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Page 1: 01 )+ 234 56 7' 8+0 9 ,+olver/q_/planeqes.pdf · ) ! * ,+- ./+0 1 )+ 234 56 7' 8+0 9 ,+ :7@badcfe chgjilk mon >.i)prq k chst>7ivu w >.s m; = @b>7gx=?czy[>]\^k

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QL>7=�� *³ ' <��~µ Y[>.G[Co=?>�=?|[> ` S M a.>(Co{ ` ¬ jyM ;!>(ADGX=?>.�O; M � N >�{ j G[a)=?AcCOG ` COG M @ M GJAD{­C N Y ' «eAD=!|;!> ` S�>.a)=¯=!C,=!|[>�@B> M ` j ;!> � � d { � AcG M Y[YJAD=?ADCHG�=?C,A µ M G[Y0AcA µ �AcADA µ b |[>   GJAD=?>9PRY[AD@B>7G ` ADCHG MON @BC~Y j[N > # A ` M ` j � ` S M a.>/CO{�� ®³BA C < .� ³/.)Tµ

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s Co=?Aca7> � |[CV«�>7gH>7; � =!| M =L«�>�Y[COG � =°| M gO> M GXv�ADGJ{­CH;!@ M =!AcCHG M ` =!CZ«e|[>.;�>�ADG�=!|[>¦STCHADGX= ` S�>.a7=!; j @CO{�% N Ac>¯=?|[>�>.AD�H>.GXg MONDj > `/³ �©� kHk µ � j ` =Z{­C j G[Y��d G/=!|[>�;�>.@ M AcGJY[>.;±CO{©=?|[A `°` >.a)=?AcCOG � «�> ` | MONDN S[;!> ` >.GX= M �H>7G[>.; MON S[;!C~a.>7Y j ;!>]{­CH;±a NcM `!` AD{ v~AcGJ�=?|J>8GJCH;!@ MON ADI M � N >^¬ jyM ` A¡P¢>)� M a)= N v ` C N g M � N >ZS�CO=!>.GX=?A MON ` ADG �� k Y[AD@B>7G ` ADCHG ` � q >7a7=?ADCHG n «eA NcN��>�Y[>7gOCO=?>7Y¨=!C"=?|[>�AD@BS N >.@F>.GX= M =?AcCOG CO{±=?|JA ` S[;�C©a7>.Y j ;!>�AcG =!|[>�a M ` > � k �yMoNcN CV«eADG[� j ` =!CCH�J= M AcG M «eAcYJ> M ;!; M v�CO{*GJ>7« G[CO;!@ MON ADI M � N >¯¬ jyM ` A¡P¢>)� M a)= N v ` C N g M � N >�S N�M G M ;ZSTCO=!>.GX=?A MON ` �b |[>   ; ` = ` =?>7S-ADG�=?|[>�a N�M `�` A   a M =!AcCHG�Co{*¬ jyM ` A¡P¢>)� M a7= N v ` C N g M � N > q a$|[;V�CHYJAcG[�H>7;ZCHS�>.; M =?CH; `AcG A C A ` =?CFa NcM `!` AD{ v�=!|[>   G[A¡=?>)P¢Y[Ac@F>.G ` AcCOG MON QLAD> ` j � MON �H>.�J; M ` CO{ C ³BA C µ j G[Y[>7;¯Y[A¡£¤>7CH@FCH;�PS[|[A ` @ `H0 � A'C�� A C M GJYÁ;�> ` a MON AcG[� ` 1 � A C � A . ��M a7=!AcG[� CHG C ³BAC�µ M a7a.CH;�Y[AcG[�=!C>.¬ jyM =?AcCOG `B³ k �Ã� µ M G[Y ³ k � n µ � b |[A `   ; ` = ` =?>.SÀ| M ` M G M = j ; MON {­CH;�@ j[NcM =?ADCHGAcG =?>7;!@ ` CO{ZQLAc>

MON �H>.�[; M a7CH|[CH@FC N CO�Ov � � �H��� d G[Y[>.>7Y �¦M GXv   G[AD=!>)P¢Y[Ac@F>.G ` AcCHG MON QLAc> ` j � MON �H>.�J; M ! CO{ C ³.A C µ| M ` M � M ` A ` CO{°=?|[>�{­CH;�@� 9 ��� 9 1,+,+�+�1 � � ��� � 1 A 9 1,+�+,+�1 A�� 1 ³ �J� kon µ

«e|[>7;!> � 9 1,+,+�+�1 � � M ;!> N AcGJ> M ; N v ADG[Y[>.S�>.GJY[>.GX=�gH>7a7=!CH;   > N Y `�` S M G[GJAcG[� M G���P¢Y[Ac@F>.G ` AcCOG MONQLAc> ` j � MON �H>.�[; M / Co{^=?|J>BQLAD> MoN �H>7�[; M CO{¦gH>7a7=?CO;   > N Y ` CHG A C �°M G[Y «e|[>.;�>F=!|[>,{ j G[a7=!AcCHG `A 9 1,+,+,+ 1 A�� M a)= M ` @ j[N =!AcS N Aca M =?ADCHGBCOST>7; M =!CH; ` CHG = ? ³BA C <EA�µ �q AcGJa.> ! A ` M QLAc> MON �O>.�[; MJ� =?|[>-{ j G[a7=!AcCHG ` A 9 1,+,+,+ 1 A�� @ j ` = G[>.a7> `!` M ;!A N v ` S M G M G / P@FC©Y jJN > 3 � = ? ³BA C <EA^µ � d G CO=!|[>.;�«^CO;!Y ` � 3 @ j ` =��T>FAcGXg M ;!A M GX= j G[Y[>7;/=!|[> M a7=?ADCHG CO{/ ³ �Xv YJ>.;!A¡g M =?ADCHG µ � p CO;!>.CVgO>.; � =?|J>-{ j G[a)=?ADCHG ` � 9 1,+,+,+ 1 � � Y[>   G[> M º PRa7C©a$| M AcG 6 � / �=@? ³BA'CD<EA^µ � M a.a7CH;!Y[ADG[�B=!C 6 < � ��� � � � � ºH� � � �R��:¯a7= jyMONcN v ��6 C j �H|X=<=!C��T>/;!>7� M ;!YJ>.YM ` M =@?Á³.A'CD<EA�µ4F�3 P�g MONcj >7Y º P¢a.C~a$| M AcG � ` ADG[a.>"=!|[> � � � º � �=� � �±M ;�>"CHG N viY[>   G[>7Y j S=!CN ADG[> M ;"a.CH@(�[AcG M =?AcCOG ` CO{8=?|[> A � � º � � � B � ½ >.a MoNcN G[CV« =!| M =,=?|J>¨a7CH��C j G[Y M ;�v CO{ M= ? ³BA C <EA^µEFG3 P�g MoNcj >7Y º PRa7C©a$| M AcG A ` =!|[> MON =?>.;�G M =!AcG[�-�[A N AcG[> M ;/@ M S[SJAcG[�� 9 6 � / � / �= ? ³BA C <EA^µEFG3 Y[>   G[>.Y-�zv�=!|[>�{­CH;!@ j[N�M

� 9 6 < � 1�� � � � ³ 6 <�� � µ N�� ³ 6 < � � µ N 6 < � � 1�� � � + ³ �J� k Ä µd GiCO;!Y[>7;8=!| M =e=?|[>/Y[AD£T>.;�>.GX=?A MON CHS�>.; M =?CO; `(³ �J� kon µ ` S M G M Q±AD> MON �H>7�[; M©� AD=8A ` G[>7a.> `�` M ;�v M G[Y` j )Ba7Ac>7Gz=F=?| M =,=?|[>0;!AD�H|X=�P¢| M G[Y ` ADY[>�CO{<>.¬ jyM =!AcCHG ³ �©� k Ä µ N Ac>�ADG =?|[> / PR@FC©Y jJN > 3 {­CO; MONcN

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a$|[CHADa.> ` CO{� M GJY � AcG / � CH;]AcGFCO=!|[>.;]«^CO;!Y ` =?| M = 6 ��> M = ?Á³BA C�<EA^µEF�3 P¢g MONDj >.Y,a7C©a)v©a N >o���GF=!|[>8CO=?|[>7;]| M G[Y � =R«�C"QLAc> ` j � MON �H>.�[; M ` CO{ C ³.A C µ «eA NcN ��>¯>7¬ j ADg MON >.GX= j G[Y[>7; M ;!> ` a MoN AcGJ��HA¡gH>.G �Xv�>.¬ jyM =?AcCOG `B³ k �Ã� µ M GJY ³ k � n µ «eAD=?| 0 � AcY����,AD{ M G[Y CHG N vA¡{¦=!|[>.AD;�a.CH;�;!> ` S�CHG[Y[ADG[�º P¢a.C~a7v~a N > ` Y[AD£T>.;��Xv M º P¢a.C~a7v~a N >�� Co{/=!|[>�{­CH;!@ �� < � � � � � � ³ N N CH�@1 µ � � � ³ N 1 µ �º���� � � � =!| M =eA ` �Xv M º P¢a.CH��C j G[Y M ;�v�� � = ³ N 1 µ � b | j ` «�>�| M gH> �������� � ��� ��� � ��� � �� � ( ,� . ,� + �� � ���� , �2 -, + �" -. � > -, #%$2�'&)(+* -, + + * ( � � � -�@, �'. � � � -, � � , (+* � $ " (+* �2 ," � ( � - C ³BA C µ (+, �� #%$ �'&)(+* -, + + * ( � � � - . � � � * � ³;/ 143 1 � 6 � µ �� � � �� ) / � � ( �@, �'. � � � -, � � , (+* � � (+* �2 ," � ( - & + . �� � -* � � ��B� )83 � = ? ³.A C <4A µ � � ( �@, �'.; � � � -, � � , (+* /� � �+$�* ���B�B� ) �76 � � � ( + � �� * � � + * ( � � �', % 9 ³;/ <,= ? ³.A C <EA^µEF�3�µ� uO>7; 9 F AD@ = �d {¤COG[> M `!` j @F> ` =?| M = =?|J> =?;!ADS N > `e³0/214351 �76 � µ | M gO>8��>.>7G,a N�M `!` A   >.Y � =?|[>7GFCOG[>Z| M ` M a7CH@,PS N >7=?> N A ` =8CO{®=?|[>(Q±AD>)P MON �H>7�[; M Aca ` >.a.COG[Y©PRCO;!Y[>7;<Y[A¡£¤>7;!>.GX=!A MON CHS�>.; M =?CO; ` �zv0= M uzAcG[�F¬ jyM Y[; M =?ADaa.CO@"�[AcG M =?ADCHG ` CO{¦=?|J>,{­CO;!@ ³ �J� k µ � b |[>Fa NcM `!` A   a M =?ADCHG�CO{¦=?;�AcS N > `,³;/ 14351 �76 � µ A ` |[CV«^>)gH>.; M|[AD�H| N v GJCHG©P¢=!;!A¡g©A MON S[;!CO� N >7@-� b |[>�a.CH@FS N >7=?> M G ` «^>7;�A ` COG N v uzG[CV«eG AcG =!|[>�a M ` >�CO{¯QLAc>

MON �H>.�[; M ` CO{�Y[A¡£¤>7;!>7Gz=!A MON COST>7; M =!CH; ` AcG0=R«^C a.CH@FS N >9�0g M ;!A M � N > ` � =!| M =¯A `   G[A¡=?>)P¢Y[Ac@F>.G ` AcCOG MON` j � MON �O>.�[; M ` ! � C ³� oµ ��� ��� �

b |[>�G[>9�©= ` =?>7S�=?CV« M ;!Y ` =!|[><a N�M `�` A   a M =!AcCHGBCO{L=?|J>�¬ jyM ` A�PR>9� M a7= N v ` C N g M � N >8STCo=?>.GX=!A MON ` A `=?C8Y[>)=?>.;�@BADG[>�«e|[Aca$|�CO{©=?|[> ³ >7¬ j ADg MON >.G[a7>�a N�M `�` > ` CO{ µ QLAc> ` j � MON �H>7�[; M ` ! � C ³BA C µ CH�J= M AcG[>7YAcG b |[>.CH;�>.@ �J� � M Y[@FAD= MÀ  G[A¡=?>)P¢Y[Ac@F>.G ` AcCOG MON @FC©Y jJN > # CO{�{ j GJa7=?ADCHG ` AcG =@?Á³.A'CD<EA^µ �:<� M AcG � =!|[A ` A ` M { M AD; N v a.CH@FS N Aca M =?>.Y¨S[;�CH� N >7@ «e|[Aca$|| M ` ��>.>7G ` C N gH>7Ya.CH@FS N >7=?> N v0ADG-=?|J>a M ` >�CO{   G[A¡=?>9PRY[AD@B>7G ` ADCHG MON ` j � MON �O>.�[; M ` ! CO{ C ³�&oµ � � � � � ½ >7@ M ;�u M � N v � {­CH; MoNcN =?|[>0QLAc>MON �H>.�[; M ` CO�J= M ADG[>.Y AcG ½ >7{­>7;!>7G[a.> � � � � =?|J>�a.CHGJY[AD=!AcCHGF=?| M =�=?|[>7;!>�>9�©A ` = M/  G[A¡=?>)P¢Y[Ac@F>.G ` AcCOG MON@FC©Y jJN >ZCO{T{ j G[a7=!AcCHG ` {­CO;!a.> ` =!|[>ea.CH|JCH@BC N CH�Ov(S M ; M @B>)=?>7; ` M ;!A ` ADG[��AcG b |[>.CO;!>.@ �©� ��=?C�= M uo>CHG N v M Y[A ` a.;!>)=?> ` >)=<CO{®g MONcj > ` � b |[A ` S[|[>7G[CH@F>.G[COG-CO{®=?|[>i§�¬ jyM GX=!AcI M =?AcCOG¨Co{ a.CO|[CH@FC N CH�ov ªA ` M { M ` a.ADG M =?ADG[��S[;�CH� N >7@4=?| M =eY[> ` >.;�gH> ` { j ;�=!|[>.;ZADGzgO> ` =?Ac� M =?ADCHG��

b |[>�G[>9�©= ` =?>7S�AcGF=?|[>�a N�M `�` A   a M =!AcCHGBCO{L¬ jyM ` A¡P¢>)� M a7= N v ` C N g M � N > q a$|[;}�CHY[ADG[�H>.;�CHS�>.; M =?CH; `A ` =!C/Y[>)=?>7;!@FAcG[>Z«e|[ADa$| CO{T=?|[>¯QLAc>)P MON �O>.�[; M Aca ` >.a7CHG[Y©P¢CH;!Y[>7;^CHS�>.; M =?CO; ` CH�J= M AcG[>7Y M ` M ;!> ` j[N =CO{�=!|[>   ; ` =�=R«^C ` =?>7S ` M ;�>¯>7¬ j ADg MON >.GX=^=!C M q a$|[;V�CHYJAcG[�H>7;^CHS�>.; M =?CO;.� b C(=!|[A ` >7£T>.a)=^«�>�@ j ` =M S[S N v0h^CO;!C NDN�M ;�v k �Ã� � =!|[>�a.CHGX=!>.GX=<Co{®«e|[ADa$|¨«�>�G[CV«¾{­CH;�@ j[N�M =?> M �[AD= @BCH;�>�>)�©S N Aca.A¡= N vH�QL>7= j `   ; ` =8;!>7«e;�AD=!>�>7¬ jyM =?ADCHG ³ �J� k µ M �[AD= Y[AD£T>.;�>.GX= N v M `

� � N k %�� G� ���� � ;�7 < � 9 = 7 <

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«e|[>7;!>�=?|[>¦QLAc>9P MON �H>.�J; M ADa®CHS�>.; M =?CO;�%�� G� �����«eA NDN ��>�;!>){­>.;!;�>.Y�=?C M ` =!|[>�§�� MOj �H>]� M @FA N =?CHGJA M G ªJ�` ADG[a.>/AD=8A ` =?CF��>(>.¬ j A¡g MON >7Gz=8=?C M q a$|J;V�CHY[ADG[�H>7;¯CHS�>.; M =?CO; j GJY[>.;8=?|[>�a.CH@(�[AcG[>7Yi>)£¤>7a7=�Co{ M;!> ` a MON ADG[�"CH;,§�� MOj �H>¯=?; M G ` {­CH;�@ M =?AcCOG ª CHG�=!|[>�Y[>7ST>7G[Y[>.GX=eg M ;!A M � N > M GJY M a$| M G[�H>�CO{°ADG[Y[>)PS�>.G[Y[>7GX=�g M ;!A M � N > ` ��M ` ST>7;�>.¬ jyM =?AcCOG `,³ k � � µ M G[Y ³ k � n µ � ³ s CO=?ADa.>/=!| M =�=!|[>�;!> ` a MON ADG[� ³ k � n µ«eAD=!| 0 � ADY���� � =!|[C j �H|BAD=¦A ` G[Co= M�j G[AD= M ;�v(=?; M G ` {­CH;�@ M =?AcCOGFCo{ � *³BA C < � � � ) 9 +,+,+ � ) C µ � A `

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G[>)gH>.;�=?|[> N > `!` M �H>7G j AcG[> j GJAD= M ;�vCOST>7; M =!CH;�{­;!CH@ � ³BA C�< 1 � � � ) 9 +,+,+ � ) CXµ CHGX=!C � ³.A'CD<� � � ) 9 +,+,+ � ) C µ � µ�� v¨>9�JSJ;!> `�` ADG[� � AcG¨=?|[>({­CO;!@ `(³ k � º µ M GJY ³ �©� k � µ �TM G[Y j ` AcG[� ³ �J� º µ � «�>CH�J= M AcG

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6�� 1 <4� � ! < 1 ³ �J�Ã� m µ=?; M G ` {­CH;!@FAcG[�"=!|[>�>.AD�H>.GXg MONcj >�S[;!CH� N >.@

%�� G� ���� <4� L < ³ �J�Ã� º µAcGX=!C,=!|[>-§�S[|Xv ` ADa MONDª >7Ac�H>7GXg MoNcj >�S[;�CH� N >.@

% 6O� L 6 1 ³ �J�Ã� k µ«e|[>7;!> % A ` =?|[> q a$|J;V�CHY[ADG[�H>7;8COST>7; M =!CH; ³ k � k©º µ � A ` =!| M =

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� � k 1 � ºk N CH� � + ³ �J�Ã� n µ

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½ Ac>.@ M G[GJA M G�@ M G[AD{­C N Y��L:Áa M ` > AcG/STCHADGX=*A ` =!|[>^{­C NDN CV«eAcG[�e>9� M @BS N >�a7CHG ` AcY[>7;!>.Y��Xv q |[A¡{­@ M GM G[Y b°j ;!�[ADG[>.; � º�� � >7¬zG�� ³ k Ä µ � �

� � ) ³ º � ) µ � � ) N k ³ º � ) µL³ º � � µ � � ) � � � � ³ º � � µ � � � � ; ; ; + ³ n � k µ

b |JA ` Y[A¡£¤>7;!>.GX=!A MON COST>7; M =!CH;ZA ` |Xv~ST>7;!��C N ADa�>7gO>.;�vz«e|[>7;!> � AcG ` =?> M Y0CO{®�T>7AcG[�,> NDN ADSJ=?ADaO�b |[> ` >7a.CHGJYB;�>.¬ j Ac;�>.@F>.GX= � «e|JAca$|�«^>ZGJC�« Y[A ` a j `!` M = N >.G[�o=?| � | M ` =?C�YJC�«eAD=?|"=!|[>ZA `�` j > `CO{ ` ¬ jyM ;�>"AcGX=?>7�H; M �[A N AD=Rv M G[Yi��C j GJY M ;�v0a7CHG[Y[A¡=?ADCHG ` � b |[>/{ j GJY M @F>.GX= MON ;�>.¬ j Ac;�>.@F>.GX=¯A ` CO{a.C j ; ` >F=!| M =�=?|J>F>7Ac�H>7GJ{ j G[a)=?ADCHG ` M ;�A ` ADG[��{­;!CO@1=?|J> M S[S N ADa M =!AcCHGiCO{�=!|[> MON �O>.�[; M Aca"@F>7=!|[C~Y��>¨GJCH;!@ MON ADI M � N > � ` C =!| M =�=!|[>7v a M G ��>¨S[|Xv ` Aca MONcN v AcGX=!>.;!SJ;!>7=!>.Y AcG ` = M G[Y M ;�Y ¬ jyM Gz= j @�P@F>.a$| M GJAca MoN { M ` |[AcCHG M ` =?|[>�S M ;�=?ADa N > � ` S[;�CH� M �[A N A¡=Rv M @BS N AD= j Y[>O� q j S[S�C ` >�=?| M =�«�>�| M gH> Mq a$|[;}�CHY[ADG[�H>.;^CHST>7; M =!CH; ³ k � k~º µ¦` j a$|�=?| M = ³ � ��� µ

A ` STC ` AD=!ADgH>9PRY[>   G[A¡=?> M GJY�| M ` I7>.;!CFE MOj `�` A M Ga j ;�g M = j ;!>¨>7gH>7;�vz«e|[>7;!>ADG A � b | j ` =!|[>.;�>¨>9�©A ` = N C©a MON a.C~CH;�Y[AcG M =?> `-³�.)�10.� µ ADG «e|[Aca$| %= M uO> ` =?|J>�{­CO;!@ %�F GIH¦�OADgH>7G0�zv0>7¬ jyM =?ADCHG ³ k � kHk µ «eA¡=?| � k �

%�F GIH � N ºkJ � � .) �

� � .� K �@? ³�.)�10.� µ�+ ³ n � � µ

d =B@ M vÁ| M S[S�>.G =?| M =F=?|J>-a$| M G[�H>CO{<g M ;!A M � N > ` «e|JAca$| S j = ` =!|[>iCOST>7; M =!CH; ³ k � k©º µ AcGÁAD= `G[CH;�@ MoN §�S[|Xv ` ADa MONDª {­CH;!@ ³ n � � µ «eA NcN @ M S"=?|[> «e|JC N > S N�M G[> A CHGX=?C M G�COST>7GFSJ;!CHS�>.; ` j � ` >7=³ ` M v M �TC j G[Y[>7YiCHS�>.G-;!>.a)= M GJ� N > µ �TM ` «�C j[N Yi��>�=!|[>�a M ` >/«eAD=!| M a.CVgH>7;!ADG[��@ M S�� " >�«eA NcN=?| j ` | M gO><=?C�YJ> MON «eAD=!|�=?|[>¯A `!` j >�CO{±��C j G[Y M ;�vFa.COG[Y[AD=!AcCHG ` {­CH;¦=?|[><« M gH>�{ j GJa7=?ADCHG ` ADG =?|J>³�.)�1 .� µ a.C~CH;!YJAcG M =!> ` M =^=!|[>���C j G[Y M ;�vBCO{L=?|[A `^` >7=}� b |[> ` >���C j G[Y M ;�vBa.CHGJY[AD=!AcCHG ` «eA NDN S N�M v Ma.; j a.A MON ;!C N >�{­CH;8=?|[>/>)�©A ` =?>7G[a.>�CO{ M Y[@BA `!` Ac� N >�« M gH>"{ j GJa7=?ADCHG ` � ` ADG[a.>/AcG�O>.G[>7; MON =?|[>)v-«eA NcNG[CO=®��> MOj =!CH@ M =?ADa MONDN v ` M =!A `   >.Y"�Xv�=?|[>�>.AD�H>.GJ{ j G[a7=!AcCHG ` {­C j GJY"�Xv M S[S N v~ADG[�8=!|[>�§ MON �H>7�[; M Aca ª@F>7=?|JC©Y��]QL>)= j ` A NcNDj ` =!; M =!>¯=?|J> ` >�AcYJ> M ` «eAD=!|�=R«^CFAcGJ{­CO;!@ M =?A¡gH>�>9� M @BS N > ` ���� � ��� � � ����� h^CHG ` AcYJ>.;Z=?|[> q a$|J;V�CHY[ADG[�H>7;8COST>7; M =!CH;

� � �Á³ º � ) µ � � ) � k ³ º � ) µL³ º � � µ � � ) � � ��� ³ º � � µ � � �

� k ³ º � ) µ � �Á³ º N µ )�N B�� � �� )� k ³ º � � µ � N ) ��� ³ º N B µ � � �� �� �Á³ N º µ ) � k B ) � ��� ³ B N º µ B�� 1 ³ n � n µ

«e|[>7;!> � � m M G[Y � � m M ;�>�;!> MON S M ; M @B>)=?>7; ` � B M G[Y M ;!>�G[COG[G[>.� M =?A¡gH>�AcGX=!>.�H>7; ` ��M GJY� � � º + ³ n � Ä µb |[A ` CHST>7; M =!CH;¤«eA NcN ��> ` |JC�«eG���> N CV« ³ ` >.> q >.a)=?ADCHG n � º � n µ =?CZ��>¦¬ jyM ` A¡P¢>)� M a)= N v ` C N g M � N > � «eAD=!|a.COG ` = M GX= S�CO=?>7Gz=!A MON�M G[Y |[ADY[Y[>7G ` v~@F@B>)=?;�v MON �H>7�[; M&! � ��� ³ k µ�� � � ³ k µ � b |[>8a.CHGX=!; M g M ;!A M GX=@F>7=?;�Aca�a7CH@FSTCHGJ>.GX= ` M ;!>��OADgH>7G-�Xv

�9 9 � �Á³ º � ) µ 1 �

9 � ³ º � ) µL³ º � � µ 1 � � � ³ º � � µ 1 ³ n � � µ

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` C8=?| M =°=!|[>¦@B>)=?;!ADa�A ` � N CH� MONDN v ½ AD>.@ M G[G[A M G M G[Y/| M ` I.>.;�C�E MOj `�` A M G/a j ;�g M = j ;!>¦>7gO>.;�vz«e|[>7;!>AcG A& � b |[>�a.C~CH;�Y[AcG M =?>,=?; M G ` {­CH;�@ M =?AcCOG M GJY ;!> ` a MON AcG[�-CO{Z=?|J> « M gO>�{ j G[a7=!AcCHGÀ@ M S[S[AcGJ�=?|J>�COST>7; M =!CH; ³ n � n µ =!C,=!|[>�G[CH;�@ MON {­CH;!@ ³ n �Ã� µ M ;�>��OADgH>7G0�zv

.) � � M ;!a)= M G ) N M ;!a)= M G � � ³ � � N º µ 1 .� � º��M ;�a7= M G � < ³ n � � µ

1 � 5 º � ) 7 ?� 5 º � � 7 ?�� + ³ n � l µ

b |[>ea.C~CH;�Y[AcG M =?>^=!; M G ` {­CH;!@ M =!AcCHG ³ n � � µ @ M S ` =?|J> «e|[C N >ZS N�M G[>^CHGX=?C M �TC j G[Y[>.YFCHS�>.G,;!>7a7=�PM G[� N > < =?|J>.;!>){­CH;!>]=?|JA ` >)� M @FS N >�YJ> ` a7;!AD�T> ` =!|[>]S[|Xv ` Aca MON ` AD= jyM =!AcCHG�CO{ M {­;�>.>]S M ;�=?ADa N >�a7CHG   GJ>.Y=?C M �TC j G[Y[>.YÀ;!>7a7= M G[� N >o� b |[> G M = j ; MON �TC j G[Y M ;�v�a.COG[Y[AD=!AcCHG ` AcG =?|[> ³�.) 10.� µ a7C©CH;�Y[AcG M =?> `M ;�>"=?| M =�=!|[>,>.AD�H>.GJ{ j G[a7=!AcCHG `�` |[C j[N Y�g M G[A ` | M =�=?|[>���C j G[Y M ;�v�Co{�=!|[>,;!>.a)= M GJ� N > � ` C�=?| M ==?|J>(S M ;�=?ADa N >�| M ` I7>.;!CBS[;!CO� M �[A N AD=Rv�CO{ �H>)=!=!AcG[�,=?CF=?|[>/�TC j G[Y M ;�v M G[Y> ` a M S[AcG[�J�e\�;�CH@ =?|J>{­CH;�@3CO{L=!|[>�� Moj �H><{ M a)=?CH;81 M ` �HA¡gH>7G��zv ³ n � l µ �[M GJY�=?|[><{ M a7= =!| M = M GXv   G[A¡=?>)P¢Y[Ac@F>.G ` AcCOG MON@FC©Y jJN >iCo{ ` @FC©CO=!| { j G[a)=?AcCOG ` {­CH; =!|[>�QLAc> MON �H>7�[; M:! A `�` S M G[G[>7Y �Xv STC N v~G[CH@FA MON ` � «�>` >7>�=?| M =<=?|[>�>7Ac�H>7GJ{ j G[a)=?AcCOG ` M ;�A ` ADG[�B{­;�CH@1=!|[> M SJS N ADa M =!AcCHG-CO{]=?|[> MON �H>.�J; M ADa(@F>7=?|JC©Yi{­CO;¬ jyM ` A¡PR>9� M a7= N v ` C N g M � N >�S[;�CH� N >7@ ` M ;!>�CO{°=?|[>�{­CH;�@

6 ³�.)�10.� µ � � ³ )�1 � µ³ º � ) µ

� ³ º � � µ � 1 ³ n � ¸ µ«e|[>7;!> � A ` M STC N v~G[CH@FA MON Co{�Y[>.�H;�>.> N > `!` =?| M G CH; >7¬ j[MON =!C AcG ) M G[Y N > `!` =!| M G CO;>.¬ jyMoN =!C B AcG � �®M G[Y ³*)�1 � µ 3 A A ` @ M S[S�>.Y =?C ³�.) 10.� µ ADGÀ=!|[>B;�>.a)= M G[� N > M a.a7CH;!Y[ADG[�-=!C=?|J> N C©a MON ADGzgO>.; ` >FCO{�=!|[>,Y[AD£T>.CO@BCH;�S[|[A ` @ ³ n � � µ � b |[>Fa.COG[Y[AD=!AcCHG=!| M = 6 ³/.)�1 .� µ g M G[A ` | M ==?|J>-��C j G[Y M ;�v CO{8=?|J>-;�>.a7= M G[� N > � =?| M =FA ` «e|J>.G ) M G[Y � =!>.G[YÁ=?C AcG   G[AD=Rv � ` |[C j[N Y G[CV«��>�Ac@FSTC ` >.Y M ` M G M Y[Y[A¡=?AcCOG MON ;!>.¬ j AD;!>7@B>7Gz=�COG=?|[>,>.AD�H>.G©{ j G[a7=!AcCHG ` CO{ % � ` AcG[a7>FA¡=<«�CHG � =MOj =!CH@ M =?ADa MONDN v,|[C N Y0AcG0�H>.GJ>.; MoN �

��� � ��� � � ���;� h^CHG ` AcYJ>.;Z=?|[> q a$|J;V�CHY[ADG[�H>7;8COST>7; M =!CH;Z�HADgO>.G0�Xv� � 5 º � ) 7 �

� ) � k ) �5 º � ) 7 �

� ) � � �5 º � ) 7 5 º � � 7 �

� � � k ³ º N µ ) 5 º � ) 7 �

� ) � k5 N � ³ º N µ ) 7 � �

� �� ³ N º µ ) � ³ � º µ � º + ³ n � ºVm µ

" > ` | MONcN ` >7>"AcG q >.a)=?AcCOG n �Ã�J� k =?| M =<=?|JA ` Y[AD£T>.;�>.GX=?A MON CHST>7; M =!CH;<A ` ¬ jyM ` A¡P¢>)� M a)= N v ` C N g M � N > �«eAD=!| |JAcY[Y[>7G ` v~@B@F>7=!;�v MON �H>.�J; M A ` CH@BCO;!S[|[ADa�=?C ! � ³ k µ�� A � b |J>-@F>7=!;!Aca � «e|JC ` >¨a.CHG~P=?; M g M ;!A M Gz=ea7CH@FSTCHGJ>.GX= ` M ;�>��HADgO>.G¨�zv

�9 9 � ³ º � ) µ 1 �

9 � ) � ³ º � ) µ 1 � � ³ º � ) µL³ º � � µ 1 ³ n � ºHº µ

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A ` M � M AcG¨� N CO� MONcN v ½ Ac>7@ M G[G[A M G�«eAD=?|¨I.>7;!C0E MOj `�` A M G-a j ;�g M = j ;!>�>7gO>.;�v~«e|J>.;!>o� b |J>(a$| M GJ�H>CO{®a.C~CH;!YJAcG M =!> ` M G[Y0;!> ` a MON AcG[�"«e|JAca$|¨@ M S�=!|[>�CHS�>.; M =?CH; ³ n � ºVm µ =!C"=?|[>�G[CH;�@ MoN {­CH;�@ ³ n � � µM ;�>��OADgH>7G0�zv

.) � M ;!a7= M G )�1 .� � M ;�a ` AcG[| �� º � ) < ³ n � º�k µ1 � � º � )

³ º � ) � � µ�� � � + ³ n � º � µb |[> a.C~CH;�Y[AcG M =?> =?; M G ` {­CH;!@ M =?ADCHG ³ n � ºVk µ @ M S ` =?|[> S NcM G[> =!C M G COST>7G3ADG   G[A¡=?> ` =?;!ADS³ N�� F k 1�� F k µ � A AcG M N C~a MoNcN vÁY[A¡£¤>7CH@FCH;!S[|JAca-« M vH� b |[> >7Ac�H>7GJ{ j G[a)=?AcCOG ` CH�J= M AcG[>7Y �zv=?|J> MoN �H>7�[; M ADa�@F>7=?|JC©Y M ;�>�CO{*=!|[>�{­CH;!@

6 ³�.)�1 .� µ � a7C ` C .)a7C ` | C � 9 .� � ³ = M G .) 1?` >7a .)�` ADG[| .� µ 1 ³ n � º}n µ«e|[>7;!> � ³ )�1 � µ A ` M S�C N v©GJCH@BA MON CO{�=?CO= MON Y[>7�H;!>7> AcG ³ )�1 � µ �*:¯� M AcG � =?|[>ZG M = j ; MON ��C j G[Y M ;�va.COG[Y[AD=!AcCHG ` M ;!>�=!| M =e=?|[>�>7Ac�H>7GJ{ j G[a)=?AcCOG ` g M G[A ` | M =Z=?|[>���C j G[Y M ;�v�Co{*=?|J> ` =?;�AcS � =!| M =eA `

6 � N � k 10.� � � 6 � � k 10.� � � m 1 � .� 3 A + ³ n � º Ä µ: ` AcG =?|J>iS[;�>7g~AcC j ` >9� M @BS N > � CHG N v ` CH@F>-Co{<=?|J>->7Ac�H>7GJ{ j G[a)=?AcCOG `³ n � º}n µ «eA NDN { j[ND [NcN =?|J>��C j G[Y M ;�v�a7CHG[Y[A¡=?AcCOG `�³ n � º}n µ � b |[>�STCo=?>.GX=!A MON ? ³�.) 10.� µ A ` ;�>.@ M ;!u M � N v ` Ac@FS N > �

? ³�.) 10.� µ � N ºk ³ º � µ�³ k � µZ` >.a$| .� + ³ n � º � µd =8A ` ADG[Y[>.S�>.GJY[>.GX=¯CO{ .) ��M G[Y0A ` M ;!> ` =?;�Aca7=!>.Y r �C ` a$| N ¹ b > NcN >.;ZS�CO=?>7GX=?A MoN AcG .� �

d = ` |JC j[N Y���>ZS�CHAcGX=?>7Y"C j = M = =?|JA `*` = M �O> =?| M =*=?|[> G M = j ; MON ��C j GJY M ;�v/a.COG[Y[AD=!AcCHG ` a$|[C ` >.GM ��CVgH> M ;!>��Xv0G[CF@B> M G ` =?|[>�CHG N v�CHGJ> ` CHG[>�a.C j[N Y0a.CHG ` AcY[>7;8{­;�CH@ M �H>7CH@B>)=?;�Aca MoN STCOAcGX=eCO{g~Ac>)«�� \yCH;BAcG ` = M GJa.> � CHG[>�a7C j[N Y AcY[>7GX=?AD{ vÁ=?|J> ` ADY[> ` CO{�=!|[> ` =!;!ADS AcG ¼ � M @FS N > n � k M G[Ya.COG ` ADY[>.;�=?|[>F@BCo=?AcCOG Co{ M S M ;�=?ADa N >FCOG M GÀAcG   GJAD=?>,a)v N AcG[YJ>.;.� b |J> ��C j G[Y M ;�v a.CHGJY[AD=!AcCHG `«�C j[N Y0=?|J>.G¨�T>�S�>.;�AcC~Y[Aca�ADG .) ������ ��

6 � N � k 10.� � � 6 � � k 1 .� � 1 � .� 3 A + ³ n � º�� µ

b |[> M �TCVgH>B>)� M @FS N > `�` |[CV« =?| M =(ADGÀ@ M GXv�a M ` > ` =?|J> ; M G[�H>,CO{ =!|[> §�S[|Xv ` Aca MONcª a.C~CH;�PY[ADG M =?> ` A ` G[CO= MONcN CO{ A � � j = M GCOST>7G ` j � ` >7=�' 3 A «eAD=!|G[CHG[>7@BS©=Rvi��C j G[Y M ;�v � ' �b |[A ` | M S[S�>.G ` =Rv~S[Aca MONcN v�AcG(=!|[> a M ` > CO{�@F>7=!;!ADa ` Co{�I.>.;�C�E Moj `!` A M G"a j ;�g M = j ;!> ¥ «e|J>.;!> =!|[>.;�>A ` M G M = j ; MON ` >7=<CO{�h M ;�=!> ` A M Ga7C©CO;!Y[ADG M =?> `t¥ AD{°=?|[>"a7C©CO;!Y[ADG M =?>�=?; M G ` {­CH;!@ M =?ADCHG0@ M S[S[AcGJ�³*)�1 � µ =?C ³�.)�1 .� µ A ` M a7CVgH>.;�AcG[�0@ M S�� d G �H>7G[>.; MON�� AD{�=?|J>.;!>�A ` M G M = j ; MON ` v ` =?>7@ CO{(§�S[|Xv ` A�Pa MoNcª a.C~CH;!Y[ADG M =!> `¦` j �H�O> ` =!>.Y��Xv,=?|J><�H>7CH@B>)=?;�v M `!` C©a7A M =!>.Y,=?C/=!|[> j G[Y[>.; N v~AcGJ� ½ Ac>7@ M GJG[A M G@F>7=?;�Aca ³­` M v M @F>7=!;!Aca�Co{�a.COG ` = M GX= a j ;�g M = j ;!>¨CHG M |Xv~ST>7;!��C N CHADY µ � =?|J>.G COG[>-| M ` =?C �HC

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=?|J;!C j �O|¨=!|[> M Y[Y[A¡=?AcCOG MON ` =?>7S ` Co{*Y[>)=?>7;!@FAcG[ADG[�"=?|[>�; M G[�H>�CO{°=?|[> ` >�a.C~CH;!YJAcG M =!> ` � a$|[C~C ` ADG[�G M = j ; MoN ��C j GJY M ;�v a7CHG[Y[A¡=?ADCHG ` {­CH;,=?|[>¨>.AD�H>.G©{ j G[a7=!AcCHG ` � M G[Y Y[>)=?>7;!@FAcG[ADG[��«e|[Aca$| CO{�=?|J>>.AD�H>.G©{ j G[a7=!AcCHG ` CH�J= M AcGJ>.Y �Xv =?|[> MON �O>.�[; M Aca,@F>7=?|JC©Y { jJND yNDN =?|[> ` >�a7CHG[Y[A¡=?AcCOG ` MoN CHG[�0«eAD=!|` ¬ jyM ;!>,AcGX=?>7�H; M �[A N AD=RvH��: `�` |[CV«eG �Xv ¼ � M @FS N > ` n � º M G[Y n � k � ` j a$| M S[;!C~a.>7Y j ;!>,A ` �zvG[C@F> M G ` j G[AD¬ j > ³ ��E� �oM a7v N ADG[Y[>.; & � � M G(ADG   G[A¡=?> ` =!;!AcS µ � d G M GXv�a M ` > � «^> ` | MONDNzMON « M v ` ;!>7¬ j Ac;�>=?|J>F� MOj �H>F� M @BA N =?COG[A M G ³ �J� k � µ =!C0�T>,Y[>   G[>.YÀCVgH>.; MONDN CO{ A AcG�=?|J> ³ )�1 � µ a.C~CH;!Y[ADG M =!> ` �M G[Y0=?C,| M gO> M S[;�AcG[a7AcS MON ` v~@"��C N CO{®STC ` AD=!ADgO>)PRYJ>   G[A¡=?> ` Ac�HG M = j ;�>�>)gH>7;�vz«e|[>.;�>O�

b |[> =?|JAc;!Y(;!>.¬ j AD;!>7@B>7Gz= A ` =!| M =*CO{�Ac;!;�>.Y j a.Ac�JA N A¡=Rv � G M @F> N v�=?| M =®=?|[>^� MOj �H> � M @FA N =?CHG[A M G³ �©� k � µ8` |JC j[N Y MoN « M v ` >9�JS N Aca7AD= N v0AcGXgOC N gO>�> N >7@B>7GX= ` � 7 CO{]=?|[>�|[ADY[Y[>7G ` v~@B@F>7=!;�v MON �O>.�[; M! «e|JAca$| � =?CH�H>)=?|[>7;F«eA¡=?| =?|J>.Ac;,a7CH@B@ j = M =!CH; ` � � 7 1 � < � � ` S M G =!|[>0>.GX=?AD;!>¨QLAc> MON �O>.�[; M ! �d G[Y[>7>.Y � AD{°=?|J> � 7 � ` �H>7G[>.; M =?>7Y M S[;�CHST>7; ` j � MON �H>.�J; M ! = � =?|[>7G-«�>/a7C j[N Y¨| M gO> M ` A¡= jyM =!AcCHG«e|[>7;!>FG[CHG©P�=?;!A¡g~A MON a.CH|[CO@BC N CH�Ovia N�M `!` > ` {­CO; ! �T>7a.CH@F>�=?;�ADg~A MON {­CH; ! = �®M G[Y =?| j ` �HADgO>F;�A ` >=?C =?>7;!@ ` AcG�=?|J>À� Moj �H> � M @BA N =?COG[A M G ³ �J� k � µ «e|[ADa$|²a7C j[N Y ��> > N AD@BADG M =!>.Y �Xv M � MOj �O>=?; M G ` {­CH;!@ M =?ADCHG��*Q±>)= j ` A NcNDj ` =!; M =!><=?|JA ` �Xv M G¨>)� M @FS N >o���� � ��� � � ��� � h^CHG ` AcYJ>.;Z=?|[>�QLAc> MoN �H>7�[; M ` S M G[G[>7Yi�Xv�=?|J>�YJAD£T>.;!>7GX=?A MoN CHS�>.; M =?CH; `

� 9 � � � 1 � � ) � � � 1 � � � ) � � � � k ³ ) N � µ 1 ³ n � ºVl µ

«e|[>7;!> M ` �T>){­CH;!> � � �� ) 1 � �

� � + ³ n � ºV¸ µb |[A ` QLAc> MON �H>.�J; MJ� «e|[Aca$|²A ` A ` CH@BCO;!S[|[ADa=?C ��� ³ k 1EA�µ � a7CH;!;�> ` STCHGJY ` =!C h M ` > º�k AcG =?|J>a NcM `!` A   a M =?ADCHG � � ��CO{�QLAD> MoN �H>7�[; M ` Co{�S NcM G M ;   ; ` =�PRCH;�Y[>.;¦Y[AD£T>.;�>.GX=?A MON CHS�>.; M =?CO; ` M Y[@FAD=�=?AcGJ� M  G[A¡=?>9PRY[AD@B>7G ` ADCHG MON @FC©Y jJN > CO{ ` @BC~CO=?|/{ j G[a7=!AcCHG ` � d = M Y[@BA¡= ` M<  G[AD=!>)PRYJAc@F>.G ` AcCHG MoN @FC~Y j[N >CO{ ` @FC©CO=!|�{ j G[a7=!AcCHG ` A¡{ M G[YBCOG N v�A¡{T=!|[>8a.CH|[CO@BC N CH�Ov/S M ; M @B>)=?>7; A ` M GBADGz=!>.�H>7;]a.CHG ` = M GX=.�� j =*=?|[>^=R«�CoP¢Y[Ac@F>.G ` AcCHG MON ` j � MON �H>.�J; M ! = ` S M G[G[>7YF�Xv � M G[Y � � A ` A ` CH@FCH;�S[|[Aca]=?C¯=?|[>eQLAc>MON �H>.�[; M / ¥ =?|[> j G[AD¬ j >-GJCHG©P M �T> N A M G ³ ` C N g M � N > µ =R«�CoPRY[AD@B>7G ` ADCHG MON Q±AD> MON �H>7�[; M ¥ «e|[ADa$|| M ` =!;!ADg~A MON a7CH|[CH@FC N CO�Ov j G[Y[>.;e=?|J> M `!` j @BSJ=!AcCHG0CO{°=?|J>�>9�©A ` =!>.G[a7>/Co{ M"  G[A¡=?>)P¢Y[Ac@F>.G ` AcCOG MON@FC©Y jJN >�CO{ ` @FC~CO=?|�{ j G[a)=?ADCHG `�³ ` >.> � � � h M ` > k � µ �� >7{­CO;!>FS[;!C~a.>7>.Y[ADG[�¨=!C0S[;!> ` >.GX=(C j ; N A ` =�CO{�G[>7« G[CH;!@ MON AcI M � N >/¬ j[M ` A�PR>)� M a)= N v ` C N g M � N >S NcM G M ; S�CO=!>.GX=?A MON ` � «^> ` |JC j[N Y0@ M uO> ` CH@B>��O>.G[>7; MON a7CH@B@F>.GX= ` COG0=!|[> ` >/S�CO=!>.GX=?A MON ` �\*Ac; ` =^CO{ MONcN � C j ; N A ` =�A ` �Xv�G[C�@F> M G ` a.CO@BS N >7=!>O� " >�;!> ` =?;�Aca)=?>.Y�C j ; ` > N gO> ` =!C(=?|[;�>.>�QLAc>

MON �H>.�[; M ` C j =�CO{�=!|[> N A ` =<CO{ k n CH�J= M AcG[>7YiADG � � � � G M @F> N v0;�> MON AcI M =?ADCHG ` CO{�=?|J>�QLAc> MoN �H>7�[; M `��� ³ k 1EA�µ � ��� ³ k 1EA�µ M G[Y ��� ³ � 1EA�µ ��MON ;!> M YJvFa.CHG ` AcYJ>.;!>7Y��Xv q |[AD{­@ M G M G[Y b°j ;��[AcG[>7; � º�� � �JM G[Y! � ³ k 1EA�µ � A ; � 9 � a7CH;!;�> ` STCHGJY[AcG[�-=?C�h M ` > kon AcG =?|[>Ba N�M `!` A   a M =?AcCOGÀCO{ ;!>7{­>7;!>7G[a.> � � � �i\yCH;> M a$|,Q±AD> MoN �H>7�[; M�!�� «^> ` | MONDN �OADgH>��T> N CV« AD= ` ;�> MON AcI M =?ADCHG/ADG/=!>.;!@ ` Co{   ; ` =�PRCO;!Y[>7;*Y[A¡£¤>7;!>.GX=!A MONCHS�>.; M =?CH; ` � 7 � º � 9D� YJAc@ !��LM G[Y�=?|J>.G S[;!> ` >7Gz=�=!|[>(g M ;!ADC j ` S M ; M @F>7=!;!ADI.>.Y-{ M @BA N AD> ` CO{G[CH;�@ MoN AcI M � N >�¬ jyM ` A�PR>9� M a7= N v ` C N g M � N >�S�CO=?>7GX=?A MoN ` «eAD=!| M �J;!Ac>){�Y[A ` a j `!` ADCHGiCo{ =?|[>7Ac; ` MON Ac>7Gz={­> M = j ;�> ` �]: ` ��>7{­CO;!> � «�> ` | MONDN�j ` >�=!|[>�G[CO= M =?ADCHG

��� ;�7 < � 9 = 7 <

�87 � < � ;�7 � 9 = 7� 7 � =>= 1 5 � YJAc@ ! + ³ n � kOm µ

kOm

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� j ;�a$|[CHADa.>,« M ` @ M Y[> M { =?>7;�@ j a$|À=!;!A MoN�M G[YÀ>.;!;�CH;�«eAD=!| =!|[>BCo=?|[>7;(QLAc> MON �H>.�J; M ` ADGÀC j ;N A ` = ��N > M YJAcG[� MON @FC ` =¯ADGXg M ;!A M � N vB=?C�@F>7=!;!Aca ` «e|JAca$|i«�>.;�>"G[CO=¯� N CO� MONcN v ½ Ac>7@ M GJG[A M G � CH;8=!C>.AD�H>.G©{ j G[a7=!AcCHG ` «e|[Aca$|0«^>7;!>�G[CO= ` ¬ jyM ;!>�AcGX=?>7�H; M � N >o�q >.a7CHG[Y N v � =?|J>/G[CO;!@ MON ADI M � N ><¬ jyM ` A¡P¢>)� M a7= N v ` C N g M � N >�S�CO=?>7Gz=!A MON ` «^>�CH�J= M AcGJ>.Y¨AcG[A¡=?A MoNcN v«�>.;!>�@ j a$|�@BCO;!><a7CH@FS N ADa M =!>.YB=!| M G =!|[>�CHGJ> ` «�>�S[;!> ` >7Gz=e��> N CV«�� " >�a$|JC ` >�=!C ` S�>.a7A MON AcI.>=?|J>,g MONDj > ` CO{ ` CH@F>,S M ; M @B>)=?>7; ` AcG CH;�Y[>.;�=?C0@ M uO>�=?|J>B>9�JSJ;!> `�` ADCHG ` @FCH;�>�a.CH@FS M a)= M G[Y=?; M a7= M � N >e«e|JA N >Z;�>7= M AcG[ADG[��=?|[>8> `�` >7Gz=!A MON S[;�CHST>7;�=!Ac> ` CO{T=?|[>8�H>7G[>.; MON STCO=!>.GX=?A MON ` � " > ` |[C j[N YMON ` CFSTCHADGX=¯C j =¯=!| M =e=?|J>(G[>)« STCO=!>.GX=?A MON ` «�>(| M gO>(CH�©= M ADG[>.Y¨{­CH;Z=?|[>/QLAc> MON �H>7�[; M ` � � ³ k µ ���� ³ k µ M GJY ��� ³ � µ MoNcN�M ;!A ` >�{­;!CH@ ` C N g©ADG[�"=?|J>�{ jJNcN a N C ` j ;!>�a.COG[Y[AD=!AcCHG `�³ �J�Ã�H� µ �

b |[Ac;�Y N v � =!|[>-SJ;!CHS�CH;�=!AcCHG MON A¡=RvÀ��>7=R«�>.>7G =?|[>0S�CO=?>7GX=?A MoNeM G[Y =!|[>-E Moj `!` A M GÁa j ;�g M = j ;�>M a7a.CH;�Y[AcG[��=!C ? � �

º ��� 1 ³ n � k©º µS[;�C�gO>.Y��XvFQLC ` >7g M G[Y b®j ;!�[ADG[>.; � ºOº �y{­CH;]¬ jyM ` A�PR>9� M a7= N v ` C N g M � N >e� M @FA N =!CHG[A M G ` M `!` C~a.A M =?>7Y=?C8=?|[>�|[AcYJY[>.G ` v~@B@F>7=!;�v MON �O>.�[; M ��� ³ k µ «eA¡=?|"I7>.;!C<a.CH|[CO@BC N CH�Ov � A ` ADG(�H>7G[>.; MON G[CO= ` M =!A `   >.Y³ >)gH>7G M ` v©@FSJ=!CO=?ADa MONDN v µ � q ST>7a.A   a�a.C j GX=!>.;!>9� M @BS N > ` M ;�>��HADgO>.G¨�zv0@ M GXv�Co{®=!|[>�STCO=!>.GX=?A MON `AcG�=!|[> N A ` =Z��> N CV«���¯CV«�>7gH>7; � «�>�| M gO>�{­C j G[Y�{ j ;�=?|[>7;Z>7g~AcYJ>.G[a7>�ADG { M gHCH;ZCo{ M a7CHG���>7a7= j ;!>�CO{ b®j ;!�[ADG[>.; � kOm �=?C¨=?|[>B>7£T>.a)="=?| M =/=!|[> ¬ jyM ` A¡P¢>)� M a7= N v ` C N g M � N >BS�CO=!>.GX=?A MON ` CHG M ´ M =/� M a$uz�H;�C j G[Y @F>7=!;!AcaM ;�> ` >.S M ; M � N >�AcG�=?|J>i§�S[|Xv ` Aca MONcª a.C~CH;�Y[AcG M =?> ` �D���� ���M ;!>�CO{°=?|[>�{­CH;�@? ³�.)�1 .� µ � � ³/.)Tµ � � ³�.� µ ³ n � kHk µAcG ` j AD= M � N >�h M ;�=!> ` A M G¨a.C~CH;!Y[ADG M =!> `�³�.)�1 .� µ ������ ����� k A��� ����� k� A��b |[>7;!>�A ` � j SÀ=?C N C©a MON Y[AD£T>.CO@BCH;�S[|[A ` @ ` M G[Y ;!> ` a MON ADG[� ` ³ k �Ã� µ M G[Y ³ k � n µ � Mij G[Ac¬ j >B;!>.S~P;!> ` >7Gz= M =?ADCHG�CO{�=?|JA ` QLAc> MON �O>.�[; M AcG =!>.;!@ ` CO{   ; ` =�PRCH;�Y[>.;�S N�M G M ; Y[A¡£¤>7;!>.GX=!A MON CHS�>.; M =?CH; `M Y[@FAD=�=?ADG[� M0  G[AD=!>F@FC~Y j[N >�Co{ ` @FC~CO=?|�{ j G[a)=?ADCHG ` # � b |[A ` ;�>.S[;�> ` >7GX= M =!AcCHG a7CH;!;�> ` STCHGJY `=?CBh M ` > ºOº ADG�=?|[>�a NcM `!` A   a M =?ADCHG�CO{®;!>){­>.;!>7G[a.> � � � ��M G[Y0A ` �HA¡gH>.G¨>)�©S N Aca7AD= N v �Xv

� 9 � � 1 � �� 1 � � � ) � 1 � ��� 1� � � ) � N )�1 � � ��� N B� 1 ³ n � k � µ«e|[>7;!>�=?|[>�¬ jyM Gz=!AcI7>.Y0a.CH|JCH@BC N CH�OvFS M ; M @F>7=!>.; ` M G[Y B M ;!>�G[COG[G[>.� M =?A¡gH>�AcGX=!>.�H>7; ` �]:¯Gzv  G[A¡=?>9PRY[AD@B>7G ` ADCHG MON ! P¢@BC~Y j[N >�CO{ ` @BC~CO=!|�{ j GJa7=?ADCHG ` M Y[@FAD= ` M � M ` A ` CO{yS�C N v~G[CO@BA MON ` � ³ )�1 � µ«e|[C ` >�Y[>7�H;!>7>�AcG ) A ` N > `!` =?| M G CH;(>7¬ j[MON =!C M GJY «e|[C ` >�Y[>.�O;!>.> AcG � A ` N > `!` =!| M G CO;>.¬ jyMoN =?C B � b |[>/>7Ac�H>7GJ{ j G[a)=?ADCHG ` M ;�A ` ADG[�"{­;!CO@3=?|J> M S[S N ADa M =!AcCHG CO{®=!|[> MON �O>.�[; M Aca�@F>7=!|[C~Y=?C�� M @FA N =?CHG[A M G ` M Y[@BA¡=!=!AcG[� ��� ³ k µ � ��� ³ k µ M ` M |[ADY[Y[>7G ` v~@F@B>)=?;�v MON �H>.�[; MBM ;!>/=!|[>.;�>7{­CH;�>CO{°=?|[>�{­CH;�@ 6 ³ )�1 � µ � 1 ³*)�1 � µ � ³*)�1 � µ 1 ³ n � kon µ«e|[>7;!> 1 A ` =?|[>�� Moj �H>�{ M a7=!CH; M G[Y � A ` M ` M ��C�gO>O�" > | M gO> {­C j G[Y�=?|[>�{­C NDN CV«eAcG[�ÀS M ; M @B>)=?;�AcI.>7Y�{ M @BA N AD> ` CO{ ` C Ncj =?AcCOG ` =?C =!|[> a N C ` j ;�>a.COG[Y[AD=!AcCHG `�³ �J�Ã�H� µ �

k©º

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����� ���b |[>   ; ` = >)� M @FS N >8A ` =?|[>¯Y[AD£T>.;�>.GX=?A MON CHST>7; M =!CH; ³ n � kOm µ Y[>   GJ>.Y0�XvB=!|[>¯{­C NDN CV«eAcGJ��g MONDj > ` CO{=?|J>�a7C©> )Fa.Ac>7GX= ` = 7 < � = 7 � º��&9 1 � �

� �

³ = 7 < µ ������������ º m m m ºº � m m º mm m º � � m m mm m m º ��� m mm º m m º ºº m m m º º

�����������1 ³ n � k Ä µ

³�= 7 µ � 5 m 1 m 1 º N ³ º � k� µ � 1 º N ³ º � k B µ � 1 m 1 m 7 1 ³ n � k � µ«eAD=!| =>= � � M G[Y � M ;!�[A¡=?; M ;�v�S M ; M @F>7=!>.; ` �

b |[>�a.CHGX=?; M g M ;!A M Gz=e@F>7=!;!ADa�a.C~> )Fa.AD>.GX= ` M ;�>��OADgH>7G0�zv

�9 9 � 5 º � ) 7 5 � � ) 7 1 ³ n � kH� µ�9 � 5 º � ) 7 5 º � � 7 1 ³ n � kOl µ�

� 5 º � � 7 5 � � � 7 + ³ n � kO¸ µb |[>�@B>)=?;�Aca<«eA NcN ��>�STC ` AD=!ADgO>�Y[>   GJAD=?>�S[;�CVg©ADY[>.Y0=?| M =

� � º 1 � � º 1 � � � º + ³ n �Ã� m µb |[>�� MOj �H>�{ M a7=?CO;ZA `

1 � � ³ � N º µ ) � ³���N º µ � � � � N º � ��³ º � ) µ � � �� ³ º � � µ � � �� + ³ n �Ã� º µ

b |[>(E Moj `!` A M G0a j ;�g M = j ;!>�A ` �HA¡gH>7G-�Xv³ � N º µ � � ��N � � ³ º � ��N k � µ �

� � ³ ��N º µ E ? ³ � � º µL³ � ��� µ � � � N º� k ³ � N º µ ) � � ³���N � µ � �� ³���N º µ E ? 9�� k ��� N n � ����� � ³ Ä � N n ��N º µ � � k 5 º � k � N k �Á³ º ��� µ ��� 7 � � ³ º N � µ ) � ³ � � ��� � Ä µ � 1 � �� º 1 ³ n �Ã� k µ

M G[Y� � N"³ º � k ) µ 1 � � º 1 ³ n �Ã�H� µ

kHk

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«e|[>7;!>E � ³ � N º µ ) � ³���N º µ � � � � N º + ³ n �Ã� n µ

b |[>�>)�©S[;�> `�` AcCOG¨{­CH;�=?|[>�S�CO=?>7GX=?A MoN A ` >)gH>7G-@FCH;!><a j @"��>.; ` CH@F> � ` C�«^> ` | MONcN G[CO=eY[A ` S NcM vBAD=|[>7;!>O� d G ` =!> M Y � «�>ZS[;�> ` >7GX=¦=R«�C�S M ;�=?ADa j[NcM ;®ADG ` = M G[a7> ` CO{y=!|[> M ��C�gO> @ j[N =?ADS M ; M @B>)=?>.;L{ M @FA N vCO{®¬ jyM ` A�PR>9� M a7= N v ` C N g M � N >�� M @FA N =?CHGJA M G ` ������ �;�q j � ` =?A¡= j =!AcG[� � � � � k ³ n �Ã�XÄ µADG�=?|[>�S[;�>7g~AcC j ` >)� M @FS N >�«�>/CO�J= M ADG

³ = 7 < µ �����������

k º m m m ºº k m m º mm m � m m mm m m � m mm º m m º ºº m m m º º

�����������1 ³ n �Ã�H� µ

³ = 7 µ � 5 m 1 m 1 N(³ º � n@ µ 1 N(³ º � n B µ 1 m 1 m 7 + ³ n �Ã� � µ" > ` | MONDNLMON ` C�= M uo>=>= � �

� B � + ³ n �Ã� l µb |[>�a.CHGX=?; M g M ;!A M Gz=e@F>7=!;!ADa�a.C~> )Fa.AD>.GX= ` ;!>7Y j a7>�=!C

�9 9 � 5 º � ) 7 5 k � ) 7 1 ³ n �Ã� ¸ µ�9 � 5 º � ) 7 5 º � � 7 1 ³ n � nXm µ�

� 5 º � � 7 5 k � � 7 + ³ n � n[º µb |[>�� MOj �O>�{ M a7=?CO; M G[YE MOj `�` A M G-a j ;�g M = j ;!>�{­;�CH@4=?|J>/S[;�>7g~AcC j ` >)� M @FS N > ` AD@BS N AD{ vF=?C,=?|J>{­C NDN CV«eAcG[�(>)�©S[;!> `!` AcCHG ` �

1 � ³ � � ) � � ?µ ��³ º � ) µ�� � �� ³ º � � µ � � �� 1 ³ n � nzk µ

� � N � N l � � � N � � ) � ³ � � � � µ� � ) � � � � ³ � � k ) � µ�³ º � � µ�³ k � � µ³ � � ) � � µ + ³ n � n � µ

\*ADG MONcN v � =?|[>�S�CO=?>7GX=?A MoN A ` �HA¡gH>7G-�Xvl ? � N � N ³ º � k� µ�³ � � k µº � ) N ³ º � k B µ�³ � � k B µº � �

N º�� � ºVk � N � � k ) � ³ � � Ä � µ� � ) � � � Ä ³ � � k ) � µ�³ º � � µ�³ k � � µ³ � � ) � � µ +

³ n � nHn µ

k �

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����� � �: ¬ jyM ` A�PR>9� M a7= N v ` C N g M � N >ZSTCo=?>.GX=!A MON ` Ac@FA NcM ;°=!C�=?|[>eS[;�>7g~AcC j ` CHGJ>ZA ` CH�J= M AcG[>7Y�«e|[>.GF«^> ` >)=

� � �k 1 � � k ³ n � n Ä µ

AcG,=?|J><�H>7G[>.; MON STCO=!>.GX=?A MON n � º � º � " >¯¬ j CO=!>¯«eA¡=?|[C j =�{ j ;�=?|[>7;�a7CH@F@B>7Gz=]=!|[><>9�JSJ;!> `�` ADCHG ` {­CO;=?|J>�a.C~> )Fa.AD>.GX= `@= 7 < � = 7 ³ º � 9 1 � �� µ M GJY =>= � =?|[>�a7CHGX=?; M g M ;�A M GX=�@F>7=!;!Aca(a.C~> )Fa.AD>.GX= ` �=?|J>�� MOj �H>�{ M a)=?CH; M G[Y¨=!|[>/E Moj `!` A M G0a j ;�g M = j ;!> �

³�= 7 < µ �����������

º m m m ºº k m m º mm m �

m m m

m m m � m mm º m m º ºº m m m º º

�����������1 ³ n � n � µ

³ = 7 µ � 5 m 1 m 1 N 5 9 � � 7 1 N"³ º � n B µ 1 m 1 m 7 1 ³ n � nz� µ

=>= � º � k ³ k B @N � )µn < ³ n � nXl µ

�9 9 � 5 º � ) 7 � � k � ) � 1 ³ n � nX¸ µ

�9 � 5 º � ) 7 5 º � � 7 1 ³ n � Ä m µ�

� 5 º � � 7 5 k � � 7 < ³ n � Ä º µ

1 � ³ n � k ) � � $µ ��³ º � ) µ � � �� ³ º � � µ � � �� + ³ n � Ä k µ

� � º N k Ä � � m ) � � ) � º � ) � � º�k ) � �n � k ) � �

�� ³ º � ) )µ�³ � � k ) 9µ�³ n � ) � k ) � µ³ n � k ) � � µ + ³ n � ÄO� µ

b |[>�STCo=?>.GX=!A MON {­CH; =?|[A ` >)� M @FS N >�A ` �HADgO>.G¨�zvº � ? � N n � N ³ º � k� µ�³ � � k� µº � ) N k ³ º � k B µ�³ � � k B µº � �

N º}l � kon ) � � k � � kOm ) � � N ¸ � n � k ) � �

�Ä ³ n � n ) � N � 9µ�³ º � � $µ�³ k � � 9µ

³ n � k ) � � µ + ³ n � Ä n µ

kon

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����� � �b |[>e{­C NcN CV«eAcG[� ` C Ncj =!AcCHG,a7CH;!;�> ` S�CHG[Y ` =?C�=?|J> q a$|J;V�CHY[ADG[�H>7;�CHS�>.; M =?CO;�Y[A ` a j `�` >.Y�ADG ¼ � M @FS N >n � º � " >�= M uO>

³�= 7 < µ ������������ º m m m ºº � m m º mm m k � m m mm m m k � m mm º m m � ºº m m m º �

�����������1 ³ n � ÄHÄ µ

³�= 7 µ � 5 m 1 m 1 N k � 1 N k � B 1 m 1 m 7 1 ³ n � ÄO� µM G[Y

=>= � N ³ � ��� B µ/+ ³ n � Ä � µb |[>�a.CHGX=?; M g M ;!A M Gz=e@F>7=!;!ADa�a.C~> )Fa.AD>.GX= ` M ;�>��OADgH>7G0�zv

�9 9 � �Á³ º � ) µ 1 ³ n � Ä l µ�9 � ³ º � ) µL³ º � � µ 1 ³ n � Ä ¸ µ�

� � ³ º � � µ + ³ n �Ã� m µb |[>�� MOj �O>�{ M a7=!CH;ZA ` �HA¡gH>7G-�Xv

1 � 5 º � ) 7 ?� 5 º � � 7 ? � + ³ n �Ã� º µ

b |[>(E Moj `!` A M G0a j ;�g M = j ;!> M G[Y0=?|[>�S�CO=?>7GX=?A MoN ��CO=?|0g M G[A ` | �� � ? � m + ³ n �Ã� k µ

b |[>(h M ;�=!> ` A M G0a.C~CH;�Y[AcG M =?> `�³/.) 10.� µ M ;!>��HA¡gH>7G-�Xv ³ n � � µ ������ ���\yCH; =?|J>�{­C NcN CV«eADG[� ` C Ncj =!AcCHG � «^>�= M uO>

³ = 7 < µ ������������ º m m m �º � m m º mm m k � m m mm m m � �J� = m mm º m m � �� m m m � � =

� ���������1 ³ n �Ã�H� µ

³ = 7 µ � 5 m 1 m 1 N k � 1 N � � ³ º � k B µ � =@1 m 1 m 7 1 ³ n �Ã� n µ

k Ä

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M G[Y=>= � º

k ³ � N�� =/µ ? 9 � k � B ³ º � B µ � N k � B ³ k � B µ = � k � =� � 5 N k � N � ³ º � k B � k B µ � = � ³ º � n B � k B µ = 7 � 1 ³ n �Ã�XÄ µ

«e|[>7;!> � � � � = M G[Y � M ;!>�G[COG[G[>.� M =?A¡gH>�;!> MON S M ; M @B>)=?>7; ` ��M G[Y � �� � = �b |[>�a.CHGX=?; M g M ;!A M Gz=e@F>7=!;!ADa�a.C~> )Fa.AD>.GX= ` M ;�>��OADgH>7G0�zv

�9 9 � �Á³ º � ) µ 1 ³ n �Ã�H� µ�9 � ³ º � ) µL³ º � ��� µ 1 ³ n �Ã� � µ�

� ³ º � ��� µL³ � � = � µ/+ ³ n �Ã� l µb |[>�@B>)=?;�Aca<«eA NcN ��>�STC ` AD=!ADgO>�Y[>   GJAD=?>�>)gH>.;�vz«e|[>.;�>"S[;!CVg~AcYJ>.Y0=?| M =

� � m 1 � � � º 1 � = � � + ³ n �Ã� ¸ µb |[>�� MOj �H>�{ M a7=?CO;ZA ` �HA¡gH>.G¨�Xv

1 � � � � N º � ³�� = N � µ � � ��³ º � ) µ

� ³ º � ��� µ � � �� + ³ n � �Om µb |[>(E Moj `!` A M G0a j ;�g M = j ;!>�A ` �HA¡gH>7G-�Xv

� � = N � ��&=JN �� N � � k ³ k � � � N�� = N � µ� � N º � ³��&= N � µ � �

� �Á³ º N � � µ.³ � � N =/µ³�� � N º � ³ � =�N � µ � µ � + ³ n � �©º µ

d =8A ` M { j G[a)=?ADCHG0CO{®=!|[> ` >7a.CHG[Y-a.C~CH;!YJAcG M =!>�CHG N v �yM GJY¨A ` M ` v~@FSJ=?Co=?Aca MONcN v a7CHG ` = M GX=}�b |[>�STCO=!>.GX=?A MON A ` �HADgO>.G¨�zv

l ?� � N =

� N(³ º � k B µL³ � � k B µº � ��� � � � N � � � ��� n � =JN � � =³ � =JN � µ�³�� � N º � ³ � = N � µ � µ� Ä �Á³�� � N º µL³ � � N =(µ³ � =JN � µ�³�� � N º � ³ � = N � µ � µ + ³ n � �Hk µ

b |[> N Ac@FAD=!AcG[�<a M ` > � � � = N > M Y ` =?C M a7CHG ` = M GX= S�CO=?>7GX=?A MoN AcG M ´ M =�� M a$uz�H;�C j G[Y � ` N Ac�H|X= N v@FCH;!>��H>7G[>.; MON =?| M G�=?|[>�CHG[>�ADG ¼ � M @FS N > n � º � n ������ ����� � A��b |[A ` Q±AD> MON �H>.�[; M | M ` M�j G[AD¬ j >�;!> MON ADI M =!AcCHG ADG =?>7;!@ ` CO{   ; ` =�PRCO;!Y[>7;�S N�M G M ;"Y[A¡£¤>7;!>.GX=!A MONCHS�>.; M =?CH; ` M Y[@FAD=�=?AcGJ� M   G[A¡=?>9PRY[AD@B>7G ` ADCHG MON @BC~Y j[N >iCO{ ` @BC~CO=?| { j G[a7=!AcCHG ` �<j S�=!C N C~a MONY[A¡£¤>7CH@BCO;!S[|[A ` @ ` M G[Y0;�> ` a MON ADG[� `�³ k � � µ M G[Y ³ k � n µ � b |JA ` ;!> MON ADI M =!AcCHG � �HA¡gH>.G0�Xv

� 9 � � 1 � �� 1 � � � ) � 1 � ��� � 1 � � � ) 1 ��� ��� 1� � � ) � � ) � N )�1 � � � ) � � � � N � 1 ³ n � � � µk �

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«eAD=!| =?|J> S M ; M @F>7=?>7; ;!> ` =?;�Aca7=!>.Y =!Ci= M uo> G[COG[G[>.� M =?A¡gH>�ADGz=!>.�H>7;/g MONDj > ` � a.CH;�;!> ` S�CHG[Y ` =!Ch M ` > º ÄeAcG�=?|[>�a N�M `!` A   a M =?AcCOG�Co{y;!>){­>.;!>7G[a.> � � ��� b |[>   GJAD=?>9PRY[AD@B>7G ` ADCHG MON @BC~Y j[N > # a7CHG ` A ` = `CO{®STC N v~G[CH@FA MON ` � ³*)�1 � µ CO{°=?CO= MON Y[>7�H;!>7>�ADG ) M G[Y � N > `!` =?| M G-CO;8>7¬ jyMON =?C � b |[>�>.AD�H>.G©P{ j G[a)=?ADCHG ` CH�J= M AcG[>7Y-�Xv M S[S N v~AcG[��=?|J> MON �H>.�[; M Aca�@F>7=!|[C~Y¨=!C M GXv-� M @BA N =?COG[A M G STC `�` > `!` ADG[���� ³ � µ M ` M |JAcY[Y[>7G ` v~@B@F>7=!;�v MON �H>.�[; M @ j ` =e=!|[>.;�>7{­CH;�>/��>/Co{*=?|J>�{­CH;�@ ³ n � kon µ � «e|[>7;!> 1ÀA `=?|J>�� MOj �H>�{ M a)=?CH;Za7CH;!;�> ` STCHGJY[AcG[�,=?C,> M a$|iS M ;�=?ADa j[NcM ;Z� M @BA N =!CHG[A M G �zM G[Y � A ` M ` ��>7{­CO;!>O�" >�| M gO>�{­C j G[Y =?|J> {­C NcN CV«eAcG[�-@ j[N =!AcS M ; M @F>7=!>.;�{ M @BA N v CO{¯� M @BA N =!CHG[A M G ` «eAD=?| � � ³ � µ|[ADY[Y[>.G ` v~@F@B>)=?;�v ����;� ���b |[>�S[;!ADG[a.ADS MON ` v~@"��C N CO{*=!|[>�@ j[N =?AcS M ; M @F>7=!>.;¦{ M @BA N vFCO{ � M @FA N =?CHG[A M G ` «^> ` | MONcN SJ;!> ` >.GX=A ` �O>.G[>7; M =!>.Y COG N v �zv =!|[>¨� M ` A ` > N >.@F>.GX= ` � 9 � � � � � M GJY � � � �¯CV«�>7gH>7; � ` AcG[a7>¨=!|[> ` >CHS�>.; M =?CH; ` {­CH;�@ M �O>.G[>7; M =!AcG[� ` >7="{­CH;/=?|[>�QLAD> MON �O>.�[; M ³ n � � � µ � =?|JA ` >9� M @BS N > @F>.>)= ` =?|J>Ac;�;!>7Y j a.AD�[A N AD=RvF;!>7¬ j Ac;�>.@F>.GX=8Y[>   GJ>.Yi> M ; N Ac>7; AcG�=?|JA ` q >7a7=?ADCHG��

b |[>�� MOj �H>�� M @FA N =!CHG[A M GB{­CH; =!|[A ` >9� M @BS N >�A ` �HA¡gH>7G¨�XvN k % � G� ��� � � � ³ � 9 µ � � ³ � µ � � = � ³ � � µ � � ³ � � µ �

��� � � � 9 1 � � � � � � 1 � � � � ³ � � k µL³ � � � � � µ � 1 ³ n � �on µ«e|[>7;!> � � 7 1 � < � � � 7 � < � � < � 7 Y[>.GJCO=?> ` =?|[> M Gz=!Aca7CH@B@ j = M =!CH;]CO{�=!|[>�Y[A¡£¤>7;!>.GX=!A MON CHS�>.;�PM =!CH; ` � 7 M GJY � < ��M GJY0=!|[>�S M ; M @B>)=?>7; ` � � � � = M G[Y � ` M =!A ` { v�=?|[>�ADG[>.¬ jyMON AD=Rv

C � � =JN � �� m + ³ n � � Ä µb |[>�a.CHGX=?; M g M ;!A M Gz=e@F>7=!;!ADa�a.C~> )Fa.AD>.GX= ` M ;�>��OADgH>7G0�zv

�9 9 � � � ) ³ � � �~µ 1 ³ n � � � µ�9 � ) � ³ � � �~µ 1 ³ n � �H� µ�

� � � � � ³ �J� �~µ 1 ³ n � �Ol µ«e|[>7;!>

� � �J� = 5 � ) � � 7 + ³ n � �O¸ µb |[>�@B>)=?;!ADa<«eA NDN ��>�STC ` AD=!ADgH>�YJ>   G[A¡=?>�>7gO>.;�v~«e|J>.;!>(AD{±=?|[>�S M ; M @F>7=!>.; `e` M =?A ` { v

� � m 1 � � m 1 = � m 1 � � m + ³ n � lHm µb |[>�� MOj �H>�{ M a7=?CO;ZA `

1 � >)�©S J � � k n � M ;!a)= M G � �� K ³ � � µ ? � � �� + ³ n � lJº µ

kH�

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�¯>7G[a.>�=!|[>�>7Ac�H>7GJ{ j G[a)=?AcCOG `0³ n � kon µ CH�J= M AcGJ>.Y M SJS N v~AcGJ�i=?|[> MON �H>7�[; M AcaF@B>)=?|[C~Y «eA NDN^Moj =?CoP@ M =?ADa MONDN v,��> ` ¬ jyM ;!>�AcGX=!>.�H; M � N >¯«eAD=?|¨;!> ` S�>.a)=8=!CF=!|[>�@B> M ` j ;!> � � � ) � � �b |[>(E MOj `!` A M G0a j ;�g M = j ;�> � «e|[ADa$|-A ` S M ;�=?Aca j[N�M ; N v ` AD@BS N ><{­CH; =!|[A ` >9� M @BS N > �� � N k � � N k � �J� = 5 � ) � � 7 � 1 ³ n � lXk µ

A ` GJ>.� M =!ADgO>�>)gH>7;�vz«e|[>.;�>O�\*AcG MONcN v � =?|[>�S�CO=?>7Gz=!A MON A ` �HA¡gH>.G¨�Xvl ? � N � � N ³ � � º � � l µ �

� ³ � � � � =JN � µ ? 9�� N º � ³ º � µ.³ k � µ � �� � ³ k � � �O� � º�k� µ � � =� � 5 º � ³ º � µL³ k � µ � N � ³ º � k� µL³ Ä � k� µ � = 7 � +

³ n � l � µd {J«�> N C©COu8{­CH; ` C Ncj =?AcCOG ` CO{~=?|[> q a$|[;}�CHY[ADG[�H>.;±>7¬ j[M =?ADCHG�«eA¡=?|�S�CO=?>7Gz=!A MON ³ n � l � µ Y[>7ST>7G[Y[ADG[�CHG N v"CHG�=!|[>B§�; M YJA MONDª a.C~CH;�Y[AcG M =?> � � «�>8>7G[Y j SF«eA¡=?| M G,>7£T>.a)=?A¡gH>eCHG[>9PRY[AD@B>7G ` ADCHG MON q a$|[;V�C PY[ADG[�H>.;ZCOST>7; M =!CH;�% � �HA¡gH>.G0�Xv

N k % � � � ³ �~µ � � � � � ³ �~µ�� � � A ³ �~µ 1 ³ n � lOn µ

«e|[>7;!>� ³ �~µ � n ³ � N �~µ 5 N � ��� N � � = 7 1� ³ �~µ

� k � ³ � N k� µ � � k ³ º � k� µ � � N ³ Ä � k� µ � � k � � = � 1A ³ �~µ � � ³ N º µ � N ³ � º µ � � + ³ n � l Ä µh^CH@FS M ;�AcG[��=?|J> ` >�{­CH;!@ j[N�M ` «eA¡=?| � ¸ � >7¬ jyM =?ADCHG ³ kOm µ � � A¡=eA `e` =!; M AD�H|X=!{­CH;�« M ;�Y¨=!C ` |[CV« =?| M ==?|J>�COG[>)P¢Y[Ac@F>.G ` AcCHG MON q a$|J;V�CHY[ADG[�H>7;8COST>7; M =!CH; ³ n � lOn µ Y[C©> ` G[CO= M Y[@FAD= ��� ³ k 1EA�µ M ` M |JAcY[Y[>7G` v~@F@B>)=?;�v MON �O>.�[; M �]�¯CV«�>7gH>7; �¤M ` j � ` >7=�Co{®=!|[>/>7Ac�H>7GJ{ j G[a)=?ADCHG ` CO{ ³ n � lOn µ a7C j[N Y0ADG-S[;�AcG[a7A¡PS N >^��> a.CH@FS j =!>.Y MON �H>.�J; M ADa MONDN v��Xv N C~CHuzAcG[� M =*=!|[> >.AD�H>.G©{ j G[a7=!AcCHG ` CO{y=?|J>^=R«^C PRY[AD@B>7G ` ADCHG MON¬ jyM ` A¡PR>9� M a7= N v ` C N g M � N >�� M @FA N =!CHG[A M G ³ n � �on µ M ;!A ` AcG[�Z{­;�CH@ =?|[> MON �H>.�[; M Aca�@F>7=!|[C~Y/«e|[ADa$| M ;�>{ j G[a)=?ADCHG ` CO{ � COG N v ³,+.- � ¼ � M @FS N >8�J� k µ � b |[A `¦` j �O�H> ` = ` =!| M =]=?|J><a NcM `!` CO{�CHG[>)P¢Y[Ac@F>.G ` AcCOG MON¬ jyM ` A¡PR>9� M a7= N v ` C N g M � N > q a$|[;}�CHY[AcGJ�H>.;eCHS�>.; M =?CH; ` a.C j[N Y-��> ` AD�HG[A   a M GX= N v�>7G N�M ;��H>.Y�g~A M ` j AD=�PM � N >�;!>7Y j a7=!AcCHG�{­;�CH@4=R«�CoPRY[AD@B>7G ` ADCHG MON ¬ jyM ` A�PR>9� M a7= N v ` C N g M � N >�� M @FA N =?CHGJA M G ` ������ ! ��� k A�� � A������b |[> NcM ` =^QLAc> MoN �H>7�[; M «�> ` | MONcN Y[> MoN «eAD=!| � «e|[Aca$|�{­;�CH@ =!|[> MON �H>.�J; M ADa¯S�CHAcGX=�CO{Lg~Ac>)«²A ` =?|J>` >7@BADY[Ac;�>.a)= ` j @ CO{ ! � ³ k 1EA�µ «eA¡=?| M ³ 5 � º µ PRY[AD@B>7G ` ADCHG MON M �T> N A M GÀADY[> MoN�� a.CH;�;!> ` STCOG[Y ` =!Ch M ` > kon AcG =?|[> a N�M `!` A   a M =?AcCOG CO{e;�>7{­>.;�>.G[a7> � � ��� b |[A ` a N�M `�` CO{8QLAc> MON �H>7�[; M ` � Y[>7ST>7G[Y[ADG[�

kOl

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CHG M S�C ` AD=?A¡gH>0AcGX=!>.�H>7; 5 � A ` j G[AD¬ j > N v ;!> MoN AcI7>.Y �¦j SÁ=?C Y[AD£T>.CH@FCH;�S[|[A ` @ ` M G[YÁ;!> ` a MON AcG[� `³ k � � µ M G[Y ³ k � n µ � ADG =?>7;!@ ` CO{±S NcM G M ;   ; ` =�P¢CH;!Y[>7;^Y[A¡£¤>7;!>7Gz=!A MON CHS�>.; M =?CH; ` S�C `!` > `!` AcG[� M/  G[AD=!>@FC©Y jJN >�CO{ ` @FC~CO=?|�{ j G[a)=?ADCHG ` � ¼ �©S N Aca.A¡= N v � =!|[A ` ;�> MON AcI M =?ADCHG�A ` �OADgH>7G � {­CH; 5 � º � �Xv

� 9 � � 1 � �� 1 � � � ) � 1 � � ) 1 � � �� 1� � � ) � � 5 ) � N )�1 ³ n � l � µ«e|[>7;!> A ` M G[COG[G[>.� M =?A¡gH>�AcGX=!>.�H>7;.� \yCH;*5 � º «�>0@ j ` = MON ` C�AcG[a Ncj Y[>B=?|[>0Y[A¡£¤>7;!>.GX=!A MONCHS�>.; M =?CH; ` � � � � � ) � � 9 1 º ���@� 5 N º + ³ n � lX� µ:<GXv ! PRADGzg M ;�A M GX=   G[A¡=?>9PRY[AD@B>7G ` ADCHG MON @FC©Y j[N >eCO{ ` @BC~CO=?|F{ j G[a)=?AcCOG ` # a.COG ` A ` = ` CO{LS�C N v~G[CoP@FA MON ` � ³*)�1 � µ CO{°=?|[>�{­CH;�@

� ³ )�1 � µ � �� ��� =� � ; � � C

9 ��� ) � � � + ³ n � lHl µ

" >¯| M gO>8{­C j G[YB=!|[>8{­C NcN CV«eADG[��@ j[N =?ADS M ; M @B>)=?>.;®{ M @BA N AD> ` Co{ ` C Ncj =!AcCHG ` {­CH; =!|[A ` QLAc> MON �H>.�J; M ���� � ���\yCH; =?|J>   ; ` = ` C Ncj =!AcCHG � «�> ` | MONcN = M uo>

5 � º 1 ³ n � lH¸ µ` C =!| M = ! A ` � P¢Y[Ac@F>.G ` AcCHG MON � b |[>�a.C~> )Fa7Ac>.GX= `�= 7 < M GJY = 7 � º � 9 1 � �

� � | M gH>�=?|J>{­C NDN CV«eAcG[�/g MoNcj > ` �

³ = 7 < µ �

�������������

� m m m m mm � m m m mm m L m = mm m m � =�4E ³ L�N k = � E�µ m mm m = m E mm m m m m = � ³ L�N =(µ

��������������1 ³ n � ¸Hm µ

³�= 7 µ � 5 m 1 m 1 L N k ³ º � µ0=@1 m 1>=JN k ³ º � µ E 1 m 7 + ³ n � ¸Jº µ\yCH;�=?|J>F@FCH@F>.GX= � =?|[>,S M ; M @F>7=?>7; =>= A ` M ;!�JAD=?; M ;�v �±M G[Y�=?|J>FCo=?|[>7;�S M ; M @F>7=!>.; ` AcG ³ n � ¸Hm µM G[Y ³ n � ¸Jº µ «eA NDN CHG N v���> M `!` j @B>7Y¨=!CF��>�G[CHG[GJ>.� M =!ADgO>O�

b |[>�a.CHGX=?; M g M ;!A M Gz=e@F>7=!;!ADa�a.C~> )Fa.AD>.GX= ` M ;�>�=!|[>.G

�9 9 � º� � � � ³ L�N =(µ ) � ³�� � = ) µ 1 ³ n � ¸Xk µ

�9 � = � ) � � � � ³ L N =/µ ) � 1 ³ n � ¸ � µ

� � = ) �4E � ³ L�N =/µ E � ��� ³ L�N k = � E�µ � � E � ��� + ³ n � ¸On µ

kO¸

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b |[A ` @B>)=?;�Aca(A ` S�C ` A¡=?A¡gH>(YJ>   G[A¡=?>�>)gH>.;�vz«e|[>.;�>BS[;�CVg©ADY[>.Y=!| M =�=!|[>"S M ; M @F>7=!>.; `<` M =!A ` { v¨=?|J>M Y[YJAD=?ADCHG MON a.CHGJY[AD=!AcCHG `

� � m 1 �� m 1 L � =@1 L � E �²k = + ³ n � ¸ Ä µ

b |[>�� MOj �H>�{ M a7=?CO;ZA `1 � � � � ³ L�N =(µ ) � �� � �4E � =�³ L�N k = � E�µ ) � ��

³ � � ��� = ) � �4E � µ�� � � + ³ n � ¸ � µq ADG[a.> 5 � º � =?|J>/>7Ac�H>7GJ{ j G[a)=?AcCOG ` M ;!A ` AcG[�,{­;!CO@ =?|[> M S[S N Aca M =?ADCHG0CO{ =?|J> MON �H>.�J; M ADa�@F>7=!|[C~Y=?C�=!|[A ` >)� M @FS N > M ;!>�CO{®=?|[>�{­CH;�@ ³ n � kon µ � «eAD=!| � M S�C N v©GJCH@BA MON CO{®=!CO= MoN Y[>.�H;�>.>�AcG ) M G[Y� N > `!` =?| M G-CH;8>.¬ jyMON =?C � b |[>.;�>7{­CH;�> � =?C >7G ` j ;!>(=!|[> MOj =?CH@ M =?ADa ` ¬ jyM ;�>"AcGX=!>.�H; M �[A N AD=RvBCO{=?|J>�>7Ac�H>7GJ{ j G[a)=?ADCHG ` «�>/@ j ` =8Ac@FSTC ` ><=!|[> M Y[Y[A¡=?AcCOG MON ;�> ` =?;!ADa7=!AcCHG `

= � m 1 E � m + ³ n � ¸X� µb |[>(E MOj `!` A M G0a j ;�g M = j ;�>�{­CH; =?|[A `Z` C NDj =?ADCHG�A ` �� � ³ L�N k =/µ = � �4E � = ³ L�N k = � E�µ ) � ? � � � E � k �Á³ L�N k =/µL³ E N =/µ ) � =�³�= N L"µL³ L�N k = � E�µ ) � +³ n � ¸Hl µb |[>�S�CO=?>7Gz=!A MON A ` =?C~C�a.CH@FS N Aca M =?>.Y¨=?C�YJA ` S N�M viADG MONDN �O>.G[>7; MON AD=RvH� " > ` | MONcN°N AD@BA¡=8C j ;�P

` > N gO> ` =?C,S[;!> ` >7Gz=!AcG[�F=R«^CFS M ;�=?ADa j[NcM ; a M ` > ` � AcG ` =?> M Y ���� � �;�d {*«�> ` >)= L � k = ³ n � ¸H¸ µAcG�=!|[>�S[;!>)g©ADC j `e` C Ncj =!AcCHG � =?|[>7G ³�= 7 < µ M G[Y ³�= 7 µ ;�>.Y j a.>�=?C

³�= 7 < µ �

�������������

� m m m m mm � m m m mm m k = m = mm m m � =� m mm m = m E mm m m m m = �

��������������1 ³ n � ºVmHm µ

M G[Y³ = 7 µ � 5 m 1 m 1 N k = 1 m 1,=�N k ³ º � µ E 1 m 7 + ³ n � ºVmJº µ

" > ` | MONDNLMON ` C ` >7==>= � N = � ³ � º µ E + ³ n � ºVmXk µ

� m

Page 32: 01 )+ 234 56 7' 8+0 9 ,+olver/q_/planeqes.pdf · ) ! * ,+- ./+0 1 )+ 234 56 7' 8+0 9 ,+ :7@badcfe chgjilk mon >.i)prq k chst>7ivu w >.s m; = @b>7gx=?czy[>]\^k

b |[>�@B>)=?;!ADa � «e|[C ` >�a.COGz=!; M g M ;!A M GX=ea.CH@FS�CHG[>.GX= ` M ;!>��HADgO>.G¨�Xv

�9 9 � º� ³ � � = ) µ 1 ³ n � ºVm � µ

�9 � = � ) � ³ � � = ) µ 1 ³ n � ºVmOn µ

� � � � = � ) ³ � � = � µ � E � 1 ³ n � ºVm Ä µ

A ` >)gH>.;�vz«e|[>.;�>�STC ` AD=!ADgH>eY[>   G[A¡=?> M G[YB´ M =}� d GF{ M a7= � =?|[A `¦` C Ncj =?AcCOGFA ` M ` N Ac�H|X=]�H>7G[>.; MON ADI M =!AcCHGCO{ ¼ � M @BS N > n � k �b |[>�� MOj �H>�{ M a7=?CO;ZA `

1 � � � � = ) ³ � � ��� = ) � �4E � µ�� � � + ³ n � ºVm � µ

b |[>�h M ;�=?> ` A M G a7C©CO;!Y[ADG M =?> `³/.)�10.� µ AcG «e|[Aca$|Á=?|[> q a$|[;}�CHY[AcGJ�H>.;FCHS�>.; M =?CH;,Y[>   G[>.Y �zv³ n � ºVmOm µ ¹ ³ n � ºVmXk µ M Y[CHSJ= ` AD= ` GJCH;!@ MON {­CH;�@ ³ k � kOk µ M ;!>

.) � º� � = M ;�a7= M G = F � )�1 ³ n � ºVmX� µ.� � º� E M ;!a ` AcGJ| � �4E �

� ³ � � = ) µ + ³ n � ºVmHl µb |[>7;!>7{­CO;!> �[M ` AcG ¼ � M @FS N > n � k � =?|[>�; M G[�H><CO{L=?|[>�§�S[|Xv ` Aca MONcª a.C~CH;!Y[ADG M =!> `�³/.)�10.� µ A ` M ` =?;!ADS³�.)�������10.)�� G�� µ � A �8�8>.G[a7> �©M ` YJA ` a j `!` >.Y�ADG ¼ � M @FS N > n � k �~M Y[YJAD=?ADCHG MON �TC j G[Y M ;�v,a.CHGJY[AD=!AcCHG `«eA NDN | M gO>�=!CF��>�Ac@FSTC ` >.Y0CHG�=!|[>�>.Ac�O>.GJ{ j GJa7=?ADCHG ` v~Ac> N Y[>7Y¨�Xv�=!|[> MON �O>.�[; M Aca�@F>7=!|[C~Y��

b |[>�STCO=!>.GX=?A MON ADG0=!|[>�S[|Xv ` Aca MON a.C~CH;�Y[AcG M =?> ` A `Z` =!;!AcuzADG[� N v ` AD@BS N > �? � N ºk ³ º � µ�³ k � µ E ` >.a$| 5 � E .� 7 + ³ n � ºVmH¸ µ

d =ZA ` AcGJY[>.S�>.G[YJ>.GX=eCO{ .) �[M GJY ³ M ` ADG ¼ � M @BS N > n � k µ A ` ` Ac@FS N v M r �C ` a$| N ¹ b > NcN >.; S�CO=?>7GX=?A MoN ADG.� � s Co=?Aca7>�=?| M =8=?|JA ` STCo=?>.GX=!A MON ` M =?A `   > ` =!|[>(a7CHG���>.a)= j ;�>(CO{ b®j ;!�[ADG[>.; �TM a.a.CO;!Y[ADG[�F=!CF«e|JAca$|M ¬ jyM ` A¡P¢>)� M a)= N v ` C N g M � N >�� M @BA N =?COG[A M G CHG M ´ M =¯@ M GJAD{­C N Y�AcG¨@BCH;�>�=?| M G-CHG[>�Y[Ac@F>.G ` AcCOG` |JC j[N Y0��> ` >.S M ; M � N >O�

b*M u~ADG[��AcGX=!C M a7a.C j GX=�>7¬ j[M =?ADCHG `,³ n � º}m � µ M G[Y ³ n � ºVmOl µ � =?|[> MON �H>7�[; M Aca MoNcN v�a.CH@FS j = M � N >>.AD�H>.G©{ j G[a7=!AcCHG ` >)�©S[;!> `!` >.Y�AcG�=!>.;�@ ` CO{°=?|[>�S[|Xv ` ADa MON a7C©CH;�Y[AcG M =?> ` M ;!>�CO{°=?|J>�{­CO;!@6 ³�.)�10.� µ � a.C `4C 5 � �&= .) 7

a7C ` | C � 9 5 � E .� 7 � ³ )�1 � µ 1 ³ n � ºHºVm µ«eAD=!|

) � � F = = M G 5 � �&=!.) 7 1 ³ n � ºHºHº µ� � � F+E ` AcG[| 5 � E .� 7 ` >.a 5 � � =!.) 7 1 ³ n � ºHº�k µ

M G[Y � ³*)�1 � µ M STC N v~G[CH@FA MON CO{°=?CO= MON Y[>7�H;!>7>/ADG ) M GJY � GJCO=e>)�©a.>7>.Y[ADG[� �� º

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��� � � �d G0=?|[A ` >)� M @FS N > � «e|[Aca$|¨A ` M � M AcG0� M ` >.Y¨CHG n �Ã�J� º � «^> ` >7=

L � k =JN E 1 ³ n � ºHº � µ{­;!CO@3«e|[ADa$|-A¡=Z{­C NcN C�« ` =?| M =

³ = 7 < µ �

������������

� m m m m mm � m m m mm m k = N E m = mm m m m m mm m = m E mm m m m m = � ³�= NOE�µ

�������������1 ³ n � ºHº}n µ

³ = 7 µ � 5 m 1 m 1 N k� =JNOE 1 m 1>=JN k ³ º � µ E 1 m 7 + ³ n � ºHº Ä µ" > ` | MONDNLMON ` C�= M uo>=>= � º

n � ³ º � k� µL³ � � k� µ E N k ³ º � k� µ = � + ³ n � ºHº � µs Co=?Aca7>^=?| M =�=?|[>Z@ M =!;!A¡� ³ n � ºOº}n µ A ` Y[>.�O>.G[>7; M =!> � ;!>)´y>.a)=?AcGJ��=!|[> { M a)=�=?| M =*=?|[>e� MOj �H>Z� M @BA N P=?COG[A M G ³ n � kom µ Y[C~> ` G[CO=FY[>7ST>7G[Y CHG =?|J>0{­C j ;�=!|Á�O>.G[>7; M =!CH;,CO{ ! AcG =?|[A ` >)� M @FS N >o� b |[>Ac;�;!>7Y j a.AD�[A N AD=Rv�a7CHG[Y[A¡=?ADCHG ADGz=!;!C~Y j a7>.Y > M ; N Ac>.;�AcGÀ=?|[A ` q >7a7=?ADCHG A ` |[CV«�>7gH>7; ` M =!A `   >.Y � ` AcG[a7>=?|J>�;�>.@ M AcGJAcG[�"�O>.G[>7; M =!CH; ` M G[Y0=?|J>.Ac;Za7CH@F@ j = M =?CH; ` M ;!>�> M ` A N v ` >.>7G-=?C ` S M G ! �

b |[>�a.CHGX=?; M g M ;!A M Gz=ea7CH@FSTCHGJ>.GX= ` CO{°=?|[>�@F>7=!;!Aca M ;!> �

�9 9 � º� ³�� � = ) µ � � � ³�= N E�µ ) � 1 ³ n � ºHº�� µ

�9 � = � ) � � � � ³ = NOE�µ ) � 1 ³ n � ºHºVl µ

� � � � = � ³ = N E�µ ) � � E � + ³ n � ºHºV¸ µ

b |[>(E Moj `!` A M G0a j ;�g M = j ;!> ` AD@BS N A   > ` =?C� � N = � � � � k ³�= N E�µ ) � 1 ³ n � º�kOm µ

M G[Y¨A ` =!|[>.;�>7{­CH;�>�G[>.� M =?ADgO>�>7gH>7;�vz«e|[>7;!> � �Xv ³ n � ¸ Ä µ � ³ n � ¸X� µ M G[Y ³ n � ºHº � µ �b |[>�� MOj �H>�{ M a7=?CO;Z;!>.Y j a.> ` =?C

1 � � � � ³ = NOE�µ ) � ��³ � � ��� = ) � �4E � µ � � � + ³ n � º�k©º µ

\*ADG MONcN v � =?|[>�S�CO=?>7GX=?A MoN A ` �HA¡gH>7G-�XvN l ? � n ³ º � µ¤³ k � µ � � E� � ��� = ) � �4E � �

�4E³ = NOE�µ ) � � �

� =� ³ = N E�µ ) + ³ n � º�kHk µs Co=?Aca7>�=?| M =°{­CH;L=?|JA ` >)� M @FS N >�=!|[>�S�CO=!>.GX=?A MONzM G[Y�=?|[>¦a j ;�g M = j ;!> M ;!>]AcG[YJ>.>.Y M ` v~@FSJ=?Co=?Aca MONcN vS[;�CHSTCO;�=?ADCHG MON �JM a.a.CO;!Y[ADG[��=?C ³ n � k©º µ �

� k

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��� � � �: ¬ jyMoN AD= M =?A¡gH> N v ` Ac@FA N�M ; ` C NDj =?ADCHG-=!CB=!|[>"S[;�>7g~AcC j ` CHG[> ��MON ` CB� M ` >7YCHG n � �J� º � A ` CH�J= M AcG[>7Y�Xv ` >)=!=!AcG[� L � E + ³ n � º�k � µ" >�=!|[>.G¨| M gH>

³�= 7 < µ �

�������������

� m m m m mm � m m m mm m E m = mm m m k � =�4E ³ E N =/µ m mm m = m E mm m m m m = � ³ E N =/µ

� ������������1 ³ n � º�kon µ

³�= 7 µ � 5 m 1 m 1 N k ³ º � µ = � E 1 m 1,=JN k ³ º � µ E 1 m 7 1 ³ n � º�k Ä µM G[Y0«�> ` | MONDNLMON ` C ` >7=

=>= � ºn � k ³ � � ºVm � n@ µ4= N ³ ºHº � º � � n µ E � ³ n � º�k � µ

b |[>�a.CHGX=?; M g M ;!A M Gz=e@F>7=!;!ADa�a.C~> )Fa.AD>.GX= ` M ;�>�=!|[>.G¨�HA¡gH>.G¨�Xv

�9 9 � º� ³ � � = ) µ � � � ³ E N =(µ ) � 1�9 � = � ) � � � � ³ E N =(µ ) � 1�

� � � E � � =�4E ) ³ E N =(µL³ k ��� E � µ�+ ³ n � º�kH� µb |[>�� MOj �H>�{ M a7=?CO;ZA `

1 � � � � ³ E N =(µ ) � �� � �4E � k = ³ E N =(µ ) � ��³ � � ��� = ) � �4E � µ�� � � + ³ n � º�kOl µ

b |[>(E MOj `!` A M G0a j ;�g M = j ;�> � «e|[ADa$|-A ` �HADgO>.G¨�Xv� � = N E k �

k �Á³ E N k =(µL³ E N =(µ�4E � k = ³ E N =/µ ) N� � E ³ E N k =(µ

k � �4E � k = ³ E N =/µ ) � 1 ³ n � º�kO¸ µA ` M ` v~@FSJ=?Co=?Aca MONcN v�a.COG ` = M GX= ³ S�C ` A¡=?A¡gH>�CH;<G[>7� M =!ADgH> � � j =�G[CO=<I.>.;�C � ` AcG[a7>"AcG¨=?| M =�a M ` >"A¡= � `> M ` v�=?C ` >.>�=?| M =Z=!|[>�Ac;�;!>.Y j a.AD�[A N AD=RvFa.CHGJY[AD=!AcCHG�«�C j[N Y¨��>�g~AcC NcM =?>7Y µ �

b |[>�>)�©S N ADa.A¡=Z>)�©S[;�> `!` AcCHG¨{­CH; =?|J>�S�CO=!>.GX=?A MON A `º � ?� � k ³ E N k =(µ� � ³ E N =(µ ) �

k ³ E N k =/µL³ Ä E N � =/µ�4E � k = ³ E N =(µ ) � Ä �4E ³ k = N E�µ � �4E � k = ³ E N =(µ ) �

� l ³ º � µL³ k � µ � � ³ E N k =/µ � k E�³ E N =(µ � �� � ��� = ) � �4E � +

³ n � º � m µ�H�

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��� � ���d G=?|JA `�` C Ncj =!AcCHG � ADGi«e|[Aca$|�«�>�G[C N CHG[�H>7;<;!> ` =!;!Aca)=�C j ; ` > N gH> ` =?C�= M uzAcG[�45 � º � =?|J>"� MOj �O>� M @BA N =?COG[A M GBA ` �HA¡gH>7G-�Xv

N k %�� G� ���� � � ³ � 9 µ � � 5 ³ º � B µ � � 9 1 � � � � � 5 ³ 5 N k B N k µL³ � � µ � �Á³ º � B µ ³ � � µ � �

7 <���� � ������ � � ��� = 7 < �87 � <� � � º � k ³ º � B µ � 5 N � � � � � N k � � ³ º � B µ � �� ��³ º � B µ � 5 N � � ³ º � B µ � � + ³ n � º � º µ

b |[>/a.C~> )Fa.AD>.GX= ` = 7 < «eA¡=?| 9 1 �3 k 1 n 1 � 1,+,+�+ 1 B � Ä � ³ ���� �� =!|[C ` > M `�` C~a.A M =?>.Y¨=?CF=?|[>��H>.G~P>.; M =?CO; ` CO{°=?|[>�{­CH;�@ ) � � mH� $ � B µ M ;!>�a$|JC ` >7GiAcG ` j a$| M « M v�=!| M =

�7 <���� � ������ � � ��� = 7 < � 7 � < � ³ � ) ��� µ � �

� � 1 ³ n � º � k µ«e|[>7;!> A ` M G M ;!�JAD=?; M ;�v ;�> MON a.CHG ` = M GX= ��M G[Y =?|[> STC ` AD=!ADgH> AcGX=?>7�H>.; B � 5 ` M =!A `   > ` =?|J>AcGJ>.¬ jyMON AD=Rv 5 �� k ³ B � º µ�+ ³ n � º �H� µb |[>�@B>)=?;�Aca � «e|[C ` >/a7CHGX=?; M g M ;�A M GX=ea.CO@BS�CHG[>7Gz= ` M ;!>��HA¡gH>.G0�Xv

�9 9 � � ) ��� 1 ³ n � º � n µ�9 � ³ º � B µ � ) � 1 ³ n � º �XÄ µ�

� ³�� ) ��� µ � � ³ º � B µ � � 1 ³ n � º �H� µA ` S�C ` A¡=?ADgO>¯YJ>   G[A¡=?>¯>7gH>7;�vz«e|[>7;!>�S[;!CVg~AcYJ>.Y =!| M =^=!|[><S M ; M @F>7=!>.; ` � � � M GJY M ;�>¯S�C ` A¡=?A¡gH>O�b |[>�� MOj �O>�{ M a7=!CH;ZA `

1 � � 5 � ) ��� 7 9 � � � � � ³ º � B µ � � ? � $ + ³ n � º � � µ�¯>7G[a.>�=!|[> MON �H>.�J; M ADa¯>7Ac�H>7GJ{ j G[a)=?AcCOG ` M ;�> ` ¬ jyM ;�>�AcGX=?>7�H; M � N >e«eAD=!|�;!> ` ST>7a7=Z=!C(=?|[>�@F> M ` j ;�>� � � ) � � {­CH; N�M ;!�H>�>.GJC j �H|ig MONDj > ` CO{ =!|[>(S M ; M @F>7=!>.; � � b |[>"a j ;�g M = j ;!>/A ` G[>.� M =?A¡gH> M G[Ya.COG ` = M GX= �

� � N � � m + ³ n � º � l µb |[>�STCo=?>.GX=!A MON A ` �HA¡gH>.G¨�Xv

? � N ºk � � ³ º � B µ � ³ º � � µ�³�� ) ��� µ � ³�� ) ��� µ 9 � � � � � ³ º � B µ � + ³ n � º � ¸ µ

q AcGJa.>"=?|J>FS�CO=!>.GX=?A MON Y[C~> ` G[Co=�Y[>.S�>.GJYÀCHG�=!|[>,a.CH|[CO@BC N CH�Ov¨S M ; M @F>7=?>7; � =!|[> M ��C�gO>� M @BA N =?COG[A M G A ` >)� M a7= N v ` C N g M � N > ³ AcG0=?|[> ` >7G ` >"Co{ ;!>){­>.;�>.G[a7> � º}l � µ � s CO=!Aca7> � { j ;�=!|[>.;�@BCO;!> �� n

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=?| M =,=?|[>¨STCo=?>.GX=!A MON A ` MON ` CÀADG[Y[>.S�>.GJY[>.GX=BCO{�5~� " >0| M gH>-=!| j ` a7CHG ` =?; j a7=?>7Y M G >)� M a7= N v` C N g M � N > � M @BA N =!CHG[A M G M `!` C©a7A M =!>.Y =!C M G ADG   G[A¡=?>FG j @"��>.;"CO{ AcG[>7¬ j ADg MON >7GX="QLAc> MON �O>.�[; M ` � ��E� � =?|J>,Q±AD> MON �H>.�J; M `�` S M G[GJ>.Y �Xv ³ n � l � µ «eAD=!|/5 � B 1 B � º 1,+,+�+ ³ M G[Y 5 �� k ³ B � º µ!µ �b |[A ` j GJY[>.; ` a.CO;!> ` =?|[>�> `�` >7Gz=!A MON G[CHG j GJAc¬ j >.GJ> `!` CO{*=!|[>�a.CH;�;!> ` STCOG[Y[>.GJa.>"��>7=R«�>.>7G�>)� M a7= N vCH;Z¬ jyM ` A¡P¢>)� M a7= N v ` C N g M � N >�� M @BA N =!CHG[A M G ` M G[Y-|JAcY[Y[>7G ` v~@B@F>7=!;�v MON �H>.�J; M ` �q AcGJa.> =!|[>�@B>)=?;�AcaFAcG =?|JA ` ADG ` = M G[a7>�| M ` a7CHG ` = M GX=�G[>7� M =?A¡gH>�a j ;�g M = j ;!> � AD="Co{eAcGX=?>7;!> ` ==?CBS M `�` =?C M ` v ` =!>.@1CO{�a.C~CH;�Y[AcG M =?> ` AcG¨«e|[Aca$|i=!|[>(@F>7=!;!ADa M YJCHSJ= ` CHG[>/CO{�AD= ` «�> NDN uzG[CV«eGG[CH;�@ MoN {­CH;!@ ` � \�CO;Z>)� M @FS N > � AcG�=?|J>�a7C©CO;!Y[ADG M =?> ` v ` =?>7@ ³ � 1���µ Y[>   G[>.Y-�Xv

) � �� � � � 1 � � º

k� �

��Á³ º � B µ �H? � ? 9 ³ º N � � � µ 1

� � � � � � < N � � � ��� 1 m � � � � ³ n � º}nXm µ=?|J>�@F>7=!;!ADa ³ n � º � n µ ¹ ³ n � º �H� µ ��>.a7CH@B> `

��� � � � � � � �� + ³ n � º}n[º µb |[A ` A ` r CHAcGJa M ;~K> � ` { M @FC j ` | MoN {�PRS N�M G[>^@BC~Y[> N {­CO; M @ M G[AD{­C N Y�CO{¤a.CHG ` = M GX=�G[>.� M =?A¡gH>8a j ;�g M P= j ;!> N�� � d G-=?|[>"GJ>7« ³ � 1��"µ a.C~CH;!Y[ADG M =!> ` � =?|[>/� MOj �O>/{ M a)=?CH; M G[YS�CO=?>7GX=?A MoN*M ;�>(;�> ` S�>.a9P=?A¡gH> N v��OADgH>7G-�Xv

1 � � � � � 9 ���³ º � � � � µ � 1 ³ n � º}nzk µ

M G[Y ? � N k � � ³ º � � µL³ º � B µ �� � �³ º � � � � µ + ³ n � º}n � µ

��G[>¦a M G   G[Y � AcG M =!CO= MONDN v M G MON CH�HC j ` { M ` |[ADCHG �oM a$| M G[�H>^Co{[a.C~CH;�Y[AcG M =?> ` @ M S[S[ADG[�Z=?|[>¦@F>7=�P;!ADa¯«eA¡=?|�a.COGz=!; M g M ;!A M GX=Za.CO@BS�CHG[>7Gz= `�³ n � º � n µ ¹ ³ n � º �H� µ =?C"=!|[> ` = M G[Y M ;!Y0a.CHG ` = M Gz=eGJ>.� M =!ADgO>a j ;�g M = j ;!>,@B>)=?;�Aca � ? 9 ³ ��� � ` AcG[| � � 0 µ CHG =!|[>�=R«^C P ` |J>.>7=!>.Y |Xv~S�>.;!��C N CHAcY��,�8CV«^>)gH>.; �=?|J> {­CH;!@ jJN�M ` ADG"=?|[A ` a M ` > M ;!> M�N A¡=!= N >¦@BCH;�> a.CO@BS N Aca M =?>7Y � ` C�«�>Z«^CHG � =¦Y[A ` S NcM v�=?|J>.@ |[>7;!>o�r >7;!| M S ` =?|[>/@BC ` =�G M = j ; MON a7C©CO;!Y[ADG M =?> ` v ` =?>.@ {­CH;e=?|[A ` S�CO=?>7Gz=!A MON A ` =?|J>(CHG[>(Y[>   GJ>.YCHG�=?|J>�ADG   G[A¡=?> ` =?;!ADS ³ N�� F k 1���F k µ � A �Xv

) � � F � = M G ��1 � � � ��

�Á³ º � B µ ` >.a � � 9 �` ADG[| ³ B � º µ�� <N � k � � � � k 1 N � � � � � � + ³ n � º}nHn µ

b |[>�>)�©S[;�> `!` AcCHG¨CO{°=?|[>�@F>7=!;!Aca�ADG�=?|[> ³ ��1��©µ a7C©CO;!Y[ADG M =?> ` A ` =!|[>.G��� � � ? 9 ` >.a ��³ � � � � � µ�+ ³ n � º}n Ä µb |[A ` a7CHGJ{­CH;�@ MONDN v-´ M =�gH>.; ` ADCHG CO{ M a.CHG ` = M Gz=(G[>.� M =?A¡gH>Fa j ;�g M = j ;�> @F>7=?;�Aca,A ` �[;�Ac>7´JvÀYJA ` Pa j `!` >7YAcG�;�>7{­>7;!>.GJa.> � n � � d G¨=!|[>�G[>7«¾a.C~CH;!YJAcG M =!> ` � =?|[>�� MOj �H>�{ M a7=!CH;Z��>.a.CO@B> `

1 � a.C ` � � � 9 � � �i` >7a$| � ³ B � º µ�� ³ n � º}n � µ�XÄ

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M G[Y0=?|J>�S�CO=!>.GX=?A MON A `? � N ºk � � ³ º � � µL³ º � B µ a.C ` �` >7a$| ³ B � º µ�� + ³ n � º}nz� µ

b |[> q a$|[;}�CHY[ADG[�H>.;�>7¬ jyM =?ADCHG A `"` >7S M ; M � N >�ADG =?|J> ³ ��1��©µ a7C©CH;�Y[AcG M =?> ` v ` =!>.@¨� d GJY[>.>7Y �{­;!CO@ ³ n � º}n Ä µ AD= {­C NcN CV« ` =!| M =M � � a7C ` � J �

� � �� � � K 1 ³ n � º}nXl µ

M G[Y�=!|[>.;�>7{­CH;�>�=?|[> q a$|J;V�CHY[ADG[�H>7; >.¬ jyM =!AcCHG % 6O� L 6 A ` > M ` A N v ` >7>.G�=?C ` >.S M ; M =?>�ADGX=?C"=?|J>=R«�CBCHGJ>)PRYJAc@F>.G ` AcCHG MoN ��C j G[Y M ;�v�g MONDj >�S[;!CO� N >7@ `N ºk���� � ³ �Tµ N L � ` >7a � � ³ �Tµ � N�� � ³ �Tµ 1

��� $ ? � $ `

>7a � � � ³ �Tµ � � � � � ³ n � º}nX¸ µM G[Y

N ºk�� � � ³��µ Nºk � ³ � � º µ ` >.a$| � � ³��µ � � � ³��µ 1� ?? ?�� ³��µ � � � � � 1 ³ n � º Ä m µ

«e|[>7;!> � A ` =?|[> ` >7S M ; M =?ADCHG-a7CHG ` = M GX= M G[Y0«^>/| M gH> ` >7= � � ³ B � º µ�� � b |[>�STCo=?>.GX=!A MON ADG³ n � º Ä m µ A ` M ;�> ` =!;!ADa7=?>7Y r �C ` a$| N ¹ b > NDN >7;¦S�CO=!>.GX=?A MON < AcGFS M ;�=?ADa j[NcM ; � «e|J>.G �>��� A ` M STC ` AD=!ADgH>AcGX=!>.�H>7; «^>�CH�J= M AcG M � P ` C N AD=?COG�;!>7´[>.a7=!AcCHG N > `�` STCO=!>.GX=?A MON �\*AcG MONcN v � G[CO=?ADa.> =!| M = AcG =!|[> a.C~CH;!Y[ADG M =!> ` v ` =!>.@ ³ n � º}nOn µ =?|[> § MoN �H>7�[; M ADa ª ` ¬ jyM ;!>9PAcGX=!>.�H; M � N >�>7Ac�H>7GJ{ j G[a)=?AcCOG ` Co{'% Moj =?CH@ M =!Aca MoNcN v ` M =?A ` { v�=?|[>/G M = j ; MON ��C j G[Y M ;�v0a7CHG[Y[A¡=?AcCOGCO{eg M G[A ` |[ADG[��CHG =?|J>��TC j G[Y M ;�v � � � � ��F k � d G[Y[>.>7Y � ` AcGJa.>�=?|J>�@B>)=?;!ADa gHC Ncj @F> {­CH;�@�A `` AD@BS N v � ? 9 ` >.a � � � � � ` ¬ jyM ;!>�AcGX=?>7�H; M �[A N AD=RvFCO{ 6 ³ � 1 �Jµ AD@BS N Ac> ` =!| M =Z=?| M =

� � $ ? � $ `

>7a � � 6 � � � � � + ³ n � º Ä º µq ADG[a.> � �Xv ³ n � lHl µ � ³ n � º}n � µ ��M G[Y ³ n � º}nHn µ � =!|[> MoN �H>7�[; M ADa�>.AD�H>.GJ{ j G[a7=!AcCHG ` M ;�>/> M ` A N v ` >7>.Gi=!C��>�Co{®=!|[>�{­CH;!@ 6 ³ ��1��©µ � a.C ` ���®³ ��1��©µ ³ n � º Ä k µ«eAD=!| �®³ ��1��©µ*` @FC©Co=?| � ³ n � º Ä º µ AD@B@F>.YJA M =!> N v�v~Ac> N Y ` � � º F k �~M G[YB=?|[>7;!>7{­CO;!> 6 g M G[A ` |[> ` M =� ��� � F k �� � �0�&�&�&� � � %

� º ��·���: N | M `�` AcY � �J� ¼ G[�H> N �¤M G[Y��J� " j¤� : N �H>7�[; M ADa M S[S[;!C M a$|i=?CF=?|[> ` a M =!=!>.;!ADG[� @ M =!;!A¡� �� � � � � � -&H� � -. . � ��� ³ ºV¸Hlon µ � º��V¹JkOm �

�H�

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� k ��·��±: N | M `�` AcY � \^�®E��j ; ` >7v �®M G[Y \^� dtM a$|[> NcN C � E�;!C j SÀ=?|J>.CH;�v M S[S[;!C M a$|À=!C ` a M =!=!>.;�AcG[� �� ,/, � � � � � � � ��� ³ ºV¸Ol � µ � � n � ¹ � lHm �

� ����·��±: N | M `�` AcY � \^�®E��j ; ` >7v �®M G[Y \^� dtM a$|[> NcN C � E�;!C j SÀ=?|J>.CH;�v M S[S[;!C M a$|À=!C ` a M =!=!>.;�AcG[�[�d!d � b |J>/> j a N AcY[> M G0a.CHG[GJ>.a7=!AcCHG � � ,/, � � � � � � ����� ³ ºV¸Hl � µ � º}lJº)¹JkOmOm �

� n � s �ÃQ�� � MONcM I ` M G[Y�:(���]CH;!C ` � h^| M C ` CHG =!|[>�S ` > j Y[C ` S[|[>7;!> � � � � � � + � � ���� . � � � �³ ºV¸Ol � µ � ºVmH¸�¹©konXm �

� ÄH� K¼ � h^CO=�=?CHG � q j ; N > ` ADGXg M ;!A M Gz= ` Y[A¡£8K>7;!>7Gz=!Ac> N ` Y[>¬ j > N ¬ j > ` K>7¬ j[M =?ADCHG ` N AcG�K> M Ac;�> ` MOj �Y�K>.;�ADg�K>.> ` S M ;�=!Ac> NcN > ` Y j ` >7a.CHG[Y-CH;!YJ;!> � � ,/, �� + * � �� � � ��� ³ ºV¸HmOm µ � k~ºHº)¹JkonOn �� ����:(�TE�CHG[ILKMoN >.I ¹ Q�KCHS�>.I �Ts �Tw M @F; M G ��M GJY r � �J��� N gH>.; � QLAD> MON �H>.�J; M ` CO{]Y[A¡£¤>7;!>.GX=!A MON CHS©P>.; M =?CH; ` AcG�=R«�CBa7CH@BS N >)� g M ;!A M � N > ` � � � � � + (+,������ (+. � �c� =?C M S[S�> M ;7�� � ��:(�±E�CHG[I�KMON >7I ¹ Q�KCHS�>.I �±s �±w M @F; M G �LM G[Y r � �J�±� N gO>.; �®��jyM ` A¡P¢>)� M a7= N v ` C N g M � N >�QLAD> MON P�H>.�J; M ` CO{   ; ` =�CH;�Y[>.;¯Y[AD£T>.;�>.GX=?A MON CHST>7; M =!CH; ` AcGi=R«�C�a.CO@BS N >)�0g M ;�A M � N > ` ����� � � � � � �� � ³ º}¸H¸Jº µ � � ¸H¸ Ä ¹~nXmHmHl �� l ��:(�~E�CH; ` uXv � ½ > N�M =!AcCHG ` |[ADS��T>)=R«^>7>.G�>9� M a7= N v ` C N g M � N > M G[YF¬ j[M ` A�PR>)� M a)= N v ` C N g M � N >�gH>.;tP

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