AD ~ 11 1fte4lt -t sk Be I

I

~ 1fe ~ stewafts t~ I

S9 DC ye(clts ~~pLJat-t2l-tt 2 Z 2

I

Ui~ -tt~ ~ S~~e~(e$S~t ta~ I -+

e ~et -tke Apollos e(fa(Cl ~r 1 Z l) XI ta froiof CeQ~~~ 1_ AEttr~ bullJJ~ 1i1b eo _ 4 ttfi-t ftlbJ c =~41I)t( _ ~A~ ~ amp~ Co 0-~

A

~ 8 1) C

-+1

lL) Let AJgt~ ike (AtIYl --~ J ~f)Jj- _ -74 MC r~ ~ araw Ceuro AOwi- E le AS

We et 4Ace ~ lSoSC~(s wr-bCA=EA 1fe ~= t- St4ltf WCl we 3et

~ co 4~ _ ks ltt ~ r ~ n - )+c- ~e~f So tf~ yklJs

to A1gt - J~c (t-s )- (b4cf middot

Ie be kAt CA ~ F ~ hIeuro A If Its AD ampE CF O~ ~bull ct ile

A ~~ lC ti lC ft=i () E rFA

amp Ii C Re~ 9y ltle lIII lpound AC fL _ CB~f I Aamp ~ - -LC 7n -_~t-or ~~ 11 rg 0

StaSiALAFc SillL CFB ~ $ 0 e se t M=Ac suY SLaLL 12ampA$OoOl ~c8~~ Famp C8~middotmiddot -1)c kSk~fA-ampA~I

-rI-e(it) is 1If 41$ A~ $ftJt4$~Sir f~_J- L ~ til

t(euro q~lclvtVt 0 at ~~ os-r I

middot

f (J

amp 1) C

CO 01gt ~O Cf OA BEmiddot

Q~c1~~ Af l fC -fl f 0-~ 31 ~tM Co -t~

_ U Ic _C6 _I I - ~-- 4wtq4IUSOf f6 c eA BE

So amp1gt ampE ~lifI1e$t 1)( Fc 14a Set c)

11 n~onU~lE~CA crf00 LJ f be f ) V _ bull bull J _ I ~ AE- sect2)t ~ -= ~o Re~l( ~ ft1~cooI olettot IS lJIe I~(g~fi i Ca s ~ If FIS)t 1gtC teA (~ of ott fOu6 Ot ile pI-e -tIlt Aft 1

CFue CcMcc1Ye-t bull Ai 6 ~(S_CA ~M~ wl~lAfs ~ A ~ roi (Ly t1lollffl~~) s S~ lgtJ= oS fir A AA6C If-tM1r~1t-0 0_ kat we It--ctIe (olt) I biseefotSqf AS o ~ itMecf 4tO

- - O-tkt ~ ha Ie~ Abl ampE 0 A ~I OA=OB-c 0amp=0( sQ-ctc 6 1) C -4lIt COI A6=F middot 61 UIfA s ~cl () S on k perptecfitr i 1ott A~n8ElCfOlII) AEx ~ltff=i t ~CA 0f4e4~epf(rt~~C - FB PC eA ~e C6CMtV60-l t () O~fk(-t)weJct f-~k~ 0 S~~t~ceqVot 4ASC rtrs~~

M= =6E -ti =~-t _ - Famp_ t ~e ~W--Sc~~trl (oCiVC4IIlG~cl) ~I

~ Fe F8 fe -Pi) F-f AIrBC1tIe~~~CdQowtbullbulllampI~ isAppi_~ iftiileafces1lbllt~_ ~so Cailtd(~8r~iiua46Aac

(4)tfAtgtBeuroCf_~~c(AABcI )( B let)(1Z~~feJ~_JI- AF Igt JC ce eA ~ 10k I 1 L L _~ -r-rshy

t FiwlgtC iA=C7i 1 ~=I middot - -e 11QUtt t t AaCA BCSoAOBElCF==~cfltfVtc~tAaC A C ~AASHCaIAx~~rAt~o CfJ) If A1gt1 BE CFore Clttitcles MBc -t Jl I bull IX~ t y Sl(~ I Y [~

- x -1 ~ 180 ~~ S bull Ct-I- -J F - D C ~At 6Jgt ce =ampOOA 02as5 V4SC igttamp1tVL Cnw l( V~ FEIt l5C eA -~Ci1S8 bcostcGosA f 1Xt 1 =1 ~ -rtiHitrdt is ~~sc~

A $0 A1gtn8eurooCF= H o~~Mac 9 rclk ~c1A~ c 0( lt -tkilrM~ 44ABC ~ (c) If AD ee CF laquo~ Q+ bisrttOlSM8c -nct gt~tS)( f ~ Ale ~ts of t-~ 1gt Co ~ Af ~x~=~~c1t)~)ft -t-a 1S(tT~ Qrct wtfl~sIleo AampcA Be

Famp Acc4~) ~d ) IJL-t~ -tfiA Aec S0 A~ 1 ~o tF I I ~odt(laquof4A~c -r JI s ~ ttWte c1---tlt fsctIA ttde of AA8c ~

-tl~ Imiddot~s ATgt BE N

A E

t)

FA ~~

CfiE) t wt poundtccl ~e $~ ~ LampAC

bt10Ni 6 410f1 C J -tlte -tampi th~~ f L eAt ~ -tlte ~O Ile

-os c 7- J~littf~s vt S t 4ACe(A

~ ~~-t At ~ tgtDiltt Ia X r-- lt cule4l 14 xce1i-te of AI8C

I f~- A ~rI Ie clr fe(f-c1oss tACA6C IIIi-4 f~t I ~J v y z

I I -- I Il~o AAS I AIIIX 6~AIIIZ6 ad IiTrC ~1iIzc S l X t 1=tr (4 -rke Crcubull4f c~ r A--4 clt~ ( IS -tct~ to AS CAee 4 xt~ z tt s clleJ ~ esc-i~ cVc1e (OY 4ccittf) 4 IiA~ MOO bull ~ ulSe cI(- tt er4c(~ 1

~A A ( r bull c

It~ 711

to ~~I ~

bullIa

II

Ill folWt QrcI~

ror ~ABC Iet A 8 e Lt clpoiwf$ ( atleAlAB et 1gt 6 F be feet of 4It-lcl-t ~s Be CA ItC bull

let kL I ~middotqe tf0t~ af I-A W61-C w4 cs-Je Itioampafv of Mac

1ke ec lgtEF rltcM_ttcoOCtclc ~ Cc~ fUaj ~ ~ clt( ~ ItIIe e--t Cull ABe ~ cefe N -ioNs cd~ is ~ clrowl 0 H ~ ((s ~s iwlTlGIC_~f AAS 0 SottIM ~AABC w see aitCA ~d (f8t t see uti it ~

8 So Cit~ Si~ eL =i M =8M

s~ AH1 a ( I Sc~ t1 $kf+ 8 A D C -na~ ~CO~I5 tcLM rs

(L Aoot C of AS ~r I Sc f 8EL1oo=L CFM eFCI~c Iso r

1I So SeEF l~f1 ~amp ~~l(

St(Irt~ ~ As OEKt 4re~~ ~ ~ qrdeHlaquoI~ tEl helCt (61 4~te ~~ rck l~i~i-d~ 4SeL)- A6( 1lgtGF ~l~ ueClW ~ SCl-e cude Note tL I CMA Gte ctOIfars qf ~Circle

c5fD Sice OA amp0 BCIICS So feufbAch s ~~rfNA o A J Crb Srll(~ly oa J Ae ~ f 11 e P int cuclc f 4 t~ bullbull Ie Oe J ampA So 0 is o~e1A1( is -t3~ 0 ike ~( c-de No LlAamp1 AA~c ~i tot~o 2 1 ()~ ~e 1k-let esUietl C47rcles

A D C So AASI A A~ 0 i rAtto 2 L r4 -tk --tY-~e 1-eO AO A~ AeAe h )Ao=iAK t(~ Ws s Qtt-t_e1y ~tfJ 5~ A 0 J Be tJMJ lt-1 foe $0 A 0 II K ~e4 tIlCl e~t~f1 ~t AOl~ ~ laquo ~~[(em bull $ ct Aj( is laquoJ~ -to rOllt oftt ~ rtt Q~c bull So t~ ~oet (lSigt t ~--------r-- ~eO~rft of QH) is 1le cet~t_tl Nt ~ middotfc~ ~ 1 AAo tJ ts ~Iamp ~ I) K ( K IS IIIlftd-af fIA ~ lt K i OA middotH Crc-~t s l AAac ) bull t

6Je UIe i MBC i~ ~ 111- 0 ~ Amiddot Note AX is ediArt~o ~d4 8c

o ( II Ltt Ofll AA c (q SCMct OAII A 1-1

--- ~N-- tA~ 0 =i A HI we sae B A Igt C A Ao AAH6 rtto i 2

o~ So 1)iErH11tt)(iio~ ~ 5 1 ~~ bull ee ae ~ ~Qj (so il~t i o ht -fIt ~ j-o~ -0 tj 411 t teampd ~ At Gt ~-t AN C fgtst ec - cetle So = dtli ~ 6-f( t~ eord-IS -l J 0 ~ N~ ~ AI$o A 3AA 0 bull ]

L

i a t e CJ

I u

Ci

CEi0 ~~N~ ~ let beQsJf~e(-f(f ~ K+O So i ampmiddot-i ACo~~ iSA )lJt4~fotmiddot A- b W~~ Co III ~ teal --~

--rfa ~t -+ A( ~rtlt 1I14us ~llloe (~~ ~ C G~cJly ct s el+J of t1SJ bull ~+Igt~ U~fPOlt (ft) Ent M~ fb 0(l +be bull c-+ ct i ec) o (0 )+ (c(-elc) (4-tc)-+(~-td)1 (410- (cot Ii) ~-c)-+ (b-clh bullreg ((H~)(-ttJC=(Ac-bcl)-t(~-t~dl 12 ~ c-td~o -flt -- c-e(-= ~ J Ne( Campmiddot c+Ji ~c+~ ~co1ts

I

~ IAtb S 4-1o~ w~4eA4 -iIu 0 C0JY-te a( Atb l~ At6t -Ilt o~oo4t ~14a (Of ~) tf at is ~ 4~ lilt middot

NoI-t i--s is ike clt9t- be-l-wu (00) a( (e)

~~ W daM ilu~Solf VAl~cf olIIt y At bmiddot=J4Iot IJt --lA-t~t=(Glt~Ga Ioc)A- 1 ~ ~Cll--bl - shy~ 1 711a L lfO

Yroee~bullbull~ Ltt wJ~e( - _ - bull - - - - - -- IJL _~-J(D Wt1 +l W-L w-aJ we=w i -n - hi

~ lt~~wt~ lzlltJ 1lzl iYI~~ - middotifUoJ

~ Jqt~~ =leampal ~=c+rk=Wie~Ji4e- I ~(eo) lit ~el~-6z)

i Wt=(p~b(c~d~)rrae bull amp ~ yo~e L~

1olot furrn n It- be e ( Ie l= 4t(i~4 fLC loi(l~ 9 b(~(EfR1IvLfDs4ttX-cN ~ to ie ro~ CO6)~l) 14~

(o(oo) Caocdlaquoclottfse cCllIctcn ats o(td 4e ~ ot o-tbi laquot it is cC~ r o~-iW)~f~ e~e oyo cs8 tl~s (fosS)+ i~9l It A~~c coseH~=YeteIIlaquoi~ to ~OftS ~ bull

ey ik cu~ I f xt~~=Ye )~ ~=r-e-roY AI( fe Z~CIsk lWtf fir ~ lee euro C o Go ro~~t~tt ~ ~t wf ~ ltII _fir ~ ~ f bull (6+l~

I - ire gt I~ J1=e ~ J

) WftreileH(Il-Imy

~s ) ~ ~CI~ W

fIrre J

l Ioh L T_ -f -t ts ofJ

W4-II4 C4S~ pound_ )

~~ 41f Wid Ja-e w)e )

I1 2~)tt~ I pin e Afe

-ltv ~t Setflaquots ~ A I~d ~ampPav3~

Cotttple~ 6eUYIUi(-ry

~ -t Ls ~ N~~tQVs e c gt e - Ccs9 +Se

~sc Obte~ ~ ~

CD 1- W claquotsr(middot t -R Ie-tt We III r ~1 ~(+ot) ~ 01 e _ 8 To yot~+f A YIi v fLe rlAlIe Iiishy

- r I 1fSj~t -to -Ie ~ ~ ~ Go)1 ~ C(

=~ r_ ik We $~fl1Ioltrb 1Ie crl foe l fA ~ - e b~ e

Acrl~1 Ie ~ ~s Iej f t ~ fl=- E

Ei-tmiddot 1- ~-tljk -t di-Yoits 1

Gi~ W W2 fke 9Qta-~c e~CM Af -tI ~ ~ ~ ~-~~k IN Wa is O~ ~ 0 +t Wa t ea - 10

W ~ So z-w bull HelllLc ~-J _-i -- ~1ecJ ~-W c

Wz-W WcW I ~_Wmiddot 0 1-kt beA ~~ olSo tJi~u -tk cJ~r

igtr -tke ~~ ferlts 4 WLJ l -to be eolheAr- eogi- of l u fcoJc ~ 1 1rllleP0rt

i CtrIz-) RottmiddotOW 1oJ1 9t W

- bull -1 II It-vL

e == Cos 1 gts = 1 bullWIw Eltot of-ike le tkn C rttr~JcJA

-to oJ W1 5 f l-C -~-c- l

0~7i-f ~

Li f~) ASS-teJ wt~ (uit) c~tctf

11 w W~ n 0 ~ tle ~-l cJe (at wi =Wzih~ l )

~ -tk trto ~~t ~O J Wt so z u

l- _ Wz-W C - - - l - = -w~lc-W t-w

Slworl~~ w~3~t ~ _ ]t +WWz t Wt W2 bull

-r~er~of -to h amp ~jl ~ ~~ lot C r~ 0 W W-z s l- C i (wamp-w)

---- -=WW1 ~-c -W(W1-W)

lt)irljj We 3 t I~-101Mh C-IVWC

1A~i~Cst

Let~ Wz~ W we ~ct ike f~Otl af ~f -tampjc--t ht t ~ i tele I)t I wI~~

(l+ lJti JW] yl ert~ -tle rey bull tcJr fa c To iIt tlaquojct

lIt cJ W is -L Wt

i(J~w) -= T(w~-~

~gt

CD C~eetfe( 0 is ~t tlv ornI reg CeV~J G is ct A-tA~ A3_

() I eurot- NH llt (-r~s rs -tf 41-1 ~- 1 A A A bull A tateo J n I l _ J i (~~Le~ ~Alll~b) s 01 SCt~eD u -pe v~GyueJ

(jOf4-hoce~t~ H l$ c AT At+ Pr3 (be(AASe O~ = 5(O~)) pound1- f lt tl~ A ~ fJclCi-r -to ALA 1s

i- A-A3 ~ -= At - A1-AJ A bl~-t ~ 1 1laquo ~ ~ r~~cJAt -to AA~ $

c- AA) == ~- A~ ~ -rktSt -fwo -ts W f~cf ltt t ampJk4J gt~~flaquos boi lut~~ u$~-f~ ~t tAll lAzI= tA- i- (e

AA = AzA - ~X3 -= ) t ~t lt e c At-tA T A~ SAiSfelt bofl ~t~01l~ 1eo t-= AT At -( ~3

17 N f t - L A+ Al-Ar) 6 Ce---+ef ~-tke ~-e foitrt Qftle $ DA l-

(be~oe 1-1 $ ~ ~Jro~ 4 o t-t) ~tCA ~ Mi-e fit arcc is -tke Ciolaquo ~t f4~SfS -tvnWJ4 ~ a Jo---~ -4le ~~es AtAl Aamp+~ As+A) ~ ~- J L -) ~) -

~Q 1eet qf ~ al-t-bAdcs H I 1 1-3 -=t ~ Wampdtoi~~ -tk ferllaquos ad ~e D~e1 ~~ raquo A~lt

(J~i(t~ ) A lltzlJ J llWW1-~ Ayt ~ito

Sol4 SifCamp ~A~R~lgttPLlCQA~ ~rJwail~e Arf A+cJQ+~~R20 I 1i~R+~~Pao C-t~1T~ZQ=-O

I ~Il I w e LV = e ~ 5 A ~t 4 ~b To ~~ fl X 1l s erltamptDI we CoM-rtf

Xt wl-t t)ll= (Ai~amp ) +w~Ct~iP )~(8+~~

= k [CM Q+ ~~)+ 1Yfgtt wR + tf )+ w (C + p+~ I = 0

~~~A I )( ts ~ (Rot 4 1 J~ ~ ~-t 4 -II 3~f1 C~cf ~ ce~-ter4cl At ~ (A e) ~ ~(f-t~) (ie ~c pOlt 3 -the amp~~c ~ ~ ~11t~ -G t- ~rid 1 ~~t AS)

COlf~selj Ikj ll~ 01 ilt G~f smiddot ~ fo~t ~ loc-s 61 )( 0-~ G~f C = i(Jlt- CA-t 8)) is -flc co~nsfo-kj lt Ov- ile ~t Clfdt

1-(t1J~ Let A~ A)e tI ~r~ 0t W1w) w~j I Y~ f~~j

fYo~ A ~ J~r - fe~~ -to -tkt -t~~ e to ~ c~tdt I

01 b w WI W 3 Got W bull skw~ ~est f~(tS ~ctCmt 1cle-t~~ ~s tmiddot~t t C)~

~otct~ JlCG ASSUllC -tL ai~cit-tle is -tlt kAtf GifC(t

~ h~ le~~tcJA -to t f~eMt oJ 1J -iklk ~ MS et--4M rll-tvJ~

bull l- A ~-A - WltWl t~ k~Wi -r ~- w - tV - 2 - - W 2 bull

Now WI bullbull f -ike ampM- ~~lc I SO Wd -= 1 i1e we ~ fJ~-te -tk ~n 4S _ _

~ bullbull Z ~ _ I T ~-t Wos 11 W + 2 Wl ~ - 1iIII I - - w

2 2-

F-oN -tk5 t ~ ~t -tk yoil-f N Jw~ -+ W3 $ 0shy

--te e lt$-I(C -t1e e1f~sS1W f Ns Sr~t~c ~~ nSFt -t oJ Jt Vis we (4 eot-t~ -tMt wtl lISO e O~ -tIt o~-- -two les -t~ e-Fc~Sto ~1 tJ -tt l s u~ -t $ -tle (fwle1 ~ -t~ )1 fO~~ (tce ~

J I W-z4 _

11Ob~ ( S~~t lYe Tko~ ) let W be D~ llt (~crclf ofJ ~1 13 c( PI Q1 R

be ~ iut ~ ~ lC ftJi~ ~ W -tt t1I 2 ll I tl ~ I ft ~ec-f~Jflj slw ifvt P Q R A-e tAl(Il (-ps Ole 5-

clt~ A $~501 11 tf A ltamp-t) ~ W) i

~ol~bo- WamplAi loss -t 3~nl~ I Wt J lS$We Je G-nIUshy

Cilampk 1s ~ ~ cttclt ~ lll llJ lls -= lw I ~ t 1kt k ii ~s ~~ l+ ll~ ~ Ii t3 --ie r~~ fw- W + 1~ Ivs ~ f-ltl ) i tJ- Zt~W So Sol lkcsc -tcdr W~ 3laquo l = ~ t L + W-lE W

2

St ~ Q ltl ott ilW --l 1(= tt f t~~1l

I sluw fQR 4t CttlfUf it S~s-t st P-R =l-amp-Nil f-R _l- Z-amp-~~ Yo-~~J (tI 4W -g ~-R

Q-~ -1-1)-1tJ --l~W X l ~-amp~w ) l2tgtW-ltl~ -lZ+ t

4t~ w- Zl~-ll-t It f- fl

- (1- R bull

-J clt~lttii lw=t ~ WW-=i

CiiID ~tlt~ firLiA BC let 1gt be A4Ie GtIlOc1tf- E 001 As loIiti DEit-CB J ~ F ie 600 Be I

ciA ~fDf oX ~~ o-rbmiddot 0 1 ltt ftt XIS G(( Gr be 01 EP ~tS~t ~ el~ttrlgtedo-r W~~~~fk~t~s X Ao D C fSfoFc-=Ep-=BYc1gt=r

~J ~sted oR we rMj Sity ~ i 7 middot PrDV~ 6i-F fs pcmI(e( -to -Me 4 b~ 1 -M CaJamp) Xl= Of-~ -tI S~1 je Y-X Sol-I Set 1ampt o~ AtAo tt(-~ IMc

For ~fS X It we e Ix-+f ~ lxl +111 ~ft Tie E 8 Gfl = C ot~~ E (0 r)klgt(d~ 1- W-11IAy f X= ~t(r-s-e t~o A~ F tB t(f-t)c 4( euroj =tE t-((-f)J) _ h Let Pbe 0 poillt el LIle )( f lJe lter t= B _ L _ amp1gt g + (_t )e~ middot gtY haYCamp oP=toX+(f-t)oy -f=~y ~ Be -- r -i1gt-t ~_

J J gt1( 8 -I io O~)y~ amp(01] ~ P-u SfjllleMt Xt E retgt I $0 IE-BI rD-cl c1

EICjl1t Call a ~1IIecent ~ ~ QjgtWelC ~l~ (I- ) Is (E -amph 1l ID-d r-(t-amp)(c(-f6-Jgtfd tl )ltLJ )M ~ ct j~ Ie ~od ~ orF9fe sk~ J i q F- Gt = t6-p)~+ (I-t)(1-9)C ~ +~hw ~t cf -tk s IIf-t4 Jgtllrl1lpounds Of ~t(tei _ IS tlt-p)amp1~$ htfampt iits~etet ~ik~litetllllorltl -tlt-p)la (amp+~~ =(~~k1NIllelo I _1 t f4IIIl ltf1ltS

Sll~ fir trl4t~ A~c~ Itt-A IlIamp 1M OjL ltf 114 (tw~-for ~ pound Me~ --ik se ~fOW twI ~ _ Igt IC-tO - f ~ if

T -poundTI-r -pound ~ I A=0 1)~D i(1el IC-BIt lo-dtll)~

UI8iC-1gt1 +11Hlt-at=Iel+ Ie-IgtI+11gt1 +1c_~(f~~t Wt ut Ie+IC-Igt ~ Iamp+c-tgtl t=~f1f)

AA IDI + IC-61 ~ 11gt+C-81 C-~AO=~8C) (gtt) holds ~Le~ft~~lcJs A81(1)C ATgt Usc _~ __

c6hf--I--l~1gt~ ItiC

~1- ~t fmiddot~~ 0+ ~ 0 ( is )(Y=tJC( (1 rsti - Ex4k+ Let 0 ~~ (i(cAt cf 4ABe 9 ~iIt J bef -fIl lfcffS Jf -IIf (t) Xi=fX (y+I)zmiddotXmiddotZ+fmiddotZ 0( (cXl-Y~(Xmiddoty) ~ I~~)(middotX I IXmiddot~~hd1I O~iOf (=) Xmiddoty-O ~~~~~~~~~~~~~~~ amp--ft 3 Let A8C b Le lmiddotts ~sfmiddotmiddot Phe

Ac~+amp~+A~-t8C~~ Ast+ctl SJt~~ Set1ie Ot~I ttt A ~~t f Jw

CmiddotC +(amp-lgtHamp-~)+D~ (8-c)~-c) ~ amp (c-b)laquo- At~(~- awl lt~~-f4ls s fu ~4S

(6 C-b)middot(S-C-lraquo ~ 0 ~~ck s (amplt-1) ~o

A ~t 1gt Ie -tLt poit ~ Aamp -L II ~ e _ ce~AAcO

p C fgtrcw _t C1gtJoe ) AS-AC Sol~~~~~~~dO~A

A a A J) A J)= ~ E=~~ =3 +~lCJ1gt-C=Aamp-2C

C1gt1 Oe- (A-tS-le)(Mc+1raquowO c) No AA~lh c C C(CUM(bull (IampSt 8 41f1$-bull (4) bec u Amiddot(Q-ltAB-ACO 1IeJtt(~) ~ OAl ~c ~ A~~AC

euro ~ toJs ~ 8lt~ 1)-A69 seAPS fWlkl ~JCOc $ firAABC jf( t ssewu-J -ptMf ~ c= - ta-+CmiddotfI AAS( its ~ttd q ~1 - If We Sampt -iU CitClIMChH- 0 AS ken -HII-srft~ ~o -t r -11 __ -~ -1 ALh--COtt - 7J 0 OtlGCnx n - ~-

A Fit iAcetft tJf ~~ c 0( lU= ~ = L

co b AI c lt-c

e ~ 1)c 1gt= te+(t-t) C t --amps ~1i~ poundL = tD ~+ cC C bI-c Gte middot I t A-t -~)tgt t-ll- A

aAtlS cc_ - tgtA - M~C 14 e middot

11l Lqt-(gt OmiddotkC Gtctal ~ICef c(H ~r J

51_ Set 5 4lt C4fColt_bull tu e -H Matel~Me1~ 1~ AA+b$-t C shy ~ 4~(

Lampil~gt 1omiddot~(i-1)l4-1) lt0 A-A 6middot~Cc=(tlJ 2ec 6amp+cc-(a-c)(amp-Q=k~middotIf (A16i)riamptc~ Rlt9~~ 11- 3( h_ Imiddotltl-C) 4l- 2(~~(H- btCi)tI~)) cttC

)(~+c) (-1)((-1) =((~ t1 -Hi+(() lt 0 of -~ f (ib -t-e) lA+Il+ ct )+ilaquoc gt~ CifI+cl+Jl(c)+ ~ ~ a(-o)(--G)-4-~-c)(b+cc-4)~)gt0 tsc4 rc s

~ Ike fRS ~ f xi xI wt -Stl-fculot 11-$9 (t)=LXOY) 0( tiYfft~e~ -fo -tkt fl~~ 1-- oxY J e

lti) ~ -f~)( ~f)-a)( l t Yltl (c~wYcxnyJ (j - )(~1 4fT~ A X0( V~~ p A of yl t1ft 0

(6laquo Q bull 1 lj 111)1 (DW~v e

eJ41~ Let AAA A _j A 1 1_ -+ V]nq DO 4 CD e I

- its ste ~tS p-Ilt1 ProiIla-t middot ClrtllAA1Ar oreAA AA So(u-tVf SeL ot - ~ -_amp I~ _L ft--A A ----- ~ fJe ~ ~ --fI 01r~~ O4St SMs ~qIt ~t)~csCA-A) I lA_-A f

E)Ctl-eIlaquo-r Let A6COf tgt ~~ pe-tft Qc e t

~~~Q~ ~ 1kfwlrids~ A88CCIgtbEpoundA 1T~ -r APamptl~J~ le ACDIIIampf6i -laquo s~O~ tk-t ~s Ooet is so eM eII bullbull ~olt4-tfN ~et -ckt O~bullbull~ rt -e ~_W f~ S~

tJ 1(t0 AXC ~ AP ofe (o(iu o=A-f- A(~ J C- 32s amp A

lltc t))tA SIA~y 8)(1)= (1(8 CxE~ C I

raquo)(A 6llgt re EJ( 6 =CcE feMtt I

eurolCAJ- E)(6-t( - ~lte+El$ ~ pound10 eImiddotmiddot

1 ~~-A~)o (As-AJ1gt(~A~ S ~~CI amp euro1tf6lc~ ~se Ac Adol~ -t(t-t Lit set - () middot At

At~ t ~It~ AsIC~ Al~-+yen+yJAI (

_t a ~ - bull

~ 2-shy

I _0 c A 6 c ~ As V ~1~Ut 1 Sjtllc -fb ~BIC~ fW(t

ftdle ~ts of BC CA AB ns~chvell -tk ft1~ -tIua-t

No A bull G 8 A I ~amp Ca A~ (orr eU egt~ 4~_ A~itlA-~lClA-As~=(~tAtAr-tAjcA -~~ StthtlI4It ~ SaJc1ttA

(Nmiddot~~i~+Ar~~l ore4 l1A AAs = Are 1J~~Ai

Aft13 amp11 C=A-ttils-A)frSollletoA~] SiCt AS e Gfe i eRe

o~ (Bt-A)K(~-A) - (A-ttz-~tl-t- t t)AxB No ~~=~~~-=amp-AH-t)e ~~1 S-a-= It-t1)A I Ct = lAt8)- c tlA +ll-t~)B ~ (amp-AI~I~(Cz-~)=(t-ttl-trtl-+t~t))Al(amp~O A S~ CL At( ccdllfttor

~t ~~ 1~~Pt

o

C[~1D --r-0 vetlOf) )( lf ate Jt~y wtt-t---t f~ t -flat ~f~ ClX~yO kAs 01 Soat~

AT 10 o T4 s tktCcStI ~~A rf KttO ~ X0 f Art NIt Co((llteor

F4t IT AX+bY+c =0 ~$ote -e 1~I(z-s 4t4l 4-+amp ott -=0 J ilQA Xf Z 4le cbullbullI btACcS( ~l AO fIe b-tc-o w X-1-KZ-tYc-6Z

(~ar~11to(~1 wr~t--J Lftai c~ s OAAampA Co

~ OeLamps 1f 1 -1z- Aa6~l~8ampR AsampIA~= ~ 6 8-c amp-S tltcl A DAR 0

~e COIIfttAt t ~1 =- 1 ~ ~ P Pl) P3S~ Set - orlll at o at A8 btt ~trs Ale LIDa (ampfbv~ ~ A~ rA Q( e s So 8 1-t S6Wt (s EIt Cll No

Pl =tAt(c-t) 8a trA+ (ct)s ~- ~3 lAAt-tQ-) 8-= tA(-aA+Cc-ct)S a S~tU~ ~ 0= ltr- CArgtA + [pound1)l -(I-I4)$]B

A~ (tally rcf~=gt tr(~ Otu( (l-tl~-laquotlt)S=C Solll fott ol -tit pt~~ -+-s f ti ~I~Js

Nt ~~e ~ 1tu~~A+ SoSzCt-rl g$t Vs- r~ r~- r~1 Pgt1s~S)A+~s(tmiddotgt8 R= rlrfgt~A ~(I)J B

Y~-r)S) ~6a-t~S) amp c) ttS +fs-1S ~ p~f~P+~sampf-tj~

~ P1 ~se~rw)~c 0 Qtlgt+CoO ~ r fL cU-1- fc-i (ove

~ 0

A - -

~ FOf~lamp~

(1 -laquo ~C

fot-CA~ to ~ t t amp -t~~ crt a ~tc ~ El(tend~ltl St L laquobe ~[A8Cl Js~~i~ R= 4 C

Let ( ~t 4ct nwts lt 4e GoismvmcJt i-R- tl 4J~)(fo~of AAsc Sr ~ l=~~Yslt) ~ bc_

S A -- - 0 21 1iltelaquoe s dolAt C~d~middot ~o~ uI1gt ~ s~amp s~~C middot T 1_ ~ rI n -rf (i-- shy

tl Ie or~ DraJ clmiddotae~t 61gt 1pound Si ~ A= ----=algt i IS lle~ ltJOiOlSA0

~~~~~~~~~~~~~-~~~~=~~~~ p adEr-l-~a~~r~ A- oS+- jtus c~ - c e c I) p(]) Let 18(1gt L~Ms

I4dtt rAsel Or S~8c1oI(lcl~ 1leflAftt Let A6nct)p -r1 ~act 0

~Me C ABC ) GlUo~kc ~ PAx P6= Pc x PD = tl b~~=Abc bull P19tpound Note L APD L (PB

4R A1BC)aHd~ckLPAtgt=LPCBS=tfA-tb~~) is ike seifieAc ~AAPDACfB~=~~ PAIPB=fxPD

amp Q C Of 4A8C Lri pc C 1amp-~ ~~ PC Is -lt-~t lat t lie i4 jCbullbullr 4l( M6C Qt r Ie -i4~ to -e -fde ~ A A8C if (JJ

C)~ ~e icltc1e ot AAec ~e p A e OYlJ c fCL p~~re [Mel =[ALel[~cl+(CI1= ~-t~+~=SIr ~ Not~ LArc=LcPB

I-tfllWlbull [A8tl~ S($-11 ) (s-b)(s-c)middot I pCs f~ot -to LACp4C ampP(~ Cos C= tt2ttoa-c (~AI Ci(~ircl 4 MBc B 2shy

[A6Ci= ~SiIlC=Qr(+coSp(i-($C) ~AAcPACBP ~~ fgtc PCPAlltPB =(Cl~-+Iot-c~t-~a~-9 ) = catlo-4 t )(A1(-c)(CoHI- b)(o-Il-~= S (s-c)(~~

2- ~ a

Ci C [AS(I A 2

~

I

~JJI LPFA-=odeg=Lpe~ ~ amp~ ~LPFeLPAE

C5Ji) ~tolt1 s-ThtOfotfll Let A 6c~ ~t dlSncf ~ts 01 bull ~c ~o - Me~IA~ 1( bull t Of~~~I ~Ot bull -Tht~ bull Sa c~tOV M1 C(liofIPT potd~ A 6 C Iie to

AI 6 C 1gt (1~t~c 1gtpound fCLR atfmiddote ZA ~A A ZA bull -~ -iA ~Co~ PAQ~clf$ WeA~ ZA~lA I tc Z~t

pFAECc1dk

bull ~ Srlloi(y taCgt6~~~-lPFB ~ pG~ f CDCCYcbull LPampb LPFI) = e 1klaquo AIJ~P LPAespoundp8C pfE _ LPeP 8EF (0(1ltlt~L PFE L~8Tgt~ LFP - L 10 collirAfampff

)fgtC)~Jl~~ ~ ASC1HAol6C=AcS]) bull (~~_ ~ktI AeCO At)ItBC ~ACdtgt 1)~c 190pound 0 sWLe AB UJlfsftfUct A ampA6

S~~41 to flCAP 1I1elt AB A~ 6eshy

6 Ai - 7ligt= (1) lBAE=LCAJgt

SO LMc L BAlgt-L1gt= LeA1gt-LMe =LEAt) Tkeuro1 A8AC~Ae-A1) So Rr-c EDAtgt~A Thet Aec~ A~8C =poundItampE AClC E~ AC80

bull A rC =c Sf-t Ell I

f1-I-4j hoW~ ~8euro~EtgtS ampb ~ E iUt~( SO - ~~oeA~LeeALtgtCA ~AsectCO Sltffc

SoSoft ~oe 1et~6cP cl-ampd-p~ 0

tI~ Let l)poundF fetf~~ff- P~ ampa Aeyen~~ ~

Asse ~Mist (so4 is 6~UA_JC ~AGSC ~O bull G ~f( Aalec~o)

tt~e9 7eff

fovlaquos X I Z ate (es Aamp ampCA D ((t~ve-()ty It X I Z (lie (dl-lflOr

A ~f f6 lhg--1 ~ xe YC LA - middot ~ lQt Dbu (~ Ac soct1IIt 81gt II J( Z -r1teuron

~g ~ ~ 1t~ ~z Se AlC 6Y c~ _At P1Q (i~ ~y Ie ~c -- _______ r tamp iU I bull laS yc fA ~Igt ZCZA middot lCI~ lIeeu~ Ie~

If ~ tL ~ =-1 iIamp )( YL MHo l~(~ Y~t~~~~ SlJ) Ltt l~ X(OCA -Thtl b Mt11Idtw 11~ Ax ay CI _ lt Cz Y Cl iiiK zA --i ~o --=-l1toobull CfIea bull _Cl -a

I I

ceDD ~MelI s lIeo~toA l~tA I ~cc t) euro ~be tc~ lO 0shy

de lw~~ ~( ft amptCtSSCti 1 tf (~ diC- (~QEf ) bull

t p Ae ti l)euro J Q Bel pound f 2= Cl)n fA ~ ~k ~ Q1t ottc(l(ea~ ~QIR~~~ -

f~ 1 ~ ltt X~EfA 1AMCD bull ~ z- C~neF Arr~l ~(atts ~ff 1e-(fM1oec~ FA

ftt- Ool~~~ 4xf l w hVII

e-- ~ X K __( It X2 ~_( t ~~II Qx 6y Ct ~y pzex I fllFxijmiddot 1I

Hul~pr~ ~ AIl ~~ tfffSfctj cofI4t tt XA)(B XEmiddotKF J (CmiddotYP=1AmiddotYS ZEmiddotZF= zeZIgt W~~et ZQ lSf~-i igt PQ~ ore rlfltelaquor

Qx Pf Itz loy c-enc ~Mee(AaS

t-rks ~ere 0 Imiddotil~ (1$($ of PoucJ s for It we tftwt Ato 8 -te I AIwIJ (3 il(cJe 1Iofl1-t i AB will b~ ~-t1l3et (iot ot B ~ It~j CIt~ we ells JpoundAoflt ~ t~ liflE Clt B b~ BR

6lCtJfC i F~~ h Cf(Ultirc~ ot Mac J f(it 1) ( ~ ~i~0yen ot -t4l~lE I~ ~tA - ~~ Be ~ e fM 1fe ttusc(e~ of-ffwf3ct (tt4-t C3L1r~ CA~ F= bt ~ ttfStd~ of -tINt ti-~-f Imiddot~t ~tC wo( Aamp 11161 PI Ell F o~ ctU

Soof~fIyen P=Mo 8C ~ E= BBnlA f=CCnAB APP~i P~f ~ ~(fo MB See I fott et 1gtpound f c-

-- =JSiiiiIii

b)lAtc ~ Let-tgt 0- eht ~cfs 0( dt101 AtCS

AS ~ AC O~~e (ilcu-R( Mac ftspciwJy l(t tgt Ilt ~f AtC sCI ~== DPn SA J R= PEn AC fro +~-t lile QR~s~(QVJ14 fttCf+~I (~ 1) ~ f9bt-Mshy~e 1)rff0--AS- CO ~SfctsLAc8

Co ~r ~ qftllCr At =lgt 6 ~LAec So 1= Cl)n G8 Sf_ eEtS

Q tgtPt SA DP 8ital R= Pe C Pre ttL PlE AI

AIP~ f~l ~ 1Ito(-to C ~ P er ~ w 1 ~ bull 1I

t Set I Q Rut tIff~ Co~~d~

~ -7

Alt IXu q j

elf (Ga1(e 3 Ltt AT3CPs e ~ +s tMDlCJe ~-rd AAfLBS Bat LeA) ccf LAB fat 1gt be ~ls (I ~cucl1t ~c4( I

DA(11)C= AU DB()CAe~ 1gtCIAB~ fgt~~ A~ r~CtfaJ T4 6v~fi ~ IAGC a~ Co((~((r

~olf- W HL-cI oy-((~( ~ AA Be Ne

AAIB~I)Cc(-=I DArBC=A 11gt1( ISc AtA f Cc -= H L lAlA I C I Cl

1t~()cD=C1 ~l (AIBl (cjAfrrr5~5Gl ~~ t DAAfCC tgtlt Se4 A HC tit c11ilaquoraquo SIt 1y ar171~ BS41s(to AS e 0cc we Su e H 6ltve c1(i~amp r A~ H C~ S4rt a(((~4~ I

-~ ALI)f ~fle1 tt P toe a ltpor i~4Mec

LtfP I~~ff~I$f- 5 -to ~CA Camp ft~t~ lttt bJ() ~_ eshy

ll 10 ~ fet ~~~N~ c-tohs API sp (~ftvtll IfQ P ~ 61bullbull Pt14 PttNQ~~ (tries ~tll~ Qfz cod A~ aft ~et

iSoLttd- $(fCJt L CPc p) LCQLP LC~P Lc (gta Palt-e J -t ~es c P ~L I PI Q p 4ftcocttc f~AfrI15 ~s middottU(Woto ~1l$1 w-tSu CPt ( gt e-= A ) P t1t( QIP= X ) (Q-a Pf P2C-= B 4re CoI~rtelr $6 Rb2-l amp1L ( AB-=Xmiddot ~ ~lIQ P~IA8 tVe ~Cqfre~

NewtDJ S

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-

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p _ c $Lt-~ -71

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No LM~-L~8-=-LIWC-LAec f~ $(amp ~st ~JO 0 Ao( ~J~~ ~ Atl 43~ t (-d 0 ~ A61PcD

fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

Page 2: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

~

~o~ 1 (2000 1MO) a~u r r1 tJe~t ~)(4IMfI( 1 (20ooAPMo) Lampt ASC ~4-t~le LdJ MJ N 1 S ( -- fcSt 044 r T ~~ M 14 1e1l2 iIe ~lts 11 UoeIItJd~ tIt -~CI+OsIdI

Ms dsc -to 1 iIIn N 5 Iampt f of r 4t A ~ ~t A~~de ~c~~y lampt Q P~ fa fi~ r1 t S let -ilo Ae -tI~ M p-Ile( -t1 ~ (0 oIk iIe ferrrc ot AI fImiddotJA ttf ~A BA r 8Ic)-t c J r1A~d 1) Iampt CAnpeeo At ( Clgt p 8N() CI) Q sit fut EP= EQmiddot

r _ 1~1~wt~ lC-4lCu-k - trt ~-tIa ce~J t~ t~4A6 ~11 c~Wcl

~=CI~ kt~-try~tlaquo~ X~I$IOt-~ ~t- seto 1 At AtpoJ f-)t~ II- RA6 ~t 6 (0) I ( t)J 0 (01) o~(fa) e~ c-= (-gtt) 1)= (-ab-St)

SICL C ) UA6 bull ( CJ) 210 2M I we ~ A EAte middot

trt~ ~ Ceuro ~eIy So E (s-t) fi~ LCD ~M ffftbJoJTo IS ePEQ tt sces -to 4w 11 i$ )(po-f

Q Sce O(4 IfAIaJ J~ OA IS ( r VE J So

~~ c( e 14111 ~ bx-+ (r~-rl)~ s~ (rl- r )t (-) ~1Ct (hfo r t -1 OMs Wt et1

(b-s)+ (t1--it rrt bull ( s(rmiddotmiddotd= fit

Stllo-tltt~-tlesfJ - 3~ b~ bs+ (n-r)ts i pl~ (bA2o) Samptf~$ (t) $0 fe MAlhllects AB Siloce MU PQI ~II rfetts P~middot 14~MQ ~P=EQ I

7cfNe(1 let 0 be -t( POlt t eJt -tIo pe~t-c(r

P to A Ute ANfYIc frw~ QOL Be

8 ~~ se1lt~ ~U~50W AtJ wl( Si ~y~t~M~ -f4Aj(~

A 0 1o5Ic-f0V AAJ of ~ BAc rte A~ c ~~s~s-frttrI(~t

~CI(~ Set No 00)-L1It X-41(s 0 tlt Ani let -f- ~ ~ Aa lilt ~=cD~ eO A=-(-otIt1 o) P=-(ob)

- tltstl ~of Ac is OJ ~-AX-b -( $ril el11 of Po is j - tx b CM-)

111 )=-o ~ qt 0- ~ )t ltIto) r - 0

~ -~~8C ~ i~cox -The gtolbullbull~c)-( 1oIe~J amp (ti c~~ ) So(vl CD -c6) Wlaquo

tl C ( -c~ - c~)~ -del( 1= ( tt b_ -c E~ cot AM ts J ~(X+ b ctqtmiddot c~t) ~ ~o ~ et C e ) S( c4- t Q =(0I ~) bull

ope C c ~( 0( amp0 5 -i - Q 0 L ~c

~~

- bull

(~y ra JMO) l fft (01 ~WfiWItll A~Ie Se~~ - LtktU~4

Liacs

er wtIfo~ Ae J 61gt Ad A8t-l)C S~rfamp ~-( 1la r-t P lAJer~middot C 2

f~ 1~-

c Itgt C71 ilt ~(re~tW ~seto1S ~AR~ ~c eet s istt(e A8Ct) gt(oVt ~ AaCD S A C1cJ~cZ~r(~bull

ipound1 ~ tfgtoly L AA8P MJ ACOP Iv~~ ef(Clt~ llpse

( Ictide) I -tc e s

$olt- Set-t- ~~ilt PbullL C) rV] ( X X ~ltgtJc ~~ rallI Ibullbull Ac fl lt4Ei-AlC$

J) lttiM~ middotAe~~)=r OIX~I~kSampbpound etI~J-f(eL __ _ ~ ~ t~ ~~ Itgt ~-l I -J1 0 1D

LetAP=6Pr~CPlgtp Sde - 51=AX~bnitt~t41+ej-tf=o CiE-)

A(-Jt~ft p) ~=(IJfJi)C=(Iti pb)=4-~) ~ eft 1l1C~cle~ Et W (4egt 4=000) bull f ~ A+O I~We ~J at ~ 4l +0

A(cL1A8(gtN-AcOP 6O1~1 JrljtI_11 -fsl-tt ( ASSue ci Icj 5 foitlts yen~ ~c cf 2 ~ ~1 -2 tr- P Wt CI4 ~-s1-t~~ to Cyenc)-to def~n- b c c( e 41 Srt p r- ( -~ I I TI I ~i(~f+tr~fiJ ~)=Jl i i Cieler ~ to ~c~ tSeltt 4t + foifts

IJ -r 2lop ls-f Jsrz )qp ~ ~ ~ y-=s 0_ rL_) tT-if t ~ JU ZlrP+lt~~fi) ~ ABc D IS ~~cf1I1~ ~( X~lp( 11 ~ CAse ~3eoocll ill( t~fc fOit is c~-fWIIWt-e

1$ (cft tik~ bull ~ol(A ~ IgI f~ 11 G ~c~~ Co fts$eS -tl~bullu -ht~ ytgt~ ~ -tao oftet ~~t- c ocl lt1ffI ~ St(~)()_S~II1 ~10ft bull 1k1u~ef-COl s of -fle -fo(1V SI6c~) $AS~~~) SOfWe ~e (( bull

G~sD 6)(Affe 6 Let 0 he -f(f -ftrtf~ crrtuW~middotJ QfAAec W It A) t tI~-fu utff~el At 1gt f~ -t-e tAftcccmiddotdt fettect iIlaquo Be -f P let Ie 1gt0 i+tfTect k~s AC1 AB t H~AI reft~ frot -tit4t 0~=aN

obeJSet ~or~ i t 0 f

p -fa

~h ~ ~ X-4lt 0 L MN

f Let plJe1fa pect~~p i~ ~sct +0 o

A Lampt p=( t))~ p~ (-po)

-rtte~ c(~a~~ ~~-t- ~to~~r-Vgtqkt ~~ I AP Ie A( -fle sI-pe t( (4Lc

8C~ n ~~of4 ~ll~~s AP~(

~~~ II( ltf4 r )tes A6 middotoflie -s of ~~ I( t_ r amp= l(1-6ctpl1l-fI amp_ ~ ~t So~ AE ~1iiiO--------___-=---__

St~ ]=0 to Jet tkX-c-Jwfts 4~N ~e Wt k~rt= I6c~ 2) (~O

So M= (coJ 0) tV (-0)0) -f SotMe ~oeuro tR ~-tt~-ht~ () bull OM ON

ec s r(1j_~(~P))(_rt~_P))=O ~~ ~ -vs

~ reApi r-Lk~ ~

(frsl) ste-~~1~~ Ceo Us ~ FotrAAOC J let Dbe O~ ~ff U - -- A Let Dbe 0- Sce ac Let p= ADU - 81gt I)l W -= cD e 1) C 2+ eln= a( )

tiV+lG PM tW yen~-~ t-=- (10deg- middot ~o

(os tCos(llodeg-l)_ -CO$~ jlell byeose I 1

~ ~ t 1 I I l tf fJo= Cos 1-+ Cos t - Wotf - C + t~p- ~4 ~t zWp + set

Aeelok-s A (0 Let AD ~ 11 1fte4lt -t sk Be I

I

~ 1fe ~ stewafts t~ I

S9 DC ye(clts ~~pLJat-t2l-tt 2 Z 2

I

Ui~ -tt~ ~ S~~e~(e$S~t ta~ I -+

e ~et -tke Apollos e(fa(Cl ~r 1 Z l) XI ta froiof CeQ~~~ 1_ AEttr~ bullJJ~ 1i1b eo _ 4 ttfi-t ftlbJ c =~41I)t( _ ~A~ ~ amp~ Co 0-~

A

~ 8 1) C

-+1

lL) Let AJgt~ ike (AtIYl --~ J ~f)Jj- _ -74 MC r~ ~ araw Ceuro AOwi- E le AS

We et 4Ace ~ lSoSC~(s wr-bCA=EA 1fe ~= t- St4ltf WCl we 3et

~ co 4~ _ ks ltt ~ r ~ n - )+c- ~e~f So tf~ yklJs

to A1gt - J~c (t-s )- (b4cf middot

Ie be kAt CA ~ F ~ hIeuro A If Its AD ampE CF O~ ~bull ct ile

A ~~ lC ti lC ft=i () E rFA

amp Ii C Re~ 9y ltle lIII lpound AC fL _ CB~f I Aamp ~ - -LC 7n -_~t-or ~~ 11 rg 0

StaSiALAFc SillL CFB ~ $ 0 e se t M=Ac suY SLaLL 12ampA$OoOl ~c8~~ Famp C8~middotmiddot -1)c kSk~fA-ampA~I

-rI-e(it) is 1If 41$ A~ $ftJt4$~Sir f~_J- L ~ til

t(euro q~lclvtVt 0 at ~~ os-r I

middot

f (J

amp 1) C

CO 01gt ~O Cf OA BEmiddot

Q~c1~~ Af l fC -fl f 0-~ 31 ~tM Co -t~

_ U Ic _C6 _I I - ~-- 4wtq4IUSOf f6 c eA BE

So amp1gt ampE ~lifI1e$t 1)( Fc 14a Set c)

11 n~onU~lE~CA crf00 LJ f be f ) V _ bull bull J _ I ~ AE- sect2)t ~ -= ~o Re~l( ~ ft1~cooI olettot IS lJIe I~(g~fi i Ca s ~ If FIS)t 1gtC teA (~ of ott fOu6 Ot ile pI-e -tIlt Aft 1

CFue CcMcc1Ye-t bull Ai 6 ~(S_CA ~M~ wl~lAfs ~ A ~ roi (Ly t1lollffl~~) s S~ lgtJ= oS fir A AA6C If-tM1r~1t-0 0_ kat we It--ctIe (olt) I biseefotSqf AS o ~ itMecf 4tO

- - O-tkt ~ ha Ie~ Abl ampE 0 A ~I OA=OB-c 0amp=0( sQ-ctc 6 1) C -4lIt COI A6=F middot 61 UIfA s ~cl () S on k perptecfitr i 1ott A~n8ElCfOlII) AEx ~ltff=i t ~CA 0f4e4~epf(rt~~C - FB PC eA ~e C6CMtV60-l t () O~fk(-t)weJct f-~k~ 0 S~~t~ceqVot 4ASC rtrs~~

M= =6E -ti =~-t _ - Famp_ t ~e ~W--Sc~~trl (oCiVC4IIlG~cl) ~I

~ Fe F8 fe -Pi) F-f AIrBC1tIe~~~CdQowtbullbulllampI~ isAppi_~ iftiileafces1lbllt~_ ~so Cailtd(~8r~iiua46Aac

(4)tfAtgtBeuroCf_~~c(AABcI )( B let)(1Z~~feJ~_JI- AF Igt JC ce eA ~ 10k I 1 L L _~ -r-rshy

t FiwlgtC iA=C7i 1 ~=I middot - -e 11QUtt t t AaCA BCSoAOBElCF==~cfltfVtc~tAaC A C ~AASHCaIAx~~rAt~o CfJ) If A1gt1 BE CFore Clttitcles MBc -t Jl I bull IX~ t y Sl(~ I Y [~

- x -1 ~ 180 ~~ S bull Ct-I- -J F - D C ~At 6Jgt ce =ampOOA 02as5 V4SC igttamp1tVL Cnw l( V~ FEIt l5C eA -~Ci1S8 bcostcGosA f 1Xt 1 =1 ~ -rtiHitrdt is ~~sc~

A $0 A1gtn8eurooCF= H o~~Mac 9 rclk ~c1A~ c 0( lt -tkilrM~ 44ABC ~ (c) If AD ee CF laquo~ Q+ bisrttOlSM8c -nct gt~tS)( f ~ Ale ~ts of t-~ 1gt Co ~ Af ~x~=~~c1t)~)ft -t-a 1S(tT~ Qrct wtfl~sIleo AampcA Be

Famp Acc4~) ~d ) IJL-t~ -tfiA Aec S0 A~ 1 ~o tF I I ~odt(laquof4A~c -r JI s ~ ttWte c1---tlt fsctIA ttde of AA8c ~

-tl~ Imiddot~s ATgt BE N

A E

t)

FA ~~

CfiE) t wt poundtccl ~e $~ ~ LampAC

bt10Ni 6 410f1 C J -tlte -tampi th~~ f L eAt ~ -tlte ~O Ile

-os c 7- J~littf~s vt S t 4ACe(A

~ ~~-t At ~ tgtDiltt Ia X r-- lt cule4l 14 xce1i-te of AI8C

I f~- A ~rI Ie clr fe(f-c1oss tACA6C IIIi-4 f~t I ~J v y z

I I -- I Il~o AAS I AIIIX 6~AIIIZ6 ad IiTrC ~1iIzc S l X t 1=tr (4 -rke Crcubull4f c~ r A--4 clt~ ( IS -tct~ to AS CAee 4 xt~ z tt s clleJ ~ esc-i~ cVc1e (OY 4ccittf) 4 IiA~ MOO bull ~ ulSe cI(- tt er4c(~ 1

~A A ( r bull c

It~ 711

to ~~I ~

bullIa

II

Ill folWt QrcI~

ror ~ABC Iet A 8 e Lt clpoiwf$ ( atleAlAB et 1gt 6 F be feet of 4It-lcl-t ~s Be CA ItC bull

let kL I ~middotqe tf0t~ af I-A W61-C w4 cs-Je Itioampafv of Mac

1ke ec lgtEF rltcM_ttcoOCtclc ~ Cc~ fUaj ~ ~ clt( ~ ItIIe e--t Cull ABe ~ cefe N -ioNs cd~ is ~ clrowl 0 H ~ ((s ~s iwlTlGIC_~f AAS 0 SottIM ~AABC w see aitCA ~d (f8t t see uti it ~

8 So Cit~ Si~ eL =i M =8M

s~ AH1 a ( I Sc~ t1 $kf+ 8 A D C -na~ ~CO~I5 tcLM rs

(L Aoot C of AS ~r I Sc f 8EL1oo=L CFM eFCI~c Iso r

1I So SeEF l~f1 ~amp ~~l(

St(Irt~ ~ As OEKt 4re~~ ~ ~ qrdeHlaquoI~ tEl helCt (61 4~te ~~ rck l~i~i-d~ 4SeL)- A6( 1lgtGF ~l~ ueClW ~ SCl-e cude Note tL I CMA Gte ctOIfars qf ~Circle

c5fD Sice OA amp0 BCIICS So feufbAch s ~~rfNA o A J Crb Srll(~ly oa J Ae ~ f 11 e P int cuclc f 4 t~ bullbull Ie Oe J ampA So 0 is o~e1A1( is -t3~ 0 ike ~( c-de No LlAamp1 AA~c ~i tot~o 2 1 ()~ ~e 1k-let esUietl C47rcles

A D C So AASI A A~ 0 i rAtto 2 L r4 -tk --tY-~e 1-eO AO A~ AeAe h )Ao=iAK t(~ Ws s Qtt-t_e1y ~tfJ 5~ A 0 J Be tJMJ lt-1 foe $0 A 0 II K ~e4 tIlCl e~t~f1 ~t AOl~ ~ laquo ~~[(em bull $ ct Aj( is laquoJ~ -to rOllt oftt ~ rtt Q~c bull So t~ ~oet (lSigt t ~--------r-- ~eO~rft of QH) is 1le cet~t_tl Nt ~ middotfc~ ~ 1 AAo tJ ts ~Iamp ~ I) K ( K IS IIIlftd-af fIA ~ lt K i OA middotH Crc-~t s l AAac ) bull t

6Je UIe i MBC i~ ~ 111- 0 ~ Amiddot Note AX is ediArt~o ~d4 8c

o ( II Ltt Ofll AA c (q SCMct OAII A 1-1

--- ~N-- tA~ 0 =i A HI we sae B A Igt C A Ao AAH6 rtto i 2

o~ So 1)iErH11tt)(iio~ ~ 5 1 ~~ bull ee ae ~ ~Qj (so il~t i o ht -fIt ~ j-o~ -0 tj 411 t teampd ~ At Gt ~-t AN C fgtst ec - cetle So = dtli ~ 6-f( t~ eord-IS -l J 0 ~ N~ ~ AI$o A 3AA 0 bull ]

L

i a t e CJ

I u

Ci

CEi0 ~~N~ ~ let beQsJf~e(-f(f ~ K+O So i ampmiddot-i ACo~~ iSA )lJt4~fotmiddot A- b W~~ Co III ~ teal --~

--rfa ~t -+ A( ~rtlt 1I14us ~llloe (~~ ~ C G~cJly ct s el+J of t1SJ bull ~+Igt~ U~fPOlt (ft) Ent M~ fb 0(l +be bull c-+ ct i ec) o (0 )+ (c(-elc) (4-tc)-+(~-td)1 (410- (cot Ii) ~-c)-+ (b-clh bullreg ((H~)(-ttJC=(Ac-bcl)-t(~-t~dl 12 ~ c-td~o -flt -- c-e(-= ~ J Ne( Campmiddot c+Ji ~c+~ ~co1ts

I

~ IAtb S 4-1o~ w~4eA4 -iIu 0 C0JY-te a( Atb l~ At6t -Ilt o~oo4t ~14a (Of ~) tf at is ~ 4~ lilt middot

NoI-t i--s is ike clt9t- be-l-wu (00) a( (e)

~~ W daM ilu~Solf VAl~cf olIIt y At bmiddot=J4Iot IJt --lA-t~t=(Glt~Ga Ioc)A- 1 ~ ~Cll--bl - shy~ 1 711a L lfO

Yroee~bullbull~ Ltt wJ~e( - _ - bull - - - - - -- IJL _~-J(D Wt1 +l W-L w-aJ we=w i -n - hi

~ lt~~wt~ lzlltJ 1lzl iYI~~ - middotifUoJ

~ Jqt~~ =leampal ~=c+rk=Wie~Ji4e- I ~(eo) lit ~el~-6z)

i Wt=(p~b(c~d~)rrae bull amp ~ yo~e L~

1olot furrn n It- be e ( Ie l= 4t(i~4 fLC loi(l~ 9 b(~(EfR1IvLfDs4ttX-cN ~ to ie ro~ CO6)~l) 14~

(o(oo) Caocdlaquoclottfse cCllIctcn ats o(td 4e ~ ot o-tbi laquot it is cC~ r o~-iW)~f~ e~e oyo cs8 tl~s (fosS)+ i~9l It A~~c coseH~=YeteIIlaquoi~ to ~OftS ~ bull

ey ik cu~ I f xt~~=Ye )~ ~=r-e-roY AI( fe Z~CIsk lWtf fir ~ lee euro C o Go ro~~t~tt ~ ~t wf ~ ltII _fir ~ ~ f bull (6+l~

I - ire gt I~ J1=e ~ J

) WftreileH(Il-Imy

~s ) ~ ~CI~ W

fIrre J

l Ioh L T_ -f -t ts ofJ

W4-II4 C4S~ pound_ )

~~ 41f Wid Ja-e w)e )

I1 2~)tt~ I pin e Afe

-ltv ~t Setflaquots ~ A I~d ~ampPav3~

Cotttple~ 6eUYIUi(-ry

~ -t Ls ~ N~~tQVs e c gt e - Ccs9 +Se

~sc Obte~ ~ ~

CD 1- W claquotsr(middot t -R Ie-tt We III r ~1 ~(+ot) ~ 01 e _ 8 To yot~+f A YIi v fLe rlAlIe Iiishy

- r I 1fSj~t -to -Ie ~ ~ ~ Go)1 ~ C(

=~ r_ ik We $~fl1Ioltrb 1Ie crl foe l fA ~ - e b~ e

Acrl~1 Ie ~ ~s Iej f t ~ fl=- E

Ei-tmiddot 1- ~-tljk -t di-Yoits 1

Gi~ W W2 fke 9Qta-~c e~CM Af -tI ~ ~ ~ ~-~~k IN Wa is O~ ~ 0 +t Wa t ea - 10

W ~ So z-w bull HelllLc ~-J _-i -- ~1ecJ ~-W c

Wz-W WcW I ~_Wmiddot 0 1-kt beA ~~ olSo tJi~u -tk cJ~r

igtr -tke ~~ ferlts 4 WLJ l -to be eolheAr- eogi- of l u fcoJc ~ 1 1rllleP0rt

i CtrIz-) RottmiddotOW 1oJ1 9t W

- bull -1 II It-vL

e == Cos 1 gts = 1 bullWIw Eltot of-ike le tkn C rttr~JcJA

-to oJ W1 5 f l-C -~-c- l

0~7i-f ~

Li f~) ASS-teJ wt~ (uit) c~tctf

11 w W~ n 0 ~ tle ~-l cJe (at wi =Wzih~ l )

~ -tk trto ~~t ~O J Wt so z u

l- _ Wz-W C - - - l - = -w~lc-W t-w

Slworl~~ w~3~t ~ _ ]t +WWz t Wt W2 bull

-r~er~of -to h amp ~jl ~ ~~ lot C r~ 0 W W-z s l- C i (wamp-w)

---- -=WW1 ~-c -W(W1-W)

lt)irljj We 3 t I~-101Mh C-IVWC

1A~i~Cst

Let~ Wz~ W we ~ct ike f~Otl af ~f -tampjc--t ht t ~ i tele I)t I wI~~

(l+ lJti JW] yl ert~ -tle rey bull tcJr fa c To iIt tlaquojct

lIt cJ W is -L Wt

i(J~w) -= T(w~-~

~gt

CD C~eetfe( 0 is ~t tlv ornI reg CeV~J G is ct A-tA~ A3_

() I eurot- NH llt (-r~s rs -tf 41-1 ~- 1 A A A bull A tateo J n I l _ J i (~~Le~ ~Alll~b) s 01 SCt~eD u -pe v~GyueJ

(jOf4-hoce~t~ H l$ c AT At+ Pr3 (be(AASe O~ = 5(O~)) pound1- f lt tl~ A ~ fJclCi-r -to ALA 1s

i- A-A3 ~ -= At - A1-AJ A bl~-t ~ 1 1laquo ~ ~ r~~cJAt -to AA~ $

c- AA) == ~- A~ ~ -rktSt -fwo -ts W f~cf ltt t ampJk4J gt~~flaquos boi lut~~ u$~-f~ ~t tAll lAzI= tA- i- (e

AA = AzA - ~X3 -= ) t ~t lt e c At-tA T A~ SAiSfelt bofl ~t~01l~ 1eo t-= AT At -( ~3

17 N f t - L A+ Al-Ar) 6 Ce---+ef ~-tke ~-e foitrt Qftle $ DA l-

(be~oe 1-1 $ ~ ~Jro~ 4 o t-t) ~tCA ~ Mi-e fit arcc is -tke Ciolaquo ~t f4~SfS -tvnWJ4 ~ a Jo---~ -4le ~~es AtAl Aamp+~ As+A) ~ ~- J L -) ~) -

~Q 1eet qf ~ al-t-bAdcs H I 1 1-3 -=t ~ Wampdtoi~~ -tk ferllaquos ad ~e D~e1 ~~ raquo A~lt

(J~i(t~ ) A lltzlJ J llWW1-~ Ayt ~ito

Sol4 SifCamp ~A~R~lgttPLlCQA~ ~rJwail~e Arf A+cJQ+~~R20 I 1i~R+~~Pao C-t~1T~ZQ=-O

I ~Il I w e LV = e ~ 5 A ~t 4 ~b To ~~ fl X 1l s erltamptDI we CoM-rtf

Xt wl-t t)ll= (Ai~amp ) +w~Ct~iP )~(8+~~

= k [CM Q+ ~~)+ 1Yfgtt wR + tf )+ w (C + p+~ I = 0

~~~A I )( ts ~ (Rot 4 1 J~ ~ ~-t 4 -II 3~f1 C~cf ~ ce~-ter4cl At ~ (A e) ~ ~(f-t~) (ie ~c pOlt 3 -the amp~~c ~ ~ ~11t~ -G t- ~rid 1 ~~t AS)

COlf~selj Ikj ll~ 01 ilt G~f smiddot ~ fo~t ~ loc-s 61 )( 0-~ G~f C = i(Jlt- CA-t 8)) is -flc co~nsfo-kj lt Ov- ile ~t Clfdt

1-(t1J~ Let A~ A)e tI ~r~ 0t W1w) w~j I Y~ f~~j

fYo~ A ~ J~r - fe~~ -to -tkt -t~~ e to ~ c~tdt I

01 b w WI W 3 Got W bull skw~ ~est f~(tS ~ctCmt 1cle-t~~ ~s tmiddot~t t C)~

~otct~ JlCG ASSUllC -tL ai~cit-tle is -tlt kAtf GifC(t

~ h~ le~~tcJA -to t f~eMt oJ 1J -iklk ~ MS et--4M rll-tvJ~

bull l- A ~-A - WltWl t~ k~Wi -r ~- w - tV - 2 - - W 2 bull

Now WI bullbull f -ike ampM- ~~lc I SO Wd -= 1 i1e we ~ fJ~-te -tk ~n 4S _ _

~ bullbull Z ~ _ I T ~-t Wos 11 W + 2 Wl ~ - 1iIII I - - w

2 2-

F-oN -tk5 t ~ ~t -tk yoil-f N Jw~ -+ W3 $ 0shy

--te e lt$-I(C -t1e e1f~sS1W f Ns Sr~t~c ~~ nSFt -t oJ Jt Vis we (4 eot-t~ -tMt wtl lISO e O~ -tIt o~-- -two les -t~ e-Fc~Sto ~1 tJ -tt l s u~ -t $ -tle (fwle1 ~ -t~ )1 fO~~ (tce ~

J I W-z4 _

11Ob~ ( S~~t lYe Tko~ ) let W be D~ llt (~crclf ofJ ~1 13 c( PI Q1 R

be ~ iut ~ ~ lC ftJi~ ~ W -tt t1I 2 ll I tl ~ I ft ~ec-f~Jflj slw ifvt P Q R A-e tAl(Il (-ps Ole 5-

clt~ A $~501 11 tf A ltamp-t) ~ W) i

~ol~bo- WamplAi loss -t 3~nl~ I Wt J lS$We Je G-nIUshy

Cilampk 1s ~ ~ cttclt ~ lll llJ lls -= lw I ~ t 1kt k ii ~s ~~ l+ ll~ ~ Ii t3 --ie r~~ fw- W + 1~ Ivs ~ f-ltl ) i tJ- Zt~W So Sol lkcsc -tcdr W~ 3laquo l = ~ t L + W-lE W

2

St ~ Q ltl ott ilW --l 1(= tt f t~~1l

I sluw fQR 4t CttlfUf it S~s-t st P-R =l-amp-Nil f-R _l- Z-amp-~~ Yo-~~J (tI 4W -g ~-R

Q-~ -1-1)-1tJ --l~W X l ~-amp~w ) l2tgtW-ltl~ -lZ+ t

4t~ w- Zl~-ll-t It f- fl

- (1- R bull

-J clt~lttii lw=t ~ WW-=i

CiiID ~tlt~ firLiA BC let 1gt be A4Ie GtIlOc1tf- E 001 As loIiti DEit-CB J ~ F ie 600 Be I

ciA ~fDf oX ~~ o-rbmiddot 0 1 ltt ftt XIS G(( Gr be 01 EP ~tS~t ~ el~ttrlgtedo-r W~~~~fk~t~s X Ao D C fSfoFc-=Ep-=BYc1gt=r

~J ~sted oR we rMj Sity ~ i 7 middot PrDV~ 6i-F fs pcmI(e( -to -Me 4 b~ 1 -M CaJamp) Xl= Of-~ -tI S~1 je Y-X Sol-I Set 1ampt o~ AtAo tt(-~ IMc

For ~fS X It we e Ix-+f ~ lxl +111 ~ft Tie E 8 Gfl = C ot~~ E (0 r)klgt(d~ 1- W-11IAy f X= ~t(r-s-e t~o A~ F tB t(f-t)c 4( euroj =tE t-((-f)J) _ h Let Pbe 0 poillt el LIle )( f lJe lter t= B _ L _ amp1gt g + (_t )e~ middot gtY haYCamp oP=toX+(f-t)oy -f=~y ~ Be -- r -i1gt-t ~_

J J gt1( 8 -I io O~)y~ amp(01] ~ P-u SfjllleMt Xt E retgt I $0 IE-BI rD-cl c1

EICjl1t Call a ~1IIecent ~ ~ QjgtWelC ~l~ (I- ) Is (E -amph 1l ID-d r-(t-amp)(c(-f6-Jgtfd tl )ltLJ )M ~ ct j~ Ie ~od ~ orF9fe sk~ J i q F- Gt = t6-p)~+ (I-t)(1-9)C ~ +~hw ~t cf -tk s IIf-t4 Jgtllrl1lpounds Of ~t(tei _ IS tlt-p)amp1~$ htfampt iits~etet ~ik~litetllllorltl -tlt-p)la (amp+~~ =(~~k1NIllelo I _1 t f4IIIl ltf1ltS

Sll~ fir trl4t~ A~c~ Itt-A IlIamp 1M OjL ltf 114 (tw~-for ~ pound Me~ --ik se ~fOW twI ~ _ Igt IC-tO - f ~ if

T -poundTI-r -pound ~ I A=0 1)~D i(1el IC-BIt lo-dtll)~

UI8iC-1gt1 +11Hlt-at=Iel+ Ie-IgtI+11gt1 +1c_~(f~~t Wt ut Ie+IC-Igt ~ Iamp+c-tgtl t=~f1f)

AA IDI + IC-61 ~ 11gt+C-81 C-~AO=~8C) (gtt) holds ~Le~ft~~lcJs A81(1)C ATgt Usc _~ __

c6hf--I--l~1gt~ ItiC

~1- ~t fmiddot~~ 0+ ~ 0 ( is )(Y=tJC( (1 rsti - Ex4k+ Let 0 ~~ (i(cAt cf 4ABe 9 ~iIt J bef -fIl lfcffS Jf -IIf (t) Xi=fX (y+I)zmiddotXmiddotZ+fmiddotZ 0( (cXl-Y~(Xmiddoty) ~ I~~)(middotX I IXmiddot~~hd1I O~iOf (=) Xmiddoty-O ~~~~~~~~~~~~~~~ amp--ft 3 Let A8C b Le lmiddotts ~sfmiddotmiddot Phe

Ac~+amp~+A~-t8C~~ Ast+ctl SJt~~ Set1ie Ot~I ttt A ~~t f Jw

CmiddotC +(amp-lgtHamp-~)+D~ (8-c)~-c) ~ amp (c-b)laquo- At~(~- awl lt~~-f4ls s fu ~4S

(6 C-b)middot(S-C-lraquo ~ 0 ~~ck s (amplt-1) ~o

A ~t 1gt Ie -tLt poit ~ Aamp -L II ~ e _ ce~AAcO

p C fgtrcw _t C1gtJoe ) AS-AC Sol~~~~~~~dO~A

A a A J) A J)= ~ E=~~ =3 +~lCJ1gt-C=Aamp-2C

C1gt1 Oe- (A-tS-le)(Mc+1raquowO c) No AA~lh c C C(CUM(bull (IampSt 8 41f1$-bull (4) bec u Amiddot(Q-ltAB-ACO 1IeJtt(~) ~ OAl ~c ~ A~~AC

euro ~ toJs ~ 8lt~ 1)-A69 seAPS fWlkl ~JCOc $ firAABC jf( t ssewu-J -ptMf ~ c= - ta-+CmiddotfI AAS( its ~ttd q ~1 - If We Sampt -iU CitClIMChH- 0 AS ken -HII-srft~ ~o -t r -11 __ -~ -1 ALh--COtt - 7J 0 OtlGCnx n - ~-

A Fit iAcetft tJf ~~ c 0( lU= ~ = L

co b AI c lt-c

e ~ 1)c 1gt= te+(t-t) C t --amps ~1i~ poundL = tD ~+ cC C bI-c Gte middot I t A-t -~)tgt t-ll- A

aAtlS cc_ - tgtA - M~C 14 e middot

11l Lqt-(gt OmiddotkC Gtctal ~ICef c(H ~r J

51_ Set 5 4lt C4fColt_bull tu e -H Matel~Me1~ 1~ AA+b$-t C shy ~ 4~(

Lampil~gt 1omiddot~(i-1)l4-1) lt0 A-A 6middot~Cc=(tlJ 2ec 6amp+cc-(a-c)(amp-Q=k~middotIf (A16i)riamptc~ Rlt9~~ 11- 3( h_ Imiddotltl-C) 4l- 2(~~(H- btCi)tI~)) cttC

)(~+c) (-1)((-1) =((~ t1 -Hi+(() lt 0 of -~ f (ib -t-e) lA+Il+ ct )+ilaquoc gt~ CifI+cl+Jl(c)+ ~ ~ a(-o)(--G)-4-~-c)(b+cc-4)~)gt0 tsc4 rc s

~ Ike fRS ~ f xi xI wt -Stl-fculot 11-$9 (t)=LXOY) 0( tiYfft~e~ -fo -tkt fl~~ 1-- oxY J e

lti) ~ -f~)( ~f)-a)( l t Yltl (c~wYcxnyJ (j - )(~1 4fT~ A X0( V~~ p A of yl t1ft 0

(6laquo Q bull 1 lj 111)1 (DW~v e

eJ41~ Let AAA A _j A 1 1_ -+ V]nq DO 4 CD e I

- its ste ~tS p-Ilt1 ProiIla-t middot ClrtllAA1Ar oreAA AA So(u-tVf SeL ot - ~ -_amp I~ _L ft--A A ----- ~ fJe ~ ~ --fI 01r~~ O4St SMs ~qIt ~t)~csCA-A) I lA_-A f

E)Ctl-eIlaquo-r Let A6COf tgt ~~ pe-tft Qc e t

~~~Q~ ~ 1kfwlrids~ A88CCIgtbEpoundA 1T~ -r APamptl~J~ le ACDIIIampf6i -laquo s~O~ tk-t ~s Ooet is so eM eII bullbull ~olt4-tfN ~et -ckt O~bullbull~ rt -e ~_W f~ S~

tJ 1(t0 AXC ~ AP ofe (o(iu o=A-f- A(~ J C- 32s amp A

lltc t))tA SIA~y 8)(1)= (1(8 CxE~ C I

raquo)(A 6llgt re EJ( 6 =CcE feMtt I

eurolCAJ- E)(6-t( - ~lte+El$ ~ pound10 eImiddotmiddot

1 ~~-A~)o (As-AJ1gt(~A~ S ~~CI amp euro1tf6lc~ ~se Ac Adol~ -t(t-t Lit set - () middot At

At~ t ~It~ AsIC~ Al~-+yen+yJAI (

_t a ~ - bull

~ 2-shy

I _0 c A 6 c ~ As V ~1~Ut 1 Sjtllc -fb ~BIC~ fW(t

ftdle ~ts of BC CA AB ns~chvell -tk ft1~ -tIua-t

No A bull G 8 A I ~amp Ca A~ (orr eU egt~ 4~_ A~itlA-~lClA-As~=(~tAtAr-tAjcA -~~ StthtlI4It ~ SaJc1ttA

(Nmiddot~~i~+Ar~~l ore4 l1A AAs = Are 1J~~Ai

Aft13 amp11 C=A-ttils-A)frSollletoA~] SiCt AS e Gfe i eRe

o~ (Bt-A)K(~-A) - (A-ttz-~tl-t- t t)AxB No ~~=~~~-=amp-AH-t)e ~~1 S-a-= It-t1)A I Ct = lAt8)- c tlA +ll-t~)B ~ (amp-AI~I~(Cz-~)=(t-ttl-trtl-+t~t))Al(amp~O A S~ CL At( ccdllfttor

~t ~~ 1~~Pt

o

C[~1D --r-0 vetlOf) )( lf ate Jt~y wtt-t---t f~ t -flat ~f~ ClX~yO kAs 01 Soat~

AT 10 o T4 s tktCcStI ~~A rf KttO ~ X0 f Art NIt Co((llteor

F4t IT AX+bY+c =0 ~$ote -e 1~I(z-s 4t4l 4-+amp ott -=0 J ilQA Xf Z 4le cbullbullI btACcS( ~l AO fIe b-tc-o w X-1-KZ-tYc-6Z

(~ar~11to(~1 wr~t--J Lftai c~ s OAAampA Co

~ OeLamps 1f 1 -1z- Aa6~l~8ampR AsampIA~= ~ 6 8-c amp-S tltcl A DAR 0

~e COIIfttAt t ~1 =- 1 ~ ~ P Pl) P3S~ Set - orlll at o at A8 btt ~trs Ale LIDa (ampfbv~ ~ A~ rA Q( e s So 8 1-t S6Wt (s EIt Cll No

Pl =tAt(c-t) 8a trA+ (ct)s ~- ~3 lAAt-tQ-) 8-= tA(-aA+Cc-ct)S a S~tU~ ~ 0= ltr- CArgtA + [pound1)l -(I-I4)$]B

A~ (tally rcf~=gt tr(~ Otu( (l-tl~-laquotlt)S=C Solll fott ol -tit pt~~ -+-s f ti ~I~Js

Nt ~~e ~ 1tu~~A+ SoSzCt-rl g$t Vs- r~ r~- r~1 Pgt1s~S)A+~s(tmiddotgt8 R= rlrfgt~A ~(I)J B

Y~-r)S) ~6a-t~S) amp c) ttS +fs-1S ~ p~f~P+~sampf-tj~

~ P1 ~se~rw)~c 0 Qtlgt+CoO ~ r fL cU-1- fc-i (ove

~ 0

A - -

~ FOf~lamp~

(1 -laquo ~C

fot-CA~ to ~ t t amp -t~~ crt a ~tc ~ El(tend~ltl St L laquobe ~[A8Cl Js~~i~ R= 4 C

Let ( ~t 4ct nwts lt 4e GoismvmcJt i-R- tl 4J~)(fo~of AAsc Sr ~ l=~~Yslt) ~ bc_

S A -- - 0 21 1iltelaquoe s dolAt C~d~middot ~o~ uI1gt ~ s~amp s~~C middot T 1_ ~ rI n -rf (i-- shy

tl Ie or~ DraJ clmiddotae~t 61gt 1pound Si ~ A= ----=algt i IS lle~ ltJOiOlSA0

~~~~~~~~~~~~~-~~~~=~~~~ p adEr-l-~a~~r~ A- oS+- jtus c~ - c e c I) p(]) Let 18(1gt L~Ms

I4dtt rAsel Or S~8c1oI(lcl~ 1leflAftt Let A6nct)p -r1 ~act 0

~Me C ABC ) GlUo~kc ~ PAx P6= Pc x PD = tl b~~=Abc bull P19tpound Note L APD L (PB

4R A1BC)aHd~ckLPAtgt=LPCBS=tfA-tb~~) is ike seifieAc ~AAPDACfB~=~~ PAIPB=fxPD

amp Q C Of 4A8C Lri pc C 1amp-~ ~~ PC Is -lt-~t lat t lie i4 jCbullbullr 4l( M6C Qt r Ie -i4~ to -e -fde ~ A A8C if (JJ

C)~ ~e icltc1e ot AAec ~e p A e OYlJ c fCL p~~re [Mel =[ALel[~cl+(CI1= ~-t~+~=SIr ~ Not~ LArc=LcPB

I-tfllWlbull [A8tl~ S($-11 ) (s-b)(s-c)middot I pCs f~ot -to LACp4C ampP(~ Cos C= tt2ttoa-c (~AI Ci(~ircl 4 MBc B 2shy

[A6Ci= ~SiIlC=Qr(+coSp(i-($C) ~AAcPACBP ~~ fgtc PCPAlltPB =(Cl~-+Iot-c~t-~a~-9 ) = catlo-4 t )(A1(-c)(CoHI- b)(o-Il-~= S (s-c)(~~

2- ~ a

Ci C [AS(I A 2

~

I

~JJI LPFA-=odeg=Lpe~ ~ amp~ ~LPFeLPAE

C5Ji) ~tolt1 s-ThtOfotfll Let A 6c~ ~t dlSncf ~ts 01 bull ~c ~o - Me~IA~ 1( bull t Of~~~I ~Ot bull -Tht~ bull Sa c~tOV M1 C(liofIPT potd~ A 6 C Iie to

AI 6 C 1gt (1~t~c 1gtpound fCLR atfmiddote ZA ~A A ZA bull -~ -iA ~Co~ PAQ~clf$ WeA~ ZA~lA I tc Z~t

pFAECc1dk

bull ~ Srlloi(y taCgt6~~~-lPFB ~ pG~ f CDCCYcbull LPampb LPFI) = e 1klaquo AIJ~P LPAespoundp8C pfE _ LPeP 8EF (0(1ltlt~L PFE L~8Tgt~ LFP - L 10 collirAfampff

)fgtC)~Jl~~ ~ ASC1HAol6C=AcS]) bull (~~_ ~ktI AeCO At)ItBC ~ACdtgt 1)~c 190pound 0 sWLe AB UJlfsftfUct A ampA6

S~~41 to flCAP 1I1elt AB A~ 6eshy

6 Ai - 7ligt= (1) lBAE=LCAJgt

SO LMc L BAlgt-L1gt= LeA1gt-LMe =LEAt) Tkeuro1 A8AC~Ae-A1) So Rr-c EDAtgt~A Thet Aec~ A~8C =poundItampE AClC E~ AC80

bull A rC =c Sf-t Ell I

f1-I-4j hoW~ ~8euro~EtgtS ampb ~ E iUt~( SO - ~~oeA~LeeALtgtCA ~AsectCO Sltffc

SoSoft ~oe 1et~6cP cl-ampd-p~ 0

tI~ Let l)poundF fetf~~ff- P~ ampa Aeyen~~ ~

Asse ~Mist (so4 is 6~UA_JC ~AGSC ~O bull G ~f( Aalec~o)

tt~e9 7eff

fovlaquos X I Z ate (es Aamp ampCA D ((t~ve-()ty It X I Z (lie (dl-lflOr

A ~f f6 lhg--1 ~ xe YC LA - middot ~ lQt Dbu (~ Ac soct1IIt 81gt II J( Z -r1teuron

~g ~ ~ 1t~ ~z Se AlC 6Y c~ _At P1Q (i~ ~y Ie ~c -- _______ r tamp iU I bull laS yc fA ~Igt ZCZA middot lCI~ lIeeu~ Ie~

If ~ tL ~ =-1 iIamp )( YL MHo l~(~ Y~t~~~~ SlJ) Ltt l~ X(OCA -Thtl b Mt11Idtw 11~ Ax ay CI _ lt Cz Y Cl iiiK zA --i ~o --=-l1toobull CfIea bull _Cl -a

I I

ceDD ~MelI s lIeo~toA l~tA I ~cc t) euro ~be tc~ lO 0shy

de lw~~ ~( ft amptCtSSCti 1 tf (~ diC- (~QEf ) bull

t p Ae ti l)euro J Q Bel pound f 2= Cl)n fA ~ ~k ~ Q1t ottc(l(ea~ ~QIR~~~ -

f~ 1 ~ ltt X~EfA 1AMCD bull ~ z- C~neF Arr~l ~(atts ~ff 1e-(fM1oec~ FA

ftt- Ool~~~ 4xf l w hVII

e-- ~ X K __( It X2 ~_( t ~~II Qx 6y Ct ~y pzex I fllFxijmiddot 1I

Hul~pr~ ~ AIl ~~ tfffSfctj cofI4t tt XA)(B XEmiddotKF J (CmiddotYP=1AmiddotYS ZEmiddotZF= zeZIgt W~~et ZQ lSf~-i igt PQ~ ore rlfltelaquor

Qx Pf Itz loy c-enc ~Mee(AaS

t-rks ~ere 0 Imiddotil~ (1$($ of PoucJ s for It we tftwt Ato 8 -te I AIwIJ (3 il(cJe 1Iofl1-t i AB will b~ ~-t1l3et (iot ot B ~ It~j CIt~ we ells JpoundAoflt ~ t~ liflE Clt B b~ BR

6lCtJfC i F~~ h Cf(Ultirc~ ot Mac J f(it 1) ( ~ ~i~0yen ot -t4l~lE I~ ~tA - ~~ Be ~ e fM 1fe ttusc(e~ of-ffwf3ct (tt4-t C3L1r~ CA~ F= bt ~ ttfStd~ of -tINt ti-~-f Imiddot~t ~tC wo( Aamp 11161 PI Ell F o~ ctU

Soof~fIyen P=Mo 8C ~ E= BBnlA f=CCnAB APP~i P~f ~ ~(fo MB See I fott et 1gtpound f c-

-- =JSiiiiIii

b)lAtc ~ Let-tgt 0- eht ~cfs 0( dt101 AtCS

AS ~ AC O~~e (ilcu-R( Mac ftspciwJy l(t tgt Ilt ~f AtC sCI ~== DPn SA J R= PEn AC fro +~-t lile QR~s~(QVJ14 fttCf+~I (~ 1) ~ f9bt-Mshy~e 1)rff0--AS- CO ~SfctsLAc8

Co ~r ~ qftllCr At =lgt 6 ~LAec So 1= Cl)n G8 Sf_ eEtS

Q tgtPt SA DP 8ital R= Pe C Pre ttL PlE AI

AIP~ f~l ~ 1Ito(-to C ~ P er ~ w 1 ~ bull 1I

t Set I Q Rut tIff~ Co~~d~

~ -7

Alt IXu q j

elf (Ga1(e 3 Ltt AT3CPs e ~ +s tMDlCJe ~-rd AAfLBS Bat LeA) ccf LAB fat 1gt be ~ls (I ~cucl1t ~c4( I

DA(11)C= AU DB()CAe~ 1gtCIAB~ fgt~~ A~ r~CtfaJ T4 6v~fi ~ IAGC a~ Co((~((r

~olf- W HL-cI oy-((~( ~ AA Be Ne

AAIB~I)Cc(-=I DArBC=A 11gt1( ISc AtA f Cc -= H L lAlA I C I Cl

1t~()cD=C1 ~l (AIBl (cjAfrrr5~5Gl ~~ t DAAfCC tgtlt Se4 A HC tit c11ilaquoraquo SIt 1y ar171~ BS41s(to AS e 0cc we Su e H 6ltve c1(i~amp r A~ H C~ S4rt a(((~4~ I

-~ ALI)f ~fle1 tt P toe a ltpor i~4Mec

LtfP I~~ff~I$f- 5 -to ~CA Camp ft~t~ lttt bJ() ~_ eshy

ll 10 ~ fet ~~~N~ c-tohs API sp (~ftvtll IfQ P ~ 61bullbull Pt14 PttNQ~~ (tries ~tll~ Qfz cod A~ aft ~et

iSoLttd- $(fCJt L CPc p) LCQLP LC~P Lc (gta Palt-e J -t ~es c P ~L I PI Q p 4ftcocttc f~AfrI15 ~s middottU(Woto ~1l$1 w-tSu CPt ( gt e-= A ) P t1t( QIP= X ) (Q-a Pf P2C-= B 4re CoI~rtelr $6 Rb2-l amp1L ( AB-=Xmiddot ~ ~lIQ P~IA8 tVe ~Cqfre~

NewtDJ S

~A ABcOS~~(laquoteJktvsa e ~SQiraquoeamp c~tkt~~ ~~

APgtsc CD) PA AXcpotlts EFG)H-~t~ C F B ~ACG~FHgD~~r~t

Sol~tcNI W E6nFHO~ Eftn FG ~X _Apply~~ ~~scJ ~ ~ -to E~ltSJ F f(f ~Sta E~ () Fr =0 ~~ ( 14 1) I G Fn H( X are ut(ltealf_ ~ltfcAy~ltP~CA(s ~e- 4 E6--()FF~~ J ~S14

EEn FF~ B euroH nf6=X amp-t-fn ~euro 0 tUllPtfcmiddotc4t

-nus ~S 0 XI oJB ~c((e4~ 7itN pound4 fl Ff n6D=O SlAry EG F-- ( AC - O ACE6 fH6DCPotrclO

1)ec~CAes ~ 0 nfAaAec ~ JACc) M

A c B actgcP J CAnCpQJ AampnAgR ~r--+--Ir-~~R If AA 613 I cc 4te ~tVt-ct ~

A e 1-~ PI ~ Rctil eo(IQ4(_

c~ rCP_ R2esrk ~-s ~ -tyenUL te~ 4 ~~cAAfIdgre IfV --IfU ~ f 4s root G-oIer ~Ns c~ AOAB ~ftJJ MeoJ- -~r ~ et QPL AEa gil

At A rltamp -7---1S ( rt l g 0 () I 4 ~ ~ Ie Be Cctf~ Lloec Ilfct-Jt ~~ C~ c~ IJOCA ~ 1te(J C~ BP Cd M oct ~

B8 PC-co ~-( ~ No CC~=-( ~(ff~~~sctmiddot~~= - ~ (IC4M~cfMtl~~~ote- ~ et eampI c-f(er

62Y ~coJ A~s tttt ~Cct~lI1tr

Let Cn-les C ~ Cz ktwe ~~t ~~-fe15 0 ~ 02

Sf 11 4st f( J 14 (cs of ( OotX w~ 1

fe- ) t ~ lt twitt ()~ -tu Cl

eo( C~ ~Ilt ue 0 K- r 4)-~ J ~ ~ li~ f(~ok( -to OO~ -rtgt Is -4 (~~a1CSof tLt -f~Cnrd u

MOtse ~3 Crce~ CJCC1 W~~ OJOaoJ(h I~ nf CiamplttJ -tfe 3 ~ ltWQs ~FoS offI Wi( i~~(JItct cent Do fgti- ((lt d4 vaJOJ aftftfT4crtfes 111$ ~It lw la-I fIwe wi(( v-espue to 4((3 ccle$

G7~~14~S

~ If 2c(c~sCp~ lte~tAt PQ ~ p Cl aJ hss fou 0 411(1 yen

middot~ Ot J To Co J C So -ky tore eM ta noe(tk( ~ 2 r(4-~ ~ pIA i~( ~~ oS

~yenI4l~~~

P------ ~ c~ Lf4rdes C e d lifest J e we c- tltANJ A f(rrzl cltJ~C

~~ ~~~eAJf- 14 1

Ci-- ntcl ~~~ CJCl ~ CCsII i~~(t et -t4 ~ C4tt p1-Cch~~

~P~ f LoDa is ~er~ AK~Of CCz _

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-

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p _ c $Lt-~ -71

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I

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I

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(~y ra JMO) l fft (01 ~WfiWItll A~Ie Se~~ - LtktU~4

Liacs

er wtIfo~ Ae J 61gt Ad A8t-l)C S~rfamp ~-( 1la r-t P lAJer~middot C 2

f~ 1~-

c Itgt C71 ilt ~(re~tW ~seto1S ~AR~ ~c eet s istt(e A8Ct) gt(oVt ~ AaCD S A C1cJ~cZ~r(~bull

ipound1 ~ tfgtoly L AA8P MJ ACOP Iv~~ ef(Clt~ llpse

( Ictide) I -tc e s

$olt- Set-t- ~~ilt PbullL C) rV] ( X X ~ltgtJc ~~ rallI Ibullbull Ac fl lt4Ei-AlC$

J) lttiM~ middotAe~~)=r OIX~I~kSampbpound etI~J-f(eL __ _ ~ ~ t~ ~~ Itgt ~-l I -J1 0 1D

LetAP=6Pr~CPlgtp Sde - 51=AX~bnitt~t41+ej-tf=o CiE-)

A(-Jt~ft p) ~=(IJfJi)C=(Iti pb)=4-~) ~ eft 1l1C~cle~ Et W (4egt 4=000) bull f ~ A+O I~We ~J at ~ 4l +0

A(cL1A8(gtN-AcOP 6O1~1 JrljtI_11 -fsl-tt ( ASSue ci Icj 5 foitlts yen~ ~c cf 2 ~ ~1 -2 tr- P Wt CI4 ~-s1-t~~ to Cyenc)-to def~n- b c c( e 41 Srt p r- ( -~ I I TI I ~i(~f+tr~fiJ ~)=Jl i i Cieler ~ to ~c~ tSeltt 4t + foifts

IJ -r 2lop ls-f Jsrz )qp ~ ~ ~ y-=s 0_ rL_) tT-if t ~ JU ZlrP+lt~~fi) ~ ABc D IS ~~cf1I1~ ~( X~lp( 11 ~ CAse ~3eoocll ill( t~fc fOit is c~-fWIIWt-e

1$ (cft tik~ bull ~ol(A ~ IgI f~ 11 G ~c~~ Co fts$eS -tl~bullu -ht~ ytgt~ ~ -tao oftet ~~t- c ocl lt1ffI ~ St(~)()_S~II1 ~10ft bull 1k1u~ef-COl s of -fle -fo(1V SI6c~) $AS~~~) SOfWe ~e (( bull

G~sD 6)(Affe 6 Let 0 he -f(f -ftrtf~ crrtuW~middotJ QfAAec W It A) t tI~-fu utff~el At 1gt f~ -t-e tAftcccmiddotdt fettect iIlaquo Be -f P let Ie 1gt0 i+tfTect k~s AC1 AB t H~AI reft~ frot -tit4t 0~=aN

obeJSet ~or~ i t 0 f

p -fa

~h ~ ~ X-4lt 0 L MN

f Let plJe1fa pect~~p i~ ~sct +0 o

A Lampt p=( t))~ p~ (-po)

-rtte~ c(~a~~ ~~-t- ~to~~r-Vgtqkt ~~ I AP Ie A( -fle sI-pe t( (4Lc

8C~ n ~~of4 ~ll~~s AP~(

~~~ II( ltf4 r )tes A6 middotoflie -s of ~~ I( t_ r amp= l(1-6ctpl1l-fI amp_ ~ ~t So~ AE ~1iiiO--------___-=---__

St~ ]=0 to Jet tkX-c-Jwfts 4~N ~e Wt k~rt= I6c~ 2) (~O

So M= (coJ 0) tV (-0)0) -f SotMe ~oeuro tR ~-tt~-ht~ () bull OM ON

ec s r(1j_~(~P))(_rt~_P))=O ~~ ~ -vs

~ reApi r-Lk~ ~

(frsl) ste-~~1~~ Ceo Us ~ FotrAAOC J let Dbe O~ ~ff U - -- A Let Dbe 0- Sce ac Let p= ADU - 81gt I)l W -= cD e 1) C 2+ eln= a( )

tiV+lG PM tW yen~-~ t-=- (10deg- middot ~o

(os tCos(llodeg-l)_ -CO$~ jlell byeose I 1

~ ~ t 1 I I l tf fJo= Cos 1-+ Cos t - Wotf - C + t~p- ~4 ~t zWp + set

Aeelok-s A (0 Let AD ~ 11 1fte4lt -t sk Be I

I

~ 1fe ~ stewafts t~ I

S9 DC ye(clts ~~pLJat-t2l-tt 2 Z 2

I

Ui~ -tt~ ~ S~~e~(e$S~t ta~ I -+

e ~et -tke Apollos e(fa(Cl ~r 1 Z l) XI ta froiof CeQ~~~ 1_ AEttr~ bullJJ~ 1i1b eo _ 4 ttfi-t ftlbJ c =~41I)t( _ ~A~ ~ amp~ Co 0-~

A

~ 8 1) C

-+1

lL) Let AJgt~ ike (AtIYl --~ J ~f)Jj- _ -74 MC r~ ~ araw Ceuro AOwi- E le AS

We et 4Ace ~ lSoSC~(s wr-bCA=EA 1fe ~= t- St4ltf WCl we 3et

~ co 4~ _ ks ltt ~ r ~ n - )+c- ~e~f So tf~ yklJs

to A1gt - J~c (t-s )- (b4cf middot

Ie be kAt CA ~ F ~ hIeuro A If Its AD ampE CF O~ ~bull ct ile

A ~~ lC ti lC ft=i () E rFA

amp Ii C Re~ 9y ltle lIII lpound AC fL _ CB~f I Aamp ~ - -LC 7n -_~t-or ~~ 11 rg 0

StaSiALAFc SillL CFB ~ $ 0 e se t M=Ac suY SLaLL 12ampA$OoOl ~c8~~ Famp C8~middotmiddot -1)c kSk~fA-ampA~I

-rI-e(it) is 1If 41$ A~ $ftJt4$~Sir f~_J- L ~ til

t(euro q~lclvtVt 0 at ~~ os-r I

middot

f (J

amp 1) C

CO 01gt ~O Cf OA BEmiddot

Q~c1~~ Af l fC -fl f 0-~ 31 ~tM Co -t~

_ U Ic _C6 _I I - ~-- 4wtq4IUSOf f6 c eA BE

So amp1gt ampE ~lifI1e$t 1)( Fc 14a Set c)

11 n~onU~lE~CA crf00 LJ f be f ) V _ bull bull J _ I ~ AE- sect2)t ~ -= ~o Re~l( ~ ft1~cooI olettot IS lJIe I~(g~fi i Ca s ~ If FIS)t 1gtC teA (~ of ott fOu6 Ot ile pI-e -tIlt Aft 1

CFue CcMcc1Ye-t bull Ai 6 ~(S_CA ~M~ wl~lAfs ~ A ~ roi (Ly t1lollffl~~) s S~ lgtJ= oS fir A AA6C If-tM1r~1t-0 0_ kat we It--ctIe (olt) I biseefotSqf AS o ~ itMecf 4tO

- - O-tkt ~ ha Ie~ Abl ampE 0 A ~I OA=OB-c 0amp=0( sQ-ctc 6 1) C -4lIt COI A6=F middot 61 UIfA s ~cl () S on k perptecfitr i 1ott A~n8ElCfOlII) AEx ~ltff=i t ~CA 0f4e4~epf(rt~~C - FB PC eA ~e C6CMtV60-l t () O~fk(-t)weJct f-~k~ 0 S~~t~ceqVot 4ASC rtrs~~

M= =6E -ti =~-t _ - Famp_ t ~e ~W--Sc~~trl (oCiVC4IIlG~cl) ~I

~ Fe F8 fe -Pi) F-f AIrBC1tIe~~~CdQowtbullbulllampI~ isAppi_~ iftiileafces1lbllt~_ ~so Cailtd(~8r~iiua46Aac

(4)tfAtgtBeuroCf_~~c(AABcI )( B let)(1Z~~feJ~_JI- AF Igt JC ce eA ~ 10k I 1 L L _~ -r-rshy

t FiwlgtC iA=C7i 1 ~=I middot - -e 11QUtt t t AaCA BCSoAOBElCF==~cfltfVtc~tAaC A C ~AASHCaIAx~~rAt~o CfJ) If A1gt1 BE CFore Clttitcles MBc -t Jl I bull IX~ t y Sl(~ I Y [~

- x -1 ~ 180 ~~ S bull Ct-I- -J F - D C ~At 6Jgt ce =ampOOA 02as5 V4SC igttamp1tVL Cnw l( V~ FEIt l5C eA -~Ci1S8 bcostcGosA f 1Xt 1 =1 ~ -rtiHitrdt is ~~sc~

A $0 A1gtn8eurooCF= H o~~Mac 9 rclk ~c1A~ c 0( lt -tkilrM~ 44ABC ~ (c) If AD ee CF laquo~ Q+ bisrttOlSM8c -nct gt~tS)( f ~ Ale ~ts of t-~ 1gt Co ~ Af ~x~=~~c1t)~)ft -t-a 1S(tT~ Qrct wtfl~sIleo AampcA Be

Famp Acc4~) ~d ) IJL-t~ -tfiA Aec S0 A~ 1 ~o tF I I ~odt(laquof4A~c -r JI s ~ ttWte c1---tlt fsctIA ttde of AA8c ~

-tl~ Imiddot~s ATgt BE N

A E

t)

FA ~~

CfiE) t wt poundtccl ~e $~ ~ LampAC

bt10Ni 6 410f1 C J -tlte -tampi th~~ f L eAt ~ -tlte ~O Ile

-os c 7- J~littf~s vt S t 4ACe(A

~ ~~-t At ~ tgtDiltt Ia X r-- lt cule4l 14 xce1i-te of AI8C

I f~- A ~rI Ie clr fe(f-c1oss tACA6C IIIi-4 f~t I ~J v y z

I I -- I Il~o AAS I AIIIX 6~AIIIZ6 ad IiTrC ~1iIzc S l X t 1=tr (4 -rke Crcubull4f c~ r A--4 clt~ ( IS -tct~ to AS CAee 4 xt~ z tt s clleJ ~ esc-i~ cVc1e (OY 4ccittf) 4 IiA~ MOO bull ~ ulSe cI(- tt er4c(~ 1

~A A ( r bull c

It~ 711

to ~~I ~

bullIa

II

Ill folWt QrcI~

ror ~ABC Iet A 8 e Lt clpoiwf$ ( atleAlAB et 1gt 6 F be feet of 4It-lcl-t ~s Be CA ItC bull

let kL I ~middotqe tf0t~ af I-A W61-C w4 cs-Je Itioampafv of Mac

1ke ec lgtEF rltcM_ttcoOCtclc ~ Cc~ fUaj ~ ~ clt( ~ ItIIe e--t Cull ABe ~ cefe N -ioNs cd~ is ~ clrowl 0 H ~ ((s ~s iwlTlGIC_~f AAS 0 SottIM ~AABC w see aitCA ~d (f8t t see uti it ~

8 So Cit~ Si~ eL =i M =8M

s~ AH1 a ( I Sc~ t1 $kf+ 8 A D C -na~ ~CO~I5 tcLM rs

(L Aoot C of AS ~r I Sc f 8EL1oo=L CFM eFCI~c Iso r

1I So SeEF l~f1 ~amp ~~l(

St(Irt~ ~ As OEKt 4re~~ ~ ~ qrdeHlaquoI~ tEl helCt (61 4~te ~~ rck l~i~i-d~ 4SeL)- A6( 1lgtGF ~l~ ueClW ~ SCl-e cude Note tL I CMA Gte ctOIfars qf ~Circle

c5fD Sice OA amp0 BCIICS So feufbAch s ~~rfNA o A J Crb Srll(~ly oa J Ae ~ f 11 e P int cuclc f 4 t~ bullbull Ie Oe J ampA So 0 is o~e1A1( is -t3~ 0 ike ~( c-de No LlAamp1 AA~c ~i tot~o 2 1 ()~ ~e 1k-let esUietl C47rcles

A D C So AASI A A~ 0 i rAtto 2 L r4 -tk --tY-~e 1-eO AO A~ AeAe h )Ao=iAK t(~ Ws s Qtt-t_e1y ~tfJ 5~ A 0 J Be tJMJ lt-1 foe $0 A 0 II K ~e4 tIlCl e~t~f1 ~t AOl~ ~ laquo ~~[(em bull $ ct Aj( is laquoJ~ -to rOllt oftt ~ rtt Q~c bull So t~ ~oet (lSigt t ~--------r-- ~eO~rft of QH) is 1le cet~t_tl Nt ~ middotfc~ ~ 1 AAo tJ ts ~Iamp ~ I) K ( K IS IIIlftd-af fIA ~ lt K i OA middotH Crc-~t s l AAac ) bull t

6Je UIe i MBC i~ ~ 111- 0 ~ Amiddot Note AX is ediArt~o ~d4 8c

o ( II Ltt Ofll AA c (q SCMct OAII A 1-1

--- ~N-- tA~ 0 =i A HI we sae B A Igt C A Ao AAH6 rtto i 2

o~ So 1)iErH11tt)(iio~ ~ 5 1 ~~ bull ee ae ~ ~Qj (so il~t i o ht -fIt ~ j-o~ -0 tj 411 t teampd ~ At Gt ~-t AN C fgtst ec - cetle So = dtli ~ 6-f( t~ eord-IS -l J 0 ~ N~ ~ AI$o A 3AA 0 bull ]

L

i a t e CJ

I u

Ci

CEi0 ~~N~ ~ let beQsJf~e(-f(f ~ K+O So i ampmiddot-i ACo~~ iSA )lJt4~fotmiddot A- b W~~ Co III ~ teal --~

--rfa ~t -+ A( ~rtlt 1I14us ~llloe (~~ ~ C G~cJly ct s el+J of t1SJ bull ~+Igt~ U~fPOlt (ft) Ent M~ fb 0(l +be bull c-+ ct i ec) o (0 )+ (c(-elc) (4-tc)-+(~-td)1 (410- (cot Ii) ~-c)-+ (b-clh bullreg ((H~)(-ttJC=(Ac-bcl)-t(~-t~dl 12 ~ c-td~o -flt -- c-e(-= ~ J Ne( Campmiddot c+Ji ~c+~ ~co1ts

I

~ IAtb S 4-1o~ w~4eA4 -iIu 0 C0JY-te a( Atb l~ At6t -Ilt o~oo4t ~14a (Of ~) tf at is ~ 4~ lilt middot

NoI-t i--s is ike clt9t- be-l-wu (00) a( (e)

~~ W daM ilu~Solf VAl~cf olIIt y At bmiddot=J4Iot IJt --lA-t~t=(Glt~Ga Ioc)A- 1 ~ ~Cll--bl - shy~ 1 711a L lfO

Yroee~bullbull~ Ltt wJ~e( - _ - bull - - - - - -- IJL _~-J(D Wt1 +l W-L w-aJ we=w i -n - hi

~ lt~~wt~ lzlltJ 1lzl iYI~~ - middotifUoJ

~ Jqt~~ =leampal ~=c+rk=Wie~Ji4e- I ~(eo) lit ~el~-6z)

i Wt=(p~b(c~d~)rrae bull amp ~ yo~e L~

1olot furrn n It- be e ( Ie l= 4t(i~4 fLC loi(l~ 9 b(~(EfR1IvLfDs4ttX-cN ~ to ie ro~ CO6)~l) 14~

(o(oo) Caocdlaquoclottfse cCllIctcn ats o(td 4e ~ ot o-tbi laquot it is cC~ r o~-iW)~f~ e~e oyo cs8 tl~s (fosS)+ i~9l It A~~c coseH~=YeteIIlaquoi~ to ~OftS ~ bull

ey ik cu~ I f xt~~=Ye )~ ~=r-e-roY AI( fe Z~CIsk lWtf fir ~ lee euro C o Go ro~~t~tt ~ ~t wf ~ ltII _fir ~ ~ f bull (6+l~

I - ire gt I~ J1=e ~ J

) WftreileH(Il-Imy

~s ) ~ ~CI~ W

fIrre J

l Ioh L T_ -f -t ts ofJ

W4-II4 C4S~ pound_ )

~~ 41f Wid Ja-e w)e )

I1 2~)tt~ I pin e Afe

-ltv ~t Setflaquots ~ A I~d ~ampPav3~

Cotttple~ 6eUYIUi(-ry

~ -t Ls ~ N~~tQVs e c gt e - Ccs9 +Se

~sc Obte~ ~ ~

CD 1- W claquotsr(middot t -R Ie-tt We III r ~1 ~(+ot) ~ 01 e _ 8 To yot~+f A YIi v fLe rlAlIe Iiishy

- r I 1fSj~t -to -Ie ~ ~ ~ Go)1 ~ C(

=~ r_ ik We $~fl1Ioltrb 1Ie crl foe l fA ~ - e b~ e

Acrl~1 Ie ~ ~s Iej f t ~ fl=- E

Ei-tmiddot 1- ~-tljk -t di-Yoits 1

Gi~ W W2 fke 9Qta-~c e~CM Af -tI ~ ~ ~ ~-~~k IN Wa is O~ ~ 0 +t Wa t ea - 10

W ~ So z-w bull HelllLc ~-J _-i -- ~1ecJ ~-W c

Wz-W WcW I ~_Wmiddot 0 1-kt beA ~~ olSo tJi~u -tk cJ~r

igtr -tke ~~ ferlts 4 WLJ l -to be eolheAr- eogi- of l u fcoJc ~ 1 1rllleP0rt

i CtrIz-) RottmiddotOW 1oJ1 9t W

- bull -1 II It-vL

e == Cos 1 gts = 1 bullWIw Eltot of-ike le tkn C rttr~JcJA

-to oJ W1 5 f l-C -~-c- l

0~7i-f ~

Li f~) ASS-teJ wt~ (uit) c~tctf

11 w W~ n 0 ~ tle ~-l cJe (at wi =Wzih~ l )

~ -tk trto ~~t ~O J Wt so z u

l- _ Wz-W C - - - l - = -w~lc-W t-w

Slworl~~ w~3~t ~ _ ]t +WWz t Wt W2 bull

-r~er~of -to h amp ~jl ~ ~~ lot C r~ 0 W W-z s l- C i (wamp-w)

---- -=WW1 ~-c -W(W1-W)

lt)irljj We 3 t I~-101Mh C-IVWC

1A~i~Cst

Let~ Wz~ W we ~ct ike f~Otl af ~f -tampjc--t ht t ~ i tele I)t I wI~~

(l+ lJti JW] yl ert~ -tle rey bull tcJr fa c To iIt tlaquojct

lIt cJ W is -L Wt

i(J~w) -= T(w~-~

~gt

CD C~eetfe( 0 is ~t tlv ornI reg CeV~J G is ct A-tA~ A3_

() I eurot- NH llt (-r~s rs -tf 41-1 ~- 1 A A A bull A tateo J n I l _ J i (~~Le~ ~Alll~b) s 01 SCt~eD u -pe v~GyueJ

(jOf4-hoce~t~ H l$ c AT At+ Pr3 (be(AASe O~ = 5(O~)) pound1- f lt tl~ A ~ fJclCi-r -to ALA 1s

i- A-A3 ~ -= At - A1-AJ A bl~-t ~ 1 1laquo ~ ~ r~~cJAt -to AA~ $

c- AA) == ~- A~ ~ -rktSt -fwo -ts W f~cf ltt t ampJk4J gt~~flaquos boi lut~~ u$~-f~ ~t tAll lAzI= tA- i- (e

AA = AzA - ~X3 -= ) t ~t lt e c At-tA T A~ SAiSfelt bofl ~t~01l~ 1eo t-= AT At -( ~3

17 N f t - L A+ Al-Ar) 6 Ce---+ef ~-tke ~-e foitrt Qftle $ DA l-

(be~oe 1-1 $ ~ ~Jro~ 4 o t-t) ~tCA ~ Mi-e fit arcc is -tke Ciolaquo ~t f4~SfS -tvnWJ4 ~ a Jo---~ -4le ~~es AtAl Aamp+~ As+A) ~ ~- J L -) ~) -

~Q 1eet qf ~ al-t-bAdcs H I 1 1-3 -=t ~ Wampdtoi~~ -tk ferllaquos ad ~e D~e1 ~~ raquo A~lt

(J~i(t~ ) A lltzlJ J llWW1-~ Ayt ~ito

Sol4 SifCamp ~A~R~lgttPLlCQA~ ~rJwail~e Arf A+cJQ+~~R20 I 1i~R+~~Pao C-t~1T~ZQ=-O

I ~Il I w e LV = e ~ 5 A ~t 4 ~b To ~~ fl X 1l s erltamptDI we CoM-rtf

Xt wl-t t)ll= (Ai~amp ) +w~Ct~iP )~(8+~~

= k [CM Q+ ~~)+ 1Yfgtt wR + tf )+ w (C + p+~ I = 0

~~~A I )( ts ~ (Rot 4 1 J~ ~ ~-t 4 -II 3~f1 C~cf ~ ce~-ter4cl At ~ (A e) ~ ~(f-t~) (ie ~c pOlt 3 -the amp~~c ~ ~ ~11t~ -G t- ~rid 1 ~~t AS)

COlf~selj Ikj ll~ 01 ilt G~f smiddot ~ fo~t ~ loc-s 61 )( 0-~ G~f C = i(Jlt- CA-t 8)) is -flc co~nsfo-kj lt Ov- ile ~t Clfdt

1-(t1J~ Let A~ A)e tI ~r~ 0t W1w) w~j I Y~ f~~j

fYo~ A ~ J~r - fe~~ -to -tkt -t~~ e to ~ c~tdt I

01 b w WI W 3 Got W bull skw~ ~est f~(tS ~ctCmt 1cle-t~~ ~s tmiddot~t t C)~

~otct~ JlCG ASSUllC -tL ai~cit-tle is -tlt kAtf GifC(t

~ h~ le~~tcJA -to t f~eMt oJ 1J -iklk ~ MS et--4M rll-tvJ~

bull l- A ~-A - WltWl t~ k~Wi -r ~- w - tV - 2 - - W 2 bull

Now WI bullbull f -ike ampM- ~~lc I SO Wd -= 1 i1e we ~ fJ~-te -tk ~n 4S _ _

~ bullbull Z ~ _ I T ~-t Wos 11 W + 2 Wl ~ - 1iIII I - - w

2 2-

F-oN -tk5 t ~ ~t -tk yoil-f N Jw~ -+ W3 $ 0shy

--te e lt$-I(C -t1e e1f~sS1W f Ns Sr~t~c ~~ nSFt -t oJ Jt Vis we (4 eot-t~ -tMt wtl lISO e O~ -tIt o~-- -two les -t~ e-Fc~Sto ~1 tJ -tt l s u~ -t $ -tle (fwle1 ~ -t~ )1 fO~~ (tce ~

J I W-z4 _

11Ob~ ( S~~t lYe Tko~ ) let W be D~ llt (~crclf ofJ ~1 13 c( PI Q1 R

be ~ iut ~ ~ lC ftJi~ ~ W -tt t1I 2 ll I tl ~ I ft ~ec-f~Jflj slw ifvt P Q R A-e tAl(Il (-ps Ole 5-

clt~ A $~501 11 tf A ltamp-t) ~ W) i

~ol~bo- WamplAi loss -t 3~nl~ I Wt J lS$We Je G-nIUshy

Cilampk 1s ~ ~ cttclt ~ lll llJ lls -= lw I ~ t 1kt k ii ~s ~~ l+ ll~ ~ Ii t3 --ie r~~ fw- W + 1~ Ivs ~ f-ltl ) i tJ- Zt~W So Sol lkcsc -tcdr W~ 3laquo l = ~ t L + W-lE W

2

St ~ Q ltl ott ilW --l 1(= tt f t~~1l

I sluw fQR 4t CttlfUf it S~s-t st P-R =l-amp-Nil f-R _l- Z-amp-~~ Yo-~~J (tI 4W -g ~-R

Q-~ -1-1)-1tJ --l~W X l ~-amp~w ) l2tgtW-ltl~ -lZ+ t

4t~ w- Zl~-ll-t It f- fl

- (1- R bull

-J clt~lttii lw=t ~ WW-=i

CiiID ~tlt~ firLiA BC let 1gt be A4Ie GtIlOc1tf- E 001 As loIiti DEit-CB J ~ F ie 600 Be I

ciA ~fDf oX ~~ o-rbmiddot 0 1 ltt ftt XIS G(( Gr be 01 EP ~tS~t ~ el~ttrlgtedo-r W~~~~fk~t~s X Ao D C fSfoFc-=Ep-=BYc1gt=r

~J ~sted oR we rMj Sity ~ i 7 middot PrDV~ 6i-F fs pcmI(e( -to -Me 4 b~ 1 -M CaJamp) Xl= Of-~ -tI S~1 je Y-X Sol-I Set 1ampt o~ AtAo tt(-~ IMc

For ~fS X It we e Ix-+f ~ lxl +111 ~ft Tie E 8 Gfl = C ot~~ E (0 r)klgt(d~ 1- W-11IAy f X= ~t(r-s-e t~o A~ F tB t(f-t)c 4( euroj =tE t-((-f)J) _ h Let Pbe 0 poillt el LIle )( f lJe lter t= B _ L _ amp1gt g + (_t )e~ middot gtY haYCamp oP=toX+(f-t)oy -f=~y ~ Be -- r -i1gt-t ~_

J J gt1( 8 -I io O~)y~ amp(01] ~ P-u SfjllleMt Xt E retgt I $0 IE-BI rD-cl c1

EICjl1t Call a ~1IIecent ~ ~ QjgtWelC ~l~ (I- ) Is (E -amph 1l ID-d r-(t-amp)(c(-f6-Jgtfd tl )ltLJ )M ~ ct j~ Ie ~od ~ orF9fe sk~ J i q F- Gt = t6-p)~+ (I-t)(1-9)C ~ +~hw ~t cf -tk s IIf-t4 Jgtllrl1lpounds Of ~t(tei _ IS tlt-p)amp1~$ htfampt iits~etet ~ik~litetllllorltl -tlt-p)la (amp+~~ =(~~k1NIllelo I _1 t f4IIIl ltf1ltS

Sll~ fir trl4t~ A~c~ Itt-A IlIamp 1M OjL ltf 114 (tw~-for ~ pound Me~ --ik se ~fOW twI ~ _ Igt IC-tO - f ~ if

T -poundTI-r -pound ~ I A=0 1)~D i(1el IC-BIt lo-dtll)~

UI8iC-1gt1 +11Hlt-at=Iel+ Ie-IgtI+11gt1 +1c_~(f~~t Wt ut Ie+IC-Igt ~ Iamp+c-tgtl t=~f1f)

AA IDI + IC-61 ~ 11gt+C-81 C-~AO=~8C) (gtt) holds ~Le~ft~~lcJs A81(1)C ATgt Usc _~ __

c6hf--I--l~1gt~ ItiC

~1- ~t fmiddot~~ 0+ ~ 0 ( is )(Y=tJC( (1 rsti - Ex4k+ Let 0 ~~ (i(cAt cf 4ABe 9 ~iIt J bef -fIl lfcffS Jf -IIf (t) Xi=fX (y+I)zmiddotXmiddotZ+fmiddotZ 0( (cXl-Y~(Xmiddoty) ~ I~~)(middotX I IXmiddot~~hd1I O~iOf (=) Xmiddoty-O ~~~~~~~~~~~~~~~ amp--ft 3 Let A8C b Le lmiddotts ~sfmiddotmiddot Phe

Ac~+amp~+A~-t8C~~ Ast+ctl SJt~~ Set1ie Ot~I ttt A ~~t f Jw

CmiddotC +(amp-lgtHamp-~)+D~ (8-c)~-c) ~ amp (c-b)laquo- At~(~- awl lt~~-f4ls s fu ~4S

(6 C-b)middot(S-C-lraquo ~ 0 ~~ck s (amplt-1) ~o

A ~t 1gt Ie -tLt poit ~ Aamp -L II ~ e _ ce~AAcO

p C fgtrcw _t C1gtJoe ) AS-AC Sol~~~~~~~dO~A

A a A J) A J)= ~ E=~~ =3 +~lCJ1gt-C=Aamp-2C

C1gt1 Oe- (A-tS-le)(Mc+1raquowO c) No AA~lh c C C(CUM(bull (IampSt 8 41f1$-bull (4) bec u Amiddot(Q-ltAB-ACO 1IeJtt(~) ~ OAl ~c ~ A~~AC

euro ~ toJs ~ 8lt~ 1)-A69 seAPS fWlkl ~JCOc $ firAABC jf( t ssewu-J -ptMf ~ c= - ta-+CmiddotfI AAS( its ~ttd q ~1 - If We Sampt -iU CitClIMChH- 0 AS ken -HII-srft~ ~o -t r -11 __ -~ -1 ALh--COtt - 7J 0 OtlGCnx n - ~-

A Fit iAcetft tJf ~~ c 0( lU= ~ = L

co b AI c lt-c

e ~ 1)c 1gt= te+(t-t) C t --amps ~1i~ poundL = tD ~+ cC C bI-c Gte middot I t A-t -~)tgt t-ll- A

aAtlS cc_ - tgtA - M~C 14 e middot

11l Lqt-(gt OmiddotkC Gtctal ~ICef c(H ~r J

51_ Set 5 4lt C4fColt_bull tu e -H Matel~Me1~ 1~ AA+b$-t C shy ~ 4~(

Lampil~gt 1omiddot~(i-1)l4-1) lt0 A-A 6middot~Cc=(tlJ 2ec 6amp+cc-(a-c)(amp-Q=k~middotIf (A16i)riamptc~ Rlt9~~ 11- 3( h_ Imiddotltl-C) 4l- 2(~~(H- btCi)tI~)) cttC

)(~+c) (-1)((-1) =((~ t1 -Hi+(() lt 0 of -~ f (ib -t-e) lA+Il+ ct )+ilaquoc gt~ CifI+cl+Jl(c)+ ~ ~ a(-o)(--G)-4-~-c)(b+cc-4)~)gt0 tsc4 rc s

~ Ike fRS ~ f xi xI wt -Stl-fculot 11-$9 (t)=LXOY) 0( tiYfft~e~ -fo -tkt fl~~ 1-- oxY J e

lti) ~ -f~)( ~f)-a)( l t Yltl (c~wYcxnyJ (j - )(~1 4fT~ A X0( V~~ p A of yl t1ft 0

(6laquo Q bull 1 lj 111)1 (DW~v e

eJ41~ Let AAA A _j A 1 1_ -+ V]nq DO 4 CD e I

- its ste ~tS p-Ilt1 ProiIla-t middot ClrtllAA1Ar oreAA AA So(u-tVf SeL ot - ~ -_amp I~ _L ft--A A ----- ~ fJe ~ ~ --fI 01r~~ O4St SMs ~qIt ~t)~csCA-A) I lA_-A f

E)Ctl-eIlaquo-r Let A6COf tgt ~~ pe-tft Qc e t

~~~Q~ ~ 1kfwlrids~ A88CCIgtbEpoundA 1T~ -r APamptl~J~ le ACDIIIampf6i -laquo s~O~ tk-t ~s Ooet is so eM eII bullbull ~olt4-tfN ~et -ckt O~bullbull~ rt -e ~_W f~ S~

tJ 1(t0 AXC ~ AP ofe (o(iu o=A-f- A(~ J C- 32s amp A

lltc t))tA SIA~y 8)(1)= (1(8 CxE~ C I

raquo)(A 6llgt re EJ( 6 =CcE feMtt I

eurolCAJ- E)(6-t( - ~lte+El$ ~ pound10 eImiddotmiddot

1 ~~-A~)o (As-AJ1gt(~A~ S ~~CI amp euro1tf6lc~ ~se Ac Adol~ -t(t-t Lit set - () middot At

At~ t ~It~ AsIC~ Al~-+yen+yJAI (

_t a ~ - bull

~ 2-shy

I _0 c A 6 c ~ As V ~1~Ut 1 Sjtllc -fb ~BIC~ fW(t

ftdle ~ts of BC CA AB ns~chvell -tk ft1~ -tIua-t

No A bull G 8 A I ~amp Ca A~ (orr eU egt~ 4~_ A~itlA-~lClA-As~=(~tAtAr-tAjcA -~~ StthtlI4It ~ SaJc1ttA

(Nmiddot~~i~+Ar~~l ore4 l1A AAs = Are 1J~~Ai

Aft13 amp11 C=A-ttils-A)frSollletoA~] SiCt AS e Gfe i eRe

o~ (Bt-A)K(~-A) - (A-ttz-~tl-t- t t)AxB No ~~=~~~-=amp-AH-t)e ~~1 S-a-= It-t1)A I Ct = lAt8)- c tlA +ll-t~)B ~ (amp-AI~I~(Cz-~)=(t-ttl-trtl-+t~t))Al(amp~O A S~ CL At( ccdllfttor

~t ~~ 1~~Pt

o

C[~1D --r-0 vetlOf) )( lf ate Jt~y wtt-t---t f~ t -flat ~f~ ClX~yO kAs 01 Soat~

AT 10 o T4 s tktCcStI ~~A rf KttO ~ X0 f Art NIt Co((llteor

F4t IT AX+bY+c =0 ~$ote -e 1~I(z-s 4t4l 4-+amp ott -=0 J ilQA Xf Z 4le cbullbullI btACcS( ~l AO fIe b-tc-o w X-1-KZ-tYc-6Z

(~ar~11to(~1 wr~t--J Lftai c~ s OAAampA Co

~ OeLamps 1f 1 -1z- Aa6~l~8ampR AsampIA~= ~ 6 8-c amp-S tltcl A DAR 0

~e COIIfttAt t ~1 =- 1 ~ ~ P Pl) P3S~ Set - orlll at o at A8 btt ~trs Ale LIDa (ampfbv~ ~ A~ rA Q( e s So 8 1-t S6Wt (s EIt Cll No

Pl =tAt(c-t) 8a trA+ (ct)s ~- ~3 lAAt-tQ-) 8-= tA(-aA+Cc-ct)S a S~tU~ ~ 0= ltr- CArgtA + [pound1)l -(I-I4)$]B

A~ (tally rcf~=gt tr(~ Otu( (l-tl~-laquotlt)S=C Solll fott ol -tit pt~~ -+-s f ti ~I~Js

Nt ~~e ~ 1tu~~A+ SoSzCt-rl g$t Vs- r~ r~- r~1 Pgt1s~S)A+~s(tmiddotgt8 R= rlrfgt~A ~(I)J B

Y~-r)S) ~6a-t~S) amp c) ttS +fs-1S ~ p~f~P+~sampf-tj~

~ P1 ~se~rw)~c 0 Qtlgt+CoO ~ r fL cU-1- fc-i (ove

~ 0

A - -

~ FOf~lamp~

(1 -laquo ~C

fot-CA~ to ~ t t amp -t~~ crt a ~tc ~ El(tend~ltl St L laquobe ~[A8Cl Js~~i~ R= 4 C

Let ( ~t 4ct nwts lt 4e GoismvmcJt i-R- tl 4J~)(fo~of AAsc Sr ~ l=~~Yslt) ~ bc_

S A -- - 0 21 1iltelaquoe s dolAt C~d~middot ~o~ uI1gt ~ s~amp s~~C middot T 1_ ~ rI n -rf (i-- shy

tl Ie or~ DraJ clmiddotae~t 61gt 1pound Si ~ A= ----=algt i IS lle~ ltJOiOlSA0

~~~~~~~~~~~~~-~~~~=~~~~ p adEr-l-~a~~r~ A- oS+- jtus c~ - c e c I) p(]) Let 18(1gt L~Ms

I4dtt rAsel Or S~8c1oI(lcl~ 1leflAftt Let A6nct)p -r1 ~act 0

~Me C ABC ) GlUo~kc ~ PAx P6= Pc x PD = tl b~~=Abc bull P19tpound Note L APD L (PB

4R A1BC)aHd~ckLPAtgt=LPCBS=tfA-tb~~) is ike seifieAc ~AAPDACfB~=~~ PAIPB=fxPD

amp Q C Of 4A8C Lri pc C 1amp-~ ~~ PC Is -lt-~t lat t lie i4 jCbullbullr 4l( M6C Qt r Ie -i4~ to -e -fde ~ A A8C if (JJ

C)~ ~e icltc1e ot AAec ~e p A e OYlJ c fCL p~~re [Mel =[ALel[~cl+(CI1= ~-t~+~=SIr ~ Not~ LArc=LcPB

I-tfllWlbull [A8tl~ S($-11 ) (s-b)(s-c)middot I pCs f~ot -to LACp4C ampP(~ Cos C= tt2ttoa-c (~AI Ci(~ircl 4 MBc B 2shy

[A6Ci= ~SiIlC=Qr(+coSp(i-($C) ~AAcPACBP ~~ fgtc PCPAlltPB =(Cl~-+Iot-c~t-~a~-9 ) = catlo-4 t )(A1(-c)(CoHI- b)(o-Il-~= S (s-c)(~~

2- ~ a

Ci C [AS(I A 2

~

I

~JJI LPFA-=odeg=Lpe~ ~ amp~ ~LPFeLPAE

C5Ji) ~tolt1 s-ThtOfotfll Let A 6c~ ~t dlSncf ~ts 01 bull ~c ~o - Me~IA~ 1( bull t Of~~~I ~Ot bull -Tht~ bull Sa c~tOV M1 C(liofIPT potd~ A 6 C Iie to

AI 6 C 1gt (1~t~c 1gtpound fCLR atfmiddote ZA ~A A ZA bull -~ -iA ~Co~ PAQ~clf$ WeA~ ZA~lA I tc Z~t

pFAECc1dk

bull ~ Srlloi(y taCgt6~~~-lPFB ~ pG~ f CDCCYcbull LPampb LPFI) = e 1klaquo AIJ~P LPAespoundp8C pfE _ LPeP 8EF (0(1ltlt~L PFE L~8Tgt~ LFP - L 10 collirAfampff

)fgtC)~Jl~~ ~ ASC1HAol6C=AcS]) bull (~~_ ~ktI AeCO At)ItBC ~ACdtgt 1)~c 190pound 0 sWLe AB UJlfsftfUct A ampA6

S~~41 to flCAP 1I1elt AB A~ 6eshy

6 Ai - 7ligt= (1) lBAE=LCAJgt

SO LMc L BAlgt-L1gt= LeA1gt-LMe =LEAt) Tkeuro1 A8AC~Ae-A1) So Rr-c EDAtgt~A Thet Aec~ A~8C =poundItampE AClC E~ AC80

bull A rC =c Sf-t Ell I

f1-I-4j hoW~ ~8euro~EtgtS ampb ~ E iUt~( SO - ~~oeA~LeeALtgtCA ~AsectCO Sltffc

SoSoft ~oe 1et~6cP cl-ampd-p~ 0

tI~ Let l)poundF fetf~~ff- P~ ampa Aeyen~~ ~

Asse ~Mist (so4 is 6~UA_JC ~AGSC ~O bull G ~f( Aalec~o)

tt~e9 7eff

fovlaquos X I Z ate (es Aamp ampCA D ((t~ve-()ty It X I Z (lie (dl-lflOr

A ~f f6 lhg--1 ~ xe YC LA - middot ~ lQt Dbu (~ Ac soct1IIt 81gt II J( Z -r1teuron

~g ~ ~ 1t~ ~z Se AlC 6Y c~ _At P1Q (i~ ~y Ie ~c -- _______ r tamp iU I bull laS yc fA ~Igt ZCZA middot lCI~ lIeeu~ Ie~

If ~ tL ~ =-1 iIamp )( YL MHo l~(~ Y~t~~~~ SlJ) Ltt l~ X(OCA -Thtl b Mt11Idtw 11~ Ax ay CI _ lt Cz Y Cl iiiK zA --i ~o --=-l1toobull CfIea bull _Cl -a

I I

ceDD ~MelI s lIeo~toA l~tA I ~cc t) euro ~be tc~ lO 0shy

de lw~~ ~( ft amptCtSSCti 1 tf (~ diC- (~QEf ) bull

t p Ae ti l)euro J Q Bel pound f 2= Cl)n fA ~ ~k ~ Q1t ottc(l(ea~ ~QIR~~~ -

f~ 1 ~ ltt X~EfA 1AMCD bull ~ z- C~neF Arr~l ~(atts ~ff 1e-(fM1oec~ FA

ftt- Ool~~~ 4xf l w hVII

e-- ~ X K __( It X2 ~_( t ~~II Qx 6y Ct ~y pzex I fllFxijmiddot 1I

Hul~pr~ ~ AIl ~~ tfffSfctj cofI4t tt XA)(B XEmiddotKF J (CmiddotYP=1AmiddotYS ZEmiddotZF= zeZIgt W~~et ZQ lSf~-i igt PQ~ ore rlfltelaquor

Qx Pf Itz loy c-enc ~Mee(AaS

t-rks ~ere 0 Imiddotil~ (1$($ of PoucJ s for It we tftwt Ato 8 -te I AIwIJ (3 il(cJe 1Iofl1-t i AB will b~ ~-t1l3et (iot ot B ~ It~j CIt~ we ells JpoundAoflt ~ t~ liflE Clt B b~ BR

6lCtJfC i F~~ h Cf(Ultirc~ ot Mac J f(it 1) ( ~ ~i~0yen ot -t4l~lE I~ ~tA - ~~ Be ~ e fM 1fe ttusc(e~ of-ffwf3ct (tt4-t C3L1r~ CA~ F= bt ~ ttfStd~ of -tINt ti-~-f Imiddot~t ~tC wo( Aamp 11161 PI Ell F o~ ctU

Soof~fIyen P=Mo 8C ~ E= BBnlA f=CCnAB APP~i P~f ~ ~(fo MB See I fott et 1gtpound f c-

-- =JSiiiiIii

b)lAtc ~ Let-tgt 0- eht ~cfs 0( dt101 AtCS

AS ~ AC O~~e (ilcu-R( Mac ftspciwJy l(t tgt Ilt ~f AtC sCI ~== DPn SA J R= PEn AC fro +~-t lile QR~s~(QVJ14 fttCf+~I (~ 1) ~ f9bt-Mshy~e 1)rff0--AS- CO ~SfctsLAc8

Co ~r ~ qftllCr At =lgt 6 ~LAec So 1= Cl)n G8 Sf_ eEtS

Q tgtPt SA DP 8ital R= Pe C Pre ttL PlE AI

AIP~ f~l ~ 1Ito(-to C ~ P er ~ w 1 ~ bull 1I

t Set I Q Rut tIff~ Co~~d~

~ -7

Alt IXu q j

elf (Ga1(e 3 Ltt AT3CPs e ~ +s tMDlCJe ~-rd AAfLBS Bat LeA) ccf LAB fat 1gt be ~ls (I ~cucl1t ~c4( I

DA(11)C= AU DB()CAe~ 1gtCIAB~ fgt~~ A~ r~CtfaJ T4 6v~fi ~ IAGC a~ Co((~((r

~olf- W HL-cI oy-((~( ~ AA Be Ne

AAIB~I)Cc(-=I DArBC=A 11gt1( ISc AtA f Cc -= H L lAlA I C I Cl

1t~()cD=C1 ~l (AIBl (cjAfrrr5~5Gl ~~ t DAAfCC tgtlt Se4 A HC tit c11ilaquoraquo SIt 1y ar171~ BS41s(to AS e 0cc we Su e H 6ltve c1(i~amp r A~ H C~ S4rt a(((~4~ I

-~ ALI)f ~fle1 tt P toe a ltpor i~4Mec

LtfP I~~ff~I$f- 5 -to ~CA Camp ft~t~ lttt bJ() ~_ eshy

ll 10 ~ fet ~~~N~ c-tohs API sp (~ftvtll IfQ P ~ 61bullbull Pt14 PttNQ~~ (tries ~tll~ Qfz cod A~ aft ~et

iSoLttd- $(fCJt L CPc p) LCQLP LC~P Lc (gta Palt-e J -t ~es c P ~L I PI Q p 4ftcocttc f~AfrI15 ~s middottU(Woto ~1l$1 w-tSu CPt ( gt e-= A ) P t1t( QIP= X ) (Q-a Pf P2C-= B 4re CoI~rtelr $6 Rb2-l amp1L ( AB-=Xmiddot ~ ~lIQ P~IA8 tVe ~Cqfre~

NewtDJ S

~A ABcOS~~(laquoteJktvsa e ~SQiraquoeamp c~tkt~~ ~~

APgtsc CD) PA AXcpotlts EFG)H-~t~ C F B ~ACG~FHgD~~r~t

Sol~tcNI W E6nFHO~ Eftn FG ~X _Apply~~ ~~scJ ~ ~ -to E~ltSJ F f(f ~Sta E~ () Fr =0 ~~ ( 14 1) I G Fn H( X are ut(ltealf_ ~ltfcAy~ltP~CA(s ~e- 4 E6--()FF~~ J ~S14

EEn FF~ B euroH nf6=X amp-t-fn ~euro 0 tUllPtfcmiddotc4t

-nus ~S 0 XI oJB ~c((e4~ 7itN pound4 fl Ff n6D=O SlAry EG F-- ( AC - O ACE6 fH6DCPotrclO

1)ec~CAes ~ 0 nfAaAec ~ JACc) M

A c B actgcP J CAnCpQJ AampnAgR ~r--+--Ir-~~R If AA 613 I cc 4te ~tVt-ct ~

A e 1-~ PI ~ Rctil eo(IQ4(_

c~ rCP_ R2esrk ~-s ~ -tyenUL te~ 4 ~~cAAfIdgre IfV --IfU ~ f 4s root G-oIer ~Ns c~ AOAB ~ftJJ MeoJ- -~r ~ et QPL AEa gil

At A rltamp -7---1S ( rt l g 0 () I 4 ~ ~ Ie Be Cctf~ Lloec Ilfct-Jt ~~ C~ c~ IJOCA ~ 1te(J C~ BP Cd M oct ~

B8 PC-co ~-( ~ No CC~=-( ~(ff~~~sctmiddot~~= - ~ (IC4M~cfMtl~~~ote- ~ et eampI c-f(er

62Y ~coJ A~s tttt ~Cct~lI1tr

Let Cn-les C ~ Cz ktwe ~~t ~~-fe15 0 ~ 02

Sf 11 4st f( J 14 (cs of ( OotX w~ 1

fe- ) t ~ lt twitt ()~ -tu Cl

eo( C~ ~Ilt ue 0 K- r 4)-~ J ~ ~ li~ f(~ok( -to OO~ -rtgt Is -4 (~~a1CSof tLt -f~Cnrd u

MOtse ~3 Crce~ CJCC1 W~~ OJOaoJ(h I~ nf CiamplttJ -tfe 3 ~ ltWQs ~FoS offI Wi( i~~(JItct cent Do fgti- ((lt d4 vaJOJ aftftfT4crtfes 111$ ~It lw la-I fIwe wi(( v-espue to 4((3 ccle$

G7~~14~S

~ If 2c(c~sCp~ lte~tAt PQ ~ p Cl aJ hss fou 0 411(1 yen

middot~ Ot J To Co J C So -ky tore eM ta noe(tk( ~ 2 r(4-~ ~ pIA i~( ~~ oS

~yenI4l~~~

P------ ~ c~ Lf4rdes C e d lifest J e we c- tltANJ A f(rrzl cltJ~C

~~ ~~~eAJf- 14 1

Ci-- ntcl ~~~ CJCl ~ CCsII i~~(t et -t4 ~ C4tt p1-Cch~~

~P~ f LoDa is ~er~ AK~Of CCz _

Let ED be ~~~ foSflctorf oft B~ MaC ~D ~S~e AC -ri Cau~tt1e c1A8JgtC ut ABtttE J(e ~ cfC4c~rc(e c1 AB D MflId 8 Ccent F-=-c --r

D (Olt ~t AE =- CF So 1$1 i te~d~ c~ ~gteJ AE~AB=ADAC II CFIltCBCD CA So~= ~~

5 ~c 81gt fsecfs L ABe WI_ Cl) ~ _ I bull It rJC AS - AD CF- f1C

------------------~ ampA~fel Let ABC be ~ ftrJMIj(e ~ soscJes 68C[)I

CAE AASF ~te~(1 to AAsC wi( ~ CA Aa 4 S bu1 tsrtdvel~ Pro~ta ~-t 141esff-1 AJSc ~ t ~ I~es t=F fEgt DE ~dJ ~uc(~t

Col Amiddot ~ SJltto i Late ~e cnl~w-f( Jgt4Sr~ ~ IE ( - eatu r4~ ~Cgt cte

a~~c~~ Iof crde middot1itE Ultoofe Y04oc Jl Y l AE=CE ( tel btcte(~w-I(Fu

c~ Cc~-tr ~cL~4S AF=8F - I -r4e-tltlfte~ A PUr~I T (~ff I ~~ fiIolu ~ ts ltfCI C1 $f lltty ~amp~ 2 lies Cltt VIIIt~~ ~c c) ~ roampoIaJIlt) of (14So -tkey ~u(4t fAa ~~ Camp~tet

63DP I

r ~e A ScIampf~ 2 LtP be 1ft l~~

~ Ii~~(-kB~lIc(~ -to FD-f _ bull 11C ra(~~ to OE -tt~ fOIts frolle M 1 Elf c(frelttf

S 7c IL ttgt ~-JC 1l rgte ~ t

I

I A~ C~ $oIf1 Let ile cncrcft~ J) ~=HF - PD eF -61) OJ rD-peuro-C~1 EAtlA~1eSamp Ql (A~ AF =SF I CD-c CEAGJPF t 81gt

2 l 1 0 F pW~ ct - fE =AF -AE S r~L pound ~ POtt 1 ~CAty4W(t t

- t_ EICIt1k 3 AC--damp l-H aat 0 P~r -fl Ie A4M C ~ usc -t ifegtSltct ~- Ae Id t W S let

Be It N Let 1k u cudcl 0(AAac -lt1 aNll~Std ~t B t ~ middot Pe ~~t OlUaM

SoIwt t ~ C4Samp 61 Be we6~ 11 aM i~ ~ ~ftthlte Qt S of cYG vtIeof poundlASC 1ICft OM =oel 8M

A~p BA18C i4e c~~In CAsamp - AUN AAec ACfo K~ 1Iotf1Ar (S1Cc iMruw Ibl~cto~ L kll Ac AC Jolaquoaret tes) s e rdeo( I

I

pound I ~e AC kN J 8M Itteet 41 4 (IOIt P I

Siell L PM N L 81lt11 l HCA s MIC PAte CDhcrkcl Q ttl I t fill pou fOitJ BMlC ~p 8M ec 80- yo Y=OA

PM r8- PNICPK POamp-r~ bull ~ $Jtmct~ 1keuro92 Ie -t 10- eo~= ampf(tM- rM) PM - 3

rJ It

OMl PB lr F6 ~t 8MPM+6I1I

OM J ~M

L I A6cb be i$(~Ibullt co_~4 tt ArllAofOo Q-t d - amp c~ f A1)1 SC ~ f (aros

Ccle i VI ( 4 E f= ~~-t t I~oes ampe Q= f-o -Ie C

8y po -t fI-t~ Po~_~ peltPD=PHxPl ~_ ft QClltQ6=~d~Qs~tAcff we1et Po~-Qo=CFM-ru) ~ fMQ~ -ns i (Ies 0ML PQ lQMO Itf oM

Ntrf Csd tIe C~C wi4 Q0 As d-cr~ 2 _ bullbull

It t-sses ME F SlAte LampMO LQ EDt -lCl fo s ~ CIC-z Ef ~ Ef -s iU c($ ef ce Let cI has ceth A( ~s tt lie

laquoa ~ ~ t JFPO _r - flMx pQ fiCa _Vi ~ P$ 01 ~ bull0I

A(Igt~ ite-sect PQ 4t M +Q -of leM _ LA0(= l paceW ac- ~ 8I(C ~ lttlclc p ~_I c 1_

let ya~s t Cltn~ I ~_0 =c bull t if crftit C fc$wt

~l~Sshy c1iW ~ 14- - l-l-~t1 A IS ~f~~J i AA6C J 0 i-tala

C(cuCttdlt~ 7Le -(kfee 4-ttJes AP eamp tMJ Cf irUktt- H EDAA6=-M FDo AC-N tp~4-dcent () 06Jl)F )OCJ1gtE

N C~) 0 J- M N middot i

Solfen bullCO LAfcc9cfLATgtC 9 A fgt l=~C6AtyJrc TktL6lgtFcLBAC AooBc-OCi--ees LOBC-=J(t~Io~Leoc)middot1tl_l8A(= ~oo~L8bFmiddot F omiddot Iamp -=gt 08 ~ tgt l= ~frly DC lDe-

B 0 c (~) CLMA ltPgtM~MIf AC~HI () I 81U AlA ~ NIi-IIIt= Aa -AltlaquoJI tgtA L

F ~c ~ l)e - ~ Aa~Ac (c~

~~b )N6oIp 13Ai~80-- OllADI (0( 1)04 ()-(~)+(()+ll)-~~ J)M~ ~_cot=OMOt)1 te

bull Ott J MAl N~-11 fI ~=C)jI 6lf1

~iet SoU- ln LAFC0 =LOC-dJACl) Fc-tkc ut J bu])M So ~t TeI [)f -ue L Jeo L 6gtF =LeAlt ~ J-f4 a~t (~e tB

4 ~t~4Yclt ~ JNle gtetpeId~ bs~CtoY til g 1 I J 1) 4te 0 ~J

=gt 0t3lJe ~oS i DF Q(A~ DCLbE wHk ~ CSV ftt Ae efT I c AC~J~DI ~ (ltt 6e If Be I I I 01 tl( AS 1POW iI f uIlh) SrlOCo Ae1gt = aq rW1d1C by d~ l~testJ~ t4PtwI- Let lc SAe -de -CA k)sU AABC f 2AamptI

NA ~ NC NF ~ rJ SI AC ~ dbullt ~fieaa~(L ofM$C ~=~ so tr~ of ~ bullbull ftc~(eNs() ~ ikatQ~oJ CoxS qf ~ Grtles Q-14III ~ if ITI ~ YM~(-l A~s 7I-e lmiddot 11M rOI(A)C1lt D ~~(S liIOH

r 6middot 1- r IAC- UComiddot

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-

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p _ c $Lt-~ -71

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I

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Page 4: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

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f Let plJe1fa pect~~p i~ ~sct +0 o

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to A1gt - J~c (t-s )- (b4cf middot

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- x -1 ~ 180 ~~ S bull Ct-I- -J F - D C ~At 6Jgt ce =ampOOA 02as5 V4SC igttamp1tVL Cnw l( V~ FEIt l5C eA -~Ci1S8 bcostcGosA f 1Xt 1 =1 ~ -rtiHitrdt is ~~sc~

A $0 A1gtn8eurooCF= H o~~Mac 9 rclk ~c1A~ c 0( lt -tkilrM~ 44ABC ~ (c) If AD ee CF laquo~ Q+ bisrttOlSM8c -nct gt~tS)( f ~ Ale ~ts of t-~ 1gt Co ~ Af ~x~=~~c1t)~)ft -t-a 1S(tT~ Qrct wtfl~sIleo AampcA Be

Famp Acc4~) ~d ) IJL-t~ -tfiA Aec S0 A~ 1 ~o tF I I ~odt(laquof4A~c -r JI s ~ ttWte c1---tlt fsctIA ttde of AA8c ~

-tl~ Imiddot~s ATgt BE N

A E

t)

FA ~~

CfiE) t wt poundtccl ~e $~ ~ LampAC

bt10Ni 6 410f1 C J -tlte -tampi th~~ f L eAt ~ -tlte ~O Ile

-os c 7- J~littf~s vt S t 4ACe(A

~ ~~-t At ~ tgtDiltt Ia X r-- lt cule4l 14 xce1i-te of AI8C

I f~- A ~rI Ie clr fe(f-c1oss tACA6C IIIi-4 f~t I ~J v y z

I I -- I Il~o AAS I AIIIX 6~AIIIZ6 ad IiTrC ~1iIzc S l X t 1=tr (4 -rke Crcubull4f c~ r A--4 clt~ ( IS -tct~ to AS CAee 4 xt~ z tt s clleJ ~ esc-i~ cVc1e (OY 4ccittf) 4 IiA~ MOO bull ~ ulSe cI(- tt er4c(~ 1

~A A ( r bull c

It~ 711

to ~~I ~

bullIa

II

Ill folWt QrcI~

ror ~ABC Iet A 8 e Lt clpoiwf$ ( atleAlAB et 1gt 6 F be feet of 4It-lcl-t ~s Be CA ItC bull

let kL I ~middotqe tf0t~ af I-A W61-C w4 cs-Je Itioampafv of Mac

1ke ec lgtEF rltcM_ttcoOCtclc ~ Cc~ fUaj ~ ~ clt( ~ ItIIe e--t Cull ABe ~ cefe N -ioNs cd~ is ~ clrowl 0 H ~ ((s ~s iwlTlGIC_~f AAS 0 SottIM ~AABC w see aitCA ~d (f8t t see uti it ~

8 So Cit~ Si~ eL =i M =8M

s~ AH1 a ( I Sc~ t1 $kf+ 8 A D C -na~ ~CO~I5 tcLM rs

(L Aoot C of AS ~r I Sc f 8EL1oo=L CFM eFCI~c Iso r

1I So SeEF l~f1 ~amp ~~l(

St(Irt~ ~ As OEKt 4re~~ ~ ~ qrdeHlaquoI~ tEl helCt (61 4~te ~~ rck l~i~i-d~ 4SeL)- A6( 1lgtGF ~l~ ueClW ~ SCl-e cude Note tL I CMA Gte ctOIfars qf ~Circle

c5fD Sice OA amp0 BCIICS So feufbAch s ~~rfNA o A J Crb Srll(~ly oa J Ae ~ f 11 e P int cuclc f 4 t~ bullbull Ie Oe J ampA So 0 is o~e1A1( is -t3~ 0 ike ~( c-de No LlAamp1 AA~c ~i tot~o 2 1 ()~ ~e 1k-let esUietl C47rcles

A D C So AASI A A~ 0 i rAtto 2 L r4 -tk --tY-~e 1-eO AO A~ AeAe h )Ao=iAK t(~ Ws s Qtt-t_e1y ~tfJ 5~ A 0 J Be tJMJ lt-1 foe $0 A 0 II K ~e4 tIlCl e~t~f1 ~t AOl~ ~ laquo ~~[(em bull $ ct Aj( is laquoJ~ -to rOllt oftt ~ rtt Q~c bull So t~ ~oet (lSigt t ~--------r-- ~eO~rft of QH) is 1le cet~t_tl Nt ~ middotfc~ ~ 1 AAo tJ ts ~Iamp ~ I) K ( K IS IIIlftd-af fIA ~ lt K i OA middotH Crc-~t s l AAac ) bull t

6Je UIe i MBC i~ ~ 111- 0 ~ Amiddot Note AX is ediArt~o ~d4 8c

o ( II Ltt Ofll AA c (q SCMct OAII A 1-1

--- ~N-- tA~ 0 =i A HI we sae B A Igt C A Ao AAH6 rtto i 2

o~ So 1)iErH11tt)(iio~ ~ 5 1 ~~ bull ee ae ~ ~Qj (so il~t i o ht -fIt ~ j-o~ -0 tj 411 t teampd ~ At Gt ~-t AN C fgtst ec - cetle So = dtli ~ 6-f( t~ eord-IS -l J 0 ~ N~ ~ AI$o A 3AA 0 bull ]

L

i a t e CJ

I u

Ci

CEi0 ~~N~ ~ let beQsJf~e(-f(f ~ K+O So i ampmiddot-i ACo~~ iSA )lJt4~fotmiddot A- b W~~ Co III ~ teal --~

--rfa ~t -+ A( ~rtlt 1I14us ~llloe (~~ ~ C G~cJly ct s el+J of t1SJ bull ~+Igt~ U~fPOlt (ft) Ent M~ fb 0(l +be bull c-+ ct i ec) o (0 )+ (c(-elc) (4-tc)-+(~-td)1 (410- (cot Ii) ~-c)-+ (b-clh bullreg ((H~)(-ttJC=(Ac-bcl)-t(~-t~dl 12 ~ c-td~o -flt -- c-e(-= ~ J Ne( Campmiddot c+Ji ~c+~ ~co1ts

I

~ IAtb S 4-1o~ w~4eA4 -iIu 0 C0JY-te a( Atb l~ At6t -Ilt o~oo4t ~14a (Of ~) tf at is ~ 4~ lilt middot

NoI-t i--s is ike clt9t- be-l-wu (00) a( (e)

~~ W daM ilu~Solf VAl~cf olIIt y At bmiddot=J4Iot IJt --lA-t~t=(Glt~Ga Ioc)A- 1 ~ ~Cll--bl - shy~ 1 711a L lfO

Yroee~bullbull~ Ltt wJ~e( - _ - bull - - - - - -- IJL _~-J(D Wt1 +l W-L w-aJ we=w i -n - hi

~ lt~~wt~ lzlltJ 1lzl iYI~~ - middotifUoJ

~ Jqt~~ =leampal ~=c+rk=Wie~Ji4e- I ~(eo) lit ~el~-6z)

i Wt=(p~b(c~d~)rrae bull amp ~ yo~e L~

1olot furrn n It- be e ( Ie l= 4t(i~4 fLC loi(l~ 9 b(~(EfR1IvLfDs4ttX-cN ~ to ie ro~ CO6)~l) 14~

(o(oo) Caocdlaquoclottfse cCllIctcn ats o(td 4e ~ ot o-tbi laquot it is cC~ r o~-iW)~f~ e~e oyo cs8 tl~s (fosS)+ i~9l It A~~c coseH~=YeteIIlaquoi~ to ~OftS ~ bull

ey ik cu~ I f xt~~=Ye )~ ~=r-e-roY AI( fe Z~CIsk lWtf fir ~ lee euro C o Go ro~~t~tt ~ ~t wf ~ ltII _fir ~ ~ f bull (6+l~

I - ire gt I~ J1=e ~ J

) WftreileH(Il-Imy

~s ) ~ ~CI~ W

fIrre J

l Ioh L T_ -f -t ts ofJ

W4-II4 C4S~ pound_ )

~~ 41f Wid Ja-e w)e )

I1 2~)tt~ I pin e Afe

-ltv ~t Setflaquots ~ A I~d ~ampPav3~

Cotttple~ 6eUYIUi(-ry

~ -t Ls ~ N~~tQVs e c gt e - Ccs9 +Se

~sc Obte~ ~ ~

CD 1- W claquotsr(middot t -R Ie-tt We III r ~1 ~(+ot) ~ 01 e _ 8 To yot~+f A YIi v fLe rlAlIe Iiishy

- r I 1fSj~t -to -Ie ~ ~ ~ Go)1 ~ C(

=~ r_ ik We $~fl1Ioltrb 1Ie crl foe l fA ~ - e b~ e

Acrl~1 Ie ~ ~s Iej f t ~ fl=- E

Ei-tmiddot 1- ~-tljk -t di-Yoits 1

Gi~ W W2 fke 9Qta-~c e~CM Af -tI ~ ~ ~ ~-~~k IN Wa is O~ ~ 0 +t Wa t ea - 10

W ~ So z-w bull HelllLc ~-J _-i -- ~1ecJ ~-W c

Wz-W WcW I ~_Wmiddot 0 1-kt beA ~~ olSo tJi~u -tk cJ~r

igtr -tke ~~ ferlts 4 WLJ l -to be eolheAr- eogi- of l u fcoJc ~ 1 1rllleP0rt

i CtrIz-) RottmiddotOW 1oJ1 9t W

- bull -1 II It-vL

e == Cos 1 gts = 1 bullWIw Eltot of-ike le tkn C rttr~JcJA

-to oJ W1 5 f l-C -~-c- l

0~7i-f ~

Li f~) ASS-teJ wt~ (uit) c~tctf

11 w W~ n 0 ~ tle ~-l cJe (at wi =Wzih~ l )

~ -tk trto ~~t ~O J Wt so z u

l- _ Wz-W C - - - l - = -w~lc-W t-w

Slworl~~ w~3~t ~ _ ]t +WWz t Wt W2 bull

-r~er~of -to h amp ~jl ~ ~~ lot C r~ 0 W W-z s l- C i (wamp-w)

---- -=WW1 ~-c -W(W1-W)

lt)irljj We 3 t I~-101Mh C-IVWC

1A~i~Cst

Let~ Wz~ W we ~ct ike f~Otl af ~f -tampjc--t ht t ~ i tele I)t I wI~~

(l+ lJti JW] yl ert~ -tle rey bull tcJr fa c To iIt tlaquojct

lIt cJ W is -L Wt

i(J~w) -= T(w~-~

~gt

CD C~eetfe( 0 is ~t tlv ornI reg CeV~J G is ct A-tA~ A3_

() I eurot- NH llt (-r~s rs -tf 41-1 ~- 1 A A A bull A tateo J n I l _ J i (~~Le~ ~Alll~b) s 01 SCt~eD u -pe v~GyueJ

(jOf4-hoce~t~ H l$ c AT At+ Pr3 (be(AASe O~ = 5(O~)) pound1- f lt tl~ A ~ fJclCi-r -to ALA 1s

i- A-A3 ~ -= At - A1-AJ A bl~-t ~ 1 1laquo ~ ~ r~~cJAt -to AA~ $

c- AA) == ~- A~ ~ -rktSt -fwo -ts W f~cf ltt t ampJk4J gt~~flaquos boi lut~~ u$~-f~ ~t tAll lAzI= tA- i- (e

AA = AzA - ~X3 -= ) t ~t lt e c At-tA T A~ SAiSfelt bofl ~t~01l~ 1eo t-= AT At -( ~3

17 N f t - L A+ Al-Ar) 6 Ce---+ef ~-tke ~-e foitrt Qftle $ DA l-

(be~oe 1-1 $ ~ ~Jro~ 4 o t-t) ~tCA ~ Mi-e fit arcc is -tke Ciolaquo ~t f4~SfS -tvnWJ4 ~ a Jo---~ -4le ~~es AtAl Aamp+~ As+A) ~ ~- J L -) ~) -

~Q 1eet qf ~ al-t-bAdcs H I 1 1-3 -=t ~ Wampdtoi~~ -tk ferllaquos ad ~e D~e1 ~~ raquo A~lt

(J~i(t~ ) A lltzlJ J llWW1-~ Ayt ~ito

Sol4 SifCamp ~A~R~lgttPLlCQA~ ~rJwail~e Arf A+cJQ+~~R20 I 1i~R+~~Pao C-t~1T~ZQ=-O

I ~Il I w e LV = e ~ 5 A ~t 4 ~b To ~~ fl X 1l s erltamptDI we CoM-rtf

Xt wl-t t)ll= (Ai~amp ) +w~Ct~iP )~(8+~~

= k [CM Q+ ~~)+ 1Yfgtt wR + tf )+ w (C + p+~ I = 0

~~~A I )( ts ~ (Rot 4 1 J~ ~ ~-t 4 -II 3~f1 C~cf ~ ce~-ter4cl At ~ (A e) ~ ~(f-t~) (ie ~c pOlt 3 -the amp~~c ~ ~ ~11t~ -G t- ~rid 1 ~~t AS)

COlf~selj Ikj ll~ 01 ilt G~f smiddot ~ fo~t ~ loc-s 61 )( 0-~ G~f C = i(Jlt- CA-t 8)) is -flc co~nsfo-kj lt Ov- ile ~t Clfdt

1-(t1J~ Let A~ A)e tI ~r~ 0t W1w) w~j I Y~ f~~j

fYo~ A ~ J~r - fe~~ -to -tkt -t~~ e to ~ c~tdt I

01 b w WI W 3 Got W bull skw~ ~est f~(tS ~ctCmt 1cle-t~~ ~s tmiddot~t t C)~

~otct~ JlCG ASSUllC -tL ai~cit-tle is -tlt kAtf GifC(t

~ h~ le~~tcJA -to t f~eMt oJ 1J -iklk ~ MS et--4M rll-tvJ~

bull l- A ~-A - WltWl t~ k~Wi -r ~- w - tV - 2 - - W 2 bull

Now WI bullbull f -ike ampM- ~~lc I SO Wd -= 1 i1e we ~ fJ~-te -tk ~n 4S _ _

~ bullbull Z ~ _ I T ~-t Wos 11 W + 2 Wl ~ - 1iIII I - - w

2 2-

F-oN -tk5 t ~ ~t -tk yoil-f N Jw~ -+ W3 $ 0shy

--te e lt$-I(C -t1e e1f~sS1W f Ns Sr~t~c ~~ nSFt -t oJ Jt Vis we (4 eot-t~ -tMt wtl lISO e O~ -tIt o~-- -two les -t~ e-Fc~Sto ~1 tJ -tt l s u~ -t $ -tle (fwle1 ~ -t~ )1 fO~~ (tce ~

J I W-z4 _

11Ob~ ( S~~t lYe Tko~ ) let W be D~ llt (~crclf ofJ ~1 13 c( PI Q1 R

be ~ iut ~ ~ lC ftJi~ ~ W -tt t1I 2 ll I tl ~ I ft ~ec-f~Jflj slw ifvt P Q R A-e tAl(Il (-ps Ole 5-

clt~ A $~501 11 tf A ltamp-t) ~ W) i

~ol~bo- WamplAi loss -t 3~nl~ I Wt J lS$We Je G-nIUshy

Cilampk 1s ~ ~ cttclt ~ lll llJ lls -= lw I ~ t 1kt k ii ~s ~~ l+ ll~ ~ Ii t3 --ie r~~ fw- W + 1~ Ivs ~ f-ltl ) i tJ- Zt~W So Sol lkcsc -tcdr W~ 3laquo l = ~ t L + W-lE W

2

St ~ Q ltl ott ilW --l 1(= tt f t~~1l

I sluw fQR 4t CttlfUf it S~s-t st P-R =l-amp-Nil f-R _l- Z-amp-~~ Yo-~~J (tI 4W -g ~-R

Q-~ -1-1)-1tJ --l~W X l ~-amp~w ) l2tgtW-ltl~ -lZ+ t

4t~ w- Zl~-ll-t It f- fl

- (1- R bull

-J clt~lttii lw=t ~ WW-=i

CiiID ~tlt~ firLiA BC let 1gt be A4Ie GtIlOc1tf- E 001 As loIiti DEit-CB J ~ F ie 600 Be I

ciA ~fDf oX ~~ o-rbmiddot 0 1 ltt ftt XIS G(( Gr be 01 EP ~tS~t ~ el~ttrlgtedo-r W~~~~fk~t~s X Ao D C fSfoFc-=Ep-=BYc1gt=r

~J ~sted oR we rMj Sity ~ i 7 middot PrDV~ 6i-F fs pcmI(e( -to -Me 4 b~ 1 -M CaJamp) Xl= Of-~ -tI S~1 je Y-X Sol-I Set 1ampt o~ AtAo tt(-~ IMc

For ~fS X It we e Ix-+f ~ lxl +111 ~ft Tie E 8 Gfl = C ot~~ E (0 r)klgt(d~ 1- W-11IAy f X= ~t(r-s-e t~o A~ F tB t(f-t)c 4( euroj =tE t-((-f)J) _ h Let Pbe 0 poillt el LIle )( f lJe lter t= B _ L _ amp1gt g + (_t )e~ middot gtY haYCamp oP=toX+(f-t)oy -f=~y ~ Be -- r -i1gt-t ~_

J J gt1( 8 -I io O~)y~ amp(01] ~ P-u SfjllleMt Xt E retgt I $0 IE-BI rD-cl c1

EICjl1t Call a ~1IIecent ~ ~ QjgtWelC ~l~ (I- ) Is (E -amph 1l ID-d r-(t-amp)(c(-f6-Jgtfd tl )ltLJ )M ~ ct j~ Ie ~od ~ orF9fe sk~ J i q F- Gt = t6-p)~+ (I-t)(1-9)C ~ +~hw ~t cf -tk s IIf-t4 Jgtllrl1lpounds Of ~t(tei _ IS tlt-p)amp1~$ htfampt iits~etet ~ik~litetllllorltl -tlt-p)la (amp+~~ =(~~k1NIllelo I _1 t f4IIIl ltf1ltS

Sll~ fir trl4t~ A~c~ Itt-A IlIamp 1M OjL ltf 114 (tw~-for ~ pound Me~ --ik se ~fOW twI ~ _ Igt IC-tO - f ~ if

T -poundTI-r -pound ~ I A=0 1)~D i(1el IC-BIt lo-dtll)~

UI8iC-1gt1 +11Hlt-at=Iel+ Ie-IgtI+11gt1 +1c_~(f~~t Wt ut Ie+IC-Igt ~ Iamp+c-tgtl t=~f1f)

AA IDI + IC-61 ~ 11gt+C-81 C-~AO=~8C) (gtt) holds ~Le~ft~~lcJs A81(1)C ATgt Usc _~ __

c6hf--I--l~1gt~ ItiC

~1- ~t fmiddot~~ 0+ ~ 0 ( is )(Y=tJC( (1 rsti - Ex4k+ Let 0 ~~ (i(cAt cf 4ABe 9 ~iIt J bef -fIl lfcffS Jf -IIf (t) Xi=fX (y+I)zmiddotXmiddotZ+fmiddotZ 0( (cXl-Y~(Xmiddoty) ~ I~~)(middotX I IXmiddot~~hd1I O~iOf (=) Xmiddoty-O ~~~~~~~~~~~~~~~ amp--ft 3 Let A8C b Le lmiddotts ~sfmiddotmiddot Phe

Ac~+amp~+A~-t8C~~ Ast+ctl SJt~~ Set1ie Ot~I ttt A ~~t f Jw

CmiddotC +(amp-lgtHamp-~)+D~ (8-c)~-c) ~ amp (c-b)laquo- At~(~- awl lt~~-f4ls s fu ~4S

(6 C-b)middot(S-C-lraquo ~ 0 ~~ck s (amplt-1) ~o

A ~t 1gt Ie -tLt poit ~ Aamp -L II ~ e _ ce~AAcO

p C fgtrcw _t C1gtJoe ) AS-AC Sol~~~~~~~dO~A

A a A J) A J)= ~ E=~~ =3 +~lCJ1gt-C=Aamp-2C

C1gt1 Oe- (A-tS-le)(Mc+1raquowO c) No AA~lh c C C(CUM(bull (IampSt 8 41f1$-bull (4) bec u Amiddot(Q-ltAB-ACO 1IeJtt(~) ~ OAl ~c ~ A~~AC

euro ~ toJs ~ 8lt~ 1)-A69 seAPS fWlkl ~JCOc $ firAABC jf( t ssewu-J -ptMf ~ c= - ta-+CmiddotfI AAS( its ~ttd q ~1 - If We Sampt -iU CitClIMChH- 0 AS ken -HII-srft~ ~o -t r -11 __ -~ -1 ALh--COtt - 7J 0 OtlGCnx n - ~-

A Fit iAcetft tJf ~~ c 0( lU= ~ = L

co b AI c lt-c

e ~ 1)c 1gt= te+(t-t) C t --amps ~1i~ poundL = tD ~+ cC C bI-c Gte middot I t A-t -~)tgt t-ll- A

aAtlS cc_ - tgtA - M~C 14 e middot

11l Lqt-(gt OmiddotkC Gtctal ~ICef c(H ~r J

51_ Set 5 4lt C4fColt_bull tu e -H Matel~Me1~ 1~ AA+b$-t C shy ~ 4~(

Lampil~gt 1omiddot~(i-1)l4-1) lt0 A-A 6middot~Cc=(tlJ 2ec 6amp+cc-(a-c)(amp-Q=k~middotIf (A16i)riamptc~ Rlt9~~ 11- 3( h_ Imiddotltl-C) 4l- 2(~~(H- btCi)tI~)) cttC

)(~+c) (-1)((-1) =((~ t1 -Hi+(() lt 0 of -~ f (ib -t-e) lA+Il+ ct )+ilaquoc gt~ CifI+cl+Jl(c)+ ~ ~ a(-o)(--G)-4-~-c)(b+cc-4)~)gt0 tsc4 rc s

~ Ike fRS ~ f xi xI wt -Stl-fculot 11-$9 (t)=LXOY) 0( tiYfft~e~ -fo -tkt fl~~ 1-- oxY J e

lti) ~ -f~)( ~f)-a)( l t Yltl (c~wYcxnyJ (j - )(~1 4fT~ A X0( V~~ p A of yl t1ft 0

(6laquo Q bull 1 lj 111)1 (DW~v e

eJ41~ Let AAA A _j A 1 1_ -+ V]nq DO 4 CD e I

- its ste ~tS p-Ilt1 ProiIla-t middot ClrtllAA1Ar oreAA AA So(u-tVf SeL ot - ~ -_amp I~ _L ft--A A ----- ~ fJe ~ ~ --fI 01r~~ O4St SMs ~qIt ~t)~csCA-A) I lA_-A f

E)Ctl-eIlaquo-r Let A6COf tgt ~~ pe-tft Qc e t

~~~Q~ ~ 1kfwlrids~ A88CCIgtbEpoundA 1T~ -r APamptl~J~ le ACDIIIampf6i -laquo s~O~ tk-t ~s Ooet is so eM eII bullbull ~olt4-tfN ~et -ckt O~bullbull~ rt -e ~_W f~ S~

tJ 1(t0 AXC ~ AP ofe (o(iu o=A-f- A(~ J C- 32s amp A

lltc t))tA SIA~y 8)(1)= (1(8 CxE~ C I

raquo)(A 6llgt re EJ( 6 =CcE feMtt I

eurolCAJ- E)(6-t( - ~lte+El$ ~ pound10 eImiddotmiddot

1 ~~-A~)o (As-AJ1gt(~A~ S ~~CI amp euro1tf6lc~ ~se Ac Adol~ -t(t-t Lit set - () middot At

At~ t ~It~ AsIC~ Al~-+yen+yJAI (

_t a ~ - bull

~ 2-shy

I _0 c A 6 c ~ As V ~1~Ut 1 Sjtllc -fb ~BIC~ fW(t

ftdle ~ts of BC CA AB ns~chvell -tk ft1~ -tIua-t

No A bull G 8 A I ~amp Ca A~ (orr eU egt~ 4~_ A~itlA-~lClA-As~=(~tAtAr-tAjcA -~~ StthtlI4It ~ SaJc1ttA

(Nmiddot~~i~+Ar~~l ore4 l1A AAs = Are 1J~~Ai

Aft13 amp11 C=A-ttils-A)frSollletoA~] SiCt AS e Gfe i eRe

o~ (Bt-A)K(~-A) - (A-ttz-~tl-t- t t)AxB No ~~=~~~-=amp-AH-t)e ~~1 S-a-= It-t1)A I Ct = lAt8)- c tlA +ll-t~)B ~ (amp-AI~I~(Cz-~)=(t-ttl-trtl-+t~t))Al(amp~O A S~ CL At( ccdllfttor

~t ~~ 1~~Pt

o

C[~1D --r-0 vetlOf) )( lf ate Jt~y wtt-t---t f~ t -flat ~f~ ClX~yO kAs 01 Soat~

AT 10 o T4 s tktCcStI ~~A rf KttO ~ X0 f Art NIt Co((llteor

F4t IT AX+bY+c =0 ~$ote -e 1~I(z-s 4t4l 4-+amp ott -=0 J ilQA Xf Z 4le cbullbullI btACcS( ~l AO fIe b-tc-o w X-1-KZ-tYc-6Z

(~ar~11to(~1 wr~t--J Lftai c~ s OAAampA Co

~ OeLamps 1f 1 -1z- Aa6~l~8ampR AsampIA~= ~ 6 8-c amp-S tltcl A DAR 0

~e COIIfttAt t ~1 =- 1 ~ ~ P Pl) P3S~ Set - orlll at o at A8 btt ~trs Ale LIDa (ampfbv~ ~ A~ rA Q( e s So 8 1-t S6Wt (s EIt Cll No

Pl =tAt(c-t) 8a trA+ (ct)s ~- ~3 lAAt-tQ-) 8-= tA(-aA+Cc-ct)S a S~tU~ ~ 0= ltr- CArgtA + [pound1)l -(I-I4)$]B

A~ (tally rcf~=gt tr(~ Otu( (l-tl~-laquotlt)S=C Solll fott ol -tit pt~~ -+-s f ti ~I~Js

Nt ~~e ~ 1tu~~A+ SoSzCt-rl g$t Vs- r~ r~- r~1 Pgt1s~S)A+~s(tmiddotgt8 R= rlrfgt~A ~(I)J B

Y~-r)S) ~6a-t~S) amp c) ttS +fs-1S ~ p~f~P+~sampf-tj~

~ P1 ~se~rw)~c 0 Qtlgt+CoO ~ r fL cU-1- fc-i (ove

~ 0

A - -

~ FOf~lamp~

(1 -laquo ~C

fot-CA~ to ~ t t amp -t~~ crt a ~tc ~ El(tend~ltl St L laquobe ~[A8Cl Js~~i~ R= 4 C

Let ( ~t 4ct nwts lt 4e GoismvmcJt i-R- tl 4J~)(fo~of AAsc Sr ~ l=~~Yslt) ~ bc_

S A -- - 0 21 1iltelaquoe s dolAt C~d~middot ~o~ uI1gt ~ s~amp s~~C middot T 1_ ~ rI n -rf (i-- shy

tl Ie or~ DraJ clmiddotae~t 61gt 1pound Si ~ A= ----=algt i IS lle~ ltJOiOlSA0

~~~~~~~~~~~~~-~~~~=~~~~ p adEr-l-~a~~r~ A- oS+- jtus c~ - c e c I) p(]) Let 18(1gt L~Ms

I4dtt rAsel Or S~8c1oI(lcl~ 1leflAftt Let A6nct)p -r1 ~act 0

~Me C ABC ) GlUo~kc ~ PAx P6= Pc x PD = tl b~~=Abc bull P19tpound Note L APD L (PB

4R A1BC)aHd~ckLPAtgt=LPCBS=tfA-tb~~) is ike seifieAc ~AAPDACfB~=~~ PAIPB=fxPD

amp Q C Of 4A8C Lri pc C 1amp-~ ~~ PC Is -lt-~t lat t lie i4 jCbullbullr 4l( M6C Qt r Ie -i4~ to -e -fde ~ A A8C if (JJ

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I-tfllWlbull [A8tl~ S($-11 ) (s-b)(s-c)middot I pCs f~ot -to LACp4C ampP(~ Cos C= tt2ttoa-c (~AI Ci(~ircl 4 MBc B 2shy

[A6Ci= ~SiIlC=Qr(+coSp(i-($C) ~AAcPACBP ~~ fgtc PCPAlltPB =(Cl~-+Iot-c~t-~a~-9 ) = catlo-4 t )(A1(-c)(CoHI- b)(o-Il-~= S (s-c)(~~

2- ~ a

Ci C [AS(I A 2

~

I

~JJI LPFA-=odeg=Lpe~ ~ amp~ ~LPFeLPAE

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AI 6 C 1gt (1~t~c 1gtpound fCLR atfmiddote ZA ~A A ZA bull -~ -iA ~Co~ PAQ~clf$ WeA~ ZA~lA I tc Z~t

pFAECc1dk

bull ~ Srlloi(y taCgt6~~~-lPFB ~ pG~ f CDCCYcbull LPampb LPFI) = e 1klaquo AIJ~P LPAespoundp8C pfE _ LPeP 8EF (0(1ltlt~L PFE L~8Tgt~ LFP - L 10 collirAfampff

)fgtC)~Jl~~ ~ ASC1HAol6C=AcS]) bull (~~_ ~ktI AeCO At)ItBC ~ACdtgt 1)~c 190pound 0 sWLe AB UJlfsftfUct A ampA6

S~~41 to flCAP 1I1elt AB A~ 6eshy

6 Ai - 7ligt= (1) lBAE=LCAJgt

SO LMc L BAlgt-L1gt= LeA1gt-LMe =LEAt) Tkeuro1 A8AC~Ae-A1) So Rr-c EDAtgt~A Thet Aec~ A~8C =poundItampE AClC E~ AC80

bull A rC =c Sf-t Ell I

f1-I-4j hoW~ ~8euro~EtgtS ampb ~ E iUt~( SO - ~~oeA~LeeALtgtCA ~AsectCO Sltffc

SoSoft ~oe 1et~6cP cl-ampd-p~ 0

tI~ Let l)poundF fetf~~ff- P~ ampa Aeyen~~ ~

Asse ~Mist (so4 is 6~UA_JC ~AGSC ~O bull G ~f( Aalec~o)

tt~e9 7eff

fovlaquos X I Z ate (es Aamp ampCA D ((t~ve-()ty It X I Z (lie (dl-lflOr

A ~f f6 lhg--1 ~ xe YC LA - middot ~ lQt Dbu (~ Ac soct1IIt 81gt II J( Z -r1teuron

~g ~ ~ 1t~ ~z Se AlC 6Y c~ _At P1Q (i~ ~y Ie ~c -- _______ r tamp iU I bull laS yc fA ~Igt ZCZA middot lCI~ lIeeu~ Ie~

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I I

ceDD ~MelI s lIeo~toA l~tA I ~cc t) euro ~be tc~ lO 0shy

de lw~~ ~( ft amptCtSSCti 1 tf (~ diC- (~QEf ) bull

t p Ae ti l)euro J Q Bel pound f 2= Cl)n fA ~ ~k ~ Q1t ottc(l(ea~ ~QIR~~~ -

f~ 1 ~ ltt X~EfA 1AMCD bull ~ z- C~neF Arr~l ~(atts ~ff 1e-(fM1oec~ FA

ftt- Ool~~~ 4xf l w hVII

e-- ~ X K __( It X2 ~_( t ~~II Qx 6y Ct ~y pzex I fllFxijmiddot 1I

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Qx Pf Itz loy c-enc ~Mee(AaS

t-rks ~ere 0 Imiddotil~ (1$($ of PoucJ s for It we tftwt Ato 8 -te I AIwIJ (3 il(cJe 1Iofl1-t i AB will b~ ~-t1l3et (iot ot B ~ It~j CIt~ we ells JpoundAoflt ~ t~ liflE Clt B b~ BR

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-- =JSiiiiIii

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Q tgtPt SA DP 8ital R= Pe C Pre ttL PlE AI

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t Set I Q Rut tIff~ Co~~d~

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-~ ALI)f ~fle1 tt P toe a ltpor i~4Mec

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A e 1-~ PI ~ Rctil eo(IQ4(_

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Col Amiddot ~ SJltto i Late ~e cnl~w-f( Jgt4Sr~ ~ IE ( - eatu r4~ ~Cgt cte

a~~c~~ Iof crde middot1itE Ultoofe Y04oc Jl Y l AE=CE ( tel btcte(~w-I(Fu

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63DP I

r ~e A ScIampf~ 2 LtP be 1ft l~~

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S 7c IL ttgt ~-JC 1l rgte ~ t

I

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I

pound I ~e AC kN J 8M Itteet 41 4 (IOIt P I

Siell L PM N L 81lt11 l HCA s MIC PAte CDhcrkcl Q ttl I t fill pou fOitJ BMlC ~p 8M ec 80- yo Y=OA

PM r8- PNICPK POamp-r~ bull ~ $Jtmct~ 1keuro92 Ie -t 10- eo~= ampf(tM- rM) PM - 3

rJ It

OMl PB lr F6 ~t 8MPM+6I1I

OM J ~M

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Ntrf Csd tIe C~C wi4 Q0 As d-cr~ 2 _ bullbull

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F ~c ~ l)e - ~ Aa~Ac (c~

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bull Ott J MAl N~-11 fI ~=C)jI 6lf1

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r 6middot 1- r IAC- UComiddot

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-tIt vtt4lfO c4 -rs T~ ~tCf AT AIT~ 7iIese if L1I $ =ll~Imiddot ~iTt~lltSl~~t~ L T t S~-LTITa S1~1

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(~p Sol~ middot Let dort FE ~wt -to nr2 4Ss(oll (iJ

Feuro () r C Lt r 1 U04s~r 111k ~y1- (M V)Sets P t r c-to K) Iiamp JE t jilt L AS

sow1 bull Ff 1Ie L ~ A is +lt1 ~roIldrc FE LNEC ~Afe~LAME I rSo L ~~eL~A~)~ LlNEcLlAMc ~ ACAeuro ~e1IA I ~ ~ pouer ~ A ltiol4Isped to r is Ac AM= AE S~M(tAfy I 16fJe t ~A i-fk -(~d -to ~~ Aft A~ A - A ~ =lttiJPOiqJ ~FeJ 56 Ae==-AF (1amp tflt11- rAAtcd - I

_ ~S AI ~ fIr2 AA~f ~ etc )~lll fu ett(4-ik1t f t fl1 pues-~r 1gt 61 sJMe~1 t ~OI)O~ wt Soc Oa I ~~t ~~ Ctgt

~ Ltgtco~=LClgto L cLeF ~s ir~S COa b~s L 9CF $ceCfiS~f rl So

Cl) is ~so~~~ -to re

E)(4flt

amp($ PI Ira Q-te ite~Iy ~ t ~ rt M N~oJtlJ ~ r fGs$es -tI- caff( 01 ~ r~

lAe r tgtit cl1illfr iii r rio MAn=C MBfr=D f (0 ~It CD $ 1~jkt to r2 bull

~ C~ IS - tYgtctStIt

~~ A ilefSVsv wi CAAer 0 oJ ugt r gt0

(amptatl 1 J(o r)) sA~f~ +lAo Se~s A~et(1 ~(t X 0 to ~ i~e VOl~t X O~bull y at sucL fut OXmiddotOlec r~ ~ CWOIelcu I fo X=0 ~ Utake )(=~ _-cl tllSo~)(-=QO Wt-take X=o

1ke Circle -w+1 C2~+e~ 0 A~ ~kCamps r gto-((ct k poundSle ~e~ ~ I~e IWJy 4fso ~ft A~ ltrs~ by sff~t ~ CrCJtL (lWt~middotcP

fGcfs CO Gift1 ~I((S~ ~ ~ bje(~~ it f~~ u~ 00 -to -t~lfmiddot ~ ~c-t J ex ) X ~

reg -If )( s-ikcRiC iwe~~1~ XI=X bull f)(~o~elf(enX~

= bull 1 ~x ~oit ofTaTl) ~t-rrl 4i~

P e ~ X1 lCT2 4~f~~-t1~ ~s iS k~

- __ OXmiddot ox ((sec LTo)()(ycsLTox)r~ ACtreJtt ~~SSi~ 14ftJUJ 0 ~~t +0 A cvdc bull ~ya16tj -4r~ O k iII-s ak~cIc -poits ~(~ St -to ~amp~ foffts l4 fOit 0) ~~fets

of -flit G~ a41~ aJa Afe utllt4r bull JotlfoItr~~tf(~-kGttk ~~set fotleceofv-f~ ~~ctrJe ~

A(fJe vaSSoVJ4-f 0 is Set -to 4 (euro reuro IS ~~~fI)~ 0 ~~s ~~k(+ifia1e-t (It( -t 44td Ito Cnverrely (A (middot1U1IIJt rssj-tlt~ 0 is Seltt -to ~Cvde (w~~ 0 Ni-l -tttllj~-t Imiddotier0 ~Itd to ~ leilt

f r A~At pCiSS~ 14 0 es SetOf ----1-- To e~setl ~ ~ _

Ifgt reg If two cr~ (f~ttIlC~ C4fVts ~(( ttlso ~~(etAf ~ fbft Pto)~~~~

9 lCo (iflaquo at ~Sdf~7e 4-( p~ oF

0 V ~-tlaat iHy~t~tOmiddotmiddot71-~R CA4f~(S ~ SQIJ-fo ~ 0 J

A Ie dI o~ctves4ltSet-f0r1f~~ ~ c () ~-t bull i- cmiddotrd~ ftftfiSttft S ~ fa-5~ 1Gtt cri(S t ( 4It ~fo-6etc~ Gllf f~S A lS 0 4laquol 0 A ~ IV~ IIG(C4((o(Af ~ oAmiddoto~ t 0Bmiddot O~ ~ OAloB OP4 ACoj

wi+lLAoB=L8~A Wt3ttLlOMdOl~ () - ~ LOA8= LogA ~

Aamp~ = OA _ r~A A6 0(3 - OB

=) Ae r lo A~

-------- --------~

)ampa-cle i (~tlcptleofto A ~cQlt$ A 1ckc ~tiatt~

ampl if tlyen~ t ampe- ACBD - A~middotq) +AD

II( V c bull I

SoJn C-sidelt -kfSiCll At 1 vuu~j l)is Cpoundlaquotef bull J ~p-J~ Ygt I) - t t e y fatH4) J -k ~ro-atdc qf ~ec ~~A~ I Q

I iIC ~ AeC SilCamp ~ IH 6e - c I

J vue b -ftt (1) We t _ 1 _AC~ r - Be - - middot

iDA ~ 01gt1gt AJ)middotC1) tt Mltrtrllj b~ lAOmiddot~]) CO~2 1aJkSimiddotces amporeJ

A6amp c) +A)xBe Acll 81gt middot

Re fICS 11L sf ~ eat be ltoftrec -to ~t -I- ~1-tllAt t MilcO + AtgtICBC =AC 1CI1~

~V Asctgt S (l u~ ~lJ4~ 0-shy

~S6~~~ kfCfS4tJ foJt of~~ -+k eampIt~ otIIIetStM Ai ~itlt ~s -fIc ~o~~ rote iIt wJere -reIs CIMif s Mesc(t _

-

6x4t~le 2 Lt ABc 0 be ~ ~tllt t(kft~ suamp~t At ampt so liltftStct At Y1tt ~r AtO P~t~( -Ke -refltecf of 0 ~fOSS AS BC C)1gtA A~ C4IIcYdtc

p _ c $Lt-~ -71

Lcent P~ ~So k ~fut f-~Wi _ 010 0 flO Msc CD lgtA Ye cdIVt bull

sc =l Ott foIIttll is ~iIr~le-t -fo site (5 -tk Ptt-RS l~~( (Sl~~14ft

e IcentS 0 0 -to tts e_~Hrlt OSAP DfBQ ~CR O~DS ~ludlC~~ J J -J ~ _ bull

-tt TltitCirtlutdts Ie CA Ca Cc CD rtsrdtuely CfSMoSmiddotd fIf~iQ 3(0 r ~r31gt0 By ~ct(s)

I~ AC Q( e04~~t ofo ~gtltS

cfct (+) I CA SIrcent to filllt LA fllAlrd to 81gt CIrs

Set to ~ IIt LB ~(c of Ac I C ~ Sci fo c tAlC -to ~lgt1 craquoisSeoet t ol1t LD~E lc ~

0 0 r~-t 0lt1

L Nen bull

CpnCa= 0r~ LAf Le P )Mjl-ly 4~t( LI) R J ll)n~ So bull

$r~ AcJ Mgt PClKs ~~Ic~4J~~ ~ fet h) PampRs is floc

~

G)Cdtpt f

Le-t P bft Af6~-t ~S~ 4l1It Appound ~~~-t LAPB-LACS LA(C-L~8C

Ltt tgt amp be ik~~tS 0( AAPS )AA~C nspecflf ~toe ~l A1gt 1gt1 ce )wtet A fOiWtshy

~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

( )tlfamp 61) biSKfs IA8PJ By ~t CT) ACAfACf~ ~ ~ I3A - XA So iSttf ACAeACampA

P ~f - xpmiddot ~ P~B6+lCApLcA8 J

C-1-1 ~=~ 5tRCt X ( 4ft AP ampt ~1It By~t (s) 1 ~ tCp~=LCitA ~ ~ I I~ fQ is Seoct of ( ~ ~~ 1 f4$s~~3C o listf SiacCrtIeO ~ -T(Alrl~f4lrgto ~~(1)1 tIIet pamp ~t(4C~I~Ois~tfo(0

A ~IgtC A~te A lU)e bullA p A APelAcIIgt f-c ~) I SIWICamp

I

~ ~ ilt3t +00 c( ~ 1 PQ fh ) Qm Q J r bull bull ~ t01 setc~ 10 t of I I

No LM~-L~8-=-LIWC-LAec f~ $(amp ~st ~JO 0 Ao( ~J~~ ~ Atl 43~ t (-d 0 ~ A61PcD

fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

Page 5: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

(frsl) ste-~~1~~ Ceo Us ~ FotrAAOC J let Dbe O~ ~ff U - -- A Let Dbe 0- Sce ac Let p= ADU - 81gt I)l W -= cD e 1) C 2+ eln= a( )

tiV+lG PM tW yen~-~ t-=- (10deg- middot ~o

(os tCos(llodeg-l)_ -CO$~ jlell byeose I 1

~ ~ t 1 I I l tf fJo= Cos 1-+ Cos t - Wotf - C + t~p- ~4 ~t zWp + set

Aeelok-s A (0 Let AD ~ 11 1fte4lt -t sk Be I

I

~ 1fe ~ stewafts t~ I

S9 DC ye(clts ~~pLJat-t2l-tt 2 Z 2

I

Ui~ -tt~ ~ S~~e~(e$S~t ta~ I -+

e ~et -tke Apollos e(fa(Cl ~r 1 Z l) XI ta froiof CeQ~~~ 1_ AEttr~ bullJJ~ 1i1b eo _ 4 ttfi-t ftlbJ c =~41I)t( _ ~A~ ~ amp~ Co 0-~

A

~ 8 1) C

-+1

lL) Let AJgt~ ike (AtIYl --~ J ~f)Jj- _ -74 MC r~ ~ araw Ceuro AOwi- E le AS

We et 4Ace ~ lSoSC~(s wr-bCA=EA 1fe ~= t- St4ltf WCl we 3et

~ co 4~ _ ks ltt ~ r ~ n - )+c- ~e~f So tf~ yklJs

to A1gt - J~c (t-s )- (b4cf middot

Ie be kAt CA ~ F ~ hIeuro A If Its AD ampE CF O~ ~bull ct ile

A ~~ lC ti lC ft=i () E rFA

amp Ii C Re~ 9y ltle lIII lpound AC fL _ CB~f I Aamp ~ - -LC 7n -_~t-or ~~ 11 rg 0

StaSiALAFc SillL CFB ~ $ 0 e se t M=Ac suY SLaLL 12ampA$OoOl ~c8~~ Famp C8~middotmiddot -1)c kSk~fA-ampA~I

-rI-e(it) is 1If 41$ A~ $ftJt4$~Sir f~_J- L ~ til

t(euro q~lclvtVt 0 at ~~ os-r I

middot

f (J

amp 1) C

CO 01gt ~O Cf OA BEmiddot

Q~c1~~ Af l fC -fl f 0-~ 31 ~tM Co -t~

_ U Ic _C6 _I I - ~-- 4wtq4IUSOf f6 c eA BE

So amp1gt ampE ~lifI1e$t 1)( Fc 14a Set c)

11 n~onU~lE~CA crf00 LJ f be f ) V _ bull bull J _ I ~ AE- sect2)t ~ -= ~o Re~l( ~ ft1~cooI olettot IS lJIe I~(g~fi i Ca s ~ If FIS)t 1gtC teA (~ of ott fOu6 Ot ile pI-e -tIlt Aft 1

CFue CcMcc1Ye-t bull Ai 6 ~(S_CA ~M~ wl~lAfs ~ A ~ roi (Ly t1lollffl~~) s S~ lgtJ= oS fir A AA6C If-tM1r~1t-0 0_ kat we It--ctIe (olt) I biseefotSqf AS o ~ itMecf 4tO

- - O-tkt ~ ha Ie~ Abl ampE 0 A ~I OA=OB-c 0amp=0( sQ-ctc 6 1) C -4lIt COI A6=F middot 61 UIfA s ~cl () S on k perptecfitr i 1ott A~n8ElCfOlII) AEx ~ltff=i t ~CA 0f4e4~epf(rt~~C - FB PC eA ~e C6CMtV60-l t () O~fk(-t)weJct f-~k~ 0 S~~t~ceqVot 4ASC rtrs~~

M= =6E -ti =~-t _ - Famp_ t ~e ~W--Sc~~trl (oCiVC4IIlG~cl) ~I

~ Fe F8 fe -Pi) F-f AIrBC1tIe~~~CdQowtbullbulllampI~ isAppi_~ iftiileafces1lbllt~_ ~so Cailtd(~8r~iiua46Aac

(4)tfAtgtBeuroCf_~~c(AABcI )( B let)(1Z~~feJ~_JI- AF Igt JC ce eA ~ 10k I 1 L L _~ -r-rshy

t FiwlgtC iA=C7i 1 ~=I middot - -e 11QUtt t t AaCA BCSoAOBElCF==~cfltfVtc~tAaC A C ~AASHCaIAx~~rAt~o CfJ) If A1gt1 BE CFore Clttitcles MBc -t Jl I bull IX~ t y Sl(~ I Y [~

- x -1 ~ 180 ~~ S bull Ct-I- -J F - D C ~At 6Jgt ce =ampOOA 02as5 V4SC igttamp1tVL Cnw l( V~ FEIt l5C eA -~Ci1S8 bcostcGosA f 1Xt 1 =1 ~ -rtiHitrdt is ~~sc~

A $0 A1gtn8eurooCF= H o~~Mac 9 rclk ~c1A~ c 0( lt -tkilrM~ 44ABC ~ (c) If AD ee CF laquo~ Q+ bisrttOlSM8c -nct gt~tS)( f ~ Ale ~ts of t-~ 1gt Co ~ Af ~x~=~~c1t)~)ft -t-a 1S(tT~ Qrct wtfl~sIleo AampcA Be

Famp Acc4~) ~d ) IJL-t~ -tfiA Aec S0 A~ 1 ~o tF I I ~odt(laquof4A~c -r JI s ~ ttWte c1---tlt fsctIA ttde of AA8c ~

-tl~ Imiddot~s ATgt BE N

A E

t)

FA ~~

CfiE) t wt poundtccl ~e $~ ~ LampAC

bt10Ni 6 410f1 C J -tlte -tampi th~~ f L eAt ~ -tlte ~O Ile

-os c 7- J~littf~s vt S t 4ACe(A

~ ~~-t At ~ tgtDiltt Ia X r-- lt cule4l 14 xce1i-te of AI8C

I f~- A ~rI Ie clr fe(f-c1oss tACA6C IIIi-4 f~t I ~J v y z

I I -- I Il~o AAS I AIIIX 6~AIIIZ6 ad IiTrC ~1iIzc S l X t 1=tr (4 -rke Crcubull4f c~ r A--4 clt~ ( IS -tct~ to AS CAee 4 xt~ z tt s clleJ ~ esc-i~ cVc1e (OY 4ccittf) 4 IiA~ MOO bull ~ ulSe cI(- tt er4c(~ 1

~A A ( r bull c

It~ 711

to ~~I ~

bullIa

II

Ill folWt QrcI~

ror ~ABC Iet A 8 e Lt clpoiwf$ ( atleAlAB et 1gt 6 F be feet of 4It-lcl-t ~s Be CA ItC bull

let kL I ~middotqe tf0t~ af I-A W61-C w4 cs-Je Itioampafv of Mac

1ke ec lgtEF rltcM_ttcoOCtclc ~ Cc~ fUaj ~ ~ clt( ~ ItIIe e--t Cull ABe ~ cefe N -ioNs cd~ is ~ clrowl 0 H ~ ((s ~s iwlTlGIC_~f AAS 0 SottIM ~AABC w see aitCA ~d (f8t t see uti it ~

8 So Cit~ Si~ eL =i M =8M

s~ AH1 a ( I Sc~ t1 $kf+ 8 A D C -na~ ~CO~I5 tcLM rs

(L Aoot C of AS ~r I Sc f 8EL1oo=L CFM eFCI~c Iso r

1I So SeEF l~f1 ~amp ~~l(

St(Irt~ ~ As OEKt 4re~~ ~ ~ qrdeHlaquoI~ tEl helCt (61 4~te ~~ rck l~i~i-d~ 4SeL)- A6( 1lgtGF ~l~ ueClW ~ SCl-e cude Note tL I CMA Gte ctOIfars qf ~Circle

c5fD Sice OA amp0 BCIICS So feufbAch s ~~rfNA o A J Crb Srll(~ly oa J Ae ~ f 11 e P int cuclc f 4 t~ bullbull Ie Oe J ampA So 0 is o~e1A1( is -t3~ 0 ike ~( c-de No LlAamp1 AA~c ~i tot~o 2 1 ()~ ~e 1k-let esUietl C47rcles

A D C So AASI A A~ 0 i rAtto 2 L r4 -tk --tY-~e 1-eO AO A~ AeAe h )Ao=iAK t(~ Ws s Qtt-t_e1y ~tfJ 5~ A 0 J Be tJMJ lt-1 foe $0 A 0 II K ~e4 tIlCl e~t~f1 ~t AOl~ ~ laquo ~~[(em bull $ ct Aj( is laquoJ~ -to rOllt oftt ~ rtt Q~c bull So t~ ~oet (lSigt t ~--------r-- ~eO~rft of QH) is 1le cet~t_tl Nt ~ middotfc~ ~ 1 AAo tJ ts ~Iamp ~ I) K ( K IS IIIlftd-af fIA ~ lt K i OA middotH Crc-~t s l AAac ) bull t

6Je UIe i MBC i~ ~ 111- 0 ~ Amiddot Note AX is ediArt~o ~d4 8c

o ( II Ltt Ofll AA c (q SCMct OAII A 1-1

--- ~N-- tA~ 0 =i A HI we sae B A Igt C A Ao AAH6 rtto i 2

o~ So 1)iErH11tt)(iio~ ~ 5 1 ~~ bull ee ae ~ ~Qj (so il~t i o ht -fIt ~ j-o~ -0 tj 411 t teampd ~ At Gt ~-t AN C fgtst ec - cetle So = dtli ~ 6-f( t~ eord-IS -l J 0 ~ N~ ~ AI$o A 3AA 0 bull ]

L

i a t e CJ

I u

Ci

CEi0 ~~N~ ~ let beQsJf~e(-f(f ~ K+O So i ampmiddot-i ACo~~ iSA )lJt4~fotmiddot A- b W~~ Co III ~ teal --~

--rfa ~t -+ A( ~rtlt 1I14us ~llloe (~~ ~ C G~cJly ct s el+J of t1SJ bull ~+Igt~ U~fPOlt (ft) Ent M~ fb 0(l +be bull c-+ ct i ec) o (0 )+ (c(-elc) (4-tc)-+(~-td)1 (410- (cot Ii) ~-c)-+ (b-clh bullreg ((H~)(-ttJC=(Ac-bcl)-t(~-t~dl 12 ~ c-td~o -flt -- c-e(-= ~ J Ne( Campmiddot c+Ji ~c+~ ~co1ts

I

~ IAtb S 4-1o~ w~4eA4 -iIu 0 C0JY-te a( Atb l~ At6t -Ilt o~oo4t ~14a (Of ~) tf at is ~ 4~ lilt middot

NoI-t i--s is ike clt9t- be-l-wu (00) a( (e)

~~ W daM ilu~Solf VAl~cf olIIt y At bmiddot=J4Iot IJt --lA-t~t=(Glt~Ga Ioc)A- 1 ~ ~Cll--bl - shy~ 1 711a L lfO

Yroee~bullbull~ Ltt wJ~e( - _ - bull - - - - - -- IJL _~-J(D Wt1 +l W-L w-aJ we=w i -n - hi

~ lt~~wt~ lzlltJ 1lzl iYI~~ - middotifUoJ

~ Jqt~~ =leampal ~=c+rk=Wie~Ji4e- I ~(eo) lit ~el~-6z)

i Wt=(p~b(c~d~)rrae bull amp ~ yo~e L~

1olot furrn n It- be e ( Ie l= 4t(i~4 fLC loi(l~ 9 b(~(EfR1IvLfDs4ttX-cN ~ to ie ro~ CO6)~l) 14~

(o(oo) Caocdlaquoclottfse cCllIctcn ats o(td 4e ~ ot o-tbi laquot it is cC~ r o~-iW)~f~ e~e oyo cs8 tl~s (fosS)+ i~9l It A~~c coseH~=YeteIIlaquoi~ to ~OftS ~ bull

ey ik cu~ I f xt~~=Ye )~ ~=r-e-roY AI( fe Z~CIsk lWtf fir ~ lee euro C o Go ro~~t~tt ~ ~t wf ~ ltII _fir ~ ~ f bull (6+l~

I - ire gt I~ J1=e ~ J

) WftreileH(Il-Imy

~s ) ~ ~CI~ W

fIrre J

l Ioh L T_ -f -t ts ofJ

W4-II4 C4S~ pound_ )

~~ 41f Wid Ja-e w)e )

I1 2~)tt~ I pin e Afe

-ltv ~t Setflaquots ~ A I~d ~ampPav3~

Cotttple~ 6eUYIUi(-ry

~ -t Ls ~ N~~tQVs e c gt e - Ccs9 +Se

~sc Obte~ ~ ~

CD 1- W claquotsr(middot t -R Ie-tt We III r ~1 ~(+ot) ~ 01 e _ 8 To yot~+f A YIi v fLe rlAlIe Iiishy

- r I 1fSj~t -to -Ie ~ ~ ~ Go)1 ~ C(

=~ r_ ik We $~fl1Ioltrb 1Ie crl foe l fA ~ - e b~ e

Acrl~1 Ie ~ ~s Iej f t ~ fl=- E

Ei-tmiddot 1- ~-tljk -t di-Yoits 1

Gi~ W W2 fke 9Qta-~c e~CM Af -tI ~ ~ ~ ~-~~k IN Wa is O~ ~ 0 +t Wa t ea - 10

W ~ So z-w bull HelllLc ~-J _-i -- ~1ecJ ~-W c

Wz-W WcW I ~_Wmiddot 0 1-kt beA ~~ olSo tJi~u -tk cJ~r

igtr -tke ~~ ferlts 4 WLJ l -to be eolheAr- eogi- of l u fcoJc ~ 1 1rllleP0rt

i CtrIz-) RottmiddotOW 1oJ1 9t W

- bull -1 II It-vL

e == Cos 1 gts = 1 bullWIw Eltot of-ike le tkn C rttr~JcJA

-to oJ W1 5 f l-C -~-c- l

0~7i-f ~

Li f~) ASS-teJ wt~ (uit) c~tctf

11 w W~ n 0 ~ tle ~-l cJe (at wi =Wzih~ l )

~ -tk trto ~~t ~O J Wt so z u

l- _ Wz-W C - - - l - = -w~lc-W t-w

Slworl~~ w~3~t ~ _ ]t +WWz t Wt W2 bull

-r~er~of -to h amp ~jl ~ ~~ lot C r~ 0 W W-z s l- C i (wamp-w)

---- -=WW1 ~-c -W(W1-W)

lt)irljj We 3 t I~-101Mh C-IVWC

1A~i~Cst

Let~ Wz~ W we ~ct ike f~Otl af ~f -tampjc--t ht t ~ i tele I)t I wI~~

(l+ lJti JW] yl ert~ -tle rey bull tcJr fa c To iIt tlaquojct

lIt cJ W is -L Wt

i(J~w) -= T(w~-~

~gt

CD C~eetfe( 0 is ~t tlv ornI reg CeV~J G is ct A-tA~ A3_

() I eurot- NH llt (-r~s rs -tf 41-1 ~- 1 A A A bull A tateo J n I l _ J i (~~Le~ ~Alll~b) s 01 SCt~eD u -pe v~GyueJ

(jOf4-hoce~t~ H l$ c AT At+ Pr3 (be(AASe O~ = 5(O~)) pound1- f lt tl~ A ~ fJclCi-r -to ALA 1s

i- A-A3 ~ -= At - A1-AJ A bl~-t ~ 1 1laquo ~ ~ r~~cJAt -to AA~ $

c- AA) == ~- A~ ~ -rktSt -fwo -ts W f~cf ltt t ampJk4J gt~~flaquos boi lut~~ u$~-f~ ~t tAll lAzI= tA- i- (e

AA = AzA - ~X3 -= ) t ~t lt e c At-tA T A~ SAiSfelt bofl ~t~01l~ 1eo t-= AT At -( ~3

17 N f t - L A+ Al-Ar) 6 Ce---+ef ~-tke ~-e foitrt Qftle $ DA l-

(be~oe 1-1 $ ~ ~Jro~ 4 o t-t) ~tCA ~ Mi-e fit arcc is -tke Ciolaquo ~t f4~SfS -tvnWJ4 ~ a Jo---~ -4le ~~es AtAl Aamp+~ As+A) ~ ~- J L -) ~) -

~Q 1eet qf ~ al-t-bAdcs H I 1 1-3 -=t ~ Wampdtoi~~ -tk ferllaquos ad ~e D~e1 ~~ raquo A~lt

(J~i(t~ ) A lltzlJ J llWW1-~ Ayt ~ito

Sol4 SifCamp ~A~R~lgttPLlCQA~ ~rJwail~e Arf A+cJQ+~~R20 I 1i~R+~~Pao C-t~1T~ZQ=-O

I ~Il I w e LV = e ~ 5 A ~t 4 ~b To ~~ fl X 1l s erltamptDI we CoM-rtf

Xt wl-t t)ll= (Ai~amp ) +w~Ct~iP )~(8+~~

= k [CM Q+ ~~)+ 1Yfgtt wR + tf )+ w (C + p+~ I = 0

~~~A I )( ts ~ (Rot 4 1 J~ ~ ~-t 4 -II 3~f1 C~cf ~ ce~-ter4cl At ~ (A e) ~ ~(f-t~) (ie ~c pOlt 3 -the amp~~c ~ ~ ~11t~ -G t- ~rid 1 ~~t AS)

COlf~selj Ikj ll~ 01 ilt G~f smiddot ~ fo~t ~ loc-s 61 )( 0-~ G~f C = i(Jlt- CA-t 8)) is -flc co~nsfo-kj lt Ov- ile ~t Clfdt

1-(t1J~ Let A~ A)e tI ~r~ 0t W1w) w~j I Y~ f~~j

fYo~ A ~ J~r - fe~~ -to -tkt -t~~ e to ~ c~tdt I

01 b w WI W 3 Got W bull skw~ ~est f~(tS ~ctCmt 1cle-t~~ ~s tmiddot~t t C)~

~otct~ JlCG ASSUllC -tL ai~cit-tle is -tlt kAtf GifC(t

~ h~ le~~tcJA -to t f~eMt oJ 1J -iklk ~ MS et--4M rll-tvJ~

bull l- A ~-A - WltWl t~ k~Wi -r ~- w - tV - 2 - - W 2 bull

Now WI bullbull f -ike ampM- ~~lc I SO Wd -= 1 i1e we ~ fJ~-te -tk ~n 4S _ _

~ bullbull Z ~ _ I T ~-t Wos 11 W + 2 Wl ~ - 1iIII I - - w

2 2-

F-oN -tk5 t ~ ~t -tk yoil-f N Jw~ -+ W3 $ 0shy

--te e lt$-I(C -t1e e1f~sS1W f Ns Sr~t~c ~~ nSFt -t oJ Jt Vis we (4 eot-t~ -tMt wtl lISO e O~ -tIt o~-- -two les -t~ e-Fc~Sto ~1 tJ -tt l s u~ -t $ -tle (fwle1 ~ -t~ )1 fO~~ (tce ~

J I W-z4 _

11Ob~ ( S~~t lYe Tko~ ) let W be D~ llt (~crclf ofJ ~1 13 c( PI Q1 R

be ~ iut ~ ~ lC ftJi~ ~ W -tt t1I 2 ll I tl ~ I ft ~ec-f~Jflj slw ifvt P Q R A-e tAl(Il (-ps Ole 5-

clt~ A $~501 11 tf A ltamp-t) ~ W) i

~ol~bo- WamplAi loss -t 3~nl~ I Wt J lS$We Je G-nIUshy

Cilampk 1s ~ ~ cttclt ~ lll llJ lls -= lw I ~ t 1kt k ii ~s ~~ l+ ll~ ~ Ii t3 --ie r~~ fw- W + 1~ Ivs ~ f-ltl ) i tJ- Zt~W So Sol lkcsc -tcdr W~ 3laquo l = ~ t L + W-lE W

2

St ~ Q ltl ott ilW --l 1(= tt f t~~1l

I sluw fQR 4t CttlfUf it S~s-t st P-R =l-amp-Nil f-R _l- Z-amp-~~ Yo-~~J (tI 4W -g ~-R

Q-~ -1-1)-1tJ --l~W X l ~-amp~w ) l2tgtW-ltl~ -lZ+ t

4t~ w- Zl~-ll-t It f- fl

- (1- R bull

-J clt~lttii lw=t ~ WW-=i

CiiID ~tlt~ firLiA BC let 1gt be A4Ie GtIlOc1tf- E 001 As loIiti DEit-CB J ~ F ie 600 Be I

ciA ~fDf oX ~~ o-rbmiddot 0 1 ltt ftt XIS G(( Gr be 01 EP ~tS~t ~ el~ttrlgtedo-r W~~~~fk~t~s X Ao D C fSfoFc-=Ep-=BYc1gt=r

~J ~sted oR we rMj Sity ~ i 7 middot PrDV~ 6i-F fs pcmI(e( -to -Me 4 b~ 1 -M CaJamp) Xl= Of-~ -tI S~1 je Y-X Sol-I Set 1ampt o~ AtAo tt(-~ IMc

For ~fS X It we e Ix-+f ~ lxl +111 ~ft Tie E 8 Gfl = C ot~~ E (0 r)klgt(d~ 1- W-11IAy f X= ~t(r-s-e t~o A~ F tB t(f-t)c 4( euroj =tE t-((-f)J) _ h Let Pbe 0 poillt el LIle )( f lJe lter t= B _ L _ amp1gt g + (_t )e~ middot gtY haYCamp oP=toX+(f-t)oy -f=~y ~ Be -- r -i1gt-t ~_

J J gt1( 8 -I io O~)y~ amp(01] ~ P-u SfjllleMt Xt E retgt I $0 IE-BI rD-cl c1

EICjl1t Call a ~1IIecent ~ ~ QjgtWelC ~l~ (I- ) Is (E -amph 1l ID-d r-(t-amp)(c(-f6-Jgtfd tl )ltLJ )M ~ ct j~ Ie ~od ~ orF9fe sk~ J i q F- Gt = t6-p)~+ (I-t)(1-9)C ~ +~hw ~t cf -tk s IIf-t4 Jgtllrl1lpounds Of ~t(tei _ IS tlt-p)amp1~$ htfampt iits~etet ~ik~litetllllorltl -tlt-p)la (amp+~~ =(~~k1NIllelo I _1 t f4IIIl ltf1ltS

Sll~ fir trl4t~ A~c~ Itt-A IlIamp 1M OjL ltf 114 (tw~-for ~ pound Me~ --ik se ~fOW twI ~ _ Igt IC-tO - f ~ if

T -poundTI-r -pound ~ I A=0 1)~D i(1el IC-BIt lo-dtll)~

UI8iC-1gt1 +11Hlt-at=Iel+ Ie-IgtI+11gt1 +1c_~(f~~t Wt ut Ie+IC-Igt ~ Iamp+c-tgtl t=~f1f)

AA IDI + IC-61 ~ 11gt+C-81 C-~AO=~8C) (gtt) holds ~Le~ft~~lcJs A81(1)C ATgt Usc _~ __

c6hf--I--l~1gt~ ItiC

~1- ~t fmiddot~~ 0+ ~ 0 ( is )(Y=tJC( (1 rsti - Ex4k+ Let 0 ~~ (i(cAt cf 4ABe 9 ~iIt J bef -fIl lfcffS Jf -IIf (t) Xi=fX (y+I)zmiddotXmiddotZ+fmiddotZ 0( (cXl-Y~(Xmiddoty) ~ I~~)(middotX I IXmiddot~~hd1I O~iOf (=) Xmiddoty-O ~~~~~~~~~~~~~~~ amp--ft 3 Let A8C b Le lmiddotts ~sfmiddotmiddot Phe

Ac~+amp~+A~-t8C~~ Ast+ctl SJt~~ Set1ie Ot~I ttt A ~~t f Jw

CmiddotC +(amp-lgtHamp-~)+D~ (8-c)~-c) ~ amp (c-b)laquo- At~(~- awl lt~~-f4ls s fu ~4S

(6 C-b)middot(S-C-lraquo ~ 0 ~~ck s (amplt-1) ~o

A ~t 1gt Ie -tLt poit ~ Aamp -L II ~ e _ ce~AAcO

p C fgtrcw _t C1gtJoe ) AS-AC Sol~~~~~~~dO~A

A a A J) A J)= ~ E=~~ =3 +~lCJ1gt-C=Aamp-2C

C1gt1 Oe- (A-tS-le)(Mc+1raquowO c) No AA~lh c C C(CUM(bull (IampSt 8 41f1$-bull (4) bec u Amiddot(Q-ltAB-ACO 1IeJtt(~) ~ OAl ~c ~ A~~AC

euro ~ toJs ~ 8lt~ 1)-A69 seAPS fWlkl ~JCOc $ firAABC jf( t ssewu-J -ptMf ~ c= - ta-+CmiddotfI AAS( its ~ttd q ~1 - If We Sampt -iU CitClIMChH- 0 AS ken -HII-srft~ ~o -t r -11 __ -~ -1 ALh--COtt - 7J 0 OtlGCnx n - ~-

A Fit iAcetft tJf ~~ c 0( lU= ~ = L

co b AI c lt-c

e ~ 1)c 1gt= te+(t-t) C t --amps ~1i~ poundL = tD ~+ cC C bI-c Gte middot I t A-t -~)tgt t-ll- A

aAtlS cc_ - tgtA - M~C 14 e middot

11l Lqt-(gt OmiddotkC Gtctal ~ICef c(H ~r J

51_ Set 5 4lt C4fColt_bull tu e -H Matel~Me1~ 1~ AA+b$-t C shy ~ 4~(

Lampil~gt 1omiddot~(i-1)l4-1) lt0 A-A 6middot~Cc=(tlJ 2ec 6amp+cc-(a-c)(amp-Q=k~middotIf (A16i)riamptc~ Rlt9~~ 11- 3( h_ Imiddotltl-C) 4l- 2(~~(H- btCi)tI~)) cttC

)(~+c) (-1)((-1) =((~ t1 -Hi+(() lt 0 of -~ f (ib -t-e) lA+Il+ ct )+ilaquoc gt~ CifI+cl+Jl(c)+ ~ ~ a(-o)(--G)-4-~-c)(b+cc-4)~)gt0 tsc4 rc s

~ Ike fRS ~ f xi xI wt -Stl-fculot 11-$9 (t)=LXOY) 0( tiYfft~e~ -fo -tkt fl~~ 1-- oxY J e

lti) ~ -f~)( ~f)-a)( l t Yltl (c~wYcxnyJ (j - )(~1 4fT~ A X0( V~~ p A of yl t1ft 0

(6laquo Q bull 1 lj 111)1 (DW~v e

eJ41~ Let AAA A _j A 1 1_ -+ V]nq DO 4 CD e I

- its ste ~tS p-Ilt1 ProiIla-t middot ClrtllAA1Ar oreAA AA So(u-tVf SeL ot - ~ -_amp I~ _L ft--A A ----- ~ fJe ~ ~ --fI 01r~~ O4St SMs ~qIt ~t)~csCA-A) I lA_-A f

E)Ctl-eIlaquo-r Let A6COf tgt ~~ pe-tft Qc e t

~~~Q~ ~ 1kfwlrids~ A88CCIgtbEpoundA 1T~ -r APamptl~J~ le ACDIIIampf6i -laquo s~O~ tk-t ~s Ooet is so eM eII bullbull ~olt4-tfN ~et -ckt O~bullbull~ rt -e ~_W f~ S~

tJ 1(t0 AXC ~ AP ofe (o(iu o=A-f- A(~ J C- 32s amp A

lltc t))tA SIA~y 8)(1)= (1(8 CxE~ C I

raquo)(A 6llgt re EJ( 6 =CcE feMtt I

eurolCAJ- E)(6-t( - ~lte+El$ ~ pound10 eImiddotmiddot

1 ~~-A~)o (As-AJ1gt(~A~ S ~~CI amp euro1tf6lc~ ~se Ac Adol~ -t(t-t Lit set - () middot At

At~ t ~It~ AsIC~ Al~-+yen+yJAI (

_t a ~ - bull

~ 2-shy

I _0 c A 6 c ~ As V ~1~Ut 1 Sjtllc -fb ~BIC~ fW(t

ftdle ~ts of BC CA AB ns~chvell -tk ft1~ -tIua-t

No A bull G 8 A I ~amp Ca A~ (orr eU egt~ 4~_ A~itlA-~lClA-As~=(~tAtAr-tAjcA -~~ StthtlI4It ~ SaJc1ttA

(Nmiddot~~i~+Ar~~l ore4 l1A AAs = Are 1J~~Ai

Aft13 amp11 C=A-ttils-A)frSollletoA~] SiCt AS e Gfe i eRe

o~ (Bt-A)K(~-A) - (A-ttz-~tl-t- t t)AxB No ~~=~~~-=amp-AH-t)e ~~1 S-a-= It-t1)A I Ct = lAt8)- c tlA +ll-t~)B ~ (amp-AI~I~(Cz-~)=(t-ttl-trtl-+t~t))Al(amp~O A S~ CL At( ccdllfttor

~t ~~ 1~~Pt

o

C[~1D --r-0 vetlOf) )( lf ate Jt~y wtt-t---t f~ t -flat ~f~ ClX~yO kAs 01 Soat~

AT 10 o T4 s tktCcStI ~~A rf KttO ~ X0 f Art NIt Co((llteor

F4t IT AX+bY+c =0 ~$ote -e 1~I(z-s 4t4l 4-+amp ott -=0 J ilQA Xf Z 4le cbullbullI btACcS( ~l AO fIe b-tc-o w X-1-KZ-tYc-6Z

(~ar~11to(~1 wr~t--J Lftai c~ s OAAampA Co

~ OeLamps 1f 1 -1z- Aa6~l~8ampR AsampIA~= ~ 6 8-c amp-S tltcl A DAR 0

~e COIIfttAt t ~1 =- 1 ~ ~ P Pl) P3S~ Set - orlll at o at A8 btt ~trs Ale LIDa (ampfbv~ ~ A~ rA Q( e s So 8 1-t S6Wt (s EIt Cll No

Pl =tAt(c-t) 8a trA+ (ct)s ~- ~3 lAAt-tQ-) 8-= tA(-aA+Cc-ct)S a S~tU~ ~ 0= ltr- CArgtA + [pound1)l -(I-I4)$]B

A~ (tally rcf~=gt tr(~ Otu( (l-tl~-laquotlt)S=C Solll fott ol -tit pt~~ -+-s f ti ~I~Js

Nt ~~e ~ 1tu~~A+ SoSzCt-rl g$t Vs- r~ r~- r~1 Pgt1s~S)A+~s(tmiddotgt8 R= rlrfgt~A ~(I)J B

Y~-r)S) ~6a-t~S) amp c) ttS +fs-1S ~ p~f~P+~sampf-tj~

~ P1 ~se~rw)~c 0 Qtlgt+CoO ~ r fL cU-1- fc-i (ove

~ 0

A - -

~ FOf~lamp~

(1 -laquo ~C

fot-CA~ to ~ t t amp -t~~ crt a ~tc ~ El(tend~ltl St L laquobe ~[A8Cl Js~~i~ R= 4 C

Let ( ~t 4ct nwts lt 4e GoismvmcJt i-R- tl 4J~)(fo~of AAsc Sr ~ l=~~Yslt) ~ bc_

S A -- - 0 21 1iltelaquoe s dolAt C~d~middot ~o~ uI1gt ~ s~amp s~~C middot T 1_ ~ rI n -rf (i-- shy

tl Ie or~ DraJ clmiddotae~t 61gt 1pound Si ~ A= ----=algt i IS lle~ ltJOiOlSA0

~~~~~~~~~~~~~-~~~~=~~~~ p adEr-l-~a~~r~ A- oS+- jtus c~ - c e c I) p(]) Let 18(1gt L~Ms

I4dtt rAsel Or S~8c1oI(lcl~ 1leflAftt Let A6nct)p -r1 ~act 0

~Me C ABC ) GlUo~kc ~ PAx P6= Pc x PD = tl b~~=Abc bull P19tpound Note L APD L (PB

4R A1BC)aHd~ckLPAtgt=LPCBS=tfA-tb~~) is ike seifieAc ~AAPDACfB~=~~ PAIPB=fxPD

amp Q C Of 4A8C Lri pc C 1amp-~ ~~ PC Is -lt-~t lat t lie i4 jCbullbullr 4l( M6C Qt r Ie -i4~ to -e -fde ~ A A8C if (JJ

C)~ ~e icltc1e ot AAec ~e p A e OYlJ c fCL p~~re [Mel =[ALel[~cl+(CI1= ~-t~+~=SIr ~ Not~ LArc=LcPB

I-tfllWlbull [A8tl~ S($-11 ) (s-b)(s-c)middot I pCs f~ot -to LACp4C ampP(~ Cos C= tt2ttoa-c (~AI Ci(~ircl 4 MBc B 2shy

[A6Ci= ~SiIlC=Qr(+coSp(i-($C) ~AAcPACBP ~~ fgtc PCPAlltPB =(Cl~-+Iot-c~t-~a~-9 ) = catlo-4 t )(A1(-c)(CoHI- b)(o-Il-~= S (s-c)(~~

2- ~ a

Ci C [AS(I A 2

~

I

~JJI LPFA-=odeg=Lpe~ ~ amp~ ~LPFeLPAE

C5Ji) ~tolt1 s-ThtOfotfll Let A 6c~ ~t dlSncf ~ts 01 bull ~c ~o - Me~IA~ 1( bull t Of~~~I ~Ot bull -Tht~ bull Sa c~tOV M1 C(liofIPT potd~ A 6 C Iie to

AI 6 C 1gt (1~t~c 1gtpound fCLR atfmiddote ZA ~A A ZA bull -~ -iA ~Co~ PAQ~clf$ WeA~ ZA~lA I tc Z~t

pFAECc1dk

bull ~ Srlloi(y taCgt6~~~-lPFB ~ pG~ f CDCCYcbull LPampb LPFI) = e 1klaquo AIJ~P LPAespoundp8C pfE _ LPeP 8EF (0(1ltlt~L PFE L~8Tgt~ LFP - L 10 collirAfampff

)fgtC)~Jl~~ ~ ASC1HAol6C=AcS]) bull (~~_ ~ktI AeCO At)ItBC ~ACdtgt 1)~c 190pound 0 sWLe AB UJlfsftfUct A ampA6

S~~41 to flCAP 1I1elt AB A~ 6eshy

6 Ai - 7ligt= (1) lBAE=LCAJgt

SO LMc L BAlgt-L1gt= LeA1gt-LMe =LEAt) Tkeuro1 A8AC~Ae-A1) So Rr-c EDAtgt~A Thet Aec~ A~8C =poundItampE AClC E~ AC80

bull A rC =c Sf-t Ell I

f1-I-4j hoW~ ~8euro~EtgtS ampb ~ E iUt~( SO - ~~oeA~LeeALtgtCA ~AsectCO Sltffc

SoSoft ~oe 1et~6cP cl-ampd-p~ 0

tI~ Let l)poundF fetf~~ff- P~ ampa Aeyen~~ ~

Asse ~Mist (so4 is 6~UA_JC ~AGSC ~O bull G ~f( Aalec~o)

tt~e9 7eff

fovlaquos X I Z ate (es Aamp ampCA D ((t~ve-()ty It X I Z (lie (dl-lflOr

A ~f f6 lhg--1 ~ xe YC LA - middot ~ lQt Dbu (~ Ac soct1IIt 81gt II J( Z -r1teuron

~g ~ ~ 1t~ ~z Se AlC 6Y c~ _At P1Q (i~ ~y Ie ~c -- _______ r tamp iU I bull laS yc fA ~Igt ZCZA middot lCI~ lIeeu~ Ie~

If ~ tL ~ =-1 iIamp )( YL MHo l~(~ Y~t~~~~ SlJ) Ltt l~ X(OCA -Thtl b Mt11Idtw 11~ Ax ay CI _ lt Cz Y Cl iiiK zA --i ~o --=-l1toobull CfIea bull _Cl -a

I I

ceDD ~MelI s lIeo~toA l~tA I ~cc t) euro ~be tc~ lO 0shy

de lw~~ ~( ft amptCtSSCti 1 tf (~ diC- (~QEf ) bull

t p Ae ti l)euro J Q Bel pound f 2= Cl)n fA ~ ~k ~ Q1t ottc(l(ea~ ~QIR~~~ -

f~ 1 ~ ltt X~EfA 1AMCD bull ~ z- C~neF Arr~l ~(atts ~ff 1e-(fM1oec~ FA

ftt- Ool~~~ 4xf l w hVII

e-- ~ X K __( It X2 ~_( t ~~II Qx 6y Ct ~y pzex I fllFxijmiddot 1I

Hul~pr~ ~ AIl ~~ tfffSfctj cofI4t tt XA)(B XEmiddotKF J (CmiddotYP=1AmiddotYS ZEmiddotZF= zeZIgt W~~et ZQ lSf~-i igt PQ~ ore rlfltelaquor

Qx Pf Itz loy c-enc ~Mee(AaS

t-rks ~ere 0 Imiddotil~ (1$($ of PoucJ s for It we tftwt Ato 8 -te I AIwIJ (3 il(cJe 1Iofl1-t i AB will b~ ~-t1l3et (iot ot B ~ It~j CIt~ we ells JpoundAoflt ~ t~ liflE Clt B b~ BR

6lCtJfC i F~~ h Cf(Ultirc~ ot Mac J f(it 1) ( ~ ~i~0yen ot -t4l~lE I~ ~tA - ~~ Be ~ e fM 1fe ttusc(e~ of-ffwf3ct (tt4-t C3L1r~ CA~ F= bt ~ ttfStd~ of -tINt ti-~-f Imiddot~t ~tC wo( Aamp 11161 PI Ell F o~ ctU

Soof~fIyen P=Mo 8C ~ E= BBnlA f=CCnAB APP~i P~f ~ ~(fo MB See I fott et 1gtpound f c-

-- =JSiiiiIii

b)lAtc ~ Let-tgt 0- eht ~cfs 0( dt101 AtCS

AS ~ AC O~~e (ilcu-R( Mac ftspciwJy l(t tgt Ilt ~f AtC sCI ~== DPn SA J R= PEn AC fro +~-t lile QR~s~(QVJ14 fttCf+~I (~ 1) ~ f9bt-Mshy~e 1)rff0--AS- CO ~SfctsLAc8

Co ~r ~ qftllCr At =lgt 6 ~LAec So 1= Cl)n G8 Sf_ eEtS

Q tgtPt SA DP 8ital R= Pe C Pre ttL PlE AI

AIP~ f~l ~ 1Ito(-to C ~ P er ~ w 1 ~ bull 1I

t Set I Q Rut tIff~ Co~~d~

~ -7

Alt IXu q j

elf (Ga1(e 3 Ltt AT3CPs e ~ +s tMDlCJe ~-rd AAfLBS Bat LeA) ccf LAB fat 1gt be ~ls (I ~cucl1t ~c4( I

DA(11)C= AU DB()CAe~ 1gtCIAB~ fgt~~ A~ r~CtfaJ T4 6v~fi ~ IAGC a~ Co((~((r

~olf- W HL-cI oy-((~( ~ AA Be Ne

AAIB~I)Cc(-=I DArBC=A 11gt1( ISc AtA f Cc -= H L lAlA I C I Cl

1t~()cD=C1 ~l (AIBl (cjAfrrr5~5Gl ~~ t DAAfCC tgtlt Se4 A HC tit c11ilaquoraquo SIt 1y ar171~ BS41s(to AS e 0cc we Su e H 6ltve c1(i~amp r A~ H C~ S4rt a(((~4~ I

-~ ALI)f ~fle1 tt P toe a ltpor i~4Mec

LtfP I~~ff~I$f- 5 -to ~CA Camp ft~t~ lttt bJ() ~_ eshy

ll 10 ~ fet ~~~N~ c-tohs API sp (~ftvtll IfQ P ~ 61bullbull Pt14 PttNQ~~ (tries ~tll~ Qfz cod A~ aft ~et

iSoLttd- $(fCJt L CPc p) LCQLP LC~P Lc (gta Palt-e J -t ~es c P ~L I PI Q p 4ftcocttc f~AfrI15 ~s middottU(Woto ~1l$1 w-tSu CPt ( gt e-= A ) P t1t( QIP= X ) (Q-a Pf P2C-= B 4re CoI~rtelr $6 Rb2-l amp1L ( AB-=Xmiddot ~ ~lIQ P~IA8 tVe ~Cqfre~

NewtDJ S

~A ABcOS~~(laquoteJktvsa e ~SQiraquoeamp c~tkt~~ ~~

APgtsc CD) PA AXcpotlts EFG)H-~t~ C F B ~ACG~FHgD~~r~t

Sol~tcNI W E6nFHO~ Eftn FG ~X _Apply~~ ~~scJ ~ ~ -to E~ltSJ F f(f ~Sta E~ () Fr =0 ~~ ( 14 1) I G Fn H( X are ut(ltealf_ ~ltfcAy~ltP~CA(s ~e- 4 E6--()FF~~ J ~S14

EEn FF~ B euroH nf6=X amp-t-fn ~euro 0 tUllPtfcmiddotc4t

-nus ~S 0 XI oJB ~c((e4~ 7itN pound4 fl Ff n6D=O SlAry EG F-- ( AC - O ACE6 fH6DCPotrclO

1)ec~CAes ~ 0 nfAaAec ~ JACc) M

A c B actgcP J CAnCpQJ AampnAgR ~r--+--Ir-~~R If AA 613 I cc 4te ~tVt-ct ~

A e 1-~ PI ~ Rctil eo(IQ4(_

c~ rCP_ R2esrk ~-s ~ -tyenUL te~ 4 ~~cAAfIdgre IfV --IfU ~ f 4s root G-oIer ~Ns c~ AOAB ~ftJJ MeoJ- -~r ~ et QPL AEa gil

At A rltamp -7---1S ( rt l g 0 () I 4 ~ ~ Ie Be Cctf~ Lloec Ilfct-Jt ~~ C~ c~ IJOCA ~ 1te(J C~ BP Cd M oct ~

B8 PC-co ~-( ~ No CC~=-( ~(ff~~~sctmiddot~~= - ~ (IC4M~cfMtl~~~ote- ~ et eampI c-f(er

62Y ~coJ A~s tttt ~Cct~lI1tr

Let Cn-les C ~ Cz ktwe ~~t ~~-fe15 0 ~ 02

Sf 11 4st f( J 14 (cs of ( OotX w~ 1

fe- ) t ~ lt twitt ()~ -tu Cl

eo( C~ ~Ilt ue 0 K- r 4)-~ J ~ ~ li~ f(~ok( -to OO~ -rtgt Is -4 (~~a1CSof tLt -f~Cnrd u

MOtse ~3 Crce~ CJCC1 W~~ OJOaoJ(h I~ nf CiamplttJ -tfe 3 ~ ltWQs ~FoS offI Wi( i~~(JItct cent Do fgti- ((lt d4 vaJOJ aftftfT4crtfes 111$ ~It lw la-I fIwe wi(( v-espue to 4((3 ccle$

G7~~14~S

~ If 2c(c~sCp~ lte~tAt PQ ~ p Cl aJ hss fou 0 411(1 yen

middot~ Ot J To Co J C So -ky tore eM ta noe(tk( ~ 2 r(4-~ ~ pIA i~( ~~ oS

~yenI4l~~~

P------ ~ c~ Lf4rdes C e d lifest J e we c- tltANJ A f(rrzl cltJ~C

~~ ~~~eAJf- 14 1

Ci-- ntcl ~~~ CJCl ~ CCsII i~~(t et -t4 ~ C4tt p1-Cch~~

~P~ f LoDa is ~er~ AK~Of CCz _

Let ED be ~~~ foSflctorf oft B~ MaC ~D ~S~e AC -ri Cau~tt1e c1A8JgtC ut ABtttE J(e ~ cfC4c~rc(e c1 AB D MflId 8 Ccent F-=-c --r

D (Olt ~t AE =- CF So 1$1 i te~d~ c~ ~gteJ AE~AB=ADAC II CFIltCBCD CA So~= ~~

5 ~c 81gt fsecfs L ABe WI_ Cl) ~ _ I bull It rJC AS - AD CF- f1C

------------------~ ampA~fel Let ABC be ~ ftrJMIj(e ~ soscJes 68C[)I

CAE AASF ~te~(1 to AAsC wi( ~ CA Aa 4 S bu1 tsrtdvel~ Pro~ta ~-t 141esff-1 AJSc ~ t ~ I~es t=F fEgt DE ~dJ ~uc(~t

Col Amiddot ~ SJltto i Late ~e cnl~w-f( Jgt4Sr~ ~ IE ( - eatu r4~ ~Cgt cte

a~~c~~ Iof crde middot1itE Ultoofe Y04oc Jl Y l AE=CE ( tel btcte(~w-I(Fu

c~ Cc~-tr ~cL~4S AF=8F - I -r4e-tltlfte~ A PUr~I T (~ff I ~~ fiIolu ~ ts ltfCI C1 $f lltty ~amp~ 2 lies Cltt VIIIt~~ ~c c) ~ roampoIaJIlt) of (14So -tkey ~u(4t fAa ~~ Camp~tet

63DP I

r ~e A ScIampf~ 2 LtP be 1ft l~~

~ Ii~~(-kB~lIc(~ -to FD-f _ bull 11C ra(~~ to OE -tt~ fOIts frolle M 1 Elf c(frelttf

S 7c IL ttgt ~-JC 1l rgte ~ t

I

I A~ C~ $oIf1 Let ile cncrcft~ J) ~=HF - PD eF -61) OJ rD-peuro-C~1 EAtlA~1eSamp Ql (A~ AF =SF I CD-c CEAGJPF t 81gt

2 l 1 0 F pW~ ct - fE =AF -AE S r~L pound ~ POtt 1 ~CAty4W(t t

- t_ EICIt1k 3 AC--damp l-H aat 0 P~r -fl Ie A4M C ~ usc -t ifegtSltct ~- Ae Id t W S let

Be It N Let 1k u cudcl 0(AAac -lt1 aNll~Std ~t B t ~ middot Pe ~~t OlUaM

SoIwt t ~ C4Samp 61 Be we6~ 11 aM i~ ~ ~ftthlte Qt S of cYG vtIeof poundlASC 1ICft OM =oel 8M

A~p BA18C i4e c~~In CAsamp - AUN AAec ACfo K~ 1Iotf1Ar (S1Cc iMruw Ibl~cto~ L kll Ac AC Jolaquoaret tes) s e rdeo( I

I

pound I ~e AC kN J 8M Itteet 41 4 (IOIt P I

Siell L PM N L 81lt11 l HCA s MIC PAte CDhcrkcl Q ttl I t fill pou fOitJ BMlC ~p 8M ec 80- yo Y=OA

PM r8- PNICPK POamp-r~ bull ~ $Jtmct~ 1keuro92 Ie -t 10- eo~= ampf(tM- rM) PM - 3

rJ It

OMl PB lr F6 ~t 8MPM+6I1I

OM J ~M

L I A6cb be i$(~Ibullt co_~4 tt ArllAofOo Q-t d - amp c~ f A1)1 SC ~ f (aros

Ccle i VI ( 4 E f= ~~-t t I~oes ampe Q= f-o -Ie C

8y po -t fI-t~ Po~_~ peltPD=PHxPl ~_ ft QClltQ6=~d~Qs~tAcff we1et Po~-Qo=CFM-ru) ~ fMQ~ -ns i (Ies 0ML PQ lQMO Itf oM

Ntrf Csd tIe C~C wi4 Q0 As d-cr~ 2 _ bullbull

It t-sses ME F SlAte LampMO LQ EDt -lCl fo s ~ CIC-z Ef ~ Ef -s iU c($ ef ce Let cI has ceth A( ~s tt lie

laquoa ~ ~ t JFPO _r - flMx pQ fiCa _Vi ~ P$ 01 ~ bull0I

A(Igt~ ite-sect PQ 4t M +Q -of leM _ LA0(= l paceW ac- ~ 8I(C ~ lttlclc p ~_I c 1_

let ya~s t Cltn~ I ~_0 =c bull t if crftit C fc$wt

~l~Sshy c1iW ~ 14- - l-l-~t1 A IS ~f~~J i AA6C J 0 i-tala

C(cuCttdlt~ 7Le -(kfee 4-ttJes AP eamp tMJ Cf irUktt- H EDAA6=-M FDo AC-N tp~4-dcent () 06Jl)F )OCJ1gtE

N C~) 0 J- M N middot i

Solfen bullCO LAfcc9cfLATgtC 9 A fgt l=~C6AtyJrc TktL6lgtFcLBAC AooBc-OCi--ees LOBC-=J(t~Io~Leoc)middot1tl_l8A(= ~oo~L8bFmiddot F omiddot Iamp -=gt 08 ~ tgt l= ~frly DC lDe-

B 0 c (~) CLMA ltPgtM~MIf AC~HI () I 81U AlA ~ NIi-IIIt= Aa -AltlaquoJI tgtA L

F ~c ~ l)e - ~ Aa~Ac (c~

~~b )N6oIp 13Ai~80-- OllADI (0( 1)04 ()-(~)+(()+ll)-~~ J)M~ ~_cot=OMOt)1 te

bull Ott J MAl N~-11 fI ~=C)jI 6lf1

~iet SoU- ln LAFC0 =LOC-dJACl) Fc-tkc ut J bu])M So ~t TeI [)f -ue L Jeo L 6gtF =LeAlt ~ J-f4 a~t (~e tB

4 ~t~4Yclt ~ JNle gtetpeId~ bs~CtoY til g 1 I J 1) 4te 0 ~J

=gt 0t3lJe ~oS i DF Q(A~ DCLbE wHk ~ CSV ftt Ae efT I c AC~J~DI ~ (ltt 6e If Be I I I 01 tl( AS 1POW iI f uIlh) SrlOCo Ae1gt = aq rW1d1C by d~ l~testJ~ t4PtwI- Let lc SAe -de -CA k)sU AABC f 2AamptI

NA ~ NC NF ~ rJ SI AC ~ dbullt ~fieaa~(L ofM$C ~=~ so tr~ of ~ bullbull ftc~(eNs() ~ ikatQ~oJ CoxS qf ~ Grtles Q-14III ~ if ITI ~ YM~(-l A~s 7I-e lmiddot 11M rOI(A)C1lt D ~~(S liIOH

r 6middot 1- r IAC- UComiddot

041(ms AhOYllo-lety wi1kceterO a-J Ptto k (cltwaof-d ~1 H(oJ 1lt) ) is Q ~CI itt setVls Jllttl r01ht X 01 ~ plAtte -t 1ile ~c~ X sampcck -tk~t OXL~ -= ieoX ~~rk~ It kl~1)~~~~ti saA3Jkf~ l-t lFl ltl J ~ -tk kPJMDffty 5 ( ~ A IrtySe~ Q -~ f ~ - ilc ~3~ ~ 12tlgteuroFbe~Js~8CCAM~ ~ (-((Ali) Secs AAsc +0 AAFE

amp 1gtJ C Let q Ie ilaquoo cttIL 0 6A-QC SiAte GiA =-2GfD GS -2GE ~tqt=-2~ s ~) ~IAbEF f AASC EXAfe L L AABC AB =AC A(iRl IS t -t t_1y to tIP cnuantt14MC4t~rMs pte AC ~tf~s P Q~ Pe 1l~ 1e totiJpoNltt (fQ

~114t llCeftgt ofAABC Sott~Let 0 bt 14 cgftt ~ -

) rele Lt 1gt foe ~t3et totlaquo 6 c 71 -t4 Circle +ipound Clttt-atd l4AOC

S 1) l3~yf A-trot ~ PQ

ADfAt -= ~~~~=~=Ic S HcAl)So04s I ib 0 S111tt O~$-iLalAltbullbullfMc t ~-tl_W-~tIecf-

CfajiV ~~ s A~t~~etsVI At AlAJ ISdVt4 well -scfes~e l A az (i) (~ts~ Sltk Cif(IOSitc Ai) fW IZ N ~~+-~~Re ~Ill~ ctrck ~ fMlf a c-~ ~lt 0 c-I

II~ iw~le laquo 3Ie -tno1 eel Ct rd -to ufS A

~ of stJes ~u+-1- middotfDItf-t G 1Cf ~fj -t4 (nuCampolttt ~~+riAe ~-tIa ~~it cO (6([e-t etft

A ~t Let A 6e ( It ~~scf 4~el cltlu ItS 54014 1 ampJ y be -fl- ~offu arcres SCrz

e ~C At otamp r 1A~f~~ ~ It 6gt Ilt

N611 Ae ~tly I B~ Iec t CAlieA Ids A is ru~ ~__~ Aamp a-( AC I So AAIb~Stt-t~ L fMc gti((y Mi~~ LMe e-l ee ir1kcts L seA So Mo( ern ee=- (-(A ~~dAIC

AI (IOOoJ 0A I De = ae r So 0 ts-tfe c~af of AAe d kt P~c4rc-ctr~AA6C

1k ~o~1 ~ (1 A) SeLs AABC f 6Aec ~ SeJ t~

scre-~-tP~MOC-tc~ OllA~~ bull middot 1 P 0 ore co((eAt

- fiscl 1( AASCGs ~IIe1lt ~~~~W (~- ~~L ~Ioc L

- L- ~ bull - 2J~ ~(IC= 8(~(s-lt)

ot t Ii -l 1pound is -(I ~K(~ ifCirde ~ Ill laf S bt-tl nf(~ ltgtf I IIIllyeltt t ~oflA bull

~ (e~ M s M~SzM)S3 ~~rrelaquo At s~ let 6 ~ bullt _ r

blse~ 4 poundA 00 ~-te 4 We c~ S~ SJ 1 M MJ

A 1iamp A --To t~t iampt elite- o~rf-tLt (i) IIIiilsrtt t Aamp1le rtfItJ-f 1 ts S I Co

-tIt vtt4lfO c4 -rs T~ ~tCf AT AIT~ 7iIese if L1I $ =ll~Imiddot ~iTt~lltSl~~t~ L T t S~-LTITa S1~1

(i) 11 A A ~ $S~ AA i MM ~ i 3 I ~ A T~ AI S~1 ~~ HzMl ~ ss I HsM bull ~ co ~ffWbull( ~dSr Nect CircCl1C(~ ~ASsz$3 reI 0 AA A~l

Ctcmiddott of A M~H IIbtepofcrceS~MAJ~r~ ~1 fLAA~AsrL f2 J ~ VAdtoos ~~

Z bullSo --Gtdes ~ 1Io(~ Ll lB~ reggt ampSt~~ AMMz toil s~~i~~ ~lt (x M- SLLt Ill ~bullbull04 S 1-ta~X l1c H ) Mz $1

~=(lttc-o)(c-M-~fl~e) 1 M M amp41 S)Jltl~ UrJ~Cost lt~~~~~(fo) ~ ()bc HSt~Zeuro~X

CT1tW EtA-f tt 1- bull ~A be ~iAt 4+etse~ ~ fwo nO~fD~fUtf Cirdes C ~C CAl-~ef0 0 (tltjreJ~ Dtte ~1MtM

~t~o c eamp 1d1t(s-et C cent~ Cztlt Pt J(e -i4af(EV (A~ ~-t-te~ctc At ~Ca~t QI Lk Me t ~~it-t~ ()Q o-J ~ ~ ~itet ~ pzCla

~-t ~ LtJAo LMAMz

~~ ~ ~

SGl~ B-t~etJ Plpt(gtzOt~~O

Ca ~lJZ~ damp bull nwy 14(0 oPa ) Q SeKds C L 0 PI

~ I ~ t -lO Z bull ~ J ~ OAn Ct =8 ~~-oflt~1 e $ Ll016M -tLl~A~~ So LOI~= LOaAHa A~ t- fs 0P 0 P ~o ltlie sjI Ie~ 00 Cgt~ ofL ~ ) 00 ~O~e-=OPct=OAIOg

t ~te~~-1 cknl4t1 ~ AO~ ~ Ate ~Itc

~ LO8M= lDAM

A~ I =gt LoAM L~AMz WIAamp~ ---

L 0cA M~ ==gt L0 A0)- L I-i A Mz bull -to _16bCrfkSf~S

Solt~p Wpound(CS JTbe reflec~ ~ S Wit-(S~ltt

fI5 Mis

~J e

t ~lwt Cgt (1Of ctImiddotd i -br3frt -+0

e $ f(~

Q cmiddotnI F -tkt bcs of tIl YOII f Sue- fut ~e-re ~)f Q

01 ~ w~ M ~ ~(eoi~ ~ l R~~ QS ~ isc~e~ C~rdamp 4 A PQ R

-to M Lt u be 04

~ A$ iudQ~~ltofe1 middot~~(R C V Lat ~ 10 ampl yo~t~14 fc

Co -fI kottcrt(e+y wfoit4 uW( P-tkt StI~ l t

~CtCte (_oppos-e P -(f ~ T middot (1 ~ Set$ U -to (Q((esr-~~-toflfobulltHf lt 1) Ii P~n (= v ut s setft~~ ~ t PQ~ ~

TR SQ=S - PR= PV- PIlt = Vlaquo=n ~ T T So 5 01 Ae ltT0 e ttl

ampruJt~J) fr p~ ltTaee~ UT ~ U

~ l(P Ifamp)Se0v4 u to ~ C(telte e to c~ l I- UtoT So TT Let 14tats~ P-4 C ~+~t5ect r ~Q~R ~

ampS-=s- Pflt=Pv- P((--Vre =TIC=-TIlt ~ tiM -i1s-MS Ti-f1T=-jiM PtSAt4t

~ El4middotrle b rio t)

Lt-A~c ~ co ftiI5le ~ ~tof scl Be A1k ~tsct- N ot l ~AC i~+fSoct ~c ct tJ ~~r~I~ k~ +0 AN -+~~ N ifersets AM 4 Q -c AB -t p -n ~f-lrJrmiddot 0 li~e to APt Pt-a~AIl laquo 0 middot Pofe Qo l Be SIt- TfABAc1kMNQfampAQMol3c

WLOG I ampS$f41111t A6gtAC Let AN MttStcf Uttucrclt fAABC j 1) ~

-- - bull c L 1gtg CL lgtAC=L~Llgtc~ e lAo M f~ r ~ ~ DC aJ PM 1 Be

~o Ho~y K(A ~StovlsA6j)(+oAgO(t4 08 O~ aq ae Itt t= Be( PN -r4~

L Ogt- L b8e =LM8=ro6_LAop=LoP~ ~ ~ D 0 tcKl orooc

I ) I J GfeCttrA J~c J~M4 ~ L 0 - Lep - 1 0 - 7 1- - 0 - 0 Igt IC tS~ amp It sc K is AM == AM l PfI=Q

I I ~ Lg eto L~~O~)oo 1~ ~o LSC g c It Be r

F l

(~p Sol~ middot Let dort FE ~wt -to nr2 4Ss(oll (iJ

Feuro () r C Lt r 1 U04s~r 111k ~y1- (M V)Sets P t r c-to K) Iiamp JE t jilt L AS

sow1 bull Ff 1Ie L ~ A is +lt1 ~roIldrc FE LNEC ~Afe~LAME I rSo L ~~eL~A~)~ LlNEcLlAMc ~ ACAeuro ~e1IA I ~ ~ pouer ~ A ltiol4Isped to r is Ac AM= AE S~M(tAfy I 16fJe t ~A i-fk -(~d -to ~~ Aft A~ A - A ~ =lttiJPOiqJ ~FeJ 56 Ae==-AF (1amp tflt11- rAAtcd - I

_ ~S AI ~ fIr2 AA~f ~ etc )~lll fu ett(4-ik1t f t fl1 pues-~r 1gt 61 sJMe~1 t ~OI)O~ wt Soc Oa I ~~t ~~ Ctgt

~ Ltgtco~=LClgto L cLeF ~s ir~S COa b~s L 9CF $ceCfiS~f rl So

Cl) is ~so~~~ -to re

E)(4flt

amp($ PI Ira Q-te ite~Iy ~ t ~ rt M N~oJtlJ ~ r fGs$es -tI- caff( 01 ~ r~

lAe r tgtit cl1illfr iii r rio MAn=C MBfr=D f (0 ~It CD $ 1~jkt to r2 bull

~ C~ IS - tYgtctStIt

~~ A ilefSVsv wi CAAer 0 oJ ugt r gt0

(amptatl 1 J(o r)) sA~f~ +lAo Se~s A~et(1 ~(t X 0 to ~ i~e VOl~t X O~bull y at sucL fut OXmiddotOlec r~ ~ CWOIelcu I fo X=0 ~ Utake )(=~ _-cl tllSo~)(-=QO Wt-take X=o

1ke Circle -w+1 C2~+e~ 0 A~ ~kCamps r gto-((ct k poundSle ~e~ ~ I~e IWJy 4fso ~ft A~ ltrs~ by sff~t ~ CrCJtL (lWt~middotcP

fGcfs CO Gift1 ~I((S~ ~ ~ bje(~~ it f~~ u~ 00 -to -t~lfmiddot ~ ~c-t J ex ) X ~

reg -If )( s-ikcRiC iwe~~1~ XI=X bull f)(~o~elf(enX~

= bull 1 ~x ~oit ofTaTl) ~t-rrl 4i~

P e ~ X1 lCT2 4~f~~-t1~ ~s iS k~

- __ OXmiddot ox ((sec LTo)()(ycsLTox)r~ ACtreJtt ~~SSi~ 14ftJUJ 0 ~~t +0 A cvdc bull ~ya16tj -4r~ O k iII-s ak~cIc -poits ~(~ St -to ~amp~ foffts l4 fOit 0) ~~fets

of -flit G~ a41~ aJa Afe utllt4r bull JotlfoItr~~tf(~-kGttk ~~set fotleceofv-f~ ~~ctrJe ~

A(fJe vaSSoVJ4-f 0 is Set -to 4 (euro reuro IS ~~~fI)~ 0 ~~s ~~k(+ifia1e-t (It( -t 44td Ito Cnverrely (A (middot1U1IIJt rssj-tlt~ 0 is Seltt -to ~Cvde (w~~ 0 Ni-l -tttllj~-t Imiddotier0 ~Itd to ~ leilt

f r A~At pCiSS~ 14 0 es SetOf ----1-- To e~setl ~ ~ _

Ifgt reg If two cr~ (f~ttIlC~ C4fVts ~(( ttlso ~~(etAf ~ fbft Pto)~~~~

9 lCo (iflaquo at ~Sdf~7e 4-( p~ oF

0 V ~-tlaat iHy~t~tOmiddotmiddot71-~R CA4f~(S ~ SQIJ-fo ~ 0 J

A Ie dI o~ctves4ltSet-f0r1f~~ ~ c () ~-t bull i- cmiddotrd~ ftftfiSttft S ~ fa-5~ 1Gtt cri(S t ( 4It ~fo-6etc~ Gllf f~S A lS 0 4laquol 0 A ~ IV~ IIG(C4((o(Af ~ oAmiddoto~ t 0Bmiddot O~ ~ OAloB OP4 ACoj

wi+lLAoB=L8~A Wt3ttLlOMdOl~ () - ~ LOA8= LogA ~

Aamp~ = OA _ r~A A6 0(3 - OB

=) Ae r lo A~

-------- --------~

)ampa-cle i (~tlcptleofto A ~cQlt$ A 1ckc ~tiatt~

ampl if tlyen~ t ampe- ACBD - A~middotq) +AD

II( V c bull I

SoJn C-sidelt -kfSiCll At 1 vuu~j l)is Cpoundlaquotef bull J ~p-J~ Ygt I) - t t e y fatH4) J -k ~ro-atdc qf ~ec ~~A~ I Q

I iIC ~ AeC SilCamp ~ IH 6e - c I

J vue b -ftt (1) We t _ 1 _AC~ r - Be - - middot

iDA ~ 01gt1gt AJ)middotC1) tt Mltrtrllj b~ lAOmiddot~]) CO~2 1aJkSimiddotces amporeJ

A6amp c) +A)xBe Acll 81gt middot

Re fICS 11L sf ~ eat be ltoftrec -to ~t -I- ~1-tllAt t MilcO + AtgtICBC =AC 1CI1~

~V Asctgt S (l u~ ~lJ4~ 0-shy

~S6~~~ kfCfS4tJ foJt of~~ -+k eampIt~ otIIIetStM Ai ~itlt ~s -fIc ~o~~ rote iIt wJere -reIs CIMif s Mesc(t _

-

6x4t~le 2 Lt ABc 0 be ~ ~tllt t(kft~ suamp~t At ampt so liltftStct At Y1tt ~r AtO P~t~( -Ke -refltecf of 0 ~fOSS AS BC C)1gtA A~ C4IIcYdtc

p _ c $Lt-~ -71

Lcent P~ ~So k ~fut f-~Wi _ 010 0 flO Msc CD lgtA Ye cdIVt bull

sc =l Ott foIIttll is ~iIr~le-t -fo site (5 -tk Ptt-RS l~~( (Sl~~14ft

e IcentS 0 0 -to tts e_~Hrlt OSAP DfBQ ~CR O~DS ~ludlC~~ J J -J ~ _ bull

-tt TltitCirtlutdts Ie CA Ca Cc CD rtsrdtuely CfSMoSmiddotd fIf~iQ 3(0 r ~r31gt0 By ~ct(s)

I~ AC Q( e04~~t ofo ~gtltS

cfct (+) I CA SIrcent to filllt LA fllAlrd to 81gt CIrs

Set to ~ IIt LB ~(c of Ac I C ~ Sci fo c tAlC -to ~lgt1 craquoisSeoet t ol1t LD~E lc ~

0 0 r~-t 0lt1

L Nen bull

CpnCa= 0r~ LAf Le P )Mjl-ly 4~t( LI) R J ll)n~ So bull

$r~ AcJ Mgt PClKs ~~Ic~4J~~ ~ fet h) PampRs is floc

~

G)Cdtpt f

Le-t P bft Af6~-t ~S~ 4l1It Appound ~~~-t LAPB-LACS LA(C-L~8C

Ltt tgt amp be ik~~tS 0( AAPS )AA~C nspecflf ~toe ~l A1gt 1gt1 ce )wtet A fOiWtshy

~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

( )tlfamp 61) biSKfs IA8PJ By ~t CT) ACAfACf~ ~ ~ I3A - XA So iSttf ACAeACampA

P ~f - xpmiddot ~ P~B6+lCApLcA8 J

C-1-1 ~=~ 5tRCt X ( 4ft AP ampt ~1It By~t (s) 1 ~ tCp~=LCitA ~ ~ I I~ fQ is Seoct of ( ~ ~~ 1 f4$s~~3C o listf SiacCrtIeO ~ -T(Alrl~f4lrgto ~~(1)1 tIIet pamp ~t(4C~I~Ois~tfo(0

A ~IgtC A~te A lU)e bullA p A APelAcIIgt f-c ~) I SIWICamp

I

~ ~ ilt3t +00 c( ~ 1 PQ fh ) Qm Q J r bull bull ~ t01 setc~ 10 t of I I

No LM~-L~8-=-LIWC-LAec f~ $(amp ~st ~JO 0 Ao( ~J~~ ~ Atl 43~ t (-d 0 ~ A61PcD

fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

Page 6: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

11 n~onU~lE~CA crf00 LJ f be f ) V _ bull bull J _ I ~ AE- sect2)t ~ -= ~o Re~l( ~ ft1~cooI olettot IS lJIe I~(g~fi i Ca s ~ If FIS)t 1gtC teA (~ of ott fOu6 Ot ile pI-e -tIlt Aft 1

CFue CcMcc1Ye-t bull Ai 6 ~(S_CA ~M~ wl~lAfs ~ A ~ roi (Ly t1lollffl~~) s S~ lgtJ= oS fir A AA6C If-tM1r~1t-0 0_ kat we It--ctIe (olt) I biseefotSqf AS o ~ itMecf 4tO

- - O-tkt ~ ha Ie~ Abl ampE 0 A ~I OA=OB-c 0amp=0( sQ-ctc 6 1) C -4lIt COI A6=F middot 61 UIfA s ~cl () S on k perptecfitr i 1ott A~n8ElCfOlII) AEx ~ltff=i t ~CA 0f4e4~epf(rt~~C - FB PC eA ~e C6CMtV60-l t () O~fk(-t)weJct f-~k~ 0 S~~t~ceqVot 4ASC rtrs~~

M= =6E -ti =~-t _ - Famp_ t ~e ~W--Sc~~trl (oCiVC4IIlG~cl) ~I

~ Fe F8 fe -Pi) F-f AIrBC1tIe~~~CdQowtbullbulllampI~ isAppi_~ iftiileafces1lbllt~_ ~so Cailtd(~8r~iiua46Aac

(4)tfAtgtBeuroCf_~~c(AABcI )( B let)(1Z~~feJ~_JI- AF Igt JC ce eA ~ 10k I 1 L L _~ -r-rshy

t FiwlgtC iA=C7i 1 ~=I middot - -e 11QUtt t t AaCA BCSoAOBElCF==~cfltfVtc~tAaC A C ~AASHCaIAx~~rAt~o CfJ) If A1gt1 BE CFore Clttitcles MBc -t Jl I bull IX~ t y Sl(~ I Y [~

- x -1 ~ 180 ~~ S bull Ct-I- -J F - D C ~At 6Jgt ce =ampOOA 02as5 V4SC igttamp1tVL Cnw l( V~ FEIt l5C eA -~Ci1S8 bcostcGosA f 1Xt 1 =1 ~ -rtiHitrdt is ~~sc~

A $0 A1gtn8eurooCF= H o~~Mac 9 rclk ~c1A~ c 0( lt -tkilrM~ 44ABC ~ (c) If AD ee CF laquo~ Q+ bisrttOlSM8c -nct gt~tS)( f ~ Ale ~ts of t-~ 1gt Co ~ Af ~x~=~~c1t)~)ft -t-a 1S(tT~ Qrct wtfl~sIleo AampcA Be

Famp Acc4~) ~d ) IJL-t~ -tfiA Aec S0 A~ 1 ~o tF I I ~odt(laquof4A~c -r JI s ~ ttWte c1---tlt fsctIA ttde of AA8c ~

-tl~ Imiddot~s ATgt BE N

A E

t)

FA ~~

CfiE) t wt poundtccl ~e $~ ~ LampAC

bt10Ni 6 410f1 C J -tlte -tampi th~~ f L eAt ~ -tlte ~O Ile

-os c 7- J~littf~s vt S t 4ACe(A

~ ~~-t At ~ tgtDiltt Ia X r-- lt cule4l 14 xce1i-te of AI8C

I f~- A ~rI Ie clr fe(f-c1oss tACA6C IIIi-4 f~t I ~J v y z

I I -- I Il~o AAS I AIIIX 6~AIIIZ6 ad IiTrC ~1iIzc S l X t 1=tr (4 -rke Crcubull4f c~ r A--4 clt~ ( IS -tct~ to AS CAee 4 xt~ z tt s clleJ ~ esc-i~ cVc1e (OY 4ccittf) 4 IiA~ MOO bull ~ ulSe cI(- tt er4c(~ 1

~A A ( r bull c

It~ 711

to ~~I ~

bullIa

II

Ill folWt QrcI~

ror ~ABC Iet A 8 e Lt clpoiwf$ ( atleAlAB et 1gt 6 F be feet of 4It-lcl-t ~s Be CA ItC bull

let kL I ~middotqe tf0t~ af I-A W61-C w4 cs-Je Itioampafv of Mac

1ke ec lgtEF rltcM_ttcoOCtclc ~ Cc~ fUaj ~ ~ clt( ~ ItIIe e--t Cull ABe ~ cefe N -ioNs cd~ is ~ clrowl 0 H ~ ((s ~s iwlTlGIC_~f AAS 0 SottIM ~AABC w see aitCA ~d (f8t t see uti it ~

8 So Cit~ Si~ eL =i M =8M

s~ AH1 a ( I Sc~ t1 $kf+ 8 A D C -na~ ~CO~I5 tcLM rs

(L Aoot C of AS ~r I Sc f 8EL1oo=L CFM eFCI~c Iso r

1I So SeEF l~f1 ~amp ~~l(

St(Irt~ ~ As OEKt 4re~~ ~ ~ qrdeHlaquoI~ tEl helCt (61 4~te ~~ rck l~i~i-d~ 4SeL)- A6( 1lgtGF ~l~ ueClW ~ SCl-e cude Note tL I CMA Gte ctOIfars qf ~Circle

c5fD Sice OA amp0 BCIICS So feufbAch s ~~rfNA o A J Crb Srll(~ly oa J Ae ~ f 11 e P int cuclc f 4 t~ bullbull Ie Oe J ampA So 0 is o~e1A1( is -t3~ 0 ike ~( c-de No LlAamp1 AA~c ~i tot~o 2 1 ()~ ~e 1k-let esUietl C47rcles

A D C So AASI A A~ 0 i rAtto 2 L r4 -tk --tY-~e 1-eO AO A~ AeAe h )Ao=iAK t(~ Ws s Qtt-t_e1y ~tfJ 5~ A 0 J Be tJMJ lt-1 foe $0 A 0 II K ~e4 tIlCl e~t~f1 ~t AOl~ ~ laquo ~~[(em bull $ ct Aj( is laquoJ~ -to rOllt oftt ~ rtt Q~c bull So t~ ~oet (lSigt t ~--------r-- ~eO~rft of QH) is 1le cet~t_tl Nt ~ middotfc~ ~ 1 AAo tJ ts ~Iamp ~ I) K ( K IS IIIlftd-af fIA ~ lt K i OA middotH Crc-~t s l AAac ) bull t

6Je UIe i MBC i~ ~ 111- 0 ~ Amiddot Note AX is ediArt~o ~d4 8c

o ( II Ltt Ofll AA c (q SCMct OAII A 1-1

--- ~N-- tA~ 0 =i A HI we sae B A Igt C A Ao AAH6 rtto i 2

o~ So 1)iErH11tt)(iio~ ~ 5 1 ~~ bull ee ae ~ ~Qj (so il~t i o ht -fIt ~ j-o~ -0 tj 411 t teampd ~ At Gt ~-t AN C fgtst ec - cetle So = dtli ~ 6-f( t~ eord-IS -l J 0 ~ N~ ~ AI$o A 3AA 0 bull ]

L

i a t e CJ

I u

Ci

CEi0 ~~N~ ~ let beQsJf~e(-f(f ~ K+O So i ampmiddot-i ACo~~ iSA )lJt4~fotmiddot A- b W~~ Co III ~ teal --~

--rfa ~t -+ A( ~rtlt 1I14us ~llloe (~~ ~ C G~cJly ct s el+J of t1SJ bull ~+Igt~ U~fPOlt (ft) Ent M~ fb 0(l +be bull c-+ ct i ec) o (0 )+ (c(-elc) (4-tc)-+(~-td)1 (410- (cot Ii) ~-c)-+ (b-clh bullreg ((H~)(-ttJC=(Ac-bcl)-t(~-t~dl 12 ~ c-td~o -flt -- c-e(-= ~ J Ne( Campmiddot c+Ji ~c+~ ~co1ts

I

~ IAtb S 4-1o~ w~4eA4 -iIu 0 C0JY-te a( Atb l~ At6t -Ilt o~oo4t ~14a (Of ~) tf at is ~ 4~ lilt middot

NoI-t i--s is ike clt9t- be-l-wu (00) a( (e)

~~ W daM ilu~Solf VAl~cf olIIt y At bmiddot=J4Iot IJt --lA-t~t=(Glt~Ga Ioc)A- 1 ~ ~Cll--bl - shy~ 1 711a L lfO

Yroee~bullbull~ Ltt wJ~e( - _ - bull - - - - - -- IJL _~-J(D Wt1 +l W-L w-aJ we=w i -n - hi

~ lt~~wt~ lzlltJ 1lzl iYI~~ - middotifUoJ

~ Jqt~~ =leampal ~=c+rk=Wie~Ji4e- I ~(eo) lit ~el~-6z)

i Wt=(p~b(c~d~)rrae bull amp ~ yo~e L~

1olot furrn n It- be e ( Ie l= 4t(i~4 fLC loi(l~ 9 b(~(EfR1IvLfDs4ttX-cN ~ to ie ro~ CO6)~l) 14~

(o(oo) Caocdlaquoclottfse cCllIctcn ats o(td 4e ~ ot o-tbi laquot it is cC~ r o~-iW)~f~ e~e oyo cs8 tl~s (fosS)+ i~9l It A~~c coseH~=YeteIIlaquoi~ to ~OftS ~ bull

ey ik cu~ I f xt~~=Ye )~ ~=r-e-roY AI( fe Z~CIsk lWtf fir ~ lee euro C o Go ro~~t~tt ~ ~t wf ~ ltII _fir ~ ~ f bull (6+l~

I - ire gt I~ J1=e ~ J

) WftreileH(Il-Imy

~s ) ~ ~CI~ W

fIrre J

l Ioh L T_ -f -t ts ofJ

W4-II4 C4S~ pound_ )

~~ 41f Wid Ja-e w)e )

I1 2~)tt~ I pin e Afe

-ltv ~t Setflaquots ~ A I~d ~ampPav3~

Cotttple~ 6eUYIUi(-ry

~ -t Ls ~ N~~tQVs e c gt e - Ccs9 +Se

~sc Obte~ ~ ~

CD 1- W claquotsr(middot t -R Ie-tt We III r ~1 ~(+ot) ~ 01 e _ 8 To yot~+f A YIi v fLe rlAlIe Iiishy

- r I 1fSj~t -to -Ie ~ ~ ~ Go)1 ~ C(

=~ r_ ik We $~fl1Ioltrb 1Ie crl foe l fA ~ - e b~ e

Acrl~1 Ie ~ ~s Iej f t ~ fl=- E

Ei-tmiddot 1- ~-tljk -t di-Yoits 1

Gi~ W W2 fke 9Qta-~c e~CM Af -tI ~ ~ ~ ~-~~k IN Wa is O~ ~ 0 +t Wa t ea - 10

W ~ So z-w bull HelllLc ~-J _-i -- ~1ecJ ~-W c

Wz-W WcW I ~_Wmiddot 0 1-kt beA ~~ olSo tJi~u -tk cJ~r

igtr -tke ~~ ferlts 4 WLJ l -to be eolheAr- eogi- of l u fcoJc ~ 1 1rllleP0rt

i CtrIz-) RottmiddotOW 1oJ1 9t W

- bull -1 II It-vL

e == Cos 1 gts = 1 bullWIw Eltot of-ike le tkn C rttr~JcJA

-to oJ W1 5 f l-C -~-c- l

0~7i-f ~

Li f~) ASS-teJ wt~ (uit) c~tctf

11 w W~ n 0 ~ tle ~-l cJe (at wi =Wzih~ l )

~ -tk trto ~~t ~O J Wt so z u

l- _ Wz-W C - - - l - = -w~lc-W t-w

Slworl~~ w~3~t ~ _ ]t +WWz t Wt W2 bull

-r~er~of -to h amp ~jl ~ ~~ lot C r~ 0 W W-z s l- C i (wamp-w)

---- -=WW1 ~-c -W(W1-W)

lt)irljj We 3 t I~-101Mh C-IVWC

1A~i~Cst

Let~ Wz~ W we ~ct ike f~Otl af ~f -tampjc--t ht t ~ i tele I)t I wI~~

(l+ lJti JW] yl ert~ -tle rey bull tcJr fa c To iIt tlaquojct

lIt cJ W is -L Wt

i(J~w) -= T(w~-~

~gt

CD C~eetfe( 0 is ~t tlv ornI reg CeV~J G is ct A-tA~ A3_

() I eurot- NH llt (-r~s rs -tf 41-1 ~- 1 A A A bull A tateo J n I l _ J i (~~Le~ ~Alll~b) s 01 SCt~eD u -pe v~GyueJ

(jOf4-hoce~t~ H l$ c AT At+ Pr3 (be(AASe O~ = 5(O~)) pound1- f lt tl~ A ~ fJclCi-r -to ALA 1s

i- A-A3 ~ -= At - A1-AJ A bl~-t ~ 1 1laquo ~ ~ r~~cJAt -to AA~ $

c- AA) == ~- A~ ~ -rktSt -fwo -ts W f~cf ltt t ampJk4J gt~~flaquos boi lut~~ u$~-f~ ~t tAll lAzI= tA- i- (e

AA = AzA - ~X3 -= ) t ~t lt e c At-tA T A~ SAiSfelt bofl ~t~01l~ 1eo t-= AT At -( ~3

17 N f t - L A+ Al-Ar) 6 Ce---+ef ~-tke ~-e foitrt Qftle $ DA l-

(be~oe 1-1 $ ~ ~Jro~ 4 o t-t) ~tCA ~ Mi-e fit arcc is -tke Ciolaquo ~t f4~SfS -tvnWJ4 ~ a Jo---~ -4le ~~es AtAl Aamp+~ As+A) ~ ~- J L -) ~) -

~Q 1eet qf ~ al-t-bAdcs H I 1 1-3 -=t ~ Wampdtoi~~ -tk ferllaquos ad ~e D~e1 ~~ raquo A~lt

(J~i(t~ ) A lltzlJ J llWW1-~ Ayt ~ito

Sol4 SifCamp ~A~R~lgttPLlCQA~ ~rJwail~e Arf A+cJQ+~~R20 I 1i~R+~~Pao C-t~1T~ZQ=-O

I ~Il I w e LV = e ~ 5 A ~t 4 ~b To ~~ fl X 1l s erltamptDI we CoM-rtf

Xt wl-t t)ll= (Ai~amp ) +w~Ct~iP )~(8+~~

= k [CM Q+ ~~)+ 1Yfgtt wR + tf )+ w (C + p+~ I = 0

~~~A I )( ts ~ (Rot 4 1 J~ ~ ~-t 4 -II 3~f1 C~cf ~ ce~-ter4cl At ~ (A e) ~ ~(f-t~) (ie ~c pOlt 3 -the amp~~c ~ ~ ~11t~ -G t- ~rid 1 ~~t AS)

COlf~selj Ikj ll~ 01 ilt G~f smiddot ~ fo~t ~ loc-s 61 )( 0-~ G~f C = i(Jlt- CA-t 8)) is -flc co~nsfo-kj lt Ov- ile ~t Clfdt

1-(t1J~ Let A~ A)e tI ~r~ 0t W1w) w~j I Y~ f~~j

fYo~ A ~ J~r - fe~~ -to -tkt -t~~ e to ~ c~tdt I

01 b w WI W 3 Got W bull skw~ ~est f~(tS ~ctCmt 1cle-t~~ ~s tmiddot~t t C)~

~otct~ JlCG ASSUllC -tL ai~cit-tle is -tlt kAtf GifC(t

~ h~ le~~tcJA -to t f~eMt oJ 1J -iklk ~ MS et--4M rll-tvJ~

bull l- A ~-A - WltWl t~ k~Wi -r ~- w - tV - 2 - - W 2 bull

Now WI bullbull f -ike ampM- ~~lc I SO Wd -= 1 i1e we ~ fJ~-te -tk ~n 4S _ _

~ bullbull Z ~ _ I T ~-t Wos 11 W + 2 Wl ~ - 1iIII I - - w

2 2-

F-oN -tk5 t ~ ~t -tk yoil-f N Jw~ -+ W3 $ 0shy

--te e lt$-I(C -t1e e1f~sS1W f Ns Sr~t~c ~~ nSFt -t oJ Jt Vis we (4 eot-t~ -tMt wtl lISO e O~ -tIt o~-- -two les -t~ e-Fc~Sto ~1 tJ -tt l s u~ -t $ -tle (fwle1 ~ -t~ )1 fO~~ (tce ~

J I W-z4 _

11Ob~ ( S~~t lYe Tko~ ) let W be D~ llt (~crclf ofJ ~1 13 c( PI Q1 R

be ~ iut ~ ~ lC ftJi~ ~ W -tt t1I 2 ll I tl ~ I ft ~ec-f~Jflj slw ifvt P Q R A-e tAl(Il (-ps Ole 5-

clt~ A $~501 11 tf A ltamp-t) ~ W) i

~ol~bo- WamplAi loss -t 3~nl~ I Wt J lS$We Je G-nIUshy

Cilampk 1s ~ ~ cttclt ~ lll llJ lls -= lw I ~ t 1kt k ii ~s ~~ l+ ll~ ~ Ii t3 --ie r~~ fw- W + 1~ Ivs ~ f-ltl ) i tJ- Zt~W So Sol lkcsc -tcdr W~ 3laquo l = ~ t L + W-lE W

2

St ~ Q ltl ott ilW --l 1(= tt f t~~1l

I sluw fQR 4t CttlfUf it S~s-t st P-R =l-amp-Nil f-R _l- Z-amp-~~ Yo-~~J (tI 4W -g ~-R

Q-~ -1-1)-1tJ --l~W X l ~-amp~w ) l2tgtW-ltl~ -lZ+ t

4t~ w- Zl~-ll-t It f- fl

- (1- R bull

-J clt~lttii lw=t ~ WW-=i

CiiID ~tlt~ firLiA BC let 1gt be A4Ie GtIlOc1tf- E 001 As loIiti DEit-CB J ~ F ie 600 Be I

ciA ~fDf oX ~~ o-rbmiddot 0 1 ltt ftt XIS G(( Gr be 01 EP ~tS~t ~ el~ttrlgtedo-r W~~~~fk~t~s X Ao D C fSfoFc-=Ep-=BYc1gt=r

~J ~sted oR we rMj Sity ~ i 7 middot PrDV~ 6i-F fs pcmI(e( -to -Me 4 b~ 1 -M CaJamp) Xl= Of-~ -tI S~1 je Y-X Sol-I Set 1ampt o~ AtAo tt(-~ IMc

For ~fS X It we e Ix-+f ~ lxl +111 ~ft Tie E 8 Gfl = C ot~~ E (0 r)klgt(d~ 1- W-11IAy f X= ~t(r-s-e t~o A~ F tB t(f-t)c 4( euroj =tE t-((-f)J) _ h Let Pbe 0 poillt el LIle )( f lJe lter t= B _ L _ amp1gt g + (_t )e~ middot gtY haYCamp oP=toX+(f-t)oy -f=~y ~ Be -- r -i1gt-t ~_

J J gt1( 8 -I io O~)y~ amp(01] ~ P-u SfjllleMt Xt E retgt I $0 IE-BI rD-cl c1

EICjl1t Call a ~1IIecent ~ ~ QjgtWelC ~l~ (I- ) Is (E -amph 1l ID-d r-(t-amp)(c(-f6-Jgtfd tl )ltLJ )M ~ ct j~ Ie ~od ~ orF9fe sk~ J i q F- Gt = t6-p)~+ (I-t)(1-9)C ~ +~hw ~t cf -tk s IIf-t4 Jgtllrl1lpounds Of ~t(tei _ IS tlt-p)amp1~$ htfampt iits~etet ~ik~litetllllorltl -tlt-p)la (amp+~~ =(~~k1NIllelo I _1 t f4IIIl ltf1ltS

Sll~ fir trl4t~ A~c~ Itt-A IlIamp 1M OjL ltf 114 (tw~-for ~ pound Me~ --ik se ~fOW twI ~ _ Igt IC-tO - f ~ if

T -poundTI-r -pound ~ I A=0 1)~D i(1el IC-BIt lo-dtll)~

UI8iC-1gt1 +11Hlt-at=Iel+ Ie-IgtI+11gt1 +1c_~(f~~t Wt ut Ie+IC-Igt ~ Iamp+c-tgtl t=~f1f)

AA IDI + IC-61 ~ 11gt+C-81 C-~AO=~8C) (gtt) holds ~Le~ft~~lcJs A81(1)C ATgt Usc _~ __

c6hf--I--l~1gt~ ItiC

~1- ~t fmiddot~~ 0+ ~ 0 ( is )(Y=tJC( (1 rsti - Ex4k+ Let 0 ~~ (i(cAt cf 4ABe 9 ~iIt J bef -fIl lfcffS Jf -IIf (t) Xi=fX (y+I)zmiddotXmiddotZ+fmiddotZ 0( (cXl-Y~(Xmiddoty) ~ I~~)(middotX I IXmiddot~~hd1I O~iOf (=) Xmiddoty-O ~~~~~~~~~~~~~~~ amp--ft 3 Let A8C b Le lmiddotts ~sfmiddotmiddot Phe

Ac~+amp~+A~-t8C~~ Ast+ctl SJt~~ Set1ie Ot~I ttt A ~~t f Jw

CmiddotC +(amp-lgtHamp-~)+D~ (8-c)~-c) ~ amp (c-b)laquo- At~(~- awl lt~~-f4ls s fu ~4S

(6 C-b)middot(S-C-lraquo ~ 0 ~~ck s (amplt-1) ~o

A ~t 1gt Ie -tLt poit ~ Aamp -L II ~ e _ ce~AAcO

p C fgtrcw _t C1gtJoe ) AS-AC Sol~~~~~~~dO~A

A a A J) A J)= ~ E=~~ =3 +~lCJ1gt-C=Aamp-2C

C1gt1 Oe- (A-tS-le)(Mc+1raquowO c) No AA~lh c C C(CUM(bull (IampSt 8 41f1$-bull (4) bec u Amiddot(Q-ltAB-ACO 1IeJtt(~) ~ OAl ~c ~ A~~AC

euro ~ toJs ~ 8lt~ 1)-A69 seAPS fWlkl ~JCOc $ firAABC jf( t ssewu-J -ptMf ~ c= - ta-+CmiddotfI AAS( its ~ttd q ~1 - If We Sampt -iU CitClIMChH- 0 AS ken -HII-srft~ ~o -t r -11 __ -~ -1 ALh--COtt - 7J 0 OtlGCnx n - ~-

A Fit iAcetft tJf ~~ c 0( lU= ~ = L

co b AI c lt-c

e ~ 1)c 1gt= te+(t-t) C t --amps ~1i~ poundL = tD ~+ cC C bI-c Gte middot I t A-t -~)tgt t-ll- A

aAtlS cc_ - tgtA - M~C 14 e middot

11l Lqt-(gt OmiddotkC Gtctal ~ICef c(H ~r J

51_ Set 5 4lt C4fColt_bull tu e -H Matel~Me1~ 1~ AA+b$-t C shy ~ 4~(

Lampil~gt 1omiddot~(i-1)l4-1) lt0 A-A 6middot~Cc=(tlJ 2ec 6amp+cc-(a-c)(amp-Q=k~middotIf (A16i)riamptc~ Rlt9~~ 11- 3( h_ Imiddotltl-C) 4l- 2(~~(H- btCi)tI~)) cttC

)(~+c) (-1)((-1) =((~ t1 -Hi+(() lt 0 of -~ f (ib -t-e) lA+Il+ ct )+ilaquoc gt~ CifI+cl+Jl(c)+ ~ ~ a(-o)(--G)-4-~-c)(b+cc-4)~)gt0 tsc4 rc s

~ Ike fRS ~ f xi xI wt -Stl-fculot 11-$9 (t)=LXOY) 0( tiYfft~e~ -fo -tkt fl~~ 1-- oxY J e

lti) ~ -f~)( ~f)-a)( l t Yltl (c~wYcxnyJ (j - )(~1 4fT~ A X0( V~~ p A of yl t1ft 0

(6laquo Q bull 1 lj 111)1 (DW~v e

eJ41~ Let AAA A _j A 1 1_ -+ V]nq DO 4 CD e I

- its ste ~tS p-Ilt1 ProiIla-t middot ClrtllAA1Ar oreAA AA So(u-tVf SeL ot - ~ -_amp I~ _L ft--A A ----- ~ fJe ~ ~ --fI 01r~~ O4St SMs ~qIt ~t)~csCA-A) I lA_-A f

E)Ctl-eIlaquo-r Let A6COf tgt ~~ pe-tft Qc e t

~~~Q~ ~ 1kfwlrids~ A88CCIgtbEpoundA 1T~ -r APamptl~J~ le ACDIIIampf6i -laquo s~O~ tk-t ~s Ooet is so eM eII bullbull ~olt4-tfN ~et -ckt O~bullbull~ rt -e ~_W f~ S~

tJ 1(t0 AXC ~ AP ofe (o(iu o=A-f- A(~ J C- 32s amp A

lltc t))tA SIA~y 8)(1)= (1(8 CxE~ C I

raquo)(A 6llgt re EJ( 6 =CcE feMtt I

eurolCAJ- E)(6-t( - ~lte+El$ ~ pound10 eImiddotmiddot

1 ~~-A~)o (As-AJ1gt(~A~ S ~~CI amp euro1tf6lc~ ~se Ac Adol~ -t(t-t Lit set - () middot At

At~ t ~It~ AsIC~ Al~-+yen+yJAI (

_t a ~ - bull

~ 2-shy

I _0 c A 6 c ~ As V ~1~Ut 1 Sjtllc -fb ~BIC~ fW(t

ftdle ~ts of BC CA AB ns~chvell -tk ft1~ -tIua-t

No A bull G 8 A I ~amp Ca A~ (orr eU egt~ 4~_ A~itlA-~lClA-As~=(~tAtAr-tAjcA -~~ StthtlI4It ~ SaJc1ttA

(Nmiddot~~i~+Ar~~l ore4 l1A AAs = Are 1J~~Ai

Aft13 amp11 C=A-ttils-A)frSollletoA~] SiCt AS e Gfe i eRe

o~ (Bt-A)K(~-A) - (A-ttz-~tl-t- t t)AxB No ~~=~~~-=amp-AH-t)e ~~1 S-a-= It-t1)A I Ct = lAt8)- c tlA +ll-t~)B ~ (amp-AI~I~(Cz-~)=(t-ttl-trtl-+t~t))Al(amp~O A S~ CL At( ccdllfttor

~t ~~ 1~~Pt

o

C[~1D --r-0 vetlOf) )( lf ate Jt~y wtt-t---t f~ t -flat ~f~ ClX~yO kAs 01 Soat~

AT 10 o T4 s tktCcStI ~~A rf KttO ~ X0 f Art NIt Co((llteor

F4t IT AX+bY+c =0 ~$ote -e 1~I(z-s 4t4l 4-+amp ott -=0 J ilQA Xf Z 4le cbullbullI btACcS( ~l AO fIe b-tc-o w X-1-KZ-tYc-6Z

(~ar~11to(~1 wr~t--J Lftai c~ s OAAampA Co

~ OeLamps 1f 1 -1z- Aa6~l~8ampR AsampIA~= ~ 6 8-c amp-S tltcl A DAR 0

~e COIIfttAt t ~1 =- 1 ~ ~ P Pl) P3S~ Set - orlll at o at A8 btt ~trs Ale LIDa (ampfbv~ ~ A~ rA Q( e s So 8 1-t S6Wt (s EIt Cll No

Pl =tAt(c-t) 8a trA+ (ct)s ~- ~3 lAAt-tQ-) 8-= tA(-aA+Cc-ct)S a S~tU~ ~ 0= ltr- CArgtA + [pound1)l -(I-I4)$]B

A~ (tally rcf~=gt tr(~ Otu( (l-tl~-laquotlt)S=C Solll fott ol -tit pt~~ -+-s f ti ~I~Js

Nt ~~e ~ 1tu~~A+ SoSzCt-rl g$t Vs- r~ r~- r~1 Pgt1s~S)A+~s(tmiddotgt8 R= rlrfgt~A ~(I)J B

Y~-r)S) ~6a-t~S) amp c) ttS +fs-1S ~ p~f~P+~sampf-tj~

~ P1 ~se~rw)~c 0 Qtlgt+CoO ~ r fL cU-1- fc-i (ove

~ 0

A - -

~ FOf~lamp~

(1 -laquo ~C

fot-CA~ to ~ t t amp -t~~ crt a ~tc ~ El(tend~ltl St L laquobe ~[A8Cl Js~~i~ R= 4 C

Let ( ~t 4ct nwts lt 4e GoismvmcJt i-R- tl 4J~)(fo~of AAsc Sr ~ l=~~Yslt) ~ bc_

S A -- - 0 21 1iltelaquoe s dolAt C~d~middot ~o~ uI1gt ~ s~amp s~~C middot T 1_ ~ rI n -rf (i-- shy

tl Ie or~ DraJ clmiddotae~t 61gt 1pound Si ~ A= ----=algt i IS lle~ ltJOiOlSA0

~~~~~~~~~~~~~-~~~~=~~~~ p adEr-l-~a~~r~ A- oS+- jtus c~ - c e c I) p(]) Let 18(1gt L~Ms

I4dtt rAsel Or S~8c1oI(lcl~ 1leflAftt Let A6nct)p -r1 ~act 0

~Me C ABC ) GlUo~kc ~ PAx P6= Pc x PD = tl b~~=Abc bull P19tpound Note L APD L (PB

4R A1BC)aHd~ckLPAtgt=LPCBS=tfA-tb~~) is ike seifieAc ~AAPDACfB~=~~ PAIPB=fxPD

amp Q C Of 4A8C Lri pc C 1amp-~ ~~ PC Is -lt-~t lat t lie i4 jCbullbullr 4l( M6C Qt r Ie -i4~ to -e -fde ~ A A8C if (JJ

C)~ ~e icltc1e ot AAec ~e p A e OYlJ c fCL p~~re [Mel =[ALel[~cl+(CI1= ~-t~+~=SIr ~ Not~ LArc=LcPB

I-tfllWlbull [A8tl~ S($-11 ) (s-b)(s-c)middot I pCs f~ot -to LACp4C ampP(~ Cos C= tt2ttoa-c (~AI Ci(~ircl 4 MBc B 2shy

[A6Ci= ~SiIlC=Qr(+coSp(i-($C) ~AAcPACBP ~~ fgtc PCPAlltPB =(Cl~-+Iot-c~t-~a~-9 ) = catlo-4 t )(A1(-c)(CoHI- b)(o-Il-~= S (s-c)(~~

2- ~ a

Ci C [AS(I A 2

~

I

~JJI LPFA-=odeg=Lpe~ ~ amp~ ~LPFeLPAE

C5Ji) ~tolt1 s-ThtOfotfll Let A 6c~ ~t dlSncf ~ts 01 bull ~c ~o - Me~IA~ 1( bull t Of~~~I ~Ot bull -Tht~ bull Sa c~tOV M1 C(liofIPT potd~ A 6 C Iie to

AI 6 C 1gt (1~t~c 1gtpound fCLR atfmiddote ZA ~A A ZA bull -~ -iA ~Co~ PAQ~clf$ WeA~ ZA~lA I tc Z~t

pFAECc1dk

bull ~ Srlloi(y taCgt6~~~-lPFB ~ pG~ f CDCCYcbull LPampb LPFI) = e 1klaquo AIJ~P LPAespoundp8C pfE _ LPeP 8EF (0(1ltlt~L PFE L~8Tgt~ LFP - L 10 collirAfampff

)fgtC)~Jl~~ ~ ASC1HAol6C=AcS]) bull (~~_ ~ktI AeCO At)ItBC ~ACdtgt 1)~c 190pound 0 sWLe AB UJlfsftfUct A ampA6

S~~41 to flCAP 1I1elt AB A~ 6eshy

6 Ai - 7ligt= (1) lBAE=LCAJgt

SO LMc L BAlgt-L1gt= LeA1gt-LMe =LEAt) Tkeuro1 A8AC~Ae-A1) So Rr-c EDAtgt~A Thet Aec~ A~8C =poundItampE AClC E~ AC80

bull A rC =c Sf-t Ell I

f1-I-4j hoW~ ~8euro~EtgtS ampb ~ E iUt~( SO - ~~oeA~LeeALtgtCA ~AsectCO Sltffc

SoSoft ~oe 1et~6cP cl-ampd-p~ 0

tI~ Let l)poundF fetf~~ff- P~ ampa Aeyen~~ ~

Asse ~Mist (so4 is 6~UA_JC ~AGSC ~O bull G ~f( Aalec~o)

tt~e9 7eff

fovlaquos X I Z ate (es Aamp ampCA D ((t~ve-()ty It X I Z (lie (dl-lflOr

A ~f f6 lhg--1 ~ xe YC LA - middot ~ lQt Dbu (~ Ac soct1IIt 81gt II J( Z -r1teuron

~g ~ ~ 1t~ ~z Se AlC 6Y c~ _At P1Q (i~ ~y Ie ~c -- _______ r tamp iU I bull laS yc fA ~Igt ZCZA middot lCI~ lIeeu~ Ie~

If ~ tL ~ =-1 iIamp )( YL MHo l~(~ Y~t~~~~ SlJ) Ltt l~ X(OCA -Thtl b Mt11Idtw 11~ Ax ay CI _ lt Cz Y Cl iiiK zA --i ~o --=-l1toobull CfIea bull _Cl -a

I I

ceDD ~MelI s lIeo~toA l~tA I ~cc t) euro ~be tc~ lO 0shy

de lw~~ ~( ft amptCtSSCti 1 tf (~ diC- (~QEf ) bull

t p Ae ti l)euro J Q Bel pound f 2= Cl)n fA ~ ~k ~ Q1t ottc(l(ea~ ~QIR~~~ -

f~ 1 ~ ltt X~EfA 1AMCD bull ~ z- C~neF Arr~l ~(atts ~ff 1e-(fM1oec~ FA

ftt- Ool~~~ 4xf l w hVII

e-- ~ X K __( It X2 ~_( t ~~II Qx 6y Ct ~y pzex I fllFxijmiddot 1I

Hul~pr~ ~ AIl ~~ tfffSfctj cofI4t tt XA)(B XEmiddotKF J (CmiddotYP=1AmiddotYS ZEmiddotZF= zeZIgt W~~et ZQ lSf~-i igt PQ~ ore rlfltelaquor

Qx Pf Itz loy c-enc ~Mee(AaS

t-rks ~ere 0 Imiddotil~ (1$($ of PoucJ s for It we tftwt Ato 8 -te I AIwIJ (3 il(cJe 1Iofl1-t i AB will b~ ~-t1l3et (iot ot B ~ It~j CIt~ we ells JpoundAoflt ~ t~ liflE Clt B b~ BR

6lCtJfC i F~~ h Cf(Ultirc~ ot Mac J f(it 1) ( ~ ~i~0yen ot -t4l~lE I~ ~tA - ~~ Be ~ e fM 1fe ttusc(e~ of-ffwf3ct (tt4-t C3L1r~ CA~ F= bt ~ ttfStd~ of -tINt ti-~-f Imiddot~t ~tC wo( Aamp 11161 PI Ell F o~ ctU

Soof~fIyen P=Mo 8C ~ E= BBnlA f=CCnAB APP~i P~f ~ ~(fo MB See I fott et 1gtpound f c-

-- =JSiiiiIii

b)lAtc ~ Let-tgt 0- eht ~cfs 0( dt101 AtCS

AS ~ AC O~~e (ilcu-R( Mac ftspciwJy l(t tgt Ilt ~f AtC sCI ~== DPn SA J R= PEn AC fro +~-t lile QR~s~(QVJ14 fttCf+~I (~ 1) ~ f9bt-Mshy~e 1)rff0--AS- CO ~SfctsLAc8

Co ~r ~ qftllCr At =lgt 6 ~LAec So 1= Cl)n G8 Sf_ eEtS

Q tgtPt SA DP 8ital R= Pe C Pre ttL PlE AI

AIP~ f~l ~ 1Ito(-to C ~ P er ~ w 1 ~ bull 1I

t Set I Q Rut tIff~ Co~~d~

~ -7

Alt IXu q j

elf (Ga1(e 3 Ltt AT3CPs e ~ +s tMDlCJe ~-rd AAfLBS Bat LeA) ccf LAB fat 1gt be ~ls (I ~cucl1t ~c4( I

DA(11)C= AU DB()CAe~ 1gtCIAB~ fgt~~ A~ r~CtfaJ T4 6v~fi ~ IAGC a~ Co((~((r

~olf- W HL-cI oy-((~( ~ AA Be Ne

AAIB~I)Cc(-=I DArBC=A 11gt1( ISc AtA f Cc -= H L lAlA I C I Cl

1t~()cD=C1 ~l (AIBl (cjAfrrr5~5Gl ~~ t DAAfCC tgtlt Se4 A HC tit c11ilaquoraquo SIt 1y ar171~ BS41s(to AS e 0cc we Su e H 6ltve c1(i~amp r A~ H C~ S4rt a(((~4~ I

-~ ALI)f ~fle1 tt P toe a ltpor i~4Mec

LtfP I~~ff~I$f- 5 -to ~CA Camp ft~t~ lttt bJ() ~_ eshy

ll 10 ~ fet ~~~N~ c-tohs API sp (~ftvtll IfQ P ~ 61bullbull Pt14 PttNQ~~ (tries ~tll~ Qfz cod A~ aft ~et

iSoLttd- $(fCJt L CPc p) LCQLP LC~P Lc (gta Palt-e J -t ~es c P ~L I PI Q p 4ftcocttc f~AfrI15 ~s middottU(Woto ~1l$1 w-tSu CPt ( gt e-= A ) P t1t( QIP= X ) (Q-a Pf P2C-= B 4re CoI~rtelr $6 Rb2-l amp1L ( AB-=Xmiddot ~ ~lIQ P~IA8 tVe ~Cqfre~

NewtDJ S

~A ABcOS~~(laquoteJktvsa e ~SQiraquoeamp c~tkt~~ ~~

APgtsc CD) PA AXcpotlts EFG)H-~t~ C F B ~ACG~FHgD~~r~t

Sol~tcNI W E6nFHO~ Eftn FG ~X _Apply~~ ~~scJ ~ ~ -to E~ltSJ F f(f ~Sta E~ () Fr =0 ~~ ( 14 1) I G Fn H( X are ut(ltealf_ ~ltfcAy~ltP~CA(s ~e- 4 E6--()FF~~ J ~S14

EEn FF~ B euroH nf6=X amp-t-fn ~euro 0 tUllPtfcmiddotc4t

-nus ~S 0 XI oJB ~c((e4~ 7itN pound4 fl Ff n6D=O SlAry EG F-- ( AC - O ACE6 fH6DCPotrclO

1)ec~CAes ~ 0 nfAaAec ~ JACc) M

A c B actgcP J CAnCpQJ AampnAgR ~r--+--Ir-~~R If AA 613 I cc 4te ~tVt-ct ~

A e 1-~ PI ~ Rctil eo(IQ4(_

c~ rCP_ R2esrk ~-s ~ -tyenUL te~ 4 ~~cAAfIdgre IfV --IfU ~ f 4s root G-oIer ~Ns c~ AOAB ~ftJJ MeoJ- -~r ~ et QPL AEa gil

At A rltamp -7---1S ( rt l g 0 () I 4 ~ ~ Ie Be Cctf~ Lloec Ilfct-Jt ~~ C~ c~ IJOCA ~ 1te(J C~ BP Cd M oct ~

B8 PC-co ~-( ~ No CC~=-( ~(ff~~~sctmiddot~~= - ~ (IC4M~cfMtl~~~ote- ~ et eampI c-f(er

62Y ~coJ A~s tttt ~Cct~lI1tr

Let Cn-les C ~ Cz ktwe ~~t ~~-fe15 0 ~ 02

Sf 11 4st f( J 14 (cs of ( OotX w~ 1

fe- ) t ~ lt twitt ()~ -tu Cl

eo( C~ ~Ilt ue 0 K- r 4)-~ J ~ ~ li~ f(~ok( -to OO~ -rtgt Is -4 (~~a1CSof tLt -f~Cnrd u

MOtse ~3 Crce~ CJCC1 W~~ OJOaoJ(h I~ nf CiamplttJ -tfe 3 ~ ltWQs ~FoS offI Wi( i~~(JItct cent Do fgti- ((lt d4 vaJOJ aftftfT4crtfes 111$ ~It lw la-I fIwe wi(( v-espue to 4((3 ccle$

G7~~14~S

~ If 2c(c~sCp~ lte~tAt PQ ~ p Cl aJ hss fou 0 411(1 yen

middot~ Ot J To Co J C So -ky tore eM ta noe(tk( ~ 2 r(4-~ ~ pIA i~( ~~ oS

~yenI4l~~~

P------ ~ c~ Lf4rdes C e d lifest J e we c- tltANJ A f(rrzl cltJ~C

~~ ~~~eAJf- 14 1

Ci-- ntcl ~~~ CJCl ~ CCsII i~~(t et -t4 ~ C4tt p1-Cch~~

~P~ f LoDa is ~er~ AK~Of CCz _

Let ED be ~~~ foSflctorf oft B~ MaC ~D ~S~e AC -ri Cau~tt1e c1A8JgtC ut ABtttE J(e ~ cfC4c~rc(e c1 AB D MflId 8 Ccent F-=-c --r

D (Olt ~t AE =- CF So 1$1 i te~d~ c~ ~gteJ AE~AB=ADAC II CFIltCBCD CA So~= ~~

5 ~c 81gt fsecfs L ABe WI_ Cl) ~ _ I bull It rJC AS - AD CF- f1C

------------------~ ampA~fel Let ABC be ~ ftrJMIj(e ~ soscJes 68C[)I

CAE AASF ~te~(1 to AAsC wi( ~ CA Aa 4 S bu1 tsrtdvel~ Pro~ta ~-t 141esff-1 AJSc ~ t ~ I~es t=F fEgt DE ~dJ ~uc(~t

Col Amiddot ~ SJltto i Late ~e cnl~w-f( Jgt4Sr~ ~ IE ( - eatu r4~ ~Cgt cte

a~~c~~ Iof crde middot1itE Ultoofe Y04oc Jl Y l AE=CE ( tel btcte(~w-I(Fu

c~ Cc~-tr ~cL~4S AF=8F - I -r4e-tltlfte~ A PUr~I T (~ff I ~~ fiIolu ~ ts ltfCI C1 $f lltty ~amp~ 2 lies Cltt VIIIt~~ ~c c) ~ roampoIaJIlt) of (14So -tkey ~u(4t fAa ~~ Camp~tet

63DP I

r ~e A ScIampf~ 2 LtP be 1ft l~~

~ Ii~~(-kB~lIc(~ -to FD-f _ bull 11C ra(~~ to OE -tt~ fOIts frolle M 1 Elf c(frelttf

S 7c IL ttgt ~-JC 1l rgte ~ t

I

I A~ C~ $oIf1 Let ile cncrcft~ J) ~=HF - PD eF -61) OJ rD-peuro-C~1 EAtlA~1eSamp Ql (A~ AF =SF I CD-c CEAGJPF t 81gt

2 l 1 0 F pW~ ct - fE =AF -AE S r~L pound ~ POtt 1 ~CAty4W(t t

- t_ EICIt1k 3 AC--damp l-H aat 0 P~r -fl Ie A4M C ~ usc -t ifegtSltct ~- Ae Id t W S let

Be It N Let 1k u cudcl 0(AAac -lt1 aNll~Std ~t B t ~ middot Pe ~~t OlUaM

SoIwt t ~ C4Samp 61 Be we6~ 11 aM i~ ~ ~ftthlte Qt S of cYG vtIeof poundlASC 1ICft OM =oel 8M

A~p BA18C i4e c~~In CAsamp - AUN AAec ACfo K~ 1Iotf1Ar (S1Cc iMruw Ibl~cto~ L kll Ac AC Jolaquoaret tes) s e rdeo( I

I

pound I ~e AC kN J 8M Itteet 41 4 (IOIt P I

Siell L PM N L 81lt11 l HCA s MIC PAte CDhcrkcl Q ttl I t fill pou fOitJ BMlC ~p 8M ec 80- yo Y=OA

PM r8- PNICPK POamp-r~ bull ~ $Jtmct~ 1keuro92 Ie -t 10- eo~= ampf(tM- rM) PM - 3

rJ It

OMl PB lr F6 ~t 8MPM+6I1I

OM J ~M

L I A6cb be i$(~Ibullt co_~4 tt ArllAofOo Q-t d - amp c~ f A1)1 SC ~ f (aros

Ccle i VI ( 4 E f= ~~-t t I~oes ampe Q= f-o -Ie C

8y po -t fI-t~ Po~_~ peltPD=PHxPl ~_ ft QClltQ6=~d~Qs~tAcff we1et Po~-Qo=CFM-ru) ~ fMQ~ -ns i (Ies 0ML PQ lQMO Itf oM

Ntrf Csd tIe C~C wi4 Q0 As d-cr~ 2 _ bullbull

It t-sses ME F SlAte LampMO LQ EDt -lCl fo s ~ CIC-z Ef ~ Ef -s iU c($ ef ce Let cI has ceth A( ~s tt lie

laquoa ~ ~ t JFPO _r - flMx pQ fiCa _Vi ~ P$ 01 ~ bull0I

A(Igt~ ite-sect PQ 4t M +Q -of leM _ LA0(= l paceW ac- ~ 8I(C ~ lttlclc p ~_I c 1_

let ya~s t Cltn~ I ~_0 =c bull t if crftit C fc$wt

~l~Sshy c1iW ~ 14- - l-l-~t1 A IS ~f~~J i AA6C J 0 i-tala

C(cuCttdlt~ 7Le -(kfee 4-ttJes AP eamp tMJ Cf irUktt- H EDAA6=-M FDo AC-N tp~4-dcent () 06Jl)F )OCJ1gtE

N C~) 0 J- M N middot i

Solfen bullCO LAfcc9cfLATgtC 9 A fgt l=~C6AtyJrc TktL6lgtFcLBAC AooBc-OCi--ees LOBC-=J(t~Io~Leoc)middot1tl_l8A(= ~oo~L8bFmiddot F omiddot Iamp -=gt 08 ~ tgt l= ~frly DC lDe-

B 0 c (~) CLMA ltPgtM~MIf AC~HI () I 81U AlA ~ NIi-IIIt= Aa -AltlaquoJI tgtA L

F ~c ~ l)e - ~ Aa~Ac (c~

~~b )N6oIp 13Ai~80-- OllADI (0( 1)04 ()-(~)+(()+ll)-~~ J)M~ ~_cot=OMOt)1 te

bull Ott J MAl N~-11 fI ~=C)jI 6lf1

~iet SoU- ln LAFC0 =LOC-dJACl) Fc-tkc ut J bu])M So ~t TeI [)f -ue L Jeo L 6gtF =LeAlt ~ J-f4 a~t (~e tB

4 ~t~4Yclt ~ JNle gtetpeId~ bs~CtoY til g 1 I J 1) 4te 0 ~J

=gt 0t3lJe ~oS i DF Q(A~ DCLbE wHk ~ CSV ftt Ae efT I c AC~J~DI ~ (ltt 6e If Be I I I 01 tl( AS 1POW iI f uIlh) SrlOCo Ae1gt = aq rW1d1C by d~ l~testJ~ t4PtwI- Let lc SAe -de -CA k)sU AABC f 2AamptI

NA ~ NC NF ~ rJ SI AC ~ dbullt ~fieaa~(L ofM$C ~=~ so tr~ of ~ bullbull ftc~(eNs() ~ ikatQ~oJ CoxS qf ~ Grtles Q-14III ~ if ITI ~ YM~(-l A~s 7I-e lmiddot 11M rOI(A)C1lt D ~~(S liIOH

r 6middot 1- r IAC- UComiddot

041(ms AhOYllo-lety wi1kceterO a-J Ptto k (cltwaof-d ~1 H(oJ 1lt) ) is Q ~CI itt setVls Jllttl r01ht X 01 ~ plAtte -t 1ile ~c~ X sampcck -tk~t OXL~ -= ieoX ~~rk~ It kl~1)~~~~ti saA3Jkf~ l-t lFl ltl J ~ -tk kPJMDffty 5 ( ~ A IrtySe~ Q -~ f ~ - ilc ~3~ ~ 12tlgteuroFbe~Js~8CCAM~ ~ (-((Ali) Secs AAsc +0 AAFE

amp 1gtJ C Let q Ie ilaquoo cttIL 0 6A-QC SiAte GiA =-2GfD GS -2GE ~tqt=-2~ s ~) ~IAbEF f AASC EXAfe L L AABC AB =AC A(iRl IS t -t t_1y to tIP cnuantt14MC4t~rMs pte AC ~tf~s P Q~ Pe 1l~ 1e totiJpoNltt (fQ

~114t llCeftgt ofAABC Sott~Let 0 bt 14 cgftt ~ -

) rele Lt 1gt foe ~t3et totlaquo 6 c 71 -t4 Circle +ipound Clttt-atd l4AOC

S 1) l3~yf A-trot ~ PQ

ADfAt -= ~~~~=~=Ic S HcAl)So04s I ib 0 S111tt O~$-iLalAltbullbullfMc t ~-tl_W-~tIecf-

CfajiV ~~ s A~t~~etsVI At AlAJ ISdVt4 well -scfes~e l A az (i) (~ts~ Sltk Cif(IOSitc Ai) fW IZ N ~~+-~~Re ~Ill~ ctrck ~ fMlf a c-~ ~lt 0 c-I

II~ iw~le laquo 3Ie -tno1 eel Ct rd -to ufS A

~ of stJes ~u+-1- middotfDItf-t G 1Cf ~fj -t4 (nuCampolttt ~~+riAe ~-tIa ~~it cO (6([e-t etft

A ~t Let A 6e ( It ~~scf 4~el cltlu ItS 54014 1 ampJ y be -fl- ~offu arcres SCrz

e ~C At otamp r 1A~f~~ ~ It 6gt Ilt

N611 Ae ~tly I B~ Iec t CAlieA Ids A is ru~ ~__~ Aamp a-( AC I So AAIb~Stt-t~ L fMc gti((y Mi~~ LMe e-l ee ir1kcts L seA So Mo( ern ee=- (-(A ~~dAIC

AI (IOOoJ 0A I De = ae r So 0 ts-tfe c~af of AAe d kt P~c4rc-ctr~AA6C

1k ~o~1 ~ (1 A) SeLs AABC f 6Aec ~ SeJ t~

scre-~-tP~MOC-tc~ OllA~~ bull middot 1 P 0 ore co((eAt

- fiscl 1( AASCGs ~IIe1lt ~~~~W (~- ~~L ~Ioc L

- L- ~ bull - 2J~ ~(IC= 8(~(s-lt)

ot t Ii -l 1pound is -(I ~K(~ ifCirde ~ Ill laf S bt-tl nf(~ ltgtf I IIIllyeltt t ~oflA bull

~ (e~ M s M~SzM)S3 ~~rrelaquo At s~ let 6 ~ bullt _ r

blse~ 4 poundA 00 ~-te 4 We c~ S~ SJ 1 M MJ

A 1iamp A --To t~t iampt elite- o~rf-tLt (i) IIIiilsrtt t Aamp1le rtfItJ-f 1 ts S I Co

-tIt vtt4lfO c4 -rs T~ ~tCf AT AIT~ 7iIese if L1I $ =ll~Imiddot ~iTt~lltSl~~t~ L T t S~-LTITa S1~1

(i) 11 A A ~ $S~ AA i MM ~ i 3 I ~ A T~ AI S~1 ~~ HzMl ~ ss I HsM bull ~ co ~ffWbull( ~dSr Nect CircCl1C(~ ~ASsz$3 reI 0 AA A~l

Ctcmiddott of A M~H IIbtepofcrceS~MAJ~r~ ~1 fLAA~AsrL f2 J ~ VAdtoos ~~

Z bullSo --Gtdes ~ 1Io(~ Ll lB~ reggt ampSt~~ AMMz toil s~~i~~ ~lt (x M- SLLt Ill ~bullbull04 S 1-ta~X l1c H ) Mz $1

~=(lttc-o)(c-M-~fl~e) 1 M M amp41 S)Jltl~ UrJ~Cost lt~~~~~(fo) ~ ()bc HSt~Zeuro~X

CT1tW EtA-f tt 1- bull ~A be ~iAt 4+etse~ ~ fwo nO~fD~fUtf Cirdes C ~C CAl-~ef0 0 (tltjreJ~ Dtte ~1MtM

~t~o c eamp 1d1t(s-et C cent~ Cztlt Pt J(e -i4af(EV (A~ ~-t-te~ctc At ~Ca~t QI Lk Me t ~~it-t~ ()Q o-J ~ ~ ~itet ~ pzCla

~-t ~ LtJAo LMAMz

~~ ~ ~

SGl~ B-t~etJ Plpt(gtzOt~~O

Ca ~lJZ~ damp bull nwy 14(0 oPa ) Q SeKds C L 0 PI

~ I ~ t -lO Z bull ~ J ~ OAn Ct =8 ~~-oflt~1 e $ Ll016M -tLl~A~~ So LOI~= LOaAHa A~ t- fs 0P 0 P ~o ltlie sjI Ie~ 00 Cgt~ ofL ~ ) 00 ~O~e-=OPct=OAIOg

t ~te~~-1 cknl4t1 ~ AO~ ~ Ate ~Itc

~ LO8M= lDAM

A~ I =gt LoAM L~AMz WIAamp~ ---

L 0cA M~ ==gt L0 A0)- L I-i A Mz bull -to _16bCrfkSf~S

Solt~p Wpound(CS JTbe reflec~ ~ S Wit-(S~ltt

fI5 Mis

~J e

t ~lwt Cgt (1Of ctImiddotd i -br3frt -+0

e $ f(~

Q cmiddotnI F -tkt bcs of tIl YOII f Sue- fut ~e-re ~)f Q

01 ~ w~ M ~ ~(eoi~ ~ l R~~ QS ~ isc~e~ C~rdamp 4 A PQ R

-to M Lt u be 04

~ A$ iudQ~~ltofe1 middot~~(R C V Lat ~ 10 ampl yo~t~14 fc

Co -fI kottcrt(e+y wfoit4 uW( P-tkt StI~ l t

~CtCte (_oppos-e P -(f ~ T middot (1 ~ Set$ U -to (Q((esr-~~-toflfobulltHf lt 1) Ii P~n (= v ut s setft~~ ~ t PQ~ ~

TR SQ=S - PR= PV- PIlt = Vlaquo=n ~ T T So 5 01 Ae ltT0 e ttl

ampruJt~J) fr p~ ltTaee~ UT ~ U

~ l(P Ifamp)Se0v4 u to ~ C(telte e to c~ l I- UtoT So TT Let 14tats~ P-4 C ~+~t5ect r ~Q~R ~

ampS-=s- Pflt=Pv- P((--Vre =TIC=-TIlt ~ tiM -i1s-MS Ti-f1T=-jiM PtSAt4t

~ El4middotrle b rio t)

Lt-A~c ~ co ftiI5le ~ ~tof scl Be A1k ~tsct- N ot l ~AC i~+fSoct ~c ct tJ ~~r~I~ k~ +0 AN -+~~ N ifersets AM 4 Q -c AB -t p -n ~f-lrJrmiddot 0 li~e to APt Pt-a~AIl laquo 0 middot Pofe Qo l Be SIt- TfABAc1kMNQfampAQMol3c

WLOG I ampS$f41111t A6gtAC Let AN MttStcf Uttucrclt fAABC j 1) ~

-- - bull c L 1gtg CL lgtAC=L~Llgtc~ e lAo M f~ r ~ ~ DC aJ PM 1 Be

~o Ho~y K(A ~StovlsA6j)(+oAgO(t4 08 O~ aq ae Itt t= Be( PN -r4~

L Ogt- L b8e =LM8=ro6_LAop=LoP~ ~ ~ D 0 tcKl orooc

I ) I J GfeCttrA J~c J~M4 ~ L 0 - Lep - 1 0 - 7 1- - 0 - 0 Igt IC tS~ amp It sc K is AM == AM l PfI=Q

I I ~ Lg eto L~~O~)oo 1~ ~o LSC g c It Be r

F l

(~p Sol~ middot Let dort FE ~wt -to nr2 4Ss(oll (iJ

Feuro () r C Lt r 1 U04s~r 111k ~y1- (M V)Sets P t r c-to K) Iiamp JE t jilt L AS

sow1 bull Ff 1Ie L ~ A is +lt1 ~roIldrc FE LNEC ~Afe~LAME I rSo L ~~eL~A~)~ LlNEcLlAMc ~ ACAeuro ~e1IA I ~ ~ pouer ~ A ltiol4Isped to r is Ac AM= AE S~M(tAfy I 16fJe t ~A i-fk -(~d -to ~~ Aft A~ A - A ~ =lttiJPOiqJ ~FeJ 56 Ae==-AF (1amp tflt11- rAAtcd - I

_ ~S AI ~ fIr2 AA~f ~ etc )~lll fu ett(4-ik1t f t fl1 pues-~r 1gt 61 sJMe~1 t ~OI)O~ wt Soc Oa I ~~t ~~ Ctgt

~ Ltgtco~=LClgto L cLeF ~s ir~S COa b~s L 9CF $ceCfiS~f rl So

Cl) is ~so~~~ -to re

E)(4flt

amp($ PI Ira Q-te ite~Iy ~ t ~ rt M N~oJtlJ ~ r fGs$es -tI- caff( 01 ~ r~

lAe r tgtit cl1illfr iii r rio MAn=C MBfr=D f (0 ~It CD $ 1~jkt to r2 bull

~ C~ IS - tYgtctStIt

~~ A ilefSVsv wi CAAer 0 oJ ugt r gt0

(amptatl 1 J(o r)) sA~f~ +lAo Se~s A~et(1 ~(t X 0 to ~ i~e VOl~t X O~bull y at sucL fut OXmiddotOlec r~ ~ CWOIelcu I fo X=0 ~ Utake )(=~ _-cl tllSo~)(-=QO Wt-take X=o

1ke Circle -w+1 C2~+e~ 0 A~ ~kCamps r gto-((ct k poundSle ~e~ ~ I~e IWJy 4fso ~ft A~ ltrs~ by sff~t ~ CrCJtL (lWt~middotcP

fGcfs CO Gift1 ~I((S~ ~ ~ bje(~~ it f~~ u~ 00 -to -t~lfmiddot ~ ~c-t J ex ) X ~

reg -If )( s-ikcRiC iwe~~1~ XI=X bull f)(~o~elf(enX~

= bull 1 ~x ~oit ofTaTl) ~t-rrl 4i~

P e ~ X1 lCT2 4~f~~-t1~ ~s iS k~

- __ OXmiddot ox ((sec LTo)()(ycsLTox)r~ ACtreJtt ~~SSi~ 14ftJUJ 0 ~~t +0 A cvdc bull ~ya16tj -4r~ O k iII-s ak~cIc -poits ~(~ St -to ~amp~ foffts l4 fOit 0) ~~fets

of -flit G~ a41~ aJa Afe utllt4r bull JotlfoItr~~tf(~-kGttk ~~set fotleceofv-f~ ~~ctrJe ~

A(fJe vaSSoVJ4-f 0 is Set -to 4 (euro reuro IS ~~~fI)~ 0 ~~s ~~k(+ifia1e-t (It( -t 44td Ito Cnverrely (A (middot1U1IIJt rssj-tlt~ 0 is Seltt -to ~Cvde (w~~ 0 Ni-l -tttllj~-t Imiddotier0 ~Itd to ~ leilt

f r A~At pCiSS~ 14 0 es SetOf ----1-- To e~setl ~ ~ _

Ifgt reg If two cr~ (f~ttIlC~ C4fVts ~(( ttlso ~~(etAf ~ fbft Pto)~~~~

9 lCo (iflaquo at ~Sdf~7e 4-( p~ oF

0 V ~-tlaat iHy~t~tOmiddotmiddot71-~R CA4f~(S ~ SQIJ-fo ~ 0 J

A Ie dI o~ctves4ltSet-f0r1f~~ ~ c () ~-t bull i- cmiddotrd~ ftftfiSttft S ~ fa-5~ 1Gtt cri(S t ( 4It ~fo-6etc~ Gllf f~S A lS 0 4laquol 0 A ~ IV~ IIG(C4((o(Af ~ oAmiddoto~ t 0Bmiddot O~ ~ OAloB OP4 ACoj

wi+lLAoB=L8~A Wt3ttLlOMdOl~ () - ~ LOA8= LogA ~

Aamp~ = OA _ r~A A6 0(3 - OB

=) Ae r lo A~

-------- --------~

)ampa-cle i (~tlcptleofto A ~cQlt$ A 1ckc ~tiatt~

ampl if tlyen~ t ampe- ACBD - A~middotq) +AD

II( V c bull I

SoJn C-sidelt -kfSiCll At 1 vuu~j l)is Cpoundlaquotef bull J ~p-J~ Ygt I) - t t e y fatH4) J -k ~ro-atdc qf ~ec ~~A~ I Q

I iIC ~ AeC SilCamp ~ IH 6e - c I

J vue b -ftt (1) We t _ 1 _AC~ r - Be - - middot

iDA ~ 01gt1gt AJ)middotC1) tt Mltrtrllj b~ lAOmiddot~]) CO~2 1aJkSimiddotces amporeJ

A6amp c) +A)xBe Acll 81gt middot

Re fICS 11L sf ~ eat be ltoftrec -to ~t -I- ~1-tllAt t MilcO + AtgtICBC =AC 1CI1~

~V Asctgt S (l u~ ~lJ4~ 0-shy

~S6~~~ kfCfS4tJ foJt of~~ -+k eampIt~ otIIIetStM Ai ~itlt ~s -fIc ~o~~ rote iIt wJere -reIs CIMif s Mesc(t _

-

6x4t~le 2 Lt ABc 0 be ~ ~tllt t(kft~ suamp~t At ampt so liltftStct At Y1tt ~r AtO P~t~( -Ke -refltecf of 0 ~fOSS AS BC C)1gtA A~ C4IIcYdtc

p _ c $Lt-~ -71

Lcent P~ ~So k ~fut f-~Wi _ 010 0 flO Msc CD lgtA Ye cdIVt bull

sc =l Ott foIIttll is ~iIr~le-t -fo site (5 -tk Ptt-RS l~~( (Sl~~14ft

e IcentS 0 0 -to tts e_~Hrlt OSAP DfBQ ~CR O~DS ~ludlC~~ J J -J ~ _ bull

-tt TltitCirtlutdts Ie CA Ca Cc CD rtsrdtuely CfSMoSmiddotd fIf~iQ 3(0 r ~r31gt0 By ~ct(s)

I~ AC Q( e04~~t ofo ~gtltS

cfct (+) I CA SIrcent to filllt LA fllAlrd to 81gt CIrs

Set to ~ IIt LB ~(c of Ac I C ~ Sci fo c tAlC -to ~lgt1 craquoisSeoet t ol1t LD~E lc ~

0 0 r~-t 0lt1

L Nen bull

CpnCa= 0r~ LAf Le P )Mjl-ly 4~t( LI) R J ll)n~ So bull

$r~ AcJ Mgt PClKs ~~Ic~4J~~ ~ fet h) PampRs is floc

~

G)Cdtpt f

Le-t P bft Af6~-t ~S~ 4l1It Appound ~~~-t LAPB-LACS LA(C-L~8C

Ltt tgt amp be ik~~tS 0( AAPS )AA~C nspecflf ~toe ~l A1gt 1gt1 ce )wtet A fOiWtshy

~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

( )tlfamp 61) biSKfs IA8PJ By ~t CT) ACAfACf~ ~ ~ I3A - XA So iSttf ACAeACampA

P ~f - xpmiddot ~ P~B6+lCApLcA8 J

C-1-1 ~=~ 5tRCt X ( 4ft AP ampt ~1It By~t (s) 1 ~ tCp~=LCitA ~ ~ I I~ fQ is Seoct of ( ~ ~~ 1 f4$s~~3C o listf SiacCrtIeO ~ -T(Alrl~f4lrgto ~~(1)1 tIIet pamp ~t(4C~I~Ois~tfo(0

A ~IgtC A~te A lU)e bullA p A APelAcIIgt f-c ~) I SIWICamp

I

~ ~ ilt3t +00 c( ~ 1 PQ fh ) Qm Q J r bull bull ~ t01 setc~ 10 t of I I

No LM~-L~8-=-LIWC-LAec f~ $(amp ~st ~JO 0 Ao( ~J~~ ~ Atl 43~ t (-d 0 ~ A61PcD

fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

Page 7: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

CfiE) t wt poundtccl ~e $~ ~ LampAC

bt10Ni 6 410f1 C J -tlte -tampi th~~ f L eAt ~ -tlte ~O Ile

-os c 7- J~littf~s vt S t 4ACe(A

~ ~~-t At ~ tgtDiltt Ia X r-- lt cule4l 14 xce1i-te of AI8C

I f~- A ~rI Ie clr fe(f-c1oss tACA6C IIIi-4 f~t I ~J v y z

I I -- I Il~o AAS I AIIIX 6~AIIIZ6 ad IiTrC ~1iIzc S l X t 1=tr (4 -rke Crcubull4f c~ r A--4 clt~ ( IS -tct~ to AS CAee 4 xt~ z tt s clleJ ~ esc-i~ cVc1e (OY 4ccittf) 4 IiA~ MOO bull ~ ulSe cI(- tt er4c(~ 1

~A A ( r bull c

It~ 711

to ~~I ~

bullIa

II

Ill folWt QrcI~

ror ~ABC Iet A 8 e Lt clpoiwf$ ( atleAlAB et 1gt 6 F be feet of 4It-lcl-t ~s Be CA ItC bull

let kL I ~middotqe tf0t~ af I-A W61-C w4 cs-Je Itioampafv of Mac

1ke ec lgtEF rltcM_ttcoOCtclc ~ Cc~ fUaj ~ ~ clt( ~ ItIIe e--t Cull ABe ~ cefe N -ioNs cd~ is ~ clrowl 0 H ~ ((s ~s iwlTlGIC_~f AAS 0 SottIM ~AABC w see aitCA ~d (f8t t see uti it ~

8 So Cit~ Si~ eL =i M =8M

s~ AH1 a ( I Sc~ t1 $kf+ 8 A D C -na~ ~CO~I5 tcLM rs

(L Aoot C of AS ~r I Sc f 8EL1oo=L CFM eFCI~c Iso r

1I So SeEF l~f1 ~amp ~~l(

St(Irt~ ~ As OEKt 4re~~ ~ ~ qrdeHlaquoI~ tEl helCt (61 4~te ~~ rck l~i~i-d~ 4SeL)- A6( 1lgtGF ~l~ ueClW ~ SCl-e cude Note tL I CMA Gte ctOIfars qf ~Circle

c5fD Sice OA amp0 BCIICS So feufbAch s ~~rfNA o A J Crb Srll(~ly oa J Ae ~ f 11 e P int cuclc f 4 t~ bullbull Ie Oe J ampA So 0 is o~e1A1( is -t3~ 0 ike ~( c-de No LlAamp1 AA~c ~i tot~o 2 1 ()~ ~e 1k-let esUietl C47rcles

A D C So AASI A A~ 0 i rAtto 2 L r4 -tk --tY-~e 1-eO AO A~ AeAe h )Ao=iAK t(~ Ws s Qtt-t_e1y ~tfJ 5~ A 0 J Be tJMJ lt-1 foe $0 A 0 II K ~e4 tIlCl e~t~f1 ~t AOl~ ~ laquo ~~[(em bull $ ct Aj( is laquoJ~ -to rOllt oftt ~ rtt Q~c bull So t~ ~oet (lSigt t ~--------r-- ~eO~rft of QH) is 1le cet~t_tl Nt ~ middotfc~ ~ 1 AAo tJ ts ~Iamp ~ I) K ( K IS IIIlftd-af fIA ~ lt K i OA middotH Crc-~t s l AAac ) bull t

6Je UIe i MBC i~ ~ 111- 0 ~ Amiddot Note AX is ediArt~o ~d4 8c

o ( II Ltt Ofll AA c (q SCMct OAII A 1-1

--- ~N-- tA~ 0 =i A HI we sae B A Igt C A Ao AAH6 rtto i 2

o~ So 1)iErH11tt)(iio~ ~ 5 1 ~~ bull ee ae ~ ~Qj (so il~t i o ht -fIt ~ j-o~ -0 tj 411 t teampd ~ At Gt ~-t AN C fgtst ec - cetle So = dtli ~ 6-f( t~ eord-IS -l J 0 ~ N~ ~ AI$o A 3AA 0 bull ]

L

i a t e CJ

I u

Ci

CEi0 ~~N~ ~ let beQsJf~e(-f(f ~ K+O So i ampmiddot-i ACo~~ iSA )lJt4~fotmiddot A- b W~~ Co III ~ teal --~

--rfa ~t -+ A( ~rtlt 1I14us ~llloe (~~ ~ C G~cJly ct s el+J of t1SJ bull ~+Igt~ U~fPOlt (ft) Ent M~ fb 0(l +be bull c-+ ct i ec) o (0 )+ (c(-elc) (4-tc)-+(~-td)1 (410- (cot Ii) ~-c)-+ (b-clh bullreg ((H~)(-ttJC=(Ac-bcl)-t(~-t~dl 12 ~ c-td~o -flt -- c-e(-= ~ J Ne( Campmiddot c+Ji ~c+~ ~co1ts

I

~ IAtb S 4-1o~ w~4eA4 -iIu 0 C0JY-te a( Atb l~ At6t -Ilt o~oo4t ~14a (Of ~) tf at is ~ 4~ lilt middot

NoI-t i--s is ike clt9t- be-l-wu (00) a( (e)

~~ W daM ilu~Solf VAl~cf olIIt y At bmiddot=J4Iot IJt --lA-t~t=(Glt~Ga Ioc)A- 1 ~ ~Cll--bl - shy~ 1 711a L lfO

Yroee~bullbull~ Ltt wJ~e( - _ - bull - - - - - -- IJL _~-J(D Wt1 +l W-L w-aJ we=w i -n - hi

~ lt~~wt~ lzlltJ 1lzl iYI~~ - middotifUoJ

~ Jqt~~ =leampal ~=c+rk=Wie~Ji4e- I ~(eo) lit ~el~-6z)

i Wt=(p~b(c~d~)rrae bull amp ~ yo~e L~

1olot furrn n It- be e ( Ie l= 4t(i~4 fLC loi(l~ 9 b(~(EfR1IvLfDs4ttX-cN ~ to ie ro~ CO6)~l) 14~

(o(oo) Caocdlaquoclottfse cCllIctcn ats o(td 4e ~ ot o-tbi laquot it is cC~ r o~-iW)~f~ e~e oyo cs8 tl~s (fosS)+ i~9l It A~~c coseH~=YeteIIlaquoi~ to ~OftS ~ bull

ey ik cu~ I f xt~~=Ye )~ ~=r-e-roY AI( fe Z~CIsk lWtf fir ~ lee euro C o Go ro~~t~tt ~ ~t wf ~ ltII _fir ~ ~ f bull (6+l~

I - ire gt I~ J1=e ~ J

) WftreileH(Il-Imy

~s ) ~ ~CI~ W

fIrre J

l Ioh L T_ -f -t ts ofJ

W4-II4 C4S~ pound_ )

~~ 41f Wid Ja-e w)e )

I1 2~)tt~ I pin e Afe

-ltv ~t Setflaquots ~ A I~d ~ampPav3~

Cotttple~ 6eUYIUi(-ry

~ -t Ls ~ N~~tQVs e c gt e - Ccs9 +Se

~sc Obte~ ~ ~

CD 1- W claquotsr(middot t -R Ie-tt We III r ~1 ~(+ot) ~ 01 e _ 8 To yot~+f A YIi v fLe rlAlIe Iiishy

- r I 1fSj~t -to -Ie ~ ~ ~ Go)1 ~ C(

=~ r_ ik We $~fl1Ioltrb 1Ie crl foe l fA ~ - e b~ e

Acrl~1 Ie ~ ~s Iej f t ~ fl=- E

Ei-tmiddot 1- ~-tljk -t di-Yoits 1

Gi~ W W2 fke 9Qta-~c e~CM Af -tI ~ ~ ~ ~-~~k IN Wa is O~ ~ 0 +t Wa t ea - 10

W ~ So z-w bull HelllLc ~-J _-i -- ~1ecJ ~-W c

Wz-W WcW I ~_Wmiddot 0 1-kt beA ~~ olSo tJi~u -tk cJ~r

igtr -tke ~~ ferlts 4 WLJ l -to be eolheAr- eogi- of l u fcoJc ~ 1 1rllleP0rt

i CtrIz-) RottmiddotOW 1oJ1 9t W

- bull -1 II It-vL

e == Cos 1 gts = 1 bullWIw Eltot of-ike le tkn C rttr~JcJA

-to oJ W1 5 f l-C -~-c- l

0~7i-f ~

Li f~) ASS-teJ wt~ (uit) c~tctf

11 w W~ n 0 ~ tle ~-l cJe (at wi =Wzih~ l )

~ -tk trto ~~t ~O J Wt so z u

l- _ Wz-W C - - - l - = -w~lc-W t-w

Slworl~~ w~3~t ~ _ ]t +WWz t Wt W2 bull

-r~er~of -to h amp ~jl ~ ~~ lot C r~ 0 W W-z s l- C i (wamp-w)

---- -=WW1 ~-c -W(W1-W)

lt)irljj We 3 t I~-101Mh C-IVWC

1A~i~Cst

Let~ Wz~ W we ~ct ike f~Otl af ~f -tampjc--t ht t ~ i tele I)t I wI~~

(l+ lJti JW] yl ert~ -tle rey bull tcJr fa c To iIt tlaquojct

lIt cJ W is -L Wt

i(J~w) -= T(w~-~

~gt

CD C~eetfe( 0 is ~t tlv ornI reg CeV~J G is ct A-tA~ A3_

() I eurot- NH llt (-r~s rs -tf 41-1 ~- 1 A A A bull A tateo J n I l _ J i (~~Le~ ~Alll~b) s 01 SCt~eD u -pe v~GyueJ

(jOf4-hoce~t~ H l$ c AT At+ Pr3 (be(AASe O~ = 5(O~)) pound1- f lt tl~ A ~ fJclCi-r -to ALA 1s

i- A-A3 ~ -= At - A1-AJ A bl~-t ~ 1 1laquo ~ ~ r~~cJAt -to AA~ $

c- AA) == ~- A~ ~ -rktSt -fwo -ts W f~cf ltt t ampJk4J gt~~flaquos boi lut~~ u$~-f~ ~t tAll lAzI= tA- i- (e

AA = AzA - ~X3 -= ) t ~t lt e c At-tA T A~ SAiSfelt bofl ~t~01l~ 1eo t-= AT At -( ~3

17 N f t - L A+ Al-Ar) 6 Ce---+ef ~-tke ~-e foitrt Qftle $ DA l-

(be~oe 1-1 $ ~ ~Jro~ 4 o t-t) ~tCA ~ Mi-e fit arcc is -tke Ciolaquo ~t f4~SfS -tvnWJ4 ~ a Jo---~ -4le ~~es AtAl Aamp+~ As+A) ~ ~- J L -) ~) -

~Q 1eet qf ~ al-t-bAdcs H I 1 1-3 -=t ~ Wampdtoi~~ -tk ferllaquos ad ~e D~e1 ~~ raquo A~lt

(J~i(t~ ) A lltzlJ J llWW1-~ Ayt ~ito

Sol4 SifCamp ~A~R~lgttPLlCQA~ ~rJwail~e Arf A+cJQ+~~R20 I 1i~R+~~Pao C-t~1T~ZQ=-O

I ~Il I w e LV = e ~ 5 A ~t 4 ~b To ~~ fl X 1l s erltamptDI we CoM-rtf

Xt wl-t t)ll= (Ai~amp ) +w~Ct~iP )~(8+~~

= k [CM Q+ ~~)+ 1Yfgtt wR + tf )+ w (C + p+~ I = 0

~~~A I )( ts ~ (Rot 4 1 J~ ~ ~-t 4 -II 3~f1 C~cf ~ ce~-ter4cl At ~ (A e) ~ ~(f-t~) (ie ~c pOlt 3 -the amp~~c ~ ~ ~11t~ -G t- ~rid 1 ~~t AS)

COlf~selj Ikj ll~ 01 ilt G~f smiddot ~ fo~t ~ loc-s 61 )( 0-~ G~f C = i(Jlt- CA-t 8)) is -flc co~nsfo-kj lt Ov- ile ~t Clfdt

1-(t1J~ Let A~ A)e tI ~r~ 0t W1w) w~j I Y~ f~~j

fYo~ A ~ J~r - fe~~ -to -tkt -t~~ e to ~ c~tdt I

01 b w WI W 3 Got W bull skw~ ~est f~(tS ~ctCmt 1cle-t~~ ~s tmiddot~t t C)~

~otct~ JlCG ASSUllC -tL ai~cit-tle is -tlt kAtf GifC(t

~ h~ le~~tcJA -to t f~eMt oJ 1J -iklk ~ MS et--4M rll-tvJ~

bull l- A ~-A - WltWl t~ k~Wi -r ~- w - tV - 2 - - W 2 bull

Now WI bullbull f -ike ampM- ~~lc I SO Wd -= 1 i1e we ~ fJ~-te -tk ~n 4S _ _

~ bullbull Z ~ _ I T ~-t Wos 11 W + 2 Wl ~ - 1iIII I - - w

2 2-

F-oN -tk5 t ~ ~t -tk yoil-f N Jw~ -+ W3 $ 0shy

--te e lt$-I(C -t1e e1f~sS1W f Ns Sr~t~c ~~ nSFt -t oJ Jt Vis we (4 eot-t~ -tMt wtl lISO e O~ -tIt o~-- -two les -t~ e-Fc~Sto ~1 tJ -tt l s u~ -t $ -tle (fwle1 ~ -t~ )1 fO~~ (tce ~

J I W-z4 _

11Ob~ ( S~~t lYe Tko~ ) let W be D~ llt (~crclf ofJ ~1 13 c( PI Q1 R

be ~ iut ~ ~ lC ftJi~ ~ W -tt t1I 2 ll I tl ~ I ft ~ec-f~Jflj slw ifvt P Q R A-e tAl(Il (-ps Ole 5-

clt~ A $~501 11 tf A ltamp-t) ~ W) i

~ol~bo- WamplAi loss -t 3~nl~ I Wt J lS$We Je G-nIUshy

Cilampk 1s ~ ~ cttclt ~ lll llJ lls -= lw I ~ t 1kt k ii ~s ~~ l+ ll~ ~ Ii t3 --ie r~~ fw- W + 1~ Ivs ~ f-ltl ) i tJ- Zt~W So Sol lkcsc -tcdr W~ 3laquo l = ~ t L + W-lE W

2

St ~ Q ltl ott ilW --l 1(= tt f t~~1l

I sluw fQR 4t CttlfUf it S~s-t st P-R =l-amp-Nil f-R _l- Z-amp-~~ Yo-~~J (tI 4W -g ~-R

Q-~ -1-1)-1tJ --l~W X l ~-amp~w ) l2tgtW-ltl~ -lZ+ t

4t~ w- Zl~-ll-t It f- fl

- (1- R bull

-J clt~lttii lw=t ~ WW-=i

CiiID ~tlt~ firLiA BC let 1gt be A4Ie GtIlOc1tf- E 001 As loIiti DEit-CB J ~ F ie 600 Be I

ciA ~fDf oX ~~ o-rbmiddot 0 1 ltt ftt XIS G(( Gr be 01 EP ~tS~t ~ el~ttrlgtedo-r W~~~~fk~t~s X Ao D C fSfoFc-=Ep-=BYc1gt=r

~J ~sted oR we rMj Sity ~ i 7 middot PrDV~ 6i-F fs pcmI(e( -to -Me 4 b~ 1 -M CaJamp) Xl= Of-~ -tI S~1 je Y-X Sol-I Set 1ampt o~ AtAo tt(-~ IMc

For ~fS X It we e Ix-+f ~ lxl +111 ~ft Tie E 8 Gfl = C ot~~ E (0 r)klgt(d~ 1- W-11IAy f X= ~t(r-s-e t~o A~ F tB t(f-t)c 4( euroj =tE t-((-f)J) _ h Let Pbe 0 poillt el LIle )( f lJe lter t= B _ L _ amp1gt g + (_t )e~ middot gtY haYCamp oP=toX+(f-t)oy -f=~y ~ Be -- r -i1gt-t ~_

J J gt1( 8 -I io O~)y~ amp(01] ~ P-u SfjllleMt Xt E retgt I $0 IE-BI rD-cl c1

EICjl1t Call a ~1IIecent ~ ~ QjgtWelC ~l~ (I- ) Is (E -amph 1l ID-d r-(t-amp)(c(-f6-Jgtfd tl )ltLJ )M ~ ct j~ Ie ~od ~ orF9fe sk~ J i q F- Gt = t6-p)~+ (I-t)(1-9)C ~ +~hw ~t cf -tk s IIf-t4 Jgtllrl1lpounds Of ~t(tei _ IS tlt-p)amp1~$ htfampt iits~etet ~ik~litetllllorltl -tlt-p)la (amp+~~ =(~~k1NIllelo I _1 t f4IIIl ltf1ltS

Sll~ fir trl4t~ A~c~ Itt-A IlIamp 1M OjL ltf 114 (tw~-for ~ pound Me~ --ik se ~fOW twI ~ _ Igt IC-tO - f ~ if

T -poundTI-r -pound ~ I A=0 1)~D i(1el IC-BIt lo-dtll)~

UI8iC-1gt1 +11Hlt-at=Iel+ Ie-IgtI+11gt1 +1c_~(f~~t Wt ut Ie+IC-Igt ~ Iamp+c-tgtl t=~f1f)

AA IDI + IC-61 ~ 11gt+C-81 C-~AO=~8C) (gtt) holds ~Le~ft~~lcJs A81(1)C ATgt Usc _~ __

c6hf--I--l~1gt~ ItiC

~1- ~t fmiddot~~ 0+ ~ 0 ( is )(Y=tJC( (1 rsti - Ex4k+ Let 0 ~~ (i(cAt cf 4ABe 9 ~iIt J bef -fIl lfcffS Jf -IIf (t) Xi=fX (y+I)zmiddotXmiddotZ+fmiddotZ 0( (cXl-Y~(Xmiddoty) ~ I~~)(middotX I IXmiddot~~hd1I O~iOf (=) Xmiddoty-O ~~~~~~~~~~~~~~~ amp--ft 3 Let A8C b Le lmiddotts ~sfmiddotmiddot Phe

Ac~+amp~+A~-t8C~~ Ast+ctl SJt~~ Set1ie Ot~I ttt A ~~t f Jw

CmiddotC +(amp-lgtHamp-~)+D~ (8-c)~-c) ~ amp (c-b)laquo- At~(~- awl lt~~-f4ls s fu ~4S

(6 C-b)middot(S-C-lraquo ~ 0 ~~ck s (amplt-1) ~o

A ~t 1gt Ie -tLt poit ~ Aamp -L II ~ e _ ce~AAcO

p C fgtrcw _t C1gtJoe ) AS-AC Sol~~~~~~~dO~A

A a A J) A J)= ~ E=~~ =3 +~lCJ1gt-C=Aamp-2C

C1gt1 Oe- (A-tS-le)(Mc+1raquowO c) No AA~lh c C C(CUM(bull (IampSt 8 41f1$-bull (4) bec u Amiddot(Q-ltAB-ACO 1IeJtt(~) ~ OAl ~c ~ A~~AC

euro ~ toJs ~ 8lt~ 1)-A69 seAPS fWlkl ~JCOc $ firAABC jf( t ssewu-J -ptMf ~ c= - ta-+CmiddotfI AAS( its ~ttd q ~1 - If We Sampt -iU CitClIMChH- 0 AS ken -HII-srft~ ~o -t r -11 __ -~ -1 ALh--COtt - 7J 0 OtlGCnx n - ~-

A Fit iAcetft tJf ~~ c 0( lU= ~ = L

co b AI c lt-c

e ~ 1)c 1gt= te+(t-t) C t --amps ~1i~ poundL = tD ~+ cC C bI-c Gte middot I t A-t -~)tgt t-ll- A

aAtlS cc_ - tgtA - M~C 14 e middot

11l Lqt-(gt OmiddotkC Gtctal ~ICef c(H ~r J

51_ Set 5 4lt C4fColt_bull tu e -H Matel~Me1~ 1~ AA+b$-t C shy ~ 4~(

Lampil~gt 1omiddot~(i-1)l4-1) lt0 A-A 6middot~Cc=(tlJ 2ec 6amp+cc-(a-c)(amp-Q=k~middotIf (A16i)riamptc~ Rlt9~~ 11- 3( h_ Imiddotltl-C) 4l- 2(~~(H- btCi)tI~)) cttC

)(~+c) (-1)((-1) =((~ t1 -Hi+(() lt 0 of -~ f (ib -t-e) lA+Il+ ct )+ilaquoc gt~ CifI+cl+Jl(c)+ ~ ~ a(-o)(--G)-4-~-c)(b+cc-4)~)gt0 tsc4 rc s

~ Ike fRS ~ f xi xI wt -Stl-fculot 11-$9 (t)=LXOY) 0( tiYfft~e~ -fo -tkt fl~~ 1-- oxY J e

lti) ~ -f~)( ~f)-a)( l t Yltl (c~wYcxnyJ (j - )(~1 4fT~ A X0( V~~ p A of yl t1ft 0

(6laquo Q bull 1 lj 111)1 (DW~v e

eJ41~ Let AAA A _j A 1 1_ -+ V]nq DO 4 CD e I

- its ste ~tS p-Ilt1 ProiIla-t middot ClrtllAA1Ar oreAA AA So(u-tVf SeL ot - ~ -_amp I~ _L ft--A A ----- ~ fJe ~ ~ --fI 01r~~ O4St SMs ~qIt ~t)~csCA-A) I lA_-A f

E)Ctl-eIlaquo-r Let A6COf tgt ~~ pe-tft Qc e t

~~~Q~ ~ 1kfwlrids~ A88CCIgtbEpoundA 1T~ -r APamptl~J~ le ACDIIIampf6i -laquo s~O~ tk-t ~s Ooet is so eM eII bullbull ~olt4-tfN ~et -ckt O~bullbull~ rt -e ~_W f~ S~

tJ 1(t0 AXC ~ AP ofe (o(iu o=A-f- A(~ J C- 32s amp A

lltc t))tA SIA~y 8)(1)= (1(8 CxE~ C I

raquo)(A 6llgt re EJ( 6 =CcE feMtt I

eurolCAJ- E)(6-t( - ~lte+El$ ~ pound10 eImiddotmiddot

1 ~~-A~)o (As-AJ1gt(~A~ S ~~CI amp euro1tf6lc~ ~se Ac Adol~ -t(t-t Lit set - () middot At

At~ t ~It~ AsIC~ Al~-+yen+yJAI (

_t a ~ - bull

~ 2-shy

I _0 c A 6 c ~ As V ~1~Ut 1 Sjtllc -fb ~BIC~ fW(t

ftdle ~ts of BC CA AB ns~chvell -tk ft1~ -tIua-t

No A bull G 8 A I ~amp Ca A~ (orr eU egt~ 4~_ A~itlA-~lClA-As~=(~tAtAr-tAjcA -~~ StthtlI4It ~ SaJc1ttA

(Nmiddot~~i~+Ar~~l ore4 l1A AAs = Are 1J~~Ai

Aft13 amp11 C=A-ttils-A)frSollletoA~] SiCt AS e Gfe i eRe

o~ (Bt-A)K(~-A) - (A-ttz-~tl-t- t t)AxB No ~~=~~~-=amp-AH-t)e ~~1 S-a-= It-t1)A I Ct = lAt8)- c tlA +ll-t~)B ~ (amp-AI~I~(Cz-~)=(t-ttl-trtl-+t~t))Al(amp~O A S~ CL At( ccdllfttor

~t ~~ 1~~Pt

o

C[~1D --r-0 vetlOf) )( lf ate Jt~y wtt-t---t f~ t -flat ~f~ ClX~yO kAs 01 Soat~

AT 10 o T4 s tktCcStI ~~A rf KttO ~ X0 f Art NIt Co((llteor

F4t IT AX+bY+c =0 ~$ote -e 1~I(z-s 4t4l 4-+amp ott -=0 J ilQA Xf Z 4le cbullbullI btACcS( ~l AO fIe b-tc-o w X-1-KZ-tYc-6Z

(~ar~11to(~1 wr~t--J Lftai c~ s OAAampA Co

~ OeLamps 1f 1 -1z- Aa6~l~8ampR AsampIA~= ~ 6 8-c amp-S tltcl A DAR 0

~e COIIfttAt t ~1 =- 1 ~ ~ P Pl) P3S~ Set - orlll at o at A8 btt ~trs Ale LIDa (ampfbv~ ~ A~ rA Q( e s So 8 1-t S6Wt (s EIt Cll No

Pl =tAt(c-t) 8a trA+ (ct)s ~- ~3 lAAt-tQ-) 8-= tA(-aA+Cc-ct)S a S~tU~ ~ 0= ltr- CArgtA + [pound1)l -(I-I4)$]B

A~ (tally rcf~=gt tr(~ Otu( (l-tl~-laquotlt)S=C Solll fott ol -tit pt~~ -+-s f ti ~I~Js

Nt ~~e ~ 1tu~~A+ SoSzCt-rl g$t Vs- r~ r~- r~1 Pgt1s~S)A+~s(tmiddotgt8 R= rlrfgt~A ~(I)J B

Y~-r)S) ~6a-t~S) amp c) ttS +fs-1S ~ p~f~P+~sampf-tj~

~ P1 ~se~rw)~c 0 Qtlgt+CoO ~ r fL cU-1- fc-i (ove

~ 0

A - -

~ FOf~lamp~

(1 -laquo ~C

fot-CA~ to ~ t t amp -t~~ crt a ~tc ~ El(tend~ltl St L laquobe ~[A8Cl Js~~i~ R= 4 C

Let ( ~t 4ct nwts lt 4e GoismvmcJt i-R- tl 4J~)(fo~of AAsc Sr ~ l=~~Yslt) ~ bc_

S A -- - 0 21 1iltelaquoe s dolAt C~d~middot ~o~ uI1gt ~ s~amp s~~C middot T 1_ ~ rI n -rf (i-- shy

tl Ie or~ DraJ clmiddotae~t 61gt 1pound Si ~ A= ----=algt i IS lle~ ltJOiOlSA0

~~~~~~~~~~~~~-~~~~=~~~~ p adEr-l-~a~~r~ A- oS+- jtus c~ - c e c I) p(]) Let 18(1gt L~Ms

I4dtt rAsel Or S~8c1oI(lcl~ 1leflAftt Let A6nct)p -r1 ~act 0

~Me C ABC ) GlUo~kc ~ PAx P6= Pc x PD = tl b~~=Abc bull P19tpound Note L APD L (PB

4R A1BC)aHd~ckLPAtgt=LPCBS=tfA-tb~~) is ike seifieAc ~AAPDACfB~=~~ PAIPB=fxPD

amp Q C Of 4A8C Lri pc C 1amp-~ ~~ PC Is -lt-~t lat t lie i4 jCbullbullr 4l( M6C Qt r Ie -i4~ to -e -fde ~ A A8C if (JJ

C)~ ~e icltc1e ot AAec ~e p A e OYlJ c fCL p~~re [Mel =[ALel[~cl+(CI1= ~-t~+~=SIr ~ Not~ LArc=LcPB

I-tfllWlbull [A8tl~ S($-11 ) (s-b)(s-c)middot I pCs f~ot -to LACp4C ampP(~ Cos C= tt2ttoa-c (~AI Ci(~ircl 4 MBc B 2shy

[A6Ci= ~SiIlC=Qr(+coSp(i-($C) ~AAcPACBP ~~ fgtc PCPAlltPB =(Cl~-+Iot-c~t-~a~-9 ) = catlo-4 t )(A1(-c)(CoHI- b)(o-Il-~= S (s-c)(~~

2- ~ a

Ci C [AS(I A 2

~

I

~JJI LPFA-=odeg=Lpe~ ~ amp~ ~LPFeLPAE

C5Ji) ~tolt1 s-ThtOfotfll Let A 6c~ ~t dlSncf ~ts 01 bull ~c ~o - Me~IA~ 1( bull t Of~~~I ~Ot bull -Tht~ bull Sa c~tOV M1 C(liofIPT potd~ A 6 C Iie to

AI 6 C 1gt (1~t~c 1gtpound fCLR atfmiddote ZA ~A A ZA bull -~ -iA ~Co~ PAQ~clf$ WeA~ ZA~lA I tc Z~t

pFAECc1dk

bull ~ Srlloi(y taCgt6~~~-lPFB ~ pG~ f CDCCYcbull LPampb LPFI) = e 1klaquo AIJ~P LPAespoundp8C pfE _ LPeP 8EF (0(1ltlt~L PFE L~8Tgt~ LFP - L 10 collirAfampff

)fgtC)~Jl~~ ~ ASC1HAol6C=AcS]) bull (~~_ ~ktI AeCO At)ItBC ~ACdtgt 1)~c 190pound 0 sWLe AB UJlfsftfUct A ampA6

S~~41 to flCAP 1I1elt AB A~ 6eshy

6 Ai - 7ligt= (1) lBAE=LCAJgt

SO LMc L BAlgt-L1gt= LeA1gt-LMe =LEAt) Tkeuro1 A8AC~Ae-A1) So Rr-c EDAtgt~A Thet Aec~ A~8C =poundItampE AClC E~ AC80

bull A rC =c Sf-t Ell I

f1-I-4j hoW~ ~8euro~EtgtS ampb ~ E iUt~( SO - ~~oeA~LeeALtgtCA ~AsectCO Sltffc

SoSoft ~oe 1et~6cP cl-ampd-p~ 0

tI~ Let l)poundF fetf~~ff- P~ ampa Aeyen~~ ~

Asse ~Mist (so4 is 6~UA_JC ~AGSC ~O bull G ~f( Aalec~o)

tt~e9 7eff

fovlaquos X I Z ate (es Aamp ampCA D ((t~ve-()ty It X I Z (lie (dl-lflOr

A ~f f6 lhg--1 ~ xe YC LA - middot ~ lQt Dbu (~ Ac soct1IIt 81gt II J( Z -r1teuron

~g ~ ~ 1t~ ~z Se AlC 6Y c~ _At P1Q (i~ ~y Ie ~c -- _______ r tamp iU I bull laS yc fA ~Igt ZCZA middot lCI~ lIeeu~ Ie~

If ~ tL ~ =-1 iIamp )( YL MHo l~(~ Y~t~~~~ SlJ) Ltt l~ X(OCA -Thtl b Mt11Idtw 11~ Ax ay CI _ lt Cz Y Cl iiiK zA --i ~o --=-l1toobull CfIea bull _Cl -a

I I

ceDD ~MelI s lIeo~toA l~tA I ~cc t) euro ~be tc~ lO 0shy

de lw~~ ~( ft amptCtSSCti 1 tf (~ diC- (~QEf ) bull

t p Ae ti l)euro J Q Bel pound f 2= Cl)n fA ~ ~k ~ Q1t ottc(l(ea~ ~QIR~~~ -

f~ 1 ~ ltt X~EfA 1AMCD bull ~ z- C~neF Arr~l ~(atts ~ff 1e-(fM1oec~ FA

ftt- Ool~~~ 4xf l w hVII

e-- ~ X K __( It X2 ~_( t ~~II Qx 6y Ct ~y pzex I fllFxijmiddot 1I

Hul~pr~ ~ AIl ~~ tfffSfctj cofI4t tt XA)(B XEmiddotKF J (CmiddotYP=1AmiddotYS ZEmiddotZF= zeZIgt W~~et ZQ lSf~-i igt PQ~ ore rlfltelaquor

Qx Pf Itz loy c-enc ~Mee(AaS

t-rks ~ere 0 Imiddotil~ (1$($ of PoucJ s for It we tftwt Ato 8 -te I AIwIJ (3 il(cJe 1Iofl1-t i AB will b~ ~-t1l3et (iot ot B ~ It~j CIt~ we ells JpoundAoflt ~ t~ liflE Clt B b~ BR

6lCtJfC i F~~ h Cf(Ultirc~ ot Mac J f(it 1) ( ~ ~i~0yen ot -t4l~lE I~ ~tA - ~~ Be ~ e fM 1fe ttusc(e~ of-ffwf3ct (tt4-t C3L1r~ CA~ F= bt ~ ttfStd~ of -tINt ti-~-f Imiddot~t ~tC wo( Aamp 11161 PI Ell F o~ ctU

Soof~fIyen P=Mo 8C ~ E= BBnlA f=CCnAB APP~i P~f ~ ~(fo MB See I fott et 1gtpound f c-

-- =JSiiiiIii

b)lAtc ~ Let-tgt 0- eht ~cfs 0( dt101 AtCS

AS ~ AC O~~e (ilcu-R( Mac ftspciwJy l(t tgt Ilt ~f AtC sCI ~== DPn SA J R= PEn AC fro +~-t lile QR~s~(QVJ14 fttCf+~I (~ 1) ~ f9bt-Mshy~e 1)rff0--AS- CO ~SfctsLAc8

Co ~r ~ qftllCr At =lgt 6 ~LAec So 1= Cl)n G8 Sf_ eEtS

Q tgtPt SA DP 8ital R= Pe C Pre ttL PlE AI

AIP~ f~l ~ 1Ito(-to C ~ P er ~ w 1 ~ bull 1I

t Set I Q Rut tIff~ Co~~d~

~ -7

Alt IXu q j

elf (Ga1(e 3 Ltt AT3CPs e ~ +s tMDlCJe ~-rd AAfLBS Bat LeA) ccf LAB fat 1gt be ~ls (I ~cucl1t ~c4( I

DA(11)C= AU DB()CAe~ 1gtCIAB~ fgt~~ A~ r~CtfaJ T4 6v~fi ~ IAGC a~ Co((~((r

~olf- W HL-cI oy-((~( ~ AA Be Ne

AAIB~I)Cc(-=I DArBC=A 11gt1( ISc AtA f Cc -= H L lAlA I C I Cl

1t~()cD=C1 ~l (AIBl (cjAfrrr5~5Gl ~~ t DAAfCC tgtlt Se4 A HC tit c11ilaquoraquo SIt 1y ar171~ BS41s(to AS e 0cc we Su e H 6ltve c1(i~amp r A~ H C~ S4rt a(((~4~ I

-~ ALI)f ~fle1 tt P toe a ltpor i~4Mec

LtfP I~~ff~I$f- 5 -to ~CA Camp ft~t~ lttt bJ() ~_ eshy

ll 10 ~ fet ~~~N~ c-tohs API sp (~ftvtll IfQ P ~ 61bullbull Pt14 PttNQ~~ (tries ~tll~ Qfz cod A~ aft ~et

iSoLttd- $(fCJt L CPc p) LCQLP LC~P Lc (gta Palt-e J -t ~es c P ~L I PI Q p 4ftcocttc f~AfrI15 ~s middottU(Woto ~1l$1 w-tSu CPt ( gt e-= A ) P t1t( QIP= X ) (Q-a Pf P2C-= B 4re CoI~rtelr $6 Rb2-l amp1L ( AB-=Xmiddot ~ ~lIQ P~IA8 tVe ~Cqfre~

NewtDJ S

~A ABcOS~~(laquoteJktvsa e ~SQiraquoeamp c~tkt~~ ~~

APgtsc CD) PA AXcpotlts EFG)H-~t~ C F B ~ACG~FHgD~~r~t

Sol~tcNI W E6nFHO~ Eftn FG ~X _Apply~~ ~~scJ ~ ~ -to E~ltSJ F f(f ~Sta E~ () Fr =0 ~~ ( 14 1) I G Fn H( X are ut(ltealf_ ~ltfcAy~ltP~CA(s ~e- 4 E6--()FF~~ J ~S14

EEn FF~ B euroH nf6=X amp-t-fn ~euro 0 tUllPtfcmiddotc4t

-nus ~S 0 XI oJB ~c((e4~ 7itN pound4 fl Ff n6D=O SlAry EG F-- ( AC - O ACE6 fH6DCPotrclO

1)ec~CAes ~ 0 nfAaAec ~ JACc) M

A c B actgcP J CAnCpQJ AampnAgR ~r--+--Ir-~~R If AA 613 I cc 4te ~tVt-ct ~

A e 1-~ PI ~ Rctil eo(IQ4(_

c~ rCP_ R2esrk ~-s ~ -tyenUL te~ 4 ~~cAAfIdgre IfV --IfU ~ f 4s root G-oIer ~Ns c~ AOAB ~ftJJ MeoJ- -~r ~ et QPL AEa gil

At A rltamp -7---1S ( rt l g 0 () I 4 ~ ~ Ie Be Cctf~ Lloec Ilfct-Jt ~~ C~ c~ IJOCA ~ 1te(J C~ BP Cd M oct ~

B8 PC-co ~-( ~ No CC~=-( ~(ff~~~sctmiddot~~= - ~ (IC4M~cfMtl~~~ote- ~ et eampI c-f(er

62Y ~coJ A~s tttt ~Cct~lI1tr

Let Cn-les C ~ Cz ktwe ~~t ~~-fe15 0 ~ 02

Sf 11 4st f( J 14 (cs of ( OotX w~ 1

fe- ) t ~ lt twitt ()~ -tu Cl

eo( C~ ~Ilt ue 0 K- r 4)-~ J ~ ~ li~ f(~ok( -to OO~ -rtgt Is -4 (~~a1CSof tLt -f~Cnrd u

MOtse ~3 Crce~ CJCC1 W~~ OJOaoJ(h I~ nf CiamplttJ -tfe 3 ~ ltWQs ~FoS offI Wi( i~~(JItct cent Do fgti- ((lt d4 vaJOJ aftftfT4crtfes 111$ ~It lw la-I fIwe wi(( v-espue to 4((3 ccle$

G7~~14~S

~ If 2c(c~sCp~ lte~tAt PQ ~ p Cl aJ hss fou 0 411(1 yen

middot~ Ot J To Co J C So -ky tore eM ta noe(tk( ~ 2 r(4-~ ~ pIA i~( ~~ oS

~yenI4l~~~

P------ ~ c~ Lf4rdes C e d lifest J e we c- tltANJ A f(rrzl cltJ~C

~~ ~~~eAJf- 14 1

Ci-- ntcl ~~~ CJCl ~ CCsII i~~(t et -t4 ~ C4tt p1-Cch~~

~P~ f LoDa is ~er~ AK~Of CCz _

Let ED be ~~~ foSflctorf oft B~ MaC ~D ~S~e AC -ri Cau~tt1e c1A8JgtC ut ABtttE J(e ~ cfC4c~rc(e c1 AB D MflId 8 Ccent F-=-c --r

D (Olt ~t AE =- CF So 1$1 i te~d~ c~ ~gteJ AE~AB=ADAC II CFIltCBCD CA So~= ~~

5 ~c 81gt fsecfs L ABe WI_ Cl) ~ _ I bull It rJC AS - AD CF- f1C

------------------~ ampA~fel Let ABC be ~ ftrJMIj(e ~ soscJes 68C[)I

CAE AASF ~te~(1 to AAsC wi( ~ CA Aa 4 S bu1 tsrtdvel~ Pro~ta ~-t 141esff-1 AJSc ~ t ~ I~es t=F fEgt DE ~dJ ~uc(~t

Col Amiddot ~ SJltto i Late ~e cnl~w-f( Jgt4Sr~ ~ IE ( - eatu r4~ ~Cgt cte

a~~c~~ Iof crde middot1itE Ultoofe Y04oc Jl Y l AE=CE ( tel btcte(~w-I(Fu

c~ Cc~-tr ~cL~4S AF=8F - I -r4e-tltlfte~ A PUr~I T (~ff I ~~ fiIolu ~ ts ltfCI C1 $f lltty ~amp~ 2 lies Cltt VIIIt~~ ~c c) ~ roampoIaJIlt) of (14So -tkey ~u(4t fAa ~~ Camp~tet

63DP I

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Page 8: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

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o ( II Ltt Ofll AA c (q SCMct OAII A 1-1

--- ~N-- tA~ 0 =i A HI we sae B A Igt C A Ao AAH6 rtto i 2

o~ So 1)iErH11tt)(iio~ ~ 5 1 ~~ bull ee ae ~ ~Qj (so il~t i o ht -fIt ~ j-o~ -0 tj 411 t teampd ~ At Gt ~-t AN C fgtst ec - cetle So = dtli ~ 6-f( t~ eord-IS -l J 0 ~ N~ ~ AI$o A 3AA 0 bull ]

L

i a t e CJ

I u

Ci

CEi0 ~~N~ ~ let beQsJf~e(-f(f ~ K+O So i ampmiddot-i ACo~~ iSA )lJt4~fotmiddot A- b W~~ Co III ~ teal --~

--rfa ~t -+ A( ~rtlt 1I14us ~llloe (~~ ~ C G~cJly ct s el+J of t1SJ bull ~+Igt~ U~fPOlt (ft) Ent M~ fb 0(l +be bull c-+ ct i ec) o (0 )+ (c(-elc) (4-tc)-+(~-td)1 (410- (cot Ii) ~-c)-+ (b-clh bullreg ((H~)(-ttJC=(Ac-bcl)-t(~-t~dl 12 ~ c-td~o -flt -- c-e(-= ~ J Ne( Campmiddot c+Ji ~c+~ ~co1ts

I

~ IAtb S 4-1o~ w~4eA4 -iIu 0 C0JY-te a( Atb l~ At6t -Ilt o~oo4t ~14a (Of ~) tf at is ~ 4~ lilt middot

NoI-t i--s is ike clt9t- be-l-wu (00) a( (e)

~~ W daM ilu~Solf VAl~cf olIIt y At bmiddot=J4Iot IJt --lA-t~t=(Glt~Ga Ioc)A- 1 ~ ~Cll--bl - shy~ 1 711a L lfO

Yroee~bullbull~ Ltt wJ~e( - _ - bull - - - - - -- IJL _~-J(D Wt1 +l W-L w-aJ we=w i -n - hi

~ lt~~wt~ lzlltJ 1lzl iYI~~ - middotifUoJ

~ Jqt~~ =leampal ~=c+rk=Wie~Ji4e- I ~(eo) lit ~el~-6z)

i Wt=(p~b(c~d~)rrae bull amp ~ yo~e L~

1olot furrn n It- be e ( Ie l= 4t(i~4 fLC loi(l~ 9 b(~(EfR1IvLfDs4ttX-cN ~ to ie ro~ CO6)~l) 14~

(o(oo) Caocdlaquoclottfse cCllIctcn ats o(td 4e ~ ot o-tbi laquot it is cC~ r o~-iW)~f~ e~e oyo cs8 tl~s (fosS)+ i~9l It A~~c coseH~=YeteIIlaquoi~ to ~OftS ~ bull

ey ik cu~ I f xt~~=Ye )~ ~=r-e-roY AI( fe Z~CIsk lWtf fir ~ lee euro C o Go ro~~t~tt ~ ~t wf ~ ltII _fir ~ ~ f bull (6+l~

I - ire gt I~ J1=e ~ J

) WftreileH(Il-Imy

~s ) ~ ~CI~ W

fIrre J

l Ioh L T_ -f -t ts ofJ

W4-II4 C4S~ pound_ )

~~ 41f Wid Ja-e w)e )

I1 2~)tt~ I pin e Afe

-ltv ~t Setflaquots ~ A I~d ~ampPav3~

Cotttple~ 6eUYIUi(-ry

~ -t Ls ~ N~~tQVs e c gt e - Ccs9 +Se

~sc Obte~ ~ ~

CD 1- W claquotsr(middot t -R Ie-tt We III r ~1 ~(+ot) ~ 01 e _ 8 To yot~+f A YIi v fLe rlAlIe Iiishy

- r I 1fSj~t -to -Ie ~ ~ ~ Go)1 ~ C(

=~ r_ ik We $~fl1Ioltrb 1Ie crl foe l fA ~ - e b~ e

Acrl~1 Ie ~ ~s Iej f t ~ fl=- E

Ei-tmiddot 1- ~-tljk -t di-Yoits 1

Gi~ W W2 fke 9Qta-~c e~CM Af -tI ~ ~ ~ ~-~~k IN Wa is O~ ~ 0 +t Wa t ea - 10

W ~ So z-w bull HelllLc ~-J _-i -- ~1ecJ ~-W c

Wz-W WcW I ~_Wmiddot 0 1-kt beA ~~ olSo tJi~u -tk cJ~r

igtr -tke ~~ ferlts 4 WLJ l -to be eolheAr- eogi- of l u fcoJc ~ 1 1rllleP0rt

i CtrIz-) RottmiddotOW 1oJ1 9t W

- bull -1 II It-vL

e == Cos 1 gts = 1 bullWIw Eltot of-ike le tkn C rttr~JcJA

-to oJ W1 5 f l-C -~-c- l

0~7i-f ~

Li f~) ASS-teJ wt~ (uit) c~tctf

11 w W~ n 0 ~ tle ~-l cJe (at wi =Wzih~ l )

~ -tk trto ~~t ~O J Wt so z u

l- _ Wz-W C - - - l - = -w~lc-W t-w

Slworl~~ w~3~t ~ _ ]t +WWz t Wt W2 bull

-r~er~of -to h amp ~jl ~ ~~ lot C r~ 0 W W-z s l- C i (wamp-w)

---- -=WW1 ~-c -W(W1-W)

lt)irljj We 3 t I~-101Mh C-IVWC

1A~i~Cst

Let~ Wz~ W we ~ct ike f~Otl af ~f -tampjc--t ht t ~ i tele I)t I wI~~

(l+ lJti JW] yl ert~ -tle rey bull tcJr fa c To iIt tlaquojct

lIt cJ W is -L Wt

i(J~w) -= T(w~-~

~gt

CD C~eetfe( 0 is ~t tlv ornI reg CeV~J G is ct A-tA~ A3_

() I eurot- NH llt (-r~s rs -tf 41-1 ~- 1 A A A bull A tateo J n I l _ J i (~~Le~ ~Alll~b) s 01 SCt~eD u -pe v~GyueJ

(jOf4-hoce~t~ H l$ c AT At+ Pr3 (be(AASe O~ = 5(O~)) pound1- f lt tl~ A ~ fJclCi-r -to ALA 1s

i- A-A3 ~ -= At - A1-AJ A bl~-t ~ 1 1laquo ~ ~ r~~cJAt -to AA~ $

c- AA) == ~- A~ ~ -rktSt -fwo -ts W f~cf ltt t ampJk4J gt~~flaquos boi lut~~ u$~-f~ ~t tAll lAzI= tA- i- (e

AA = AzA - ~X3 -= ) t ~t lt e c At-tA T A~ SAiSfelt bofl ~t~01l~ 1eo t-= AT At -( ~3

17 N f t - L A+ Al-Ar) 6 Ce---+ef ~-tke ~-e foitrt Qftle $ DA l-

(be~oe 1-1 $ ~ ~Jro~ 4 o t-t) ~tCA ~ Mi-e fit arcc is -tke Ciolaquo ~t f4~SfS -tvnWJ4 ~ a Jo---~ -4le ~~es AtAl Aamp+~ As+A) ~ ~- J L -) ~) -

~Q 1eet qf ~ al-t-bAdcs H I 1 1-3 -=t ~ Wampdtoi~~ -tk ferllaquos ad ~e D~e1 ~~ raquo A~lt

(J~i(t~ ) A lltzlJ J llWW1-~ Ayt ~ito

Sol4 SifCamp ~A~R~lgttPLlCQA~ ~rJwail~e Arf A+cJQ+~~R20 I 1i~R+~~Pao C-t~1T~ZQ=-O

I ~Il I w e LV = e ~ 5 A ~t 4 ~b To ~~ fl X 1l s erltamptDI we CoM-rtf

Xt wl-t t)ll= (Ai~amp ) +w~Ct~iP )~(8+~~

= k [CM Q+ ~~)+ 1Yfgtt wR + tf )+ w (C + p+~ I = 0

~~~A I )( ts ~ (Rot 4 1 J~ ~ ~-t 4 -II 3~f1 C~cf ~ ce~-ter4cl At ~ (A e) ~ ~(f-t~) (ie ~c pOlt 3 -the amp~~c ~ ~ ~11t~ -G t- ~rid 1 ~~t AS)

COlf~selj Ikj ll~ 01 ilt G~f smiddot ~ fo~t ~ loc-s 61 )( 0-~ G~f C = i(Jlt- CA-t 8)) is -flc co~nsfo-kj lt Ov- ile ~t Clfdt

1-(t1J~ Let A~ A)e tI ~r~ 0t W1w) w~j I Y~ f~~j

fYo~ A ~ J~r - fe~~ -to -tkt -t~~ e to ~ c~tdt I

01 b w WI W 3 Got W bull skw~ ~est f~(tS ~ctCmt 1cle-t~~ ~s tmiddot~t t C)~

~otct~ JlCG ASSUllC -tL ai~cit-tle is -tlt kAtf GifC(t

~ h~ le~~tcJA -to t f~eMt oJ 1J -iklk ~ MS et--4M rll-tvJ~

bull l- A ~-A - WltWl t~ k~Wi -r ~- w - tV - 2 - - W 2 bull

Now WI bullbull f -ike ampM- ~~lc I SO Wd -= 1 i1e we ~ fJ~-te -tk ~n 4S _ _

~ bullbull Z ~ _ I T ~-t Wos 11 W + 2 Wl ~ - 1iIII I - - w

2 2-

F-oN -tk5 t ~ ~t -tk yoil-f N Jw~ -+ W3 $ 0shy

--te e lt$-I(C -t1e e1f~sS1W f Ns Sr~t~c ~~ nSFt -t oJ Jt Vis we (4 eot-t~ -tMt wtl lISO e O~ -tIt o~-- -two les -t~ e-Fc~Sto ~1 tJ -tt l s u~ -t $ -tle (fwle1 ~ -t~ )1 fO~~ (tce ~

J I W-z4 _

11Ob~ ( S~~t lYe Tko~ ) let W be D~ llt (~crclf ofJ ~1 13 c( PI Q1 R

be ~ iut ~ ~ lC ftJi~ ~ W -tt t1I 2 ll I tl ~ I ft ~ec-f~Jflj slw ifvt P Q R A-e tAl(Il (-ps Ole 5-

clt~ A $~501 11 tf A ltamp-t) ~ W) i

~ol~bo- WamplAi loss -t 3~nl~ I Wt J lS$We Je G-nIUshy

Cilampk 1s ~ ~ cttclt ~ lll llJ lls -= lw I ~ t 1kt k ii ~s ~~ l+ ll~ ~ Ii t3 --ie r~~ fw- W + 1~ Ivs ~ f-ltl ) i tJ- Zt~W So Sol lkcsc -tcdr W~ 3laquo l = ~ t L + W-lE W

2

St ~ Q ltl ott ilW --l 1(= tt f t~~1l

I sluw fQR 4t CttlfUf it S~s-t st P-R =l-amp-Nil f-R _l- Z-amp-~~ Yo-~~J (tI 4W -g ~-R

Q-~ -1-1)-1tJ --l~W X l ~-amp~w ) l2tgtW-ltl~ -lZ+ t

4t~ w- Zl~-ll-t It f- fl

- (1- R bull

-J clt~lttii lw=t ~ WW-=i

CiiID ~tlt~ firLiA BC let 1gt be A4Ie GtIlOc1tf- E 001 As loIiti DEit-CB J ~ F ie 600 Be I

ciA ~fDf oX ~~ o-rbmiddot 0 1 ltt ftt XIS G(( Gr be 01 EP ~tS~t ~ el~ttrlgtedo-r W~~~~fk~t~s X Ao D C fSfoFc-=Ep-=BYc1gt=r

~J ~sted oR we rMj Sity ~ i 7 middot PrDV~ 6i-F fs pcmI(e( -to -Me 4 b~ 1 -M CaJamp) Xl= Of-~ -tI S~1 je Y-X Sol-I Set 1ampt o~ AtAo tt(-~ IMc

For ~fS X It we e Ix-+f ~ lxl +111 ~ft Tie E 8 Gfl = C ot~~ E (0 r)klgt(d~ 1- W-11IAy f X= ~t(r-s-e t~o A~ F tB t(f-t)c 4( euroj =tE t-((-f)J) _ h Let Pbe 0 poillt el LIle )( f lJe lter t= B _ L _ amp1gt g + (_t )e~ middot gtY haYCamp oP=toX+(f-t)oy -f=~y ~ Be -- r -i1gt-t ~_

J J gt1( 8 -I io O~)y~ amp(01] ~ P-u SfjllleMt Xt E retgt I $0 IE-BI rD-cl c1

EICjl1t Call a ~1IIecent ~ ~ QjgtWelC ~l~ (I- ) Is (E -amph 1l ID-d r-(t-amp)(c(-f6-Jgtfd tl )ltLJ )M ~ ct j~ Ie ~od ~ orF9fe sk~ J i q F- Gt = t6-p)~+ (I-t)(1-9)C ~ +~hw ~t cf -tk s IIf-t4 Jgtllrl1lpounds Of ~t(tei _ IS tlt-p)amp1~$ htfampt iits~etet ~ik~litetllllorltl -tlt-p)la (amp+~~ =(~~k1NIllelo I _1 t f4IIIl ltf1ltS

Sll~ fir trl4t~ A~c~ Itt-A IlIamp 1M OjL ltf 114 (tw~-for ~ pound Me~ --ik se ~fOW twI ~ _ Igt IC-tO - f ~ if

T -poundTI-r -pound ~ I A=0 1)~D i(1el IC-BIt lo-dtll)~

UI8iC-1gt1 +11Hlt-at=Iel+ Ie-IgtI+11gt1 +1c_~(f~~t Wt ut Ie+IC-Igt ~ Iamp+c-tgtl t=~f1f)

AA IDI + IC-61 ~ 11gt+C-81 C-~AO=~8C) (gtt) holds ~Le~ft~~lcJs A81(1)C ATgt Usc _~ __

c6hf--I--l~1gt~ ItiC

~1- ~t fmiddot~~ 0+ ~ 0 ( is )(Y=tJC( (1 rsti - Ex4k+ Let 0 ~~ (i(cAt cf 4ABe 9 ~iIt J bef -fIl lfcffS Jf -IIf (t) Xi=fX (y+I)zmiddotXmiddotZ+fmiddotZ 0( (cXl-Y~(Xmiddoty) ~ I~~)(middotX I IXmiddot~~hd1I O~iOf (=) Xmiddoty-O ~~~~~~~~~~~~~~~ amp--ft 3 Let A8C b Le lmiddotts ~sfmiddotmiddot Phe

Ac~+amp~+A~-t8C~~ Ast+ctl SJt~~ Set1ie Ot~I ttt A ~~t f Jw

CmiddotC +(amp-lgtHamp-~)+D~ (8-c)~-c) ~ amp (c-b)laquo- At~(~- awl lt~~-f4ls s fu ~4S

(6 C-b)middot(S-C-lraquo ~ 0 ~~ck s (amplt-1) ~o

A ~t 1gt Ie -tLt poit ~ Aamp -L II ~ e _ ce~AAcO

p C fgtrcw _t C1gtJoe ) AS-AC Sol~~~~~~~dO~A

A a A J) A J)= ~ E=~~ =3 +~lCJ1gt-C=Aamp-2C

C1gt1 Oe- (A-tS-le)(Mc+1raquowO c) No AA~lh c C C(CUM(bull (IampSt 8 41f1$-bull (4) bec u Amiddot(Q-ltAB-ACO 1IeJtt(~) ~ OAl ~c ~ A~~AC

euro ~ toJs ~ 8lt~ 1)-A69 seAPS fWlkl ~JCOc $ firAABC jf( t ssewu-J -ptMf ~ c= - ta-+CmiddotfI AAS( its ~ttd q ~1 - If We Sampt -iU CitClIMChH- 0 AS ken -HII-srft~ ~o -t r -11 __ -~ -1 ALh--COtt - 7J 0 OtlGCnx n - ~-

A Fit iAcetft tJf ~~ c 0( lU= ~ = L

co b AI c lt-c

e ~ 1)c 1gt= te+(t-t) C t --amps ~1i~ poundL = tD ~+ cC C bI-c Gte middot I t A-t -~)tgt t-ll- A

aAtlS cc_ - tgtA - M~C 14 e middot

11l Lqt-(gt OmiddotkC Gtctal ~ICef c(H ~r J

51_ Set 5 4lt C4fColt_bull tu e -H Matel~Me1~ 1~ AA+b$-t C shy ~ 4~(

Lampil~gt 1omiddot~(i-1)l4-1) lt0 A-A 6middot~Cc=(tlJ 2ec 6amp+cc-(a-c)(amp-Q=k~middotIf (A16i)riamptc~ Rlt9~~ 11- 3( h_ Imiddotltl-C) 4l- 2(~~(H- btCi)tI~)) cttC

)(~+c) (-1)((-1) =((~ t1 -Hi+(() lt 0 of -~ f (ib -t-e) lA+Il+ ct )+ilaquoc gt~ CifI+cl+Jl(c)+ ~ ~ a(-o)(--G)-4-~-c)(b+cc-4)~)gt0 tsc4 rc s

~ Ike fRS ~ f xi xI wt -Stl-fculot 11-$9 (t)=LXOY) 0( tiYfft~e~ -fo -tkt fl~~ 1-- oxY J e

lti) ~ -f~)( ~f)-a)( l t Yltl (c~wYcxnyJ (j - )(~1 4fT~ A X0( V~~ p A of yl t1ft 0

(6laquo Q bull 1 lj 111)1 (DW~v e

eJ41~ Let AAA A _j A 1 1_ -+ V]nq DO 4 CD e I

- its ste ~tS p-Ilt1 ProiIla-t middot ClrtllAA1Ar oreAA AA So(u-tVf SeL ot - ~ -_amp I~ _L ft--A A ----- ~ fJe ~ ~ --fI 01r~~ O4St SMs ~qIt ~t)~csCA-A) I lA_-A f

E)Ctl-eIlaquo-r Let A6COf tgt ~~ pe-tft Qc e t

~~~Q~ ~ 1kfwlrids~ A88CCIgtbEpoundA 1T~ -r APamptl~J~ le ACDIIIampf6i -laquo s~O~ tk-t ~s Ooet is so eM eII bullbull ~olt4-tfN ~et -ckt O~bullbull~ rt -e ~_W f~ S~

tJ 1(t0 AXC ~ AP ofe (o(iu o=A-f- A(~ J C- 32s amp A

lltc t))tA SIA~y 8)(1)= (1(8 CxE~ C I

raquo)(A 6llgt re EJ( 6 =CcE feMtt I

eurolCAJ- E)(6-t( - ~lte+El$ ~ pound10 eImiddotmiddot

1 ~~-A~)o (As-AJ1gt(~A~ S ~~CI amp euro1tf6lc~ ~se Ac Adol~ -t(t-t Lit set - () middot At

At~ t ~It~ AsIC~ Al~-+yen+yJAI (

_t a ~ - bull

~ 2-shy

I _0 c A 6 c ~ As V ~1~Ut 1 Sjtllc -fb ~BIC~ fW(t

ftdle ~ts of BC CA AB ns~chvell -tk ft1~ -tIua-t

No A bull G 8 A I ~amp Ca A~ (orr eU egt~ 4~_ A~itlA-~lClA-As~=(~tAtAr-tAjcA -~~ StthtlI4It ~ SaJc1ttA

(Nmiddot~~i~+Ar~~l ore4 l1A AAs = Are 1J~~Ai

Aft13 amp11 C=A-ttils-A)frSollletoA~] SiCt AS e Gfe i eRe

o~ (Bt-A)K(~-A) - (A-ttz-~tl-t- t t)AxB No ~~=~~~-=amp-AH-t)e ~~1 S-a-= It-t1)A I Ct = lAt8)- c tlA +ll-t~)B ~ (amp-AI~I~(Cz-~)=(t-ttl-trtl-+t~t))Al(amp~O A S~ CL At( ccdllfttor

~t ~~ 1~~Pt

o

C[~1D --r-0 vetlOf) )( lf ate Jt~y wtt-t---t f~ t -flat ~f~ ClX~yO kAs 01 Soat~

AT 10 o T4 s tktCcStI ~~A rf KttO ~ X0 f Art NIt Co((llteor

F4t IT AX+bY+c =0 ~$ote -e 1~I(z-s 4t4l 4-+amp ott -=0 J ilQA Xf Z 4le cbullbullI btACcS( ~l AO fIe b-tc-o w X-1-KZ-tYc-6Z

(~ar~11to(~1 wr~t--J Lftai c~ s OAAampA Co

~ OeLamps 1f 1 -1z- Aa6~l~8ampR AsampIA~= ~ 6 8-c amp-S tltcl A DAR 0

~e COIIfttAt t ~1 =- 1 ~ ~ P Pl) P3S~ Set - orlll at o at A8 btt ~trs Ale LIDa (ampfbv~ ~ A~ rA Q( e s So 8 1-t S6Wt (s EIt Cll No

Pl =tAt(c-t) 8a trA+ (ct)s ~- ~3 lAAt-tQ-) 8-= tA(-aA+Cc-ct)S a S~tU~ ~ 0= ltr- CArgtA + [pound1)l -(I-I4)$]B

A~ (tally rcf~=gt tr(~ Otu( (l-tl~-laquotlt)S=C Solll fott ol -tit pt~~ -+-s f ti ~I~Js

Nt ~~e ~ 1tu~~A+ SoSzCt-rl g$t Vs- r~ r~- r~1 Pgt1s~S)A+~s(tmiddotgt8 R= rlrfgt~A ~(I)J B

Y~-r)S) ~6a-t~S) amp c) ttS +fs-1S ~ p~f~P+~sampf-tj~

~ P1 ~se~rw)~c 0 Qtlgt+CoO ~ r fL cU-1- fc-i (ove

~ 0

A - -

~ FOf~lamp~

(1 -laquo ~C

fot-CA~ to ~ t t amp -t~~ crt a ~tc ~ El(tend~ltl St L laquobe ~[A8Cl Js~~i~ R= 4 C

Let ( ~t 4ct nwts lt 4e GoismvmcJt i-R- tl 4J~)(fo~of AAsc Sr ~ l=~~Yslt) ~ bc_

S A -- - 0 21 1iltelaquoe s dolAt C~d~middot ~o~ uI1gt ~ s~amp s~~C middot T 1_ ~ rI n -rf (i-- shy

tl Ie or~ DraJ clmiddotae~t 61gt 1pound Si ~ A= ----=algt i IS lle~ ltJOiOlSA0

~~~~~~~~~~~~~-~~~~=~~~~ p adEr-l-~a~~r~ A- oS+- jtus c~ - c e c I) p(]) Let 18(1gt L~Ms

I4dtt rAsel Or S~8c1oI(lcl~ 1leflAftt Let A6nct)p -r1 ~act 0

~Me C ABC ) GlUo~kc ~ PAx P6= Pc x PD = tl b~~=Abc bull P19tpound Note L APD L (PB

4R A1BC)aHd~ckLPAtgt=LPCBS=tfA-tb~~) is ike seifieAc ~AAPDACfB~=~~ PAIPB=fxPD

amp Q C Of 4A8C Lri pc C 1amp-~ ~~ PC Is -lt-~t lat t lie i4 jCbullbullr 4l( M6C Qt r Ie -i4~ to -e -fde ~ A A8C if (JJ

C)~ ~e icltc1e ot AAec ~e p A e OYlJ c fCL p~~re [Mel =[ALel[~cl+(CI1= ~-t~+~=SIr ~ Not~ LArc=LcPB

I-tfllWlbull [A8tl~ S($-11 ) (s-b)(s-c)middot I pCs f~ot -to LACp4C ampP(~ Cos C= tt2ttoa-c (~AI Ci(~ircl 4 MBc B 2shy

[A6Ci= ~SiIlC=Qr(+coSp(i-($C) ~AAcPACBP ~~ fgtc PCPAlltPB =(Cl~-+Iot-c~t-~a~-9 ) = catlo-4 t )(A1(-c)(CoHI- b)(o-Il-~= S (s-c)(~~

2- ~ a

Ci C [AS(I A 2

~

I

~JJI LPFA-=odeg=Lpe~ ~ amp~ ~LPFeLPAE

C5Ji) ~tolt1 s-ThtOfotfll Let A 6c~ ~t dlSncf ~ts 01 bull ~c ~o - Me~IA~ 1( bull t Of~~~I ~Ot bull -Tht~ bull Sa c~tOV M1 C(liofIPT potd~ A 6 C Iie to

AI 6 C 1gt (1~t~c 1gtpound fCLR atfmiddote ZA ~A A ZA bull -~ -iA ~Co~ PAQ~clf$ WeA~ ZA~lA I tc Z~t

pFAECc1dk

bull ~ Srlloi(y taCgt6~~~-lPFB ~ pG~ f CDCCYcbull LPampb LPFI) = e 1klaquo AIJ~P LPAespoundp8C pfE _ LPeP 8EF (0(1ltlt~L PFE L~8Tgt~ LFP - L 10 collirAfampff

)fgtC)~Jl~~ ~ ASC1HAol6C=AcS]) bull (~~_ ~ktI AeCO At)ItBC ~ACdtgt 1)~c 190pound 0 sWLe AB UJlfsftfUct A ampA6

S~~41 to flCAP 1I1elt AB A~ 6eshy

6 Ai - 7ligt= (1) lBAE=LCAJgt

SO LMc L BAlgt-L1gt= LeA1gt-LMe =LEAt) Tkeuro1 A8AC~Ae-A1) So Rr-c EDAtgt~A Thet Aec~ A~8C =poundItampE AClC E~ AC80

bull A rC =c Sf-t Ell I

f1-I-4j hoW~ ~8euro~EtgtS ampb ~ E iUt~( SO - ~~oeA~LeeALtgtCA ~AsectCO Sltffc

SoSoft ~oe 1et~6cP cl-ampd-p~ 0

tI~ Let l)poundF fetf~~ff- P~ ampa Aeyen~~ ~

Asse ~Mist (so4 is 6~UA_JC ~AGSC ~O bull G ~f( Aalec~o)

tt~e9 7eff

fovlaquos X I Z ate (es Aamp ampCA D ((t~ve-()ty It X I Z (lie (dl-lflOr

A ~f f6 lhg--1 ~ xe YC LA - middot ~ lQt Dbu (~ Ac soct1IIt 81gt II J( Z -r1teuron

~g ~ ~ 1t~ ~z Se AlC 6Y c~ _At P1Q (i~ ~y Ie ~c -- _______ r tamp iU I bull laS yc fA ~Igt ZCZA middot lCI~ lIeeu~ Ie~

If ~ tL ~ =-1 iIamp )( YL MHo l~(~ Y~t~~~~ SlJ) Ltt l~ X(OCA -Thtl b Mt11Idtw 11~ Ax ay CI _ lt Cz Y Cl iiiK zA --i ~o --=-l1toobull CfIea bull _Cl -a

I I

ceDD ~MelI s lIeo~toA l~tA I ~cc t) euro ~be tc~ lO 0shy

de lw~~ ~( ft amptCtSSCti 1 tf (~ diC- (~QEf ) bull

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I iIC ~ AeC SilCamp ~ IH 6e - c I

J vue b -ftt (1) We t _ 1 _AC~ r - Be - - middot

iDA ~ 01gt1gt AJ)middotC1) tt Mltrtrllj b~ lAOmiddot~]) CO~2 1aJkSimiddotces amporeJ

A6amp c) +A)xBe Acll 81gt middot

Re fICS 11L sf ~ eat be ltoftrec -to ~t -I- ~1-tllAt t MilcO + AtgtICBC =AC 1CI1~

~V Asctgt S (l u~ ~lJ4~ 0-shy

~S6~~~ kfCfS4tJ foJt of~~ -+k eampIt~ otIIIetStM Ai ~itlt ~s -fIc ~o~~ rote iIt wJere -reIs CIMif s Mesc(t _

-

6x4t~le 2 Lt ABc 0 be ~ ~tllt t(kft~ suamp~t At ampt so liltftStct At Y1tt ~r AtO P~t~( -Ke -refltecf of 0 ~fOSS AS BC C)1gtA A~ C4IIcYdtc

p _ c $Lt-~ -71

Lcent P~ ~So k ~fut f-~Wi _ 010 0 flO Msc CD lgtA Ye cdIVt bull

sc =l Ott foIIttll is ~iIr~le-t -fo site (5 -tk Ptt-RS l~~( (Sl~~14ft

e IcentS 0 0 -to tts e_~Hrlt OSAP DfBQ ~CR O~DS ~ludlC~~ J J -J ~ _ bull

-tt TltitCirtlutdts Ie CA Ca Cc CD rtsrdtuely CfSMoSmiddotd fIf~iQ 3(0 r ~r31gt0 By ~ct(s)

I~ AC Q( e04~~t ofo ~gtltS

cfct (+) I CA SIrcent to filllt LA fllAlrd to 81gt CIrs

Set to ~ IIt LB ~(c of Ac I C ~ Sci fo c tAlC -to ~lgt1 craquoisSeoet t ol1t LD~E lc ~

0 0 r~-t 0lt1

L Nen bull

CpnCa= 0r~ LAf Le P )Mjl-ly 4~t( LI) R J ll)n~ So bull

$r~ AcJ Mgt PClKs ~~Ic~4J~~ ~ fet h) PampRs is floc

~

G)Cdtpt f

Le-t P bft Af6~-t ~S~ 4l1It Appound ~~~-t LAPB-LACS LA(C-L~8C

Ltt tgt amp be ik~~tS 0( AAPS )AA~C nspecflf ~toe ~l A1gt 1gt1 ce )wtet A fOiWtshy

~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

( )tlfamp 61) biSKfs IA8PJ By ~t CT) ACAfACf~ ~ ~ I3A - XA So iSttf ACAeACampA

P ~f - xpmiddot ~ P~B6+lCApLcA8 J

C-1-1 ~=~ 5tRCt X ( 4ft AP ampt ~1It By~t (s) 1 ~ tCp~=LCitA ~ ~ I I~ fQ is Seoct of ( ~ ~~ 1 f4$s~~3C o listf SiacCrtIeO ~ -T(Alrl~f4lrgto ~~(1)1 tIIet pamp ~t(4C~I~Ois~tfo(0

A ~IgtC A~te A lU)e bullA p A APelAcIIgt f-c ~) I SIWICamp

I

~ ~ ilt3t +00 c( ~ 1 PQ fh ) Qm Q J r bull bull ~ t01 setc~ 10 t of I I

No LM~-L~8-=-LIWC-LAec f~ $(amp ~st ~JO 0 Ao( ~J~~ ~ Atl 43~ t (-d 0 ~ A61PcD

fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

Page 9: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

CEi0 ~~N~ ~ let beQsJf~e(-f(f ~ K+O So i ampmiddot-i ACo~~ iSA )lJt4~fotmiddot A- b W~~ Co III ~ teal --~

--rfa ~t -+ A( ~rtlt 1I14us ~llloe (~~ ~ C G~cJly ct s el+J of t1SJ bull ~+Igt~ U~fPOlt (ft) Ent M~ fb 0(l +be bull c-+ ct i ec) o (0 )+ (c(-elc) (4-tc)-+(~-td)1 (410- (cot Ii) ~-c)-+ (b-clh bullreg ((H~)(-ttJC=(Ac-bcl)-t(~-t~dl 12 ~ c-td~o -flt -- c-e(-= ~ J Ne( Campmiddot c+Ji ~c+~ ~co1ts

I

~ IAtb S 4-1o~ w~4eA4 -iIu 0 C0JY-te a( Atb l~ At6t -Ilt o~oo4t ~14a (Of ~) tf at is ~ 4~ lilt middot

NoI-t i--s is ike clt9t- be-l-wu (00) a( (e)

~~ W daM ilu~Solf VAl~cf olIIt y At bmiddot=J4Iot IJt --lA-t~t=(Glt~Ga Ioc)A- 1 ~ ~Cll--bl - shy~ 1 711a L lfO

Yroee~bullbull~ Ltt wJ~e( - _ - bull - - - - - -- IJL _~-J(D Wt1 +l W-L w-aJ we=w i -n - hi

~ lt~~wt~ lzlltJ 1lzl iYI~~ - middotifUoJ

~ Jqt~~ =leampal ~=c+rk=Wie~Ji4e- I ~(eo) lit ~el~-6z)

i Wt=(p~b(c~d~)rrae bull amp ~ yo~e L~

1olot furrn n It- be e ( Ie l= 4t(i~4 fLC loi(l~ 9 b(~(EfR1IvLfDs4ttX-cN ~ to ie ro~ CO6)~l) 14~

(o(oo) Caocdlaquoclottfse cCllIctcn ats o(td 4e ~ ot o-tbi laquot it is cC~ r o~-iW)~f~ e~e oyo cs8 tl~s (fosS)+ i~9l It A~~c coseH~=YeteIIlaquoi~ to ~OftS ~ bull

ey ik cu~ I f xt~~=Ye )~ ~=r-e-roY AI( fe Z~CIsk lWtf fir ~ lee euro C o Go ro~~t~tt ~ ~t wf ~ ltII _fir ~ ~ f bull (6+l~

I - ire gt I~ J1=e ~ J

) WftreileH(Il-Imy

~s ) ~ ~CI~ W

fIrre J

l Ioh L T_ -f -t ts ofJ

W4-II4 C4S~ pound_ )

~~ 41f Wid Ja-e w)e )

I1 2~)tt~ I pin e Afe

-ltv ~t Setflaquots ~ A I~d ~ampPav3~

Cotttple~ 6eUYIUi(-ry

~ -t Ls ~ N~~tQVs e c gt e - Ccs9 +Se

~sc Obte~ ~ ~

CD 1- W claquotsr(middot t -R Ie-tt We III r ~1 ~(+ot) ~ 01 e _ 8 To yot~+f A YIi v fLe rlAlIe Iiishy

- r I 1fSj~t -to -Ie ~ ~ ~ Go)1 ~ C(

=~ r_ ik We $~fl1Ioltrb 1Ie crl foe l fA ~ - e b~ e

Acrl~1 Ie ~ ~s Iej f t ~ fl=- E

Ei-tmiddot 1- ~-tljk -t di-Yoits 1

Gi~ W W2 fke 9Qta-~c e~CM Af -tI ~ ~ ~ ~-~~k IN Wa is O~ ~ 0 +t Wa t ea - 10

W ~ So z-w bull HelllLc ~-J _-i -- ~1ecJ ~-W c

Wz-W WcW I ~_Wmiddot 0 1-kt beA ~~ olSo tJi~u -tk cJ~r

igtr -tke ~~ ferlts 4 WLJ l -to be eolheAr- eogi- of l u fcoJc ~ 1 1rllleP0rt

i CtrIz-) RottmiddotOW 1oJ1 9t W

- bull -1 II It-vL

e == Cos 1 gts = 1 bullWIw Eltot of-ike le tkn C rttr~JcJA

-to oJ W1 5 f l-C -~-c- l

0~7i-f ~

Li f~) ASS-teJ wt~ (uit) c~tctf

11 w W~ n 0 ~ tle ~-l cJe (at wi =Wzih~ l )

~ -tk trto ~~t ~O J Wt so z u

l- _ Wz-W C - - - l - = -w~lc-W t-w

Slworl~~ w~3~t ~ _ ]t +WWz t Wt W2 bull

-r~er~of -to h amp ~jl ~ ~~ lot C r~ 0 W W-z s l- C i (wamp-w)

---- -=WW1 ~-c -W(W1-W)

lt)irljj We 3 t I~-101Mh C-IVWC

1A~i~Cst

Let~ Wz~ W we ~ct ike f~Otl af ~f -tampjc--t ht t ~ i tele I)t I wI~~

(l+ lJti JW] yl ert~ -tle rey bull tcJr fa c To iIt tlaquojct

lIt cJ W is -L Wt

i(J~w) -= T(w~-~

~gt

CD C~eetfe( 0 is ~t tlv ornI reg CeV~J G is ct A-tA~ A3_

() I eurot- NH llt (-r~s rs -tf 41-1 ~- 1 A A A bull A tateo J n I l _ J i (~~Le~ ~Alll~b) s 01 SCt~eD u -pe v~GyueJ

(jOf4-hoce~t~ H l$ c AT At+ Pr3 (be(AASe O~ = 5(O~)) pound1- f lt tl~ A ~ fJclCi-r -to ALA 1s

i- A-A3 ~ -= At - A1-AJ A bl~-t ~ 1 1laquo ~ ~ r~~cJAt -to AA~ $

c- AA) == ~- A~ ~ -rktSt -fwo -ts W f~cf ltt t ampJk4J gt~~flaquos boi lut~~ u$~-f~ ~t tAll lAzI= tA- i- (e

AA = AzA - ~X3 -= ) t ~t lt e c At-tA T A~ SAiSfelt bofl ~t~01l~ 1eo t-= AT At -( ~3

17 N f t - L A+ Al-Ar) 6 Ce---+ef ~-tke ~-e foitrt Qftle $ DA l-

(be~oe 1-1 $ ~ ~Jro~ 4 o t-t) ~tCA ~ Mi-e fit arcc is -tke Ciolaquo ~t f4~SfS -tvnWJ4 ~ a Jo---~ -4le ~~es AtAl Aamp+~ As+A) ~ ~- J L -) ~) -

~Q 1eet qf ~ al-t-bAdcs H I 1 1-3 -=t ~ Wampdtoi~~ -tk ferllaquos ad ~e D~e1 ~~ raquo A~lt

(J~i(t~ ) A lltzlJ J llWW1-~ Ayt ~ito

Sol4 SifCamp ~A~R~lgttPLlCQA~ ~rJwail~e Arf A+cJQ+~~R20 I 1i~R+~~Pao C-t~1T~ZQ=-O

I ~Il I w e LV = e ~ 5 A ~t 4 ~b To ~~ fl X 1l s erltamptDI we CoM-rtf

Xt wl-t t)ll= (Ai~amp ) +w~Ct~iP )~(8+~~

= k [CM Q+ ~~)+ 1Yfgtt wR + tf )+ w (C + p+~ I = 0

~~~A I )( ts ~ (Rot 4 1 J~ ~ ~-t 4 -II 3~f1 C~cf ~ ce~-ter4cl At ~ (A e) ~ ~(f-t~) (ie ~c pOlt 3 -the amp~~c ~ ~ ~11t~ -G t- ~rid 1 ~~t AS)

COlf~selj Ikj ll~ 01 ilt G~f smiddot ~ fo~t ~ loc-s 61 )( 0-~ G~f C = i(Jlt- CA-t 8)) is -flc co~nsfo-kj lt Ov- ile ~t Clfdt

1-(t1J~ Let A~ A)e tI ~r~ 0t W1w) w~j I Y~ f~~j

fYo~ A ~ J~r - fe~~ -to -tkt -t~~ e to ~ c~tdt I

01 b w WI W 3 Got W bull skw~ ~est f~(tS ~ctCmt 1cle-t~~ ~s tmiddot~t t C)~

~otct~ JlCG ASSUllC -tL ai~cit-tle is -tlt kAtf GifC(t

~ h~ le~~tcJA -to t f~eMt oJ 1J -iklk ~ MS et--4M rll-tvJ~

bull l- A ~-A - WltWl t~ k~Wi -r ~- w - tV - 2 - - W 2 bull

Now WI bullbull f -ike ampM- ~~lc I SO Wd -= 1 i1e we ~ fJ~-te -tk ~n 4S _ _

~ bullbull Z ~ _ I T ~-t Wos 11 W + 2 Wl ~ - 1iIII I - - w

2 2-

F-oN -tk5 t ~ ~t -tk yoil-f N Jw~ -+ W3 $ 0shy

--te e lt$-I(C -t1e e1f~sS1W f Ns Sr~t~c ~~ nSFt -t oJ Jt Vis we (4 eot-t~ -tMt wtl lISO e O~ -tIt o~-- -two les -t~ e-Fc~Sto ~1 tJ -tt l s u~ -t $ -tle (fwle1 ~ -t~ )1 fO~~ (tce ~

J I W-z4 _

11Ob~ ( S~~t lYe Tko~ ) let W be D~ llt (~crclf ofJ ~1 13 c( PI Q1 R

be ~ iut ~ ~ lC ftJi~ ~ W -tt t1I 2 ll I tl ~ I ft ~ec-f~Jflj slw ifvt P Q R A-e tAl(Il (-ps Ole 5-

clt~ A $~501 11 tf A ltamp-t) ~ W) i

~ol~bo- WamplAi loss -t 3~nl~ I Wt J lS$We Je G-nIUshy

Cilampk 1s ~ ~ cttclt ~ lll llJ lls -= lw I ~ t 1kt k ii ~s ~~ l+ ll~ ~ Ii t3 --ie r~~ fw- W + 1~ Ivs ~ f-ltl ) i tJ- Zt~W So Sol lkcsc -tcdr W~ 3laquo l = ~ t L + W-lE W

2

St ~ Q ltl ott ilW --l 1(= tt f t~~1l

I sluw fQR 4t CttlfUf it S~s-t st P-R =l-amp-Nil f-R _l- Z-amp-~~ Yo-~~J (tI 4W -g ~-R

Q-~ -1-1)-1tJ --l~W X l ~-amp~w ) l2tgtW-ltl~ -lZ+ t

4t~ w- Zl~-ll-t It f- fl

- (1- R bull

-J clt~lttii lw=t ~ WW-=i

CiiID ~tlt~ firLiA BC let 1gt be A4Ie GtIlOc1tf- E 001 As loIiti DEit-CB J ~ F ie 600 Be I

ciA ~fDf oX ~~ o-rbmiddot 0 1 ltt ftt XIS G(( Gr be 01 EP ~tS~t ~ el~ttrlgtedo-r W~~~~fk~t~s X Ao D C fSfoFc-=Ep-=BYc1gt=r

~J ~sted oR we rMj Sity ~ i 7 middot PrDV~ 6i-F fs pcmI(e( -to -Me 4 b~ 1 -M CaJamp) Xl= Of-~ -tI S~1 je Y-X Sol-I Set 1ampt o~ AtAo tt(-~ IMc

For ~fS X It we e Ix-+f ~ lxl +111 ~ft Tie E 8 Gfl = C ot~~ E (0 r)klgt(d~ 1- W-11IAy f X= ~t(r-s-e t~o A~ F tB t(f-t)c 4( euroj =tE t-((-f)J) _ h Let Pbe 0 poillt el LIle )( f lJe lter t= B _ L _ amp1gt g + (_t )e~ middot gtY haYCamp oP=toX+(f-t)oy -f=~y ~ Be -- r -i1gt-t ~_

J J gt1( 8 -I io O~)y~ amp(01] ~ P-u SfjllleMt Xt E retgt I $0 IE-BI rD-cl c1

EICjl1t Call a ~1IIecent ~ ~ QjgtWelC ~l~ (I- ) Is (E -amph 1l ID-d r-(t-amp)(c(-f6-Jgtfd tl )ltLJ )M ~ ct j~ Ie ~od ~ orF9fe sk~ J i q F- Gt = t6-p)~+ (I-t)(1-9)C ~ +~hw ~t cf -tk s IIf-t4 Jgtllrl1lpounds Of ~t(tei _ IS tlt-p)amp1~$ htfampt iits~etet ~ik~litetllllorltl -tlt-p)la (amp+~~ =(~~k1NIllelo I _1 t f4IIIl ltf1ltS

Sll~ fir trl4t~ A~c~ Itt-A IlIamp 1M OjL ltf 114 (tw~-for ~ pound Me~ --ik se ~fOW twI ~ _ Igt IC-tO - f ~ if

T -poundTI-r -pound ~ I A=0 1)~D i(1el IC-BIt lo-dtll)~

UI8iC-1gt1 +11Hlt-at=Iel+ Ie-IgtI+11gt1 +1c_~(f~~t Wt ut Ie+IC-Igt ~ Iamp+c-tgtl t=~f1f)

AA IDI + IC-61 ~ 11gt+C-81 C-~AO=~8C) (gtt) holds ~Le~ft~~lcJs A81(1)C ATgt Usc _~ __

c6hf--I--l~1gt~ ItiC

~1- ~t fmiddot~~ 0+ ~ 0 ( is )(Y=tJC( (1 rsti - Ex4k+ Let 0 ~~ (i(cAt cf 4ABe 9 ~iIt J bef -fIl lfcffS Jf -IIf (t) Xi=fX (y+I)zmiddotXmiddotZ+fmiddotZ 0( (cXl-Y~(Xmiddoty) ~ I~~)(middotX I IXmiddot~~hd1I O~iOf (=) Xmiddoty-O ~~~~~~~~~~~~~~~ amp--ft 3 Let A8C b Le lmiddotts ~sfmiddotmiddot Phe

Ac~+amp~+A~-t8C~~ Ast+ctl SJt~~ Set1ie Ot~I ttt A ~~t f Jw

CmiddotC +(amp-lgtHamp-~)+D~ (8-c)~-c) ~ amp (c-b)laquo- At~(~- awl lt~~-f4ls s fu ~4S

(6 C-b)middot(S-C-lraquo ~ 0 ~~ck s (amplt-1) ~o

A ~t 1gt Ie -tLt poit ~ Aamp -L II ~ e _ ce~AAcO

p C fgtrcw _t C1gtJoe ) AS-AC Sol~~~~~~~dO~A

A a A J) A J)= ~ E=~~ =3 +~lCJ1gt-C=Aamp-2C

C1gt1 Oe- (A-tS-le)(Mc+1raquowO c) No AA~lh c C C(CUM(bull (IampSt 8 41f1$-bull (4) bec u Amiddot(Q-ltAB-ACO 1IeJtt(~) ~ OAl ~c ~ A~~AC

euro ~ toJs ~ 8lt~ 1)-A69 seAPS fWlkl ~JCOc $ firAABC jf( t ssewu-J -ptMf ~ c= - ta-+CmiddotfI AAS( its ~ttd q ~1 - If We Sampt -iU CitClIMChH- 0 AS ken -HII-srft~ ~o -t r -11 __ -~ -1 ALh--COtt - 7J 0 OtlGCnx n - ~-

A Fit iAcetft tJf ~~ c 0( lU= ~ = L

co b AI c lt-c

e ~ 1)c 1gt= te+(t-t) C t --amps ~1i~ poundL = tD ~+ cC C bI-c Gte middot I t A-t -~)tgt t-ll- A

aAtlS cc_ - tgtA - M~C 14 e middot

11l Lqt-(gt OmiddotkC Gtctal ~ICef c(H ~r J

51_ Set 5 4lt C4fColt_bull tu e -H Matel~Me1~ 1~ AA+b$-t C shy ~ 4~(

Lampil~gt 1omiddot~(i-1)l4-1) lt0 A-A 6middot~Cc=(tlJ 2ec 6amp+cc-(a-c)(amp-Q=k~middotIf (A16i)riamptc~ Rlt9~~ 11- 3( h_ Imiddotltl-C) 4l- 2(~~(H- btCi)tI~)) cttC

)(~+c) (-1)((-1) =((~ t1 -Hi+(() lt 0 of -~ f (ib -t-e) lA+Il+ ct )+ilaquoc gt~ CifI+cl+Jl(c)+ ~ ~ a(-o)(--G)-4-~-c)(b+cc-4)~)gt0 tsc4 rc s

~ Ike fRS ~ f xi xI wt -Stl-fculot 11-$9 (t)=LXOY) 0( tiYfft~e~ -fo -tkt fl~~ 1-- oxY J e

lti) ~ -f~)( ~f)-a)( l t Yltl (c~wYcxnyJ (j - )(~1 4fT~ A X0( V~~ p A of yl t1ft 0

(6laquo Q bull 1 lj 111)1 (DW~v e

eJ41~ Let AAA A _j A 1 1_ -+ V]nq DO 4 CD e I

- its ste ~tS p-Ilt1 ProiIla-t middot ClrtllAA1Ar oreAA AA So(u-tVf SeL ot - ~ -_amp I~ _L ft--A A ----- ~ fJe ~ ~ --fI 01r~~ O4St SMs ~qIt ~t)~csCA-A) I lA_-A f

E)Ctl-eIlaquo-r Let A6COf tgt ~~ pe-tft Qc e t

~~~Q~ ~ 1kfwlrids~ A88CCIgtbEpoundA 1T~ -r APamptl~J~ le ACDIIIampf6i -laquo s~O~ tk-t ~s Ooet is so eM eII bullbull ~olt4-tfN ~et -ckt O~bullbull~ rt -e ~_W f~ S~

tJ 1(t0 AXC ~ AP ofe (o(iu o=A-f- A(~ J C- 32s amp A

lltc t))tA SIA~y 8)(1)= (1(8 CxE~ C I

raquo)(A 6llgt re EJ( 6 =CcE feMtt I

eurolCAJ- E)(6-t( - ~lte+El$ ~ pound10 eImiddotmiddot

1 ~~-A~)o (As-AJ1gt(~A~ S ~~CI amp euro1tf6lc~ ~se Ac Adol~ -t(t-t Lit set - () middot At

At~ t ~It~ AsIC~ Al~-+yen+yJAI (

_t a ~ - bull

~ 2-shy

I _0 c A 6 c ~ As V ~1~Ut 1 Sjtllc -fb ~BIC~ fW(t

ftdle ~ts of BC CA AB ns~chvell -tk ft1~ -tIua-t

No A bull G 8 A I ~amp Ca A~ (orr eU egt~ 4~_ A~itlA-~lClA-As~=(~tAtAr-tAjcA -~~ StthtlI4It ~ SaJc1ttA

(Nmiddot~~i~+Ar~~l ore4 l1A AAs = Are 1J~~Ai

Aft13 amp11 C=A-ttils-A)frSollletoA~] SiCt AS e Gfe i eRe

o~ (Bt-A)K(~-A) - (A-ttz-~tl-t- t t)AxB No ~~=~~~-=amp-AH-t)e ~~1 S-a-= It-t1)A I Ct = lAt8)- c tlA +ll-t~)B ~ (amp-AI~I~(Cz-~)=(t-ttl-trtl-+t~t))Al(amp~O A S~ CL At( ccdllfttor

~t ~~ 1~~Pt

o

C[~1D --r-0 vetlOf) )( lf ate Jt~y wtt-t---t f~ t -flat ~f~ ClX~yO kAs 01 Soat~

AT 10 o T4 s tktCcStI ~~A rf KttO ~ X0 f Art NIt Co((llteor

F4t IT AX+bY+c =0 ~$ote -e 1~I(z-s 4t4l 4-+amp ott -=0 J ilQA Xf Z 4le cbullbullI btACcS( ~l AO fIe b-tc-o w X-1-KZ-tYc-6Z

(~ar~11to(~1 wr~t--J Lftai c~ s OAAampA Co

~ OeLamps 1f 1 -1z- Aa6~l~8ampR AsampIA~= ~ 6 8-c amp-S tltcl A DAR 0

~e COIIfttAt t ~1 =- 1 ~ ~ P Pl) P3S~ Set - orlll at o at A8 btt ~trs Ale LIDa (ampfbv~ ~ A~ rA Q( e s So 8 1-t S6Wt (s EIt Cll No

Pl =tAt(c-t) 8a trA+ (ct)s ~- ~3 lAAt-tQ-) 8-= tA(-aA+Cc-ct)S a S~tU~ ~ 0= ltr- CArgtA + [pound1)l -(I-I4)$]B

A~ (tally rcf~=gt tr(~ Otu( (l-tl~-laquotlt)S=C Solll fott ol -tit pt~~ -+-s f ti ~I~Js

Nt ~~e ~ 1tu~~A+ SoSzCt-rl g$t Vs- r~ r~- r~1 Pgt1s~S)A+~s(tmiddotgt8 R= rlrfgt~A ~(I)J B

Y~-r)S) ~6a-t~S) amp c) ttS +fs-1S ~ p~f~P+~sampf-tj~

~ P1 ~se~rw)~c 0 Qtlgt+CoO ~ r fL cU-1- fc-i (ove

~ 0

A - -

~ FOf~lamp~

(1 -laquo ~C

fot-CA~ to ~ t t amp -t~~ crt a ~tc ~ El(tend~ltl St L laquobe ~[A8Cl Js~~i~ R= 4 C

Let ( ~t 4ct nwts lt 4e GoismvmcJt i-R- tl 4J~)(fo~of AAsc Sr ~ l=~~Yslt) ~ bc_

S A -- - 0 21 1iltelaquoe s dolAt C~d~middot ~o~ uI1gt ~ s~amp s~~C middot T 1_ ~ rI n -rf (i-- shy

tl Ie or~ DraJ clmiddotae~t 61gt 1pound Si ~ A= ----=algt i IS lle~ ltJOiOlSA0

~~~~~~~~~~~~~-~~~~=~~~~ p adEr-l-~a~~r~ A- oS+- jtus c~ - c e c I) p(]) Let 18(1gt L~Ms

I4dtt rAsel Or S~8c1oI(lcl~ 1leflAftt Let A6nct)p -r1 ~act 0

~Me C ABC ) GlUo~kc ~ PAx P6= Pc x PD = tl b~~=Abc bull P19tpound Note L APD L (PB

4R A1BC)aHd~ckLPAtgt=LPCBS=tfA-tb~~) is ike seifieAc ~AAPDACfB~=~~ PAIPB=fxPD

amp Q C Of 4A8C Lri pc C 1amp-~ ~~ PC Is -lt-~t lat t lie i4 jCbullbullr 4l( M6C Qt r Ie -i4~ to -e -fde ~ A A8C if (JJ

C)~ ~e icltc1e ot AAec ~e p A e OYlJ c fCL p~~re [Mel =[ALel[~cl+(CI1= ~-t~+~=SIr ~ Not~ LArc=LcPB

I-tfllWlbull [A8tl~ S($-11 ) (s-b)(s-c)middot I pCs f~ot -to LACp4C ampP(~ Cos C= tt2ttoa-c (~AI Ci(~ircl 4 MBc B 2shy

[A6Ci= ~SiIlC=Qr(+coSp(i-($C) ~AAcPACBP ~~ fgtc PCPAlltPB =(Cl~-+Iot-c~t-~a~-9 ) = catlo-4 t )(A1(-c)(CoHI- b)(o-Il-~= S (s-c)(~~

2- ~ a

Ci C [AS(I A 2

~

I

~JJI LPFA-=odeg=Lpe~ ~ amp~ ~LPFeLPAE

C5Ji) ~tolt1 s-ThtOfotfll Let A 6c~ ~t dlSncf ~ts 01 bull ~c ~o - Me~IA~ 1( bull t Of~~~I ~Ot bull -Tht~ bull Sa c~tOV M1 C(liofIPT potd~ A 6 C Iie to

AI 6 C 1gt (1~t~c 1gtpound fCLR atfmiddote ZA ~A A ZA bull -~ -iA ~Co~ PAQ~clf$ WeA~ ZA~lA I tc Z~t

pFAECc1dk

bull ~ Srlloi(y taCgt6~~~-lPFB ~ pG~ f CDCCYcbull LPampb LPFI) = e 1klaquo AIJ~P LPAespoundp8C pfE _ LPeP 8EF (0(1ltlt~L PFE L~8Tgt~ LFP - L 10 collirAfampff

)fgtC)~Jl~~ ~ ASC1HAol6C=AcS]) bull (~~_ ~ktI AeCO At)ItBC ~ACdtgt 1)~c 190pound 0 sWLe AB UJlfsftfUct A ampA6

S~~41 to flCAP 1I1elt AB A~ 6eshy

6 Ai - 7ligt= (1) lBAE=LCAJgt

SO LMc L BAlgt-L1gt= LeA1gt-LMe =LEAt) Tkeuro1 A8AC~Ae-A1) So Rr-c EDAtgt~A Thet Aec~ A~8C =poundItampE AClC E~ AC80

bull A rC =c Sf-t Ell I

f1-I-4j hoW~ ~8euro~EtgtS ampb ~ E iUt~( SO - ~~oeA~LeeALtgtCA ~AsectCO Sltffc

SoSoft ~oe 1et~6cP cl-ampd-p~ 0

tI~ Let l)poundF fetf~~ff- P~ ampa Aeyen~~ ~

Asse ~Mist (so4 is 6~UA_JC ~AGSC ~O bull G ~f( Aalec~o)

tt~e9 7eff

fovlaquos X I Z ate (es Aamp ampCA D ((t~ve-()ty It X I Z (lie (dl-lflOr

A ~f f6 lhg--1 ~ xe YC LA - middot ~ lQt Dbu (~ Ac soct1IIt 81gt II J( Z -r1teuron

~g ~ ~ 1t~ ~z Se AlC 6Y c~ _At P1Q (i~ ~y Ie ~c -- _______ r tamp iU I bull laS yc fA ~Igt ZCZA middot lCI~ lIeeu~ Ie~

If ~ tL ~ =-1 iIamp )( YL MHo l~(~ Y~t~~~~ SlJ) Ltt l~ X(OCA -Thtl b Mt11Idtw 11~ Ax ay CI _ lt Cz Y Cl iiiK zA --i ~o --=-l1toobull CfIea bull _Cl -a

I I

ceDD ~MelI s lIeo~toA l~tA I ~cc t) euro ~be tc~ lO 0shy

de lw~~ ~( ft amptCtSSCti 1 tf (~ diC- (~QEf ) bull

t p Ae ti l)euro J Q Bel pound f 2= Cl)n fA ~ ~k ~ Q1t ottc(l(ea~ ~QIR~~~ -

f~ 1 ~ ltt X~EfA 1AMCD bull ~ z- C~neF Arr~l ~(atts ~ff 1e-(fM1oec~ FA

ftt- Ool~~~ 4xf l w hVII

e-- ~ X K __( It X2 ~_( t ~~II Qx 6y Ct ~y pzex I fllFxijmiddot 1I

Hul~pr~ ~ AIl ~~ tfffSfctj cofI4t tt XA)(B XEmiddotKF J (CmiddotYP=1AmiddotYS ZEmiddotZF= zeZIgt W~~et ZQ lSf~-i igt PQ~ ore rlfltelaquor

Qx Pf Itz loy c-enc ~Mee(AaS

t-rks ~ere 0 Imiddotil~ (1$($ of PoucJ s for It we tftwt Ato 8 -te I AIwIJ (3 il(cJe 1Iofl1-t i AB will b~ ~-t1l3et (iot ot B ~ It~j CIt~ we ells JpoundAoflt ~ t~ liflE Clt B b~ BR

6lCtJfC i F~~ h Cf(Ultirc~ ot Mac J f(it 1) ( ~ ~i~0yen ot -t4l~lE I~ ~tA - ~~ Be ~ e fM 1fe ttusc(e~ of-ffwf3ct (tt4-t C3L1r~ CA~ F= bt ~ ttfStd~ of -tINt ti-~-f Imiddot~t ~tC wo( Aamp 11161 PI Ell F o~ ctU

Soof~fIyen P=Mo 8C ~ E= BBnlA f=CCnAB APP~i P~f ~ ~(fo MB See I fott et 1gtpound f c-

-- =JSiiiiIii

b)lAtc ~ Let-tgt 0- eht ~cfs 0( dt101 AtCS

AS ~ AC O~~e (ilcu-R( Mac ftspciwJy l(t tgt Ilt ~f AtC sCI ~== DPn SA J R= PEn AC fro +~-t lile QR~s~(QVJ14 fttCf+~I (~ 1) ~ f9bt-Mshy~e 1)rff0--AS- CO ~SfctsLAc8

Co ~r ~ qftllCr At =lgt 6 ~LAec So 1= Cl)n G8 Sf_ eEtS

Q tgtPt SA DP 8ital R= Pe C Pre ttL PlE AI

AIP~ f~l ~ 1Ito(-to C ~ P er ~ w 1 ~ bull 1I

t Set I Q Rut tIff~ Co~~d~

~ -7

Alt IXu q j

elf (Ga1(e 3 Ltt AT3CPs e ~ +s tMDlCJe ~-rd AAfLBS Bat LeA) ccf LAB fat 1gt be ~ls (I ~cucl1t ~c4( I

DA(11)C= AU DB()CAe~ 1gtCIAB~ fgt~~ A~ r~CtfaJ T4 6v~fi ~ IAGC a~ Co((~((r

~olf- W HL-cI oy-((~( ~ AA Be Ne

AAIB~I)Cc(-=I DArBC=A 11gt1( ISc AtA f Cc -= H L lAlA I C I Cl

1t~()cD=C1 ~l (AIBl (cjAfrrr5~5Gl ~~ t DAAfCC tgtlt Se4 A HC tit c11ilaquoraquo SIt 1y ar171~ BS41s(to AS e 0cc we Su e H 6ltve c1(i~amp r A~ H C~ S4rt a(((~4~ I

-~ ALI)f ~fle1 tt P toe a ltpor i~4Mec

LtfP I~~ff~I$f- 5 -to ~CA Camp ft~t~ lttt bJ() ~_ eshy

ll 10 ~ fet ~~~N~ c-tohs API sp (~ftvtll IfQ P ~ 61bullbull Pt14 PttNQ~~ (tries ~tll~ Qfz cod A~ aft ~et

iSoLttd- $(fCJt L CPc p) LCQLP LC~P Lc (gta Palt-e J -t ~es c P ~L I PI Q p 4ftcocttc f~AfrI15 ~s middottU(Woto ~1l$1 w-tSu CPt ( gt e-= A ) P t1t( QIP= X ) (Q-a Pf P2C-= B 4re CoI~rtelr $6 Rb2-l amp1L ( AB-=Xmiddot ~ ~lIQ P~IA8 tVe ~Cqfre~

NewtDJ S

~A ABcOS~~(laquoteJktvsa e ~SQiraquoeamp c~tkt~~ ~~

APgtsc CD) PA AXcpotlts EFG)H-~t~ C F B ~ACG~FHgD~~r~t

Sol~tcNI W E6nFHO~ Eftn FG ~X _Apply~~ ~~scJ ~ ~ -to E~ltSJ F f(f ~Sta E~ () Fr =0 ~~ ( 14 1) I G Fn H( X are ut(ltealf_ ~ltfcAy~ltP~CA(s ~e- 4 E6--()FF~~ J ~S14

EEn FF~ B euroH nf6=X amp-t-fn ~euro 0 tUllPtfcmiddotc4t

-nus ~S 0 XI oJB ~c((e4~ 7itN pound4 fl Ff n6D=O SlAry EG F-- ( AC - O ACE6 fH6DCPotrclO

1)ec~CAes ~ 0 nfAaAec ~ JACc) M

A c B actgcP J CAnCpQJ AampnAgR ~r--+--Ir-~~R If AA 613 I cc 4te ~tVt-ct ~

A e 1-~ PI ~ Rctil eo(IQ4(_

c~ rCP_ R2esrk ~-s ~ -tyenUL te~ 4 ~~cAAfIdgre IfV --IfU ~ f 4s root G-oIer ~Ns c~ AOAB ~ftJJ MeoJ- -~r ~ et QPL AEa gil

At A rltamp -7---1S ( rt l g 0 () I 4 ~ ~ Ie Be Cctf~ Lloec Ilfct-Jt ~~ C~ c~ IJOCA ~ 1te(J C~ BP Cd M oct ~

B8 PC-co ~-( ~ No CC~=-( ~(ff~~~sctmiddot~~= - ~ (IC4M~cfMtl~~~ote- ~ et eampI c-f(er

62Y ~coJ A~s tttt ~Cct~lI1tr

Let Cn-les C ~ Cz ktwe ~~t ~~-fe15 0 ~ 02

Sf 11 4st f( J 14 (cs of ( OotX w~ 1

fe- ) t ~ lt twitt ()~ -tu Cl

eo( C~ ~Ilt ue 0 K- r 4)-~ J ~ ~ li~ f(~ok( -to OO~ -rtgt Is -4 (~~a1CSof tLt -f~Cnrd u

MOtse ~3 Crce~ CJCC1 W~~ OJOaoJ(h I~ nf CiamplttJ -tfe 3 ~ ltWQs ~FoS offI Wi( i~~(JItct cent Do fgti- ((lt d4 vaJOJ aftftfT4crtfes 111$ ~It lw la-I fIwe wi(( v-espue to 4((3 ccle$

G7~~14~S

~ If 2c(c~sCp~ lte~tAt PQ ~ p Cl aJ hss fou 0 411(1 yen

middot~ Ot J To Co J C So -ky tore eM ta noe(tk( ~ 2 r(4-~ ~ pIA i~( ~~ oS

~yenI4l~~~

P------ ~ c~ Lf4rdes C e d lifest J e we c- tltANJ A f(rrzl cltJ~C

~~ ~~~eAJf- 14 1

Ci-- ntcl ~~~ CJCl ~ CCsII i~~(t et -t4 ~ C4tt p1-Cch~~

~P~ f LoDa is ~er~ AK~Of CCz _

Let ED be ~~~ foSflctorf oft B~ MaC ~D ~S~e AC -ri Cau~tt1e c1A8JgtC ut ABtttE J(e ~ cfC4c~rc(e c1 AB D MflId 8 Ccent F-=-c --r

D (Olt ~t AE =- CF So 1$1 i te~d~ c~ ~gteJ AE~AB=ADAC II CFIltCBCD CA So~= ~~

5 ~c 81gt fsecfs L ABe WI_ Cl) ~ _ I bull It rJC AS - AD CF- f1C

------------------~ ampA~fel Let ABC be ~ ftrJMIj(e ~ soscJes 68C[)I

CAE AASF ~te~(1 to AAsC wi( ~ CA Aa 4 S bu1 tsrtdvel~ Pro~ta ~-t 141esff-1 AJSc ~ t ~ I~es t=F fEgt DE ~dJ ~uc(~t

Col Amiddot ~ SJltto i Late ~e cnl~w-f( Jgt4Sr~ ~ IE ( - eatu r4~ ~Cgt cte

a~~c~~ Iof crde middot1itE Ultoofe Y04oc Jl Y l AE=CE ( tel btcte(~w-I(Fu

c~ Cc~-tr ~cL~4S AF=8F - I -r4e-tltlfte~ A PUr~I T (~ff I ~~ fiIolu ~ ts ltfCI C1 $f lltty ~amp~ 2 lies Cltt VIIIt~~ ~c c) ~ roampoIaJIlt) of (14So -tkey ~u(4t fAa ~~ Camp~tet

63DP I

r ~e A ScIampf~ 2 LtP be 1ft l~~

~ Ii~~(-kB~lIc(~ -to FD-f _ bull 11C ra(~~ to OE -tt~ fOIts frolle M 1 Elf c(frelttf

S 7c IL ttgt ~-JC 1l rgte ~ t

I

I A~ C~ $oIf1 Let ile cncrcft~ J) ~=HF - PD eF -61) OJ rD-peuro-C~1 EAtlA~1eSamp Ql (A~ AF =SF I CD-c CEAGJPF t 81gt

2 l 1 0 F pW~ ct - fE =AF -AE S r~L pound ~ POtt 1 ~CAty4W(t t

- t_ EICIt1k 3 AC--damp l-H aat 0 P~r -fl Ie A4M C ~ usc -t ifegtSltct ~- Ae Id t W S let

Be It N Let 1k u cudcl 0(AAac -lt1 aNll~Std ~t B t ~ middot Pe ~~t OlUaM

SoIwt t ~ C4Samp 61 Be we6~ 11 aM i~ ~ ~ftthlte Qt S of cYG vtIeof poundlASC 1ICft OM =oel 8M

A~p BA18C i4e c~~In CAsamp - AUN AAec ACfo K~ 1Iotf1Ar (S1Cc iMruw Ibl~cto~ L kll Ac AC Jolaquoaret tes) s e rdeo( I

I

pound I ~e AC kN J 8M Itteet 41 4 (IOIt P I

Siell L PM N L 81lt11 l HCA s MIC PAte CDhcrkcl Q ttl I t fill pou fOitJ BMlC ~p 8M ec 80- yo Y=OA

PM r8- PNICPK POamp-r~ bull ~ $Jtmct~ 1keuro92 Ie -t 10- eo~= ampf(tM- rM) PM - 3

rJ It

OMl PB lr F6 ~t 8MPM+6I1I

OM J ~M

L I A6cb be i$(~Ibullt co_~4 tt ArllAofOo Q-t d - amp c~ f A1)1 SC ~ f (aros

Ccle i VI ( 4 E f= ~~-t t I~oes ampe Q= f-o -Ie C

8y po -t fI-t~ Po~_~ peltPD=PHxPl ~_ ft QClltQ6=~d~Qs~tAcff we1et Po~-Qo=CFM-ru) ~ fMQ~ -ns i (Ies 0ML PQ lQMO Itf oM

Ntrf Csd tIe C~C wi4 Q0 As d-cr~ 2 _ bullbull

It t-sses ME F SlAte LampMO LQ EDt -lCl fo s ~ CIC-z Ef ~ Ef -s iU c($ ef ce Let cI has ceth A( ~s tt lie

laquoa ~ ~ t JFPO _r - flMx pQ fiCa _Vi ~ P$ 01 ~ bull0I

A(Igt~ ite-sect PQ 4t M +Q -of leM _ LA0(= l paceW ac- ~ 8I(C ~ lttlclc p ~_I c 1_

let ya~s t Cltn~ I ~_0 =c bull t if crftit C fc$wt

~l~Sshy c1iW ~ 14- - l-l-~t1 A IS ~f~~J i AA6C J 0 i-tala

C(cuCttdlt~ 7Le -(kfee 4-ttJes AP eamp tMJ Cf irUktt- H EDAA6=-M FDo AC-N tp~4-dcent () 06Jl)F )OCJ1gtE

N C~) 0 J- M N middot i

Solfen bullCO LAfcc9cfLATgtC 9 A fgt l=~C6AtyJrc TktL6lgtFcLBAC AooBc-OCi--ees LOBC-=J(t~Io~Leoc)middot1tl_l8A(= ~oo~L8bFmiddot F omiddot Iamp -=gt 08 ~ tgt l= ~frly DC lDe-

B 0 c (~) CLMA ltPgtM~MIf AC~HI () I 81U AlA ~ NIi-IIIt= Aa -AltlaquoJI tgtA L

F ~c ~ l)e - ~ Aa~Ac (c~

~~b )N6oIp 13Ai~80-- OllADI (0( 1)04 ()-(~)+(()+ll)-~~ J)M~ ~_cot=OMOt)1 te

bull Ott J MAl N~-11 fI ~=C)jI 6lf1

~iet SoU- ln LAFC0 =LOC-dJACl) Fc-tkc ut J bu])M So ~t TeI [)f -ue L Jeo L 6gtF =LeAlt ~ J-f4 a~t (~e tB

4 ~t~4Yclt ~ JNle gtetpeId~ bs~CtoY til g 1 I J 1) 4te 0 ~J

=gt 0t3lJe ~oS i DF Q(A~ DCLbE wHk ~ CSV ftt Ae efT I c AC~J~DI ~ (ltt 6e If Be I I I 01 tl( AS 1POW iI f uIlh) SrlOCo Ae1gt = aq rW1d1C by d~ l~testJ~ t4PtwI- Let lc SAe -de -CA k)sU AABC f 2AamptI

NA ~ NC NF ~ rJ SI AC ~ dbullt ~fieaa~(L ofM$C ~=~ so tr~ of ~ bullbull ftc~(eNs() ~ ikatQ~oJ CoxS qf ~ Grtles Q-14III ~ if ITI ~ YM~(-l A~s 7I-e lmiddot 11M rOI(A)C1lt D ~~(S liIOH

r 6middot 1- r IAC- UComiddot

041(ms AhOYllo-lety wi1kceterO a-J Ptto k (cltwaof-d ~1 H(oJ 1lt) ) is Q ~CI itt setVls Jllttl r01ht X 01 ~ plAtte -t 1ile ~c~ X sampcck -tk~t OXL~ -= ieoX ~~rk~ It kl~1)~~~~ti saA3Jkf~ l-t lFl ltl J ~ -tk kPJMDffty 5 ( ~ A IrtySe~ Q -~ f ~ - ilc ~3~ ~ 12tlgteuroFbe~Js~8CCAM~ ~ (-((Ali) Secs AAsc +0 AAFE

amp 1gtJ C Let q Ie ilaquoo cttIL 0 6A-QC SiAte GiA =-2GfD GS -2GE ~tqt=-2~ s ~) ~IAbEF f AASC EXAfe L L AABC AB =AC A(iRl IS t -t t_1y to tIP cnuantt14MC4t~rMs pte AC ~tf~s P Q~ Pe 1l~ 1e totiJpoNltt (fQ

~114t llCeftgt ofAABC Sott~Let 0 bt 14 cgftt ~ -

) rele Lt 1gt foe ~t3et totlaquo 6 c 71 -t4 Circle +ipound Clttt-atd l4AOC

S 1) l3~yf A-trot ~ PQ

ADfAt -= ~~~~=~=Ic S HcAl)So04s I ib 0 S111tt O~$-iLalAltbullbullfMc t ~-tl_W-~tIecf-

CfajiV ~~ s A~t~~etsVI At AlAJ ISdVt4 well -scfes~e l A az (i) (~ts~ Sltk Cif(IOSitc Ai) fW IZ N ~~+-~~Re ~Ill~ ctrck ~ fMlf a c-~ ~lt 0 c-I

II~ iw~le laquo 3Ie -tno1 eel Ct rd -to ufS A

~ of stJes ~u+-1- middotfDItf-t G 1Cf ~fj -t4 (nuCampolttt ~~+riAe ~-tIa ~~it cO (6([e-t etft

A ~t Let A 6e ( It ~~scf 4~el cltlu ItS 54014 1 ampJ y be -fl- ~offu arcres SCrz

e ~C At otamp r 1A~f~~ ~ It 6gt Ilt

N611 Ae ~tly I B~ Iec t CAlieA Ids A is ru~ ~__~ Aamp a-( AC I So AAIb~Stt-t~ L fMc gti((y Mi~~ LMe e-l ee ir1kcts L seA So Mo( ern ee=- (-(A ~~dAIC

AI (IOOoJ 0A I De = ae r So 0 ts-tfe c~af of AAe d kt P~c4rc-ctr~AA6C

1k ~o~1 ~ (1 A) SeLs AABC f 6Aec ~ SeJ t~

scre-~-tP~MOC-tc~ OllA~~ bull middot 1 P 0 ore co((eAt

- fiscl 1( AASCGs ~IIe1lt ~~~~W (~- ~~L ~Ioc L

- L- ~ bull - 2J~ ~(IC= 8(~(s-lt)

ot t Ii -l 1pound is -(I ~K(~ ifCirde ~ Ill laf S bt-tl nf(~ ltgtf I IIIllyeltt t ~oflA bull

~ (e~ M s M~SzM)S3 ~~rrelaquo At s~ let 6 ~ bullt _ r

blse~ 4 poundA 00 ~-te 4 We c~ S~ SJ 1 M MJ

A 1iamp A --To t~t iampt elite- o~rf-tLt (i) IIIiilsrtt t Aamp1le rtfItJ-f 1 ts S I Co

-tIt vtt4lfO c4 -rs T~ ~tCf AT AIT~ 7iIese if L1I $ =ll~Imiddot ~iTt~lltSl~~t~ L T t S~-LTITa S1~1

(i) 11 A A ~ $S~ AA i MM ~ i 3 I ~ A T~ AI S~1 ~~ HzMl ~ ss I HsM bull ~ co ~ffWbull( ~dSr Nect CircCl1C(~ ~ASsz$3 reI 0 AA A~l

Ctcmiddott of A M~H IIbtepofcrceS~MAJ~r~ ~1 fLAA~AsrL f2 J ~ VAdtoos ~~

Z bullSo --Gtdes ~ 1Io(~ Ll lB~ reggt ampSt~~ AMMz toil s~~i~~ ~lt (x M- SLLt Ill ~bullbull04 S 1-ta~X l1c H ) Mz $1

~=(lttc-o)(c-M-~fl~e) 1 M M amp41 S)Jltl~ UrJ~Cost lt~~~~~(fo) ~ ()bc HSt~Zeuro~X

CT1tW EtA-f tt 1- bull ~A be ~iAt 4+etse~ ~ fwo nO~fD~fUtf Cirdes C ~C CAl-~ef0 0 (tltjreJ~ Dtte ~1MtM

~t~o c eamp 1d1t(s-et C cent~ Cztlt Pt J(e -i4af(EV (A~ ~-t-te~ctc At ~Ca~t QI Lk Me t ~~it-t~ ()Q o-J ~ ~ ~itet ~ pzCla

~-t ~ LtJAo LMAMz

~~ ~ ~

SGl~ B-t~etJ Plpt(gtzOt~~O

Ca ~lJZ~ damp bull nwy 14(0 oPa ) Q SeKds C L 0 PI

~ I ~ t -lO Z bull ~ J ~ OAn Ct =8 ~~-oflt~1 e $ Ll016M -tLl~A~~ So LOI~= LOaAHa A~ t- fs 0P 0 P ~o ltlie sjI Ie~ 00 Cgt~ ofL ~ ) 00 ~O~e-=OPct=OAIOg

t ~te~~-1 cknl4t1 ~ AO~ ~ Ate ~Itc

~ LO8M= lDAM

A~ I =gt LoAM L~AMz WIAamp~ ---

L 0cA M~ ==gt L0 A0)- L I-i A Mz bull -to _16bCrfkSf~S

Solt~p Wpound(CS JTbe reflec~ ~ S Wit-(S~ltt

fI5 Mis

~J e

t ~lwt Cgt (1Of ctImiddotd i -br3frt -+0

e $ f(~

Q cmiddotnI F -tkt bcs of tIl YOII f Sue- fut ~e-re ~)f Q

01 ~ w~ M ~ ~(eoi~ ~ l R~~ QS ~ isc~e~ C~rdamp 4 A PQ R

-to M Lt u be 04

~ A$ iudQ~~ltofe1 middot~~(R C V Lat ~ 10 ampl yo~t~14 fc

Co -fI kottcrt(e+y wfoit4 uW( P-tkt StI~ l t

~CtCte (_oppos-e P -(f ~ T middot (1 ~ Set$ U -to (Q((esr-~~-toflfobulltHf lt 1) Ii P~n (= v ut s setft~~ ~ t PQ~ ~

TR SQ=S - PR= PV- PIlt = Vlaquo=n ~ T T So 5 01 Ae ltT0 e ttl

ampruJt~J) fr p~ ltTaee~ UT ~ U

~ l(P Ifamp)Se0v4 u to ~ C(telte e to c~ l I- UtoT So TT Let 14tats~ P-4 C ~+~t5ect r ~Q~R ~

ampS-=s- Pflt=Pv- P((--Vre =TIC=-TIlt ~ tiM -i1s-MS Ti-f1T=-jiM PtSAt4t

~ El4middotrle b rio t)

Lt-A~c ~ co ftiI5le ~ ~tof scl Be A1k ~tsct- N ot l ~AC i~+fSoct ~c ct tJ ~~r~I~ k~ +0 AN -+~~ N ifersets AM 4 Q -c AB -t p -n ~f-lrJrmiddot 0 li~e to APt Pt-a~AIl laquo 0 middot Pofe Qo l Be SIt- TfABAc1kMNQfampAQMol3c

WLOG I ampS$f41111t A6gtAC Let AN MttStcf Uttucrclt fAABC j 1) ~

-- - bull c L 1gtg CL lgtAC=L~Llgtc~ e lAo M f~ r ~ ~ DC aJ PM 1 Be

~o Ho~y K(A ~StovlsA6j)(+oAgO(t4 08 O~ aq ae Itt t= Be( PN -r4~

L Ogt- L b8e =LM8=ro6_LAop=LoP~ ~ ~ D 0 tcKl orooc

I ) I J GfeCttrA J~c J~M4 ~ L 0 - Lep - 1 0 - 7 1- - 0 - 0 Igt IC tS~ amp It sc K is AM == AM l PfI=Q

I I ~ Lg eto L~~O~)oo 1~ ~o LSC g c It Be r

F l

(~p Sol~ middot Let dort FE ~wt -to nr2 4Ss(oll (iJ

Feuro () r C Lt r 1 U04s~r 111k ~y1- (M V)Sets P t r c-to K) Iiamp JE t jilt L AS

sow1 bull Ff 1Ie L ~ A is +lt1 ~roIldrc FE LNEC ~Afe~LAME I rSo L ~~eL~A~)~ LlNEcLlAMc ~ ACAeuro ~e1IA I ~ ~ pouer ~ A ltiol4Isped to r is Ac AM= AE S~M(tAfy I 16fJe t ~A i-fk -(~d -to ~~ Aft A~ A - A ~ =lttiJPOiqJ ~FeJ 56 Ae==-AF (1amp tflt11- rAAtcd - I

_ ~S AI ~ fIr2 AA~f ~ etc )~lll fu ett(4-ik1t f t fl1 pues-~r 1gt 61 sJMe~1 t ~OI)O~ wt Soc Oa I ~~t ~~ Ctgt

~ Ltgtco~=LClgto L cLeF ~s ir~S COa b~s L 9CF $ceCfiS~f rl So

Cl) is ~so~~~ -to re

E)(4flt

amp($ PI Ira Q-te ite~Iy ~ t ~ rt M N~oJtlJ ~ r fGs$es -tI- caff( 01 ~ r~

lAe r tgtit cl1illfr iii r rio MAn=C MBfr=D f (0 ~It CD $ 1~jkt to r2 bull

~ C~ IS - tYgtctStIt

~~ A ilefSVsv wi CAAer 0 oJ ugt r gt0

(amptatl 1 J(o r)) sA~f~ +lAo Se~s A~et(1 ~(t X 0 to ~ i~e VOl~t X O~bull y at sucL fut OXmiddotOlec r~ ~ CWOIelcu I fo X=0 ~ Utake )(=~ _-cl tllSo~)(-=QO Wt-take X=o

1ke Circle -w+1 C2~+e~ 0 A~ ~kCamps r gto-((ct k poundSle ~e~ ~ I~e IWJy 4fso ~ft A~ ltrs~ by sff~t ~ CrCJtL (lWt~middotcP

fGcfs CO Gift1 ~I((S~ ~ ~ bje(~~ it f~~ u~ 00 -to -t~lfmiddot ~ ~c-t J ex ) X ~

reg -If )( s-ikcRiC iwe~~1~ XI=X bull f)(~o~elf(enX~

= bull 1 ~x ~oit ofTaTl) ~t-rrl 4i~

P e ~ X1 lCT2 4~f~~-t1~ ~s iS k~

- __ OXmiddot ox ((sec LTo)()(ycsLTox)r~ ACtreJtt ~~SSi~ 14ftJUJ 0 ~~t +0 A cvdc bull ~ya16tj -4r~ O k iII-s ak~cIc -poits ~(~ St -to ~amp~ foffts l4 fOit 0) ~~fets

of -flit G~ a41~ aJa Afe utllt4r bull JotlfoItr~~tf(~-kGttk ~~set fotleceofv-f~ ~~ctrJe ~

A(fJe vaSSoVJ4-f 0 is Set -to 4 (euro reuro IS ~~~fI)~ 0 ~~s ~~k(+ifia1e-t (It( -t 44td Ito Cnverrely (A (middot1U1IIJt rssj-tlt~ 0 is Seltt -to ~Cvde (w~~ 0 Ni-l -tttllj~-t Imiddotier0 ~Itd to ~ leilt

f r A~At pCiSS~ 14 0 es SetOf ----1-- To e~setl ~ ~ _

Ifgt reg If two cr~ (f~ttIlC~ C4fVts ~(( ttlso ~~(etAf ~ fbft Pto)~~~~

9 lCo (iflaquo at ~Sdf~7e 4-( p~ oF

0 V ~-tlaat iHy~t~tOmiddotmiddot71-~R CA4f~(S ~ SQIJ-fo ~ 0 J

A Ie dI o~ctves4ltSet-f0r1f~~ ~ c () ~-t bull i- cmiddotrd~ ftftfiSttft S ~ fa-5~ 1Gtt cri(S t ( 4It ~fo-6etc~ Gllf f~S A lS 0 4laquol 0 A ~ IV~ IIG(C4((o(Af ~ oAmiddoto~ t 0Bmiddot O~ ~ OAloB OP4 ACoj

wi+lLAoB=L8~A Wt3ttLlOMdOl~ () - ~ LOA8= LogA ~

Aamp~ = OA _ r~A A6 0(3 - OB

=) Ae r lo A~

-------- --------~

)ampa-cle i (~tlcptleofto A ~cQlt$ A 1ckc ~tiatt~

ampl if tlyen~ t ampe- ACBD - A~middotq) +AD

II( V c bull I

SoJn C-sidelt -kfSiCll At 1 vuu~j l)is Cpoundlaquotef bull J ~p-J~ Ygt I) - t t e y fatH4) J -k ~ro-atdc qf ~ec ~~A~ I Q

I iIC ~ AeC SilCamp ~ IH 6e - c I

J vue b -ftt (1) We t _ 1 _AC~ r - Be - - middot

iDA ~ 01gt1gt AJ)middotC1) tt Mltrtrllj b~ lAOmiddot~]) CO~2 1aJkSimiddotces amporeJ

A6amp c) +A)xBe Acll 81gt middot

Re fICS 11L sf ~ eat be ltoftrec -to ~t -I- ~1-tllAt t MilcO + AtgtICBC =AC 1CI1~

~V Asctgt S (l u~ ~lJ4~ 0-shy

~S6~~~ kfCfS4tJ foJt of~~ -+k eampIt~ otIIIetStM Ai ~itlt ~s -fIc ~o~~ rote iIt wJere -reIs CIMif s Mesc(t _

-

6x4t~le 2 Lt ABc 0 be ~ ~tllt t(kft~ suamp~t At ampt so liltftStct At Y1tt ~r AtO P~t~( -Ke -refltecf of 0 ~fOSS AS BC C)1gtA A~ C4IIcYdtc

p _ c $Lt-~ -71

Lcent P~ ~So k ~fut f-~Wi _ 010 0 flO Msc CD lgtA Ye cdIVt bull

sc =l Ott foIIttll is ~iIr~le-t -fo site (5 -tk Ptt-RS l~~( (Sl~~14ft

e IcentS 0 0 -to tts e_~Hrlt OSAP DfBQ ~CR O~DS ~ludlC~~ J J -J ~ _ bull

-tt TltitCirtlutdts Ie CA Ca Cc CD rtsrdtuely CfSMoSmiddotd fIf~iQ 3(0 r ~r31gt0 By ~ct(s)

I~ AC Q( e04~~t ofo ~gtltS

cfct (+) I CA SIrcent to filllt LA fllAlrd to 81gt CIrs

Set to ~ IIt LB ~(c of Ac I C ~ Sci fo c tAlC -to ~lgt1 craquoisSeoet t ol1t LD~E lc ~

0 0 r~-t 0lt1

L Nen bull

CpnCa= 0r~ LAf Le P )Mjl-ly 4~t( LI) R J ll)n~ So bull

$r~ AcJ Mgt PClKs ~~Ic~4J~~ ~ fet h) PampRs is floc

~

G)Cdtpt f

Le-t P bft Af6~-t ~S~ 4l1It Appound ~~~-t LAPB-LACS LA(C-L~8C

Ltt tgt amp be ik~~tS 0( AAPS )AA~C nspecflf ~toe ~l A1gt 1gt1 ce )wtet A fOiWtshy

~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

( )tlfamp 61) biSKfs IA8PJ By ~t CT) ACAfACf~ ~ ~ I3A - XA So iSttf ACAeACampA

P ~f - xpmiddot ~ P~B6+lCApLcA8 J

C-1-1 ~=~ 5tRCt X ( 4ft AP ampt ~1It By~t (s) 1 ~ tCp~=LCitA ~ ~ I I~ fQ is Seoct of ( ~ ~~ 1 f4$s~~3C o listf SiacCrtIeO ~ -T(Alrl~f4lrgto ~~(1)1 tIIet pamp ~t(4C~I~Ois~tfo(0

A ~IgtC A~te A lU)e bullA p A APelAcIIgt f-c ~) I SIWICamp

I

~ ~ ilt3t +00 c( ~ 1 PQ fh ) Qm Q J r bull bull ~ t01 setc~ 10 t of I I

No LM~-L~8-=-LIWC-LAec f~ $(amp ~st ~JO 0 Ao( ~J~~ ~ Atl 43~ t (-d 0 ~ A61PcD

fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

Page 10: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

Cotttple~ 6eUYIUi(-ry

~ -t Ls ~ N~~tQVs e c gt e - Ccs9 +Se

~sc Obte~ ~ ~

CD 1- W claquotsr(middot t -R Ie-tt We III r ~1 ~(+ot) ~ 01 e _ 8 To yot~+f A YIi v fLe rlAlIe Iiishy

- r I 1fSj~t -to -Ie ~ ~ ~ Go)1 ~ C(

=~ r_ ik We $~fl1Ioltrb 1Ie crl foe l fA ~ - e b~ e

Acrl~1 Ie ~ ~s Iej f t ~ fl=- E

Ei-tmiddot 1- ~-tljk -t di-Yoits 1

Gi~ W W2 fke 9Qta-~c e~CM Af -tI ~ ~ ~ ~-~~k IN Wa is O~ ~ 0 +t Wa t ea - 10

W ~ So z-w bull HelllLc ~-J _-i -- ~1ecJ ~-W c

Wz-W WcW I ~_Wmiddot 0 1-kt beA ~~ olSo tJi~u -tk cJ~r

igtr -tke ~~ ferlts 4 WLJ l -to be eolheAr- eogi- of l u fcoJc ~ 1 1rllleP0rt

i CtrIz-) RottmiddotOW 1oJ1 9t W

- bull -1 II It-vL

e == Cos 1 gts = 1 bullWIw Eltot of-ike le tkn C rttr~JcJA

-to oJ W1 5 f l-C -~-c- l

0~7i-f ~

Li f~) ASS-teJ wt~ (uit) c~tctf

11 w W~ n 0 ~ tle ~-l cJe (at wi =Wzih~ l )

~ -tk trto ~~t ~O J Wt so z u

l- _ Wz-W C - - - l - = -w~lc-W t-w

Slworl~~ w~3~t ~ _ ]t +WWz t Wt W2 bull

-r~er~of -to h amp ~jl ~ ~~ lot C r~ 0 W W-z s l- C i (wamp-w)

---- -=WW1 ~-c -W(W1-W)

lt)irljj We 3 t I~-101Mh C-IVWC

1A~i~Cst

Let~ Wz~ W we ~ct ike f~Otl af ~f -tampjc--t ht t ~ i tele I)t I wI~~

(l+ lJti JW] yl ert~ -tle rey bull tcJr fa c To iIt tlaquojct

lIt cJ W is -L Wt

i(J~w) -= T(w~-~

~gt

CD C~eetfe( 0 is ~t tlv ornI reg CeV~J G is ct A-tA~ A3_

() I eurot- NH llt (-r~s rs -tf 41-1 ~- 1 A A A bull A tateo J n I l _ J i (~~Le~ ~Alll~b) s 01 SCt~eD u -pe v~GyueJ

(jOf4-hoce~t~ H l$ c AT At+ Pr3 (be(AASe O~ = 5(O~)) pound1- f lt tl~ A ~ fJclCi-r -to ALA 1s

i- A-A3 ~ -= At - A1-AJ A bl~-t ~ 1 1laquo ~ ~ r~~cJAt -to AA~ $

c- AA) == ~- A~ ~ -rktSt -fwo -ts W f~cf ltt t ampJk4J gt~~flaquos boi lut~~ u$~-f~ ~t tAll lAzI= tA- i- (e

AA = AzA - ~X3 -= ) t ~t lt e c At-tA T A~ SAiSfelt bofl ~t~01l~ 1eo t-= AT At -( ~3

17 N f t - L A+ Al-Ar) 6 Ce---+ef ~-tke ~-e foitrt Qftle $ DA l-

(be~oe 1-1 $ ~ ~Jro~ 4 o t-t) ~tCA ~ Mi-e fit arcc is -tke Ciolaquo ~t f4~SfS -tvnWJ4 ~ a Jo---~ -4le ~~es AtAl Aamp+~ As+A) ~ ~- J L -) ~) -

~Q 1eet qf ~ al-t-bAdcs H I 1 1-3 -=t ~ Wampdtoi~~ -tk ferllaquos ad ~e D~e1 ~~ raquo A~lt

(J~i(t~ ) A lltzlJ J llWW1-~ Ayt ~ito

Sol4 SifCamp ~A~R~lgttPLlCQA~ ~rJwail~e Arf A+cJQ+~~R20 I 1i~R+~~Pao C-t~1T~ZQ=-O

I ~Il I w e LV = e ~ 5 A ~t 4 ~b To ~~ fl X 1l s erltamptDI we CoM-rtf

Xt wl-t t)ll= (Ai~amp ) +w~Ct~iP )~(8+~~

= k [CM Q+ ~~)+ 1Yfgtt wR + tf )+ w (C + p+~ I = 0

~~~A I )( ts ~ (Rot 4 1 J~ ~ ~-t 4 -II 3~f1 C~cf ~ ce~-ter4cl At ~ (A e) ~ ~(f-t~) (ie ~c pOlt 3 -the amp~~c ~ ~ ~11t~ -G t- ~rid 1 ~~t AS)

COlf~selj Ikj ll~ 01 ilt G~f smiddot ~ fo~t ~ loc-s 61 )( 0-~ G~f C = i(Jlt- CA-t 8)) is -flc co~nsfo-kj lt Ov- ile ~t Clfdt

1-(t1J~ Let A~ A)e tI ~r~ 0t W1w) w~j I Y~ f~~j

fYo~ A ~ J~r - fe~~ -to -tkt -t~~ e to ~ c~tdt I

01 b w WI W 3 Got W bull skw~ ~est f~(tS ~ctCmt 1cle-t~~ ~s tmiddot~t t C)~

~otct~ JlCG ASSUllC -tL ai~cit-tle is -tlt kAtf GifC(t

~ h~ le~~tcJA -to t f~eMt oJ 1J -iklk ~ MS et--4M rll-tvJ~

bull l- A ~-A - WltWl t~ k~Wi -r ~- w - tV - 2 - - W 2 bull

Now WI bullbull f -ike ampM- ~~lc I SO Wd -= 1 i1e we ~ fJ~-te -tk ~n 4S _ _

~ bullbull Z ~ _ I T ~-t Wos 11 W + 2 Wl ~ - 1iIII I - - w

2 2-

F-oN -tk5 t ~ ~t -tk yoil-f N Jw~ -+ W3 $ 0shy

--te e lt$-I(C -t1e e1f~sS1W f Ns Sr~t~c ~~ nSFt -t oJ Jt Vis we (4 eot-t~ -tMt wtl lISO e O~ -tIt o~-- -two les -t~ e-Fc~Sto ~1 tJ -tt l s u~ -t $ -tle (fwle1 ~ -t~ )1 fO~~ (tce ~

J I W-z4 _

11Ob~ ( S~~t lYe Tko~ ) let W be D~ llt (~crclf ofJ ~1 13 c( PI Q1 R

be ~ iut ~ ~ lC ftJi~ ~ W -tt t1I 2 ll I tl ~ I ft ~ec-f~Jflj slw ifvt P Q R A-e tAl(Il (-ps Ole 5-

clt~ A $~501 11 tf A ltamp-t) ~ W) i

~ol~bo- WamplAi loss -t 3~nl~ I Wt J lS$We Je G-nIUshy

Cilampk 1s ~ ~ cttclt ~ lll llJ lls -= lw I ~ t 1kt k ii ~s ~~ l+ ll~ ~ Ii t3 --ie r~~ fw- W + 1~ Ivs ~ f-ltl ) i tJ- Zt~W So Sol lkcsc -tcdr W~ 3laquo l = ~ t L + W-lE W

2

St ~ Q ltl ott ilW --l 1(= tt f t~~1l

I sluw fQR 4t CttlfUf it S~s-t st P-R =l-amp-Nil f-R _l- Z-amp-~~ Yo-~~J (tI 4W -g ~-R

Q-~ -1-1)-1tJ --l~W X l ~-amp~w ) l2tgtW-ltl~ -lZ+ t

4t~ w- Zl~-ll-t It f- fl

- (1- R bull

-J clt~lttii lw=t ~ WW-=i

CiiID ~tlt~ firLiA BC let 1gt be A4Ie GtIlOc1tf- E 001 As loIiti DEit-CB J ~ F ie 600 Be I

ciA ~fDf oX ~~ o-rbmiddot 0 1 ltt ftt XIS G(( Gr be 01 EP ~tS~t ~ el~ttrlgtedo-r W~~~~fk~t~s X Ao D C fSfoFc-=Ep-=BYc1gt=r

~J ~sted oR we rMj Sity ~ i 7 middot PrDV~ 6i-F fs pcmI(e( -to -Me 4 b~ 1 -M CaJamp) Xl= Of-~ -tI S~1 je Y-X Sol-I Set 1ampt o~ AtAo tt(-~ IMc

For ~fS X It we e Ix-+f ~ lxl +111 ~ft Tie E 8 Gfl = C ot~~ E (0 r)klgt(d~ 1- W-11IAy f X= ~t(r-s-e t~o A~ F tB t(f-t)c 4( euroj =tE t-((-f)J) _ h Let Pbe 0 poillt el LIle )( f lJe lter t= B _ L _ amp1gt g + (_t )e~ middot gtY haYCamp oP=toX+(f-t)oy -f=~y ~ Be -- r -i1gt-t ~_

J J gt1( 8 -I io O~)y~ amp(01] ~ P-u SfjllleMt Xt E retgt I $0 IE-BI rD-cl c1

EICjl1t Call a ~1IIecent ~ ~ QjgtWelC ~l~ (I- ) Is (E -amph 1l ID-d r-(t-amp)(c(-f6-Jgtfd tl )ltLJ )M ~ ct j~ Ie ~od ~ orF9fe sk~ J i q F- Gt = t6-p)~+ (I-t)(1-9)C ~ +~hw ~t cf -tk s IIf-t4 Jgtllrl1lpounds Of ~t(tei _ IS tlt-p)amp1~$ htfampt iits~etet ~ik~litetllllorltl -tlt-p)la (amp+~~ =(~~k1NIllelo I _1 t f4IIIl ltf1ltS

Sll~ fir trl4t~ A~c~ Itt-A IlIamp 1M OjL ltf 114 (tw~-for ~ pound Me~ --ik se ~fOW twI ~ _ Igt IC-tO - f ~ if

T -poundTI-r -pound ~ I A=0 1)~D i(1el IC-BIt lo-dtll)~

UI8iC-1gt1 +11Hlt-at=Iel+ Ie-IgtI+11gt1 +1c_~(f~~t Wt ut Ie+IC-Igt ~ Iamp+c-tgtl t=~f1f)

AA IDI + IC-61 ~ 11gt+C-81 C-~AO=~8C) (gtt) holds ~Le~ft~~lcJs A81(1)C ATgt Usc _~ __

c6hf--I--l~1gt~ ItiC

~1- ~t fmiddot~~ 0+ ~ 0 ( is )(Y=tJC( (1 rsti - Ex4k+ Let 0 ~~ (i(cAt cf 4ABe 9 ~iIt J bef -fIl lfcffS Jf -IIf (t) Xi=fX (y+I)zmiddotXmiddotZ+fmiddotZ 0( (cXl-Y~(Xmiddoty) ~ I~~)(middotX I IXmiddot~~hd1I O~iOf (=) Xmiddoty-O ~~~~~~~~~~~~~~~ amp--ft 3 Let A8C b Le lmiddotts ~sfmiddotmiddot Phe

Ac~+amp~+A~-t8C~~ Ast+ctl SJt~~ Set1ie Ot~I ttt A ~~t f Jw

CmiddotC +(amp-lgtHamp-~)+D~ (8-c)~-c) ~ amp (c-b)laquo- At~(~- awl lt~~-f4ls s fu ~4S

(6 C-b)middot(S-C-lraquo ~ 0 ~~ck s (amplt-1) ~o

A ~t 1gt Ie -tLt poit ~ Aamp -L II ~ e _ ce~AAcO

p C fgtrcw _t C1gtJoe ) AS-AC Sol~~~~~~~dO~A

A a A J) A J)= ~ E=~~ =3 +~lCJ1gt-C=Aamp-2C

C1gt1 Oe- (A-tS-le)(Mc+1raquowO c) No AA~lh c C C(CUM(bull (IampSt 8 41f1$-bull (4) bec u Amiddot(Q-ltAB-ACO 1IeJtt(~) ~ OAl ~c ~ A~~AC

euro ~ toJs ~ 8lt~ 1)-A69 seAPS fWlkl ~JCOc $ firAABC jf( t ssewu-J -ptMf ~ c= - ta-+CmiddotfI AAS( its ~ttd q ~1 - If We Sampt -iU CitClIMChH- 0 AS ken -HII-srft~ ~o -t r -11 __ -~ -1 ALh--COtt - 7J 0 OtlGCnx n - ~-

A Fit iAcetft tJf ~~ c 0( lU= ~ = L

co b AI c lt-c

e ~ 1)c 1gt= te+(t-t) C t --amps ~1i~ poundL = tD ~+ cC C bI-c Gte middot I t A-t -~)tgt t-ll- A

aAtlS cc_ - tgtA - M~C 14 e middot

11l Lqt-(gt OmiddotkC Gtctal ~ICef c(H ~r J

51_ Set 5 4lt C4fColt_bull tu e -H Matel~Me1~ 1~ AA+b$-t C shy ~ 4~(

Lampil~gt 1omiddot~(i-1)l4-1) lt0 A-A 6middot~Cc=(tlJ 2ec 6amp+cc-(a-c)(amp-Q=k~middotIf (A16i)riamptc~ Rlt9~~ 11- 3( h_ Imiddotltl-C) 4l- 2(~~(H- btCi)tI~)) cttC

)(~+c) (-1)((-1) =((~ t1 -Hi+(() lt 0 of -~ f (ib -t-e) lA+Il+ ct )+ilaquoc gt~ CifI+cl+Jl(c)+ ~ ~ a(-o)(--G)-4-~-c)(b+cc-4)~)gt0 tsc4 rc s

~ Ike fRS ~ f xi xI wt -Stl-fculot 11-$9 (t)=LXOY) 0( tiYfft~e~ -fo -tkt fl~~ 1-- oxY J e

lti) ~ -f~)( ~f)-a)( l t Yltl (c~wYcxnyJ (j - )(~1 4fT~ A X0( V~~ p A of yl t1ft 0

(6laquo Q bull 1 lj 111)1 (DW~v e

eJ41~ Let AAA A _j A 1 1_ -+ V]nq DO 4 CD e I

- its ste ~tS p-Ilt1 ProiIla-t middot ClrtllAA1Ar oreAA AA So(u-tVf SeL ot - ~ -_amp I~ _L ft--A A ----- ~ fJe ~ ~ --fI 01r~~ O4St SMs ~qIt ~t)~csCA-A) I lA_-A f

E)Ctl-eIlaquo-r Let A6COf tgt ~~ pe-tft Qc e t

~~~Q~ ~ 1kfwlrids~ A88CCIgtbEpoundA 1T~ -r APamptl~J~ le ACDIIIampf6i -laquo s~O~ tk-t ~s Ooet is so eM eII bullbull ~olt4-tfN ~et -ckt O~bullbull~ rt -e ~_W f~ S~

tJ 1(t0 AXC ~ AP ofe (o(iu o=A-f- A(~ J C- 32s amp A

lltc t))tA SIA~y 8)(1)= (1(8 CxE~ C I

raquo)(A 6llgt re EJ( 6 =CcE feMtt I

eurolCAJ- E)(6-t( - ~lte+El$ ~ pound10 eImiddotmiddot

1 ~~-A~)o (As-AJ1gt(~A~ S ~~CI amp euro1tf6lc~ ~se Ac Adol~ -t(t-t Lit set - () middot At

At~ t ~It~ AsIC~ Al~-+yen+yJAI (

_t a ~ - bull

~ 2-shy

I _0 c A 6 c ~ As V ~1~Ut 1 Sjtllc -fb ~BIC~ fW(t

ftdle ~ts of BC CA AB ns~chvell -tk ft1~ -tIua-t

No A bull G 8 A I ~amp Ca A~ (orr eU egt~ 4~_ A~itlA-~lClA-As~=(~tAtAr-tAjcA -~~ StthtlI4It ~ SaJc1ttA

(Nmiddot~~i~+Ar~~l ore4 l1A AAs = Are 1J~~Ai

Aft13 amp11 C=A-ttils-A)frSollletoA~] SiCt AS e Gfe i eRe

o~ (Bt-A)K(~-A) - (A-ttz-~tl-t- t t)AxB No ~~=~~~-=amp-AH-t)e ~~1 S-a-= It-t1)A I Ct = lAt8)- c tlA +ll-t~)B ~ (amp-AI~I~(Cz-~)=(t-ttl-trtl-+t~t))Al(amp~O A S~ CL At( ccdllfttor

~t ~~ 1~~Pt

o

C[~1D --r-0 vetlOf) )( lf ate Jt~y wtt-t---t f~ t -flat ~f~ ClX~yO kAs 01 Soat~

AT 10 o T4 s tktCcStI ~~A rf KttO ~ X0 f Art NIt Co((llteor

F4t IT AX+bY+c =0 ~$ote -e 1~I(z-s 4t4l 4-+amp ott -=0 J ilQA Xf Z 4le cbullbullI btACcS( ~l AO fIe b-tc-o w X-1-KZ-tYc-6Z

(~ar~11to(~1 wr~t--J Lftai c~ s OAAampA Co

~ OeLamps 1f 1 -1z- Aa6~l~8ampR AsampIA~= ~ 6 8-c amp-S tltcl A DAR 0

~e COIIfttAt t ~1 =- 1 ~ ~ P Pl) P3S~ Set - orlll at o at A8 btt ~trs Ale LIDa (ampfbv~ ~ A~ rA Q( e s So 8 1-t S6Wt (s EIt Cll No

Pl =tAt(c-t) 8a trA+ (ct)s ~- ~3 lAAt-tQ-) 8-= tA(-aA+Cc-ct)S a S~tU~ ~ 0= ltr- CArgtA + [pound1)l -(I-I4)$]B

A~ (tally rcf~=gt tr(~ Otu( (l-tl~-laquotlt)S=C Solll fott ol -tit pt~~ -+-s f ti ~I~Js

Nt ~~e ~ 1tu~~A+ SoSzCt-rl g$t Vs- r~ r~- r~1 Pgt1s~S)A+~s(tmiddotgt8 R= rlrfgt~A ~(I)J B

Y~-r)S) ~6a-t~S) amp c) ttS +fs-1S ~ p~f~P+~sampf-tj~

~ P1 ~se~rw)~c 0 Qtlgt+CoO ~ r fL cU-1- fc-i (ove

~ 0

A - -

~ FOf~lamp~

(1 -laquo ~C

fot-CA~ to ~ t t amp -t~~ crt a ~tc ~ El(tend~ltl St L laquobe ~[A8Cl Js~~i~ R= 4 C

Let ( ~t 4ct nwts lt 4e GoismvmcJt i-R- tl 4J~)(fo~of AAsc Sr ~ l=~~Yslt) ~ bc_

S A -- - 0 21 1iltelaquoe s dolAt C~d~middot ~o~ uI1gt ~ s~amp s~~C middot T 1_ ~ rI n -rf (i-- shy

tl Ie or~ DraJ clmiddotae~t 61gt 1pound Si ~ A= ----=algt i IS lle~ ltJOiOlSA0

~~~~~~~~~~~~~-~~~~=~~~~ p adEr-l-~a~~r~ A- oS+- jtus c~ - c e c I) p(]) Let 18(1gt L~Ms

I4dtt rAsel Or S~8c1oI(lcl~ 1leflAftt Let A6nct)p -r1 ~act 0

~Me C ABC ) GlUo~kc ~ PAx P6= Pc x PD = tl b~~=Abc bull P19tpound Note L APD L (PB

4R A1BC)aHd~ckLPAtgt=LPCBS=tfA-tb~~) is ike seifieAc ~AAPDACfB~=~~ PAIPB=fxPD

amp Q C Of 4A8C Lri pc C 1amp-~ ~~ PC Is -lt-~t lat t lie i4 jCbullbullr 4l( M6C Qt r Ie -i4~ to -e -fde ~ A A8C if (JJ

C)~ ~e icltc1e ot AAec ~e p A e OYlJ c fCL p~~re [Mel =[ALel[~cl+(CI1= ~-t~+~=SIr ~ Not~ LArc=LcPB

I-tfllWlbull [A8tl~ S($-11 ) (s-b)(s-c)middot I pCs f~ot -to LACp4C ampP(~ Cos C= tt2ttoa-c (~AI Ci(~ircl 4 MBc B 2shy

[A6Ci= ~SiIlC=Qr(+coSp(i-($C) ~AAcPACBP ~~ fgtc PCPAlltPB =(Cl~-+Iot-c~t-~a~-9 ) = catlo-4 t )(A1(-c)(CoHI- b)(o-Il-~= S (s-c)(~~

2- ~ a

Ci C [AS(I A 2

~

I

~JJI LPFA-=odeg=Lpe~ ~ amp~ ~LPFeLPAE

C5Ji) ~tolt1 s-ThtOfotfll Let A 6c~ ~t dlSncf ~ts 01 bull ~c ~o - Me~IA~ 1( bull t Of~~~I ~Ot bull -Tht~ bull Sa c~tOV M1 C(liofIPT potd~ A 6 C Iie to

AI 6 C 1gt (1~t~c 1gtpound fCLR atfmiddote ZA ~A A ZA bull -~ -iA ~Co~ PAQ~clf$ WeA~ ZA~lA I tc Z~t

pFAECc1dk

bull ~ Srlloi(y taCgt6~~~-lPFB ~ pG~ f CDCCYcbull LPampb LPFI) = e 1klaquo AIJ~P LPAespoundp8C pfE _ LPeP 8EF (0(1ltlt~L PFE L~8Tgt~ LFP - L 10 collirAfampff

)fgtC)~Jl~~ ~ ASC1HAol6C=AcS]) bull (~~_ ~ktI AeCO At)ItBC ~ACdtgt 1)~c 190pound 0 sWLe AB UJlfsftfUct A ampA6

S~~41 to flCAP 1I1elt AB A~ 6eshy

6 Ai - 7ligt= (1) lBAE=LCAJgt

SO LMc L BAlgt-L1gt= LeA1gt-LMe =LEAt) Tkeuro1 A8AC~Ae-A1) So Rr-c EDAtgt~A Thet Aec~ A~8C =poundItampE AClC E~ AC80

bull A rC =c Sf-t Ell I

f1-I-4j hoW~ ~8euro~EtgtS ampb ~ E iUt~( SO - ~~oeA~LeeALtgtCA ~AsectCO Sltffc

SoSoft ~oe 1et~6cP cl-ampd-p~ 0

tI~ Let l)poundF fetf~~ff- P~ ampa Aeyen~~ ~

Asse ~Mist (so4 is 6~UA_JC ~AGSC ~O bull G ~f( Aalec~o)

tt~e9 7eff

fovlaquos X I Z ate (es Aamp ampCA D ((t~ve-()ty It X I Z (lie (dl-lflOr

A ~f f6 lhg--1 ~ xe YC LA - middot ~ lQt Dbu (~ Ac soct1IIt 81gt II J( Z -r1teuron

~g ~ ~ 1t~ ~z Se AlC 6Y c~ _At P1Q (i~ ~y Ie ~c -- _______ r tamp iU I bull laS yc fA ~Igt ZCZA middot lCI~ lIeeu~ Ie~

If ~ tL ~ =-1 iIamp )( YL MHo l~(~ Y~t~~~~ SlJ) Ltt l~ X(OCA -Thtl b Mt11Idtw 11~ Ax ay CI _ lt Cz Y Cl iiiK zA --i ~o --=-l1toobull CfIea bull _Cl -a

I I

ceDD ~MelI s lIeo~toA l~tA I ~cc t) euro ~be tc~ lO 0shy

de lw~~ ~( ft amptCtSSCti 1 tf (~ diC- (~QEf ) bull

t p Ae ti l)euro J Q Bel pound f 2= Cl)n fA ~ ~k ~ Q1t ottc(l(ea~ ~QIR~~~ -

f~ 1 ~ ltt X~EfA 1AMCD bull ~ z- C~neF Arr~l ~(atts ~ff 1e-(fM1oec~ FA

ftt- Ool~~~ 4xf l w hVII

e-- ~ X K __( It X2 ~_( t ~~II Qx 6y Ct ~y pzex I fllFxijmiddot 1I

Hul~pr~ ~ AIl ~~ tfffSfctj cofI4t tt XA)(B XEmiddotKF J (CmiddotYP=1AmiddotYS ZEmiddotZF= zeZIgt W~~et ZQ lSf~-i igt PQ~ ore rlfltelaquor

Qx Pf Itz loy c-enc ~Mee(AaS

t-rks ~ere 0 Imiddotil~ (1$($ of PoucJ s for It we tftwt Ato 8 -te I AIwIJ (3 il(cJe 1Iofl1-t i AB will b~ ~-t1l3et (iot ot B ~ It~j CIt~ we ells JpoundAoflt ~ t~ liflE Clt B b~ BR

6lCtJfC i F~~ h Cf(Ultirc~ ot Mac J f(it 1) ( ~ ~i~0yen ot -t4l~lE I~ ~tA - ~~ Be ~ e fM 1fe ttusc(e~ of-ffwf3ct (tt4-t C3L1r~ CA~ F= bt ~ ttfStd~ of -tINt ti-~-f Imiddot~t ~tC wo( Aamp 11161 PI Ell F o~ ctU

Soof~fIyen P=Mo 8C ~ E= BBnlA f=CCnAB APP~i P~f ~ ~(fo MB See I fott et 1gtpound f c-

-- =JSiiiiIii

b)lAtc ~ Let-tgt 0- eht ~cfs 0( dt101 AtCS

AS ~ AC O~~e (ilcu-R( Mac ftspciwJy l(t tgt Ilt ~f AtC sCI ~== DPn SA J R= PEn AC fro +~-t lile QR~s~(QVJ14 fttCf+~I (~ 1) ~ f9bt-Mshy~e 1)rff0--AS- CO ~SfctsLAc8

Co ~r ~ qftllCr At =lgt 6 ~LAec So 1= Cl)n G8 Sf_ eEtS

Q tgtPt SA DP 8ital R= Pe C Pre ttL PlE AI

AIP~ f~l ~ 1Ito(-to C ~ P er ~ w 1 ~ bull 1I

t Set I Q Rut tIff~ Co~~d~

~ -7

Alt IXu q j

elf (Ga1(e 3 Ltt AT3CPs e ~ +s tMDlCJe ~-rd AAfLBS Bat LeA) ccf LAB fat 1gt be ~ls (I ~cucl1t ~c4( I

DA(11)C= AU DB()CAe~ 1gtCIAB~ fgt~~ A~ r~CtfaJ T4 6v~fi ~ IAGC a~ Co((~((r

~olf- W HL-cI oy-((~( ~ AA Be Ne

AAIB~I)Cc(-=I DArBC=A 11gt1( ISc AtA f Cc -= H L lAlA I C I Cl

1t~()cD=C1 ~l (AIBl (cjAfrrr5~5Gl ~~ t DAAfCC tgtlt Se4 A HC tit c11ilaquoraquo SIt 1y ar171~ BS41s(to AS e 0cc we Su e H 6ltve c1(i~amp r A~ H C~ S4rt a(((~4~ I

-~ ALI)f ~fle1 tt P toe a ltpor i~4Mec

LtfP I~~ff~I$f- 5 -to ~CA Camp ft~t~ lttt bJ() ~_ eshy

ll 10 ~ fet ~~~N~ c-tohs API sp (~ftvtll IfQ P ~ 61bullbull Pt14 PttNQ~~ (tries ~tll~ Qfz cod A~ aft ~et

iSoLttd- $(fCJt L CPc p) LCQLP LC~P Lc (gta Palt-e J -t ~es c P ~L I PI Q p 4ftcocttc f~AfrI15 ~s middottU(Woto ~1l$1 w-tSu CPt ( gt e-= A ) P t1t( QIP= X ) (Q-a Pf P2C-= B 4re CoI~rtelr $6 Rb2-l amp1L ( AB-=Xmiddot ~ ~lIQ P~IA8 tVe ~Cqfre~

NewtDJ S

~A ABcOS~~(laquoteJktvsa e ~SQiraquoeamp c~tkt~~ ~~

APgtsc CD) PA AXcpotlts EFG)H-~t~ C F B ~ACG~FHgD~~r~t

Sol~tcNI W E6nFHO~ Eftn FG ~X _Apply~~ ~~scJ ~ ~ -to E~ltSJ F f(f ~Sta E~ () Fr =0 ~~ ( 14 1) I G Fn H( X are ut(ltealf_ ~ltfcAy~ltP~CA(s ~e- 4 E6--()FF~~ J ~S14

EEn FF~ B euroH nf6=X amp-t-fn ~euro 0 tUllPtfcmiddotc4t

-nus ~S 0 XI oJB ~c((e4~ 7itN pound4 fl Ff n6D=O SlAry EG F-- ( AC - O ACE6 fH6DCPotrclO

1)ec~CAes ~ 0 nfAaAec ~ JACc) M

A c B actgcP J CAnCpQJ AampnAgR ~r--+--Ir-~~R If AA 613 I cc 4te ~tVt-ct ~

A e 1-~ PI ~ Rctil eo(IQ4(_

c~ rCP_ R2esrk ~-s ~ -tyenUL te~ 4 ~~cAAfIdgre IfV --IfU ~ f 4s root G-oIer ~Ns c~ AOAB ~ftJJ MeoJ- -~r ~ et QPL AEa gil

At A rltamp -7---1S ( rt l g 0 () I 4 ~ ~ Ie Be Cctf~ Lloec Ilfct-Jt ~~ C~ c~ IJOCA ~ 1te(J C~ BP Cd M oct ~

B8 PC-co ~-( ~ No CC~=-( ~(ff~~~sctmiddot~~= - ~ (IC4M~cfMtl~~~ote- ~ et eampI c-f(er

62Y ~coJ A~s tttt ~Cct~lI1tr

Let Cn-les C ~ Cz ktwe ~~t ~~-fe15 0 ~ 02

Sf 11 4st f( J 14 (cs of ( OotX w~ 1

fe- ) t ~ lt twitt ()~ -tu Cl

eo( C~ ~Ilt ue 0 K- r 4)-~ J ~ ~ li~ f(~ok( -to OO~ -rtgt Is -4 (~~a1CSof tLt -f~Cnrd u

MOtse ~3 Crce~ CJCC1 W~~ OJOaoJ(h I~ nf CiamplttJ -tfe 3 ~ ltWQs ~FoS offI Wi( i~~(JItct cent Do fgti- ((lt d4 vaJOJ aftftfT4crtfes 111$ ~It lw la-I fIwe wi(( v-espue to 4((3 ccle$

G7~~14~S

~ If 2c(c~sCp~ lte~tAt PQ ~ p Cl aJ hss fou 0 411(1 yen

middot~ Ot J To Co J C So -ky tore eM ta noe(tk( ~ 2 r(4-~ ~ pIA i~( ~~ oS

~yenI4l~~~

P------ ~ c~ Lf4rdes C e d lifest J e we c- tltANJ A f(rrzl cltJ~C

~~ ~~~eAJf- 14 1

Ci-- ntcl ~~~ CJCl ~ CCsII i~~(t et -t4 ~ C4tt p1-Cch~~

~P~ f LoDa is ~er~ AK~Of CCz _

Let ED be ~~~ foSflctorf oft B~ MaC ~D ~S~e AC -ri Cau~tt1e c1A8JgtC ut ABtttE J(e ~ cfC4c~rc(e c1 AB D MflId 8 Ccent F-=-c --r

D (Olt ~t AE =- CF So 1$1 i te~d~ c~ ~gteJ AE~AB=ADAC II CFIltCBCD CA So~= ~~

5 ~c 81gt fsecfs L ABe WI_ Cl) ~ _ I bull It rJC AS - AD CF- f1C

------------------~ ampA~fel Let ABC be ~ ftrJMIj(e ~ soscJes 68C[)I

CAE AASF ~te~(1 to AAsC wi( ~ CA Aa 4 S bu1 tsrtdvel~ Pro~ta ~-t 141esff-1 AJSc ~ t ~ I~es t=F fEgt DE ~dJ ~uc(~t

Col Amiddot ~ SJltto i Late ~e cnl~w-f( Jgt4Sr~ ~ IE ( - eatu r4~ ~Cgt cte

a~~c~~ Iof crde middot1itE Ultoofe Y04oc Jl Y l AE=CE ( tel btcte(~w-I(Fu

c~ Cc~-tr ~cL~4S AF=8F - I -r4e-tltlfte~ A PUr~I T (~ff I ~~ fiIolu ~ ts ltfCI C1 $f lltty ~amp~ 2 lies Cltt VIIIt~~ ~c c) ~ roampoIaJIlt) of (14So -tkey ~u(4t fAa ~~ Camp~tet

63DP I

r ~e A ScIampf~ 2 LtP be 1ft l~~

~ Ii~~(-kB~lIc(~ -to FD-f _ bull 11C ra(~~ to OE -tt~ fOIts frolle M 1 Elf c(frelttf

S 7c IL ttgt ~-JC 1l rgte ~ t

I

I A~ C~ $oIf1 Let ile cncrcft~ J) ~=HF - PD eF -61) OJ rD-peuro-C~1 EAtlA~1eSamp Ql (A~ AF =SF I CD-c CEAGJPF t 81gt

2 l 1 0 F pW~ ct - fE =AF -AE S r~L pound ~ POtt 1 ~CAty4W(t t

- t_ EICIt1k 3 AC--damp l-H aat 0 P~r -fl Ie A4M C ~ usc -t ifegtSltct ~- Ae Id t W S let

Be It N Let 1k u cudcl 0(AAac -lt1 aNll~Std ~t B t ~ middot Pe ~~t OlUaM

SoIwt t ~ C4Samp 61 Be we6~ 11 aM i~ ~ ~ftthlte Qt S of cYG vtIeof poundlASC 1ICft OM =oel 8M

A~p BA18C i4e c~~In CAsamp - AUN AAec ACfo K~ 1Iotf1Ar (S1Cc iMruw Ibl~cto~ L kll Ac AC Jolaquoaret tes) s e rdeo( I

I

pound I ~e AC kN J 8M Itteet 41 4 (IOIt P I

Siell L PM N L 81lt11 l HCA s MIC PAte CDhcrkcl Q ttl I t fill pou fOitJ BMlC ~p 8M ec 80- yo Y=OA

PM r8- PNICPK POamp-r~ bull ~ $Jtmct~ 1keuro92 Ie -t 10- eo~= ampf(tM- rM) PM - 3

rJ It

OMl PB lr F6 ~t 8MPM+6I1I

OM J ~M

L I A6cb be i$(~Ibullt co_~4 tt ArllAofOo Q-t d - amp c~ f A1)1 SC ~ f (aros

Ccle i VI ( 4 E f= ~~-t t I~oes ampe Q= f-o -Ie C

8y po -t fI-t~ Po~_~ peltPD=PHxPl ~_ ft QClltQ6=~d~Qs~tAcff we1et Po~-Qo=CFM-ru) ~ fMQ~ -ns i (Ies 0ML PQ lQMO Itf oM

Ntrf Csd tIe C~C wi4 Q0 As d-cr~ 2 _ bullbull

It t-sses ME F SlAte LampMO LQ EDt -lCl fo s ~ CIC-z Ef ~ Ef -s iU c($ ef ce Let cI has ceth A( ~s tt lie

laquoa ~ ~ t JFPO _r - flMx pQ fiCa _Vi ~ P$ 01 ~ bull0I

A(Igt~ ite-sect PQ 4t M +Q -of leM _ LA0(= l paceW ac- ~ 8I(C ~ lttlclc p ~_I c 1_

let ya~s t Cltn~ I ~_0 =c bull t if crftit C fc$wt

~l~Sshy c1iW ~ 14- - l-l-~t1 A IS ~f~~J i AA6C J 0 i-tala

C(cuCttdlt~ 7Le -(kfee 4-ttJes AP eamp tMJ Cf irUktt- H EDAA6=-M FDo AC-N tp~4-dcent () 06Jl)F )OCJ1gtE

N C~) 0 J- M N middot i

Solfen bullCO LAfcc9cfLATgtC 9 A fgt l=~C6AtyJrc TktL6lgtFcLBAC AooBc-OCi--ees LOBC-=J(t~Io~Leoc)middot1tl_l8A(= ~oo~L8bFmiddot F omiddot Iamp -=gt 08 ~ tgt l= ~frly DC lDe-

B 0 c (~) CLMA ltPgtM~MIf AC~HI () I 81U AlA ~ NIi-IIIt= Aa -AltlaquoJI tgtA L

F ~c ~ l)e - ~ Aa~Ac (c~

~~b )N6oIp 13Ai~80-- OllADI (0( 1)04 ()-(~)+(()+ll)-~~ J)M~ ~_cot=OMOt)1 te

bull Ott J MAl N~-11 fI ~=C)jI 6lf1

~iet SoU- ln LAFC0 =LOC-dJACl) Fc-tkc ut J bu])M So ~t TeI [)f -ue L Jeo L 6gtF =LeAlt ~ J-f4 a~t (~e tB

4 ~t~4Yclt ~ JNle gtetpeId~ bs~CtoY til g 1 I J 1) 4te 0 ~J

=gt 0t3lJe ~oS i DF Q(A~ DCLbE wHk ~ CSV ftt Ae efT I c AC~J~DI ~ (ltt 6e If Be I I I 01 tl( AS 1POW iI f uIlh) SrlOCo Ae1gt = aq rW1d1C by d~ l~testJ~ t4PtwI- Let lc SAe -de -CA k)sU AABC f 2AamptI

NA ~ NC NF ~ rJ SI AC ~ dbullt ~fieaa~(L ofM$C ~=~ so tr~ of ~ bullbull ftc~(eNs() ~ ikatQ~oJ CoxS qf ~ Grtles Q-14III ~ if ITI ~ YM~(-l A~s 7I-e lmiddot 11M rOI(A)C1lt D ~~(S liIOH

r 6middot 1- r IAC- UComiddot

041(ms AhOYllo-lety wi1kceterO a-J Ptto k (cltwaof-d ~1 H(oJ 1lt) ) is Q ~CI itt setVls Jllttl r01ht X 01 ~ plAtte -t 1ile ~c~ X sampcck -tk~t OXL~ -= ieoX ~~rk~ It kl~1)~~~~ti saA3Jkf~ l-t lFl ltl J ~ -tk kPJMDffty 5 ( ~ A IrtySe~ Q -~ f ~ - ilc ~3~ ~ 12tlgteuroFbe~Js~8CCAM~ ~ (-((Ali) Secs AAsc +0 AAFE

amp 1gtJ C Let q Ie ilaquoo cttIL 0 6A-QC SiAte GiA =-2GfD GS -2GE ~tqt=-2~ s ~) ~IAbEF f AASC EXAfe L L AABC AB =AC A(iRl IS t -t t_1y to tIP cnuantt14MC4t~rMs pte AC ~tf~s P Q~ Pe 1l~ 1e totiJpoNltt (fQ

~114t llCeftgt ofAABC Sott~Let 0 bt 14 cgftt ~ -

) rele Lt 1gt foe ~t3et totlaquo 6 c 71 -t4 Circle +ipound Clttt-atd l4AOC

S 1) l3~yf A-trot ~ PQ

ADfAt -= ~~~~=~=Ic S HcAl)So04s I ib 0 S111tt O~$-iLalAltbullbullfMc t ~-tl_W-~tIecf-

CfajiV ~~ s A~t~~etsVI At AlAJ ISdVt4 well -scfes~e l A az (i) (~ts~ Sltk Cif(IOSitc Ai) fW IZ N ~~+-~~Re ~Ill~ ctrck ~ fMlf a c-~ ~lt 0 c-I

II~ iw~le laquo 3Ie -tno1 eel Ct rd -to ufS A

~ of stJes ~u+-1- middotfDItf-t G 1Cf ~fj -t4 (nuCampolttt ~~+riAe ~-tIa ~~it cO (6([e-t etft

A ~t Let A 6e ( It ~~scf 4~el cltlu ItS 54014 1 ampJ y be -fl- ~offu arcres SCrz

e ~C At otamp r 1A~f~~ ~ It 6gt Ilt

N611 Ae ~tly I B~ Iec t CAlieA Ids A is ru~ ~__~ Aamp a-( AC I So AAIb~Stt-t~ L fMc gti((y Mi~~ LMe e-l ee ir1kcts L seA So Mo( ern ee=- (-(A ~~dAIC

AI (IOOoJ 0A I De = ae r So 0 ts-tfe c~af of AAe d kt P~c4rc-ctr~AA6C

1k ~o~1 ~ (1 A) SeLs AABC f 6Aec ~ SeJ t~

scre-~-tP~MOC-tc~ OllA~~ bull middot 1 P 0 ore co((eAt

- fiscl 1( AASCGs ~IIe1lt ~~~~W (~- ~~L ~Ioc L

- L- ~ bull - 2J~ ~(IC= 8(~(s-lt)

ot t Ii -l 1pound is -(I ~K(~ ifCirde ~ Ill laf S bt-tl nf(~ ltgtf I IIIllyeltt t ~oflA bull

~ (e~ M s M~SzM)S3 ~~rrelaquo At s~ let 6 ~ bullt _ r

blse~ 4 poundA 00 ~-te 4 We c~ S~ SJ 1 M MJ

A 1iamp A --To t~t iampt elite- o~rf-tLt (i) IIIiilsrtt t Aamp1le rtfItJ-f 1 ts S I Co

-tIt vtt4lfO c4 -rs T~ ~tCf AT AIT~ 7iIese if L1I $ =ll~Imiddot ~iTt~lltSl~~t~ L T t S~-LTITa S1~1

(i) 11 A A ~ $S~ AA i MM ~ i 3 I ~ A T~ AI S~1 ~~ HzMl ~ ss I HsM bull ~ co ~ffWbull( ~dSr Nect CircCl1C(~ ~ASsz$3 reI 0 AA A~l

Ctcmiddott of A M~H IIbtepofcrceS~MAJ~r~ ~1 fLAA~AsrL f2 J ~ VAdtoos ~~

Z bullSo --Gtdes ~ 1Io(~ Ll lB~ reggt ampSt~~ AMMz toil s~~i~~ ~lt (x M- SLLt Ill ~bullbull04 S 1-ta~X l1c H ) Mz $1

~=(lttc-o)(c-M-~fl~e) 1 M M amp41 S)Jltl~ UrJ~Cost lt~~~~~(fo) ~ ()bc HSt~Zeuro~X

CT1tW EtA-f tt 1- bull ~A be ~iAt 4+etse~ ~ fwo nO~fD~fUtf Cirdes C ~C CAl-~ef0 0 (tltjreJ~ Dtte ~1MtM

~t~o c eamp 1d1t(s-et C cent~ Cztlt Pt J(e -i4af(EV (A~ ~-t-te~ctc At ~Ca~t QI Lk Me t ~~it-t~ ()Q o-J ~ ~ ~itet ~ pzCla

~-t ~ LtJAo LMAMz

~~ ~ ~

SGl~ B-t~etJ Plpt(gtzOt~~O

Ca ~lJZ~ damp bull nwy 14(0 oPa ) Q SeKds C L 0 PI

~ I ~ t -lO Z bull ~ J ~ OAn Ct =8 ~~-oflt~1 e $ Ll016M -tLl~A~~ So LOI~= LOaAHa A~ t- fs 0P 0 P ~o ltlie sjI Ie~ 00 Cgt~ ofL ~ ) 00 ~O~e-=OPct=OAIOg

t ~te~~-1 cknl4t1 ~ AO~ ~ Ate ~Itc

~ LO8M= lDAM

A~ I =gt LoAM L~AMz WIAamp~ ---

L 0cA M~ ==gt L0 A0)- L I-i A Mz bull -to _16bCrfkSf~S

Solt~p Wpound(CS JTbe reflec~ ~ S Wit-(S~ltt

fI5 Mis

~J e

t ~lwt Cgt (1Of ctImiddotd i -br3frt -+0

e $ f(~

Q cmiddotnI F -tkt bcs of tIl YOII f Sue- fut ~e-re ~)f Q

01 ~ w~ M ~ ~(eoi~ ~ l R~~ QS ~ isc~e~ C~rdamp 4 A PQ R

-to M Lt u be 04

~ A$ iudQ~~ltofe1 middot~~(R C V Lat ~ 10 ampl yo~t~14 fc

Co -fI kottcrt(e+y wfoit4 uW( P-tkt StI~ l t

~CtCte (_oppos-e P -(f ~ T middot (1 ~ Set$ U -to (Q((esr-~~-toflfobulltHf lt 1) Ii P~n (= v ut s setft~~ ~ t PQ~ ~

TR SQ=S - PR= PV- PIlt = Vlaquo=n ~ T T So 5 01 Ae ltT0 e ttl

ampruJt~J) fr p~ ltTaee~ UT ~ U

~ l(P Ifamp)Se0v4 u to ~ C(telte e to c~ l I- UtoT So TT Let 14tats~ P-4 C ~+~t5ect r ~Q~R ~

ampS-=s- Pflt=Pv- P((--Vre =TIC=-TIlt ~ tiM -i1s-MS Ti-f1T=-jiM PtSAt4t

~ El4middotrle b rio t)

Lt-A~c ~ co ftiI5le ~ ~tof scl Be A1k ~tsct- N ot l ~AC i~+fSoct ~c ct tJ ~~r~I~ k~ +0 AN -+~~ N ifersets AM 4 Q -c AB -t p -n ~f-lrJrmiddot 0 li~e to APt Pt-a~AIl laquo 0 middot Pofe Qo l Be SIt- TfABAc1kMNQfampAQMol3c

WLOG I ampS$f41111t A6gtAC Let AN MttStcf Uttucrclt fAABC j 1) ~

-- - bull c L 1gtg CL lgtAC=L~Llgtc~ e lAo M f~ r ~ ~ DC aJ PM 1 Be

~o Ho~y K(A ~StovlsA6j)(+oAgO(t4 08 O~ aq ae Itt t= Be( PN -r4~

L Ogt- L b8e =LM8=ro6_LAop=LoP~ ~ ~ D 0 tcKl orooc

I ) I J GfeCttrA J~c J~M4 ~ L 0 - Lep - 1 0 - 7 1- - 0 - 0 Igt IC tS~ amp It sc K is AM == AM l PfI=Q

I I ~ Lg eto L~~O~)oo 1~ ~o LSC g c It Be r

F l

(~p Sol~ middot Let dort FE ~wt -to nr2 4Ss(oll (iJ

Feuro () r C Lt r 1 U04s~r 111k ~y1- (M V)Sets P t r c-to K) Iiamp JE t jilt L AS

sow1 bull Ff 1Ie L ~ A is +lt1 ~roIldrc FE LNEC ~Afe~LAME I rSo L ~~eL~A~)~ LlNEcLlAMc ~ ACAeuro ~e1IA I ~ ~ pouer ~ A ltiol4Isped to r is Ac AM= AE S~M(tAfy I 16fJe t ~A i-fk -(~d -to ~~ Aft A~ A - A ~ =lttiJPOiqJ ~FeJ 56 Ae==-AF (1amp tflt11- rAAtcd - I

_ ~S AI ~ fIr2 AA~f ~ etc )~lll fu ett(4-ik1t f t fl1 pues-~r 1gt 61 sJMe~1 t ~OI)O~ wt Soc Oa I ~~t ~~ Ctgt

~ Ltgtco~=LClgto L cLeF ~s ir~S COa b~s L 9CF $ceCfiS~f rl So

Cl) is ~so~~~ -to re

E)(4flt

amp($ PI Ira Q-te ite~Iy ~ t ~ rt M N~oJtlJ ~ r fGs$es -tI- caff( 01 ~ r~

lAe r tgtit cl1illfr iii r rio MAn=C MBfr=D f (0 ~It CD $ 1~jkt to r2 bull

~ C~ IS - tYgtctStIt

~~ A ilefSVsv wi CAAer 0 oJ ugt r gt0

(amptatl 1 J(o r)) sA~f~ +lAo Se~s A~et(1 ~(t X 0 to ~ i~e VOl~t X O~bull y at sucL fut OXmiddotOlec r~ ~ CWOIelcu I fo X=0 ~ Utake )(=~ _-cl tllSo~)(-=QO Wt-take X=o

1ke Circle -w+1 C2~+e~ 0 A~ ~kCamps r gto-((ct k poundSle ~e~ ~ I~e IWJy 4fso ~ft A~ ltrs~ by sff~t ~ CrCJtL (lWt~middotcP

fGcfs CO Gift1 ~I((S~ ~ ~ bje(~~ it f~~ u~ 00 -to -t~lfmiddot ~ ~c-t J ex ) X ~

reg -If )( s-ikcRiC iwe~~1~ XI=X bull f)(~o~elf(enX~

= bull 1 ~x ~oit ofTaTl) ~t-rrl 4i~

P e ~ X1 lCT2 4~f~~-t1~ ~s iS k~

- __ OXmiddot ox ((sec LTo)()(ycsLTox)r~ ACtreJtt ~~SSi~ 14ftJUJ 0 ~~t +0 A cvdc bull ~ya16tj -4r~ O k iII-s ak~cIc -poits ~(~ St -to ~amp~ foffts l4 fOit 0) ~~fets

of -flit G~ a41~ aJa Afe utllt4r bull JotlfoItr~~tf(~-kGttk ~~set fotleceofv-f~ ~~ctrJe ~

A(fJe vaSSoVJ4-f 0 is Set -to 4 (euro reuro IS ~~~fI)~ 0 ~~s ~~k(+ifia1e-t (It( -t 44td Ito Cnverrely (A (middot1U1IIJt rssj-tlt~ 0 is Seltt -to ~Cvde (w~~ 0 Ni-l -tttllj~-t Imiddotier0 ~Itd to ~ leilt

f r A~At pCiSS~ 14 0 es SetOf ----1-- To e~setl ~ ~ _

Ifgt reg If two cr~ (f~ttIlC~ C4fVts ~(( ttlso ~~(etAf ~ fbft Pto)~~~~

9 lCo (iflaquo at ~Sdf~7e 4-( p~ oF

0 V ~-tlaat iHy~t~tOmiddotmiddot71-~R CA4f~(S ~ SQIJ-fo ~ 0 J

A Ie dI o~ctves4ltSet-f0r1f~~ ~ c () ~-t bull i- cmiddotrd~ ftftfiSttft S ~ fa-5~ 1Gtt cri(S t ( 4It ~fo-6etc~ Gllf f~S A lS 0 4laquol 0 A ~ IV~ IIG(C4((o(Af ~ oAmiddoto~ t 0Bmiddot O~ ~ OAloB OP4 ACoj

wi+lLAoB=L8~A Wt3ttLlOMdOl~ () - ~ LOA8= LogA ~

Aamp~ = OA _ r~A A6 0(3 - OB

=) Ae r lo A~

-------- --------~

)ampa-cle i (~tlcptleofto A ~cQlt$ A 1ckc ~tiatt~

ampl if tlyen~ t ampe- ACBD - A~middotq) +AD

II( V c bull I

SoJn C-sidelt -kfSiCll At 1 vuu~j l)is Cpoundlaquotef bull J ~p-J~ Ygt I) - t t e y fatH4) J -k ~ro-atdc qf ~ec ~~A~ I Q

I iIC ~ AeC SilCamp ~ IH 6e - c I

J vue b -ftt (1) We t _ 1 _AC~ r - Be - - middot

iDA ~ 01gt1gt AJ)middotC1) tt Mltrtrllj b~ lAOmiddot~]) CO~2 1aJkSimiddotces amporeJ

A6amp c) +A)xBe Acll 81gt middot

Re fICS 11L sf ~ eat be ltoftrec -to ~t -I- ~1-tllAt t MilcO + AtgtICBC =AC 1CI1~

~V Asctgt S (l u~ ~lJ4~ 0-shy

~S6~~~ kfCfS4tJ foJt of~~ -+k eampIt~ otIIIetStM Ai ~itlt ~s -fIc ~o~~ rote iIt wJere -reIs CIMif s Mesc(t _

-

6x4t~le 2 Lt ABc 0 be ~ ~tllt t(kft~ suamp~t At ampt so liltftStct At Y1tt ~r AtO P~t~( -Ke -refltecf of 0 ~fOSS AS BC C)1gtA A~ C4IIcYdtc

p _ c $Lt-~ -71

Lcent P~ ~So k ~fut f-~Wi _ 010 0 flO Msc CD lgtA Ye cdIVt bull

sc =l Ott foIIttll is ~iIr~le-t -fo site (5 -tk Ptt-RS l~~( (Sl~~14ft

e IcentS 0 0 -to tts e_~Hrlt OSAP DfBQ ~CR O~DS ~ludlC~~ J J -J ~ _ bull

-tt TltitCirtlutdts Ie CA Ca Cc CD rtsrdtuely CfSMoSmiddotd fIf~iQ 3(0 r ~r31gt0 By ~ct(s)

I~ AC Q( e04~~t ofo ~gtltS

cfct (+) I CA SIrcent to filllt LA fllAlrd to 81gt CIrs

Set to ~ IIt LB ~(c of Ac I C ~ Sci fo c tAlC -to ~lgt1 craquoisSeoet t ol1t LD~E lc ~

0 0 r~-t 0lt1

L Nen bull

CpnCa= 0r~ LAf Le P )Mjl-ly 4~t( LI) R J ll)n~ So bull

$r~ AcJ Mgt PClKs ~~Ic~4J~~ ~ fet h) PampRs is floc

~

G)Cdtpt f

Le-t P bft Af6~-t ~S~ 4l1It Appound ~~~-t LAPB-LACS LA(C-L~8C

Ltt tgt amp be ik~~tS 0( AAPS )AA~C nspecflf ~toe ~l A1gt 1gt1 ce )wtet A fOiWtshy

~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

( )tlfamp 61) biSKfs IA8PJ By ~t CT) ACAfACf~ ~ ~ I3A - XA So iSttf ACAeACampA

P ~f - xpmiddot ~ P~B6+lCApLcA8 J

C-1-1 ~=~ 5tRCt X ( 4ft AP ampt ~1It By~t (s) 1 ~ tCp~=LCitA ~ ~ I I~ fQ is Seoct of ( ~ ~~ 1 f4$s~~3C o listf SiacCrtIeO ~ -T(Alrl~f4lrgto ~~(1)1 tIIet pamp ~t(4C~I~Ois~tfo(0

A ~IgtC A~te A lU)e bullA p A APelAcIIgt f-c ~) I SIWICamp

I

~ ~ ilt3t +00 c( ~ 1 PQ fh ) Qm Q J r bull bull ~ t01 setc~ 10 t of I I

No LM~-L~8-=-LIWC-LAec f~ $(amp ~st ~JO 0 Ao( ~J~~ ~ Atl 43~ t (-d 0 ~ A61PcD

fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

Page 11: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

~gt

CD C~eetfe( 0 is ~t tlv ornI reg CeV~J G is ct A-tA~ A3_

() I eurot- NH llt (-r~s rs -tf 41-1 ~- 1 A A A bull A tateo J n I l _ J i (~~Le~ ~Alll~b) s 01 SCt~eD u -pe v~GyueJ

(jOf4-hoce~t~ H l$ c AT At+ Pr3 (be(AASe O~ = 5(O~)) pound1- f lt tl~ A ~ fJclCi-r -to ALA 1s

i- A-A3 ~ -= At - A1-AJ A bl~-t ~ 1 1laquo ~ ~ r~~cJAt -to AA~ $

c- AA) == ~- A~ ~ -rktSt -fwo -ts W f~cf ltt t ampJk4J gt~~flaquos boi lut~~ u$~-f~ ~t tAll lAzI= tA- i- (e

AA = AzA - ~X3 -= ) t ~t lt e c At-tA T A~ SAiSfelt bofl ~t~01l~ 1eo t-= AT At -( ~3

17 N f t - L A+ Al-Ar) 6 Ce---+ef ~-tke ~-e foitrt Qftle $ DA l-

(be~oe 1-1 $ ~ ~Jro~ 4 o t-t) ~tCA ~ Mi-e fit arcc is -tke Ciolaquo ~t f4~SfS -tvnWJ4 ~ a Jo---~ -4le ~~es AtAl Aamp+~ As+A) ~ ~- J L -) ~) -

~Q 1eet qf ~ al-t-bAdcs H I 1 1-3 -=t ~ Wampdtoi~~ -tk ferllaquos ad ~e D~e1 ~~ raquo A~lt

(J~i(t~ ) A lltzlJ J llWW1-~ Ayt ~ito

Sol4 SifCamp ~A~R~lgttPLlCQA~ ~rJwail~e Arf A+cJQ+~~R20 I 1i~R+~~Pao C-t~1T~ZQ=-O

I ~Il I w e LV = e ~ 5 A ~t 4 ~b To ~~ fl X 1l s erltamptDI we CoM-rtf

Xt wl-t t)ll= (Ai~amp ) +w~Ct~iP )~(8+~~

= k [CM Q+ ~~)+ 1Yfgtt wR + tf )+ w (C + p+~ I = 0

~~~A I )( ts ~ (Rot 4 1 J~ ~ ~-t 4 -II 3~f1 C~cf ~ ce~-ter4cl At ~ (A e) ~ ~(f-t~) (ie ~c pOlt 3 -the amp~~c ~ ~ ~11t~ -G t- ~rid 1 ~~t AS)

COlf~selj Ikj ll~ 01 ilt G~f smiddot ~ fo~t ~ loc-s 61 )( 0-~ G~f C = i(Jlt- CA-t 8)) is -flc co~nsfo-kj lt Ov- ile ~t Clfdt

1-(t1J~ Let A~ A)e tI ~r~ 0t W1w) w~j I Y~ f~~j

fYo~ A ~ J~r - fe~~ -to -tkt -t~~ e to ~ c~tdt I

01 b w WI W 3 Got W bull skw~ ~est f~(tS ~ctCmt 1cle-t~~ ~s tmiddot~t t C)~

~otct~ JlCG ASSUllC -tL ai~cit-tle is -tlt kAtf GifC(t

~ h~ le~~tcJA -to t f~eMt oJ 1J -iklk ~ MS et--4M rll-tvJ~

bull l- A ~-A - WltWl t~ k~Wi -r ~- w - tV - 2 - - W 2 bull

Now WI bullbull f -ike ampM- ~~lc I SO Wd -= 1 i1e we ~ fJ~-te -tk ~n 4S _ _

~ bullbull Z ~ _ I T ~-t Wos 11 W + 2 Wl ~ - 1iIII I - - w

2 2-

F-oN -tk5 t ~ ~t -tk yoil-f N Jw~ -+ W3 $ 0shy

--te e lt$-I(C -t1e e1f~sS1W f Ns Sr~t~c ~~ nSFt -t oJ Jt Vis we (4 eot-t~ -tMt wtl lISO e O~ -tIt o~-- -two les -t~ e-Fc~Sto ~1 tJ -tt l s u~ -t $ -tle (fwle1 ~ -t~ )1 fO~~ (tce ~

J I W-z4 _

11Ob~ ( S~~t lYe Tko~ ) let W be D~ llt (~crclf ofJ ~1 13 c( PI Q1 R

be ~ iut ~ ~ lC ftJi~ ~ W -tt t1I 2 ll I tl ~ I ft ~ec-f~Jflj slw ifvt P Q R A-e tAl(Il (-ps Ole 5-

clt~ A $~501 11 tf A ltamp-t) ~ W) i

~ol~bo- WamplAi loss -t 3~nl~ I Wt J lS$We Je G-nIUshy

Cilampk 1s ~ ~ cttclt ~ lll llJ lls -= lw I ~ t 1kt k ii ~s ~~ l+ ll~ ~ Ii t3 --ie r~~ fw- W + 1~ Ivs ~ f-ltl ) i tJ- Zt~W So Sol lkcsc -tcdr W~ 3laquo l = ~ t L + W-lE W

2

St ~ Q ltl ott ilW --l 1(= tt f t~~1l

I sluw fQR 4t CttlfUf it S~s-t st P-R =l-amp-Nil f-R _l- Z-amp-~~ Yo-~~J (tI 4W -g ~-R

Q-~ -1-1)-1tJ --l~W X l ~-amp~w ) l2tgtW-ltl~ -lZ+ t

4t~ w- Zl~-ll-t It f- fl

- (1- R bull

-J clt~lttii lw=t ~ WW-=i

CiiID ~tlt~ firLiA BC let 1gt be A4Ie GtIlOc1tf- E 001 As loIiti DEit-CB J ~ F ie 600 Be I

ciA ~fDf oX ~~ o-rbmiddot 0 1 ltt ftt XIS G(( Gr be 01 EP ~tS~t ~ el~ttrlgtedo-r W~~~~fk~t~s X Ao D C fSfoFc-=Ep-=BYc1gt=r

~J ~sted oR we rMj Sity ~ i 7 middot PrDV~ 6i-F fs pcmI(e( -to -Me 4 b~ 1 -M CaJamp) Xl= Of-~ -tI S~1 je Y-X Sol-I Set 1ampt o~ AtAo tt(-~ IMc

For ~fS X It we e Ix-+f ~ lxl +111 ~ft Tie E 8 Gfl = C ot~~ E (0 r)klgt(d~ 1- W-11IAy f X= ~t(r-s-e t~o A~ F tB t(f-t)c 4( euroj =tE t-((-f)J) _ h Let Pbe 0 poillt el LIle )( f lJe lter t= B _ L _ amp1gt g + (_t )e~ middot gtY haYCamp oP=toX+(f-t)oy -f=~y ~ Be -- r -i1gt-t ~_

J J gt1( 8 -I io O~)y~ amp(01] ~ P-u SfjllleMt Xt E retgt I $0 IE-BI rD-cl c1

EICjl1t Call a ~1IIecent ~ ~ QjgtWelC ~l~ (I- ) Is (E -amph 1l ID-d r-(t-amp)(c(-f6-Jgtfd tl )ltLJ )M ~ ct j~ Ie ~od ~ orF9fe sk~ J i q F- Gt = t6-p)~+ (I-t)(1-9)C ~ +~hw ~t cf -tk s IIf-t4 Jgtllrl1lpounds Of ~t(tei _ IS tlt-p)amp1~$ htfampt iits~etet ~ik~litetllllorltl -tlt-p)la (amp+~~ =(~~k1NIllelo I _1 t f4IIIl ltf1ltS

Sll~ fir trl4t~ A~c~ Itt-A IlIamp 1M OjL ltf 114 (tw~-for ~ pound Me~ --ik se ~fOW twI ~ _ Igt IC-tO - f ~ if

T -poundTI-r -pound ~ I A=0 1)~D i(1el IC-BIt lo-dtll)~

UI8iC-1gt1 +11Hlt-at=Iel+ Ie-IgtI+11gt1 +1c_~(f~~t Wt ut Ie+IC-Igt ~ Iamp+c-tgtl t=~f1f)

AA IDI + IC-61 ~ 11gt+C-81 C-~AO=~8C) (gtt) holds ~Le~ft~~lcJs A81(1)C ATgt Usc _~ __

c6hf--I--l~1gt~ ItiC

~1- ~t fmiddot~~ 0+ ~ 0 ( is )(Y=tJC( (1 rsti - Ex4k+ Let 0 ~~ (i(cAt cf 4ABe 9 ~iIt J bef -fIl lfcffS Jf -IIf (t) Xi=fX (y+I)zmiddotXmiddotZ+fmiddotZ 0( (cXl-Y~(Xmiddoty) ~ I~~)(middotX I IXmiddot~~hd1I O~iOf (=) Xmiddoty-O ~~~~~~~~~~~~~~~ amp--ft 3 Let A8C b Le lmiddotts ~sfmiddotmiddot Phe

Ac~+amp~+A~-t8C~~ Ast+ctl SJt~~ Set1ie Ot~I ttt A ~~t f Jw

CmiddotC +(amp-lgtHamp-~)+D~ (8-c)~-c) ~ amp (c-b)laquo- At~(~- awl lt~~-f4ls s fu ~4S

(6 C-b)middot(S-C-lraquo ~ 0 ~~ck s (amplt-1) ~o

A ~t 1gt Ie -tLt poit ~ Aamp -L II ~ e _ ce~AAcO

p C fgtrcw _t C1gtJoe ) AS-AC Sol~~~~~~~dO~A

A a A J) A J)= ~ E=~~ =3 +~lCJ1gt-C=Aamp-2C

C1gt1 Oe- (A-tS-le)(Mc+1raquowO c) No AA~lh c C C(CUM(bull (IampSt 8 41f1$-bull (4) bec u Amiddot(Q-ltAB-ACO 1IeJtt(~) ~ OAl ~c ~ A~~AC

euro ~ toJs ~ 8lt~ 1)-A69 seAPS fWlkl ~JCOc $ firAABC jf( t ssewu-J -ptMf ~ c= - ta-+CmiddotfI AAS( its ~ttd q ~1 - If We Sampt -iU CitClIMChH- 0 AS ken -HII-srft~ ~o -t r -11 __ -~ -1 ALh--COtt - 7J 0 OtlGCnx n - ~-

A Fit iAcetft tJf ~~ c 0( lU= ~ = L

co b AI c lt-c

e ~ 1)c 1gt= te+(t-t) C t --amps ~1i~ poundL = tD ~+ cC C bI-c Gte middot I t A-t -~)tgt t-ll- A

aAtlS cc_ - tgtA - M~C 14 e middot

11l Lqt-(gt OmiddotkC Gtctal ~ICef c(H ~r J

51_ Set 5 4lt C4fColt_bull tu e -H Matel~Me1~ 1~ AA+b$-t C shy ~ 4~(

Lampil~gt 1omiddot~(i-1)l4-1) lt0 A-A 6middot~Cc=(tlJ 2ec 6amp+cc-(a-c)(amp-Q=k~middotIf (A16i)riamptc~ Rlt9~~ 11- 3( h_ Imiddotltl-C) 4l- 2(~~(H- btCi)tI~)) cttC

)(~+c) (-1)((-1) =((~ t1 -Hi+(() lt 0 of -~ f (ib -t-e) lA+Il+ ct )+ilaquoc gt~ CifI+cl+Jl(c)+ ~ ~ a(-o)(--G)-4-~-c)(b+cc-4)~)gt0 tsc4 rc s

~ Ike fRS ~ f xi xI wt -Stl-fculot 11-$9 (t)=LXOY) 0( tiYfft~e~ -fo -tkt fl~~ 1-- oxY J e

lti) ~ -f~)( ~f)-a)( l t Yltl (c~wYcxnyJ (j - )(~1 4fT~ A X0( V~~ p A of yl t1ft 0

(6laquo Q bull 1 lj 111)1 (DW~v e

eJ41~ Let AAA A _j A 1 1_ -+ V]nq DO 4 CD e I

- its ste ~tS p-Ilt1 ProiIla-t middot ClrtllAA1Ar oreAA AA So(u-tVf SeL ot - ~ -_amp I~ _L ft--A A ----- ~ fJe ~ ~ --fI 01r~~ O4St SMs ~qIt ~t)~csCA-A) I lA_-A f

E)Ctl-eIlaquo-r Let A6COf tgt ~~ pe-tft Qc e t

~~~Q~ ~ 1kfwlrids~ A88CCIgtbEpoundA 1T~ -r APamptl~J~ le ACDIIIampf6i -laquo s~O~ tk-t ~s Ooet is so eM eII bullbull ~olt4-tfN ~et -ckt O~bullbull~ rt -e ~_W f~ S~

tJ 1(t0 AXC ~ AP ofe (o(iu o=A-f- A(~ J C- 32s amp A

lltc t))tA SIA~y 8)(1)= (1(8 CxE~ C I

raquo)(A 6llgt re EJ( 6 =CcE feMtt I

eurolCAJ- E)(6-t( - ~lte+El$ ~ pound10 eImiddotmiddot

1 ~~-A~)o (As-AJ1gt(~A~ S ~~CI amp euro1tf6lc~ ~se Ac Adol~ -t(t-t Lit set - () middot At

At~ t ~It~ AsIC~ Al~-+yen+yJAI (

_t a ~ - bull

~ 2-shy

I _0 c A 6 c ~ As V ~1~Ut 1 Sjtllc -fb ~BIC~ fW(t

ftdle ~ts of BC CA AB ns~chvell -tk ft1~ -tIua-t

No A bull G 8 A I ~amp Ca A~ (orr eU egt~ 4~_ A~itlA-~lClA-As~=(~tAtAr-tAjcA -~~ StthtlI4It ~ SaJc1ttA

(Nmiddot~~i~+Ar~~l ore4 l1A AAs = Are 1J~~Ai

Aft13 amp11 C=A-ttils-A)frSollletoA~] SiCt AS e Gfe i eRe

o~ (Bt-A)K(~-A) - (A-ttz-~tl-t- t t)AxB No ~~=~~~-=amp-AH-t)e ~~1 S-a-= It-t1)A I Ct = lAt8)- c tlA +ll-t~)B ~ (amp-AI~I~(Cz-~)=(t-ttl-trtl-+t~t))Al(amp~O A S~ CL At( ccdllfttor

~t ~~ 1~~Pt

o

C[~1D --r-0 vetlOf) )( lf ate Jt~y wtt-t---t f~ t -flat ~f~ ClX~yO kAs 01 Soat~

AT 10 o T4 s tktCcStI ~~A rf KttO ~ X0 f Art NIt Co((llteor

F4t IT AX+bY+c =0 ~$ote -e 1~I(z-s 4t4l 4-+amp ott -=0 J ilQA Xf Z 4le cbullbullI btACcS( ~l AO fIe b-tc-o w X-1-KZ-tYc-6Z

(~ar~11to(~1 wr~t--J Lftai c~ s OAAampA Co

~ OeLamps 1f 1 -1z- Aa6~l~8ampR AsampIA~= ~ 6 8-c amp-S tltcl A DAR 0

~e COIIfttAt t ~1 =- 1 ~ ~ P Pl) P3S~ Set - orlll at o at A8 btt ~trs Ale LIDa (ampfbv~ ~ A~ rA Q( e s So 8 1-t S6Wt (s EIt Cll No

Pl =tAt(c-t) 8a trA+ (ct)s ~- ~3 lAAt-tQ-) 8-= tA(-aA+Cc-ct)S a S~tU~ ~ 0= ltr- CArgtA + [pound1)l -(I-I4)$]B

A~ (tally rcf~=gt tr(~ Otu( (l-tl~-laquotlt)S=C Solll fott ol -tit pt~~ -+-s f ti ~I~Js

Nt ~~e ~ 1tu~~A+ SoSzCt-rl g$t Vs- r~ r~- r~1 Pgt1s~S)A+~s(tmiddotgt8 R= rlrfgt~A ~(I)J B

Y~-r)S) ~6a-t~S) amp c) ttS +fs-1S ~ p~f~P+~sampf-tj~

~ P1 ~se~rw)~c 0 Qtlgt+CoO ~ r fL cU-1- fc-i (ove

~ 0

A - -

~ FOf~lamp~

(1 -laquo ~C

fot-CA~ to ~ t t amp -t~~ crt a ~tc ~ El(tend~ltl St L laquobe ~[A8Cl Js~~i~ R= 4 C

Let ( ~t 4ct nwts lt 4e GoismvmcJt i-R- tl 4J~)(fo~of AAsc Sr ~ l=~~Yslt) ~ bc_

S A -- - 0 21 1iltelaquoe s dolAt C~d~middot ~o~ uI1gt ~ s~amp s~~C middot T 1_ ~ rI n -rf (i-- shy

tl Ie or~ DraJ clmiddotae~t 61gt 1pound Si ~ A= ----=algt i IS lle~ ltJOiOlSA0

~~~~~~~~~~~~~-~~~~=~~~~ p adEr-l-~a~~r~ A- oS+- jtus c~ - c e c I) p(]) Let 18(1gt L~Ms

I4dtt rAsel Or S~8c1oI(lcl~ 1leflAftt Let A6nct)p -r1 ~act 0

~Me C ABC ) GlUo~kc ~ PAx P6= Pc x PD = tl b~~=Abc bull P19tpound Note L APD L (PB

4R A1BC)aHd~ckLPAtgt=LPCBS=tfA-tb~~) is ike seifieAc ~AAPDACfB~=~~ PAIPB=fxPD

amp Q C Of 4A8C Lri pc C 1amp-~ ~~ PC Is -lt-~t lat t lie i4 jCbullbullr 4l( M6C Qt r Ie -i4~ to -e -fde ~ A A8C if (JJ

C)~ ~e icltc1e ot AAec ~e p A e OYlJ c fCL p~~re [Mel =[ALel[~cl+(CI1= ~-t~+~=SIr ~ Not~ LArc=LcPB

I-tfllWlbull [A8tl~ S($-11 ) (s-b)(s-c)middot I pCs f~ot -to LACp4C ampP(~ Cos C= tt2ttoa-c (~AI Ci(~ircl 4 MBc B 2shy

[A6Ci= ~SiIlC=Qr(+coSp(i-($C) ~AAcPACBP ~~ fgtc PCPAlltPB =(Cl~-+Iot-c~t-~a~-9 ) = catlo-4 t )(A1(-c)(CoHI- b)(o-Il-~= S (s-c)(~~

2- ~ a

Ci C [AS(I A 2

~

I

~JJI LPFA-=odeg=Lpe~ ~ amp~ ~LPFeLPAE

C5Ji) ~tolt1 s-ThtOfotfll Let A 6c~ ~t dlSncf ~ts 01 bull ~c ~o - Me~IA~ 1( bull t Of~~~I ~Ot bull -Tht~ bull Sa c~tOV M1 C(liofIPT potd~ A 6 C Iie to

AI 6 C 1gt (1~t~c 1gtpound fCLR atfmiddote ZA ~A A ZA bull -~ -iA ~Co~ PAQ~clf$ WeA~ ZA~lA I tc Z~t

pFAECc1dk

bull ~ Srlloi(y taCgt6~~~-lPFB ~ pG~ f CDCCYcbull LPampb LPFI) = e 1klaquo AIJ~P LPAespoundp8C pfE _ LPeP 8EF (0(1ltlt~L PFE L~8Tgt~ LFP - L 10 collirAfampff

)fgtC)~Jl~~ ~ ASC1HAol6C=AcS]) bull (~~_ ~ktI AeCO At)ItBC ~ACdtgt 1)~c 190pound 0 sWLe AB UJlfsftfUct A ampA6

S~~41 to flCAP 1I1elt AB A~ 6eshy

6 Ai - 7ligt= (1) lBAE=LCAJgt

SO LMc L BAlgt-L1gt= LeA1gt-LMe =LEAt) Tkeuro1 A8AC~Ae-A1) So Rr-c EDAtgt~A Thet Aec~ A~8C =poundItampE AClC E~ AC80

bull A rC =c Sf-t Ell I

f1-I-4j hoW~ ~8euro~EtgtS ampb ~ E iUt~( SO - ~~oeA~LeeALtgtCA ~AsectCO Sltffc

SoSoft ~oe 1et~6cP cl-ampd-p~ 0

tI~ Let l)poundF fetf~~ff- P~ ampa Aeyen~~ ~

Asse ~Mist (so4 is 6~UA_JC ~AGSC ~O bull G ~f( Aalec~o)

tt~e9 7eff

fovlaquos X I Z ate (es Aamp ampCA D ((t~ve-()ty It X I Z (lie (dl-lflOr

A ~f f6 lhg--1 ~ xe YC LA - middot ~ lQt Dbu (~ Ac soct1IIt 81gt II J( Z -r1teuron

~g ~ ~ 1t~ ~z Se AlC 6Y c~ _At P1Q (i~ ~y Ie ~c -- _______ r tamp iU I bull laS yc fA ~Igt ZCZA middot lCI~ lIeeu~ Ie~

If ~ tL ~ =-1 iIamp )( YL MHo l~(~ Y~t~~~~ SlJ) Ltt l~ X(OCA -Thtl b Mt11Idtw 11~ Ax ay CI _ lt Cz Y Cl iiiK zA --i ~o --=-l1toobull CfIea bull _Cl -a

I I

ceDD ~MelI s lIeo~toA l~tA I ~cc t) euro ~be tc~ lO 0shy

de lw~~ ~( ft amptCtSSCti 1 tf (~ diC- (~QEf ) bull

t p Ae ti l)euro J Q Bel pound f 2= Cl)n fA ~ ~k ~ Q1t ottc(l(ea~ ~QIR~~~ -

f~ 1 ~ ltt X~EfA 1AMCD bull ~ z- C~neF Arr~l ~(atts ~ff 1e-(fM1oec~ FA

ftt- Ool~~~ 4xf l w hVII

e-- ~ X K __( It X2 ~_( t ~~II Qx 6y Ct ~y pzex I fllFxijmiddot 1I

Hul~pr~ ~ AIl ~~ tfffSfctj cofI4t tt XA)(B XEmiddotKF J (CmiddotYP=1AmiddotYS ZEmiddotZF= zeZIgt W~~et ZQ lSf~-i igt PQ~ ore rlfltelaquor

Qx Pf Itz loy c-enc ~Mee(AaS

t-rks ~ere 0 Imiddotil~ (1$($ of PoucJ s for It we tftwt Ato 8 -te I AIwIJ (3 il(cJe 1Iofl1-t i AB will b~ ~-t1l3et (iot ot B ~ It~j CIt~ we ells JpoundAoflt ~ t~ liflE Clt B b~ BR

6lCtJfC i F~~ h Cf(Ultirc~ ot Mac J f(it 1) ( ~ ~i~0yen ot -t4l~lE I~ ~tA - ~~ Be ~ e fM 1fe ttusc(e~ of-ffwf3ct (tt4-t C3L1r~ CA~ F= bt ~ ttfStd~ of -tINt ti-~-f Imiddot~t ~tC wo( Aamp 11161 PI Ell F o~ ctU

Soof~fIyen P=Mo 8C ~ E= BBnlA f=CCnAB APP~i P~f ~ ~(fo MB See I fott et 1gtpound f c-

-- =JSiiiiIii

b)lAtc ~ Let-tgt 0- eht ~cfs 0( dt101 AtCS

AS ~ AC O~~e (ilcu-R( Mac ftspciwJy l(t tgt Ilt ~f AtC sCI ~== DPn SA J R= PEn AC fro +~-t lile QR~s~(QVJ14 fttCf+~I (~ 1) ~ f9bt-Mshy~e 1)rff0--AS- CO ~SfctsLAc8

Co ~r ~ qftllCr At =lgt 6 ~LAec So 1= Cl)n G8 Sf_ eEtS

Q tgtPt SA DP 8ital R= Pe C Pre ttL PlE AI

AIP~ f~l ~ 1Ito(-to C ~ P er ~ w 1 ~ bull 1I

t Set I Q Rut tIff~ Co~~d~

~ -7

Alt IXu q j

elf (Ga1(e 3 Ltt AT3CPs e ~ +s tMDlCJe ~-rd AAfLBS Bat LeA) ccf LAB fat 1gt be ~ls (I ~cucl1t ~c4( I

DA(11)C= AU DB()CAe~ 1gtCIAB~ fgt~~ A~ r~CtfaJ T4 6v~fi ~ IAGC a~ Co((~((r

~olf- W HL-cI oy-((~( ~ AA Be Ne

AAIB~I)Cc(-=I DArBC=A 11gt1( ISc AtA f Cc -= H L lAlA I C I Cl

1t~()cD=C1 ~l (AIBl (cjAfrrr5~5Gl ~~ t DAAfCC tgtlt Se4 A HC tit c11ilaquoraquo SIt 1y ar171~ BS41s(to AS e 0cc we Su e H 6ltve c1(i~amp r A~ H C~ S4rt a(((~4~ I

-~ ALI)f ~fle1 tt P toe a ltpor i~4Mec

LtfP I~~ff~I$f- 5 -to ~CA Camp ft~t~ lttt bJ() ~_ eshy

ll 10 ~ fet ~~~N~ c-tohs API sp (~ftvtll IfQ P ~ 61bullbull Pt14 PttNQ~~ (tries ~tll~ Qfz cod A~ aft ~et

iSoLttd- $(fCJt L CPc p) LCQLP LC~P Lc (gta Palt-e J -t ~es c P ~L I PI Q p 4ftcocttc f~AfrI15 ~s middottU(Woto ~1l$1 w-tSu CPt ( gt e-= A ) P t1t( QIP= X ) (Q-a Pf P2C-= B 4re CoI~rtelr $6 Rb2-l amp1L ( AB-=Xmiddot ~ ~lIQ P~IA8 tVe ~Cqfre~

NewtDJ S

~A ABcOS~~(laquoteJktvsa e ~SQiraquoeamp c~tkt~~ ~~

APgtsc CD) PA AXcpotlts EFG)H-~t~ C F B ~ACG~FHgD~~r~t

Sol~tcNI W E6nFHO~ Eftn FG ~X _Apply~~ ~~scJ ~ ~ -to E~ltSJ F f(f ~Sta E~ () Fr =0 ~~ ( 14 1) I G Fn H( X are ut(ltealf_ ~ltfcAy~ltP~CA(s ~e- 4 E6--()FF~~ J ~S14

EEn FF~ B euroH nf6=X amp-t-fn ~euro 0 tUllPtfcmiddotc4t

-nus ~S 0 XI oJB ~c((e4~ 7itN pound4 fl Ff n6D=O SlAry EG F-- ( AC - O ACE6 fH6DCPotrclO

1)ec~CAes ~ 0 nfAaAec ~ JACc) M

A c B actgcP J CAnCpQJ AampnAgR ~r--+--Ir-~~R If AA 613 I cc 4te ~tVt-ct ~

A e 1-~ PI ~ Rctil eo(IQ4(_

c~ rCP_ R2esrk ~-s ~ -tyenUL te~ 4 ~~cAAfIdgre IfV --IfU ~ f 4s root G-oIer ~Ns c~ AOAB ~ftJJ MeoJ- -~r ~ et QPL AEa gil

At A rltamp -7---1S ( rt l g 0 () I 4 ~ ~ Ie Be Cctf~ Lloec Ilfct-Jt ~~ C~ c~ IJOCA ~ 1te(J C~ BP Cd M oct ~

B8 PC-co ~-( ~ No CC~=-( ~(ff~~~sctmiddot~~= - ~ (IC4M~cfMtl~~~ote- ~ et eampI c-f(er

62Y ~coJ A~s tttt ~Cct~lI1tr

Let Cn-les C ~ Cz ktwe ~~t ~~-fe15 0 ~ 02

Sf 11 4st f( J 14 (cs of ( OotX w~ 1

fe- ) t ~ lt twitt ()~ -tu Cl

eo( C~ ~Ilt ue 0 K- r 4)-~ J ~ ~ li~ f(~ok( -to OO~ -rtgt Is -4 (~~a1CSof tLt -f~Cnrd u

MOtse ~3 Crce~ CJCC1 W~~ OJOaoJ(h I~ nf CiamplttJ -tfe 3 ~ ltWQs ~FoS offI Wi( i~~(JItct cent Do fgti- ((lt d4 vaJOJ aftftfT4crtfes 111$ ~It lw la-I fIwe wi(( v-espue to 4((3 ccle$

G7~~14~S

~ If 2c(c~sCp~ lte~tAt PQ ~ p Cl aJ hss fou 0 411(1 yen

middot~ Ot J To Co J C So -ky tore eM ta noe(tk( ~ 2 r(4-~ ~ pIA i~( ~~ oS

~yenI4l~~~

P------ ~ c~ Lf4rdes C e d lifest J e we c- tltANJ A f(rrzl cltJ~C

~~ ~~~eAJf- 14 1

Ci-- ntcl ~~~ CJCl ~ CCsII i~~(t et -t4 ~ C4tt p1-Cch~~

~P~ f LoDa is ~er~ AK~Of CCz _

Let ED be ~~~ foSflctorf oft B~ MaC ~D ~S~e AC -ri Cau~tt1e c1A8JgtC ut ABtttE J(e ~ cfC4c~rc(e c1 AB D MflId 8 Ccent F-=-c --r

D (Olt ~t AE =- CF So 1$1 i te~d~ c~ ~gteJ AE~AB=ADAC II CFIltCBCD CA So~= ~~

5 ~c 81gt fsecfs L ABe WI_ Cl) ~ _ I bull It rJC AS - AD CF- f1C

------------------~ ampA~fel Let ABC be ~ ftrJMIj(e ~ soscJes 68C[)I

CAE AASF ~te~(1 to AAsC wi( ~ CA Aa 4 S bu1 tsrtdvel~ Pro~ta ~-t 141esff-1 AJSc ~ t ~ I~es t=F fEgt DE ~dJ ~uc(~t

Col Amiddot ~ SJltto i Late ~e cnl~w-f( Jgt4Sr~ ~ IE ( - eatu r4~ ~Cgt cte

a~~c~~ Iof crde middot1itE Ultoofe Y04oc Jl Y l AE=CE ( tel btcte(~w-I(Fu

c~ Cc~-tr ~cL~4S AF=8F - I -r4e-tltlfte~ A PUr~I T (~ff I ~~ fiIolu ~ ts ltfCI C1 $f lltty ~amp~ 2 lies Cltt VIIIt~~ ~c c) ~ roampoIaJIlt) of (14So -tkey ~u(4t fAa ~~ Camp~tet

63DP I

r ~e A ScIampf~ 2 LtP be 1ft l~~

~ Ii~~(-kB~lIc(~ -to FD-f _ bull 11C ra(~~ to OE -tt~ fOIts frolle M 1 Elf c(frelttf

S 7c IL ttgt ~-JC 1l rgte ~ t

I

I A~ C~ $oIf1 Let ile cncrcft~ J) ~=HF - PD eF -61) OJ rD-peuro-C~1 EAtlA~1eSamp Ql (A~ AF =SF I CD-c CEAGJPF t 81gt

2 l 1 0 F pW~ ct - fE =AF -AE S r~L pound ~ POtt 1 ~CAty4W(t t

- t_ EICIt1k 3 AC--damp l-H aat 0 P~r -fl Ie A4M C ~ usc -t ifegtSltct ~- Ae Id t W S let

Be It N Let 1k u cudcl 0(AAac -lt1 aNll~Std ~t B t ~ middot Pe ~~t OlUaM

SoIwt t ~ C4Samp 61 Be we6~ 11 aM i~ ~ ~ftthlte Qt S of cYG vtIeof poundlASC 1ICft OM =oel 8M

A~p BA18C i4e c~~In CAsamp - AUN AAec ACfo K~ 1Iotf1Ar (S1Cc iMruw Ibl~cto~ L kll Ac AC Jolaquoaret tes) s e rdeo( I

I

pound I ~e AC kN J 8M Itteet 41 4 (IOIt P I

Siell L PM N L 81lt11 l HCA s MIC PAte CDhcrkcl Q ttl I t fill pou fOitJ BMlC ~p 8M ec 80- yo Y=OA

PM r8- PNICPK POamp-r~ bull ~ $Jtmct~ 1keuro92 Ie -t 10- eo~= ampf(tM- rM) PM - 3

rJ It

OMl PB lr F6 ~t 8MPM+6I1I

OM J ~M

L I A6cb be i$(~Ibullt co_~4 tt ArllAofOo Q-t d - amp c~ f A1)1 SC ~ f (aros

Ccle i VI ( 4 E f= ~~-t t I~oes ampe Q= f-o -Ie C

8y po -t fI-t~ Po~_~ peltPD=PHxPl ~_ ft QClltQ6=~d~Qs~tAcff we1et Po~-Qo=CFM-ru) ~ fMQ~ -ns i (Ies 0ML PQ lQMO Itf oM

Ntrf Csd tIe C~C wi4 Q0 As d-cr~ 2 _ bullbull

It t-sses ME F SlAte LampMO LQ EDt -lCl fo s ~ CIC-z Ef ~ Ef -s iU c($ ef ce Let cI has ceth A( ~s tt lie

laquoa ~ ~ t JFPO _r - flMx pQ fiCa _Vi ~ P$ 01 ~ bull0I

A(Igt~ ite-sect PQ 4t M +Q -of leM _ LA0(= l paceW ac- ~ 8I(C ~ lttlclc p ~_I c 1_

let ya~s t Cltn~ I ~_0 =c bull t if crftit C fc$wt

~l~Sshy c1iW ~ 14- - l-l-~t1 A IS ~f~~J i AA6C J 0 i-tala

C(cuCttdlt~ 7Le -(kfee 4-ttJes AP eamp tMJ Cf irUktt- H EDAA6=-M FDo AC-N tp~4-dcent () 06Jl)F )OCJ1gtE

N C~) 0 J- M N middot i

Solfen bullCO LAfcc9cfLATgtC 9 A fgt l=~C6AtyJrc TktL6lgtFcLBAC AooBc-OCi--ees LOBC-=J(t~Io~Leoc)middot1tl_l8A(= ~oo~L8bFmiddot F omiddot Iamp -=gt 08 ~ tgt l= ~frly DC lDe-

B 0 c (~) CLMA ltPgtM~MIf AC~HI () I 81U AlA ~ NIi-IIIt= Aa -AltlaquoJI tgtA L

F ~c ~ l)e - ~ Aa~Ac (c~

~~b )N6oIp 13Ai~80-- OllADI (0( 1)04 ()-(~)+(()+ll)-~~ J)M~ ~_cot=OMOt)1 te

bull Ott J MAl N~-11 fI ~=C)jI 6lf1

~iet SoU- ln LAFC0 =LOC-dJACl) Fc-tkc ut J bu])M So ~t TeI [)f -ue L Jeo L 6gtF =LeAlt ~ J-f4 a~t (~e tB

4 ~t~4Yclt ~ JNle gtetpeId~ bs~CtoY til g 1 I J 1) 4te 0 ~J

=gt 0t3lJe ~oS i DF Q(A~ DCLbE wHk ~ CSV ftt Ae efT I c AC~J~DI ~ (ltt 6e If Be I I I 01 tl( AS 1POW iI f uIlh) SrlOCo Ae1gt = aq rW1d1C by d~ l~testJ~ t4PtwI- Let lc SAe -de -CA k)sU AABC f 2AamptI

NA ~ NC NF ~ rJ SI AC ~ dbullt ~fieaa~(L ofM$C ~=~ so tr~ of ~ bullbull ftc~(eNs() ~ ikatQ~oJ CoxS qf ~ Grtles Q-14III ~ if ITI ~ YM~(-l A~s 7I-e lmiddot 11M rOI(A)C1lt D ~~(S liIOH

r 6middot 1- r IAC- UComiddot

041(ms AhOYllo-lety wi1kceterO a-J Ptto k (cltwaof-d ~1 H(oJ 1lt) ) is Q ~CI itt setVls Jllttl r01ht X 01 ~ plAtte -t 1ile ~c~ X sampcck -tk~t OXL~ -= ieoX ~~rk~ It kl~1)~~~~ti saA3Jkf~ l-t lFl ltl J ~ -tk kPJMDffty 5 ( ~ A IrtySe~ Q -~ f ~ - ilc ~3~ ~ 12tlgteuroFbe~Js~8CCAM~ ~ (-((Ali) Secs AAsc +0 AAFE

amp 1gtJ C Let q Ie ilaquoo cttIL 0 6A-QC SiAte GiA =-2GfD GS -2GE ~tqt=-2~ s ~) ~IAbEF f AASC EXAfe L L AABC AB =AC A(iRl IS t -t t_1y to tIP cnuantt14MC4t~rMs pte AC ~tf~s P Q~ Pe 1l~ 1e totiJpoNltt (fQ

~114t llCeftgt ofAABC Sott~Let 0 bt 14 cgftt ~ -

) rele Lt 1gt foe ~t3et totlaquo 6 c 71 -t4 Circle +ipound Clttt-atd l4AOC

S 1) l3~yf A-trot ~ PQ

ADfAt -= ~~~~=~=Ic S HcAl)So04s I ib 0 S111tt O~$-iLalAltbullbullfMc t ~-tl_W-~tIecf-

CfajiV ~~ s A~t~~etsVI At AlAJ ISdVt4 well -scfes~e l A az (i) (~ts~ Sltk Cif(IOSitc Ai) fW IZ N ~~+-~~Re ~Ill~ ctrck ~ fMlf a c-~ ~lt 0 c-I

II~ iw~le laquo 3Ie -tno1 eel Ct rd -to ufS A

~ of stJes ~u+-1- middotfDItf-t G 1Cf ~fj -t4 (nuCampolttt ~~+riAe ~-tIa ~~it cO (6([e-t etft

A ~t Let A 6e ( It ~~scf 4~el cltlu ItS 54014 1 ampJ y be -fl- ~offu arcres SCrz

e ~C At otamp r 1A~f~~ ~ It 6gt Ilt

N611 Ae ~tly I B~ Iec t CAlieA Ids A is ru~ ~__~ Aamp a-( AC I So AAIb~Stt-t~ L fMc gti((y Mi~~ LMe e-l ee ir1kcts L seA So Mo( ern ee=- (-(A ~~dAIC

AI (IOOoJ 0A I De = ae r So 0 ts-tfe c~af of AAe d kt P~c4rc-ctr~AA6C

1k ~o~1 ~ (1 A) SeLs AABC f 6Aec ~ SeJ t~

scre-~-tP~MOC-tc~ OllA~~ bull middot 1 P 0 ore co((eAt

- fiscl 1( AASCGs ~IIe1lt ~~~~W (~- ~~L ~Ioc L

- L- ~ bull - 2J~ ~(IC= 8(~(s-lt)

ot t Ii -l 1pound is -(I ~K(~ ifCirde ~ Ill laf S bt-tl nf(~ ltgtf I IIIllyeltt t ~oflA bull

~ (e~ M s M~SzM)S3 ~~rrelaquo At s~ let 6 ~ bullt _ r

blse~ 4 poundA 00 ~-te 4 We c~ S~ SJ 1 M MJ

A 1iamp A --To t~t iampt elite- o~rf-tLt (i) IIIiilsrtt t Aamp1le rtfItJ-f 1 ts S I Co

-tIt vtt4lfO c4 -rs T~ ~tCf AT AIT~ 7iIese if L1I $ =ll~Imiddot ~iTt~lltSl~~t~ L T t S~-LTITa S1~1

(i) 11 A A ~ $S~ AA i MM ~ i 3 I ~ A T~ AI S~1 ~~ HzMl ~ ss I HsM bull ~ co ~ffWbull( ~dSr Nect CircCl1C(~ ~ASsz$3 reI 0 AA A~l

Ctcmiddott of A M~H IIbtepofcrceS~MAJ~r~ ~1 fLAA~AsrL f2 J ~ VAdtoos ~~

Z bullSo --Gtdes ~ 1Io(~ Ll lB~ reggt ampSt~~ AMMz toil s~~i~~ ~lt (x M- SLLt Ill ~bullbull04 S 1-ta~X l1c H ) Mz $1

~=(lttc-o)(c-M-~fl~e) 1 M M amp41 S)Jltl~ UrJ~Cost lt~~~~~(fo) ~ ()bc HSt~Zeuro~X

CT1tW EtA-f tt 1- bull ~A be ~iAt 4+etse~ ~ fwo nO~fD~fUtf Cirdes C ~C CAl-~ef0 0 (tltjreJ~ Dtte ~1MtM

~t~o c eamp 1d1t(s-et C cent~ Cztlt Pt J(e -i4af(EV (A~ ~-t-te~ctc At ~Ca~t QI Lk Me t ~~it-t~ ()Q o-J ~ ~ ~itet ~ pzCla

~-t ~ LtJAo LMAMz

~~ ~ ~

SGl~ B-t~etJ Plpt(gtzOt~~O

Ca ~lJZ~ damp bull nwy 14(0 oPa ) Q SeKds C L 0 PI

~ I ~ t -lO Z bull ~ J ~ OAn Ct =8 ~~-oflt~1 e $ Ll016M -tLl~A~~ So LOI~= LOaAHa A~ t- fs 0P 0 P ~o ltlie sjI Ie~ 00 Cgt~ ofL ~ ) 00 ~O~e-=OPct=OAIOg

t ~te~~-1 cknl4t1 ~ AO~ ~ Ate ~Itc

~ LO8M= lDAM

A~ I =gt LoAM L~AMz WIAamp~ ---

L 0cA M~ ==gt L0 A0)- L I-i A Mz bull -to _16bCrfkSf~S

Solt~p Wpound(CS JTbe reflec~ ~ S Wit-(S~ltt

fI5 Mis

~J e

t ~lwt Cgt (1Of ctImiddotd i -br3frt -+0

e $ f(~

Q cmiddotnI F -tkt bcs of tIl YOII f Sue- fut ~e-re ~)f Q

01 ~ w~ M ~ ~(eoi~ ~ l R~~ QS ~ isc~e~ C~rdamp 4 A PQ R

-to M Lt u be 04

~ A$ iudQ~~ltofe1 middot~~(R C V Lat ~ 10 ampl yo~t~14 fc

Co -fI kottcrt(e+y wfoit4 uW( P-tkt StI~ l t

~CtCte (_oppos-e P -(f ~ T middot (1 ~ Set$ U -to (Q((esr-~~-toflfobulltHf lt 1) Ii P~n (= v ut s setft~~ ~ t PQ~ ~

TR SQ=S - PR= PV- PIlt = Vlaquo=n ~ T T So 5 01 Ae ltT0 e ttl

ampruJt~J) fr p~ ltTaee~ UT ~ U

~ l(P Ifamp)Se0v4 u to ~ C(telte e to c~ l I- UtoT So TT Let 14tats~ P-4 C ~+~t5ect r ~Q~R ~

ampS-=s- Pflt=Pv- P((--Vre =TIC=-TIlt ~ tiM -i1s-MS Ti-f1T=-jiM PtSAt4t

~ El4middotrle b rio t)

Lt-A~c ~ co ftiI5le ~ ~tof scl Be A1k ~tsct- N ot l ~AC i~+fSoct ~c ct tJ ~~r~I~ k~ +0 AN -+~~ N ifersets AM 4 Q -c AB -t p -n ~f-lrJrmiddot 0 li~e to APt Pt-a~AIl laquo 0 middot Pofe Qo l Be SIt- TfABAc1kMNQfampAQMol3c

WLOG I ampS$f41111t A6gtAC Let AN MttStcf Uttucrclt fAABC j 1) ~

-- - bull c L 1gtg CL lgtAC=L~Llgtc~ e lAo M f~ r ~ ~ DC aJ PM 1 Be

~o Ho~y K(A ~StovlsA6j)(+oAgO(t4 08 O~ aq ae Itt t= Be( PN -r4~

L Ogt- L b8e =LM8=ro6_LAop=LoP~ ~ ~ D 0 tcKl orooc

I ) I J GfeCttrA J~c J~M4 ~ L 0 - Lep - 1 0 - 7 1- - 0 - 0 Igt IC tS~ amp It sc K is AM == AM l PfI=Q

I I ~ Lg eto L~~O~)oo 1~ ~o LSC g c It Be r

F l

(~p Sol~ middot Let dort FE ~wt -to nr2 4Ss(oll (iJ

Feuro () r C Lt r 1 U04s~r 111k ~y1- (M V)Sets P t r c-to K) Iiamp JE t jilt L AS

sow1 bull Ff 1Ie L ~ A is +lt1 ~roIldrc FE LNEC ~Afe~LAME I rSo L ~~eL~A~)~ LlNEcLlAMc ~ ACAeuro ~e1IA I ~ ~ pouer ~ A ltiol4Isped to r is Ac AM= AE S~M(tAfy I 16fJe t ~A i-fk -(~d -to ~~ Aft A~ A - A ~ =lttiJPOiqJ ~FeJ 56 Ae==-AF (1amp tflt11- rAAtcd - I

_ ~S AI ~ fIr2 AA~f ~ etc )~lll fu ett(4-ik1t f t fl1 pues-~r 1gt 61 sJMe~1 t ~OI)O~ wt Soc Oa I ~~t ~~ Ctgt

~ Ltgtco~=LClgto L cLeF ~s ir~S COa b~s L 9CF $ceCfiS~f rl So

Cl) is ~so~~~ -to re

E)(4flt

amp($ PI Ira Q-te ite~Iy ~ t ~ rt M N~oJtlJ ~ r fGs$es -tI- caff( 01 ~ r~

lAe r tgtit cl1illfr iii r rio MAn=C MBfr=D f (0 ~It CD $ 1~jkt to r2 bull

~ C~ IS - tYgtctStIt

~~ A ilefSVsv wi CAAer 0 oJ ugt r gt0

(amptatl 1 J(o r)) sA~f~ +lAo Se~s A~et(1 ~(t X 0 to ~ i~e VOl~t X O~bull y at sucL fut OXmiddotOlec r~ ~ CWOIelcu I fo X=0 ~ Utake )(=~ _-cl tllSo~)(-=QO Wt-take X=o

1ke Circle -w+1 C2~+e~ 0 A~ ~kCamps r gto-((ct k poundSle ~e~ ~ I~e IWJy 4fso ~ft A~ ltrs~ by sff~t ~ CrCJtL (lWt~middotcP

fGcfs CO Gift1 ~I((S~ ~ ~ bje(~~ it f~~ u~ 00 -to -t~lfmiddot ~ ~c-t J ex ) X ~

reg -If )( s-ikcRiC iwe~~1~ XI=X bull f)(~o~elf(enX~

= bull 1 ~x ~oit ofTaTl) ~t-rrl 4i~

P e ~ X1 lCT2 4~f~~-t1~ ~s iS k~

- __ OXmiddot ox ((sec LTo)()(ycsLTox)r~ ACtreJtt ~~SSi~ 14ftJUJ 0 ~~t +0 A cvdc bull ~ya16tj -4r~ O k iII-s ak~cIc -poits ~(~ St -to ~amp~ foffts l4 fOit 0) ~~fets

of -flit G~ a41~ aJa Afe utllt4r bull JotlfoItr~~tf(~-kGttk ~~set fotleceofv-f~ ~~ctrJe ~

A(fJe vaSSoVJ4-f 0 is Set -to 4 (euro reuro IS ~~~fI)~ 0 ~~s ~~k(+ifia1e-t (It( -t 44td Ito Cnverrely (A (middot1U1IIJt rssj-tlt~ 0 is Seltt -to ~Cvde (w~~ 0 Ni-l -tttllj~-t Imiddotier0 ~Itd to ~ leilt

f r A~At pCiSS~ 14 0 es SetOf ----1-- To e~setl ~ ~ _

Ifgt reg If two cr~ (f~ttIlC~ C4fVts ~(( ttlso ~~(etAf ~ fbft Pto)~~~~

9 lCo (iflaquo at ~Sdf~7e 4-( p~ oF

0 V ~-tlaat iHy~t~tOmiddotmiddot71-~R CA4f~(S ~ SQIJ-fo ~ 0 J

A Ie dI o~ctves4ltSet-f0r1f~~ ~ c () ~-t bull i- cmiddotrd~ ftftfiSttft S ~ fa-5~ 1Gtt cri(S t ( 4It ~fo-6etc~ Gllf f~S A lS 0 4laquol 0 A ~ IV~ IIG(C4((o(Af ~ oAmiddoto~ t 0Bmiddot O~ ~ OAloB OP4 ACoj

wi+lLAoB=L8~A Wt3ttLlOMdOl~ () - ~ LOA8= LogA ~

Aamp~ = OA _ r~A A6 0(3 - OB

=) Ae r lo A~

-------- --------~

)ampa-cle i (~tlcptleofto A ~cQlt$ A 1ckc ~tiatt~

ampl if tlyen~ t ampe- ACBD - A~middotq) +AD

II( V c bull I

SoJn C-sidelt -kfSiCll At 1 vuu~j l)is Cpoundlaquotef bull J ~p-J~ Ygt I) - t t e y fatH4) J -k ~ro-atdc qf ~ec ~~A~ I Q

I iIC ~ AeC SilCamp ~ IH 6e - c I

J vue b -ftt (1) We t _ 1 _AC~ r - Be - - middot

iDA ~ 01gt1gt AJ)middotC1) tt Mltrtrllj b~ lAOmiddot~]) CO~2 1aJkSimiddotces amporeJ

A6amp c) +A)xBe Acll 81gt middot

Re fICS 11L sf ~ eat be ltoftrec -to ~t -I- ~1-tllAt t MilcO + AtgtICBC =AC 1CI1~

~V Asctgt S (l u~ ~lJ4~ 0-shy

~S6~~~ kfCfS4tJ foJt of~~ -+k eampIt~ otIIIetStM Ai ~itlt ~s -fIc ~o~~ rote iIt wJere -reIs CIMif s Mesc(t _

-

6x4t~le 2 Lt ABc 0 be ~ ~tllt t(kft~ suamp~t At ampt so liltftStct At Y1tt ~r AtO P~t~( -Ke -refltecf of 0 ~fOSS AS BC C)1gtA A~ C4IIcYdtc

p _ c $Lt-~ -71

Lcent P~ ~So k ~fut f-~Wi _ 010 0 flO Msc CD lgtA Ye cdIVt bull

sc =l Ott foIIttll is ~iIr~le-t -fo site (5 -tk Ptt-RS l~~( (Sl~~14ft

e IcentS 0 0 -to tts e_~Hrlt OSAP DfBQ ~CR O~DS ~ludlC~~ J J -J ~ _ bull

-tt TltitCirtlutdts Ie CA Ca Cc CD rtsrdtuely CfSMoSmiddotd fIf~iQ 3(0 r ~r31gt0 By ~ct(s)

I~ AC Q( e04~~t ofo ~gtltS

cfct (+) I CA SIrcent to filllt LA fllAlrd to 81gt CIrs

Set to ~ IIt LB ~(c of Ac I C ~ Sci fo c tAlC -to ~lgt1 craquoisSeoet t ol1t LD~E lc ~

0 0 r~-t 0lt1

L Nen bull

CpnCa= 0r~ LAf Le P )Mjl-ly 4~t( LI) R J ll)n~ So bull

$r~ AcJ Mgt PClKs ~~Ic~4J~~ ~ fet h) PampRs is floc

~

G)Cdtpt f

Le-t P bft Af6~-t ~S~ 4l1It Appound ~~~-t LAPB-LACS LA(C-L~8C

Ltt tgt amp be ik~~tS 0( AAPS )AA~C nspecflf ~toe ~l A1gt 1gt1 ce )wtet A fOiWtshy

~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

( )tlfamp 61) biSKfs IA8PJ By ~t CT) ACAfACf~ ~ ~ I3A - XA So iSttf ACAeACampA

P ~f - xpmiddot ~ P~B6+lCApLcA8 J

C-1-1 ~=~ 5tRCt X ( 4ft AP ampt ~1It By~t (s) 1 ~ tCp~=LCitA ~ ~ I I~ fQ is Seoct of ( ~ ~~ 1 f4$s~~3C o listf SiacCrtIeO ~ -T(Alrl~f4lrgto ~~(1)1 tIIet pamp ~t(4C~I~Ois~tfo(0

A ~IgtC A~te A lU)e bullA p A APelAcIIgt f-c ~) I SIWICamp

I

~ ~ ilt3t +00 c( ~ 1 PQ fh ) Qm Q J r bull bull ~ t01 setc~ 10 t of I I

No LM~-L~8-=-LIWC-LAec f~ $(amp ~st ~JO 0 Ao( ~J~~ ~ Atl 43~ t (-d 0 ~ A61PcD

fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

Page 12: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

Sol4 SifCamp ~A~R~lgttPLlCQA~ ~rJwail~e Arf A+cJQ+~~R20 I 1i~R+~~Pao C-t~1T~ZQ=-O

I ~Il I w e LV = e ~ 5 A ~t 4 ~b To ~~ fl X 1l s erltamptDI we CoM-rtf

Xt wl-t t)ll= (Ai~amp ) +w~Ct~iP )~(8+~~

= k [CM Q+ ~~)+ 1Yfgtt wR + tf )+ w (C + p+~ I = 0

~~~A I )( ts ~ (Rot 4 1 J~ ~ ~-t 4 -II 3~f1 C~cf ~ ce~-ter4cl At ~ (A e) ~ ~(f-t~) (ie ~c pOlt 3 -the amp~~c ~ ~ ~11t~ -G t- ~rid 1 ~~t AS)

COlf~selj Ikj ll~ 01 ilt G~f smiddot ~ fo~t ~ loc-s 61 )( 0-~ G~f C = i(Jlt- CA-t 8)) is -flc co~nsfo-kj lt Ov- ile ~t Clfdt

1-(t1J~ Let A~ A)e tI ~r~ 0t W1w) w~j I Y~ f~~j

fYo~ A ~ J~r - fe~~ -to -tkt -t~~ e to ~ c~tdt I

01 b w WI W 3 Got W bull skw~ ~est f~(tS ~ctCmt 1cle-t~~ ~s tmiddot~t t C)~

~otct~ JlCG ASSUllC -tL ai~cit-tle is -tlt kAtf GifC(t

~ h~ le~~tcJA -to t f~eMt oJ 1J -iklk ~ MS et--4M rll-tvJ~

bull l- A ~-A - WltWl t~ k~Wi -r ~- w - tV - 2 - - W 2 bull

Now WI bullbull f -ike ampM- ~~lc I SO Wd -= 1 i1e we ~ fJ~-te -tk ~n 4S _ _

~ bullbull Z ~ _ I T ~-t Wos 11 W + 2 Wl ~ - 1iIII I - - w

2 2-

F-oN -tk5 t ~ ~t -tk yoil-f N Jw~ -+ W3 $ 0shy

--te e lt$-I(C -t1e e1f~sS1W f Ns Sr~t~c ~~ nSFt -t oJ Jt Vis we (4 eot-t~ -tMt wtl lISO e O~ -tIt o~-- -two les -t~ e-Fc~Sto ~1 tJ -tt l s u~ -t $ -tle (fwle1 ~ -t~ )1 fO~~ (tce ~

J I W-z4 _

11Ob~ ( S~~t lYe Tko~ ) let W be D~ llt (~crclf ofJ ~1 13 c( PI Q1 R

be ~ iut ~ ~ lC ftJi~ ~ W -tt t1I 2 ll I tl ~ I ft ~ec-f~Jflj slw ifvt P Q R A-e tAl(Il (-ps Ole 5-

clt~ A $~501 11 tf A ltamp-t) ~ W) i

~ol~bo- WamplAi loss -t 3~nl~ I Wt J lS$We Je G-nIUshy

Cilampk 1s ~ ~ cttclt ~ lll llJ lls -= lw I ~ t 1kt k ii ~s ~~ l+ ll~ ~ Ii t3 --ie r~~ fw- W + 1~ Ivs ~ f-ltl ) i tJ- Zt~W So Sol lkcsc -tcdr W~ 3laquo l = ~ t L + W-lE W

2

St ~ Q ltl ott ilW --l 1(= tt f t~~1l

I sluw fQR 4t CttlfUf it S~s-t st P-R =l-amp-Nil f-R _l- Z-amp-~~ Yo-~~J (tI 4W -g ~-R

Q-~ -1-1)-1tJ --l~W X l ~-amp~w ) l2tgtW-ltl~ -lZ+ t

4t~ w- Zl~-ll-t It f- fl

- (1- R bull

-J clt~lttii lw=t ~ WW-=i

CiiID ~tlt~ firLiA BC let 1gt be A4Ie GtIlOc1tf- E 001 As loIiti DEit-CB J ~ F ie 600 Be I

ciA ~fDf oX ~~ o-rbmiddot 0 1 ltt ftt XIS G(( Gr be 01 EP ~tS~t ~ el~ttrlgtedo-r W~~~~fk~t~s X Ao D C fSfoFc-=Ep-=BYc1gt=r

~J ~sted oR we rMj Sity ~ i 7 middot PrDV~ 6i-F fs pcmI(e( -to -Me 4 b~ 1 -M CaJamp) Xl= Of-~ -tI S~1 je Y-X Sol-I Set 1ampt o~ AtAo tt(-~ IMc

For ~fS X It we e Ix-+f ~ lxl +111 ~ft Tie E 8 Gfl = C ot~~ E (0 r)klgt(d~ 1- W-11IAy f X= ~t(r-s-e t~o A~ F tB t(f-t)c 4( euroj =tE t-((-f)J) _ h Let Pbe 0 poillt el LIle )( f lJe lter t= B _ L _ amp1gt g + (_t )e~ middot gtY haYCamp oP=toX+(f-t)oy -f=~y ~ Be -- r -i1gt-t ~_

J J gt1( 8 -I io O~)y~ amp(01] ~ P-u SfjllleMt Xt E retgt I $0 IE-BI rD-cl c1

EICjl1t Call a ~1IIecent ~ ~ QjgtWelC ~l~ (I- ) Is (E -amph 1l ID-d r-(t-amp)(c(-f6-Jgtfd tl )ltLJ )M ~ ct j~ Ie ~od ~ orF9fe sk~ J i q F- Gt = t6-p)~+ (I-t)(1-9)C ~ +~hw ~t cf -tk s IIf-t4 Jgtllrl1lpounds Of ~t(tei _ IS tlt-p)amp1~$ htfampt iits~etet ~ik~litetllllorltl -tlt-p)la (amp+~~ =(~~k1NIllelo I _1 t f4IIIl ltf1ltS

Sll~ fir trl4t~ A~c~ Itt-A IlIamp 1M OjL ltf 114 (tw~-for ~ pound Me~ --ik se ~fOW twI ~ _ Igt IC-tO - f ~ if

T -poundTI-r -pound ~ I A=0 1)~D i(1el IC-BIt lo-dtll)~

UI8iC-1gt1 +11Hlt-at=Iel+ Ie-IgtI+11gt1 +1c_~(f~~t Wt ut Ie+IC-Igt ~ Iamp+c-tgtl t=~f1f)

AA IDI + IC-61 ~ 11gt+C-81 C-~AO=~8C) (gtt) holds ~Le~ft~~lcJs A81(1)C ATgt Usc _~ __

c6hf--I--l~1gt~ ItiC

~1- ~t fmiddot~~ 0+ ~ 0 ( is )(Y=tJC( (1 rsti - Ex4k+ Let 0 ~~ (i(cAt cf 4ABe 9 ~iIt J bef -fIl lfcffS Jf -IIf (t) Xi=fX (y+I)zmiddotXmiddotZ+fmiddotZ 0( (cXl-Y~(Xmiddoty) ~ I~~)(middotX I IXmiddot~~hd1I O~iOf (=) Xmiddoty-O ~~~~~~~~~~~~~~~ amp--ft 3 Let A8C b Le lmiddotts ~sfmiddotmiddot Phe

Ac~+amp~+A~-t8C~~ Ast+ctl SJt~~ Set1ie Ot~I ttt A ~~t f Jw

CmiddotC +(amp-lgtHamp-~)+D~ (8-c)~-c) ~ amp (c-b)laquo- At~(~- awl lt~~-f4ls s fu ~4S

(6 C-b)middot(S-C-lraquo ~ 0 ~~ck s (amplt-1) ~o

A ~t 1gt Ie -tLt poit ~ Aamp -L II ~ e _ ce~AAcO

p C fgtrcw _t C1gtJoe ) AS-AC Sol~~~~~~~dO~A

A a A J) A J)= ~ E=~~ =3 +~lCJ1gt-C=Aamp-2C

C1gt1 Oe- (A-tS-le)(Mc+1raquowO c) No AA~lh c C C(CUM(bull (IampSt 8 41f1$-bull (4) bec u Amiddot(Q-ltAB-ACO 1IeJtt(~) ~ OAl ~c ~ A~~AC

euro ~ toJs ~ 8lt~ 1)-A69 seAPS fWlkl ~JCOc $ firAABC jf( t ssewu-J -ptMf ~ c= - ta-+CmiddotfI AAS( its ~ttd q ~1 - If We Sampt -iU CitClIMChH- 0 AS ken -HII-srft~ ~o -t r -11 __ -~ -1 ALh--COtt - 7J 0 OtlGCnx n - ~-

A Fit iAcetft tJf ~~ c 0( lU= ~ = L

co b AI c lt-c

e ~ 1)c 1gt= te+(t-t) C t --amps ~1i~ poundL = tD ~+ cC C bI-c Gte middot I t A-t -~)tgt t-ll- A

aAtlS cc_ - tgtA - M~C 14 e middot

11l Lqt-(gt OmiddotkC Gtctal ~ICef c(H ~r J

51_ Set 5 4lt C4fColt_bull tu e -H Matel~Me1~ 1~ AA+b$-t C shy ~ 4~(

Lampil~gt 1omiddot~(i-1)l4-1) lt0 A-A 6middot~Cc=(tlJ 2ec 6amp+cc-(a-c)(amp-Q=k~middotIf (A16i)riamptc~ Rlt9~~ 11- 3( h_ Imiddotltl-C) 4l- 2(~~(H- btCi)tI~)) cttC

)(~+c) (-1)((-1) =((~ t1 -Hi+(() lt 0 of -~ f (ib -t-e) lA+Il+ ct )+ilaquoc gt~ CifI+cl+Jl(c)+ ~ ~ a(-o)(--G)-4-~-c)(b+cc-4)~)gt0 tsc4 rc s

~ Ike fRS ~ f xi xI wt -Stl-fculot 11-$9 (t)=LXOY) 0( tiYfft~e~ -fo -tkt fl~~ 1-- oxY J e

lti) ~ -f~)( ~f)-a)( l t Yltl (c~wYcxnyJ (j - )(~1 4fT~ A X0( V~~ p A of yl t1ft 0

(6laquo Q bull 1 lj 111)1 (DW~v e

eJ41~ Let AAA A _j A 1 1_ -+ V]nq DO 4 CD e I

- its ste ~tS p-Ilt1 ProiIla-t middot ClrtllAA1Ar oreAA AA So(u-tVf SeL ot - ~ -_amp I~ _L ft--A A ----- ~ fJe ~ ~ --fI 01r~~ O4St SMs ~qIt ~t)~csCA-A) I lA_-A f

E)Ctl-eIlaquo-r Let A6COf tgt ~~ pe-tft Qc e t

~~~Q~ ~ 1kfwlrids~ A88CCIgtbEpoundA 1T~ -r APamptl~J~ le ACDIIIampf6i -laquo s~O~ tk-t ~s Ooet is so eM eII bullbull ~olt4-tfN ~et -ckt O~bullbull~ rt -e ~_W f~ S~

tJ 1(t0 AXC ~ AP ofe (o(iu o=A-f- A(~ J C- 32s amp A

lltc t))tA SIA~y 8)(1)= (1(8 CxE~ C I

raquo)(A 6llgt re EJ( 6 =CcE feMtt I

eurolCAJ- E)(6-t( - ~lte+El$ ~ pound10 eImiddotmiddot

1 ~~-A~)o (As-AJ1gt(~A~ S ~~CI amp euro1tf6lc~ ~se Ac Adol~ -t(t-t Lit set - () middot At

At~ t ~It~ AsIC~ Al~-+yen+yJAI (

_t a ~ - bull

~ 2-shy

I _0 c A 6 c ~ As V ~1~Ut 1 Sjtllc -fb ~BIC~ fW(t

ftdle ~ts of BC CA AB ns~chvell -tk ft1~ -tIua-t

No A bull G 8 A I ~amp Ca A~ (orr eU egt~ 4~_ A~itlA-~lClA-As~=(~tAtAr-tAjcA -~~ StthtlI4It ~ SaJc1ttA

(Nmiddot~~i~+Ar~~l ore4 l1A AAs = Are 1J~~Ai

Aft13 amp11 C=A-ttils-A)frSollletoA~] SiCt AS e Gfe i eRe

o~ (Bt-A)K(~-A) - (A-ttz-~tl-t- t t)AxB No ~~=~~~-=amp-AH-t)e ~~1 S-a-= It-t1)A I Ct = lAt8)- c tlA +ll-t~)B ~ (amp-AI~I~(Cz-~)=(t-ttl-trtl-+t~t))Al(amp~O A S~ CL At( ccdllfttor

~t ~~ 1~~Pt

o

C[~1D --r-0 vetlOf) )( lf ate Jt~y wtt-t---t f~ t -flat ~f~ ClX~yO kAs 01 Soat~

AT 10 o T4 s tktCcStI ~~A rf KttO ~ X0 f Art NIt Co((llteor

F4t IT AX+bY+c =0 ~$ote -e 1~I(z-s 4t4l 4-+amp ott -=0 J ilQA Xf Z 4le cbullbullI btACcS( ~l AO fIe b-tc-o w X-1-KZ-tYc-6Z

(~ar~11to(~1 wr~t--J Lftai c~ s OAAampA Co

~ OeLamps 1f 1 -1z- Aa6~l~8ampR AsampIA~= ~ 6 8-c amp-S tltcl A DAR 0

~e COIIfttAt t ~1 =- 1 ~ ~ P Pl) P3S~ Set - orlll at o at A8 btt ~trs Ale LIDa (ampfbv~ ~ A~ rA Q( e s So 8 1-t S6Wt (s EIt Cll No

Pl =tAt(c-t) 8a trA+ (ct)s ~- ~3 lAAt-tQ-) 8-= tA(-aA+Cc-ct)S a S~tU~ ~ 0= ltr- CArgtA + [pound1)l -(I-I4)$]B

A~ (tally rcf~=gt tr(~ Otu( (l-tl~-laquotlt)S=C Solll fott ol -tit pt~~ -+-s f ti ~I~Js

Nt ~~e ~ 1tu~~A+ SoSzCt-rl g$t Vs- r~ r~- r~1 Pgt1s~S)A+~s(tmiddotgt8 R= rlrfgt~A ~(I)J B

Y~-r)S) ~6a-t~S) amp c) ttS +fs-1S ~ p~f~P+~sampf-tj~

~ P1 ~se~rw)~c 0 Qtlgt+CoO ~ r fL cU-1- fc-i (ove

~ 0

A - -

~ FOf~lamp~

(1 -laquo ~C

fot-CA~ to ~ t t amp -t~~ crt a ~tc ~ El(tend~ltl St L laquobe ~[A8Cl Js~~i~ R= 4 C

Let ( ~t 4ct nwts lt 4e GoismvmcJt i-R- tl 4J~)(fo~of AAsc Sr ~ l=~~Yslt) ~ bc_

S A -- - 0 21 1iltelaquoe s dolAt C~d~middot ~o~ uI1gt ~ s~amp s~~C middot T 1_ ~ rI n -rf (i-- shy

tl Ie or~ DraJ clmiddotae~t 61gt 1pound Si ~ A= ----=algt i IS lle~ ltJOiOlSA0

~~~~~~~~~~~~~-~~~~=~~~~ p adEr-l-~a~~r~ A- oS+- jtus c~ - c e c I) p(]) Let 18(1gt L~Ms

I4dtt rAsel Or S~8c1oI(lcl~ 1leflAftt Let A6nct)p -r1 ~act 0

~Me C ABC ) GlUo~kc ~ PAx P6= Pc x PD = tl b~~=Abc bull P19tpound Note L APD L (PB

4R A1BC)aHd~ckLPAtgt=LPCBS=tfA-tb~~) is ike seifieAc ~AAPDACfB~=~~ PAIPB=fxPD

amp Q C Of 4A8C Lri pc C 1amp-~ ~~ PC Is -lt-~t lat t lie i4 jCbullbullr 4l( M6C Qt r Ie -i4~ to -e -fde ~ A A8C if (JJ

C)~ ~e icltc1e ot AAec ~e p A e OYlJ c fCL p~~re [Mel =[ALel[~cl+(CI1= ~-t~+~=SIr ~ Not~ LArc=LcPB

I-tfllWlbull [A8tl~ S($-11 ) (s-b)(s-c)middot I pCs f~ot -to LACp4C ampP(~ Cos C= tt2ttoa-c (~AI Ci(~ircl 4 MBc B 2shy

[A6Ci= ~SiIlC=Qr(+coSp(i-($C) ~AAcPACBP ~~ fgtc PCPAlltPB =(Cl~-+Iot-c~t-~a~-9 ) = catlo-4 t )(A1(-c)(CoHI- b)(o-Il-~= S (s-c)(~~

2- ~ a

Ci C [AS(I A 2

~

I

~JJI LPFA-=odeg=Lpe~ ~ amp~ ~LPFeLPAE

C5Ji) ~tolt1 s-ThtOfotfll Let A 6c~ ~t dlSncf ~ts 01 bull ~c ~o - Me~IA~ 1( bull t Of~~~I ~Ot bull -Tht~ bull Sa c~tOV M1 C(liofIPT potd~ A 6 C Iie to

AI 6 C 1gt (1~t~c 1gtpound fCLR atfmiddote ZA ~A A ZA bull -~ -iA ~Co~ PAQ~clf$ WeA~ ZA~lA I tc Z~t

pFAECc1dk

bull ~ Srlloi(y taCgt6~~~-lPFB ~ pG~ f CDCCYcbull LPampb LPFI) = e 1klaquo AIJ~P LPAespoundp8C pfE _ LPeP 8EF (0(1ltlt~L PFE L~8Tgt~ LFP - L 10 collirAfampff

)fgtC)~Jl~~ ~ ASC1HAol6C=AcS]) bull (~~_ ~ktI AeCO At)ItBC ~ACdtgt 1)~c 190pound 0 sWLe AB UJlfsftfUct A ampA6

S~~41 to flCAP 1I1elt AB A~ 6eshy

6 Ai - 7ligt= (1) lBAE=LCAJgt

SO LMc L BAlgt-L1gt= LeA1gt-LMe =LEAt) Tkeuro1 A8AC~Ae-A1) So Rr-c EDAtgt~A Thet Aec~ A~8C =poundItampE AClC E~ AC80

bull A rC =c Sf-t Ell I

f1-I-4j hoW~ ~8euro~EtgtS ampb ~ E iUt~( SO - ~~oeA~LeeALtgtCA ~AsectCO Sltffc

SoSoft ~oe 1et~6cP cl-ampd-p~ 0

tI~ Let l)poundF fetf~~ff- P~ ampa Aeyen~~ ~

Asse ~Mist (so4 is 6~UA_JC ~AGSC ~O bull G ~f( Aalec~o)

tt~e9 7eff

fovlaquos X I Z ate (es Aamp ampCA D ((t~ve-()ty It X I Z (lie (dl-lflOr

A ~f f6 lhg--1 ~ xe YC LA - middot ~ lQt Dbu (~ Ac soct1IIt 81gt II J( Z -r1teuron

~g ~ ~ 1t~ ~z Se AlC 6Y c~ _At P1Q (i~ ~y Ie ~c -- _______ r tamp iU I bull laS yc fA ~Igt ZCZA middot lCI~ lIeeu~ Ie~

If ~ tL ~ =-1 iIamp )( YL MHo l~(~ Y~t~~~~ SlJ) Ltt l~ X(OCA -Thtl b Mt11Idtw 11~ Ax ay CI _ lt Cz Y Cl iiiK zA --i ~o --=-l1toobull CfIea bull _Cl -a

I I

ceDD ~MelI s lIeo~toA l~tA I ~cc t) euro ~be tc~ lO 0shy

de lw~~ ~( ft amptCtSSCti 1 tf (~ diC- (~QEf ) bull

t p Ae ti l)euro J Q Bel pound f 2= Cl)n fA ~ ~k ~ Q1t ottc(l(ea~ ~QIR~~~ -

f~ 1 ~ ltt X~EfA 1AMCD bull ~ z- C~neF Arr~l ~(atts ~ff 1e-(fM1oec~ FA

ftt- Ool~~~ 4xf l w hVII

e-- ~ X K __( It X2 ~_( t ~~II Qx 6y Ct ~y pzex I fllFxijmiddot 1I

Hul~pr~ ~ AIl ~~ tfffSfctj cofI4t tt XA)(B XEmiddotKF J (CmiddotYP=1AmiddotYS ZEmiddotZF= zeZIgt W~~et ZQ lSf~-i igt PQ~ ore rlfltelaquor

Qx Pf Itz loy c-enc ~Mee(AaS

t-rks ~ere 0 Imiddotil~ (1$($ of PoucJ s for It we tftwt Ato 8 -te I AIwIJ (3 il(cJe 1Iofl1-t i AB will b~ ~-t1l3et (iot ot B ~ It~j CIt~ we ells JpoundAoflt ~ t~ liflE Clt B b~ BR

6lCtJfC i F~~ h Cf(Ultirc~ ot Mac J f(it 1) ( ~ ~i~0yen ot -t4l~lE I~ ~tA - ~~ Be ~ e fM 1fe ttusc(e~ of-ffwf3ct (tt4-t C3L1r~ CA~ F= bt ~ ttfStd~ of -tINt ti-~-f Imiddot~t ~tC wo( Aamp 11161 PI Ell F o~ ctU

Soof~fIyen P=Mo 8C ~ E= BBnlA f=CCnAB APP~i P~f ~ ~(fo MB See I fott et 1gtpound f c-

-- =JSiiiiIii

b)lAtc ~ Let-tgt 0- eht ~cfs 0( dt101 AtCS

AS ~ AC O~~e (ilcu-R( Mac ftspciwJy l(t tgt Ilt ~f AtC sCI ~== DPn SA J R= PEn AC fro +~-t lile QR~s~(QVJ14 fttCf+~I (~ 1) ~ f9bt-Mshy~e 1)rff0--AS- CO ~SfctsLAc8

Co ~r ~ qftllCr At =lgt 6 ~LAec So 1= Cl)n G8 Sf_ eEtS

Q tgtPt SA DP 8ital R= Pe C Pre ttL PlE AI

AIP~ f~l ~ 1Ito(-to C ~ P er ~ w 1 ~ bull 1I

t Set I Q Rut tIff~ Co~~d~

~ -7

Alt IXu q j

elf (Ga1(e 3 Ltt AT3CPs e ~ +s tMDlCJe ~-rd AAfLBS Bat LeA) ccf LAB fat 1gt be ~ls (I ~cucl1t ~c4( I

DA(11)C= AU DB()CAe~ 1gtCIAB~ fgt~~ A~ r~CtfaJ T4 6v~fi ~ IAGC a~ Co((~((r

~olf- W HL-cI oy-((~( ~ AA Be Ne

AAIB~I)Cc(-=I DArBC=A 11gt1( ISc AtA f Cc -= H L lAlA I C I Cl

1t~()cD=C1 ~l (AIBl (cjAfrrr5~5Gl ~~ t DAAfCC tgtlt Se4 A HC tit c11ilaquoraquo SIt 1y ar171~ BS41s(to AS e 0cc we Su e H 6ltve c1(i~amp r A~ H C~ S4rt a(((~4~ I

-~ ALI)f ~fle1 tt P toe a ltpor i~4Mec

LtfP I~~ff~I$f- 5 -to ~CA Camp ft~t~ lttt bJ() ~_ eshy

ll 10 ~ fet ~~~N~ c-tohs API sp (~ftvtll IfQ P ~ 61bullbull Pt14 PttNQ~~ (tries ~tll~ Qfz cod A~ aft ~et

iSoLttd- $(fCJt L CPc p) LCQLP LC~P Lc (gta Palt-e J -t ~es c P ~L I PI Q p 4ftcocttc f~AfrI15 ~s middottU(Woto ~1l$1 w-tSu CPt ( gt e-= A ) P t1t( QIP= X ) (Q-a Pf P2C-= B 4re CoI~rtelr $6 Rb2-l amp1L ( AB-=Xmiddot ~ ~lIQ P~IA8 tVe ~Cqfre~

NewtDJ S

~A ABcOS~~(laquoteJktvsa e ~SQiraquoeamp c~tkt~~ ~~

APgtsc CD) PA AXcpotlts EFG)H-~t~ C F B ~ACG~FHgD~~r~t

Sol~tcNI W E6nFHO~ Eftn FG ~X _Apply~~ ~~scJ ~ ~ -to E~ltSJ F f(f ~Sta E~ () Fr =0 ~~ ( 14 1) I G Fn H( X are ut(ltealf_ ~ltfcAy~ltP~CA(s ~e- 4 E6--()FF~~ J ~S14

EEn FF~ B euroH nf6=X amp-t-fn ~euro 0 tUllPtfcmiddotc4t

-nus ~S 0 XI oJB ~c((e4~ 7itN pound4 fl Ff n6D=O SlAry EG F-- ( AC - O ACE6 fH6DCPotrclO

1)ec~CAes ~ 0 nfAaAec ~ JACc) M

A c B actgcP J CAnCpQJ AampnAgR ~r--+--Ir-~~R If AA 613 I cc 4te ~tVt-ct ~

A e 1-~ PI ~ Rctil eo(IQ4(_

c~ rCP_ R2esrk ~-s ~ -tyenUL te~ 4 ~~cAAfIdgre IfV --IfU ~ f 4s root G-oIer ~Ns c~ AOAB ~ftJJ MeoJ- -~r ~ et QPL AEa gil

At A rltamp -7---1S ( rt l g 0 () I 4 ~ ~ Ie Be Cctf~ Lloec Ilfct-Jt ~~ C~ c~ IJOCA ~ 1te(J C~ BP Cd M oct ~

B8 PC-co ~-( ~ No CC~=-( ~(ff~~~sctmiddot~~= - ~ (IC4M~cfMtl~~~ote- ~ et eampI c-f(er

62Y ~coJ A~s tttt ~Cct~lI1tr

Let Cn-les C ~ Cz ktwe ~~t ~~-fe15 0 ~ 02

Sf 11 4st f( J 14 (cs of ( OotX w~ 1

fe- ) t ~ lt twitt ()~ -tu Cl

eo( C~ ~Ilt ue 0 K- r 4)-~ J ~ ~ li~ f(~ok( -to OO~ -rtgt Is -4 (~~a1CSof tLt -f~Cnrd u

MOtse ~3 Crce~ CJCC1 W~~ OJOaoJ(h I~ nf CiamplttJ -tfe 3 ~ ltWQs ~FoS offI Wi( i~~(JItct cent Do fgti- ((lt d4 vaJOJ aftftfT4crtfes 111$ ~It lw la-I fIwe wi(( v-espue to 4((3 ccle$

G7~~14~S

~ If 2c(c~sCp~ lte~tAt PQ ~ p Cl aJ hss fou 0 411(1 yen

middot~ Ot J To Co J C So -ky tore eM ta noe(tk( ~ 2 r(4-~ ~ pIA i~( ~~ oS

~yenI4l~~~

P------ ~ c~ Lf4rdes C e d lifest J e we c- tltANJ A f(rrzl cltJ~C

~~ ~~~eAJf- 14 1

Ci-- ntcl ~~~ CJCl ~ CCsII i~~(t et -t4 ~ C4tt p1-Cch~~

~P~ f LoDa is ~er~ AK~Of CCz _

Let ED be ~~~ foSflctorf oft B~ MaC ~D ~S~e AC -ri Cau~tt1e c1A8JgtC ut ABtttE J(e ~ cfC4c~rc(e c1 AB D MflId 8 Ccent F-=-c --r

D (Olt ~t AE =- CF So 1$1 i te~d~ c~ ~gteJ AE~AB=ADAC II CFIltCBCD CA So~= ~~

5 ~c 81gt fsecfs L ABe WI_ Cl) ~ _ I bull It rJC AS - AD CF- f1C

------------------~ ampA~fel Let ABC be ~ ftrJMIj(e ~ soscJes 68C[)I

CAE AASF ~te~(1 to AAsC wi( ~ CA Aa 4 S bu1 tsrtdvel~ Pro~ta ~-t 141esff-1 AJSc ~ t ~ I~es t=F fEgt DE ~dJ ~uc(~t

Col Amiddot ~ SJltto i Late ~e cnl~w-f( Jgt4Sr~ ~ IE ( - eatu r4~ ~Cgt cte

a~~c~~ Iof crde middot1itE Ultoofe Y04oc Jl Y l AE=CE ( tel btcte(~w-I(Fu

c~ Cc~-tr ~cL~4S AF=8F - I -r4e-tltlfte~ A PUr~I T (~ff I ~~ fiIolu ~ ts ltfCI C1 $f lltty ~amp~ 2 lies Cltt VIIIt~~ ~c c) ~ roampoIaJIlt) of (14So -tkey ~u(4t fAa ~~ Camp~tet

63DP I

r ~e A ScIampf~ 2 LtP be 1ft l~~

~ Ii~~(-kB~lIc(~ -to FD-f _ bull 11C ra(~~ to OE -tt~ fOIts frolle M 1 Elf c(frelttf

S 7c IL ttgt ~-JC 1l rgte ~ t

I

I A~ C~ $oIf1 Let ile cncrcft~ J) ~=HF - PD eF -61) OJ rD-peuro-C~1 EAtlA~1eSamp Ql (A~ AF =SF I CD-c CEAGJPF t 81gt

2 l 1 0 F pW~ ct - fE =AF -AE S r~L pound ~ POtt 1 ~CAty4W(t t

- t_ EICIt1k 3 AC--damp l-H aat 0 P~r -fl Ie A4M C ~ usc -t ifegtSltct ~- Ae Id t W S let

Be It N Let 1k u cudcl 0(AAac -lt1 aNll~Std ~t B t ~ middot Pe ~~t OlUaM

SoIwt t ~ C4Samp 61 Be we6~ 11 aM i~ ~ ~ftthlte Qt S of cYG vtIeof poundlASC 1ICft OM =oel 8M

A~p BA18C i4e c~~In CAsamp - AUN AAec ACfo K~ 1Iotf1Ar (S1Cc iMruw Ibl~cto~ L kll Ac AC Jolaquoaret tes) s e rdeo( I

I

pound I ~e AC kN J 8M Itteet 41 4 (IOIt P I

Siell L PM N L 81lt11 l HCA s MIC PAte CDhcrkcl Q ttl I t fill pou fOitJ BMlC ~p 8M ec 80- yo Y=OA

PM r8- PNICPK POamp-r~ bull ~ $Jtmct~ 1keuro92 Ie -t 10- eo~= ampf(tM- rM) PM - 3

rJ It

OMl PB lr F6 ~t 8MPM+6I1I

OM J ~M

L I A6cb be i$(~Ibullt co_~4 tt ArllAofOo Q-t d - amp c~ f A1)1 SC ~ f (aros

Ccle i VI ( 4 E f= ~~-t t I~oes ampe Q= f-o -Ie C

8y po -t fI-t~ Po~_~ peltPD=PHxPl ~_ ft QClltQ6=~d~Qs~tAcff we1et Po~-Qo=CFM-ru) ~ fMQ~ -ns i (Ies 0ML PQ lQMO Itf oM

Ntrf Csd tIe C~C wi4 Q0 As d-cr~ 2 _ bullbull

It t-sses ME F SlAte LampMO LQ EDt -lCl fo s ~ CIC-z Ef ~ Ef -s iU c($ ef ce Let cI has ceth A( ~s tt lie

laquoa ~ ~ t JFPO _r - flMx pQ fiCa _Vi ~ P$ 01 ~ bull0I

A(Igt~ ite-sect PQ 4t M +Q -of leM _ LA0(= l paceW ac- ~ 8I(C ~ lttlclc p ~_I c 1_

let ya~s t Cltn~ I ~_0 =c bull t if crftit C fc$wt

~l~Sshy c1iW ~ 14- - l-l-~t1 A IS ~f~~J i AA6C J 0 i-tala

C(cuCttdlt~ 7Le -(kfee 4-ttJes AP eamp tMJ Cf irUktt- H EDAA6=-M FDo AC-N tp~4-dcent () 06Jl)F )OCJ1gtE

N C~) 0 J- M N middot i

Solfen bullCO LAfcc9cfLATgtC 9 A fgt l=~C6AtyJrc TktL6lgtFcLBAC AooBc-OCi--ees LOBC-=J(t~Io~Leoc)middot1tl_l8A(= ~oo~L8bFmiddot F omiddot Iamp -=gt 08 ~ tgt l= ~frly DC lDe-

B 0 c (~) CLMA ltPgtM~MIf AC~HI () I 81U AlA ~ NIi-IIIt= Aa -AltlaquoJI tgtA L

F ~c ~ l)e - ~ Aa~Ac (c~

~~b )N6oIp 13Ai~80-- OllADI (0( 1)04 ()-(~)+(()+ll)-~~ J)M~ ~_cot=OMOt)1 te

bull Ott J MAl N~-11 fI ~=C)jI 6lf1

~iet SoU- ln LAFC0 =LOC-dJACl) Fc-tkc ut J bu])M So ~t TeI [)f -ue L Jeo L 6gtF =LeAlt ~ J-f4 a~t (~e tB

4 ~t~4Yclt ~ JNle gtetpeId~ bs~CtoY til g 1 I J 1) 4te 0 ~J

=gt 0t3lJe ~oS i DF Q(A~ DCLbE wHk ~ CSV ftt Ae efT I c AC~J~DI ~ (ltt 6e If Be I I I 01 tl( AS 1POW iI f uIlh) SrlOCo Ae1gt = aq rW1d1C by d~ l~testJ~ t4PtwI- Let lc SAe -de -CA k)sU AABC f 2AamptI

NA ~ NC NF ~ rJ SI AC ~ dbullt ~fieaa~(L ofM$C ~=~ so tr~ of ~ bullbull ftc~(eNs() ~ ikatQ~oJ CoxS qf ~ Grtles Q-14III ~ if ITI ~ YM~(-l A~s 7I-e lmiddot 11M rOI(A)C1lt D ~~(S liIOH

r 6middot 1- r IAC- UComiddot

041(ms AhOYllo-lety wi1kceterO a-J Ptto k (cltwaof-d ~1 H(oJ 1lt) ) is Q ~CI itt setVls Jllttl r01ht X 01 ~ plAtte -t 1ile ~c~ X sampcck -tk~t OXL~ -= ieoX ~~rk~ It kl~1)~~~~ti saA3Jkf~ l-t lFl ltl J ~ -tk kPJMDffty 5 ( ~ A IrtySe~ Q -~ f ~ - ilc ~3~ ~ 12tlgteuroFbe~Js~8CCAM~ ~ (-((Ali) Secs AAsc +0 AAFE

amp 1gtJ C Let q Ie ilaquoo cttIL 0 6A-QC SiAte GiA =-2GfD GS -2GE ~tqt=-2~ s ~) ~IAbEF f AASC EXAfe L L AABC AB =AC A(iRl IS t -t t_1y to tIP cnuantt14MC4t~rMs pte AC ~tf~s P Q~ Pe 1l~ 1e totiJpoNltt (fQ

~114t llCeftgt ofAABC Sott~Let 0 bt 14 cgftt ~ -

) rele Lt 1gt foe ~t3et totlaquo 6 c 71 -t4 Circle +ipound Clttt-atd l4AOC

S 1) l3~yf A-trot ~ PQ

ADfAt -= ~~~~=~=Ic S HcAl)So04s I ib 0 S111tt O~$-iLalAltbullbullfMc t ~-tl_W-~tIecf-

CfajiV ~~ s A~t~~etsVI At AlAJ ISdVt4 well -scfes~e l A az (i) (~ts~ Sltk Cif(IOSitc Ai) fW IZ N ~~+-~~Re ~Ill~ ctrck ~ fMlf a c-~ ~lt 0 c-I

II~ iw~le laquo 3Ie -tno1 eel Ct rd -to ufS A

~ of stJes ~u+-1- middotfDItf-t G 1Cf ~fj -t4 (nuCampolttt ~~+riAe ~-tIa ~~it cO (6([e-t etft

A ~t Let A 6e ( It ~~scf 4~el cltlu ItS 54014 1 ampJ y be -fl- ~offu arcres SCrz

e ~C At otamp r 1A~f~~ ~ It 6gt Ilt

N611 Ae ~tly I B~ Iec t CAlieA Ids A is ru~ ~__~ Aamp a-( AC I So AAIb~Stt-t~ L fMc gti((y Mi~~ LMe e-l ee ir1kcts L seA So Mo( ern ee=- (-(A ~~dAIC

AI (IOOoJ 0A I De = ae r So 0 ts-tfe c~af of AAe d kt P~c4rc-ctr~AA6C

1k ~o~1 ~ (1 A) SeLs AABC f 6Aec ~ SeJ t~

scre-~-tP~MOC-tc~ OllA~~ bull middot 1 P 0 ore co((eAt

- fiscl 1( AASCGs ~IIe1lt ~~~~W (~- ~~L ~Ioc L

- L- ~ bull - 2J~ ~(IC= 8(~(s-lt)

ot t Ii -l 1pound is -(I ~K(~ ifCirde ~ Ill laf S bt-tl nf(~ ltgtf I IIIllyeltt t ~oflA bull

~ (e~ M s M~SzM)S3 ~~rrelaquo At s~ let 6 ~ bullt _ r

blse~ 4 poundA 00 ~-te 4 We c~ S~ SJ 1 M MJ

A 1iamp A --To t~t iampt elite- o~rf-tLt (i) IIIiilsrtt t Aamp1le rtfItJ-f 1 ts S I Co

-tIt vtt4lfO c4 -rs T~ ~tCf AT AIT~ 7iIese if L1I $ =ll~Imiddot ~iTt~lltSl~~t~ L T t S~-LTITa S1~1

(i) 11 A A ~ $S~ AA i MM ~ i 3 I ~ A T~ AI S~1 ~~ HzMl ~ ss I HsM bull ~ co ~ffWbull( ~dSr Nect CircCl1C(~ ~ASsz$3 reI 0 AA A~l

Ctcmiddott of A M~H IIbtepofcrceS~MAJ~r~ ~1 fLAA~AsrL f2 J ~ VAdtoos ~~

Z bullSo --Gtdes ~ 1Io(~ Ll lB~ reggt ampSt~~ AMMz toil s~~i~~ ~lt (x M- SLLt Ill ~bullbull04 S 1-ta~X l1c H ) Mz $1

~=(lttc-o)(c-M-~fl~e) 1 M M amp41 S)Jltl~ UrJ~Cost lt~~~~~(fo) ~ ()bc HSt~Zeuro~X

CT1tW EtA-f tt 1- bull ~A be ~iAt 4+etse~ ~ fwo nO~fD~fUtf Cirdes C ~C CAl-~ef0 0 (tltjreJ~ Dtte ~1MtM

~t~o c eamp 1d1t(s-et C cent~ Cztlt Pt J(e -i4af(EV (A~ ~-t-te~ctc At ~Ca~t QI Lk Me t ~~it-t~ ()Q o-J ~ ~ ~itet ~ pzCla

~-t ~ LtJAo LMAMz

~~ ~ ~

SGl~ B-t~etJ Plpt(gtzOt~~O

Ca ~lJZ~ damp bull nwy 14(0 oPa ) Q SeKds C L 0 PI

~ I ~ t -lO Z bull ~ J ~ OAn Ct =8 ~~-oflt~1 e $ Ll016M -tLl~A~~ So LOI~= LOaAHa A~ t- fs 0P 0 P ~o ltlie sjI Ie~ 00 Cgt~ ofL ~ ) 00 ~O~e-=OPct=OAIOg

t ~te~~-1 cknl4t1 ~ AO~ ~ Ate ~Itc

~ LO8M= lDAM

A~ I =gt LoAM L~AMz WIAamp~ ---

L 0cA M~ ==gt L0 A0)- L I-i A Mz bull -to _16bCrfkSf~S

Solt~p Wpound(CS JTbe reflec~ ~ S Wit-(S~ltt

fI5 Mis

~J e

t ~lwt Cgt (1Of ctImiddotd i -br3frt -+0

e $ f(~

Q cmiddotnI F -tkt bcs of tIl YOII f Sue- fut ~e-re ~)f Q

01 ~ w~ M ~ ~(eoi~ ~ l R~~ QS ~ isc~e~ C~rdamp 4 A PQ R

-to M Lt u be 04

~ A$ iudQ~~ltofe1 middot~~(R C V Lat ~ 10 ampl yo~t~14 fc

Co -fI kottcrt(e+y wfoit4 uW( P-tkt StI~ l t

~CtCte (_oppos-e P -(f ~ T middot (1 ~ Set$ U -to (Q((esr-~~-toflfobulltHf lt 1) Ii P~n (= v ut s setft~~ ~ t PQ~ ~

TR SQ=S - PR= PV- PIlt = Vlaquo=n ~ T T So 5 01 Ae ltT0 e ttl

ampruJt~J) fr p~ ltTaee~ UT ~ U

~ l(P Ifamp)Se0v4 u to ~ C(telte e to c~ l I- UtoT So TT Let 14tats~ P-4 C ~+~t5ect r ~Q~R ~

ampS-=s- Pflt=Pv- P((--Vre =TIC=-TIlt ~ tiM -i1s-MS Ti-f1T=-jiM PtSAt4t

~ El4middotrle b rio t)

Lt-A~c ~ co ftiI5le ~ ~tof scl Be A1k ~tsct- N ot l ~AC i~+fSoct ~c ct tJ ~~r~I~ k~ +0 AN -+~~ N ifersets AM 4 Q -c AB -t p -n ~f-lrJrmiddot 0 li~e to APt Pt-a~AIl laquo 0 middot Pofe Qo l Be SIt- TfABAc1kMNQfampAQMol3c

WLOG I ampS$f41111t A6gtAC Let AN MttStcf Uttucrclt fAABC j 1) ~

-- - bull c L 1gtg CL lgtAC=L~Llgtc~ e lAo M f~ r ~ ~ DC aJ PM 1 Be

~o Ho~y K(A ~StovlsA6j)(+oAgO(t4 08 O~ aq ae Itt t= Be( PN -r4~

L Ogt- L b8e =LM8=ro6_LAop=LoP~ ~ ~ D 0 tcKl orooc

I ) I J GfeCttrA J~c J~M4 ~ L 0 - Lep - 1 0 - 7 1- - 0 - 0 Igt IC tS~ amp It sc K is AM == AM l PfI=Q

I I ~ Lg eto L~~O~)oo 1~ ~o LSC g c It Be r

F l

(~p Sol~ middot Let dort FE ~wt -to nr2 4Ss(oll (iJ

Feuro () r C Lt r 1 U04s~r 111k ~y1- (M V)Sets P t r c-to K) Iiamp JE t jilt L AS

sow1 bull Ff 1Ie L ~ A is +lt1 ~roIldrc FE LNEC ~Afe~LAME I rSo L ~~eL~A~)~ LlNEcLlAMc ~ ACAeuro ~e1IA I ~ ~ pouer ~ A ltiol4Isped to r is Ac AM= AE S~M(tAfy I 16fJe t ~A i-fk -(~d -to ~~ Aft A~ A - A ~ =lttiJPOiqJ ~FeJ 56 Ae==-AF (1amp tflt11- rAAtcd - I

_ ~S AI ~ fIr2 AA~f ~ etc )~lll fu ett(4-ik1t f t fl1 pues-~r 1gt 61 sJMe~1 t ~OI)O~ wt Soc Oa I ~~t ~~ Ctgt

~ Ltgtco~=LClgto L cLeF ~s ir~S COa b~s L 9CF $ceCfiS~f rl So

Cl) is ~so~~~ -to re

E)(4flt

amp($ PI Ira Q-te ite~Iy ~ t ~ rt M N~oJtlJ ~ r fGs$es -tI- caff( 01 ~ r~

lAe r tgtit cl1illfr iii r rio MAn=C MBfr=D f (0 ~It CD $ 1~jkt to r2 bull

~ C~ IS - tYgtctStIt

~~ A ilefSVsv wi CAAer 0 oJ ugt r gt0

(amptatl 1 J(o r)) sA~f~ +lAo Se~s A~et(1 ~(t X 0 to ~ i~e VOl~t X O~bull y at sucL fut OXmiddotOlec r~ ~ CWOIelcu I fo X=0 ~ Utake )(=~ _-cl tllSo~)(-=QO Wt-take X=o

1ke Circle -w+1 C2~+e~ 0 A~ ~kCamps r gto-((ct k poundSle ~e~ ~ I~e IWJy 4fso ~ft A~ ltrs~ by sff~t ~ CrCJtL (lWt~middotcP

fGcfs CO Gift1 ~I((S~ ~ ~ bje(~~ it f~~ u~ 00 -to -t~lfmiddot ~ ~c-t J ex ) X ~

reg -If )( s-ikcRiC iwe~~1~ XI=X bull f)(~o~elf(enX~

= bull 1 ~x ~oit ofTaTl) ~t-rrl 4i~

P e ~ X1 lCT2 4~f~~-t1~ ~s iS k~

- __ OXmiddot ox ((sec LTo)()(ycsLTox)r~ ACtreJtt ~~SSi~ 14ftJUJ 0 ~~t +0 A cvdc bull ~ya16tj -4r~ O k iII-s ak~cIc -poits ~(~ St -to ~amp~ foffts l4 fOit 0) ~~fets

of -flit G~ a41~ aJa Afe utllt4r bull JotlfoItr~~tf(~-kGttk ~~set fotleceofv-f~ ~~ctrJe ~

A(fJe vaSSoVJ4-f 0 is Set -to 4 (euro reuro IS ~~~fI)~ 0 ~~s ~~k(+ifia1e-t (It( -t 44td Ito Cnverrely (A (middot1U1IIJt rssj-tlt~ 0 is Seltt -to ~Cvde (w~~ 0 Ni-l -tttllj~-t Imiddotier0 ~Itd to ~ leilt

f r A~At pCiSS~ 14 0 es SetOf ----1-- To e~setl ~ ~ _

Ifgt reg If two cr~ (f~ttIlC~ C4fVts ~(( ttlso ~~(etAf ~ fbft Pto)~~~~

9 lCo (iflaquo at ~Sdf~7e 4-( p~ oF

0 V ~-tlaat iHy~t~tOmiddotmiddot71-~R CA4f~(S ~ SQIJ-fo ~ 0 J

A Ie dI o~ctves4ltSet-f0r1f~~ ~ c () ~-t bull i- cmiddotrd~ ftftfiSttft S ~ fa-5~ 1Gtt cri(S t ( 4It ~fo-6etc~ Gllf f~S A lS 0 4laquol 0 A ~ IV~ IIG(C4((o(Af ~ oAmiddoto~ t 0Bmiddot O~ ~ OAloB OP4 ACoj

wi+lLAoB=L8~A Wt3ttLlOMdOl~ () - ~ LOA8= LogA ~

Aamp~ = OA _ r~A A6 0(3 - OB

=) Ae r lo A~

-------- --------~

)ampa-cle i (~tlcptleofto A ~cQlt$ A 1ckc ~tiatt~

ampl if tlyen~ t ampe- ACBD - A~middotq) +AD

II( V c bull I

SoJn C-sidelt -kfSiCll At 1 vuu~j l)is Cpoundlaquotef bull J ~p-J~ Ygt I) - t t e y fatH4) J -k ~ro-atdc qf ~ec ~~A~ I Q

I iIC ~ AeC SilCamp ~ IH 6e - c I

J vue b -ftt (1) We t _ 1 _AC~ r - Be - - middot

iDA ~ 01gt1gt AJ)middotC1) tt Mltrtrllj b~ lAOmiddot~]) CO~2 1aJkSimiddotces amporeJ

A6amp c) +A)xBe Acll 81gt middot

Re fICS 11L sf ~ eat be ltoftrec -to ~t -I- ~1-tllAt t MilcO + AtgtICBC =AC 1CI1~

~V Asctgt S (l u~ ~lJ4~ 0-shy

~S6~~~ kfCfS4tJ foJt of~~ -+k eampIt~ otIIIetStM Ai ~itlt ~s -fIc ~o~~ rote iIt wJere -reIs CIMif s Mesc(t _

-

6x4t~le 2 Lt ABc 0 be ~ ~tllt t(kft~ suamp~t At ampt so liltftStct At Y1tt ~r AtO P~t~( -Ke -refltecf of 0 ~fOSS AS BC C)1gtA A~ C4IIcYdtc

p _ c $Lt-~ -71

Lcent P~ ~So k ~fut f-~Wi _ 010 0 flO Msc CD lgtA Ye cdIVt bull

sc =l Ott foIIttll is ~iIr~le-t -fo site (5 -tk Ptt-RS l~~( (Sl~~14ft

e IcentS 0 0 -to tts e_~Hrlt OSAP DfBQ ~CR O~DS ~ludlC~~ J J -J ~ _ bull

-tt TltitCirtlutdts Ie CA Ca Cc CD rtsrdtuely CfSMoSmiddotd fIf~iQ 3(0 r ~r31gt0 By ~ct(s)

I~ AC Q( e04~~t ofo ~gtltS

cfct (+) I CA SIrcent to filllt LA fllAlrd to 81gt CIrs

Set to ~ IIt LB ~(c of Ac I C ~ Sci fo c tAlC -to ~lgt1 craquoisSeoet t ol1t LD~E lc ~

0 0 r~-t 0lt1

L Nen bull

CpnCa= 0r~ LAf Le P )Mjl-ly 4~t( LI) R J ll)n~ So bull

$r~ AcJ Mgt PClKs ~~Ic~4J~~ ~ fet h) PampRs is floc

~

G)Cdtpt f

Le-t P bft Af6~-t ~S~ 4l1It Appound ~~~-t LAPB-LACS LA(C-L~8C

Ltt tgt amp be ik~~tS 0( AAPS )AA~C nspecflf ~toe ~l A1gt 1gt1 ce )wtet A fOiWtshy

~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

( )tlfamp 61) biSKfs IA8PJ By ~t CT) ACAfACf~ ~ ~ I3A - XA So iSttf ACAeACampA

P ~f - xpmiddot ~ P~B6+lCApLcA8 J

C-1-1 ~=~ 5tRCt X ( 4ft AP ampt ~1It By~t (s) 1 ~ tCp~=LCitA ~ ~ I I~ fQ is Seoct of ( ~ ~~ 1 f4$s~~3C o listf SiacCrtIeO ~ -T(Alrl~f4lrgto ~~(1)1 tIIet pamp ~t(4C~I~Ois~tfo(0

A ~IgtC A~te A lU)e bullA p A APelAcIIgt f-c ~) I SIWICamp

I

~ ~ ilt3t +00 c( ~ 1 PQ fh ) Qm Q J r bull bull ~ t01 setc~ 10 t of I I

No LM~-L~8-=-LIWC-LAec f~ $(amp ~st ~JO 0 Ao( ~J~~ ~ Atl 43~ t (-d 0 ~ A61PcD

fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

Page 13: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

1-(t1J~ Let A~ A)e tI ~r~ 0t W1w) w~j I Y~ f~~j

fYo~ A ~ J~r - fe~~ -to -tkt -t~~ e to ~ c~tdt I

01 b w WI W 3 Got W bull skw~ ~est f~(tS ~ctCmt 1cle-t~~ ~s tmiddot~t t C)~

~otct~ JlCG ASSUllC -tL ai~cit-tle is -tlt kAtf GifC(t

~ h~ le~~tcJA -to t f~eMt oJ 1J -iklk ~ MS et--4M rll-tvJ~

bull l- A ~-A - WltWl t~ k~Wi -r ~- w - tV - 2 - - W 2 bull

Now WI bullbull f -ike ampM- ~~lc I SO Wd -= 1 i1e we ~ fJ~-te -tk ~n 4S _ _

~ bullbull Z ~ _ I T ~-t Wos 11 W + 2 Wl ~ - 1iIII I - - w

2 2-

F-oN -tk5 t ~ ~t -tk yoil-f N Jw~ -+ W3 $ 0shy

--te e lt$-I(C -t1e e1f~sS1W f Ns Sr~t~c ~~ nSFt -t oJ Jt Vis we (4 eot-t~ -tMt wtl lISO e O~ -tIt o~-- -two les -t~ e-Fc~Sto ~1 tJ -tt l s u~ -t $ -tle (fwle1 ~ -t~ )1 fO~~ (tce ~

J I W-z4 _

11Ob~ ( S~~t lYe Tko~ ) let W be D~ llt (~crclf ofJ ~1 13 c( PI Q1 R

be ~ iut ~ ~ lC ftJi~ ~ W -tt t1I 2 ll I tl ~ I ft ~ec-f~Jflj slw ifvt P Q R A-e tAl(Il (-ps Ole 5-

clt~ A $~501 11 tf A ltamp-t) ~ W) i

~ol~bo- WamplAi loss -t 3~nl~ I Wt J lS$We Je G-nIUshy

Cilampk 1s ~ ~ cttclt ~ lll llJ lls -= lw I ~ t 1kt k ii ~s ~~ l+ ll~ ~ Ii t3 --ie r~~ fw- W + 1~ Ivs ~ f-ltl ) i tJ- Zt~W So Sol lkcsc -tcdr W~ 3laquo l = ~ t L + W-lE W

2

St ~ Q ltl ott ilW --l 1(= tt f t~~1l

I sluw fQR 4t CttlfUf it S~s-t st P-R =l-amp-Nil f-R _l- Z-amp-~~ Yo-~~J (tI 4W -g ~-R

Q-~ -1-1)-1tJ --l~W X l ~-amp~w ) l2tgtW-ltl~ -lZ+ t

4t~ w- Zl~-ll-t It f- fl

- (1- R bull

-J clt~lttii lw=t ~ WW-=i

CiiID ~tlt~ firLiA BC let 1gt be A4Ie GtIlOc1tf- E 001 As loIiti DEit-CB J ~ F ie 600 Be I

ciA ~fDf oX ~~ o-rbmiddot 0 1 ltt ftt XIS G(( Gr be 01 EP ~tS~t ~ el~ttrlgtedo-r W~~~~fk~t~s X Ao D C fSfoFc-=Ep-=BYc1gt=r

~J ~sted oR we rMj Sity ~ i 7 middot PrDV~ 6i-F fs pcmI(e( -to -Me 4 b~ 1 -M CaJamp) Xl= Of-~ -tI S~1 je Y-X Sol-I Set 1ampt o~ AtAo tt(-~ IMc

For ~fS X It we e Ix-+f ~ lxl +111 ~ft Tie E 8 Gfl = C ot~~ E (0 r)klgt(d~ 1- W-11IAy f X= ~t(r-s-e t~o A~ F tB t(f-t)c 4( euroj =tE t-((-f)J) _ h Let Pbe 0 poillt el LIle )( f lJe lter t= B _ L _ amp1gt g + (_t )e~ middot gtY haYCamp oP=toX+(f-t)oy -f=~y ~ Be -- r -i1gt-t ~_

J J gt1( 8 -I io O~)y~ amp(01] ~ P-u SfjllleMt Xt E retgt I $0 IE-BI rD-cl c1

EICjl1t Call a ~1IIecent ~ ~ QjgtWelC ~l~ (I- ) Is (E -amph 1l ID-d r-(t-amp)(c(-f6-Jgtfd tl )ltLJ )M ~ ct j~ Ie ~od ~ orF9fe sk~ J i q F- Gt = t6-p)~+ (I-t)(1-9)C ~ +~hw ~t cf -tk s IIf-t4 Jgtllrl1lpounds Of ~t(tei _ IS tlt-p)amp1~$ htfampt iits~etet ~ik~litetllllorltl -tlt-p)la (amp+~~ =(~~k1NIllelo I _1 t f4IIIl ltf1ltS

Sll~ fir trl4t~ A~c~ Itt-A IlIamp 1M OjL ltf 114 (tw~-for ~ pound Me~ --ik se ~fOW twI ~ _ Igt IC-tO - f ~ if

T -poundTI-r -pound ~ I A=0 1)~D i(1el IC-BIt lo-dtll)~

UI8iC-1gt1 +11Hlt-at=Iel+ Ie-IgtI+11gt1 +1c_~(f~~t Wt ut Ie+IC-Igt ~ Iamp+c-tgtl t=~f1f)

AA IDI + IC-61 ~ 11gt+C-81 C-~AO=~8C) (gtt) holds ~Le~ft~~lcJs A81(1)C ATgt Usc _~ __

c6hf--I--l~1gt~ ItiC

~1- ~t fmiddot~~ 0+ ~ 0 ( is )(Y=tJC( (1 rsti - Ex4k+ Let 0 ~~ (i(cAt cf 4ABe 9 ~iIt J bef -fIl lfcffS Jf -IIf (t) Xi=fX (y+I)zmiddotXmiddotZ+fmiddotZ 0( (cXl-Y~(Xmiddoty) ~ I~~)(middotX I IXmiddot~~hd1I O~iOf (=) Xmiddoty-O ~~~~~~~~~~~~~~~ amp--ft 3 Let A8C b Le lmiddotts ~sfmiddotmiddot Phe

Ac~+amp~+A~-t8C~~ Ast+ctl SJt~~ Set1ie Ot~I ttt A ~~t f Jw

CmiddotC +(amp-lgtHamp-~)+D~ (8-c)~-c) ~ amp (c-b)laquo- At~(~- awl lt~~-f4ls s fu ~4S

(6 C-b)middot(S-C-lraquo ~ 0 ~~ck s (amplt-1) ~o

A ~t 1gt Ie -tLt poit ~ Aamp -L II ~ e _ ce~AAcO

p C fgtrcw _t C1gtJoe ) AS-AC Sol~~~~~~~dO~A

A a A J) A J)= ~ E=~~ =3 +~lCJ1gt-C=Aamp-2C

C1gt1 Oe- (A-tS-le)(Mc+1raquowO c) No AA~lh c C C(CUM(bull (IampSt 8 41f1$-bull (4) bec u Amiddot(Q-ltAB-ACO 1IeJtt(~) ~ OAl ~c ~ A~~AC

euro ~ toJs ~ 8lt~ 1)-A69 seAPS fWlkl ~JCOc $ firAABC jf( t ssewu-J -ptMf ~ c= - ta-+CmiddotfI AAS( its ~ttd q ~1 - If We Sampt -iU CitClIMChH- 0 AS ken -HII-srft~ ~o -t r -11 __ -~ -1 ALh--COtt - 7J 0 OtlGCnx n - ~-

A Fit iAcetft tJf ~~ c 0( lU= ~ = L

co b AI c lt-c

e ~ 1)c 1gt= te+(t-t) C t --amps ~1i~ poundL = tD ~+ cC C bI-c Gte middot I t A-t -~)tgt t-ll- A

aAtlS cc_ - tgtA - M~C 14 e middot

11l Lqt-(gt OmiddotkC Gtctal ~ICef c(H ~r J

51_ Set 5 4lt C4fColt_bull tu e -H Matel~Me1~ 1~ AA+b$-t C shy ~ 4~(

Lampil~gt 1omiddot~(i-1)l4-1) lt0 A-A 6middot~Cc=(tlJ 2ec 6amp+cc-(a-c)(amp-Q=k~middotIf (A16i)riamptc~ Rlt9~~ 11- 3( h_ Imiddotltl-C) 4l- 2(~~(H- btCi)tI~)) cttC

)(~+c) (-1)((-1) =((~ t1 -Hi+(() lt 0 of -~ f (ib -t-e) lA+Il+ ct )+ilaquoc gt~ CifI+cl+Jl(c)+ ~ ~ a(-o)(--G)-4-~-c)(b+cc-4)~)gt0 tsc4 rc s

~ Ike fRS ~ f xi xI wt -Stl-fculot 11-$9 (t)=LXOY) 0( tiYfft~e~ -fo -tkt fl~~ 1-- oxY J e

lti) ~ -f~)( ~f)-a)( l t Yltl (c~wYcxnyJ (j - )(~1 4fT~ A X0( V~~ p A of yl t1ft 0

(6laquo Q bull 1 lj 111)1 (DW~v e

eJ41~ Let AAA A _j A 1 1_ -+ V]nq DO 4 CD e I

- its ste ~tS p-Ilt1 ProiIla-t middot ClrtllAA1Ar oreAA AA So(u-tVf SeL ot - ~ -_amp I~ _L ft--A A ----- ~ fJe ~ ~ --fI 01r~~ O4St SMs ~qIt ~t)~csCA-A) I lA_-A f

E)Ctl-eIlaquo-r Let A6COf tgt ~~ pe-tft Qc e t

~~~Q~ ~ 1kfwlrids~ A88CCIgtbEpoundA 1T~ -r APamptl~J~ le ACDIIIampf6i -laquo s~O~ tk-t ~s Ooet is so eM eII bullbull ~olt4-tfN ~et -ckt O~bullbull~ rt -e ~_W f~ S~

tJ 1(t0 AXC ~ AP ofe (o(iu o=A-f- A(~ J C- 32s amp A

lltc t))tA SIA~y 8)(1)= (1(8 CxE~ C I

raquo)(A 6llgt re EJ( 6 =CcE feMtt I

eurolCAJ- E)(6-t( - ~lte+El$ ~ pound10 eImiddotmiddot

1 ~~-A~)o (As-AJ1gt(~A~ S ~~CI amp euro1tf6lc~ ~se Ac Adol~ -t(t-t Lit set - () middot At

At~ t ~It~ AsIC~ Al~-+yen+yJAI (

_t a ~ - bull

~ 2-shy

I _0 c A 6 c ~ As V ~1~Ut 1 Sjtllc -fb ~BIC~ fW(t

ftdle ~ts of BC CA AB ns~chvell -tk ft1~ -tIua-t

No A bull G 8 A I ~amp Ca A~ (orr eU egt~ 4~_ A~itlA-~lClA-As~=(~tAtAr-tAjcA -~~ StthtlI4It ~ SaJc1ttA

(Nmiddot~~i~+Ar~~l ore4 l1A AAs = Are 1J~~Ai

Aft13 amp11 C=A-ttils-A)frSollletoA~] SiCt AS e Gfe i eRe

o~ (Bt-A)K(~-A) - (A-ttz-~tl-t- t t)AxB No ~~=~~~-=amp-AH-t)e ~~1 S-a-= It-t1)A I Ct = lAt8)- c tlA +ll-t~)B ~ (amp-AI~I~(Cz-~)=(t-ttl-trtl-+t~t))Al(amp~O A S~ CL At( ccdllfttor

~t ~~ 1~~Pt

o

C[~1D --r-0 vetlOf) )( lf ate Jt~y wtt-t---t f~ t -flat ~f~ ClX~yO kAs 01 Soat~

AT 10 o T4 s tktCcStI ~~A rf KttO ~ X0 f Art NIt Co((llteor

F4t IT AX+bY+c =0 ~$ote -e 1~I(z-s 4t4l 4-+amp ott -=0 J ilQA Xf Z 4le cbullbullI btACcS( ~l AO fIe b-tc-o w X-1-KZ-tYc-6Z

(~ar~11to(~1 wr~t--J Lftai c~ s OAAampA Co

~ OeLamps 1f 1 -1z- Aa6~l~8ampR AsampIA~= ~ 6 8-c amp-S tltcl A DAR 0

~e COIIfttAt t ~1 =- 1 ~ ~ P Pl) P3S~ Set - orlll at o at A8 btt ~trs Ale LIDa (ampfbv~ ~ A~ rA Q( e s So 8 1-t S6Wt (s EIt Cll No

Pl =tAt(c-t) 8a trA+ (ct)s ~- ~3 lAAt-tQ-) 8-= tA(-aA+Cc-ct)S a S~tU~ ~ 0= ltr- CArgtA + [pound1)l -(I-I4)$]B

A~ (tally rcf~=gt tr(~ Otu( (l-tl~-laquotlt)S=C Solll fott ol -tit pt~~ -+-s f ti ~I~Js

Nt ~~e ~ 1tu~~A+ SoSzCt-rl g$t Vs- r~ r~- r~1 Pgt1s~S)A+~s(tmiddotgt8 R= rlrfgt~A ~(I)J B

Y~-r)S) ~6a-t~S) amp c) ttS +fs-1S ~ p~f~P+~sampf-tj~

~ P1 ~se~rw)~c 0 Qtlgt+CoO ~ r fL cU-1- fc-i (ove

~ 0

A - -

~ FOf~lamp~

(1 -laquo ~C

fot-CA~ to ~ t t amp -t~~ crt a ~tc ~ El(tend~ltl St L laquobe ~[A8Cl Js~~i~ R= 4 C

Let ( ~t 4ct nwts lt 4e GoismvmcJt i-R- tl 4J~)(fo~of AAsc Sr ~ l=~~Yslt) ~ bc_

S A -- - 0 21 1iltelaquoe s dolAt C~d~middot ~o~ uI1gt ~ s~amp s~~C middot T 1_ ~ rI n -rf (i-- shy

tl Ie or~ DraJ clmiddotae~t 61gt 1pound Si ~ A= ----=algt i IS lle~ ltJOiOlSA0

~~~~~~~~~~~~~-~~~~=~~~~ p adEr-l-~a~~r~ A- oS+- jtus c~ - c e c I) p(]) Let 18(1gt L~Ms

I4dtt rAsel Or S~8c1oI(lcl~ 1leflAftt Let A6nct)p -r1 ~act 0

~Me C ABC ) GlUo~kc ~ PAx P6= Pc x PD = tl b~~=Abc bull P19tpound Note L APD L (PB

4R A1BC)aHd~ckLPAtgt=LPCBS=tfA-tb~~) is ike seifieAc ~AAPDACfB~=~~ PAIPB=fxPD

amp Q C Of 4A8C Lri pc C 1amp-~ ~~ PC Is -lt-~t lat t lie i4 jCbullbullr 4l( M6C Qt r Ie -i4~ to -e -fde ~ A A8C if (JJ

C)~ ~e icltc1e ot AAec ~e p A e OYlJ c fCL p~~re [Mel =[ALel[~cl+(CI1= ~-t~+~=SIr ~ Not~ LArc=LcPB

I-tfllWlbull [A8tl~ S($-11 ) (s-b)(s-c)middot I pCs f~ot -to LACp4C ampP(~ Cos C= tt2ttoa-c (~AI Ci(~ircl 4 MBc B 2shy

[A6Ci= ~SiIlC=Qr(+coSp(i-($C) ~AAcPACBP ~~ fgtc PCPAlltPB =(Cl~-+Iot-c~t-~a~-9 ) = catlo-4 t )(A1(-c)(CoHI- b)(o-Il-~= S (s-c)(~~

2- ~ a

Ci C [AS(I A 2

~

I

~JJI LPFA-=odeg=Lpe~ ~ amp~ ~LPFeLPAE

C5Ji) ~tolt1 s-ThtOfotfll Let A 6c~ ~t dlSncf ~ts 01 bull ~c ~o - Me~IA~ 1( bull t Of~~~I ~Ot bull -Tht~ bull Sa c~tOV M1 C(liofIPT potd~ A 6 C Iie to

AI 6 C 1gt (1~t~c 1gtpound fCLR atfmiddote ZA ~A A ZA bull -~ -iA ~Co~ PAQ~clf$ WeA~ ZA~lA I tc Z~t

pFAECc1dk

bull ~ Srlloi(y taCgt6~~~-lPFB ~ pG~ f CDCCYcbull LPampb LPFI) = e 1klaquo AIJ~P LPAespoundp8C pfE _ LPeP 8EF (0(1ltlt~L PFE L~8Tgt~ LFP - L 10 collirAfampff

)fgtC)~Jl~~ ~ ASC1HAol6C=AcS]) bull (~~_ ~ktI AeCO At)ItBC ~ACdtgt 1)~c 190pound 0 sWLe AB UJlfsftfUct A ampA6

S~~41 to flCAP 1I1elt AB A~ 6eshy

6 Ai - 7ligt= (1) lBAE=LCAJgt

SO LMc L BAlgt-L1gt= LeA1gt-LMe =LEAt) Tkeuro1 A8AC~Ae-A1) So Rr-c EDAtgt~A Thet Aec~ A~8C =poundItampE AClC E~ AC80

bull A rC =c Sf-t Ell I

f1-I-4j hoW~ ~8euro~EtgtS ampb ~ E iUt~( SO - ~~oeA~LeeALtgtCA ~AsectCO Sltffc

SoSoft ~oe 1et~6cP cl-ampd-p~ 0

tI~ Let l)poundF fetf~~ff- P~ ampa Aeyen~~ ~

Asse ~Mist (so4 is 6~UA_JC ~AGSC ~O bull G ~f( Aalec~o)

tt~e9 7eff

fovlaquos X I Z ate (es Aamp ampCA D ((t~ve-()ty It X I Z (lie (dl-lflOr

A ~f f6 lhg--1 ~ xe YC LA - middot ~ lQt Dbu (~ Ac soct1IIt 81gt II J( Z -r1teuron

~g ~ ~ 1t~ ~z Se AlC 6Y c~ _At P1Q (i~ ~y Ie ~c -- _______ r tamp iU I bull laS yc fA ~Igt ZCZA middot lCI~ lIeeu~ Ie~

If ~ tL ~ =-1 iIamp )( YL MHo l~(~ Y~t~~~~ SlJ) Ltt l~ X(OCA -Thtl b Mt11Idtw 11~ Ax ay CI _ lt Cz Y Cl iiiK zA --i ~o --=-l1toobull CfIea bull _Cl -a

I I

ceDD ~MelI s lIeo~toA l~tA I ~cc t) euro ~be tc~ lO 0shy

de lw~~ ~( ft amptCtSSCti 1 tf (~ diC- (~QEf ) bull

t p Ae ti l)euro J Q Bel pound f 2= Cl)n fA ~ ~k ~ Q1t ottc(l(ea~ ~QIR~~~ -

f~ 1 ~ ltt X~EfA 1AMCD bull ~ z- C~neF Arr~l ~(atts ~ff 1e-(fM1oec~ FA

ftt- Ool~~~ 4xf l w hVII

e-- ~ X K __( It X2 ~_( t ~~II Qx 6y Ct ~y pzex I fllFxijmiddot 1I

Hul~pr~ ~ AIl ~~ tfffSfctj cofI4t tt XA)(B XEmiddotKF J (CmiddotYP=1AmiddotYS ZEmiddotZF= zeZIgt W~~et ZQ lSf~-i igt PQ~ ore rlfltelaquor

Qx Pf Itz loy c-enc ~Mee(AaS

t-rks ~ere 0 Imiddotil~ (1$($ of PoucJ s for It we tftwt Ato 8 -te I AIwIJ (3 il(cJe 1Iofl1-t i AB will b~ ~-t1l3et (iot ot B ~ It~j CIt~ we ells JpoundAoflt ~ t~ liflE Clt B b~ BR

6lCtJfC i F~~ h Cf(Ultirc~ ot Mac J f(it 1) ( ~ ~i~0yen ot -t4l~lE I~ ~tA - ~~ Be ~ e fM 1fe ttusc(e~ of-ffwf3ct (tt4-t C3L1r~ CA~ F= bt ~ ttfStd~ of -tINt ti-~-f Imiddot~t ~tC wo( Aamp 11161 PI Ell F o~ ctU

Soof~fIyen P=Mo 8C ~ E= BBnlA f=CCnAB APP~i P~f ~ ~(fo MB See I fott et 1gtpound f c-

-- =JSiiiiIii

b)lAtc ~ Let-tgt 0- eht ~cfs 0( dt101 AtCS

AS ~ AC O~~e (ilcu-R( Mac ftspciwJy l(t tgt Ilt ~f AtC sCI ~== DPn SA J R= PEn AC fro +~-t lile QR~s~(QVJ14 fttCf+~I (~ 1) ~ f9bt-Mshy~e 1)rff0--AS- CO ~SfctsLAc8

Co ~r ~ qftllCr At =lgt 6 ~LAec So 1= Cl)n G8 Sf_ eEtS

Q tgtPt SA DP 8ital R= Pe C Pre ttL PlE AI

AIP~ f~l ~ 1Ito(-to C ~ P er ~ w 1 ~ bull 1I

t Set I Q Rut tIff~ Co~~d~

~ -7

Alt IXu q j

elf (Ga1(e 3 Ltt AT3CPs e ~ +s tMDlCJe ~-rd AAfLBS Bat LeA) ccf LAB fat 1gt be ~ls (I ~cucl1t ~c4( I

DA(11)C= AU DB()CAe~ 1gtCIAB~ fgt~~ A~ r~CtfaJ T4 6v~fi ~ IAGC a~ Co((~((r

~olf- W HL-cI oy-((~( ~ AA Be Ne

AAIB~I)Cc(-=I DArBC=A 11gt1( ISc AtA f Cc -= H L lAlA I C I Cl

1t~()cD=C1 ~l (AIBl (cjAfrrr5~5Gl ~~ t DAAfCC tgtlt Se4 A HC tit c11ilaquoraquo SIt 1y ar171~ BS41s(to AS e 0cc we Su e H 6ltve c1(i~amp r A~ H C~ S4rt a(((~4~ I

-~ ALI)f ~fle1 tt P toe a ltpor i~4Mec

LtfP I~~ff~I$f- 5 -to ~CA Camp ft~t~ lttt bJ() ~_ eshy

ll 10 ~ fet ~~~N~ c-tohs API sp (~ftvtll IfQ P ~ 61bullbull Pt14 PttNQ~~ (tries ~tll~ Qfz cod A~ aft ~et

iSoLttd- $(fCJt L CPc p) LCQLP LC~P Lc (gta Palt-e J -t ~es c P ~L I PI Q p 4ftcocttc f~AfrI15 ~s middottU(Woto ~1l$1 w-tSu CPt ( gt e-= A ) P t1t( QIP= X ) (Q-a Pf P2C-= B 4re CoI~rtelr $6 Rb2-l amp1L ( AB-=Xmiddot ~ ~lIQ P~IA8 tVe ~Cqfre~

NewtDJ S

~A ABcOS~~(laquoteJktvsa e ~SQiraquoeamp c~tkt~~ ~~

APgtsc CD) PA AXcpotlts EFG)H-~t~ C F B ~ACG~FHgD~~r~t

Sol~tcNI W E6nFHO~ Eftn FG ~X _Apply~~ ~~scJ ~ ~ -to E~ltSJ F f(f ~Sta E~ () Fr =0 ~~ ( 14 1) I G Fn H( X are ut(ltealf_ ~ltfcAy~ltP~CA(s ~e- 4 E6--()FF~~ J ~S14

EEn FF~ B euroH nf6=X amp-t-fn ~euro 0 tUllPtfcmiddotc4t

-nus ~S 0 XI oJB ~c((e4~ 7itN pound4 fl Ff n6D=O SlAry EG F-- ( AC - O ACE6 fH6DCPotrclO

1)ec~CAes ~ 0 nfAaAec ~ JACc) M

A c B actgcP J CAnCpQJ AampnAgR ~r--+--Ir-~~R If AA 613 I cc 4te ~tVt-ct ~

A e 1-~ PI ~ Rctil eo(IQ4(_

c~ rCP_ R2esrk ~-s ~ -tyenUL te~ 4 ~~cAAfIdgre IfV --IfU ~ f 4s root G-oIer ~Ns c~ AOAB ~ftJJ MeoJ- -~r ~ et QPL AEa gil

At A rltamp -7---1S ( rt l g 0 () I 4 ~ ~ Ie Be Cctf~ Lloec Ilfct-Jt ~~ C~ c~ IJOCA ~ 1te(J C~ BP Cd M oct ~

B8 PC-co ~-( ~ No CC~=-( ~(ff~~~sctmiddot~~= - ~ (IC4M~cfMtl~~~ote- ~ et eampI c-f(er

62Y ~coJ A~s tttt ~Cct~lI1tr

Let Cn-les C ~ Cz ktwe ~~t ~~-fe15 0 ~ 02

Sf 11 4st f( J 14 (cs of ( OotX w~ 1

fe- ) t ~ lt twitt ()~ -tu Cl

eo( C~ ~Ilt ue 0 K- r 4)-~ J ~ ~ li~ f(~ok( -to OO~ -rtgt Is -4 (~~a1CSof tLt -f~Cnrd u

MOtse ~3 Crce~ CJCC1 W~~ OJOaoJ(h I~ nf CiamplttJ -tfe 3 ~ ltWQs ~FoS offI Wi( i~~(JItct cent Do fgti- ((lt d4 vaJOJ aftftfT4crtfes 111$ ~It lw la-I fIwe wi(( v-espue to 4((3 ccle$

G7~~14~S

~ If 2c(c~sCp~ lte~tAt PQ ~ p Cl aJ hss fou 0 411(1 yen

middot~ Ot J To Co J C So -ky tore eM ta noe(tk( ~ 2 r(4-~ ~ pIA i~( ~~ oS

~yenI4l~~~

P------ ~ c~ Lf4rdes C e d lifest J e we c- tltANJ A f(rrzl cltJ~C

~~ ~~~eAJf- 14 1

Ci-- ntcl ~~~ CJCl ~ CCsII i~~(t et -t4 ~ C4tt p1-Cch~~

~P~ f LoDa is ~er~ AK~Of CCz _

Let ED be ~~~ foSflctorf oft B~ MaC ~D ~S~e AC -ri Cau~tt1e c1A8JgtC ut ABtttE J(e ~ cfC4c~rc(e c1 AB D MflId 8 Ccent F-=-c --r

D (Olt ~t AE =- CF So 1$1 i te~d~ c~ ~gteJ AE~AB=ADAC II CFIltCBCD CA So~= ~~

5 ~c 81gt fsecfs L ABe WI_ Cl) ~ _ I bull It rJC AS - AD CF- f1C

------------------~ ampA~fel Let ABC be ~ ftrJMIj(e ~ soscJes 68C[)I

CAE AASF ~te~(1 to AAsC wi( ~ CA Aa 4 S bu1 tsrtdvel~ Pro~ta ~-t 141esff-1 AJSc ~ t ~ I~es t=F fEgt DE ~dJ ~uc(~t

Col Amiddot ~ SJltto i Late ~e cnl~w-f( Jgt4Sr~ ~ IE ( - eatu r4~ ~Cgt cte

a~~c~~ Iof crde middot1itE Ultoofe Y04oc Jl Y l AE=CE ( tel btcte(~w-I(Fu

c~ Cc~-tr ~cL~4S AF=8F - I -r4e-tltlfte~ A PUr~I T (~ff I ~~ fiIolu ~ ts ltfCI C1 $f lltty ~amp~ 2 lies Cltt VIIIt~~ ~c c) ~ roampoIaJIlt) of (14So -tkey ~u(4t fAa ~~ Camp~tet

63DP I

r ~e A ScIampf~ 2 LtP be 1ft l~~

~ Ii~~(-kB~lIc(~ -to FD-f _ bull 11C ra(~~ to OE -tt~ fOIts frolle M 1 Elf c(frelttf

S 7c IL ttgt ~-JC 1l rgte ~ t

I

I A~ C~ $oIf1 Let ile cncrcft~ J) ~=HF - PD eF -61) OJ rD-peuro-C~1 EAtlA~1eSamp Ql (A~ AF =SF I CD-c CEAGJPF t 81gt

2 l 1 0 F pW~ ct - fE =AF -AE S r~L pound ~ POtt 1 ~CAty4W(t t

- t_ EICIt1k 3 AC--damp l-H aat 0 P~r -fl Ie A4M C ~ usc -t ifegtSltct ~- Ae Id t W S let

Be It N Let 1k u cudcl 0(AAac -lt1 aNll~Std ~t B t ~ middot Pe ~~t OlUaM

SoIwt t ~ C4Samp 61 Be we6~ 11 aM i~ ~ ~ftthlte Qt S of cYG vtIeof poundlASC 1ICft OM =oel 8M

A~p BA18C i4e c~~In CAsamp - AUN AAec ACfo K~ 1Iotf1Ar (S1Cc iMruw Ibl~cto~ L kll Ac AC Jolaquoaret tes) s e rdeo( I

I

pound I ~e AC kN J 8M Itteet 41 4 (IOIt P I

Siell L PM N L 81lt11 l HCA s MIC PAte CDhcrkcl Q ttl I t fill pou fOitJ BMlC ~p 8M ec 80- yo Y=OA

PM r8- PNICPK POamp-r~ bull ~ $Jtmct~ 1keuro92 Ie -t 10- eo~= ampf(tM- rM) PM - 3

rJ It

OMl PB lr F6 ~t 8MPM+6I1I

OM J ~M

L I A6cb be i$(~Ibullt co_~4 tt ArllAofOo Q-t d - amp c~ f A1)1 SC ~ f (aros

Ccle i VI ( 4 E f= ~~-t t I~oes ampe Q= f-o -Ie C

8y po -t fI-t~ Po~_~ peltPD=PHxPl ~_ ft QClltQ6=~d~Qs~tAcff we1et Po~-Qo=CFM-ru) ~ fMQ~ -ns i (Ies 0ML PQ lQMO Itf oM

Ntrf Csd tIe C~C wi4 Q0 As d-cr~ 2 _ bullbull

It t-sses ME F SlAte LampMO LQ EDt -lCl fo s ~ CIC-z Ef ~ Ef -s iU c($ ef ce Let cI has ceth A( ~s tt lie

laquoa ~ ~ t JFPO _r - flMx pQ fiCa _Vi ~ P$ 01 ~ bull0I

A(Igt~ ite-sect PQ 4t M +Q -of leM _ LA0(= l paceW ac- ~ 8I(C ~ lttlclc p ~_I c 1_

let ya~s t Cltn~ I ~_0 =c bull t if crftit C fc$wt

~l~Sshy c1iW ~ 14- - l-l-~t1 A IS ~f~~J i AA6C J 0 i-tala

C(cuCttdlt~ 7Le -(kfee 4-ttJes AP eamp tMJ Cf irUktt- H EDAA6=-M FDo AC-N tp~4-dcent () 06Jl)F )OCJ1gtE

N C~) 0 J- M N middot i

Solfen bullCO LAfcc9cfLATgtC 9 A fgt l=~C6AtyJrc TktL6lgtFcLBAC AooBc-OCi--ees LOBC-=J(t~Io~Leoc)middot1tl_l8A(= ~oo~L8bFmiddot F omiddot Iamp -=gt 08 ~ tgt l= ~frly DC lDe-

B 0 c (~) CLMA ltPgtM~MIf AC~HI () I 81U AlA ~ NIi-IIIt= Aa -AltlaquoJI tgtA L

F ~c ~ l)e - ~ Aa~Ac (c~

~~b )N6oIp 13Ai~80-- OllADI (0( 1)04 ()-(~)+(()+ll)-~~ J)M~ ~_cot=OMOt)1 te

bull Ott J MAl N~-11 fI ~=C)jI 6lf1

~iet SoU- ln LAFC0 =LOC-dJACl) Fc-tkc ut J bu])M So ~t TeI [)f -ue L Jeo L 6gtF =LeAlt ~ J-f4 a~t (~e tB

4 ~t~4Yclt ~ JNle gtetpeId~ bs~CtoY til g 1 I J 1) 4te 0 ~J

=gt 0t3lJe ~oS i DF Q(A~ DCLbE wHk ~ CSV ftt Ae efT I c AC~J~DI ~ (ltt 6e If Be I I I 01 tl( AS 1POW iI f uIlh) SrlOCo Ae1gt = aq rW1d1C by d~ l~testJ~ t4PtwI- Let lc SAe -de -CA k)sU AABC f 2AamptI

NA ~ NC NF ~ rJ SI AC ~ dbullt ~fieaa~(L ofM$C ~=~ so tr~ of ~ bullbull ftc~(eNs() ~ ikatQ~oJ CoxS qf ~ Grtles Q-14III ~ if ITI ~ YM~(-l A~s 7I-e lmiddot 11M rOI(A)C1lt D ~~(S liIOH

r 6middot 1- r IAC- UComiddot

041(ms AhOYllo-lety wi1kceterO a-J Ptto k (cltwaof-d ~1 H(oJ 1lt) ) is Q ~CI itt setVls Jllttl r01ht X 01 ~ plAtte -t 1ile ~c~ X sampcck -tk~t OXL~ -= ieoX ~~rk~ It kl~1)~~~~ti saA3Jkf~ l-t lFl ltl J ~ -tk kPJMDffty 5 ( ~ A IrtySe~ Q -~ f ~ - ilc ~3~ ~ 12tlgteuroFbe~Js~8CCAM~ ~ (-((Ali) Secs AAsc +0 AAFE

amp 1gtJ C Let q Ie ilaquoo cttIL 0 6A-QC SiAte GiA =-2GfD GS -2GE ~tqt=-2~ s ~) ~IAbEF f AASC EXAfe L L AABC AB =AC A(iRl IS t -t t_1y to tIP cnuantt14MC4t~rMs pte AC ~tf~s P Q~ Pe 1l~ 1e totiJpoNltt (fQ

~114t llCeftgt ofAABC Sott~Let 0 bt 14 cgftt ~ -

) rele Lt 1gt foe ~t3et totlaquo 6 c 71 -t4 Circle +ipound Clttt-atd l4AOC

S 1) l3~yf A-trot ~ PQ

ADfAt -= ~~~~=~=Ic S HcAl)So04s I ib 0 S111tt O~$-iLalAltbullbullfMc t ~-tl_W-~tIecf-

CfajiV ~~ s A~t~~etsVI At AlAJ ISdVt4 well -scfes~e l A az (i) (~ts~ Sltk Cif(IOSitc Ai) fW IZ N ~~+-~~Re ~Ill~ ctrck ~ fMlf a c-~ ~lt 0 c-I

II~ iw~le laquo 3Ie -tno1 eel Ct rd -to ufS A

~ of stJes ~u+-1- middotfDItf-t G 1Cf ~fj -t4 (nuCampolttt ~~+riAe ~-tIa ~~it cO (6([e-t etft

A ~t Let A 6e ( It ~~scf 4~el cltlu ItS 54014 1 ampJ y be -fl- ~offu arcres SCrz

e ~C At otamp r 1A~f~~ ~ It 6gt Ilt

N611 Ae ~tly I B~ Iec t CAlieA Ids A is ru~ ~__~ Aamp a-( AC I So AAIb~Stt-t~ L fMc gti((y Mi~~ LMe e-l ee ir1kcts L seA So Mo( ern ee=- (-(A ~~dAIC

AI (IOOoJ 0A I De = ae r So 0 ts-tfe c~af of AAe d kt P~c4rc-ctr~AA6C

1k ~o~1 ~ (1 A) SeLs AABC f 6Aec ~ SeJ t~

scre-~-tP~MOC-tc~ OllA~~ bull middot 1 P 0 ore co((eAt

- fiscl 1( AASCGs ~IIe1lt ~~~~W (~- ~~L ~Ioc L

- L- ~ bull - 2J~ ~(IC= 8(~(s-lt)

ot t Ii -l 1pound is -(I ~K(~ ifCirde ~ Ill laf S bt-tl nf(~ ltgtf I IIIllyeltt t ~oflA bull

~ (e~ M s M~SzM)S3 ~~rrelaquo At s~ let 6 ~ bullt _ r

blse~ 4 poundA 00 ~-te 4 We c~ S~ SJ 1 M MJ

A 1iamp A --To t~t iampt elite- o~rf-tLt (i) IIIiilsrtt t Aamp1le rtfItJ-f 1 ts S I Co

-tIt vtt4lfO c4 -rs T~ ~tCf AT AIT~ 7iIese if L1I $ =ll~Imiddot ~iTt~lltSl~~t~ L T t S~-LTITa S1~1

(i) 11 A A ~ $S~ AA i MM ~ i 3 I ~ A T~ AI S~1 ~~ HzMl ~ ss I HsM bull ~ co ~ffWbull( ~dSr Nect CircCl1C(~ ~ASsz$3 reI 0 AA A~l

Ctcmiddott of A M~H IIbtepofcrceS~MAJ~r~ ~1 fLAA~AsrL f2 J ~ VAdtoos ~~

Z bullSo --Gtdes ~ 1Io(~ Ll lB~ reggt ampSt~~ AMMz toil s~~i~~ ~lt (x M- SLLt Ill ~bullbull04 S 1-ta~X l1c H ) Mz $1

~=(lttc-o)(c-M-~fl~e) 1 M M amp41 S)Jltl~ UrJ~Cost lt~~~~~(fo) ~ ()bc HSt~Zeuro~X

CT1tW EtA-f tt 1- bull ~A be ~iAt 4+etse~ ~ fwo nO~fD~fUtf Cirdes C ~C CAl-~ef0 0 (tltjreJ~ Dtte ~1MtM

~t~o c eamp 1d1t(s-et C cent~ Cztlt Pt J(e -i4af(EV (A~ ~-t-te~ctc At ~Ca~t QI Lk Me t ~~it-t~ ()Q o-J ~ ~ ~itet ~ pzCla

~-t ~ LtJAo LMAMz

~~ ~ ~

SGl~ B-t~etJ Plpt(gtzOt~~O

Ca ~lJZ~ damp bull nwy 14(0 oPa ) Q SeKds C L 0 PI

~ I ~ t -lO Z bull ~ J ~ OAn Ct =8 ~~-oflt~1 e $ Ll016M -tLl~A~~ So LOI~= LOaAHa A~ t- fs 0P 0 P ~o ltlie sjI Ie~ 00 Cgt~ ofL ~ ) 00 ~O~e-=OPct=OAIOg

t ~te~~-1 cknl4t1 ~ AO~ ~ Ate ~Itc

~ LO8M= lDAM

A~ I =gt LoAM L~AMz WIAamp~ ---

L 0cA M~ ==gt L0 A0)- L I-i A Mz bull -to _16bCrfkSf~S

Solt~p Wpound(CS JTbe reflec~ ~ S Wit-(S~ltt

fI5 Mis

~J e

t ~lwt Cgt (1Of ctImiddotd i -br3frt -+0

e $ f(~

Q cmiddotnI F -tkt bcs of tIl YOII f Sue- fut ~e-re ~)f Q

01 ~ w~ M ~ ~(eoi~ ~ l R~~ QS ~ isc~e~ C~rdamp 4 A PQ R

-to M Lt u be 04

~ A$ iudQ~~ltofe1 middot~~(R C V Lat ~ 10 ampl yo~t~14 fc

Co -fI kottcrt(e+y wfoit4 uW( P-tkt StI~ l t

~CtCte (_oppos-e P -(f ~ T middot (1 ~ Set$ U -to (Q((esr-~~-toflfobulltHf lt 1) Ii P~n (= v ut s setft~~ ~ t PQ~ ~

TR SQ=S - PR= PV- PIlt = Vlaquo=n ~ T T So 5 01 Ae ltT0 e ttl

ampruJt~J) fr p~ ltTaee~ UT ~ U

~ l(P Ifamp)Se0v4 u to ~ C(telte e to c~ l I- UtoT So TT Let 14tats~ P-4 C ~+~t5ect r ~Q~R ~

ampS-=s- Pflt=Pv- P((--Vre =TIC=-TIlt ~ tiM -i1s-MS Ti-f1T=-jiM PtSAt4t

~ El4middotrle b rio t)

Lt-A~c ~ co ftiI5le ~ ~tof scl Be A1k ~tsct- N ot l ~AC i~+fSoct ~c ct tJ ~~r~I~ k~ +0 AN -+~~ N ifersets AM 4 Q -c AB -t p -n ~f-lrJrmiddot 0 li~e to APt Pt-a~AIl laquo 0 middot Pofe Qo l Be SIt- TfABAc1kMNQfampAQMol3c

WLOG I ampS$f41111t A6gtAC Let AN MttStcf Uttucrclt fAABC j 1) ~

-- - bull c L 1gtg CL lgtAC=L~Llgtc~ e lAo M f~ r ~ ~ DC aJ PM 1 Be

~o Ho~y K(A ~StovlsA6j)(+oAgO(t4 08 O~ aq ae Itt t= Be( PN -r4~

L Ogt- L b8e =LM8=ro6_LAop=LoP~ ~ ~ D 0 tcKl orooc

I ) I J GfeCttrA J~c J~M4 ~ L 0 - Lep - 1 0 - 7 1- - 0 - 0 Igt IC tS~ amp It sc K is AM == AM l PfI=Q

I I ~ Lg eto L~~O~)oo 1~ ~o LSC g c It Be r

F l

(~p Sol~ middot Let dort FE ~wt -to nr2 4Ss(oll (iJ

Feuro () r C Lt r 1 U04s~r 111k ~y1- (M V)Sets P t r c-to K) Iiamp JE t jilt L AS

sow1 bull Ff 1Ie L ~ A is +lt1 ~roIldrc FE LNEC ~Afe~LAME I rSo L ~~eL~A~)~ LlNEcLlAMc ~ ACAeuro ~e1IA I ~ ~ pouer ~ A ltiol4Isped to r is Ac AM= AE S~M(tAfy I 16fJe t ~A i-fk -(~d -to ~~ Aft A~ A - A ~ =lttiJPOiqJ ~FeJ 56 Ae==-AF (1amp tflt11- rAAtcd - I

_ ~S AI ~ fIr2 AA~f ~ etc )~lll fu ett(4-ik1t f t fl1 pues-~r 1gt 61 sJMe~1 t ~OI)O~ wt Soc Oa I ~~t ~~ Ctgt

~ Ltgtco~=LClgto L cLeF ~s ir~S COa b~s L 9CF $ceCfiS~f rl So

Cl) is ~so~~~ -to re

E)(4flt

amp($ PI Ira Q-te ite~Iy ~ t ~ rt M N~oJtlJ ~ r fGs$es -tI- caff( 01 ~ r~

lAe r tgtit cl1illfr iii r rio MAn=C MBfr=D f (0 ~It CD $ 1~jkt to r2 bull

~ C~ IS - tYgtctStIt

~~ A ilefSVsv wi CAAer 0 oJ ugt r gt0

(amptatl 1 J(o r)) sA~f~ +lAo Se~s A~et(1 ~(t X 0 to ~ i~e VOl~t X O~bull y at sucL fut OXmiddotOlec r~ ~ CWOIelcu I fo X=0 ~ Utake )(=~ _-cl tllSo~)(-=QO Wt-take X=o

1ke Circle -w+1 C2~+e~ 0 A~ ~kCamps r gto-((ct k poundSle ~e~ ~ I~e IWJy 4fso ~ft A~ ltrs~ by sff~t ~ CrCJtL (lWt~middotcP

fGcfs CO Gift1 ~I((S~ ~ ~ bje(~~ it f~~ u~ 00 -to -t~lfmiddot ~ ~c-t J ex ) X ~

reg -If )( s-ikcRiC iwe~~1~ XI=X bull f)(~o~elf(enX~

= bull 1 ~x ~oit ofTaTl) ~t-rrl 4i~

P e ~ X1 lCT2 4~f~~-t1~ ~s iS k~

- __ OXmiddot ox ((sec LTo)()(ycsLTox)r~ ACtreJtt ~~SSi~ 14ftJUJ 0 ~~t +0 A cvdc bull ~ya16tj -4r~ O k iII-s ak~cIc -poits ~(~ St -to ~amp~ foffts l4 fOit 0) ~~fets

of -flit G~ a41~ aJa Afe utllt4r bull JotlfoItr~~tf(~-kGttk ~~set fotleceofv-f~ ~~ctrJe ~

A(fJe vaSSoVJ4-f 0 is Set -to 4 (euro reuro IS ~~~fI)~ 0 ~~s ~~k(+ifia1e-t (It( -t 44td Ito Cnverrely (A (middot1U1IIJt rssj-tlt~ 0 is Seltt -to ~Cvde (w~~ 0 Ni-l -tttllj~-t Imiddotier0 ~Itd to ~ leilt

f r A~At pCiSS~ 14 0 es SetOf ----1-- To e~setl ~ ~ _

Ifgt reg If two cr~ (f~ttIlC~ C4fVts ~(( ttlso ~~(etAf ~ fbft Pto)~~~~

9 lCo (iflaquo at ~Sdf~7e 4-( p~ oF

0 V ~-tlaat iHy~t~tOmiddotmiddot71-~R CA4f~(S ~ SQIJ-fo ~ 0 J

A Ie dI o~ctves4ltSet-f0r1f~~ ~ c () ~-t bull i- cmiddotrd~ ftftfiSttft S ~ fa-5~ 1Gtt cri(S t ( 4It ~fo-6etc~ Gllf f~S A lS 0 4laquol 0 A ~ IV~ IIG(C4((o(Af ~ oAmiddoto~ t 0Bmiddot O~ ~ OAloB OP4 ACoj

wi+lLAoB=L8~A Wt3ttLlOMdOl~ () - ~ LOA8= LogA ~

Aamp~ = OA _ r~A A6 0(3 - OB

=) Ae r lo A~

-------- --------~

)ampa-cle i (~tlcptleofto A ~cQlt$ A 1ckc ~tiatt~

ampl if tlyen~ t ampe- ACBD - A~middotq) +AD

II( V c bull I

SoJn C-sidelt -kfSiCll At 1 vuu~j l)is Cpoundlaquotef bull J ~p-J~ Ygt I) - t t e y fatH4) J -k ~ro-atdc qf ~ec ~~A~ I Q

I iIC ~ AeC SilCamp ~ IH 6e - c I

J vue b -ftt (1) We t _ 1 _AC~ r - Be - - middot

iDA ~ 01gt1gt AJ)middotC1) tt Mltrtrllj b~ lAOmiddot~]) CO~2 1aJkSimiddotces amporeJ

A6amp c) +A)xBe Acll 81gt middot

Re fICS 11L sf ~ eat be ltoftrec -to ~t -I- ~1-tllAt t MilcO + AtgtICBC =AC 1CI1~

~V Asctgt S (l u~ ~lJ4~ 0-shy

~S6~~~ kfCfS4tJ foJt of~~ -+k eampIt~ otIIIetStM Ai ~itlt ~s -fIc ~o~~ rote iIt wJere -reIs CIMif s Mesc(t _

-

6x4t~le 2 Lt ABc 0 be ~ ~tllt t(kft~ suamp~t At ampt so liltftStct At Y1tt ~r AtO P~t~( -Ke -refltecf of 0 ~fOSS AS BC C)1gtA A~ C4IIcYdtc

p _ c $Lt-~ -71

Lcent P~ ~So k ~fut f-~Wi _ 010 0 flO Msc CD lgtA Ye cdIVt bull

sc =l Ott foIIttll is ~iIr~le-t -fo site (5 -tk Ptt-RS l~~( (Sl~~14ft

e IcentS 0 0 -to tts e_~Hrlt OSAP DfBQ ~CR O~DS ~ludlC~~ J J -J ~ _ bull

-tt TltitCirtlutdts Ie CA Ca Cc CD rtsrdtuely CfSMoSmiddotd fIf~iQ 3(0 r ~r31gt0 By ~ct(s)

I~ AC Q( e04~~t ofo ~gtltS

cfct (+) I CA SIrcent to filllt LA fllAlrd to 81gt CIrs

Set to ~ IIt LB ~(c of Ac I C ~ Sci fo c tAlC -to ~lgt1 craquoisSeoet t ol1t LD~E lc ~

0 0 r~-t 0lt1

L Nen bull

CpnCa= 0r~ LAf Le P )Mjl-ly 4~t( LI) R J ll)n~ So bull

$r~ AcJ Mgt PClKs ~~Ic~4J~~ ~ fet h) PampRs is floc

~

G)Cdtpt f

Le-t P bft Af6~-t ~S~ 4l1It Appound ~~~-t LAPB-LACS LA(C-L~8C

Ltt tgt amp be ik~~tS 0( AAPS )AA~C nspecflf ~toe ~l A1gt 1gt1 ce )wtet A fOiWtshy

~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

( )tlfamp 61) biSKfs IA8PJ By ~t CT) ACAfACf~ ~ ~ I3A - XA So iSttf ACAeACampA

P ~f - xpmiddot ~ P~B6+lCApLcA8 J

C-1-1 ~=~ 5tRCt X ( 4ft AP ampt ~1It By~t (s) 1 ~ tCp~=LCitA ~ ~ I I~ fQ is Seoct of ( ~ ~~ 1 f4$s~~3C o listf SiacCrtIeO ~ -T(Alrl~f4lrgto ~~(1)1 tIIet pamp ~t(4C~I~Ois~tfo(0

A ~IgtC A~te A lU)e bullA p A APelAcIIgt f-c ~) I SIWICamp

I

~ ~ ilt3t +00 c( ~ 1 PQ fh ) Qm Q J r bull bull ~ t01 setc~ 10 t of I I

No LM~-L~8-=-LIWC-LAec f~ $(amp ~st ~JO 0 Ao( ~J~~ ~ Atl 43~ t (-d 0 ~ A61PcD

fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

Page 14: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

CiiID ~tlt~ firLiA BC let 1gt be A4Ie GtIlOc1tf- E 001 As loIiti DEit-CB J ~ F ie 600 Be I

ciA ~fDf oX ~~ o-rbmiddot 0 1 ltt ftt XIS G(( Gr be 01 EP ~tS~t ~ el~ttrlgtedo-r W~~~~fk~t~s X Ao D C fSfoFc-=Ep-=BYc1gt=r

~J ~sted oR we rMj Sity ~ i 7 middot PrDV~ 6i-F fs pcmI(e( -to -Me 4 b~ 1 -M CaJamp) Xl= Of-~ -tI S~1 je Y-X Sol-I Set 1ampt o~ AtAo tt(-~ IMc

For ~fS X It we e Ix-+f ~ lxl +111 ~ft Tie E 8 Gfl = C ot~~ E (0 r)klgt(d~ 1- W-11IAy f X= ~t(r-s-e t~o A~ F tB t(f-t)c 4( euroj =tE t-((-f)J) _ h Let Pbe 0 poillt el LIle )( f lJe lter t= B _ L _ amp1gt g + (_t )e~ middot gtY haYCamp oP=toX+(f-t)oy -f=~y ~ Be -- r -i1gt-t ~_

J J gt1( 8 -I io O~)y~ amp(01] ~ P-u SfjllleMt Xt E retgt I $0 IE-BI rD-cl c1

EICjl1t Call a ~1IIecent ~ ~ QjgtWelC ~l~ (I- ) Is (E -amph 1l ID-d r-(t-amp)(c(-f6-Jgtfd tl )ltLJ )M ~ ct j~ Ie ~od ~ orF9fe sk~ J i q F- Gt = t6-p)~+ (I-t)(1-9)C ~ +~hw ~t cf -tk s IIf-t4 Jgtllrl1lpounds Of ~t(tei _ IS tlt-p)amp1~$ htfampt iits~etet ~ik~litetllllorltl -tlt-p)la (amp+~~ =(~~k1NIllelo I _1 t f4IIIl ltf1ltS

Sll~ fir trl4t~ A~c~ Itt-A IlIamp 1M OjL ltf 114 (tw~-for ~ pound Me~ --ik se ~fOW twI ~ _ Igt IC-tO - f ~ if

T -poundTI-r -pound ~ I A=0 1)~D i(1el IC-BIt lo-dtll)~

UI8iC-1gt1 +11Hlt-at=Iel+ Ie-IgtI+11gt1 +1c_~(f~~t Wt ut Ie+IC-Igt ~ Iamp+c-tgtl t=~f1f)

AA IDI + IC-61 ~ 11gt+C-81 C-~AO=~8C) (gtt) holds ~Le~ft~~lcJs A81(1)C ATgt Usc _~ __

c6hf--I--l~1gt~ ItiC

~1- ~t fmiddot~~ 0+ ~ 0 ( is )(Y=tJC( (1 rsti - Ex4k+ Let 0 ~~ (i(cAt cf 4ABe 9 ~iIt J bef -fIl lfcffS Jf -IIf (t) Xi=fX (y+I)zmiddotXmiddotZ+fmiddotZ 0( (cXl-Y~(Xmiddoty) ~ I~~)(middotX I IXmiddot~~hd1I O~iOf (=) Xmiddoty-O ~~~~~~~~~~~~~~~ amp--ft 3 Let A8C b Le lmiddotts ~sfmiddotmiddot Phe

Ac~+amp~+A~-t8C~~ Ast+ctl SJt~~ Set1ie Ot~I ttt A ~~t f Jw

CmiddotC +(amp-lgtHamp-~)+D~ (8-c)~-c) ~ amp (c-b)laquo- At~(~- awl lt~~-f4ls s fu ~4S

(6 C-b)middot(S-C-lraquo ~ 0 ~~ck s (amplt-1) ~o

A ~t 1gt Ie -tLt poit ~ Aamp -L II ~ e _ ce~AAcO

p C fgtrcw _t C1gtJoe ) AS-AC Sol~~~~~~~dO~A

A a A J) A J)= ~ E=~~ =3 +~lCJ1gt-C=Aamp-2C

C1gt1 Oe- (A-tS-le)(Mc+1raquowO c) No AA~lh c C C(CUM(bull (IampSt 8 41f1$-bull (4) bec u Amiddot(Q-ltAB-ACO 1IeJtt(~) ~ OAl ~c ~ A~~AC

euro ~ toJs ~ 8lt~ 1)-A69 seAPS fWlkl ~JCOc $ firAABC jf( t ssewu-J -ptMf ~ c= - ta-+CmiddotfI AAS( its ~ttd q ~1 - If We Sampt -iU CitClIMChH- 0 AS ken -HII-srft~ ~o -t r -11 __ -~ -1 ALh--COtt - 7J 0 OtlGCnx n - ~-

A Fit iAcetft tJf ~~ c 0( lU= ~ = L

co b AI c lt-c

e ~ 1)c 1gt= te+(t-t) C t --amps ~1i~ poundL = tD ~+ cC C bI-c Gte middot I t A-t -~)tgt t-ll- A

aAtlS cc_ - tgtA - M~C 14 e middot

11l Lqt-(gt OmiddotkC Gtctal ~ICef c(H ~r J

51_ Set 5 4lt C4fColt_bull tu e -H Matel~Me1~ 1~ AA+b$-t C shy ~ 4~(

Lampil~gt 1omiddot~(i-1)l4-1) lt0 A-A 6middot~Cc=(tlJ 2ec 6amp+cc-(a-c)(amp-Q=k~middotIf (A16i)riamptc~ Rlt9~~ 11- 3( h_ Imiddotltl-C) 4l- 2(~~(H- btCi)tI~)) cttC

)(~+c) (-1)((-1) =((~ t1 -Hi+(() lt 0 of -~ f (ib -t-e) lA+Il+ ct )+ilaquoc gt~ CifI+cl+Jl(c)+ ~ ~ a(-o)(--G)-4-~-c)(b+cc-4)~)gt0 tsc4 rc s

~ Ike fRS ~ f xi xI wt -Stl-fculot 11-$9 (t)=LXOY) 0( tiYfft~e~ -fo -tkt fl~~ 1-- oxY J e

lti) ~ -f~)( ~f)-a)( l t Yltl (c~wYcxnyJ (j - )(~1 4fT~ A X0( V~~ p A of yl t1ft 0

(6laquo Q bull 1 lj 111)1 (DW~v e

eJ41~ Let AAA A _j A 1 1_ -+ V]nq DO 4 CD e I

- its ste ~tS p-Ilt1 ProiIla-t middot ClrtllAA1Ar oreAA AA So(u-tVf SeL ot - ~ -_amp I~ _L ft--A A ----- ~ fJe ~ ~ --fI 01r~~ O4St SMs ~qIt ~t)~csCA-A) I lA_-A f

E)Ctl-eIlaquo-r Let A6COf tgt ~~ pe-tft Qc e t

~~~Q~ ~ 1kfwlrids~ A88CCIgtbEpoundA 1T~ -r APamptl~J~ le ACDIIIampf6i -laquo s~O~ tk-t ~s Ooet is so eM eII bullbull ~olt4-tfN ~et -ckt O~bullbull~ rt -e ~_W f~ S~

tJ 1(t0 AXC ~ AP ofe (o(iu o=A-f- A(~ J C- 32s amp A

lltc t))tA SIA~y 8)(1)= (1(8 CxE~ C I

raquo)(A 6llgt re EJ( 6 =CcE feMtt I

eurolCAJ- E)(6-t( - ~lte+El$ ~ pound10 eImiddotmiddot

1 ~~-A~)o (As-AJ1gt(~A~ S ~~CI amp euro1tf6lc~ ~se Ac Adol~ -t(t-t Lit set - () middot At

At~ t ~It~ AsIC~ Al~-+yen+yJAI (

_t a ~ - bull

~ 2-shy

I _0 c A 6 c ~ As V ~1~Ut 1 Sjtllc -fb ~BIC~ fW(t

ftdle ~ts of BC CA AB ns~chvell -tk ft1~ -tIua-t

No A bull G 8 A I ~amp Ca A~ (orr eU egt~ 4~_ A~itlA-~lClA-As~=(~tAtAr-tAjcA -~~ StthtlI4It ~ SaJc1ttA

(Nmiddot~~i~+Ar~~l ore4 l1A AAs = Are 1J~~Ai

Aft13 amp11 C=A-ttils-A)frSollletoA~] SiCt AS e Gfe i eRe

o~ (Bt-A)K(~-A) - (A-ttz-~tl-t- t t)AxB No ~~=~~~-=amp-AH-t)e ~~1 S-a-= It-t1)A I Ct = lAt8)- c tlA +ll-t~)B ~ (amp-AI~I~(Cz-~)=(t-ttl-trtl-+t~t))Al(amp~O A S~ CL At( ccdllfttor

~t ~~ 1~~Pt

o

C[~1D --r-0 vetlOf) )( lf ate Jt~y wtt-t---t f~ t -flat ~f~ ClX~yO kAs 01 Soat~

AT 10 o T4 s tktCcStI ~~A rf KttO ~ X0 f Art NIt Co((llteor

F4t IT AX+bY+c =0 ~$ote -e 1~I(z-s 4t4l 4-+amp ott -=0 J ilQA Xf Z 4le cbullbullI btACcS( ~l AO fIe b-tc-o w X-1-KZ-tYc-6Z

(~ar~11to(~1 wr~t--J Lftai c~ s OAAampA Co

~ OeLamps 1f 1 -1z- Aa6~l~8ampR AsampIA~= ~ 6 8-c amp-S tltcl A DAR 0

~e COIIfttAt t ~1 =- 1 ~ ~ P Pl) P3S~ Set - orlll at o at A8 btt ~trs Ale LIDa (ampfbv~ ~ A~ rA Q( e s So 8 1-t S6Wt (s EIt Cll No

Pl =tAt(c-t) 8a trA+ (ct)s ~- ~3 lAAt-tQ-) 8-= tA(-aA+Cc-ct)S a S~tU~ ~ 0= ltr- CArgtA + [pound1)l -(I-I4)$]B

A~ (tally rcf~=gt tr(~ Otu( (l-tl~-laquotlt)S=C Solll fott ol -tit pt~~ -+-s f ti ~I~Js

Nt ~~e ~ 1tu~~A+ SoSzCt-rl g$t Vs- r~ r~- r~1 Pgt1s~S)A+~s(tmiddotgt8 R= rlrfgt~A ~(I)J B

Y~-r)S) ~6a-t~S) amp c) ttS +fs-1S ~ p~f~P+~sampf-tj~

~ P1 ~se~rw)~c 0 Qtlgt+CoO ~ r fL cU-1- fc-i (ove

~ 0

A - -

~ FOf~lamp~

(1 -laquo ~C

fot-CA~ to ~ t t amp -t~~ crt a ~tc ~ El(tend~ltl St L laquobe ~[A8Cl Js~~i~ R= 4 C

Let ( ~t 4ct nwts lt 4e GoismvmcJt i-R- tl 4J~)(fo~of AAsc Sr ~ l=~~Yslt) ~ bc_

S A -- - 0 21 1iltelaquoe s dolAt C~d~middot ~o~ uI1gt ~ s~amp s~~C middot T 1_ ~ rI n -rf (i-- shy

tl Ie or~ DraJ clmiddotae~t 61gt 1pound Si ~ A= ----=algt i IS lle~ ltJOiOlSA0

~~~~~~~~~~~~~-~~~~=~~~~ p adEr-l-~a~~r~ A- oS+- jtus c~ - c e c I) p(]) Let 18(1gt L~Ms

I4dtt rAsel Or S~8c1oI(lcl~ 1leflAftt Let A6nct)p -r1 ~act 0

~Me C ABC ) GlUo~kc ~ PAx P6= Pc x PD = tl b~~=Abc bull P19tpound Note L APD L (PB

4R A1BC)aHd~ckLPAtgt=LPCBS=tfA-tb~~) is ike seifieAc ~AAPDACfB~=~~ PAIPB=fxPD

amp Q C Of 4A8C Lri pc C 1amp-~ ~~ PC Is -lt-~t lat t lie i4 jCbullbullr 4l( M6C Qt r Ie -i4~ to -e -fde ~ A A8C if (JJ

C)~ ~e icltc1e ot AAec ~e p A e OYlJ c fCL p~~re [Mel =[ALel[~cl+(CI1= ~-t~+~=SIr ~ Not~ LArc=LcPB

I-tfllWlbull [A8tl~ S($-11 ) (s-b)(s-c)middot I pCs f~ot -to LACp4C ampP(~ Cos C= tt2ttoa-c (~AI Ci(~ircl 4 MBc B 2shy

[A6Ci= ~SiIlC=Qr(+coSp(i-($C) ~AAcPACBP ~~ fgtc PCPAlltPB =(Cl~-+Iot-c~t-~a~-9 ) = catlo-4 t )(A1(-c)(CoHI- b)(o-Il-~= S (s-c)(~~

2- ~ a

Ci C [AS(I A 2

~

I

~JJI LPFA-=odeg=Lpe~ ~ amp~ ~LPFeLPAE

C5Ji) ~tolt1 s-ThtOfotfll Let A 6c~ ~t dlSncf ~ts 01 bull ~c ~o - Me~IA~ 1( bull t Of~~~I ~Ot bull -Tht~ bull Sa c~tOV M1 C(liofIPT potd~ A 6 C Iie to

AI 6 C 1gt (1~t~c 1gtpound fCLR atfmiddote ZA ~A A ZA bull -~ -iA ~Co~ PAQ~clf$ WeA~ ZA~lA I tc Z~t

pFAECc1dk

bull ~ Srlloi(y taCgt6~~~-lPFB ~ pG~ f CDCCYcbull LPampb LPFI) = e 1klaquo AIJ~P LPAespoundp8C pfE _ LPeP 8EF (0(1ltlt~L PFE L~8Tgt~ LFP - L 10 collirAfampff

)fgtC)~Jl~~ ~ ASC1HAol6C=AcS]) bull (~~_ ~ktI AeCO At)ItBC ~ACdtgt 1)~c 190pound 0 sWLe AB UJlfsftfUct A ampA6

S~~41 to flCAP 1I1elt AB A~ 6eshy

6 Ai - 7ligt= (1) lBAE=LCAJgt

SO LMc L BAlgt-L1gt= LeA1gt-LMe =LEAt) Tkeuro1 A8AC~Ae-A1) So Rr-c EDAtgt~A Thet Aec~ A~8C =poundItampE AClC E~ AC80

bull A rC =c Sf-t Ell I

f1-I-4j hoW~ ~8euro~EtgtS ampb ~ E iUt~( SO - ~~oeA~LeeALtgtCA ~AsectCO Sltffc

SoSoft ~oe 1et~6cP cl-ampd-p~ 0

tI~ Let l)poundF fetf~~ff- P~ ampa Aeyen~~ ~

Asse ~Mist (so4 is 6~UA_JC ~AGSC ~O bull G ~f( Aalec~o)

tt~e9 7eff

fovlaquos X I Z ate (es Aamp ampCA D ((t~ve-()ty It X I Z (lie (dl-lflOr

A ~f f6 lhg--1 ~ xe YC LA - middot ~ lQt Dbu (~ Ac soct1IIt 81gt II J( Z -r1teuron

~g ~ ~ 1t~ ~z Se AlC 6Y c~ _At P1Q (i~ ~y Ie ~c -- _______ r tamp iU I bull laS yc fA ~Igt ZCZA middot lCI~ lIeeu~ Ie~

If ~ tL ~ =-1 iIamp )( YL MHo l~(~ Y~t~~~~ SlJ) Ltt l~ X(OCA -Thtl b Mt11Idtw 11~ Ax ay CI _ lt Cz Y Cl iiiK zA --i ~o --=-l1toobull CfIea bull _Cl -a

I I

ceDD ~MelI s lIeo~toA l~tA I ~cc t) euro ~be tc~ lO 0shy

de lw~~ ~( ft amptCtSSCti 1 tf (~ diC- (~QEf ) bull

t p Ae ti l)euro J Q Bel pound f 2= Cl)n fA ~ ~k ~ Q1t ottc(l(ea~ ~QIR~~~ -

f~ 1 ~ ltt X~EfA 1AMCD bull ~ z- C~neF Arr~l ~(atts ~ff 1e-(fM1oec~ FA

ftt- Ool~~~ 4xf l w hVII

e-- ~ X K __( It X2 ~_( t ~~II Qx 6y Ct ~y pzex I fllFxijmiddot 1I

Hul~pr~ ~ AIl ~~ tfffSfctj cofI4t tt XA)(B XEmiddotKF J (CmiddotYP=1AmiddotYS ZEmiddotZF= zeZIgt W~~et ZQ lSf~-i igt PQ~ ore rlfltelaquor

Qx Pf Itz loy c-enc ~Mee(AaS

t-rks ~ere 0 Imiddotil~ (1$($ of PoucJ s for It we tftwt Ato 8 -te I AIwIJ (3 il(cJe 1Iofl1-t i AB will b~ ~-t1l3et (iot ot B ~ It~j CIt~ we ells JpoundAoflt ~ t~ liflE Clt B b~ BR

6lCtJfC i F~~ h Cf(Ultirc~ ot Mac J f(it 1) ( ~ ~i~0yen ot -t4l~lE I~ ~tA - ~~ Be ~ e fM 1fe ttusc(e~ of-ffwf3ct (tt4-t C3L1r~ CA~ F= bt ~ ttfStd~ of -tINt ti-~-f Imiddot~t ~tC wo( Aamp 11161 PI Ell F o~ ctU

Soof~fIyen P=Mo 8C ~ E= BBnlA f=CCnAB APP~i P~f ~ ~(fo MB See I fott et 1gtpound f c-

-- =JSiiiiIii

b)lAtc ~ Let-tgt 0- eht ~cfs 0( dt101 AtCS

AS ~ AC O~~e (ilcu-R( Mac ftspciwJy l(t tgt Ilt ~f AtC sCI ~== DPn SA J R= PEn AC fro +~-t lile QR~s~(QVJ14 fttCf+~I (~ 1) ~ f9bt-Mshy~e 1)rff0--AS- CO ~SfctsLAc8

Co ~r ~ qftllCr At =lgt 6 ~LAec So 1= Cl)n G8 Sf_ eEtS

Q tgtPt SA DP 8ital R= Pe C Pre ttL PlE AI

AIP~ f~l ~ 1Ito(-to C ~ P er ~ w 1 ~ bull 1I

t Set I Q Rut tIff~ Co~~d~

~ -7

Alt IXu q j

elf (Ga1(e 3 Ltt AT3CPs e ~ +s tMDlCJe ~-rd AAfLBS Bat LeA) ccf LAB fat 1gt be ~ls (I ~cucl1t ~c4( I

DA(11)C= AU DB()CAe~ 1gtCIAB~ fgt~~ A~ r~CtfaJ T4 6v~fi ~ IAGC a~ Co((~((r

~olf- W HL-cI oy-((~( ~ AA Be Ne

AAIB~I)Cc(-=I DArBC=A 11gt1( ISc AtA f Cc -= H L lAlA I C I Cl

1t~()cD=C1 ~l (AIBl (cjAfrrr5~5Gl ~~ t DAAfCC tgtlt Se4 A HC tit c11ilaquoraquo SIt 1y ar171~ BS41s(to AS e 0cc we Su e H 6ltve c1(i~amp r A~ H C~ S4rt a(((~4~ I

-~ ALI)f ~fle1 tt P toe a ltpor i~4Mec

LtfP I~~ff~I$f- 5 -to ~CA Camp ft~t~ lttt bJ() ~_ eshy

ll 10 ~ fet ~~~N~ c-tohs API sp (~ftvtll IfQ P ~ 61bullbull Pt14 PttNQ~~ (tries ~tll~ Qfz cod A~ aft ~et

iSoLttd- $(fCJt L CPc p) LCQLP LC~P Lc (gta Palt-e J -t ~es c P ~L I PI Q p 4ftcocttc f~AfrI15 ~s middottU(Woto ~1l$1 w-tSu CPt ( gt e-= A ) P t1t( QIP= X ) (Q-a Pf P2C-= B 4re CoI~rtelr $6 Rb2-l amp1L ( AB-=Xmiddot ~ ~lIQ P~IA8 tVe ~Cqfre~

NewtDJ S

~A ABcOS~~(laquoteJktvsa e ~SQiraquoeamp c~tkt~~ ~~

APgtsc CD) PA AXcpotlts EFG)H-~t~ C F B ~ACG~FHgD~~r~t

Sol~tcNI W E6nFHO~ Eftn FG ~X _Apply~~ ~~scJ ~ ~ -to E~ltSJ F f(f ~Sta E~ () Fr =0 ~~ ( 14 1) I G Fn H( X are ut(ltealf_ ~ltfcAy~ltP~CA(s ~e- 4 E6--()FF~~ J ~S14

EEn FF~ B euroH nf6=X amp-t-fn ~euro 0 tUllPtfcmiddotc4t

-nus ~S 0 XI oJB ~c((e4~ 7itN pound4 fl Ff n6D=O SlAry EG F-- ( AC - O ACE6 fH6DCPotrclO

1)ec~CAes ~ 0 nfAaAec ~ JACc) M

A c B actgcP J CAnCpQJ AampnAgR ~r--+--Ir-~~R If AA 613 I cc 4te ~tVt-ct ~

A e 1-~ PI ~ Rctil eo(IQ4(_

c~ rCP_ R2esrk ~-s ~ -tyenUL te~ 4 ~~cAAfIdgre IfV --IfU ~ f 4s root G-oIer ~Ns c~ AOAB ~ftJJ MeoJ- -~r ~ et QPL AEa gil

At A rltamp -7---1S ( rt l g 0 () I 4 ~ ~ Ie Be Cctf~ Lloec Ilfct-Jt ~~ C~ c~ IJOCA ~ 1te(J C~ BP Cd M oct ~

B8 PC-co ~-( ~ No CC~=-( ~(ff~~~sctmiddot~~= - ~ (IC4M~cfMtl~~~ote- ~ et eampI c-f(er

62Y ~coJ A~s tttt ~Cct~lI1tr

Let Cn-les C ~ Cz ktwe ~~t ~~-fe15 0 ~ 02

Sf 11 4st f( J 14 (cs of ( OotX w~ 1

fe- ) t ~ lt twitt ()~ -tu Cl

eo( C~ ~Ilt ue 0 K- r 4)-~ J ~ ~ li~ f(~ok( -to OO~ -rtgt Is -4 (~~a1CSof tLt -f~Cnrd u

MOtse ~3 Crce~ CJCC1 W~~ OJOaoJ(h I~ nf CiamplttJ -tfe 3 ~ ltWQs ~FoS offI Wi( i~~(JItct cent Do fgti- ((lt d4 vaJOJ aftftfT4crtfes 111$ ~It lw la-I fIwe wi(( v-espue to 4((3 ccle$

G7~~14~S

~ If 2c(c~sCp~ lte~tAt PQ ~ p Cl aJ hss fou 0 411(1 yen

middot~ Ot J To Co J C So -ky tore eM ta noe(tk( ~ 2 r(4-~ ~ pIA i~( ~~ oS

~yenI4l~~~

P------ ~ c~ Lf4rdes C e d lifest J e we c- tltANJ A f(rrzl cltJ~C

~~ ~~~eAJf- 14 1

Ci-- ntcl ~~~ CJCl ~ CCsII i~~(t et -t4 ~ C4tt p1-Cch~~

~P~ f LoDa is ~er~ AK~Of CCz _

Let ED be ~~~ foSflctorf oft B~ MaC ~D ~S~e AC -ri Cau~tt1e c1A8JgtC ut ABtttE J(e ~ cfC4c~rc(e c1 AB D MflId 8 Ccent F-=-c --r

D (Olt ~t AE =- CF So 1$1 i te~d~ c~ ~gteJ AE~AB=ADAC II CFIltCBCD CA So~= ~~

5 ~c 81gt fsecfs L ABe WI_ Cl) ~ _ I bull It rJC AS - AD CF- f1C

------------------~ ampA~fel Let ABC be ~ ftrJMIj(e ~ soscJes 68C[)I

CAE AASF ~te~(1 to AAsC wi( ~ CA Aa 4 S bu1 tsrtdvel~ Pro~ta ~-t 141esff-1 AJSc ~ t ~ I~es t=F fEgt DE ~dJ ~uc(~t

Col Amiddot ~ SJltto i Late ~e cnl~w-f( Jgt4Sr~ ~ IE ( - eatu r4~ ~Cgt cte

a~~c~~ Iof crde middot1itE Ultoofe Y04oc Jl Y l AE=CE ( tel btcte(~w-I(Fu

c~ Cc~-tr ~cL~4S AF=8F - I -r4e-tltlfte~ A PUr~I T (~ff I ~~ fiIolu ~ ts ltfCI C1 $f lltty ~amp~ 2 lies Cltt VIIIt~~ ~c c) ~ roampoIaJIlt) of (14So -tkey ~u(4t fAa ~~ Camp~tet

63DP I

r ~e A ScIampf~ 2 LtP be 1ft l~~

~ Ii~~(-kB~lIc(~ -to FD-f _ bull 11C ra(~~ to OE -tt~ fOIts frolle M 1 Elf c(frelttf

S 7c IL ttgt ~-JC 1l rgte ~ t

I

I A~ C~ $oIf1 Let ile cncrcft~ J) ~=HF - PD eF -61) OJ rD-peuro-C~1 EAtlA~1eSamp Ql (A~ AF =SF I CD-c CEAGJPF t 81gt

2 l 1 0 F pW~ ct - fE =AF -AE S r~L pound ~ POtt 1 ~CAty4W(t t

- t_ EICIt1k 3 AC--damp l-H aat 0 P~r -fl Ie A4M C ~ usc -t ifegtSltct ~- Ae Id t W S let

Be It N Let 1k u cudcl 0(AAac -lt1 aNll~Std ~t B t ~ middot Pe ~~t OlUaM

SoIwt t ~ C4Samp 61 Be we6~ 11 aM i~ ~ ~ftthlte Qt S of cYG vtIeof poundlASC 1ICft OM =oel 8M

A~p BA18C i4e c~~In CAsamp - AUN AAec ACfo K~ 1Iotf1Ar (S1Cc iMruw Ibl~cto~ L kll Ac AC Jolaquoaret tes) s e rdeo( I

I

pound I ~e AC kN J 8M Itteet 41 4 (IOIt P I

Siell L PM N L 81lt11 l HCA s MIC PAte CDhcrkcl Q ttl I t fill pou fOitJ BMlC ~p 8M ec 80- yo Y=OA

PM r8- PNICPK POamp-r~ bull ~ $Jtmct~ 1keuro92 Ie -t 10- eo~= ampf(tM- rM) PM - 3

rJ It

OMl PB lr F6 ~t 8MPM+6I1I

OM J ~M

L I A6cb be i$(~Ibullt co_~4 tt ArllAofOo Q-t d - amp c~ f A1)1 SC ~ f (aros

Ccle i VI ( 4 E f= ~~-t t I~oes ampe Q= f-o -Ie C

8y po -t fI-t~ Po~_~ peltPD=PHxPl ~_ ft QClltQ6=~d~Qs~tAcff we1et Po~-Qo=CFM-ru) ~ fMQ~ -ns i (Ies 0ML PQ lQMO Itf oM

Ntrf Csd tIe C~C wi4 Q0 As d-cr~ 2 _ bullbull

It t-sses ME F SlAte LampMO LQ EDt -lCl fo s ~ CIC-z Ef ~ Ef -s iU c($ ef ce Let cI has ceth A( ~s tt lie

laquoa ~ ~ t JFPO _r - flMx pQ fiCa _Vi ~ P$ 01 ~ bull0I

A(Igt~ ite-sect PQ 4t M +Q -of leM _ LA0(= l paceW ac- ~ 8I(C ~ lttlclc p ~_I c 1_

let ya~s t Cltn~ I ~_0 =c bull t if crftit C fc$wt

~l~Sshy c1iW ~ 14- - l-l-~t1 A IS ~f~~J i AA6C J 0 i-tala

C(cuCttdlt~ 7Le -(kfee 4-ttJes AP eamp tMJ Cf irUktt- H EDAA6=-M FDo AC-N tp~4-dcent () 06Jl)F )OCJ1gtE

N C~) 0 J- M N middot i

Solfen bullCO LAfcc9cfLATgtC 9 A fgt l=~C6AtyJrc TktL6lgtFcLBAC AooBc-OCi--ees LOBC-=J(t~Io~Leoc)middot1tl_l8A(= ~oo~L8bFmiddot F omiddot Iamp -=gt 08 ~ tgt l= ~frly DC lDe-

B 0 c (~) CLMA ltPgtM~MIf AC~HI () I 81U AlA ~ NIi-IIIt= Aa -AltlaquoJI tgtA L

F ~c ~ l)e - ~ Aa~Ac (c~

~~b )N6oIp 13Ai~80-- OllADI (0( 1)04 ()-(~)+(()+ll)-~~ J)M~ ~_cot=OMOt)1 te

bull Ott J MAl N~-11 fI ~=C)jI 6lf1

~iet SoU- ln LAFC0 =LOC-dJACl) Fc-tkc ut J bu])M So ~t TeI [)f -ue L Jeo L 6gtF =LeAlt ~ J-f4 a~t (~e tB

4 ~t~4Yclt ~ JNle gtetpeId~ bs~CtoY til g 1 I J 1) 4te 0 ~J

=gt 0t3lJe ~oS i DF Q(A~ DCLbE wHk ~ CSV ftt Ae efT I c AC~J~DI ~ (ltt 6e If Be I I I 01 tl( AS 1POW iI f uIlh) SrlOCo Ae1gt = aq rW1d1C by d~ l~testJ~ t4PtwI- Let lc SAe -de -CA k)sU AABC f 2AamptI

NA ~ NC NF ~ rJ SI AC ~ dbullt ~fieaa~(L ofM$C ~=~ so tr~ of ~ bullbull ftc~(eNs() ~ ikatQ~oJ CoxS qf ~ Grtles Q-14III ~ if ITI ~ YM~(-l A~s 7I-e lmiddot 11M rOI(A)C1lt D ~~(S liIOH

r 6middot 1- r IAC- UComiddot

041(ms AhOYllo-lety wi1kceterO a-J Ptto k (cltwaof-d ~1 H(oJ 1lt) ) is Q ~CI itt setVls Jllttl r01ht X 01 ~ plAtte -t 1ile ~c~ X sampcck -tk~t OXL~ -= ieoX ~~rk~ It kl~1)~~~~ti saA3Jkf~ l-t lFl ltl J ~ -tk kPJMDffty 5 ( ~ A IrtySe~ Q -~ f ~ - ilc ~3~ ~ 12tlgteuroFbe~Js~8CCAM~ ~ (-((Ali) Secs AAsc +0 AAFE

amp 1gtJ C Let q Ie ilaquoo cttIL 0 6A-QC SiAte GiA =-2GfD GS -2GE ~tqt=-2~ s ~) ~IAbEF f AASC EXAfe L L AABC AB =AC A(iRl IS t -t t_1y to tIP cnuantt14MC4t~rMs pte AC ~tf~s P Q~ Pe 1l~ 1e totiJpoNltt (fQ

~114t llCeftgt ofAABC Sott~Let 0 bt 14 cgftt ~ -

) rele Lt 1gt foe ~t3et totlaquo 6 c 71 -t4 Circle +ipound Clttt-atd l4AOC

S 1) l3~yf A-trot ~ PQ

ADfAt -= ~~~~=~=Ic S HcAl)So04s I ib 0 S111tt O~$-iLalAltbullbullfMc t ~-tl_W-~tIecf-

CfajiV ~~ s A~t~~etsVI At AlAJ ISdVt4 well -scfes~e l A az (i) (~ts~ Sltk Cif(IOSitc Ai) fW IZ N ~~+-~~Re ~Ill~ ctrck ~ fMlf a c-~ ~lt 0 c-I

II~ iw~le laquo 3Ie -tno1 eel Ct rd -to ufS A

~ of stJes ~u+-1- middotfDItf-t G 1Cf ~fj -t4 (nuCampolttt ~~+riAe ~-tIa ~~it cO (6([e-t etft

A ~t Let A 6e ( It ~~scf 4~el cltlu ItS 54014 1 ampJ y be -fl- ~offu arcres SCrz

e ~C At otamp r 1A~f~~ ~ It 6gt Ilt

N611 Ae ~tly I B~ Iec t CAlieA Ids A is ru~ ~__~ Aamp a-( AC I So AAIb~Stt-t~ L fMc gti((y Mi~~ LMe e-l ee ir1kcts L seA So Mo( ern ee=- (-(A ~~dAIC

AI (IOOoJ 0A I De = ae r So 0 ts-tfe c~af of AAe d kt P~c4rc-ctr~AA6C

1k ~o~1 ~ (1 A) SeLs AABC f 6Aec ~ SeJ t~

scre-~-tP~MOC-tc~ OllA~~ bull middot 1 P 0 ore co((eAt

- fiscl 1( AASCGs ~IIe1lt ~~~~W (~- ~~L ~Ioc L

- L- ~ bull - 2J~ ~(IC= 8(~(s-lt)

ot t Ii -l 1pound is -(I ~K(~ ifCirde ~ Ill laf S bt-tl nf(~ ltgtf I IIIllyeltt t ~oflA bull

~ (e~ M s M~SzM)S3 ~~rrelaquo At s~ let 6 ~ bullt _ r

blse~ 4 poundA 00 ~-te 4 We c~ S~ SJ 1 M MJ

A 1iamp A --To t~t iampt elite- o~rf-tLt (i) IIIiilsrtt t Aamp1le rtfItJ-f 1 ts S I Co

-tIt vtt4lfO c4 -rs T~ ~tCf AT AIT~ 7iIese if L1I $ =ll~Imiddot ~iTt~lltSl~~t~ L T t S~-LTITa S1~1

(i) 11 A A ~ $S~ AA i MM ~ i 3 I ~ A T~ AI S~1 ~~ HzMl ~ ss I HsM bull ~ co ~ffWbull( ~dSr Nect CircCl1C(~ ~ASsz$3 reI 0 AA A~l

Ctcmiddott of A M~H IIbtepofcrceS~MAJ~r~ ~1 fLAA~AsrL f2 J ~ VAdtoos ~~

Z bullSo --Gtdes ~ 1Io(~ Ll lB~ reggt ampSt~~ AMMz toil s~~i~~ ~lt (x M- SLLt Ill ~bullbull04 S 1-ta~X l1c H ) Mz $1

~=(lttc-o)(c-M-~fl~e) 1 M M amp41 S)Jltl~ UrJ~Cost lt~~~~~(fo) ~ ()bc HSt~Zeuro~X

CT1tW EtA-f tt 1- bull ~A be ~iAt 4+etse~ ~ fwo nO~fD~fUtf Cirdes C ~C CAl-~ef0 0 (tltjreJ~ Dtte ~1MtM

~t~o c eamp 1d1t(s-et C cent~ Cztlt Pt J(e -i4af(EV (A~ ~-t-te~ctc At ~Ca~t QI Lk Me t ~~it-t~ ()Q o-J ~ ~ ~itet ~ pzCla

~-t ~ LtJAo LMAMz

~~ ~ ~

SGl~ B-t~etJ Plpt(gtzOt~~O

Ca ~lJZ~ damp bull nwy 14(0 oPa ) Q SeKds C L 0 PI

~ I ~ t -lO Z bull ~ J ~ OAn Ct =8 ~~-oflt~1 e $ Ll016M -tLl~A~~ So LOI~= LOaAHa A~ t- fs 0P 0 P ~o ltlie sjI Ie~ 00 Cgt~ ofL ~ ) 00 ~O~e-=OPct=OAIOg

t ~te~~-1 cknl4t1 ~ AO~ ~ Ate ~Itc

~ LO8M= lDAM

A~ I =gt LoAM L~AMz WIAamp~ ---

L 0cA M~ ==gt L0 A0)- L I-i A Mz bull -to _16bCrfkSf~S

Solt~p Wpound(CS JTbe reflec~ ~ S Wit-(S~ltt

fI5 Mis

~J e

t ~lwt Cgt (1Of ctImiddotd i -br3frt -+0

e $ f(~

Q cmiddotnI F -tkt bcs of tIl YOII f Sue- fut ~e-re ~)f Q

01 ~ w~ M ~ ~(eoi~ ~ l R~~ QS ~ isc~e~ C~rdamp 4 A PQ R

-to M Lt u be 04

~ A$ iudQ~~ltofe1 middot~~(R C V Lat ~ 10 ampl yo~t~14 fc

Co -fI kottcrt(e+y wfoit4 uW( P-tkt StI~ l t

~CtCte (_oppos-e P -(f ~ T middot (1 ~ Set$ U -to (Q((esr-~~-toflfobulltHf lt 1) Ii P~n (= v ut s setft~~ ~ t PQ~ ~

TR SQ=S - PR= PV- PIlt = Vlaquo=n ~ T T So 5 01 Ae ltT0 e ttl

ampruJt~J) fr p~ ltTaee~ UT ~ U

~ l(P Ifamp)Se0v4 u to ~ C(telte e to c~ l I- UtoT So TT Let 14tats~ P-4 C ~+~t5ect r ~Q~R ~

ampS-=s- Pflt=Pv- P((--Vre =TIC=-TIlt ~ tiM -i1s-MS Ti-f1T=-jiM PtSAt4t

~ El4middotrle b rio t)

Lt-A~c ~ co ftiI5le ~ ~tof scl Be A1k ~tsct- N ot l ~AC i~+fSoct ~c ct tJ ~~r~I~ k~ +0 AN -+~~ N ifersets AM 4 Q -c AB -t p -n ~f-lrJrmiddot 0 li~e to APt Pt-a~AIl laquo 0 middot Pofe Qo l Be SIt- TfABAc1kMNQfampAQMol3c

WLOG I ampS$f41111t A6gtAC Let AN MttStcf Uttucrclt fAABC j 1) ~

-- - bull c L 1gtg CL lgtAC=L~Llgtc~ e lAo M f~ r ~ ~ DC aJ PM 1 Be

~o Ho~y K(A ~StovlsA6j)(+oAgO(t4 08 O~ aq ae Itt t= Be( PN -r4~

L Ogt- L b8e =LM8=ro6_LAop=LoP~ ~ ~ D 0 tcKl orooc

I ) I J GfeCttrA J~c J~M4 ~ L 0 - Lep - 1 0 - 7 1- - 0 - 0 Igt IC tS~ amp It sc K is AM == AM l PfI=Q

I I ~ Lg eto L~~O~)oo 1~ ~o LSC g c It Be r

F l

(~p Sol~ middot Let dort FE ~wt -to nr2 4Ss(oll (iJ

Feuro () r C Lt r 1 U04s~r 111k ~y1- (M V)Sets P t r c-to K) Iiamp JE t jilt L AS

sow1 bull Ff 1Ie L ~ A is +lt1 ~roIldrc FE LNEC ~Afe~LAME I rSo L ~~eL~A~)~ LlNEcLlAMc ~ ACAeuro ~e1IA I ~ ~ pouer ~ A ltiol4Isped to r is Ac AM= AE S~M(tAfy I 16fJe t ~A i-fk -(~d -to ~~ Aft A~ A - A ~ =lttiJPOiqJ ~FeJ 56 Ae==-AF (1amp tflt11- rAAtcd - I

_ ~S AI ~ fIr2 AA~f ~ etc )~lll fu ett(4-ik1t f t fl1 pues-~r 1gt 61 sJMe~1 t ~OI)O~ wt Soc Oa I ~~t ~~ Ctgt

~ Ltgtco~=LClgto L cLeF ~s ir~S COa b~s L 9CF $ceCfiS~f rl So

Cl) is ~so~~~ -to re

E)(4flt

amp($ PI Ira Q-te ite~Iy ~ t ~ rt M N~oJtlJ ~ r fGs$es -tI- caff( 01 ~ r~

lAe r tgtit cl1illfr iii r rio MAn=C MBfr=D f (0 ~It CD $ 1~jkt to r2 bull

~ C~ IS - tYgtctStIt

~~ A ilefSVsv wi CAAer 0 oJ ugt r gt0

(amptatl 1 J(o r)) sA~f~ +lAo Se~s A~et(1 ~(t X 0 to ~ i~e VOl~t X O~bull y at sucL fut OXmiddotOlec r~ ~ CWOIelcu I fo X=0 ~ Utake )(=~ _-cl tllSo~)(-=QO Wt-take X=o

1ke Circle -w+1 C2~+e~ 0 A~ ~kCamps r gto-((ct k poundSle ~e~ ~ I~e IWJy 4fso ~ft A~ ltrs~ by sff~t ~ CrCJtL (lWt~middotcP

fGcfs CO Gift1 ~I((S~ ~ ~ bje(~~ it f~~ u~ 00 -to -t~lfmiddot ~ ~c-t J ex ) X ~

reg -If )( s-ikcRiC iwe~~1~ XI=X bull f)(~o~elf(enX~

= bull 1 ~x ~oit ofTaTl) ~t-rrl 4i~

P e ~ X1 lCT2 4~f~~-t1~ ~s iS k~

- __ OXmiddot ox ((sec LTo)()(ycsLTox)r~ ACtreJtt ~~SSi~ 14ftJUJ 0 ~~t +0 A cvdc bull ~ya16tj -4r~ O k iII-s ak~cIc -poits ~(~ St -to ~amp~ foffts l4 fOit 0) ~~fets

of -flit G~ a41~ aJa Afe utllt4r bull JotlfoItr~~tf(~-kGttk ~~set fotleceofv-f~ ~~ctrJe ~

A(fJe vaSSoVJ4-f 0 is Set -to 4 (euro reuro IS ~~~fI)~ 0 ~~s ~~k(+ifia1e-t (It( -t 44td Ito Cnverrely (A (middot1U1IIJt rssj-tlt~ 0 is Seltt -to ~Cvde (w~~ 0 Ni-l -tttllj~-t Imiddotier0 ~Itd to ~ leilt

f r A~At pCiSS~ 14 0 es SetOf ----1-- To e~setl ~ ~ _

Ifgt reg If two cr~ (f~ttIlC~ C4fVts ~(( ttlso ~~(etAf ~ fbft Pto)~~~~

9 lCo (iflaquo at ~Sdf~7e 4-( p~ oF

0 V ~-tlaat iHy~t~tOmiddotmiddot71-~R CA4f~(S ~ SQIJ-fo ~ 0 J

A Ie dI o~ctves4ltSet-f0r1f~~ ~ c () ~-t bull i- cmiddotrd~ ftftfiSttft S ~ fa-5~ 1Gtt cri(S t ( 4It ~fo-6etc~ Gllf f~S A lS 0 4laquol 0 A ~ IV~ IIG(C4((o(Af ~ oAmiddoto~ t 0Bmiddot O~ ~ OAloB OP4 ACoj

wi+lLAoB=L8~A Wt3ttLlOMdOl~ () - ~ LOA8= LogA ~

Aamp~ = OA _ r~A A6 0(3 - OB

=) Ae r lo A~

-------- --------~

)ampa-cle i (~tlcptleofto A ~cQlt$ A 1ckc ~tiatt~

ampl if tlyen~ t ampe- ACBD - A~middotq) +AD

II( V c bull I

SoJn C-sidelt -kfSiCll At 1 vuu~j l)is Cpoundlaquotef bull J ~p-J~ Ygt I) - t t e y fatH4) J -k ~ro-atdc qf ~ec ~~A~ I Q

I iIC ~ AeC SilCamp ~ IH 6e - c I

J vue b -ftt (1) We t _ 1 _AC~ r - Be - - middot

iDA ~ 01gt1gt AJ)middotC1) tt Mltrtrllj b~ lAOmiddot~]) CO~2 1aJkSimiddotces amporeJ

A6amp c) +A)xBe Acll 81gt middot

Re fICS 11L sf ~ eat be ltoftrec -to ~t -I- ~1-tllAt t MilcO + AtgtICBC =AC 1CI1~

~V Asctgt S (l u~ ~lJ4~ 0-shy

~S6~~~ kfCfS4tJ foJt of~~ -+k eampIt~ otIIIetStM Ai ~itlt ~s -fIc ~o~~ rote iIt wJere -reIs CIMif s Mesc(t _

-

6x4t~le 2 Lt ABc 0 be ~ ~tllt t(kft~ suamp~t At ampt so liltftStct At Y1tt ~r AtO P~t~( -Ke -refltecf of 0 ~fOSS AS BC C)1gtA A~ C4IIcYdtc

p _ c $Lt-~ -71

Lcent P~ ~So k ~fut f-~Wi _ 010 0 flO Msc CD lgtA Ye cdIVt bull

sc =l Ott foIIttll is ~iIr~le-t -fo site (5 -tk Ptt-RS l~~( (Sl~~14ft

e IcentS 0 0 -to tts e_~Hrlt OSAP DfBQ ~CR O~DS ~ludlC~~ J J -J ~ _ bull

-tt TltitCirtlutdts Ie CA Ca Cc CD rtsrdtuely CfSMoSmiddotd fIf~iQ 3(0 r ~r31gt0 By ~ct(s)

I~ AC Q( e04~~t ofo ~gtltS

cfct (+) I CA SIrcent to filllt LA fllAlrd to 81gt CIrs

Set to ~ IIt LB ~(c of Ac I C ~ Sci fo c tAlC -to ~lgt1 craquoisSeoet t ol1t LD~E lc ~

0 0 r~-t 0lt1

L Nen bull

CpnCa= 0r~ LAf Le P )Mjl-ly 4~t( LI) R J ll)n~ So bull

$r~ AcJ Mgt PClKs ~~Ic~4J~~ ~ fet h) PampRs is floc

~

G)Cdtpt f

Le-t P bft Af6~-t ~S~ 4l1It Appound ~~~-t LAPB-LACS LA(C-L~8C

Ltt tgt amp be ik~~tS 0( AAPS )AA~C nspecflf ~toe ~l A1gt 1gt1 ce )wtet A fOiWtshy

~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

( )tlfamp 61) biSKfs IA8PJ By ~t CT) ACAfACf~ ~ ~ I3A - XA So iSttf ACAeACampA

P ~f - xpmiddot ~ P~B6+lCApLcA8 J

C-1-1 ~=~ 5tRCt X ( 4ft AP ampt ~1It By~t (s) 1 ~ tCp~=LCitA ~ ~ I I~ fQ is Seoct of ( ~ ~~ 1 f4$s~~3C o listf SiacCrtIeO ~ -T(Alrl~f4lrgto ~~(1)1 tIIet pamp ~t(4C~I~Ois~tfo(0

A ~IgtC A~te A lU)e bullA p A APelAcIIgt f-c ~) I SIWICamp

I

~ ~ ilt3t +00 c( ~ 1 PQ fh ) Qm Q J r bull bull ~ t01 setc~ 10 t of I I

No LM~-L~8-=-LIWC-LAec f~ $(amp ~st ~JO 0 Ao( ~J~~ ~ Atl 43~ t (-d 0 ~ A61PcD

fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

Page 15: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

~1- ~t fmiddot~~ 0+ ~ 0 ( is )(Y=tJC( (1 rsti - Ex4k+ Let 0 ~~ (i(cAt cf 4ABe 9 ~iIt J bef -fIl lfcffS Jf -IIf (t) Xi=fX (y+I)zmiddotXmiddotZ+fmiddotZ 0( (cXl-Y~(Xmiddoty) ~ I~~)(middotX I IXmiddot~~hd1I O~iOf (=) Xmiddoty-O ~~~~~~~~~~~~~~~ amp--ft 3 Let A8C b Le lmiddotts ~sfmiddotmiddot Phe

Ac~+amp~+A~-t8C~~ Ast+ctl SJt~~ Set1ie Ot~I ttt A ~~t f Jw

CmiddotC +(amp-lgtHamp-~)+D~ (8-c)~-c) ~ amp (c-b)laquo- At~(~- awl lt~~-f4ls s fu ~4S

(6 C-b)middot(S-C-lraquo ~ 0 ~~ck s (amplt-1) ~o

A ~t 1gt Ie -tLt poit ~ Aamp -L II ~ e _ ce~AAcO

p C fgtrcw _t C1gtJoe ) AS-AC Sol~~~~~~~dO~A

A a A J) A J)= ~ E=~~ =3 +~lCJ1gt-C=Aamp-2C

C1gt1 Oe- (A-tS-le)(Mc+1raquowO c) No AA~lh c C C(CUM(bull (IampSt 8 41f1$-bull (4) bec u Amiddot(Q-ltAB-ACO 1IeJtt(~) ~ OAl ~c ~ A~~AC

euro ~ toJs ~ 8lt~ 1)-A69 seAPS fWlkl ~JCOc $ firAABC jf( t ssewu-J -ptMf ~ c= - ta-+CmiddotfI AAS( its ~ttd q ~1 - If We Sampt -iU CitClIMChH- 0 AS ken -HII-srft~ ~o -t r -11 __ -~ -1 ALh--COtt - 7J 0 OtlGCnx n - ~-

A Fit iAcetft tJf ~~ c 0( lU= ~ = L

co b AI c lt-c

e ~ 1)c 1gt= te+(t-t) C t --amps ~1i~ poundL = tD ~+ cC C bI-c Gte middot I t A-t -~)tgt t-ll- A

aAtlS cc_ - tgtA - M~C 14 e middot

11l Lqt-(gt OmiddotkC Gtctal ~ICef c(H ~r J

51_ Set 5 4lt C4fColt_bull tu e -H Matel~Me1~ 1~ AA+b$-t C shy ~ 4~(

Lampil~gt 1omiddot~(i-1)l4-1) lt0 A-A 6middot~Cc=(tlJ 2ec 6amp+cc-(a-c)(amp-Q=k~middotIf (A16i)riamptc~ Rlt9~~ 11- 3( h_ Imiddotltl-C) 4l- 2(~~(H- btCi)tI~)) cttC

)(~+c) (-1)((-1) =((~ t1 -Hi+(() lt 0 of -~ f (ib -t-e) lA+Il+ ct )+ilaquoc gt~ CifI+cl+Jl(c)+ ~ ~ a(-o)(--G)-4-~-c)(b+cc-4)~)gt0 tsc4 rc s

~ Ike fRS ~ f xi xI wt -Stl-fculot 11-$9 (t)=LXOY) 0( tiYfft~e~ -fo -tkt fl~~ 1-- oxY J e

lti) ~ -f~)( ~f)-a)( l t Yltl (c~wYcxnyJ (j - )(~1 4fT~ A X0( V~~ p A of yl t1ft 0

(6laquo Q bull 1 lj 111)1 (DW~v e

eJ41~ Let AAA A _j A 1 1_ -+ V]nq DO 4 CD e I

- its ste ~tS p-Ilt1 ProiIla-t middot ClrtllAA1Ar oreAA AA So(u-tVf SeL ot - ~ -_amp I~ _L ft--A A ----- ~ fJe ~ ~ --fI 01r~~ O4St SMs ~qIt ~t)~csCA-A) I lA_-A f

E)Ctl-eIlaquo-r Let A6COf tgt ~~ pe-tft Qc e t

~~~Q~ ~ 1kfwlrids~ A88CCIgtbEpoundA 1T~ -r APamptl~J~ le ACDIIIampf6i -laquo s~O~ tk-t ~s Ooet is so eM eII bullbull ~olt4-tfN ~et -ckt O~bullbull~ rt -e ~_W f~ S~

tJ 1(t0 AXC ~ AP ofe (o(iu o=A-f- A(~ J C- 32s amp A

lltc t))tA SIA~y 8)(1)= (1(8 CxE~ C I

raquo)(A 6llgt re EJ( 6 =CcE feMtt I

eurolCAJ- E)(6-t( - ~lte+El$ ~ pound10 eImiddotmiddot

1 ~~-A~)o (As-AJ1gt(~A~ S ~~CI amp euro1tf6lc~ ~se Ac Adol~ -t(t-t Lit set - () middot At

At~ t ~It~ AsIC~ Al~-+yen+yJAI (

_t a ~ - bull

~ 2-shy

I _0 c A 6 c ~ As V ~1~Ut 1 Sjtllc -fb ~BIC~ fW(t

ftdle ~ts of BC CA AB ns~chvell -tk ft1~ -tIua-t

No A bull G 8 A I ~amp Ca A~ (orr eU egt~ 4~_ A~itlA-~lClA-As~=(~tAtAr-tAjcA -~~ StthtlI4It ~ SaJc1ttA

(Nmiddot~~i~+Ar~~l ore4 l1A AAs = Are 1J~~Ai

Aft13 amp11 C=A-ttils-A)frSollletoA~] SiCt AS e Gfe i eRe

o~ (Bt-A)K(~-A) - (A-ttz-~tl-t- t t)AxB No ~~=~~~-=amp-AH-t)e ~~1 S-a-= It-t1)A I Ct = lAt8)- c tlA +ll-t~)B ~ (amp-AI~I~(Cz-~)=(t-ttl-trtl-+t~t))Al(amp~O A S~ CL At( ccdllfttor

~t ~~ 1~~Pt

o

C[~1D --r-0 vetlOf) )( lf ate Jt~y wtt-t---t f~ t -flat ~f~ ClX~yO kAs 01 Soat~

AT 10 o T4 s tktCcStI ~~A rf KttO ~ X0 f Art NIt Co((llteor

F4t IT AX+bY+c =0 ~$ote -e 1~I(z-s 4t4l 4-+amp ott -=0 J ilQA Xf Z 4le cbullbullI btACcS( ~l AO fIe b-tc-o w X-1-KZ-tYc-6Z

(~ar~11to(~1 wr~t--J Lftai c~ s OAAampA Co

~ OeLamps 1f 1 -1z- Aa6~l~8ampR AsampIA~= ~ 6 8-c amp-S tltcl A DAR 0

~e COIIfttAt t ~1 =- 1 ~ ~ P Pl) P3S~ Set - orlll at o at A8 btt ~trs Ale LIDa (ampfbv~ ~ A~ rA Q( e s So 8 1-t S6Wt (s EIt Cll No

Pl =tAt(c-t) 8a trA+ (ct)s ~- ~3 lAAt-tQ-) 8-= tA(-aA+Cc-ct)S a S~tU~ ~ 0= ltr- CArgtA + [pound1)l -(I-I4)$]B

A~ (tally rcf~=gt tr(~ Otu( (l-tl~-laquotlt)S=C Solll fott ol -tit pt~~ -+-s f ti ~I~Js

Nt ~~e ~ 1tu~~A+ SoSzCt-rl g$t Vs- r~ r~- r~1 Pgt1s~S)A+~s(tmiddotgt8 R= rlrfgt~A ~(I)J B

Y~-r)S) ~6a-t~S) amp c) ttS +fs-1S ~ p~f~P+~sampf-tj~

~ P1 ~se~rw)~c 0 Qtlgt+CoO ~ r fL cU-1- fc-i (ove

~ 0

A - -

~ FOf~lamp~

(1 -laquo ~C

fot-CA~ to ~ t t amp -t~~ crt a ~tc ~ El(tend~ltl St L laquobe ~[A8Cl Js~~i~ R= 4 C

Let ( ~t 4ct nwts lt 4e GoismvmcJt i-R- tl 4J~)(fo~of AAsc Sr ~ l=~~Yslt) ~ bc_

S A -- - 0 21 1iltelaquoe s dolAt C~d~middot ~o~ uI1gt ~ s~amp s~~C middot T 1_ ~ rI n -rf (i-- shy

tl Ie or~ DraJ clmiddotae~t 61gt 1pound Si ~ A= ----=algt i IS lle~ ltJOiOlSA0

~~~~~~~~~~~~~-~~~~=~~~~ p adEr-l-~a~~r~ A- oS+- jtus c~ - c e c I) p(]) Let 18(1gt L~Ms

I4dtt rAsel Or S~8c1oI(lcl~ 1leflAftt Let A6nct)p -r1 ~act 0

~Me C ABC ) GlUo~kc ~ PAx P6= Pc x PD = tl b~~=Abc bull P19tpound Note L APD L (PB

4R A1BC)aHd~ckLPAtgt=LPCBS=tfA-tb~~) is ike seifieAc ~AAPDACfB~=~~ PAIPB=fxPD

amp Q C Of 4A8C Lri pc C 1amp-~ ~~ PC Is -lt-~t lat t lie i4 jCbullbullr 4l( M6C Qt r Ie -i4~ to -e -fde ~ A A8C if (JJ

C)~ ~e icltc1e ot AAec ~e p A e OYlJ c fCL p~~re [Mel =[ALel[~cl+(CI1= ~-t~+~=SIr ~ Not~ LArc=LcPB

I-tfllWlbull [A8tl~ S($-11 ) (s-b)(s-c)middot I pCs f~ot -to LACp4C ampP(~ Cos C= tt2ttoa-c (~AI Ci(~ircl 4 MBc B 2shy

[A6Ci= ~SiIlC=Qr(+coSp(i-($C) ~AAcPACBP ~~ fgtc PCPAlltPB =(Cl~-+Iot-c~t-~a~-9 ) = catlo-4 t )(A1(-c)(CoHI- b)(o-Il-~= S (s-c)(~~

2- ~ a

Ci C [AS(I A 2

~

I

~JJI LPFA-=odeg=Lpe~ ~ amp~ ~LPFeLPAE

C5Ji) ~tolt1 s-ThtOfotfll Let A 6c~ ~t dlSncf ~ts 01 bull ~c ~o - Me~IA~ 1( bull t Of~~~I ~Ot bull -Tht~ bull Sa c~tOV M1 C(liofIPT potd~ A 6 C Iie to

AI 6 C 1gt (1~t~c 1gtpound fCLR atfmiddote ZA ~A A ZA bull -~ -iA ~Co~ PAQ~clf$ WeA~ ZA~lA I tc Z~t

pFAECc1dk

bull ~ Srlloi(y taCgt6~~~-lPFB ~ pG~ f CDCCYcbull LPampb LPFI) = e 1klaquo AIJ~P LPAespoundp8C pfE _ LPeP 8EF (0(1ltlt~L PFE L~8Tgt~ LFP - L 10 collirAfampff

)fgtC)~Jl~~ ~ ASC1HAol6C=AcS]) bull (~~_ ~ktI AeCO At)ItBC ~ACdtgt 1)~c 190pound 0 sWLe AB UJlfsftfUct A ampA6

S~~41 to flCAP 1I1elt AB A~ 6eshy

6 Ai - 7ligt= (1) lBAE=LCAJgt

SO LMc L BAlgt-L1gt= LeA1gt-LMe =LEAt) Tkeuro1 A8AC~Ae-A1) So Rr-c EDAtgt~A Thet Aec~ A~8C =poundItampE AClC E~ AC80

bull A rC =c Sf-t Ell I

f1-I-4j hoW~ ~8euro~EtgtS ampb ~ E iUt~( SO - ~~oeA~LeeALtgtCA ~AsectCO Sltffc

SoSoft ~oe 1et~6cP cl-ampd-p~ 0

tI~ Let l)poundF fetf~~ff- P~ ampa Aeyen~~ ~

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9 lCo (iflaquo at ~Sdf~7e 4-( p~ oF

0 V ~-tlaat iHy~t~tOmiddotmiddot71-~R CA4f~(S ~ SQIJ-fo ~ 0 J

A Ie dI o~ctves4ltSet-f0r1f~~ ~ c () ~-t bull i- cmiddotrd~ ftftfiSttft S ~ fa-5~ 1Gtt cri(S t ( 4It ~fo-6etc~ Gllf f~S A lS 0 4laquol 0 A ~ IV~ IIG(C4((o(Af ~ oAmiddoto~ t 0Bmiddot O~ ~ OAloB OP4 ACoj

wi+lLAoB=L8~A Wt3ttLlOMdOl~ () - ~ LOA8= LogA ~

Aamp~ = OA _ r~A A6 0(3 - OB

=) Ae r lo A~

-------- --------~

)ampa-cle i (~tlcptleofto A ~cQlt$ A 1ckc ~tiatt~

ampl if tlyen~ t ampe- ACBD - A~middotq) +AD

II( V c bull I

SoJn C-sidelt -kfSiCll At 1 vuu~j l)is Cpoundlaquotef bull J ~p-J~ Ygt I) - t t e y fatH4) J -k ~ro-atdc qf ~ec ~~A~ I Q

I iIC ~ AeC SilCamp ~ IH 6e - c I

J vue b -ftt (1) We t _ 1 _AC~ r - Be - - middot

iDA ~ 01gt1gt AJ)middotC1) tt Mltrtrllj b~ lAOmiddot~]) CO~2 1aJkSimiddotces amporeJ

A6amp c) +A)xBe Acll 81gt middot

Re fICS 11L sf ~ eat be ltoftrec -to ~t -I- ~1-tllAt t MilcO + AtgtICBC =AC 1CI1~

~V Asctgt S (l u~ ~lJ4~ 0-shy

~S6~~~ kfCfS4tJ foJt of~~ -+k eampIt~ otIIIetStM Ai ~itlt ~s -fIc ~o~~ rote iIt wJere -reIs CIMif s Mesc(t _

-

6x4t~le 2 Lt ABc 0 be ~ ~tllt t(kft~ suamp~t At ampt so liltftStct At Y1tt ~r AtO P~t~( -Ke -refltecf of 0 ~fOSS AS BC C)1gtA A~ C4IIcYdtc

p _ c $Lt-~ -71

Lcent P~ ~So k ~fut f-~Wi _ 010 0 flO Msc CD lgtA Ye cdIVt bull

sc =l Ott foIIttll is ~iIr~le-t -fo site (5 -tk Ptt-RS l~~( (Sl~~14ft

e IcentS 0 0 -to tts e_~Hrlt OSAP DfBQ ~CR O~DS ~ludlC~~ J J -J ~ _ bull

-tt TltitCirtlutdts Ie CA Ca Cc CD rtsrdtuely CfSMoSmiddotd fIf~iQ 3(0 r ~r31gt0 By ~ct(s)

I~ AC Q( e04~~t ofo ~gtltS

cfct (+) I CA SIrcent to filllt LA fllAlrd to 81gt CIrs

Set to ~ IIt LB ~(c of Ac I C ~ Sci fo c tAlC -to ~lgt1 craquoisSeoet t ol1t LD~E lc ~

0 0 r~-t 0lt1

L Nen bull

CpnCa= 0r~ LAf Le P )Mjl-ly 4~t( LI) R J ll)n~ So bull

$r~ AcJ Mgt PClKs ~~Ic~4J~~ ~ fet h) PampRs is floc

~

G)Cdtpt f

Le-t P bft Af6~-t ~S~ 4l1It Appound ~~~-t LAPB-LACS LA(C-L~8C

Ltt tgt amp be ik~~tS 0( AAPS )AA~C nspecflf ~toe ~l A1gt 1gt1 ce )wtet A fOiWtshy

~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

( )tlfamp 61) biSKfs IA8PJ By ~t CT) ACAfACf~ ~ ~ I3A - XA So iSttf ACAeACampA

P ~f - xpmiddot ~ P~B6+lCApLcA8 J

C-1-1 ~=~ 5tRCt X ( 4ft AP ampt ~1It By~t (s) 1 ~ tCp~=LCitA ~ ~ I I~ fQ is Seoct of ( ~ ~~ 1 f4$s~~3C o listf SiacCrtIeO ~ -T(Alrl~f4lrgto ~~(1)1 tIIet pamp ~t(4C~I~Ois~tfo(0

A ~IgtC A~te A lU)e bullA p A APelAcIIgt f-c ~) I SIWICamp

I

~ ~ ilt3t +00 c( ~ 1 PQ fh ) Qm Q J r bull bull ~ t01 setc~ 10 t of I I

No LM~-L~8-=-LIWC-LAec f~ $(amp ~st ~JO 0 Ao( ~J~~ ~ Atl 43~ t (-d 0 ~ A61PcD

fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

Page 16: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

~ Ike fRS ~ f xi xI wt -Stl-fculot 11-$9 (t)=LXOY) 0( tiYfft~e~ -fo -tkt fl~~ 1-- oxY J e

lti) ~ -f~)( ~f)-a)( l t Yltl (c~wYcxnyJ (j - )(~1 4fT~ A X0( V~~ p A of yl t1ft 0

(6laquo Q bull 1 lj 111)1 (DW~v e

eJ41~ Let AAA A _j A 1 1_ -+ V]nq DO 4 CD e I

- its ste ~tS p-Ilt1 ProiIla-t middot ClrtllAA1Ar oreAA AA So(u-tVf SeL ot - ~ -_amp I~ _L ft--A A ----- ~ fJe ~ ~ --fI 01r~~ O4St SMs ~qIt ~t)~csCA-A) I lA_-A f

E)Ctl-eIlaquo-r Let A6COf tgt ~~ pe-tft Qc e t

~~~Q~ ~ 1kfwlrids~ A88CCIgtbEpoundA 1T~ -r APamptl~J~ le ACDIIIampf6i -laquo s~O~ tk-t ~s Ooet is so eM eII bullbull ~olt4-tfN ~et -ckt O~bullbull~ rt -e ~_W f~ S~

tJ 1(t0 AXC ~ AP ofe (o(iu o=A-f- A(~ J C- 32s amp A

lltc t))tA SIA~y 8)(1)= (1(8 CxE~ C I

raquo)(A 6llgt re EJ( 6 =CcE feMtt I

eurolCAJ- E)(6-t( - ~lte+El$ ~ pound10 eImiddotmiddot

1 ~~-A~)o (As-AJ1gt(~A~ S ~~CI amp euro1tf6lc~ ~se Ac Adol~ -t(t-t Lit set - () middot At

At~ t ~It~ AsIC~ Al~-+yen+yJAI (

_t a ~ - bull

~ 2-shy

I _0 c A 6 c ~ As V ~1~Ut 1 Sjtllc -fb ~BIC~ fW(t

ftdle ~ts of BC CA AB ns~chvell -tk ft1~ -tIua-t

No A bull G 8 A I ~amp Ca A~ (orr eU egt~ 4~_ A~itlA-~lClA-As~=(~tAtAr-tAjcA -~~ StthtlI4It ~ SaJc1ttA

(Nmiddot~~i~+Ar~~l ore4 l1A AAs = Are 1J~~Ai

Aft13 amp11 C=A-ttils-A)frSollletoA~] SiCt AS e Gfe i eRe

o~ (Bt-A)K(~-A) - (A-ttz-~tl-t- t t)AxB No ~~=~~~-=amp-AH-t)e ~~1 S-a-= It-t1)A I Ct = lAt8)- c tlA +ll-t~)B ~ (amp-AI~I~(Cz-~)=(t-ttl-trtl-+t~t))Al(amp~O A S~ CL At( ccdllfttor

~t ~~ 1~~Pt

o

C[~1D --r-0 vetlOf) )( lf ate Jt~y wtt-t---t f~ t -flat ~f~ ClX~yO kAs 01 Soat~

AT 10 o T4 s tktCcStI ~~A rf KttO ~ X0 f Art NIt Co((llteor

F4t IT AX+bY+c =0 ~$ote -e 1~I(z-s 4t4l 4-+amp ott -=0 J ilQA Xf Z 4le cbullbullI btACcS( ~l AO fIe b-tc-o w X-1-KZ-tYc-6Z

(~ar~11to(~1 wr~t--J Lftai c~ s OAAampA Co

~ OeLamps 1f 1 -1z- Aa6~l~8ampR AsampIA~= ~ 6 8-c amp-S tltcl A DAR 0

~e COIIfttAt t ~1 =- 1 ~ ~ P Pl) P3S~ Set - orlll at o at A8 btt ~trs Ale LIDa (ampfbv~ ~ A~ rA Q( e s So 8 1-t S6Wt (s EIt Cll No

Pl =tAt(c-t) 8a trA+ (ct)s ~- ~3 lAAt-tQ-) 8-= tA(-aA+Cc-ct)S a S~tU~ ~ 0= ltr- CArgtA + [pound1)l -(I-I4)$]B

A~ (tally rcf~=gt tr(~ Otu( (l-tl~-laquotlt)S=C Solll fott ol -tit pt~~ -+-s f ti ~I~Js

Nt ~~e ~ 1tu~~A+ SoSzCt-rl g$t Vs- r~ r~- r~1 Pgt1s~S)A+~s(tmiddotgt8 R= rlrfgt~A ~(I)J B

Y~-r)S) ~6a-t~S) amp c) ttS +fs-1S ~ p~f~P+~sampf-tj~

~ P1 ~se~rw)~c 0 Qtlgt+CoO ~ r fL cU-1- fc-i (ove

~ 0

A - -

~ FOf~lamp~

(1 -laquo ~C

fot-CA~ to ~ t t amp -t~~ crt a ~tc ~ El(tend~ltl St L laquobe ~[A8Cl Js~~i~ R= 4 C

Let ( ~t 4ct nwts lt 4e GoismvmcJt i-R- tl 4J~)(fo~of AAsc Sr ~ l=~~Yslt) ~ bc_

S A -- - 0 21 1iltelaquoe s dolAt C~d~middot ~o~ uI1gt ~ s~amp s~~C middot T 1_ ~ rI n -rf (i-- shy

tl Ie or~ DraJ clmiddotae~t 61gt 1pound Si ~ A= ----=algt i IS lle~ ltJOiOlSA0

~~~~~~~~~~~~~-~~~~=~~~~ p adEr-l-~a~~r~ A- oS+- jtus c~ - c e c I) p(]) Let 18(1gt L~Ms

I4dtt rAsel Or S~8c1oI(lcl~ 1leflAftt Let A6nct)p -r1 ~act 0

~Me C ABC ) GlUo~kc ~ PAx P6= Pc x PD = tl b~~=Abc bull P19tpound Note L APD L (PB

4R A1BC)aHd~ckLPAtgt=LPCBS=tfA-tb~~) is ike seifieAc ~AAPDACfB~=~~ PAIPB=fxPD

amp Q C Of 4A8C Lri pc C 1amp-~ ~~ PC Is -lt-~t lat t lie i4 jCbullbullr 4l( M6C Qt r Ie -i4~ to -e -fde ~ A A8C if (JJ

C)~ ~e icltc1e ot AAec ~e p A e OYlJ c fCL p~~re [Mel =[ALel[~cl+(CI1= ~-t~+~=SIr ~ Not~ LArc=LcPB

I-tfllWlbull [A8tl~ S($-11 ) (s-b)(s-c)middot I pCs f~ot -to LACp4C ampP(~ Cos C= tt2ttoa-c (~AI Ci(~ircl 4 MBc B 2shy

[A6Ci= ~SiIlC=Qr(+coSp(i-($C) ~AAcPACBP ~~ fgtc PCPAlltPB =(Cl~-+Iot-c~t-~a~-9 ) = catlo-4 t )(A1(-c)(CoHI- b)(o-Il-~= S (s-c)(~~

2- ~ a

Ci C [AS(I A 2

~

I

~JJI LPFA-=odeg=Lpe~ ~ amp~ ~LPFeLPAE

C5Ji) ~tolt1 s-ThtOfotfll Let A 6c~ ~t dlSncf ~ts 01 bull ~c ~o - Me~IA~ 1( bull t Of~~~I ~Ot bull -Tht~ bull Sa c~tOV M1 C(liofIPT potd~ A 6 C Iie to

AI 6 C 1gt (1~t~c 1gtpound fCLR atfmiddote ZA ~A A ZA bull -~ -iA ~Co~ PAQ~clf$ WeA~ ZA~lA I tc Z~t

pFAECc1dk

bull ~ Srlloi(y taCgt6~~~-lPFB ~ pG~ f CDCCYcbull LPampb LPFI) = e 1klaquo AIJ~P LPAespoundp8C pfE _ LPeP 8EF (0(1ltlt~L PFE L~8Tgt~ LFP - L 10 collirAfampff

)fgtC)~Jl~~ ~ ASC1HAol6C=AcS]) bull (~~_ ~ktI AeCO At)ItBC ~ACdtgt 1)~c 190pound 0 sWLe AB UJlfsftfUct A ampA6

S~~41 to flCAP 1I1elt AB A~ 6eshy

6 Ai - 7ligt= (1) lBAE=LCAJgt

SO LMc L BAlgt-L1gt= LeA1gt-LMe =LEAt) Tkeuro1 A8AC~Ae-A1) So Rr-c EDAtgt~A Thet Aec~ A~8C =poundItampE AClC E~ AC80

bull A rC =c Sf-t Ell I

f1-I-4j hoW~ ~8euro~EtgtS ampb ~ E iUt~( SO - ~~oeA~LeeALtgtCA ~AsectCO Sltffc

SoSoft ~oe 1et~6cP cl-ampd-p~ 0

tI~ Let l)poundF fetf~~ff- P~ ampa Aeyen~~ ~

Asse ~Mist (so4 is 6~UA_JC ~AGSC ~O bull G ~f( Aalec~o)

tt~e9 7eff

fovlaquos X I Z ate (es Aamp ampCA D ((t~ve-()ty It X I Z (lie (dl-lflOr

A ~f f6 lhg--1 ~ xe YC LA - middot ~ lQt Dbu (~ Ac soct1IIt 81gt II J( Z -r1teuron

~g ~ ~ 1t~ ~z Se AlC 6Y c~ _At P1Q (i~ ~y Ie ~c -- _______ r tamp iU I bull laS yc fA ~Igt ZCZA middot lCI~ lIeeu~ Ie~

If ~ tL ~ =-1 iIamp )( YL MHo l~(~ Y~t~~~~ SlJ) Ltt l~ X(OCA -Thtl b Mt11Idtw 11~ Ax ay CI _ lt Cz Y Cl iiiK zA --i ~o --=-l1toobull CfIea bull _Cl -a

I I

ceDD ~MelI s lIeo~toA l~tA I ~cc t) euro ~be tc~ lO 0shy

de lw~~ ~( ft amptCtSSCti 1 tf (~ diC- (~QEf ) bull

t p Ae ti l)euro J Q Bel pound f 2= Cl)n fA ~ ~k ~ Q1t ottc(l(ea~ ~QIR~~~ -

f~ 1 ~ ltt X~EfA 1AMCD bull ~ z- C~neF Arr~l ~(atts ~ff 1e-(fM1oec~ FA

ftt- Ool~~~ 4xf l w hVII

e-- ~ X K __( It X2 ~_( t ~~II Qx 6y Ct ~y pzex I fllFxijmiddot 1I

Hul~pr~ ~ AIl ~~ tfffSfctj cofI4t tt XA)(B XEmiddotKF J (CmiddotYP=1AmiddotYS ZEmiddotZF= zeZIgt W~~et ZQ lSf~-i igt PQ~ ore rlfltelaquor

Qx Pf Itz loy c-enc ~Mee(AaS

t-rks ~ere 0 Imiddotil~ (1$($ of PoucJ s for It we tftwt Ato 8 -te I AIwIJ (3 il(cJe 1Iofl1-t i AB will b~ ~-t1l3et (iot ot B ~ It~j CIt~ we ells JpoundAoflt ~ t~ liflE Clt B b~ BR

6lCtJfC i F~~ h Cf(Ultirc~ ot Mac J f(it 1) ( ~ ~i~0yen ot -t4l~lE I~ ~tA - ~~ Be ~ e fM 1fe ttusc(e~ of-ffwf3ct (tt4-t C3L1r~ CA~ F= bt ~ ttfStd~ of -tINt ti-~-f Imiddot~t ~tC wo( Aamp 11161 PI Ell F o~ ctU

Soof~fIyen P=Mo 8C ~ E= BBnlA f=CCnAB APP~i P~f ~ ~(fo MB See I fott et 1gtpound f c-

-- =JSiiiiIii

b)lAtc ~ Let-tgt 0- eht ~cfs 0( dt101 AtCS

AS ~ AC O~~e (ilcu-R( Mac ftspciwJy l(t tgt Ilt ~f AtC sCI ~== DPn SA J R= PEn AC fro +~-t lile QR~s~(QVJ14 fttCf+~I (~ 1) ~ f9bt-Mshy~e 1)rff0--AS- CO ~SfctsLAc8

Co ~r ~ qftllCr At =lgt 6 ~LAec So 1= Cl)n G8 Sf_ eEtS

Q tgtPt SA DP 8ital R= Pe C Pre ttL PlE AI

AIP~ f~l ~ 1Ito(-to C ~ P er ~ w 1 ~ bull 1I

t Set I Q Rut tIff~ Co~~d~

~ -7

Alt IXu q j

elf (Ga1(e 3 Ltt AT3CPs e ~ +s tMDlCJe ~-rd AAfLBS Bat LeA) ccf LAB fat 1gt be ~ls (I ~cucl1t ~c4( I

DA(11)C= AU DB()CAe~ 1gtCIAB~ fgt~~ A~ r~CtfaJ T4 6v~fi ~ IAGC a~ Co((~((r

~olf- W HL-cI oy-((~( ~ AA Be Ne

AAIB~I)Cc(-=I DArBC=A 11gt1( ISc AtA f Cc -= H L lAlA I C I Cl

1t~()cD=C1 ~l (AIBl (cjAfrrr5~5Gl ~~ t DAAfCC tgtlt Se4 A HC tit c11ilaquoraquo SIt 1y ar171~ BS41s(to AS e 0cc we Su e H 6ltve c1(i~amp r A~ H C~ S4rt a(((~4~ I

-~ ALI)f ~fle1 tt P toe a ltpor i~4Mec

LtfP I~~ff~I$f- 5 -to ~CA Camp ft~t~ lttt bJ() ~_ eshy

ll 10 ~ fet ~~~N~ c-tohs API sp (~ftvtll IfQ P ~ 61bullbull Pt14 PttNQ~~ (tries ~tll~ Qfz cod A~ aft ~et

iSoLttd- $(fCJt L CPc p) LCQLP LC~P Lc (gta Palt-e J -t ~es c P ~L I PI Q p 4ftcocttc f~AfrI15 ~s middottU(Woto ~1l$1 w-tSu CPt ( gt e-= A ) P t1t( QIP= X ) (Q-a Pf P2C-= B 4re CoI~rtelr $6 Rb2-l amp1L ( AB-=Xmiddot ~ ~lIQ P~IA8 tVe ~Cqfre~

NewtDJ S

~A ABcOS~~(laquoteJktvsa e ~SQiraquoeamp c~tkt~~ ~~

APgtsc CD) PA AXcpotlts EFG)H-~t~ C F B ~ACG~FHgD~~r~t

Sol~tcNI W E6nFHO~ Eftn FG ~X _Apply~~ ~~scJ ~ ~ -to E~ltSJ F f(f ~Sta E~ () Fr =0 ~~ ( 14 1) I G Fn H( X are ut(ltealf_ ~ltfcAy~ltP~CA(s ~e- 4 E6--()FF~~ J ~S14

EEn FF~ B euroH nf6=X amp-t-fn ~euro 0 tUllPtfcmiddotc4t

-nus ~S 0 XI oJB ~c((e4~ 7itN pound4 fl Ff n6D=O SlAry EG F-- ( AC - O ACE6 fH6DCPotrclO

1)ec~CAes ~ 0 nfAaAec ~ JACc) M

A c B actgcP J CAnCpQJ AampnAgR ~r--+--Ir-~~R If AA 613 I cc 4te ~tVt-ct ~

A e 1-~ PI ~ Rctil eo(IQ4(_

c~ rCP_ R2esrk ~-s ~ -tyenUL te~ 4 ~~cAAfIdgre IfV --IfU ~ f 4s root G-oIer ~Ns c~ AOAB ~ftJJ MeoJ- -~r ~ et QPL AEa gil

At A rltamp -7---1S ( rt l g 0 () I 4 ~ ~ Ie Be Cctf~ Lloec Ilfct-Jt ~~ C~ c~ IJOCA ~ 1te(J C~ BP Cd M oct ~

B8 PC-co ~-( ~ No CC~=-( ~(ff~~~sctmiddot~~= - ~ (IC4M~cfMtl~~~ote- ~ et eampI c-f(er

62Y ~coJ A~s tttt ~Cct~lI1tr

Let Cn-les C ~ Cz ktwe ~~t ~~-fe15 0 ~ 02

Sf 11 4st f( J 14 (cs of ( OotX w~ 1

fe- ) t ~ lt twitt ()~ -tu Cl

eo( C~ ~Ilt ue 0 K- r 4)-~ J ~ ~ li~ f(~ok( -to OO~ -rtgt Is -4 (~~a1CSof tLt -f~Cnrd u

MOtse ~3 Crce~ CJCC1 W~~ OJOaoJ(h I~ nf CiamplttJ -tfe 3 ~ ltWQs ~FoS offI Wi( i~~(JItct cent Do fgti- ((lt d4 vaJOJ aftftfT4crtfes 111$ ~It lw la-I fIwe wi(( v-espue to 4((3 ccle$

G7~~14~S

~ If 2c(c~sCp~ lte~tAt PQ ~ p Cl aJ hss fou 0 411(1 yen

middot~ Ot J To Co J C So -ky tore eM ta noe(tk( ~ 2 r(4-~ ~ pIA i~( ~~ oS

~yenI4l~~~

P------ ~ c~ Lf4rdes C e d lifest J e we c- tltANJ A f(rrzl cltJ~C

~~ ~~~eAJf- 14 1

Ci-- ntcl ~~~ CJCl ~ CCsII i~~(t et -t4 ~ C4tt p1-Cch~~

~P~ f LoDa is ~er~ AK~Of CCz _

Let ED be ~~~ foSflctorf oft B~ MaC ~D ~S~e AC -ri Cau~tt1e c1A8JgtC ut ABtttE J(e ~ cfC4c~rc(e c1 AB D MflId 8 Ccent F-=-c --r

D (Olt ~t AE =- CF So 1$1 i te~d~ c~ ~gteJ AE~AB=ADAC II CFIltCBCD CA So~= ~~

5 ~c 81gt fsecfs L ABe WI_ Cl) ~ _ I bull It rJC AS - AD CF- f1C

------------------~ ampA~fel Let ABC be ~ ftrJMIj(e ~ soscJes 68C[)I

CAE AASF ~te~(1 to AAsC wi( ~ CA Aa 4 S bu1 tsrtdvel~ Pro~ta ~-t 141esff-1 AJSc ~ t ~ I~es t=F fEgt DE ~dJ ~uc(~t

Col Amiddot ~ SJltto i Late ~e cnl~w-f( Jgt4Sr~ ~ IE ( - eatu r4~ ~Cgt cte

a~~c~~ Iof crde middot1itE Ultoofe Y04oc Jl Y l AE=CE ( tel btcte(~w-I(Fu

c~ Cc~-tr ~cL~4S AF=8F - I -r4e-tltlfte~ A PUr~I T (~ff I ~~ fiIolu ~ ts ltfCI C1 $f lltty ~amp~ 2 lies Cltt VIIIt~~ ~c c) ~ roampoIaJIlt) of (14So -tkey ~u(4t fAa ~~ Camp~tet

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r ~e A ScIampf~ 2 LtP be 1ft l~~

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Y~-r)S) ~6a-t~S) amp c) ttS +fs-1S ~ p~f~P+~sampf-tj~

~ P1 ~se~rw)~c 0 Qtlgt+CoO ~ r fL cU-1- fc-i (ove

~ 0

A - -

~ FOf~lamp~

(1 -laquo ~C

fot-CA~ to ~ t t amp -t~~ crt a ~tc ~ El(tend~ltl St L laquobe ~[A8Cl Js~~i~ R= 4 C

Let ( ~t 4ct nwts lt 4e GoismvmcJt i-R- tl 4J~)(fo~of AAsc Sr ~ l=~~Yslt) ~ bc_

S A -- - 0 21 1iltelaquoe s dolAt C~d~middot ~o~ uI1gt ~ s~amp s~~C middot T 1_ ~ rI n -rf (i-- shy

tl Ie or~ DraJ clmiddotae~t 61gt 1pound Si ~ A= ----=algt i IS lle~ ltJOiOlSA0

~~~~~~~~~~~~~-~~~~=~~~~ p adEr-l-~a~~r~ A- oS+- jtus c~ - c e c I) p(]) Let 18(1gt L~Ms

I4dtt rAsel Or S~8c1oI(lcl~ 1leflAftt Let A6nct)p -r1 ~act 0

~Me C ABC ) GlUo~kc ~ PAx P6= Pc x PD = tl b~~=Abc bull P19tpound Note L APD L (PB

4R A1BC)aHd~ckLPAtgt=LPCBS=tfA-tb~~) is ike seifieAc ~AAPDACfB~=~~ PAIPB=fxPD

amp Q C Of 4A8C Lri pc C 1amp-~ ~~ PC Is -lt-~t lat t lie i4 jCbullbullr 4l( M6C Qt r Ie -i4~ to -e -fde ~ A A8C if (JJ

C)~ ~e icltc1e ot AAec ~e p A e OYlJ c fCL p~~re [Mel =[ALel[~cl+(CI1= ~-t~+~=SIr ~ Not~ LArc=LcPB

I-tfllWlbull [A8tl~ S($-11 ) (s-b)(s-c)middot I pCs f~ot -to LACp4C ampP(~ Cos C= tt2ttoa-c (~AI Ci(~ircl 4 MBc B 2shy

[A6Ci= ~SiIlC=Qr(+coSp(i-($C) ~AAcPACBP ~~ fgtc PCPAlltPB =(Cl~-+Iot-c~t-~a~-9 ) = catlo-4 t )(A1(-c)(CoHI- b)(o-Il-~= S (s-c)(~~

2- ~ a

Ci C [AS(I A 2

~

I

~JJI LPFA-=odeg=Lpe~ ~ amp~ ~LPFeLPAE

C5Ji) ~tolt1 s-ThtOfotfll Let A 6c~ ~t dlSncf ~ts 01 bull ~c ~o - Me~IA~ 1( bull t Of~~~I ~Ot bull -Tht~ bull Sa c~tOV M1 C(liofIPT potd~ A 6 C Iie to

AI 6 C 1gt (1~t~c 1gtpound fCLR atfmiddote ZA ~A A ZA bull -~ -iA ~Co~ PAQ~clf$ WeA~ ZA~lA I tc Z~t

pFAECc1dk

bull ~ Srlloi(y taCgt6~~~-lPFB ~ pG~ f CDCCYcbull LPampb LPFI) = e 1klaquo AIJ~P LPAespoundp8C pfE _ LPeP 8EF (0(1ltlt~L PFE L~8Tgt~ LFP - L 10 collirAfampff

)fgtC)~Jl~~ ~ ASC1HAol6C=AcS]) bull (~~_ ~ktI AeCO At)ItBC ~ACdtgt 1)~c 190pound 0 sWLe AB UJlfsftfUct A ampA6

S~~41 to flCAP 1I1elt AB A~ 6eshy

6 Ai - 7ligt= (1) lBAE=LCAJgt

SO LMc L BAlgt-L1gt= LeA1gt-LMe =LEAt) Tkeuro1 A8AC~Ae-A1) So Rr-c EDAtgt~A Thet Aec~ A~8C =poundItampE AClC E~ AC80

bull A rC =c Sf-t Ell I

f1-I-4j hoW~ ~8euro~EtgtS ampb ~ E iUt~( SO - ~~oeA~LeeALtgtCA ~AsectCO Sltffc

SoSoft ~oe 1et~6cP cl-ampd-p~ 0

tI~ Let l)poundF fetf~~ff- P~ ampa Aeyen~~ ~

Asse ~Mist (so4 is 6~UA_JC ~AGSC ~O bull G ~f( Aalec~o)

tt~e9 7eff

fovlaquos X I Z ate (es Aamp ampCA D ((t~ve-()ty It X I Z (lie (dl-lflOr

A ~f f6 lhg--1 ~ xe YC LA - middot ~ lQt Dbu (~ Ac soct1IIt 81gt II J( Z -r1teuron

~g ~ ~ 1t~ ~z Se AlC 6Y c~ _At P1Q (i~ ~y Ie ~c -- _______ r tamp iU I bull laS yc fA ~Igt ZCZA middot lCI~ lIeeu~ Ie~

If ~ tL ~ =-1 iIamp )( YL MHo l~(~ Y~t~~~~ SlJ) Ltt l~ X(OCA -Thtl b Mt11Idtw 11~ Ax ay CI _ lt Cz Y Cl iiiK zA --i ~o --=-l1toobull CfIea bull _Cl -a

I I

ceDD ~MelI s lIeo~toA l~tA I ~cc t) euro ~be tc~ lO 0shy

de lw~~ ~( ft amptCtSSCti 1 tf (~ diC- (~QEf ) bull

t p Ae ti l)euro J Q Bel pound f 2= Cl)n fA ~ ~k ~ Q1t ottc(l(ea~ ~QIR~~~ -

f~ 1 ~ ltt X~EfA 1AMCD bull ~ z- C~neF Arr~l ~(atts ~ff 1e-(fM1oec~ FA

ftt- Ool~~~ 4xf l w hVII

e-- ~ X K __( It X2 ~_( t ~~II Qx 6y Ct ~y pzex I fllFxijmiddot 1I

Hul~pr~ ~ AIl ~~ tfffSfctj cofI4t tt XA)(B XEmiddotKF J (CmiddotYP=1AmiddotYS ZEmiddotZF= zeZIgt W~~et ZQ lSf~-i igt PQ~ ore rlfltelaquor

Qx Pf Itz loy c-enc ~Mee(AaS

t-rks ~ere 0 Imiddotil~ (1$($ of PoucJ s for It we tftwt Ato 8 -te I AIwIJ (3 il(cJe 1Iofl1-t i AB will b~ ~-t1l3et (iot ot B ~ It~j CIt~ we ells JpoundAoflt ~ t~ liflE Clt B b~ BR

6lCtJfC i F~~ h Cf(Ultirc~ ot Mac J f(it 1) ( ~ ~i~0yen ot -t4l~lE I~ ~tA - ~~ Be ~ e fM 1fe ttusc(e~ of-ffwf3ct (tt4-t C3L1r~ CA~ F= bt ~ ttfStd~ of -tINt ti-~-f Imiddot~t ~tC wo( Aamp 11161 PI Ell F o~ ctU

Soof~fIyen P=Mo 8C ~ E= BBnlA f=CCnAB APP~i P~f ~ ~(fo MB See I fott et 1gtpound f c-

-- =JSiiiiIii

b)lAtc ~ Let-tgt 0- eht ~cfs 0( dt101 AtCS

AS ~ AC O~~e (ilcu-R( Mac ftspciwJy l(t tgt Ilt ~f AtC sCI ~== DPn SA J R= PEn AC fro +~-t lile QR~s~(QVJ14 fttCf+~I (~ 1) ~ f9bt-Mshy~e 1)rff0--AS- CO ~SfctsLAc8

Co ~r ~ qftllCr At =lgt 6 ~LAec So 1= Cl)n G8 Sf_ eEtS

Q tgtPt SA DP 8ital R= Pe C Pre ttL PlE AI

AIP~ f~l ~ 1Ito(-to C ~ P er ~ w 1 ~ bull 1I

t Set I Q Rut tIff~ Co~~d~

~ -7

Alt IXu q j

elf (Ga1(e 3 Ltt AT3CPs e ~ +s tMDlCJe ~-rd AAfLBS Bat LeA) ccf LAB fat 1gt be ~ls (I ~cucl1t ~c4( I

DA(11)C= AU DB()CAe~ 1gtCIAB~ fgt~~ A~ r~CtfaJ T4 6v~fi ~ IAGC a~ Co((~((r

~olf- W HL-cI oy-((~( ~ AA Be Ne

AAIB~I)Cc(-=I DArBC=A 11gt1( ISc AtA f Cc -= H L lAlA I C I Cl

1t~()cD=C1 ~l (AIBl (cjAfrrr5~5Gl ~~ t DAAfCC tgtlt Se4 A HC tit c11ilaquoraquo SIt 1y ar171~ BS41s(to AS e 0cc we Su e H 6ltve c1(i~amp r A~ H C~ S4rt a(((~4~ I

-~ ALI)f ~fle1 tt P toe a ltpor i~4Mec

LtfP I~~ff~I$f- 5 -to ~CA Camp ft~t~ lttt bJ() ~_ eshy

ll 10 ~ fet ~~~N~ c-tohs API sp (~ftvtll IfQ P ~ 61bullbull Pt14 PttNQ~~ (tries ~tll~ Qfz cod A~ aft ~et

iSoLttd- $(fCJt L CPc p) LCQLP LC~P Lc (gta Palt-e J -t ~es c P ~L I PI Q p 4ftcocttc f~AfrI15 ~s middottU(Woto ~1l$1 w-tSu CPt ( gt e-= A ) P t1t( QIP= X ) (Q-a Pf P2C-= B 4re CoI~rtelr $6 Rb2-l amp1L ( AB-=Xmiddot ~ ~lIQ P~IA8 tVe ~Cqfre~

NewtDJ S

~A ABcOS~~(laquoteJktvsa e ~SQiraquoeamp c~tkt~~ ~~

APgtsc CD) PA AXcpotlts EFG)H-~t~ C F B ~ACG~FHgD~~r~t

Sol~tcNI W E6nFHO~ Eftn FG ~X _Apply~~ ~~scJ ~ ~ -to E~ltSJ F f(f ~Sta E~ () Fr =0 ~~ ( 14 1) I G Fn H( X are ut(ltealf_ ~ltfcAy~ltP~CA(s ~e- 4 E6--()FF~~ J ~S14

EEn FF~ B euroH nf6=X amp-t-fn ~euro 0 tUllPtfcmiddotc4t

-nus ~S 0 XI oJB ~c((e4~ 7itN pound4 fl Ff n6D=O SlAry EG F-- ( AC - O ACE6 fH6DCPotrclO

1)ec~CAes ~ 0 nfAaAec ~ JACc) M

A c B actgcP J CAnCpQJ AampnAgR ~r--+--Ir-~~R If AA 613 I cc 4te ~tVt-ct ~

A e 1-~ PI ~ Rctil eo(IQ4(_

c~ rCP_ R2esrk ~-s ~ -tyenUL te~ 4 ~~cAAfIdgre IfV --IfU ~ f 4s root G-oIer ~Ns c~ AOAB ~ftJJ MeoJ- -~r ~ et QPL AEa gil

At A rltamp -7---1S ( rt l g 0 () I 4 ~ ~ Ie Be Cctf~ Lloec Ilfct-Jt ~~ C~ c~ IJOCA ~ 1te(J C~ BP Cd M oct ~

B8 PC-co ~-( ~ No CC~=-( ~(ff~~~sctmiddot~~= - ~ (IC4M~cfMtl~~~ote- ~ et eampI c-f(er

62Y ~coJ A~s tttt ~Cct~lI1tr

Let Cn-les C ~ Cz ktwe ~~t ~~-fe15 0 ~ 02

Sf 11 4st f( J 14 (cs of ( OotX w~ 1

fe- ) t ~ lt twitt ()~ -tu Cl

eo( C~ ~Ilt ue 0 K- r 4)-~ J ~ ~ li~ f(~ok( -to OO~ -rtgt Is -4 (~~a1CSof tLt -f~Cnrd u

MOtse ~3 Crce~ CJCC1 W~~ OJOaoJ(h I~ nf CiamplttJ -tfe 3 ~ ltWQs ~FoS offI Wi( i~~(JItct cent Do fgti- ((lt d4 vaJOJ aftftfT4crtfes 111$ ~It lw la-I fIwe wi(( v-espue to 4((3 ccle$

G7~~14~S

~ If 2c(c~sCp~ lte~tAt PQ ~ p Cl aJ hss fou 0 411(1 yen

middot~ Ot J To Co J C So -ky tore eM ta noe(tk( ~ 2 r(4-~ ~ pIA i~( ~~ oS

~yenI4l~~~

P------ ~ c~ Lf4rdes C e d lifest J e we c- tltANJ A f(rrzl cltJ~C

~~ ~~~eAJf- 14 1

Ci-- ntcl ~~~ CJCl ~ CCsII i~~(t et -t4 ~ C4tt p1-Cch~~

~P~ f LoDa is ~er~ AK~Of CCz _

Let ED be ~~~ foSflctorf oft B~ MaC ~D ~S~e AC -ri Cau~tt1e c1A8JgtC ut ABtttE J(e ~ cfC4c~rc(e c1 AB D MflId 8 Ccent F-=-c --r

D (Olt ~t AE =- CF So 1$1 i te~d~ c~ ~gteJ AE~AB=ADAC II CFIltCBCD CA So~= ~~

5 ~c 81gt fsecfs L ABe WI_ Cl) ~ _ I bull It rJC AS - AD CF- f1C

------------------~ ampA~fel Let ABC be ~ ftrJMIj(e ~ soscJes 68C[)I

CAE AASF ~te~(1 to AAsC wi( ~ CA Aa 4 S bu1 tsrtdvel~ Pro~ta ~-t 141esff-1 AJSc ~ t ~ I~es t=F fEgt DE ~dJ ~uc(~t

Col Amiddot ~ SJltto i Late ~e cnl~w-f( Jgt4Sr~ ~ IE ( - eatu r4~ ~Cgt cte

a~~c~~ Iof crde middot1itE Ultoofe Y04oc Jl Y l AE=CE ( tel btcte(~w-I(Fu

c~ Cc~-tr ~cL~4S AF=8F - I -r4e-tltlfte~ A PUr~I T (~ff I ~~ fiIolu ~ ts ltfCI C1 $f lltty ~amp~ 2 lies Cltt VIIIt~~ ~c c) ~ roampoIaJIlt) of (14So -tkey ~u(4t fAa ~~ Camp~tet

63DP I

r ~e A ScIampf~ 2 LtP be 1ft l~~

~ Ii~~(-kB~lIc(~ -to FD-f _ bull 11C ra(~~ to OE -tt~ fOIts frolle M 1 Elf c(frelttf

S 7c IL ttgt ~-JC 1l rgte ~ t

I

I A~ C~ $oIf1 Let ile cncrcft~ J) ~=HF - PD eF -61) OJ rD-peuro-C~1 EAtlA~1eSamp Ql (A~ AF =SF I CD-c CEAGJPF t 81gt

2 l 1 0 F pW~ ct - fE =AF -AE S r~L pound ~ POtt 1 ~CAty4W(t t

- t_ EICIt1k 3 AC--damp l-H aat 0 P~r -fl Ie A4M C ~ usc -t ifegtSltct ~- Ae Id t W S let

Be It N Let 1k u cudcl 0(AAac -lt1 aNll~Std ~t B t ~ middot Pe ~~t OlUaM

SoIwt t ~ C4Samp 61 Be we6~ 11 aM i~ ~ ~ftthlte Qt S of cYG vtIeof poundlASC 1ICft OM =oel 8M

A~p BA18C i4e c~~In CAsamp - AUN AAec ACfo K~ 1Iotf1Ar (S1Cc iMruw Ibl~cto~ L kll Ac AC Jolaquoaret tes) s e rdeo( I

I

pound I ~e AC kN J 8M Itteet 41 4 (IOIt P I

Siell L PM N L 81lt11 l HCA s MIC PAte CDhcrkcl Q ttl I t fill pou fOitJ BMlC ~p 8M ec 80- yo Y=OA

PM r8- PNICPK POamp-r~ bull ~ $Jtmct~ 1keuro92 Ie -t 10- eo~= ampf(tM- rM) PM - 3

rJ It

OMl PB lr F6 ~t 8MPM+6I1I

OM J ~M

L I A6cb be i$(~Ibullt co_~4 tt ArllAofOo Q-t d - amp c~ f A1)1 SC ~ f (aros

Ccle i VI ( 4 E f= ~~-t t I~oes ampe Q= f-o -Ie C

8y po -t fI-t~ Po~_~ peltPD=PHxPl ~_ ft QClltQ6=~d~Qs~tAcff we1et Po~-Qo=CFM-ru) ~ fMQ~ -ns i (Ies 0ML PQ lQMO Itf oM

Ntrf Csd tIe C~C wi4 Q0 As d-cr~ 2 _ bullbull

It t-sses ME F SlAte LampMO LQ EDt -lCl fo s ~ CIC-z Ef ~ Ef -s iU c($ ef ce Let cI has ceth A( ~s tt lie

laquoa ~ ~ t JFPO _r - flMx pQ fiCa _Vi ~ P$ 01 ~ bull0I

A(Igt~ ite-sect PQ 4t M +Q -of leM _ LA0(= l paceW ac- ~ 8I(C ~ lttlclc p ~_I c 1_

let ya~s t Cltn~ I ~_0 =c bull t if crftit C fc$wt

~l~Sshy c1iW ~ 14- - l-l-~t1 A IS ~f~~J i AA6C J 0 i-tala

C(cuCttdlt~ 7Le -(kfee 4-ttJes AP eamp tMJ Cf irUktt- H EDAA6=-M FDo AC-N tp~4-dcent () 06Jl)F )OCJ1gtE

N C~) 0 J- M N middot i

Solfen bullCO LAfcc9cfLATgtC 9 A fgt l=~C6AtyJrc TktL6lgtFcLBAC AooBc-OCi--ees LOBC-=J(t~Io~Leoc)middot1tl_l8A(= ~oo~L8bFmiddot F omiddot Iamp -=gt 08 ~ tgt l= ~frly DC lDe-

B 0 c (~) CLMA ltPgtM~MIf AC~HI () I 81U AlA ~ NIi-IIIt= Aa -AltlaquoJI tgtA L

F ~c ~ l)e - ~ Aa~Ac (c~

~~b )N6oIp 13Ai~80-- OllADI (0( 1)04 ()-(~)+(()+ll)-~~ J)M~ ~_cot=OMOt)1 te

bull Ott J MAl N~-11 fI ~=C)jI 6lf1

~iet SoU- ln LAFC0 =LOC-dJACl) Fc-tkc ut J bu])M So ~t TeI [)f -ue L Jeo L 6gtF =LeAlt ~ J-f4 a~t (~e tB

4 ~t~4Yclt ~ JNle gtetpeId~ bs~CtoY til g 1 I J 1) 4te 0 ~J

=gt 0t3lJe ~oS i DF Q(A~ DCLbE wHk ~ CSV ftt Ae efT I c AC~J~DI ~ (ltt 6e If Be I I I 01 tl( AS 1POW iI f uIlh) SrlOCo Ae1gt = aq rW1d1C by d~ l~testJ~ t4PtwI- Let lc SAe -de -CA k)sU AABC f 2AamptI

NA ~ NC NF ~ rJ SI AC ~ dbullt ~fieaa~(L ofM$C ~=~ so tr~ of ~ bullbull ftc~(eNs() ~ ikatQ~oJ CoxS qf ~ Grtles Q-14III ~ if ITI ~ YM~(-l A~s 7I-e lmiddot 11M rOI(A)C1lt D ~~(S liIOH

r 6middot 1- r IAC- UComiddot

041(ms AhOYllo-lety wi1kceterO a-J Ptto k (cltwaof-d ~1 H(oJ 1lt) ) is Q ~CI itt setVls Jllttl r01ht X 01 ~ plAtte -t 1ile ~c~ X sampcck -tk~t OXL~ -= ieoX ~~rk~ It kl~1)~~~~ti saA3Jkf~ l-t lFl ltl J ~ -tk kPJMDffty 5 ( ~ A IrtySe~ Q -~ f ~ - ilc ~3~ ~ 12tlgteuroFbe~Js~8CCAM~ ~ (-((Ali) Secs AAsc +0 AAFE

amp 1gtJ C Let q Ie ilaquoo cttIL 0 6A-QC SiAte GiA =-2GfD GS -2GE ~tqt=-2~ s ~) ~IAbEF f AASC EXAfe L L AABC AB =AC A(iRl IS t -t t_1y to tIP cnuantt14MC4t~rMs pte AC ~tf~s P Q~ Pe 1l~ 1e totiJpoNltt (fQ

~114t llCeftgt ofAABC Sott~Let 0 bt 14 cgftt ~ -

) rele Lt 1gt foe ~t3et totlaquo 6 c 71 -t4 Circle +ipound Clttt-atd l4AOC

S 1) l3~yf A-trot ~ PQ

ADfAt -= ~~~~=~=Ic S HcAl)So04s I ib 0 S111tt O~$-iLalAltbullbullfMc t ~-tl_W-~tIecf-

CfajiV ~~ s A~t~~etsVI At AlAJ ISdVt4 well -scfes~e l A az (i) (~ts~ Sltk Cif(IOSitc Ai) fW IZ N ~~+-~~Re ~Ill~ ctrck ~ fMlf a c-~ ~lt 0 c-I

II~ iw~le laquo 3Ie -tno1 eel Ct rd -to ufS A

~ of stJes ~u+-1- middotfDItf-t G 1Cf ~fj -t4 (nuCampolttt ~~+riAe ~-tIa ~~it cO (6([e-t etft

A ~t Let A 6e ( It ~~scf 4~el cltlu ItS 54014 1 ampJ y be -fl- ~offu arcres SCrz

e ~C At otamp r 1A~f~~ ~ It 6gt Ilt

N611 Ae ~tly I B~ Iec t CAlieA Ids A is ru~ ~__~ Aamp a-( AC I So AAIb~Stt-t~ L fMc gti((y Mi~~ LMe e-l ee ir1kcts L seA So Mo( ern ee=- (-(A ~~dAIC

AI (IOOoJ 0A I De = ae r So 0 ts-tfe c~af of AAe d kt P~c4rc-ctr~AA6C

1k ~o~1 ~ (1 A) SeLs AABC f 6Aec ~ SeJ t~

scre-~-tP~MOC-tc~ OllA~~ bull middot 1 P 0 ore co((eAt

- fiscl 1( AASCGs ~IIe1lt ~~~~W (~- ~~L ~Ioc L

- L- ~ bull - 2J~ ~(IC= 8(~(s-lt)

ot t Ii -l 1pound is -(I ~K(~ ifCirde ~ Ill laf S bt-tl nf(~ ltgtf I IIIllyeltt t ~oflA bull

~ (e~ M s M~SzM)S3 ~~rrelaquo At s~ let 6 ~ bullt _ r

blse~ 4 poundA 00 ~-te 4 We c~ S~ SJ 1 M MJ

A 1iamp A --To t~t iampt elite- o~rf-tLt (i) IIIiilsrtt t Aamp1le rtfItJ-f 1 ts S I Co

-tIt vtt4lfO c4 -rs T~ ~tCf AT AIT~ 7iIese if L1I $ =ll~Imiddot ~iTt~lltSl~~t~ L T t S~-LTITa S1~1

(i) 11 A A ~ $S~ AA i MM ~ i 3 I ~ A T~ AI S~1 ~~ HzMl ~ ss I HsM bull ~ co ~ffWbull( ~dSr Nect CircCl1C(~ ~ASsz$3 reI 0 AA A~l

Ctcmiddott of A M~H IIbtepofcrceS~MAJ~r~ ~1 fLAA~AsrL f2 J ~ VAdtoos ~~

Z bullSo --Gtdes ~ 1Io(~ Ll lB~ reggt ampSt~~ AMMz toil s~~i~~ ~lt (x M- SLLt Ill ~bullbull04 S 1-ta~X l1c H ) Mz $1

~=(lttc-o)(c-M-~fl~e) 1 M M amp41 S)Jltl~ UrJ~Cost lt~~~~~(fo) ~ ()bc HSt~Zeuro~X

CT1tW EtA-f tt 1- bull ~A be ~iAt 4+etse~ ~ fwo nO~fD~fUtf Cirdes C ~C CAl-~ef0 0 (tltjreJ~ Dtte ~1MtM

~t~o c eamp 1d1t(s-et C cent~ Cztlt Pt J(e -i4af(EV (A~ ~-t-te~ctc At ~Ca~t QI Lk Me t ~~it-t~ ()Q o-J ~ ~ ~itet ~ pzCla

~-t ~ LtJAo LMAMz

~~ ~ ~

SGl~ B-t~etJ Plpt(gtzOt~~O

Ca ~lJZ~ damp bull nwy 14(0 oPa ) Q SeKds C L 0 PI

~ I ~ t -lO Z bull ~ J ~ OAn Ct =8 ~~-oflt~1 e $ Ll016M -tLl~A~~ So LOI~= LOaAHa A~ t- fs 0P 0 P ~o ltlie sjI Ie~ 00 Cgt~ ofL ~ ) 00 ~O~e-=OPct=OAIOg

t ~te~~-1 cknl4t1 ~ AO~ ~ Ate ~Itc

~ LO8M= lDAM

A~ I =gt LoAM L~AMz WIAamp~ ---

L 0cA M~ ==gt L0 A0)- L I-i A Mz bull -to _16bCrfkSf~S

Solt~p Wpound(CS JTbe reflec~ ~ S Wit-(S~ltt

fI5 Mis

~J e

t ~lwt Cgt (1Of ctImiddotd i -br3frt -+0

e $ f(~

Q cmiddotnI F -tkt bcs of tIl YOII f Sue- fut ~e-re ~)f Q

01 ~ w~ M ~ ~(eoi~ ~ l R~~ QS ~ isc~e~ C~rdamp 4 A PQ R

-to M Lt u be 04

~ A$ iudQ~~ltofe1 middot~~(R C V Lat ~ 10 ampl yo~t~14 fc

Co -fI kottcrt(e+y wfoit4 uW( P-tkt StI~ l t

~CtCte (_oppos-e P -(f ~ T middot (1 ~ Set$ U -to (Q((esr-~~-toflfobulltHf lt 1) Ii P~n (= v ut s setft~~ ~ t PQ~ ~

TR SQ=S - PR= PV- PIlt = Vlaquo=n ~ T T So 5 01 Ae ltT0 e ttl

ampruJt~J) fr p~ ltTaee~ UT ~ U

~ l(P Ifamp)Se0v4 u to ~ C(telte e to c~ l I- UtoT So TT Let 14tats~ P-4 C ~+~t5ect r ~Q~R ~

ampS-=s- Pflt=Pv- P((--Vre =TIC=-TIlt ~ tiM -i1s-MS Ti-f1T=-jiM PtSAt4t

~ El4middotrle b rio t)

Lt-A~c ~ co ftiI5le ~ ~tof scl Be A1k ~tsct- N ot l ~AC i~+fSoct ~c ct tJ ~~r~I~ k~ +0 AN -+~~ N ifersets AM 4 Q -c AB -t p -n ~f-lrJrmiddot 0 li~e to APt Pt-a~AIl laquo 0 middot Pofe Qo l Be SIt- TfABAc1kMNQfampAQMol3c

WLOG I ampS$f41111t A6gtAC Let AN MttStcf Uttucrclt fAABC j 1) ~

-- - bull c L 1gtg CL lgtAC=L~Llgtc~ e lAo M f~ r ~ ~ DC aJ PM 1 Be

~o Ho~y K(A ~StovlsA6j)(+oAgO(t4 08 O~ aq ae Itt t= Be( PN -r4~

L Ogt- L b8e =LM8=ro6_LAop=LoP~ ~ ~ D 0 tcKl orooc

I ) I J GfeCttrA J~c J~M4 ~ L 0 - Lep - 1 0 - 7 1- - 0 - 0 Igt IC tS~ amp It sc K is AM == AM l PfI=Q

I I ~ Lg eto L~~O~)oo 1~ ~o LSC g c It Be r

F l

(~p Sol~ middot Let dort FE ~wt -to nr2 4Ss(oll (iJ

Feuro () r C Lt r 1 U04s~r 111k ~y1- (M V)Sets P t r c-to K) Iiamp JE t jilt L AS

sow1 bull Ff 1Ie L ~ A is +lt1 ~roIldrc FE LNEC ~Afe~LAME I rSo L ~~eL~A~)~ LlNEcLlAMc ~ ACAeuro ~e1IA I ~ ~ pouer ~ A ltiol4Isped to r is Ac AM= AE S~M(tAfy I 16fJe t ~A i-fk -(~d -to ~~ Aft A~ A - A ~ =lttiJPOiqJ ~FeJ 56 Ae==-AF (1amp tflt11- rAAtcd - I

_ ~S AI ~ fIr2 AA~f ~ etc )~lll fu ett(4-ik1t f t fl1 pues-~r 1gt 61 sJMe~1 t ~OI)O~ wt Soc Oa I ~~t ~~ Ctgt

~ Ltgtco~=LClgto L cLeF ~s ir~S COa b~s L 9CF $ceCfiS~f rl So

Cl) is ~so~~~ -to re

E)(4flt

amp($ PI Ira Q-te ite~Iy ~ t ~ rt M N~oJtlJ ~ r fGs$es -tI- caff( 01 ~ r~

lAe r tgtit cl1illfr iii r rio MAn=C MBfr=D f (0 ~It CD $ 1~jkt to r2 bull

~ C~ IS - tYgtctStIt

~~ A ilefSVsv wi CAAer 0 oJ ugt r gt0

(amptatl 1 J(o r)) sA~f~ +lAo Se~s A~et(1 ~(t X 0 to ~ i~e VOl~t X O~bull y at sucL fut OXmiddotOlec r~ ~ CWOIelcu I fo X=0 ~ Utake )(=~ _-cl tllSo~)(-=QO Wt-take X=o

1ke Circle -w+1 C2~+e~ 0 A~ ~kCamps r gto-((ct k poundSle ~e~ ~ I~e IWJy 4fso ~ft A~ ltrs~ by sff~t ~ CrCJtL (lWt~middotcP

fGcfs CO Gift1 ~I((S~ ~ ~ bje(~~ it f~~ u~ 00 -to -t~lfmiddot ~ ~c-t J ex ) X ~

reg -If )( s-ikcRiC iwe~~1~ XI=X bull f)(~o~elf(enX~

= bull 1 ~x ~oit ofTaTl) ~t-rrl 4i~

P e ~ X1 lCT2 4~f~~-t1~ ~s iS k~

- __ OXmiddot ox ((sec LTo)()(ycsLTox)r~ ACtreJtt ~~SSi~ 14ftJUJ 0 ~~t +0 A cvdc bull ~ya16tj -4r~ O k iII-s ak~cIc -poits ~(~ St -to ~amp~ foffts l4 fOit 0) ~~fets

of -flit G~ a41~ aJa Afe utllt4r bull JotlfoItr~~tf(~-kGttk ~~set fotleceofv-f~ ~~ctrJe ~

A(fJe vaSSoVJ4-f 0 is Set -to 4 (euro reuro IS ~~~fI)~ 0 ~~s ~~k(+ifia1e-t (It( -t 44td Ito Cnverrely (A (middot1U1IIJt rssj-tlt~ 0 is Seltt -to ~Cvde (w~~ 0 Ni-l -tttllj~-t Imiddotier0 ~Itd to ~ leilt

f r A~At pCiSS~ 14 0 es SetOf ----1-- To e~setl ~ ~ _

Ifgt reg If two cr~ (f~ttIlC~ C4fVts ~(( ttlso ~~(etAf ~ fbft Pto)~~~~

9 lCo (iflaquo at ~Sdf~7e 4-( p~ oF

0 V ~-tlaat iHy~t~tOmiddotmiddot71-~R CA4f~(S ~ SQIJ-fo ~ 0 J

A Ie dI o~ctves4ltSet-f0r1f~~ ~ c () ~-t bull i- cmiddotrd~ ftftfiSttft S ~ fa-5~ 1Gtt cri(S t ( 4It ~fo-6etc~ Gllf f~S A lS 0 4laquol 0 A ~ IV~ IIG(C4((o(Af ~ oAmiddoto~ t 0Bmiddot O~ ~ OAloB OP4 ACoj

wi+lLAoB=L8~A Wt3ttLlOMdOl~ () - ~ LOA8= LogA ~

Aamp~ = OA _ r~A A6 0(3 - OB

=) Ae r lo A~

-------- --------~

)ampa-cle i (~tlcptleofto A ~cQlt$ A 1ckc ~tiatt~

ampl if tlyen~ t ampe- ACBD - A~middotq) +AD

II( V c bull I

SoJn C-sidelt -kfSiCll At 1 vuu~j l)is Cpoundlaquotef bull J ~p-J~ Ygt I) - t t e y fatH4) J -k ~ro-atdc qf ~ec ~~A~ I Q

I iIC ~ AeC SilCamp ~ IH 6e - c I

J vue b -ftt (1) We t _ 1 _AC~ r - Be - - middot

iDA ~ 01gt1gt AJ)middotC1) tt Mltrtrllj b~ lAOmiddot~]) CO~2 1aJkSimiddotces amporeJ

A6amp c) +A)xBe Acll 81gt middot

Re fICS 11L sf ~ eat be ltoftrec -to ~t -I- ~1-tllAt t MilcO + AtgtICBC =AC 1CI1~

~V Asctgt S (l u~ ~lJ4~ 0-shy

~S6~~~ kfCfS4tJ foJt of~~ -+k eampIt~ otIIIetStM Ai ~itlt ~s -fIc ~o~~ rote iIt wJere -reIs CIMif s Mesc(t _

-

6x4t~le 2 Lt ABc 0 be ~ ~tllt t(kft~ suamp~t At ampt so liltftStct At Y1tt ~r AtO P~t~( -Ke -refltecf of 0 ~fOSS AS BC C)1gtA A~ C4IIcYdtc

p _ c $Lt-~ -71

Lcent P~ ~So k ~fut f-~Wi _ 010 0 flO Msc CD lgtA Ye cdIVt bull

sc =l Ott foIIttll is ~iIr~le-t -fo site (5 -tk Ptt-RS l~~( (Sl~~14ft

e IcentS 0 0 -to tts e_~Hrlt OSAP DfBQ ~CR O~DS ~ludlC~~ J J -J ~ _ bull

-tt TltitCirtlutdts Ie CA Ca Cc CD rtsrdtuely CfSMoSmiddotd fIf~iQ 3(0 r ~r31gt0 By ~ct(s)

I~ AC Q( e04~~t ofo ~gtltS

cfct (+) I CA SIrcent to filllt LA fllAlrd to 81gt CIrs

Set to ~ IIt LB ~(c of Ac I C ~ Sci fo c tAlC -to ~lgt1 craquoisSeoet t ol1t LD~E lc ~

0 0 r~-t 0lt1

L Nen bull

CpnCa= 0r~ LAf Le P )Mjl-ly 4~t( LI) R J ll)n~ So bull

$r~ AcJ Mgt PClKs ~~Ic~4J~~ ~ fet h) PampRs is floc

~

G)Cdtpt f

Le-t P bft Af6~-t ~S~ 4l1It Appound ~~~-t LAPB-LACS LA(C-L~8C

Ltt tgt amp be ik~~tS 0( AAPS )AA~C nspecflf ~toe ~l A1gt 1gt1 ce )wtet A fOiWtshy

~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

( )tlfamp 61) biSKfs IA8PJ By ~t CT) ACAfACf~ ~ ~ I3A - XA So iSttf ACAeACampA

P ~f - xpmiddot ~ P~B6+lCApLcA8 J

C-1-1 ~=~ 5tRCt X ( 4ft AP ampt ~1It By~t (s) 1 ~ tCp~=LCitA ~ ~ I I~ fQ is Seoct of ( ~ ~~ 1 f4$s~~3C o listf SiacCrtIeO ~ -T(Alrl~f4lrgto ~~(1)1 tIIet pamp ~t(4C~I~Ois~tfo(0

A ~IgtC A~te A lU)e bullA p A APelAcIIgt f-c ~) I SIWICamp

I

~ ~ ilt3t +00 c( ~ 1 PQ fh ) Qm Q J r bull bull ~ t01 setc~ 10 t of I I

No LM~-L~8-=-LIWC-LAec f~ $(amp ~st ~JO 0 Ao( ~J~~ ~ Atl 43~ t (-d 0 ~ A61PcD

fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

Page 18: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

A - -

~ FOf~lamp~

(1 -laquo ~C

fot-CA~ to ~ t t amp -t~~ crt a ~tc ~ El(tend~ltl St L laquobe ~[A8Cl Js~~i~ R= 4 C

Let ( ~t 4ct nwts lt 4e GoismvmcJt i-R- tl 4J~)(fo~of AAsc Sr ~ l=~~Yslt) ~ bc_

S A -- - 0 21 1iltelaquoe s dolAt C~d~middot ~o~ uI1gt ~ s~amp s~~C middot T 1_ ~ rI n -rf (i-- shy

tl Ie or~ DraJ clmiddotae~t 61gt 1pound Si ~ A= ----=algt i IS lle~ ltJOiOlSA0

~~~~~~~~~~~~~-~~~~=~~~~ p adEr-l-~a~~r~ A- oS+- jtus c~ - c e c I) p(]) Let 18(1gt L~Ms

I4dtt rAsel Or S~8c1oI(lcl~ 1leflAftt Let A6nct)p -r1 ~act 0

~Me C ABC ) GlUo~kc ~ PAx P6= Pc x PD = tl b~~=Abc bull P19tpound Note L APD L (PB

4R A1BC)aHd~ckLPAtgt=LPCBS=tfA-tb~~) is ike seifieAc ~AAPDACfB~=~~ PAIPB=fxPD

amp Q C Of 4A8C Lri pc C 1amp-~ ~~ PC Is -lt-~t lat t lie i4 jCbullbullr 4l( M6C Qt r Ie -i4~ to -e -fde ~ A A8C if (JJ

C)~ ~e icltc1e ot AAec ~e p A e OYlJ c fCL p~~re [Mel =[ALel[~cl+(CI1= ~-t~+~=SIr ~ Not~ LArc=LcPB

I-tfllWlbull [A8tl~ S($-11 ) (s-b)(s-c)middot I pCs f~ot -to LACp4C ampP(~ Cos C= tt2ttoa-c (~AI Ci(~ircl 4 MBc B 2shy

[A6Ci= ~SiIlC=Qr(+coSp(i-($C) ~AAcPACBP ~~ fgtc PCPAlltPB =(Cl~-+Iot-c~t-~a~-9 ) = catlo-4 t )(A1(-c)(CoHI- b)(o-Il-~= S (s-c)(~~

2- ~ a

Ci C [AS(I A 2

~

I

~JJI LPFA-=odeg=Lpe~ ~ amp~ ~LPFeLPAE

C5Ji) ~tolt1 s-ThtOfotfll Let A 6c~ ~t dlSncf ~ts 01 bull ~c ~o - Me~IA~ 1( bull t Of~~~I ~Ot bull -Tht~ bull Sa c~tOV M1 C(liofIPT potd~ A 6 C Iie to

AI 6 C 1gt (1~t~c 1gtpound fCLR atfmiddote ZA ~A A ZA bull -~ -iA ~Co~ PAQ~clf$ WeA~ ZA~lA I tc Z~t

pFAECc1dk

bull ~ Srlloi(y taCgt6~~~-lPFB ~ pG~ f CDCCYcbull LPampb LPFI) = e 1klaquo AIJ~P LPAespoundp8C pfE _ LPeP 8EF (0(1ltlt~L PFE L~8Tgt~ LFP - L 10 collirAfampff

)fgtC)~Jl~~ ~ ASC1HAol6C=AcS]) bull (~~_ ~ktI AeCO At)ItBC ~ACdtgt 1)~c 190pound 0 sWLe AB UJlfsftfUct A ampA6

S~~41 to flCAP 1I1elt AB A~ 6eshy

6 Ai - 7ligt= (1) lBAE=LCAJgt

SO LMc L BAlgt-L1gt= LeA1gt-LMe =LEAt) Tkeuro1 A8AC~Ae-A1) So Rr-c EDAtgt~A Thet Aec~ A~8C =poundItampE AClC E~ AC80

bull A rC =c Sf-t Ell I

f1-I-4j hoW~ ~8euro~EtgtS ampb ~ E iUt~( SO - ~~oeA~LeeALtgtCA ~AsectCO Sltffc

SoSoft ~oe 1et~6cP cl-ampd-p~ 0

tI~ Let l)poundF fetf~~ff- P~ ampa Aeyen~~ ~

Asse ~Mist (so4 is 6~UA_JC ~AGSC ~O bull G ~f( Aalec~o)

tt~e9 7eff

fovlaquos X I Z ate (es Aamp ampCA D ((t~ve-()ty It X I Z (lie (dl-lflOr

A ~f f6 lhg--1 ~ xe YC LA - middot ~ lQt Dbu (~ Ac soct1IIt 81gt II J( Z -r1teuron

~g ~ ~ 1t~ ~z Se AlC 6Y c~ _At P1Q (i~ ~y Ie ~c -- _______ r tamp iU I bull laS yc fA ~Igt ZCZA middot lCI~ lIeeu~ Ie~

If ~ tL ~ =-1 iIamp )( YL MHo l~(~ Y~t~~~~ SlJ) Ltt l~ X(OCA -Thtl b Mt11Idtw 11~ Ax ay CI _ lt Cz Y Cl iiiK zA --i ~o --=-l1toobull CfIea bull _Cl -a

I I

ceDD ~MelI s lIeo~toA l~tA I ~cc t) euro ~be tc~ lO 0shy

de lw~~ ~( ft amptCtSSCti 1 tf (~ diC- (~QEf ) bull

t p Ae ti l)euro J Q Bel pound f 2= Cl)n fA ~ ~k ~ Q1t ottc(l(ea~ ~QIR~~~ -

f~ 1 ~ ltt X~EfA 1AMCD bull ~ z- C~neF Arr~l ~(atts ~ff 1e-(fM1oec~ FA

ftt- Ool~~~ 4xf l w hVII

e-- ~ X K __( It X2 ~_( t ~~II Qx 6y Ct ~y pzex I fllFxijmiddot 1I

Hul~pr~ ~ AIl ~~ tfffSfctj cofI4t tt XA)(B XEmiddotKF J (CmiddotYP=1AmiddotYS ZEmiddotZF= zeZIgt W~~et ZQ lSf~-i igt PQ~ ore rlfltelaquor

Qx Pf Itz loy c-enc ~Mee(AaS

t-rks ~ere 0 Imiddotil~ (1$($ of PoucJ s for It we tftwt Ato 8 -te I AIwIJ (3 il(cJe 1Iofl1-t i AB will b~ ~-t1l3et (iot ot B ~ It~j CIt~ we ells JpoundAoflt ~ t~ liflE Clt B b~ BR

6lCtJfC i F~~ h Cf(Ultirc~ ot Mac J f(it 1) ( ~ ~i~0yen ot -t4l~lE I~ ~tA - ~~ Be ~ e fM 1fe ttusc(e~ of-ffwf3ct (tt4-t C3L1r~ CA~ F= bt ~ ttfStd~ of -tINt ti-~-f Imiddot~t ~tC wo( Aamp 11161 PI Ell F o~ ctU

Soof~fIyen P=Mo 8C ~ E= BBnlA f=CCnAB APP~i P~f ~ ~(fo MB See I fott et 1gtpound f c-

-- =JSiiiiIii

b)lAtc ~ Let-tgt 0- eht ~cfs 0( dt101 AtCS

AS ~ AC O~~e (ilcu-R( Mac ftspciwJy l(t tgt Ilt ~f AtC sCI ~== DPn SA J R= PEn AC fro +~-t lile QR~s~(QVJ14 fttCf+~I (~ 1) ~ f9bt-Mshy~e 1)rff0--AS- CO ~SfctsLAc8

Co ~r ~ qftllCr At =lgt 6 ~LAec So 1= Cl)n G8 Sf_ eEtS

Q tgtPt SA DP 8ital R= Pe C Pre ttL PlE AI

AIP~ f~l ~ 1Ito(-to C ~ P er ~ w 1 ~ bull 1I

t Set I Q Rut tIff~ Co~~d~

~ -7

Alt IXu q j

elf (Ga1(e 3 Ltt AT3CPs e ~ +s tMDlCJe ~-rd AAfLBS Bat LeA) ccf LAB fat 1gt be ~ls (I ~cucl1t ~c4( I

DA(11)C= AU DB()CAe~ 1gtCIAB~ fgt~~ A~ r~CtfaJ T4 6v~fi ~ IAGC a~ Co((~((r

~olf- W HL-cI oy-((~( ~ AA Be Ne

AAIB~I)Cc(-=I DArBC=A 11gt1( ISc AtA f Cc -= H L lAlA I C I Cl

1t~()cD=C1 ~l (AIBl (cjAfrrr5~5Gl ~~ t DAAfCC tgtlt Se4 A HC tit c11ilaquoraquo SIt 1y ar171~ BS41s(to AS e 0cc we Su e H 6ltve c1(i~amp r A~ H C~ S4rt a(((~4~ I

-~ ALI)f ~fle1 tt P toe a ltpor i~4Mec

LtfP I~~ff~I$f- 5 -to ~CA Camp ft~t~ lttt bJ() ~_ eshy

ll 10 ~ fet ~~~N~ c-tohs API sp (~ftvtll IfQ P ~ 61bullbull Pt14 PttNQ~~ (tries ~tll~ Qfz cod A~ aft ~et

iSoLttd- $(fCJt L CPc p) LCQLP LC~P Lc (gta Palt-e J -t ~es c P ~L I PI Q p 4ftcocttc f~AfrI15 ~s middottU(Woto ~1l$1 w-tSu CPt ( gt e-= A ) P t1t( QIP= X ) (Q-a Pf P2C-= B 4re CoI~rtelr $6 Rb2-l amp1L ( AB-=Xmiddot ~ ~lIQ P~IA8 tVe ~Cqfre~

NewtDJ S

~A ABcOS~~(laquoteJktvsa e ~SQiraquoeamp c~tkt~~ ~~

APgtsc CD) PA AXcpotlts EFG)H-~t~ C F B ~ACG~FHgD~~r~t

Sol~tcNI W E6nFHO~ Eftn FG ~X _Apply~~ ~~scJ ~ ~ -to E~ltSJ F f(f ~Sta E~ () Fr =0 ~~ ( 14 1) I G Fn H( X are ut(ltealf_ ~ltfcAy~ltP~CA(s ~e- 4 E6--()FF~~ J ~S14

EEn FF~ B euroH nf6=X amp-t-fn ~euro 0 tUllPtfcmiddotc4t

-nus ~S 0 XI oJB ~c((e4~ 7itN pound4 fl Ff n6D=O SlAry EG F-- ( AC - O ACE6 fH6DCPotrclO

1)ec~CAes ~ 0 nfAaAec ~ JACc) M

A c B actgcP J CAnCpQJ AampnAgR ~r--+--Ir-~~R If AA 613 I cc 4te ~tVt-ct ~

A e 1-~ PI ~ Rctil eo(IQ4(_

c~ rCP_ R2esrk ~-s ~ -tyenUL te~ 4 ~~cAAfIdgre IfV --IfU ~ f 4s root G-oIer ~Ns c~ AOAB ~ftJJ MeoJ- -~r ~ et QPL AEa gil

At A rltamp -7---1S ( rt l g 0 () I 4 ~ ~ Ie Be Cctf~ Lloec Ilfct-Jt ~~ C~ c~ IJOCA ~ 1te(J C~ BP Cd M oct ~

B8 PC-co ~-( ~ No CC~=-( ~(ff~~~sctmiddot~~= - ~ (IC4M~cfMtl~~~ote- ~ et eampI c-f(er

62Y ~coJ A~s tttt ~Cct~lI1tr

Let Cn-les C ~ Cz ktwe ~~t ~~-fe15 0 ~ 02

Sf 11 4st f( J 14 (cs of ( OotX w~ 1

fe- ) t ~ lt twitt ()~ -tu Cl

eo( C~ ~Ilt ue 0 K- r 4)-~ J ~ ~ li~ f(~ok( -to OO~ -rtgt Is -4 (~~a1CSof tLt -f~Cnrd u

MOtse ~3 Crce~ CJCC1 W~~ OJOaoJ(h I~ nf CiamplttJ -tfe 3 ~ ltWQs ~FoS offI Wi( i~~(JItct cent Do fgti- ((lt d4 vaJOJ aftftfT4crtfes 111$ ~It lw la-I fIwe wi(( v-espue to 4((3 ccle$

G7~~14~S

~ If 2c(c~sCp~ lte~tAt PQ ~ p Cl aJ hss fou 0 411(1 yen

middot~ Ot J To Co J C So -ky tore eM ta noe(tk( ~ 2 r(4-~ ~ pIA i~( ~~ oS

~yenI4l~~~

P------ ~ c~ Lf4rdes C e d lifest J e we c- tltANJ A f(rrzl cltJ~C

~~ ~~~eAJf- 14 1

Ci-- ntcl ~~~ CJCl ~ CCsII i~~(t et -t4 ~ C4tt p1-Cch~~

~P~ f LoDa is ~er~ AK~Of CCz _

Let ED be ~~~ foSflctorf oft B~ MaC ~D ~S~e AC -ri Cau~tt1e c1A8JgtC ut ABtttE J(e ~ cfC4c~rc(e c1 AB D MflId 8 Ccent F-=-c --r

D (Olt ~t AE =- CF So 1$1 i te~d~ c~ ~gteJ AE~AB=ADAC II CFIltCBCD CA So~= ~~

5 ~c 81gt fsecfs L ABe WI_ Cl) ~ _ I bull It rJC AS - AD CF- f1C

------------------~ ampA~fel Let ABC be ~ ftrJMIj(e ~ soscJes 68C[)I

CAE AASF ~te~(1 to AAsC wi( ~ CA Aa 4 S bu1 tsrtdvel~ Pro~ta ~-t 141esff-1 AJSc ~ t ~ I~es t=F fEgt DE ~dJ ~uc(~t

Col Amiddot ~ SJltto i Late ~e cnl~w-f( Jgt4Sr~ ~ IE ( - eatu r4~ ~Cgt cte

a~~c~~ Iof crde middot1itE Ultoofe Y04oc Jl Y l AE=CE ( tel btcte(~w-I(Fu

c~ Cc~-tr ~cL~4S AF=8F - I -r4e-tltlfte~ A PUr~I T (~ff I ~~ fiIolu ~ ts ltfCI C1 $f lltty ~amp~ 2 lies Cltt VIIIt~~ ~c c) ~ roampoIaJIlt) of (14So -tkey ~u(4t fAa ~~ Camp~tet

63DP I

r ~e A ScIampf~ 2 LtP be 1ft l~~

~ Ii~~(-kB~lIc(~ -to FD-f _ bull 11C ra(~~ to OE -tt~ fOIts frolle M 1 Elf c(frelttf

S 7c IL ttgt ~-JC 1l rgte ~ t

I

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wi+lLAoB=L8~A Wt3ttLlOMdOl~ () - ~ LOA8= LogA ~

Aamp~ = OA _ r~A A6 0(3 - OB

=) Ae r lo A~

-------- --------~

)ampa-cle i (~tlcptleofto A ~cQlt$ A 1ckc ~tiatt~

ampl if tlyen~ t ampe- ACBD - A~middotq) +AD

II( V c bull I

SoJn C-sidelt -kfSiCll At 1 vuu~j l)is Cpoundlaquotef bull J ~p-J~ Ygt I) - t t e y fatH4) J -k ~ro-atdc qf ~ec ~~A~ I Q

I iIC ~ AeC SilCamp ~ IH 6e - c I

J vue b -ftt (1) We t _ 1 _AC~ r - Be - - middot

iDA ~ 01gt1gt AJ)middotC1) tt Mltrtrllj b~ lAOmiddot~]) CO~2 1aJkSimiddotces amporeJ

A6amp c) +A)xBe Acll 81gt middot

Re fICS 11L sf ~ eat be ltoftrec -to ~t -I- ~1-tllAt t MilcO + AtgtICBC =AC 1CI1~

~V Asctgt S (l u~ ~lJ4~ 0-shy

~S6~~~ kfCfS4tJ foJt of~~ -+k eampIt~ otIIIetStM Ai ~itlt ~s -fIc ~o~~ rote iIt wJere -reIs CIMif s Mesc(t _

-

6x4t~le 2 Lt ABc 0 be ~ ~tllt t(kft~ suamp~t At ampt so liltftStct At Y1tt ~r AtO P~t~( -Ke -refltecf of 0 ~fOSS AS BC C)1gtA A~ C4IIcYdtc

p _ c $Lt-~ -71

Lcent P~ ~So k ~fut f-~Wi _ 010 0 flO Msc CD lgtA Ye cdIVt bull

sc =l Ott foIIttll is ~iIr~le-t -fo site (5 -tk Ptt-RS l~~( (Sl~~14ft

e IcentS 0 0 -to tts e_~Hrlt OSAP DfBQ ~CR O~DS ~ludlC~~ J J -J ~ _ bull

-tt TltitCirtlutdts Ie CA Ca Cc CD rtsrdtuely CfSMoSmiddotd fIf~iQ 3(0 r ~r31gt0 By ~ct(s)

I~ AC Q( e04~~t ofo ~gtltS

cfct (+) I CA SIrcent to filllt LA fllAlrd to 81gt CIrs

Set to ~ IIt LB ~(c of Ac I C ~ Sci fo c tAlC -to ~lgt1 craquoisSeoet t ol1t LD~E lc ~

0 0 r~-t 0lt1

L Nen bull

CpnCa= 0r~ LAf Le P )Mjl-ly 4~t( LI) R J ll)n~ So bull

$r~ AcJ Mgt PClKs ~~Ic~4J~~ ~ fet h) PampRs is floc

~

G)Cdtpt f

Le-t P bft Af6~-t ~S~ 4l1It Appound ~~~-t LAPB-LACS LA(C-L~8C

Ltt tgt amp be ik~~tS 0( AAPS )AA~C nspecflf ~toe ~l A1gt 1gt1 ce )wtet A fOiWtshy

~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

( )tlfamp 61) biSKfs IA8PJ By ~t CT) ACAfACf~ ~ ~ I3A - XA So iSttf ACAeACampA

P ~f - xpmiddot ~ P~B6+lCApLcA8 J

C-1-1 ~=~ 5tRCt X ( 4ft AP ampt ~1It By~t (s) 1 ~ tCp~=LCitA ~ ~ I I~ fQ is Seoct of ( ~ ~~ 1 f4$s~~3C o listf SiacCrtIeO ~ -T(Alrl~f4lrgto ~~(1)1 tIIet pamp ~t(4C~I~Ois~tfo(0

A ~IgtC A~te A lU)e bullA p A APelAcIIgt f-c ~) I SIWICamp

I

~ ~ ilt3t +00 c( ~ 1 PQ fh ) Qm Q J r bull bull ~ t01 setc~ 10 t of I I

No LM~-L~8-=-LIWC-LAec f~ $(amp ~st ~JO 0 Ao( ~J~~ ~ Atl 43~ t (-d 0 ~ A61PcD

fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

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ceDD ~MelI s lIeo~toA l~tA I ~cc t) euro ~be tc~ lO 0shy

de lw~~ ~( ft amptCtSSCti 1 tf (~ diC- (~QEf ) bull

t p Ae ti l)euro J Q Bel pound f 2= Cl)n fA ~ ~k ~ Q1t ottc(l(ea~ ~QIR~~~ -

f~ 1 ~ ltt X~EfA 1AMCD bull ~ z- C~neF Arr~l ~(atts ~ff 1e-(fM1oec~ FA

ftt- Ool~~~ 4xf l w hVII

e-- ~ X K __( It X2 ~_( t ~~II Qx 6y Ct ~y pzex I fllFxijmiddot 1I

Hul~pr~ ~ AIl ~~ tfffSfctj cofI4t tt XA)(B XEmiddotKF J (CmiddotYP=1AmiddotYS ZEmiddotZF= zeZIgt W~~et ZQ lSf~-i igt PQ~ ore rlfltelaquor

Qx Pf Itz loy c-enc ~Mee(AaS

t-rks ~ere 0 Imiddotil~ (1$($ of PoucJ s for It we tftwt Ato 8 -te I AIwIJ (3 il(cJe 1Iofl1-t i AB will b~ ~-t1l3et (iot ot B ~ It~j CIt~ we ells JpoundAoflt ~ t~ liflE Clt B b~ BR

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Soof~fIyen P=Mo 8C ~ E= BBnlA f=CCnAB APP~i P~f ~ ~(fo MB See I fott et 1gtpound f c-

-- =JSiiiiIii

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Q tgtPt SA DP 8ital R= Pe C Pre ttL PlE AI

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t Set I Q Rut tIff~ Co~~d~

~ -7

Alt IXu q j

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~olf- W HL-cI oy-((~( ~ AA Be Ne

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-~ ALI)f ~fle1 tt P toe a ltpor i~4Mec

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NewtDJ S

~A ABcOS~~(laquoteJktvsa e ~SQiraquoeamp c~tkt~~ ~~

APgtsc CD) PA AXcpotlts EFG)H-~t~ C F B ~ACG~FHgD~~r~t

Sol~tcNI W E6nFHO~ Eftn FG ~X _Apply~~ ~~scJ ~ ~ -to E~ltSJ F f(f ~Sta E~ () Fr =0 ~~ ( 14 1) I G Fn H( X are ut(ltealf_ ~ltfcAy~ltP~CA(s ~e- 4 E6--()FF~~ J ~S14

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A e 1-~ PI ~ Rctil eo(IQ4(_

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Sf 11 4st f( J 14 (cs of ( OotX w~ 1

fe- ) t ~ lt twitt ()~ -tu Cl

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~yenI4l~~~

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~~ ~~~eAJf- 14 1

Ci-- ntcl ~~~ CJCl ~ CCsII i~~(t et -t4 ~ C4tt p1-Cch~~

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------------------~ ampA~fel Let ABC be ~ ftrJMIj(e ~ soscJes 68C[)I

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Col Amiddot ~ SJltto i Late ~e cnl~w-f( Jgt4Sr~ ~ IE ( - eatu r4~ ~Cgt cte

a~~c~~ Iof crde middot1itE Ultoofe Y04oc Jl Y l AE=CE ( tel btcte(~w-I(Fu

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63DP I

r ~e A ScIampf~ 2 LtP be 1ft l~~

~ Ii~~(-kB~lIc(~ -to FD-f _ bull 11C ra(~~ to OE -tt~ fOIts frolle M 1 Elf c(frelttf

S 7c IL ttgt ~-JC 1l rgte ~ t

I

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I

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Siell L PM N L 81lt11 l HCA s MIC PAte CDhcrkcl Q ttl I t fill pou fOitJ BMlC ~p 8M ec 80- yo Y=OA

PM r8- PNICPK POamp-r~ bull ~ $Jtmct~ 1keuro92 Ie -t 10- eo~= ampf(tM- rM) PM - 3

rJ It

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OM J ~M

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F ~c ~ l)e - ~ Aa~Ac (c~

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scre-~-tP~MOC-tc~ OllA~~ bull middot 1 P 0 ore co((eAt

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- L- ~ bull - 2J~ ~(IC= 8(~(s-lt)

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-tIt vtt4lfO c4 -rs T~ ~tCf AT AIT~ 7iIese if L1I $ =ll~Imiddot ~iTt~lltSl~~t~ L T t S~-LTITa S1~1

(i) 11 A A ~ $S~ AA i MM ~ i 3 I ~ A T~ AI S~1 ~~ HzMl ~ ss I HsM bull ~ co ~ffWbull( ~dSr Nect CircCl1C(~ ~ASsz$3 reI 0 AA A~l

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Z bullSo --Gtdes ~ 1Io(~ Ll lB~ reggt ampSt~~ AMMz toil s~~i~~ ~lt (x M- SLLt Ill ~bullbull04 S 1-ta~X l1c H ) Mz $1

~=(lttc-o)(c-M-~fl~e) 1 M M amp41 S)Jltl~ UrJ~Cost lt~~~~~(fo) ~ ()bc HSt~Zeuro~X

CT1tW EtA-f tt 1- bull ~A be ~iAt 4+etse~ ~ fwo nO~fD~fUtf Cirdes C ~C CAl-~ef0 0 (tltjreJ~ Dtte ~1MtM

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~-t ~ LtJAo LMAMz

~~ ~ ~

SGl~ B-t~etJ Plpt(gtzOt~~O

Ca ~lJZ~ damp bull nwy 14(0 oPa ) Q SeKds C L 0 PI

~ I ~ t -lO Z bull ~ J ~ OAn Ct =8 ~~-oflt~1 e $ Ll016M -tLl~A~~ So LOI~= LOaAHa A~ t- fs 0P 0 P ~o ltlie sjI Ie~ 00 Cgt~ ofL ~ ) 00 ~O~e-=OPct=OAIOg

t ~te~~-1 cknl4t1 ~ AO~ ~ Ate ~Itc

~ LO8M= lDAM

A~ I =gt LoAM L~AMz WIAamp~ ---

L 0cA M~ ==gt L0 A0)- L I-i A Mz bull -to _16bCrfkSf~S

Solt~p Wpound(CS JTbe reflec~ ~ S Wit-(S~ltt

fI5 Mis

~J e

t ~lwt Cgt (1Of ctImiddotd i -br3frt -+0

e $ f(~

Q cmiddotnI F -tkt bcs of tIl YOII f Sue- fut ~e-re ~)f Q

01 ~ w~ M ~ ~(eoi~ ~ l R~~ QS ~ isc~e~ C~rdamp 4 A PQ R

-to M Lt u be 04

~ A$ iudQ~~ltofe1 middot~~(R C V Lat ~ 10 ampl yo~t~14 fc

Co -fI kottcrt(e+y wfoit4 uW( P-tkt StI~ l t

~CtCte (_oppos-e P -(f ~ T middot (1 ~ Set$ U -to (Q((esr-~~-toflfobulltHf lt 1) Ii P~n (= v ut s setft~~ ~ t PQ~ ~

TR SQ=S - PR= PV- PIlt = Vlaquo=n ~ T T So 5 01 Ae ltT0 e ttl

ampruJt~J) fr p~ ltTaee~ UT ~ U

~ l(P Ifamp)Se0v4 u to ~ C(telte e to c~ l I- UtoT So TT Let 14tats~ P-4 C ~+~t5ect r ~Q~R ~

ampS-=s- Pflt=Pv- P((--Vre =TIC=-TIlt ~ tiM -i1s-MS Ti-f1T=-jiM PtSAt4t

~ El4middotrle b rio t)

Lt-A~c ~ co ftiI5le ~ ~tof scl Be A1k ~tsct- N ot l ~AC i~+fSoct ~c ct tJ ~~r~I~ k~ +0 AN -+~~ N ifersets AM 4 Q -c AB -t p -n ~f-lrJrmiddot 0 li~e to APt Pt-a~AIl laquo 0 middot Pofe Qo l Be SIt- TfABAc1kMNQfampAQMol3c

WLOG I ampS$f41111t A6gtAC Let AN MttStcf Uttucrclt fAABC j 1) ~

-- - bull c L 1gtg CL lgtAC=L~Llgtc~ e lAo M f~ r ~ ~ DC aJ PM 1 Be

~o Ho~y K(A ~StovlsA6j)(+oAgO(t4 08 O~ aq ae Itt t= Be( PN -r4~

L Ogt- L b8e =LM8=ro6_LAop=LoP~ ~ ~ D 0 tcKl orooc

I ) I J GfeCttrA J~c J~M4 ~ L 0 - Lep - 1 0 - 7 1- - 0 - 0 Igt IC tS~ amp It sc K is AM == AM l PfI=Q

I I ~ Lg eto L~~O~)oo 1~ ~o LSC g c It Be r

F l

(~p Sol~ middot Let dort FE ~wt -to nr2 4Ss(oll (iJ

Feuro () r C Lt r 1 U04s~r 111k ~y1- (M V)Sets P t r c-to K) Iiamp JE t jilt L AS

sow1 bull Ff 1Ie L ~ A is +lt1 ~roIldrc FE LNEC ~Afe~LAME I rSo L ~~eL~A~)~ LlNEcLlAMc ~ ACAeuro ~e1IA I ~ ~ pouer ~ A ltiol4Isped to r is Ac AM= AE S~M(tAfy I 16fJe t ~A i-fk -(~d -to ~~ Aft A~ A - A ~ =lttiJPOiqJ ~FeJ 56 Ae==-AF (1amp tflt11- rAAtcd - I

_ ~S AI ~ fIr2 AA~f ~ etc )~lll fu ett(4-ik1t f t fl1 pues-~r 1gt 61 sJMe~1 t ~OI)O~ wt Soc Oa I ~~t ~~ Ctgt

~ Ltgtco~=LClgto L cLeF ~s ir~S COa b~s L 9CF $ceCfiS~f rl So

Cl) is ~so~~~ -to re

E)(4flt

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lAe r tgtit cl1illfr iii r rio MAn=C MBfr=D f (0 ~It CD $ 1~jkt to r2 bull

~ C~ IS - tYgtctStIt

~~ A ilefSVsv wi CAAer 0 oJ ugt r gt0

(amptatl 1 J(o r)) sA~f~ +lAo Se~s A~et(1 ~(t X 0 to ~ i~e VOl~t X O~bull y at sucL fut OXmiddotOlec r~ ~ CWOIelcu I fo X=0 ~ Utake )(=~ _-cl tllSo~)(-=QO Wt-take X=o

1ke Circle -w+1 C2~+e~ 0 A~ ~kCamps r gto-((ct k poundSle ~e~ ~ I~e IWJy 4fso ~ft A~ ltrs~ by sff~t ~ CrCJtL (lWt~middotcP

fGcfs CO Gift1 ~I((S~ ~ ~ bje(~~ it f~~ u~ 00 -to -t~lfmiddot ~ ~c-t J ex ) X ~

reg -If )( s-ikcRiC iwe~~1~ XI=X bull f)(~o~elf(enX~

= bull 1 ~x ~oit ofTaTl) ~t-rrl 4i~

P e ~ X1 lCT2 4~f~~-t1~ ~s iS k~

- __ OXmiddot ox ((sec LTo)()(ycsLTox)r~ ACtreJtt ~~SSi~ 14ftJUJ 0 ~~t +0 A cvdc bull ~ya16tj -4r~ O k iII-s ak~cIc -poits ~(~ St -to ~amp~ foffts l4 fOit 0) ~~fets

of -flit G~ a41~ aJa Afe utllt4r bull JotlfoItr~~tf(~-kGttk ~~set fotleceofv-f~ ~~ctrJe ~

A(fJe vaSSoVJ4-f 0 is Set -to 4 (euro reuro IS ~~~fI)~ 0 ~~s ~~k(+ifia1e-t (It( -t 44td Ito Cnverrely (A (middot1U1IIJt rssj-tlt~ 0 is Seltt -to ~Cvde (w~~ 0 Ni-l -tttllj~-t Imiddotier0 ~Itd to ~ leilt

f r A~At pCiSS~ 14 0 es SetOf ----1-- To e~setl ~ ~ _

Ifgt reg If two cr~ (f~ttIlC~ C4fVts ~(( ttlso ~~(etAf ~ fbft Pto)~~~~

9 lCo (iflaquo at ~Sdf~7e 4-( p~ oF

0 V ~-tlaat iHy~t~tOmiddotmiddot71-~R CA4f~(S ~ SQIJ-fo ~ 0 J

A Ie dI o~ctves4ltSet-f0r1f~~ ~ c () ~-t bull i- cmiddotrd~ ftftfiSttft S ~ fa-5~ 1Gtt cri(S t ( 4It ~fo-6etc~ Gllf f~S A lS 0 4laquol 0 A ~ IV~ IIG(C4((o(Af ~ oAmiddoto~ t 0Bmiddot O~ ~ OAloB OP4 ACoj

wi+lLAoB=L8~A Wt3ttLlOMdOl~ () - ~ LOA8= LogA ~

Aamp~ = OA _ r~A A6 0(3 - OB

=) Ae r lo A~

-------- --------~

)ampa-cle i (~tlcptleofto A ~cQlt$ A 1ckc ~tiatt~

ampl if tlyen~ t ampe- ACBD - A~middotq) +AD

II( V c bull I

SoJn C-sidelt -kfSiCll At 1 vuu~j l)is Cpoundlaquotef bull J ~p-J~ Ygt I) - t t e y fatH4) J -k ~ro-atdc qf ~ec ~~A~ I Q

I iIC ~ AeC SilCamp ~ IH 6e - c I

J vue b -ftt (1) We t _ 1 _AC~ r - Be - - middot

iDA ~ 01gt1gt AJ)middotC1) tt Mltrtrllj b~ lAOmiddot~]) CO~2 1aJkSimiddotces amporeJ

A6amp c) +A)xBe Acll 81gt middot

Re fICS 11L sf ~ eat be ltoftrec -to ~t -I- ~1-tllAt t MilcO + AtgtICBC =AC 1CI1~

~V Asctgt S (l u~ ~lJ4~ 0-shy

~S6~~~ kfCfS4tJ foJt of~~ -+k eampIt~ otIIIetStM Ai ~itlt ~s -fIc ~o~~ rote iIt wJere -reIs CIMif s Mesc(t _

-

6x4t~le 2 Lt ABc 0 be ~ ~tllt t(kft~ suamp~t At ampt so liltftStct At Y1tt ~r AtO P~t~( -Ke -refltecf of 0 ~fOSS AS BC C)1gtA A~ C4IIcYdtc

p _ c $Lt-~ -71

Lcent P~ ~So k ~fut f-~Wi _ 010 0 flO Msc CD lgtA Ye cdIVt bull

sc =l Ott foIIttll is ~iIr~le-t -fo site (5 -tk Ptt-RS l~~( (Sl~~14ft

e IcentS 0 0 -to tts e_~Hrlt OSAP DfBQ ~CR O~DS ~ludlC~~ J J -J ~ _ bull

-tt TltitCirtlutdts Ie CA Ca Cc CD rtsrdtuely CfSMoSmiddotd fIf~iQ 3(0 r ~r31gt0 By ~ct(s)

I~ AC Q( e04~~t ofo ~gtltS

cfct (+) I CA SIrcent to filllt LA fllAlrd to 81gt CIrs

Set to ~ IIt LB ~(c of Ac I C ~ Sci fo c tAlC -to ~lgt1 craquoisSeoet t ol1t LD~E lc ~

0 0 r~-t 0lt1

L Nen bull

CpnCa= 0r~ LAf Le P )Mjl-ly 4~t( LI) R J ll)n~ So bull

$r~ AcJ Mgt PClKs ~~Ic~4J~~ ~ fet h) PampRs is floc

~

G)Cdtpt f

Le-t P bft Af6~-t ~S~ 4l1It Appound ~~~-t LAPB-LACS LA(C-L~8C

Ltt tgt amp be ik~~tS 0( AAPS )AA~C nspecflf ~toe ~l A1gt 1gt1 ce )wtet A fOiWtshy

~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

( )tlfamp 61) biSKfs IA8PJ By ~t CT) ACAfACf~ ~ ~ I3A - XA So iSttf ACAeACampA

P ~f - xpmiddot ~ P~B6+lCApLcA8 J

C-1-1 ~=~ 5tRCt X ( 4ft AP ampt ~1It By~t (s) 1 ~ tCp~=LCitA ~ ~ I I~ fQ is Seoct of ( ~ ~~ 1 f4$s~~3C o listf SiacCrtIeO ~ -T(Alrl~f4lrgto ~~(1)1 tIIet pamp ~t(4C~I~Ois~tfo(0

A ~IgtC A~te A lU)e bullA p A APelAcIIgt f-c ~) I SIWICamp

I

~ ~ ilt3t +00 c( ~ 1 PQ fh ) Qm Q J r bull bull ~ t01 setc~ 10 t of I I

No LM~-L~8-=-LIWC-LAec f~ $(amp ~st ~JO 0 Ao( ~J~~ ~ Atl 43~ t (-d 0 ~ A61PcD

fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

Page 21: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

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Alt IXu q j

elf (Ga1(e 3 Ltt AT3CPs e ~ +s tMDlCJe ~-rd AAfLBS Bat LeA) ccf LAB fat 1gt be ~ls (I ~cucl1t ~c4( I

DA(11)C= AU DB()CAe~ 1gtCIAB~ fgt~~ A~ r~CtfaJ T4 6v~fi ~ IAGC a~ Co((~((r

~olf- W HL-cI oy-((~( ~ AA Be Ne

AAIB~I)Cc(-=I DArBC=A 11gt1( ISc AtA f Cc -= H L lAlA I C I Cl

1t~()cD=C1 ~l (AIBl (cjAfrrr5~5Gl ~~ t DAAfCC tgtlt Se4 A HC tit c11ilaquoraquo SIt 1y ar171~ BS41s(to AS e 0cc we Su e H 6ltve c1(i~amp r A~ H C~ S4rt a(((~4~ I

-~ ALI)f ~fle1 tt P toe a ltpor i~4Mec

LtfP I~~ff~I$f- 5 -to ~CA Camp ft~t~ lttt bJ() ~_ eshy

ll 10 ~ fet ~~~N~ c-tohs API sp (~ftvtll IfQ P ~ 61bullbull Pt14 PttNQ~~ (tries ~tll~ Qfz cod A~ aft ~et

iSoLttd- $(fCJt L CPc p) LCQLP LC~P Lc (gta Palt-e J -t ~es c P ~L I PI Q p 4ftcocttc f~AfrI15 ~s middottU(Woto ~1l$1 w-tSu CPt ( gt e-= A ) P t1t( QIP= X ) (Q-a Pf P2C-= B 4re CoI~rtelr $6 Rb2-l amp1L ( AB-=Xmiddot ~ ~lIQ P~IA8 tVe ~Cqfre~

NewtDJ S

~A ABcOS~~(laquoteJktvsa e ~SQiraquoeamp c~tkt~~ ~~

APgtsc CD) PA AXcpotlts EFG)H-~t~ C F B ~ACG~FHgD~~r~t

Sol~tcNI W E6nFHO~ Eftn FG ~X _Apply~~ ~~scJ ~ ~ -to E~ltSJ F f(f ~Sta E~ () Fr =0 ~~ ( 14 1) I G Fn H( X are ut(ltealf_ ~ltfcAy~ltP~CA(s ~e- 4 E6--()FF~~ J ~S14

EEn FF~ B euroH nf6=X amp-t-fn ~euro 0 tUllPtfcmiddotc4t

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1)ec~CAes ~ 0 nfAaAec ~ JACc) M

A c B actgcP J CAnCpQJ AampnAgR ~r--+--Ir-~~R If AA 613 I cc 4te ~tVt-ct ~

A e 1-~ PI ~ Rctil eo(IQ4(_

c~ rCP_ R2esrk ~-s ~ -tyenUL te~ 4 ~~cAAfIdgre IfV --IfU ~ f 4s root G-oIer ~Ns c~ AOAB ~ftJJ MeoJ- -~r ~ et QPL AEa gil

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62Y ~coJ A~s tttt ~Cct~lI1tr

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Sf 11 4st f( J 14 (cs of ( OotX w~ 1

fe- ) t ~ lt twitt ()~ -tu Cl

eo( C~ ~Ilt ue 0 K- r 4)-~ J ~ ~ li~ f(~ok( -to OO~ -rtgt Is -4 (~~a1CSof tLt -f~Cnrd u

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G7~~14~S

~ If 2c(c~sCp~ lte~tAt PQ ~ p Cl aJ hss fou 0 411(1 yen

middot~ Ot J To Co J C So -ky tore eM ta noe(tk( ~ 2 r(4-~ ~ pIA i~( ~~ oS

~yenI4l~~~

P------ ~ c~ Lf4rdes C e d lifest J e we c- tltANJ A f(rrzl cltJ~C

~~ ~~~eAJf- 14 1

Ci-- ntcl ~~~ CJCl ~ CCsII i~~(t et -t4 ~ C4tt p1-Cch~~

~P~ f LoDa is ~er~ AK~Of CCz _

Let ED be ~~~ foSflctorf oft B~ MaC ~D ~S~e AC -ri Cau~tt1e c1A8JgtC ut ABtttE J(e ~ cfC4c~rc(e c1 AB D MflId 8 Ccent F-=-c --r

D (Olt ~t AE =- CF So 1$1 i te~d~ c~ ~gteJ AE~AB=ADAC II CFIltCBCD CA So~= ~~

5 ~c 81gt fsecfs L ABe WI_ Cl) ~ _ I bull It rJC AS - AD CF- f1C

------------------~ ampA~fel Let ABC be ~ ftrJMIj(e ~ soscJes 68C[)I

CAE AASF ~te~(1 to AAsC wi( ~ CA Aa 4 S bu1 tsrtdvel~ Pro~ta ~-t 141esff-1 AJSc ~ t ~ I~es t=F fEgt DE ~dJ ~uc(~t

Col Amiddot ~ SJltto i Late ~e cnl~w-f( Jgt4Sr~ ~ IE ( - eatu r4~ ~Cgt cte

a~~c~~ Iof crde middot1itE Ultoofe Y04oc Jl Y l AE=CE ( tel btcte(~w-I(Fu

c~ Cc~-tr ~cL~4S AF=8F - I -r4e-tltlfte~ A PUr~I T (~ff I ~~ fiIolu ~ ts ltfCI C1 $f lltty ~amp~ 2 lies Cltt VIIIt~~ ~c c) ~ roampoIaJIlt) of (14So -tkey ~u(4t fAa ~~ Camp~tet

63DP I

r ~e A ScIampf~ 2 LtP be 1ft l~~

~ Ii~~(-kB~lIc(~ -to FD-f _ bull 11C ra(~~ to OE -tt~ fOIts frolle M 1 Elf c(frelttf

S 7c IL ttgt ~-JC 1l rgte ~ t

I

I A~ C~ $oIf1 Let ile cncrcft~ J) ~=HF - PD eF -61) OJ rD-peuro-C~1 EAtlA~1eSamp Ql (A~ AF =SF I CD-c CEAGJPF t 81gt

2 l 1 0 F pW~ ct - fE =AF -AE S r~L pound ~ POtt 1 ~CAty4W(t t

- t_ EICIt1k 3 AC--damp l-H aat 0 P~r -fl Ie A4M C ~ usc -t ifegtSltct ~- Ae Id t W S let

Be It N Let 1k u cudcl 0(AAac -lt1 aNll~Std ~t B t ~ middot Pe ~~t OlUaM

SoIwt t ~ C4Samp 61 Be we6~ 11 aM i~ ~ ~ftthlte Qt S of cYG vtIeof poundlASC 1ICft OM =oel 8M

A~p BA18C i4e c~~In CAsamp - AUN AAec ACfo K~ 1Iotf1Ar (S1Cc iMruw Ibl~cto~ L kll Ac AC Jolaquoaret tes) s e rdeo( I

I

pound I ~e AC kN J 8M Itteet 41 4 (IOIt P I

Siell L PM N L 81lt11 l HCA s MIC PAte CDhcrkcl Q ttl I t fill pou fOitJ BMlC ~p 8M ec 80- yo Y=OA

PM r8- PNICPK POamp-r~ bull ~ $Jtmct~ 1keuro92 Ie -t 10- eo~= ampf(tM- rM) PM - 3

rJ It

OMl PB lr F6 ~t 8MPM+6I1I

OM J ~M

L I A6cb be i$(~Ibullt co_~4 tt ArllAofOo Q-t d - amp c~ f A1)1 SC ~ f (aros

Ccle i VI ( 4 E f= ~~-t t I~oes ampe Q= f-o -Ie C

8y po -t fI-t~ Po~_~ peltPD=PHxPl ~_ ft QClltQ6=~d~Qs~tAcff we1et Po~-Qo=CFM-ru) ~ fMQ~ -ns i (Ies 0ML PQ lQMO Itf oM

Ntrf Csd tIe C~C wi4 Q0 As d-cr~ 2 _ bullbull

It t-sses ME F SlAte LampMO LQ EDt -lCl fo s ~ CIC-z Ef ~ Ef -s iU c($ ef ce Let cI has ceth A( ~s tt lie

laquoa ~ ~ t JFPO _r - flMx pQ fiCa _Vi ~ P$ 01 ~ bull0I

A(Igt~ ite-sect PQ 4t M +Q -of leM _ LA0(= l paceW ac- ~ 8I(C ~ lttlclc p ~_I c 1_

let ya~s t Cltn~ I ~_0 =c bull t if crftit C fc$wt

~l~Sshy c1iW ~ 14- - l-l-~t1 A IS ~f~~J i AA6C J 0 i-tala

C(cuCttdlt~ 7Le -(kfee 4-ttJes AP eamp tMJ Cf irUktt- H EDAA6=-M FDo AC-N tp~4-dcent () 06Jl)F )OCJ1gtE

N C~) 0 J- M N middot i

Solfen bullCO LAfcc9cfLATgtC 9 A fgt l=~C6AtyJrc TktL6lgtFcLBAC AooBc-OCi--ees LOBC-=J(t~Io~Leoc)middot1tl_l8A(= ~oo~L8bFmiddot F omiddot Iamp -=gt 08 ~ tgt l= ~frly DC lDe-

B 0 c (~) CLMA ltPgtM~MIf AC~HI () I 81U AlA ~ NIi-IIIt= Aa -AltlaquoJI tgtA L

F ~c ~ l)e - ~ Aa~Ac (c~

~~b )N6oIp 13Ai~80-- OllADI (0( 1)04 ()-(~)+(()+ll)-~~ J)M~ ~_cot=OMOt)1 te

bull Ott J MAl N~-11 fI ~=C)jI 6lf1

~iet SoU- ln LAFC0 =LOC-dJACl) Fc-tkc ut J bu])M So ~t TeI [)f -ue L Jeo L 6gtF =LeAlt ~ J-f4 a~t (~e tB

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f r A~At pCiSS~ 14 0 es SetOf ----1-- To e~setl ~ ~ _

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9 lCo (iflaquo at ~Sdf~7e 4-( p~ oF

0 V ~-tlaat iHy~t~tOmiddotmiddot71-~R CA4f~(S ~ SQIJ-fo ~ 0 J

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wi+lLAoB=L8~A Wt3ttLlOMdOl~ () - ~ LOA8= LogA ~

Aamp~ = OA _ r~A A6 0(3 - OB

=) Ae r lo A~

-------- --------~

)ampa-cle i (~tlcptleofto A ~cQlt$ A 1ckc ~tiatt~

ampl if tlyen~ t ampe- ACBD - A~middotq) +AD

II( V c bull I

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I iIC ~ AeC SilCamp ~ IH 6e - c I

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A6amp c) +A)xBe Acll 81gt middot

Re fICS 11L sf ~ eat be ltoftrec -to ~t -I- ~1-tllAt t MilcO + AtgtICBC =AC 1CI1~

~V Asctgt S (l u~ ~lJ4~ 0-shy

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-

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p _ c $Lt-~ -71

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sc =l Ott foIIttll is ~iIr~le-t -fo site (5 -tk Ptt-RS l~~( (Sl~~14ft

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-tt TltitCirtlutdts Ie CA Ca Cc CD rtsrdtuely CfSMoSmiddotd fIf~iQ 3(0 r ~r31gt0 By ~ct(s)

I~ AC Q( e04~~t ofo ~gtltS

cfct (+) I CA SIrcent to filllt LA fllAlrd to 81gt CIrs

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0 0 r~-t 0lt1

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CpnCa= 0r~ LAf Le P )Mjl-ly 4~t( LI) R J ll)n~ So bull

$r~ AcJ Mgt PClKs ~~Ic~4J~~ ~ fet h) PampRs is floc

~

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~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

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P ~f - xpmiddot ~ P~B6+lCApLcA8 J

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I

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s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

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I

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Page 22: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

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Sf 11 4st f( J 14 (cs of ( OotX w~ 1

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------------------~ ampA~fel Let ABC be ~ ftrJMIj(e ~ soscJes 68C[)I

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I

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- t_ EICIt1k 3 AC--damp l-H aat 0 P~r -fl Ie A4M C ~ usc -t ifegtSltct ~- Ae Id t W S let

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Siell L PM N L 81lt11 l HCA s MIC PAte CDhcrkcl Q ttl I t fill pou fOitJ BMlC ~p 8M ec 80- yo Y=OA

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rJ It

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let ya~s t Cltn~ I ~_0 =c bull t if crftit C fc$wt

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Page 25: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

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of -flit G~ a41~ aJa Afe utllt4r bull JotlfoItr~~tf(~-kGttk ~~set fotleceofv-f~ ~~ctrJe ~

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f r A~At pCiSS~ 14 0 es SetOf ----1-- To e~setl ~ ~ _

Ifgt reg If two cr~ (f~ttIlC~ C4fVts ~(( ttlso ~~(etAf ~ fbft Pto)~~~~

9 lCo (iflaquo at ~Sdf~7e 4-( p~ oF

0 V ~-tlaat iHy~t~tOmiddotmiddot71-~R CA4f~(S ~ SQIJ-fo ~ 0 J

A Ie dI o~ctves4ltSet-f0r1f~~ ~ c () ~-t bull i- cmiddotrd~ ftftfiSttft S ~ fa-5~ 1Gtt cri(S t ( 4It ~fo-6etc~ Gllf f~S A lS 0 4laquol 0 A ~ IV~ IIG(C4((o(Af ~ oAmiddoto~ t 0Bmiddot O~ ~ OAloB OP4 ACoj

wi+lLAoB=L8~A Wt3ttLlOMdOl~ () - ~ LOA8= LogA ~

Aamp~ = OA _ r~A A6 0(3 - OB

=) Ae r lo A~

-------- --------~

)ampa-cle i (~tlcptleofto A ~cQlt$ A 1ckc ~tiatt~

ampl if tlyen~ t ampe- ACBD - A~middotq) +AD

II( V c bull I

SoJn C-sidelt -kfSiCll At 1 vuu~j l)is Cpoundlaquotef bull J ~p-J~ Ygt I) - t t e y fatH4) J -k ~ro-atdc qf ~ec ~~A~ I Q

I iIC ~ AeC SilCamp ~ IH 6e - c I

J vue b -ftt (1) We t _ 1 _AC~ r - Be - - middot

iDA ~ 01gt1gt AJ)middotC1) tt Mltrtrllj b~ lAOmiddot~]) CO~2 1aJkSimiddotces amporeJ

A6amp c) +A)xBe Acll 81gt middot

Re fICS 11L sf ~ eat be ltoftrec -to ~t -I- ~1-tllAt t MilcO + AtgtICBC =AC 1CI1~

~V Asctgt S (l u~ ~lJ4~ 0-shy

~S6~~~ kfCfS4tJ foJt of~~ -+k eampIt~ otIIIetStM Ai ~itlt ~s -fIc ~o~~ rote iIt wJere -reIs CIMif s Mesc(t _

-

6x4t~le 2 Lt ABc 0 be ~ ~tllt t(kft~ suamp~t At ampt so liltftStct At Y1tt ~r AtO P~t~( -Ke -refltecf of 0 ~fOSS AS BC C)1gtA A~ C4IIcYdtc

p _ c $Lt-~ -71

Lcent P~ ~So k ~fut f-~Wi _ 010 0 flO Msc CD lgtA Ye cdIVt bull

sc =l Ott foIIttll is ~iIr~le-t -fo site (5 -tk Ptt-RS l~~( (Sl~~14ft

e IcentS 0 0 -to tts e_~Hrlt OSAP DfBQ ~CR O~DS ~ludlC~~ J J -J ~ _ bull

-tt TltitCirtlutdts Ie CA Ca Cc CD rtsrdtuely CfSMoSmiddotd fIf~iQ 3(0 r ~r31gt0 By ~ct(s)

I~ AC Q( e04~~t ofo ~gtltS

cfct (+) I CA SIrcent to filllt LA fllAlrd to 81gt CIrs

Set to ~ IIt LB ~(c of Ac I C ~ Sci fo c tAlC -to ~lgt1 craquoisSeoet t ol1t LD~E lc ~

0 0 r~-t 0lt1

L Nen bull

CpnCa= 0r~ LAf Le P )Mjl-ly 4~t( LI) R J ll)n~ So bull

$r~ AcJ Mgt PClKs ~~Ic~4J~~ ~ fet h) PampRs is floc

~

G)Cdtpt f

Le-t P bft Af6~-t ~S~ 4l1It Appound ~~~-t LAPB-LACS LA(C-L~8C

Ltt tgt amp be ik~~tS 0( AAPS )AA~C nspecflf ~toe ~l A1gt 1gt1 ce )wtet A fOiWtshy

~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

( )tlfamp 61) biSKfs IA8PJ By ~t CT) ACAfACf~ ~ ~ I3A - XA So iSttf ACAeACampA

P ~f - xpmiddot ~ P~B6+lCApLcA8 J

C-1-1 ~=~ 5tRCt X ( 4ft AP ampt ~1It By~t (s) 1 ~ tCp~=LCitA ~ ~ I I~ fQ is Seoct of ( ~ ~~ 1 f4$s~~3C o listf SiacCrtIeO ~ -T(Alrl~f4lrgto ~~(1)1 tIIet pamp ~t(4C~I~Ois~tfo(0

A ~IgtC A~te A lU)e bullA p A APelAcIIgt f-c ~) I SIWICamp

I

~ ~ ilt3t +00 c( ~ 1 PQ fh ) Qm Q J r bull bull ~ t01 setc~ 10 t of I I

No LM~-L~8-=-LIWC-LAec f~ $(amp ~st ~JO 0 Ao( ~J~~ ~ Atl 43~ t (-d 0 ~ A61PcD

fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

Page 26: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

CT1tW EtA-f tt 1- bull ~A be ~iAt 4+etse~ ~ fwo nO~fD~fUtf Cirdes C ~C CAl-~ef0 0 (tltjreJ~ Dtte ~1MtM

~t~o c eamp 1d1t(s-et C cent~ Cztlt Pt J(e -i4af(EV (A~ ~-t-te~ctc At ~Ca~t QI Lk Me t ~~it-t~ ()Q o-J ~ ~ ~itet ~ pzCla

~-t ~ LtJAo LMAMz

~~ ~ ~

SGl~ B-t~etJ Plpt(gtzOt~~O

Ca ~lJZ~ damp bull nwy 14(0 oPa ) Q SeKds C L 0 PI

~ I ~ t -lO Z bull ~ J ~ OAn Ct =8 ~~-oflt~1 e $ Ll016M -tLl~A~~ So LOI~= LOaAHa A~ t- fs 0P 0 P ~o ltlie sjI Ie~ 00 Cgt~ ofL ~ ) 00 ~O~e-=OPct=OAIOg

t ~te~~-1 cknl4t1 ~ AO~ ~ Ate ~Itc

~ LO8M= lDAM

A~ I =gt LoAM L~AMz WIAamp~ ---

L 0cA M~ ==gt L0 A0)- L I-i A Mz bull -to _16bCrfkSf~S

Solt~p Wpound(CS JTbe reflec~ ~ S Wit-(S~ltt

fI5 Mis

~J e

t ~lwt Cgt (1Of ctImiddotd i -br3frt -+0

e $ f(~

Q cmiddotnI F -tkt bcs of tIl YOII f Sue- fut ~e-re ~)f Q

01 ~ w~ M ~ ~(eoi~ ~ l R~~ QS ~ isc~e~ C~rdamp 4 A PQ R

-to M Lt u be 04

~ A$ iudQ~~ltofe1 middot~~(R C V Lat ~ 10 ampl yo~t~14 fc

Co -fI kottcrt(e+y wfoit4 uW( P-tkt StI~ l t

~CtCte (_oppos-e P -(f ~ T middot (1 ~ Set$ U -to (Q((esr-~~-toflfobulltHf lt 1) Ii P~n (= v ut s setft~~ ~ t PQ~ ~

TR SQ=S - PR= PV- PIlt = Vlaquo=n ~ T T So 5 01 Ae ltT0 e ttl

ampruJt~J) fr p~ ltTaee~ UT ~ U

~ l(P Ifamp)Se0v4 u to ~ C(telte e to c~ l I- UtoT So TT Let 14tats~ P-4 C ~+~t5ect r ~Q~R ~

ampS-=s- Pflt=Pv- P((--Vre =TIC=-TIlt ~ tiM -i1s-MS Ti-f1T=-jiM PtSAt4t

~ El4middotrle b rio t)

Lt-A~c ~ co ftiI5le ~ ~tof scl Be A1k ~tsct- N ot l ~AC i~+fSoct ~c ct tJ ~~r~I~ k~ +0 AN -+~~ N ifersets AM 4 Q -c AB -t p -n ~f-lrJrmiddot 0 li~e to APt Pt-a~AIl laquo 0 middot Pofe Qo l Be SIt- TfABAc1kMNQfampAQMol3c

WLOG I ampS$f41111t A6gtAC Let AN MttStcf Uttucrclt fAABC j 1) ~

-- - bull c L 1gtg CL lgtAC=L~Llgtc~ e lAo M f~ r ~ ~ DC aJ PM 1 Be

~o Ho~y K(A ~StovlsA6j)(+oAgO(t4 08 O~ aq ae Itt t= Be( PN -r4~

L Ogt- L b8e =LM8=ro6_LAop=LoP~ ~ ~ D 0 tcKl orooc

I ) I J GfeCttrA J~c J~M4 ~ L 0 - Lep - 1 0 - 7 1- - 0 - 0 Igt IC tS~ amp It sc K is AM == AM l PfI=Q

I I ~ Lg eto L~~O~)oo 1~ ~o LSC g c It Be r

F l

(~p Sol~ middot Let dort FE ~wt -to nr2 4Ss(oll (iJ

Feuro () r C Lt r 1 U04s~r 111k ~y1- (M V)Sets P t r c-to K) Iiamp JE t jilt L AS

sow1 bull Ff 1Ie L ~ A is +lt1 ~roIldrc FE LNEC ~Afe~LAME I rSo L ~~eL~A~)~ LlNEcLlAMc ~ ACAeuro ~e1IA I ~ ~ pouer ~ A ltiol4Isped to r is Ac AM= AE S~M(tAfy I 16fJe t ~A i-fk -(~d -to ~~ Aft A~ A - A ~ =lttiJPOiqJ ~FeJ 56 Ae==-AF (1amp tflt11- rAAtcd - I

_ ~S AI ~ fIr2 AA~f ~ etc )~lll fu ett(4-ik1t f t fl1 pues-~r 1gt 61 sJMe~1 t ~OI)O~ wt Soc Oa I ~~t ~~ Ctgt

~ Ltgtco~=LClgto L cLeF ~s ir~S COa b~s L 9CF $ceCfiS~f rl So

Cl) is ~so~~~ -to re

E)(4flt

amp($ PI Ira Q-te ite~Iy ~ t ~ rt M N~oJtlJ ~ r fGs$es -tI- caff( 01 ~ r~

lAe r tgtit cl1illfr iii r rio MAn=C MBfr=D f (0 ~It CD $ 1~jkt to r2 bull

~ C~ IS - tYgtctStIt

~~ A ilefSVsv wi CAAer 0 oJ ugt r gt0

(amptatl 1 J(o r)) sA~f~ +lAo Se~s A~et(1 ~(t X 0 to ~ i~e VOl~t X O~bull y at sucL fut OXmiddotOlec r~ ~ CWOIelcu I fo X=0 ~ Utake )(=~ _-cl tllSo~)(-=QO Wt-take X=o

1ke Circle -w+1 C2~+e~ 0 A~ ~kCamps r gto-((ct k poundSle ~e~ ~ I~e IWJy 4fso ~ft A~ ltrs~ by sff~t ~ CrCJtL (lWt~middotcP

fGcfs CO Gift1 ~I((S~ ~ ~ bje(~~ it f~~ u~ 00 -to -t~lfmiddot ~ ~c-t J ex ) X ~

reg -If )( s-ikcRiC iwe~~1~ XI=X bull f)(~o~elf(enX~

= bull 1 ~x ~oit ofTaTl) ~t-rrl 4i~

P e ~ X1 lCT2 4~f~~-t1~ ~s iS k~

- __ OXmiddot ox ((sec LTo)()(ycsLTox)r~ ACtreJtt ~~SSi~ 14ftJUJ 0 ~~t +0 A cvdc bull ~ya16tj -4r~ O k iII-s ak~cIc -poits ~(~ St -to ~amp~ foffts l4 fOit 0) ~~fets

of -flit G~ a41~ aJa Afe utllt4r bull JotlfoItr~~tf(~-kGttk ~~set fotleceofv-f~ ~~ctrJe ~

A(fJe vaSSoVJ4-f 0 is Set -to 4 (euro reuro IS ~~~fI)~ 0 ~~s ~~k(+ifia1e-t (It( -t 44td Ito Cnverrely (A (middot1U1IIJt rssj-tlt~ 0 is Seltt -to ~Cvde (w~~ 0 Ni-l -tttllj~-t Imiddotier0 ~Itd to ~ leilt

f r A~At pCiSS~ 14 0 es SetOf ----1-- To e~setl ~ ~ _

Ifgt reg If two cr~ (f~ttIlC~ C4fVts ~(( ttlso ~~(etAf ~ fbft Pto)~~~~

9 lCo (iflaquo at ~Sdf~7e 4-( p~ oF

0 V ~-tlaat iHy~t~tOmiddotmiddot71-~R CA4f~(S ~ SQIJ-fo ~ 0 J

A Ie dI o~ctves4ltSet-f0r1f~~ ~ c () ~-t bull i- cmiddotrd~ ftftfiSttft S ~ fa-5~ 1Gtt cri(S t ( 4It ~fo-6etc~ Gllf f~S A lS 0 4laquol 0 A ~ IV~ IIG(C4((o(Af ~ oAmiddoto~ t 0Bmiddot O~ ~ OAloB OP4 ACoj

wi+lLAoB=L8~A Wt3ttLlOMdOl~ () - ~ LOA8= LogA ~

Aamp~ = OA _ r~A A6 0(3 - OB

=) Ae r lo A~

-------- --------~

)ampa-cle i (~tlcptleofto A ~cQlt$ A 1ckc ~tiatt~

ampl if tlyen~ t ampe- ACBD - A~middotq) +AD

II( V c bull I

SoJn C-sidelt -kfSiCll At 1 vuu~j l)is Cpoundlaquotef bull J ~p-J~ Ygt I) - t t e y fatH4) J -k ~ro-atdc qf ~ec ~~A~ I Q

I iIC ~ AeC SilCamp ~ IH 6e - c I

J vue b -ftt (1) We t _ 1 _AC~ r - Be - - middot

iDA ~ 01gt1gt AJ)middotC1) tt Mltrtrllj b~ lAOmiddot~]) CO~2 1aJkSimiddotces amporeJ

A6amp c) +A)xBe Acll 81gt middot

Re fICS 11L sf ~ eat be ltoftrec -to ~t -I- ~1-tllAt t MilcO + AtgtICBC =AC 1CI1~

~V Asctgt S (l u~ ~lJ4~ 0-shy

~S6~~~ kfCfS4tJ foJt of~~ -+k eampIt~ otIIIetStM Ai ~itlt ~s -fIc ~o~~ rote iIt wJere -reIs CIMif s Mesc(t _

-

6x4t~le 2 Lt ABc 0 be ~ ~tllt t(kft~ suamp~t At ampt so liltftStct At Y1tt ~r AtO P~t~( -Ke -refltecf of 0 ~fOSS AS BC C)1gtA A~ C4IIcYdtc

p _ c $Lt-~ -71

Lcent P~ ~So k ~fut f-~Wi _ 010 0 flO Msc CD lgtA Ye cdIVt bull

sc =l Ott foIIttll is ~iIr~le-t -fo site (5 -tk Ptt-RS l~~( (Sl~~14ft

e IcentS 0 0 -to tts e_~Hrlt OSAP DfBQ ~CR O~DS ~ludlC~~ J J -J ~ _ bull

-tt TltitCirtlutdts Ie CA Ca Cc CD rtsrdtuely CfSMoSmiddotd fIf~iQ 3(0 r ~r31gt0 By ~ct(s)

I~ AC Q( e04~~t ofo ~gtltS

cfct (+) I CA SIrcent to filllt LA fllAlrd to 81gt CIrs

Set to ~ IIt LB ~(c of Ac I C ~ Sci fo c tAlC -to ~lgt1 craquoisSeoet t ol1t LD~E lc ~

0 0 r~-t 0lt1

L Nen bull

CpnCa= 0r~ LAf Le P )Mjl-ly 4~t( LI) R J ll)n~ So bull

$r~ AcJ Mgt PClKs ~~Ic~4J~~ ~ fet h) PampRs is floc

~

G)Cdtpt f

Le-t P bft Af6~-t ~S~ 4l1It Appound ~~~-t LAPB-LACS LA(C-L~8C

Ltt tgt amp be ik~~tS 0( AAPS )AA~C nspecflf ~toe ~l A1gt 1gt1 ce )wtet A fOiWtshy

~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

( )tlfamp 61) biSKfs IA8PJ By ~t CT) ACAfACf~ ~ ~ I3A - XA So iSttf ACAeACampA

P ~f - xpmiddot ~ P~B6+lCApLcA8 J

C-1-1 ~=~ 5tRCt X ( 4ft AP ampt ~1It By~t (s) 1 ~ tCp~=LCitA ~ ~ I I~ fQ is Seoct of ( ~ ~~ 1 f4$s~~3C o listf SiacCrtIeO ~ -T(Alrl~f4lrgto ~~(1)1 tIIet pamp ~t(4C~I~Ois~tfo(0

A ~IgtC A~te A lU)e bullA p A APelAcIIgt f-c ~) I SIWICamp

I

~ ~ ilt3t +00 c( ~ 1 PQ fh ) Qm Q J r bull bull ~ t01 setc~ 10 t of I I

No LM~-L~8-=-LIWC-LAec f~ $(amp ~st ~JO 0 Ao( ~J~~ ~ Atl 43~ t (-d 0 ~ A61PcD

fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

Page 27: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

~ El4middotrle b rio t)

Lt-A~c ~ co ftiI5le ~ ~tof scl Be A1k ~tsct- N ot l ~AC i~+fSoct ~c ct tJ ~~r~I~ k~ +0 AN -+~~ N ifersets AM 4 Q -c AB -t p -n ~f-lrJrmiddot 0 li~e to APt Pt-a~AIl laquo 0 middot Pofe Qo l Be SIt- TfABAc1kMNQfampAQMol3c

WLOG I ampS$f41111t A6gtAC Let AN MttStcf Uttucrclt fAABC j 1) ~

-- - bull c L 1gtg CL lgtAC=L~Llgtc~ e lAo M f~ r ~ ~ DC aJ PM 1 Be

~o Ho~y K(A ~StovlsA6j)(+oAgO(t4 08 O~ aq ae Itt t= Be( PN -r4~

L Ogt- L b8e =LM8=ro6_LAop=LoP~ ~ ~ D 0 tcKl orooc

I ) I J GfeCttrA J~c J~M4 ~ L 0 - Lep - 1 0 - 7 1- - 0 - 0 Igt IC tS~ amp It sc K is AM == AM l PfI=Q

I I ~ Lg eto L~~O~)oo 1~ ~o LSC g c It Be r

F l

(~p Sol~ middot Let dort FE ~wt -to nr2 4Ss(oll (iJ

Feuro () r C Lt r 1 U04s~r 111k ~y1- (M V)Sets P t r c-to K) Iiamp JE t jilt L AS

sow1 bull Ff 1Ie L ~ A is +lt1 ~roIldrc FE LNEC ~Afe~LAME I rSo L ~~eL~A~)~ LlNEcLlAMc ~ ACAeuro ~e1IA I ~ ~ pouer ~ A ltiol4Isped to r is Ac AM= AE S~M(tAfy I 16fJe t ~A i-fk -(~d -to ~~ Aft A~ A - A ~ =lttiJPOiqJ ~FeJ 56 Ae==-AF (1amp tflt11- rAAtcd - I

_ ~S AI ~ fIr2 AA~f ~ etc )~lll fu ett(4-ik1t f t fl1 pues-~r 1gt 61 sJMe~1 t ~OI)O~ wt Soc Oa I ~~t ~~ Ctgt

~ Ltgtco~=LClgto L cLeF ~s ir~S COa b~s L 9CF $ceCfiS~f rl So

Cl) is ~so~~~ -to re

E)(4flt

amp($ PI Ira Q-te ite~Iy ~ t ~ rt M N~oJtlJ ~ r fGs$es -tI- caff( 01 ~ r~

lAe r tgtit cl1illfr iii r rio MAn=C MBfr=D f (0 ~It CD $ 1~jkt to r2 bull

~ C~ IS - tYgtctStIt

~~ A ilefSVsv wi CAAer 0 oJ ugt r gt0

(amptatl 1 J(o r)) sA~f~ +lAo Se~s A~et(1 ~(t X 0 to ~ i~e VOl~t X O~bull y at sucL fut OXmiddotOlec r~ ~ CWOIelcu I fo X=0 ~ Utake )(=~ _-cl tllSo~)(-=QO Wt-take X=o

1ke Circle -w+1 C2~+e~ 0 A~ ~kCamps r gto-((ct k poundSle ~e~ ~ I~e IWJy 4fso ~ft A~ ltrs~ by sff~t ~ CrCJtL (lWt~middotcP

fGcfs CO Gift1 ~I((S~ ~ ~ bje(~~ it f~~ u~ 00 -to -t~lfmiddot ~ ~c-t J ex ) X ~

reg -If )( s-ikcRiC iwe~~1~ XI=X bull f)(~o~elf(enX~

= bull 1 ~x ~oit ofTaTl) ~t-rrl 4i~

P e ~ X1 lCT2 4~f~~-t1~ ~s iS k~

- __ OXmiddot ox ((sec LTo)()(ycsLTox)r~ ACtreJtt ~~SSi~ 14ftJUJ 0 ~~t +0 A cvdc bull ~ya16tj -4r~ O k iII-s ak~cIc -poits ~(~ St -to ~amp~ foffts l4 fOit 0) ~~fets

of -flit G~ a41~ aJa Afe utllt4r bull JotlfoItr~~tf(~-kGttk ~~set fotleceofv-f~ ~~ctrJe ~

A(fJe vaSSoVJ4-f 0 is Set -to 4 (euro reuro IS ~~~fI)~ 0 ~~s ~~k(+ifia1e-t (It( -t 44td Ito Cnverrely (A (middot1U1IIJt rssj-tlt~ 0 is Seltt -to ~Cvde (w~~ 0 Ni-l -tttllj~-t Imiddotier0 ~Itd to ~ leilt

f r A~At pCiSS~ 14 0 es SetOf ----1-- To e~setl ~ ~ _

Ifgt reg If two cr~ (f~ttIlC~ C4fVts ~(( ttlso ~~(etAf ~ fbft Pto)~~~~

9 lCo (iflaquo at ~Sdf~7e 4-( p~ oF

0 V ~-tlaat iHy~t~tOmiddotmiddot71-~R CA4f~(S ~ SQIJ-fo ~ 0 J

A Ie dI o~ctves4ltSet-f0r1f~~ ~ c () ~-t bull i- cmiddotrd~ ftftfiSttft S ~ fa-5~ 1Gtt cri(S t ( 4It ~fo-6etc~ Gllf f~S A lS 0 4laquol 0 A ~ IV~ IIG(C4((o(Af ~ oAmiddoto~ t 0Bmiddot O~ ~ OAloB OP4 ACoj

wi+lLAoB=L8~A Wt3ttLlOMdOl~ () - ~ LOA8= LogA ~

Aamp~ = OA _ r~A A6 0(3 - OB

=) Ae r lo A~

-------- --------~

)ampa-cle i (~tlcptleofto A ~cQlt$ A 1ckc ~tiatt~

ampl if tlyen~ t ampe- ACBD - A~middotq) +AD

II( V c bull I

SoJn C-sidelt -kfSiCll At 1 vuu~j l)is Cpoundlaquotef bull J ~p-J~ Ygt I) - t t e y fatH4) J -k ~ro-atdc qf ~ec ~~A~ I Q

I iIC ~ AeC SilCamp ~ IH 6e - c I

J vue b -ftt (1) We t _ 1 _AC~ r - Be - - middot

iDA ~ 01gt1gt AJ)middotC1) tt Mltrtrllj b~ lAOmiddot~]) CO~2 1aJkSimiddotces amporeJ

A6amp c) +A)xBe Acll 81gt middot

Re fICS 11L sf ~ eat be ltoftrec -to ~t -I- ~1-tllAt t MilcO + AtgtICBC =AC 1CI1~

~V Asctgt S (l u~ ~lJ4~ 0-shy

~S6~~~ kfCfS4tJ foJt of~~ -+k eampIt~ otIIIetStM Ai ~itlt ~s -fIc ~o~~ rote iIt wJere -reIs CIMif s Mesc(t _

-

6x4t~le 2 Lt ABc 0 be ~ ~tllt t(kft~ suamp~t At ampt so liltftStct At Y1tt ~r AtO P~t~( -Ke -refltecf of 0 ~fOSS AS BC C)1gtA A~ C4IIcYdtc

p _ c $Lt-~ -71

Lcent P~ ~So k ~fut f-~Wi _ 010 0 flO Msc CD lgtA Ye cdIVt bull

sc =l Ott foIIttll is ~iIr~le-t -fo site (5 -tk Ptt-RS l~~( (Sl~~14ft

e IcentS 0 0 -to tts e_~Hrlt OSAP DfBQ ~CR O~DS ~ludlC~~ J J -J ~ _ bull

-tt TltitCirtlutdts Ie CA Ca Cc CD rtsrdtuely CfSMoSmiddotd fIf~iQ 3(0 r ~r31gt0 By ~ct(s)

I~ AC Q( e04~~t ofo ~gtltS

cfct (+) I CA SIrcent to filllt LA fllAlrd to 81gt CIrs

Set to ~ IIt LB ~(c of Ac I C ~ Sci fo c tAlC -to ~lgt1 craquoisSeoet t ol1t LD~E lc ~

0 0 r~-t 0lt1

L Nen bull

CpnCa= 0r~ LAf Le P )Mjl-ly 4~t( LI) R J ll)n~ So bull

$r~ AcJ Mgt PClKs ~~Ic~4J~~ ~ fet h) PampRs is floc

~

G)Cdtpt f

Le-t P bft Af6~-t ~S~ 4l1It Appound ~~~-t LAPB-LACS LA(C-L~8C

Ltt tgt amp be ik~~tS 0( AAPS )AA~C nspecflf ~toe ~l A1gt 1gt1 ce )wtet A fOiWtshy

~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

( )tlfamp 61) biSKfs IA8PJ By ~t CT) ACAfACf~ ~ ~ I3A - XA So iSttf ACAeACampA

P ~f - xpmiddot ~ P~B6+lCApLcA8 J

C-1-1 ~=~ 5tRCt X ( 4ft AP ampt ~1It By~t (s) 1 ~ tCp~=LCitA ~ ~ I I~ fQ is Seoct of ( ~ ~~ 1 f4$s~~3C o listf SiacCrtIeO ~ -T(Alrl~f4lrgto ~~(1)1 tIIet pamp ~t(4C~I~Ois~tfo(0

A ~IgtC A~te A lU)e bullA p A APelAcIIgt f-c ~) I SIWICamp

I

~ ~ ilt3t +00 c( ~ 1 PQ fh ) Qm Q J r bull bull ~ t01 setc~ 10 t of I I

No LM~-L~8-=-LIWC-LAec f~ $(amp ~st ~JO 0 Ao( ~J~~ ~ Atl 43~ t (-d 0 ~ A61PcD

fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

Page 28: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

~ C~ IS - tYgtctStIt

~~ A ilefSVsv wi CAAer 0 oJ ugt r gt0

(amptatl 1 J(o r)) sA~f~ +lAo Se~s A~et(1 ~(t X 0 to ~ i~e VOl~t X O~bull y at sucL fut OXmiddotOlec r~ ~ CWOIelcu I fo X=0 ~ Utake )(=~ _-cl tllSo~)(-=QO Wt-take X=o

1ke Circle -w+1 C2~+e~ 0 A~ ~kCamps r gto-((ct k poundSle ~e~ ~ I~e IWJy 4fso ~ft A~ ltrs~ by sff~t ~ CrCJtL (lWt~middotcP

fGcfs CO Gift1 ~I((S~ ~ ~ bje(~~ it f~~ u~ 00 -to -t~lfmiddot ~ ~c-t J ex ) X ~

reg -If )( s-ikcRiC iwe~~1~ XI=X bull f)(~o~elf(enX~

= bull 1 ~x ~oit ofTaTl) ~t-rrl 4i~

P e ~ X1 lCT2 4~f~~-t1~ ~s iS k~

- __ OXmiddot ox ((sec LTo)()(ycsLTox)r~ ACtreJtt ~~SSi~ 14ftJUJ 0 ~~t +0 A cvdc bull ~ya16tj -4r~ O k iII-s ak~cIc -poits ~(~ St -to ~amp~ foffts l4 fOit 0) ~~fets

of -flit G~ a41~ aJa Afe utllt4r bull JotlfoItr~~tf(~-kGttk ~~set fotleceofv-f~ ~~ctrJe ~

A(fJe vaSSoVJ4-f 0 is Set -to 4 (euro reuro IS ~~~fI)~ 0 ~~s ~~k(+ifia1e-t (It( -t 44td Ito Cnverrely (A (middot1U1IIJt rssj-tlt~ 0 is Seltt -to ~Cvde (w~~ 0 Ni-l -tttllj~-t Imiddotier0 ~Itd to ~ leilt

f r A~At pCiSS~ 14 0 es SetOf ----1-- To e~setl ~ ~ _

Ifgt reg If two cr~ (f~ttIlC~ C4fVts ~(( ttlso ~~(etAf ~ fbft Pto)~~~~

9 lCo (iflaquo at ~Sdf~7e 4-( p~ oF

0 V ~-tlaat iHy~t~tOmiddotmiddot71-~R CA4f~(S ~ SQIJ-fo ~ 0 J

A Ie dI o~ctves4ltSet-f0r1f~~ ~ c () ~-t bull i- cmiddotrd~ ftftfiSttft S ~ fa-5~ 1Gtt cri(S t ( 4It ~fo-6etc~ Gllf f~S A lS 0 4laquol 0 A ~ IV~ IIG(C4((o(Af ~ oAmiddoto~ t 0Bmiddot O~ ~ OAloB OP4 ACoj

wi+lLAoB=L8~A Wt3ttLlOMdOl~ () - ~ LOA8= LogA ~

Aamp~ = OA _ r~A A6 0(3 - OB

=) Ae r lo A~

-------- --------~

)ampa-cle i (~tlcptleofto A ~cQlt$ A 1ckc ~tiatt~

ampl if tlyen~ t ampe- ACBD - A~middotq) +AD

II( V c bull I

SoJn C-sidelt -kfSiCll At 1 vuu~j l)is Cpoundlaquotef bull J ~p-J~ Ygt I) - t t e y fatH4) J -k ~ro-atdc qf ~ec ~~A~ I Q

I iIC ~ AeC SilCamp ~ IH 6e - c I

J vue b -ftt (1) We t _ 1 _AC~ r - Be - - middot

iDA ~ 01gt1gt AJ)middotC1) tt Mltrtrllj b~ lAOmiddot~]) CO~2 1aJkSimiddotces amporeJ

A6amp c) +A)xBe Acll 81gt middot

Re fICS 11L sf ~ eat be ltoftrec -to ~t -I- ~1-tllAt t MilcO + AtgtICBC =AC 1CI1~

~V Asctgt S (l u~ ~lJ4~ 0-shy

~S6~~~ kfCfS4tJ foJt of~~ -+k eampIt~ otIIIetStM Ai ~itlt ~s -fIc ~o~~ rote iIt wJere -reIs CIMif s Mesc(t _

-

6x4t~le 2 Lt ABc 0 be ~ ~tllt t(kft~ suamp~t At ampt so liltftStct At Y1tt ~r AtO P~t~( -Ke -refltecf of 0 ~fOSS AS BC C)1gtA A~ C4IIcYdtc

p _ c $Lt-~ -71

Lcent P~ ~So k ~fut f-~Wi _ 010 0 flO Msc CD lgtA Ye cdIVt bull

sc =l Ott foIIttll is ~iIr~le-t -fo site (5 -tk Ptt-RS l~~( (Sl~~14ft

e IcentS 0 0 -to tts e_~Hrlt OSAP DfBQ ~CR O~DS ~ludlC~~ J J -J ~ _ bull

-tt TltitCirtlutdts Ie CA Ca Cc CD rtsrdtuely CfSMoSmiddotd fIf~iQ 3(0 r ~r31gt0 By ~ct(s)

I~ AC Q( e04~~t ofo ~gtltS

cfct (+) I CA SIrcent to filllt LA fllAlrd to 81gt CIrs

Set to ~ IIt LB ~(c of Ac I C ~ Sci fo c tAlC -to ~lgt1 craquoisSeoet t ol1t LD~E lc ~

0 0 r~-t 0lt1

L Nen bull

CpnCa= 0r~ LAf Le P )Mjl-ly 4~t( LI) R J ll)n~ So bull

$r~ AcJ Mgt PClKs ~~Ic~4J~~ ~ fet h) PampRs is floc

~

G)Cdtpt f

Le-t P bft Af6~-t ~S~ 4l1It Appound ~~~-t LAPB-LACS LA(C-L~8C

Ltt tgt amp be ik~~tS 0( AAPS )AA~C nspecflf ~toe ~l A1gt 1gt1 ce )wtet A fOiWtshy

~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

( )tlfamp 61) biSKfs IA8PJ By ~t CT) ACAfACf~ ~ ~ I3A - XA So iSttf ACAeACampA

P ~f - xpmiddot ~ P~B6+lCApLcA8 J

C-1-1 ~=~ 5tRCt X ( 4ft AP ampt ~1It By~t (s) 1 ~ tCp~=LCitA ~ ~ I I~ fQ is Seoct of ( ~ ~~ 1 f4$s~~3C o listf SiacCrtIeO ~ -T(Alrl~f4lrgto ~~(1)1 tIIet pamp ~t(4C~I~Ois~tfo(0

A ~IgtC A~te A lU)e bullA p A APelAcIIgt f-c ~) I SIWICamp

I

~ ~ ilt3t +00 c( ~ 1 PQ fh ) Qm Q J r bull bull ~ t01 setc~ 10 t of I I

No LM~-L~8-=-LIWC-LAec f~ $(amp ~st ~JO 0 Ao( ~J~~ ~ Atl 43~ t (-d 0 ~ A61PcD

fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

Page 29: (I umakyli/2731/2012-2013Sp/2731_pp55-86.… · sp ~ ~~ {> "= ... ~. .,.... ~~~*~ ... _ ~~ ~ ~. / ~ ~, ~ ~ ~.. ~ ~, ~ ~

-------- --------~

)ampa-cle i (~tlcptleofto A ~cQlt$ A 1ckc ~tiatt~

ampl if tlyen~ t ampe- ACBD - A~middotq) +AD

II( V c bull I

SoJn C-sidelt -kfSiCll At 1 vuu~j l)is Cpoundlaquotef bull J ~p-J~ Ygt I) - t t e y fatH4) J -k ~ro-atdc qf ~ec ~~A~ I Q

I iIC ~ AeC SilCamp ~ IH 6e - c I

J vue b -ftt (1) We t _ 1 _AC~ r - Be - - middot

iDA ~ 01gt1gt AJ)middotC1) tt Mltrtrllj b~ lAOmiddot~]) CO~2 1aJkSimiddotces amporeJ

A6amp c) +A)xBe Acll 81gt middot

Re fICS 11L sf ~ eat be ltoftrec -to ~t -I- ~1-tllAt t MilcO + AtgtICBC =AC 1CI1~

~V Asctgt S (l u~ ~lJ4~ 0-shy

~S6~~~ kfCfS4tJ foJt of~~ -+k eampIt~ otIIIetStM Ai ~itlt ~s -fIc ~o~~ rote iIt wJere -reIs CIMif s Mesc(t _

-

6x4t~le 2 Lt ABc 0 be ~ ~tllt t(kft~ suamp~t At ampt so liltftStct At Y1tt ~r AtO P~t~( -Ke -refltecf of 0 ~fOSS AS BC C)1gtA A~ C4IIcYdtc

p _ c $Lt-~ -71

Lcent P~ ~So k ~fut f-~Wi _ 010 0 flO Msc CD lgtA Ye cdIVt bull

sc =l Ott foIIttll is ~iIr~le-t -fo site (5 -tk Ptt-RS l~~( (Sl~~14ft

e IcentS 0 0 -to tts e_~Hrlt OSAP DfBQ ~CR O~DS ~ludlC~~ J J -J ~ _ bull

-tt TltitCirtlutdts Ie CA Ca Cc CD rtsrdtuely CfSMoSmiddotd fIf~iQ 3(0 r ~r31gt0 By ~ct(s)

I~ AC Q( e04~~t ofo ~gtltS

cfct (+) I CA SIrcent to filllt LA fllAlrd to 81gt CIrs

Set to ~ IIt LB ~(c of Ac I C ~ Sci fo c tAlC -to ~lgt1 craquoisSeoet t ol1t LD~E lc ~

0 0 r~-t 0lt1

L Nen bull

CpnCa= 0r~ LAf Le P )Mjl-ly 4~t( LI) R J ll)n~ So bull

$r~ AcJ Mgt PClKs ~~Ic~4J~~ ~ fet h) PampRs is floc

~

G)Cdtpt f

Le-t P bft Af6~-t ~S~ 4l1It Appound ~~~-t LAPB-LACS LA(C-L~8C

Ltt tgt amp be ik~~tS 0( AAPS )AA~C nspecflf ~toe ~l A1gt 1gt1 ce )wtet A fOiWtshy

~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

( )tlfamp 61) biSKfs IA8PJ By ~t CT) ACAfACf~ ~ ~ I3A - XA So iSttf ACAeACampA

P ~f - xpmiddot ~ P~B6+lCApLcA8 J

C-1-1 ~=~ 5tRCt X ( 4ft AP ampt ~1It By~t (s) 1 ~ tCp~=LCitA ~ ~ I I~ fQ is Seoct of ( ~ ~~ 1 f4$s~~3C o listf SiacCrtIeO ~ -T(Alrl~f4lrgto ~~(1)1 tIIet pamp ~t(4C~I~Ois~tfo(0

A ~IgtC A~te A lU)e bullA p A APelAcIIgt f-c ~) I SIWICamp

I

~ ~ ilt3t +00 c( ~ 1 PQ fh ) Qm Q J r bull bull ~ t01 setc~ 10 t of I I

No LM~-L~8-=-LIWC-LAec f~ $(amp ~st ~JO 0 Ao( ~J~~ ~ Atl 43~ t (-d 0 ~ A61PcD

fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

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~

G)Cdtpt f

Le-t P bft Af6~-t ~S~ 4l1It Appound ~~~-t LAPB-LACS LA(C-L~8C

Ltt tgt amp be ik~~tS 0( AAPS )AA~C nspecflf ~toe ~l A1gt 1gt1 ce )wtet A fOiWtshy

~ SfAt~ -Let APn ~D-=)( ~ A~nCE~f

r $L We wt -to ~oa )( ~

( )tlfamp 61) biSKfs IA8PJ By ~t CT) ACAfACf~ ~ ~ I3A - XA So iSttf ACAeACampA

P ~f - xpmiddot ~ P~B6+lCApLcA8 J

C-1-1 ~=~ 5tRCt X ( 4ft AP ampt ~1It By~t (s) 1 ~ tCp~=LCitA ~ ~ I I~ fQ is Seoct of ( ~ ~~ 1 f4$s~~3C o listf SiacCrtIeO ~ -T(Alrl~f4lrgto ~~(1)1 tIIet pamp ~t(4C~I~Ois~tfo(0

A ~IgtC A~te A lU)e bullA p A APelAcIIgt f-c ~) I SIWICamp

I

~ ~ ilt3t +00 c( ~ 1 PQ fh ) Qm Q J r bull bull ~ t01 setc~ 10 t of I I

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fAGpl- LAte I LAC~ - LAc8 r~7 ~ ~ -to Ate AtA 1- Se-cCrtld -t ~ Ltp L B~P bull ~ 0 aA hAScit Ce

s A~c p i~ iwsMs I-tece I ps= p~ U$i~ Nt4cS1y bWMt 1lml 4ktc A64J arc Atp4~sIJ AAPs Mee - I1APC4ACP ~- ~(t to ~f~1v_tr ft

GA _ fA _ n -CA _ f bull er1amp L CPA-= LCBmiddot middot Pip - 8 - rt - [p middot middot It - i bull

(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP

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(fig) Eiclaquo~le S- (I11S 13ss~ cAtfJ) ~flt (111S-~t MJI OJrr~) GtrlleVl ) ltSe ~tJQ Wi Jiifu A8 aJ a4O ~ Let MI ~) Pbe if (1O~s ~lt~ qf14~ jtltide of ~ il$ J tI~d i ftampk(la ~rdQAt C~ tgt c AAsc Witk ~tJES Aca at CA (tlaquofcllely Rt~-f 1(_tI~ A- M (M6lt MA MJgt ~ JI4 c) Let KIoe -t4 flt o-~~t ofA MNp -tIt iIlCIIfar ~ Me( a( ~ fDitl-t of fto5laquot-of f4artcife So4 fI-L ((rcce coF 11ampC A~ Coli~r AAOC a( Asgto~ fh f4vIt L M(()=10 - SoIfttf Ob~ of(t ~ - Soltmiddot illCi(cc (M6C~t~(cluf

Co~ if~_ j (0 t) So bull L I A AMIJP I(~ ~ ~ AA l~lqt(~t4 ecA~o~ w 4t t frI~ 8 I=~ft( AMNP

1h~t(z)ABCDMt~to~x~ 1kklic~4tf-ey fact (4-) ~Ctrrde~ All C-s $ellti fo~~eAc ~ cclaquott AM NPis~Gkdit MNP

tkt Cle~raquoClB ~s Seot to ~ie 1gt8 ~l II(~ deg~~b cltmG Of M82~~ -kI(I IUs Set To Je ACII Stgt~ b Ut ilMN

M is Seect t~ M ~C~) A It-aA6) OJ iJft iIfVSM wle~r -Io-c~de1~A6t vmiddot Wa_ ce~V 1 (-) = ltnlt tI~OIt Ie traquo1 AS e c_t( ) A 6 c

S~lt~MK i)sc-tt ~14 h~ J (lmiddotB~t-fo fkMW( f$Apoundc) OM t PM N NPlte

I

~tVt bull -1shy6yfact (1) I l fit KO J 106 ~ L M _ II ~ amp11 -tk GtclUbtltr~------=----4ttt7~~W-=-LUJ - YtCf V u~ I ___ ~ l rge ~~(L eeL AK J Algti ~(~ 0 -t -( A6 middotmiddotllMNP _ ~oil~jCMPCA~~ef40CDi-s-fk~_fOIt Sy i) I-fLCi~4Aecd~~er C(--ct~ ~ AM~K) s4ck jte~ts IItAS of AA$r ~c((middotlfA~ ~~CL-ter4 at ike foctt c fH~lar-f-o io Aamp AAampc gt 141laquo~if ~1IIC(dcrof c1 MNP ik f o IS 11 L KM0 = 10middot ~~ eet of4e fWamp p1If coUt ~MNP kd

b~() middot tS~Gdr l~_AMNP