Chapter 2 Complex analysis 2.1 Complex numbers and functions We ...

Report 5 Downloads 57 Views
   

       !#" $&%('*) +-,&" .'0/21435+&6 78,&+&9;:=?+&1 @A0BCA>DFEHGJIKEMLON-PRQFS#A0NTEUPVLOQXWREHY(ZX[\B]ZXY_^`DFWRQXaTGTb-LOQcY(QFS#dT[UAfegGhaiSjBCA>WRP>kmlmQXS?dT[UAfe G`aTSjB\A(WVPKInA(WVAoQXWREHDXEHG]ZX[U[UpcEUG`LRWRQhbTaTY>A(b-LOQcPRQF[MqFA0LONiArEUGTQhY(A(G8Ls[HQhQF^`EHGiDjA(t`a]ZuLREHQFG vxwzy|{~}€ ƒ‚ k {„ IKNTEUY_N…EUGJLONTA~WRA†Zu[HS!QX‡ˆWRA†Zu[‰G`aTSjB\A(WRP;NTZXP;GTQŠPRQX[HaiLREHQFGJB\A(Y(ZXaTPVArEML‹WVA(t`aTEHWVA(P;LONiA PRt`a]ZuWRAŒQX‡Z5G`aTSjB\A(WnLRQ5B\AŒZ5GiA(D8ZuLREUqXA*t`a]ZXG8LREULpFk2Ž;NTEUPn[UA(bgLRQoLRNTA~EUG`LRWRQhbTaTYfLOEHQXG QX‡ˆLONTAEUSgZXDXEHG]ZXWp#aTGTEULKEbiA>‘]GTA>b’ZXP E }”“ •r{~– E wm} •o{ ƒ‚ k ‚X„ IKNTEUY_N—PVQF[UqXA(b—LRNTAQFWREUDFEHGTZX[CdiWRQFBT[UA(SPVA(A>S?EUGTDF[Up?B8p-BTWRa˜LOA0‡™QFWRY>AXkšŽ;NTEHP;PVQF[Ha˜LOEHQXG NTQInA>qFA>W(›]N]Zub?‡œZXWšWRA(ZXY_NTEHGiDjEHS#dT[HEUY†ZuLREHQFGiP(kˆ]QFWnPL_ZXWLOA>WRP(›hLONTA~ZXB\QžqXA~A>thaTZuLOEUQFGgEUP Ÿ aTPL~ZŠPVdCA>Y(E Zu[Y†ZXPVArQu‡LRNTAPRA(Y>QFGTb˜¡¢QFWRbiA(WsdCQF[MphGTQFS#E ZX[\A(t`a]ZuLREHQFG £8vxwy¥¤Ovcy§¦;}¨ ƒ‚ kª© „ Ž;NTAraTPRaTZX[PRQF[UaiLOEUQFGTP‹Qu‡LRNTEHPKA(t`a]Z«LOEHQXG-‡™QXWK¬­  ZXWRA v} •~¤® ‚u£ “ ¬ ƒ‚ k°¯ „ BTaiL~LONTA>WRAcZXWVA5GTQ&±O²R³X´xPRQF[UaiLOEUQFGTPK‡™QFW0¬ µ  kŒ@¶EULRN·LONTA5aTPRAŠQX‡=LRNTAŠEHS?ZXDFEUG]ZXWp aTGTEML†›i‡™QXWK¬µ  LONTAPVQF[HaiLREHQFGiP‹BCA>Y(QFS#AX¸ ¹5} •~¤=® ‚XE»£ º ¼ ¬’¼ ƒ‚ k¾½ „ ©8½

©



 "!$#%!

¹@EHA—PZ'bTA>&)GT(+QX*LR,\A—´H².LO-0NiA·/213WR*'A(ZX4f[K²f±d]ZXIKWEULgLON5QXWR‡ŒA†ZZu[iY>d]QFZXS?WL di•*[HAfe§¤65X‚XG`£ aTS5ZuGTBCbŠA>W EHS?ZXB8DFpEUG]ZXWVpŒd]ZXWVL A:9® º Zu¼ GT¬’b ¼ 5FLO‚uNi£ A k EHS?ZXDFEUG]ZXWp5d]ZuWVLšB8p>= }@? S9 ¹+; k=Ž;N`aTP>›˜LONiAsEUG8LOWRQhbTaTYfLO¹ EUQFGcQX‡ vLRNT}8A*EU7SgZuDF¹<EH; G]ZuWVpoaTGTEUL S?ZXbTAŠPRaiWRAŠLON]Z«L0LONTAcPRA>Y(QFGib˜¡QFWVbTA(Wd\QF[UphGTQXS?EHZX[A>t`a]ZuLOEUQFG ZX[UImZ†phPrNTZXPAfeiZXY>LR[Up LInQ…PVQF[Ha˜LOEHQXGTP  Zu[HPRQgY†ZX[U[HA(Bb AVWRQhQXLO.P C „ k ? G&‡œZXY>L(›‰A>qXA(Wp&dCQX[UphGTQFS#E ZX[ A>thaTZuLOEUQFG&QX‡ bTA>DFWRA>AED £ Fuv F y¥£ F+G2H v FQ˜OA N#Y(EHA>G8LOP Q£ P+RTSj}¨ R({ R $‚ RVUWUVUXR DJN]ZXPzAfeiZXY>LR[U0p DJPRQX[HaiLREHQFGTPEU‡]InAKZX[H[UQI LONiA(SLRQ?B\A0Y(QFS#dT[UAfeG`aTS5BCA>WRP(k Y PREHDXGTEU‘]Y(ZXG8LrBTWRA(ZX^8LONTWVQFaTDFN EHG&InQFWR^`EHGiD…IKEMLON Y(QFS#dT[HA e&G`aTSjB\A(WVPrImZXPrEHG˜¡ LOWVQ˜biaTY(A>b&B`p—LONTA5WRA(diWRA(PVA(G8L_Z«LOEHQXG&QX‡2LONTAjY>QFS#dT[HA e·G`aTS5BCA>W ¹J} v?y ZE =-QFG’LONiA PRQ«¡Y†Zu[H[HA>b[AVY(QFS#dT[UAferdT[HZXGTAWCKIKEULRN5ZuBTPRY>EHPRPRZ ™vC„ ZX[UQFGTDKLONTAšWRA(ZX[hZ«e˜EHP  NTQFWVEZ\>QFG8L_ZX[ „ › ZXGTb…QFWVbTEHG]Z«LOA  = „ ZX[UQFGTDŠLONiArEUSgZuDFEHG]ZuWVp?Z«e˜EHP  qXA(WLOEHY(ZX[ „ k=Ž;NTEHPKEUP;EH[H[UaTPVLRWOZuLRA(bEUG zEUDTk ‚ k { k imaginary axis

x

z

r θ 0

x = r cos(θ) y = r sin( θ)

y real axis

rszhQEUt{DFaTp3WR^_Ansu|‚ p3k { ^}eJ¸ j:nJ]T~:^_f_^_j`3acbcbcn)d%d%eVtobgfia"hQjkhJl€hJfilbgabgm:dgnonXeJdg^‚n)ƒp3dgeJnXjLacnX„…jW*ZuGTb-EULOP;Y>QFG Ÿ aTDFZuLOAN]Z†qFArA(t`a]Zu[SgZXDXGTEULRaTbTAX›iDFEUqXA(G…B`p ¼ ¹ ¼ } “ o¹ I ¹5} º v w y = w ƒ‚ k „ @ A;A eiZXS?EUGTA;GTA e˜L=LRNTA‹‡™QFWVS LONTZuL=bTE A>WRA(G8L2QFd\A(WRZuLOEUQFGTPzIKEMLONŠY>QFS?di[HAfejG`aTSc¡ B\A(WRP‹LOZX^XAu¸2Ž;NTA0dTWRQhbTaTYfLKZXGTbLRNTAŒt`aTQXLREHA(G8LKQX‡LInQcY(QFS#dT[UAfegGhaiSjBCA>WRP EUG LOA>WRS#P‹QX‡LRNTA(EUWmWRA(ZX[‰ZuGTbEHS?ZXDFEUG]ZXWVpjY(QFS#dCQXGTA(G8LOP>› P‹ZŠSgZudTdTEHGiD#Qu‡LRNTA ¹ ¡dT[HZXGTAŒLRQcLRNTA ¡¢dT[ ZXGiAX›]ZjLOQXdTEHYŒInA bTEUPRY(aiPRPsEHG-DFWRA(ZuLKbTAfL_ZXEU[‰EHG-PRA>Y>LREHQFG ‚ k°©ik @ AcIKEH[U[zY>QFGTPREUbTA(WPVA>qFA>WOZX[šEHPVPRaTA>PoWVA([HZuLOA>b LRQLONTA#BCA>N]Z†qhEHQFW0QX‡n‡™aTGTYfLOEHQXGTP0QX‡ Y(QXS?dT[UAfecquZXWVE ZXBT[UA(P>›`ZXPšInAŒbTEUb#‡™QXWš‡™aTGiY>LOEUQFGTPšQX‡‰WVA†ZX[]quZXWVE ZXBT[UA(P>kzŽ;NTAs‘]WRPL‹EHP2LONiA EHPVPRaTAKQX‡ Y(QFG8LREHG`aiLOEMLpFkˆ@ AsbTA>‘TGTA*Y>QFG8LOEUGhaiEULpŠQX‡ ZŒ‡™aTGTYfLOEHQXG  QX‡\LONTAKY(QXS?dT[UAfe quZXWREHZXBT[UA ¹ ZuPc‡™QX[H[HQIKP>¸JLONTA‡™aTGTYfLOEUQFG EHPŠY(QXG`LREHG`aTQFaiP?EM‡s‡™QXW?œZu¹8G`„ p   ›šLRNTA(WVA Afe˜EUPVLOP  PVaTY_N—LRN]ZuL ¼ ¹0• V¹ K ¼`µ  – ¼  œ¹8„z•  œV¹ Kf„ ¼`µ »‚ k ‚ „ EHGrY([UQFPRAnZXG]Zu[HQFDXp*LOQsIKN]ZuLˆI‹ZXPˆbTQFGiAn‡™QFWˆZ;‡™aTGTY>LREHQFGrQX‡xZKWRA(ZX[8quZXWREHZXBT[HA=EUGoY_NTZXdiLOA>W kŽ;NiA*A>PRPRA>GTY(A~QX‡ LRNTEHP2Y(QXGTbTEULREHQFGcEUPšEU[H[UaTPVLRWOZuLRA(bcEHG?zEHDik k°©ik sPRa]Zu[H[UpX›FImA*SjaTPL L_{ Zu^XA jPRS?ZX[H[UA(WšIKNTA(G…ImAL_ZX^uA sPVSgZX[U[HA>W(›iBiaiL;LONTEUPKEHP;GTQX‚LsZu[UImZphPKGTA>Y(A(PVPOZXWpFk Y PsZXG…AfeiZXS#dT[HAu›TY(QXGTPREUbTA(W;LONiA‡™aiGTY>LREHQFG |}  œ¹8„2}¨¹Xw G Kµ  InA~NTZqXA~LOQoPRNTQI ? GJQFWVbTA(W2LOQoPRNTQI¶LONTZuLmEMLšEHPšY(QFG8LOEUG`aTQFaTP>›˜‡™QFWnZXG8p#DFEUqXA( LONTZuLIKNTA(G|¼ ¹Š• ¹VK ¼ µ h› LONTA>GInA?Y(ZXG SgZXGTZXDFAŠLOQ…SgZu^XA&¼ €• K ¼ µ >k?@A SjaTPLK‘]GTb—ZŠImZ†pLOQcWRA>[ ZuLRA *ZuGTb `k 0EUqFA>G…LRN]ZuLм ¹• V¹ K ¼`µ h›iInAIKEH[H[CN]Z†qFAu¸ ¼ • K ¼ } ¼ ¹Xwn• ¹XKw ¼ } ¼ œ¹• ¹VK_„(ƒ¹*y¥¹VKf„ ¼`µ ]¼ ¹sy¥¹VK ¼ } ]¼ œ¹0• ¹VKf„y ‚X¹VK ¼ *PVEHGTDŠLRNTA0LOWREHZXGTDF[UAŒEHGiA(t`a]ZX[UEULpF›hImArQFBiLOZXEHGJ‡™WVQFSLRNTA[ ZXPLKWRA([HZuLOEUQFG‰¸ ¼ • K ¼ $9 ¼ ¹r• V¹ K ¼ y ¼ ‚XV¹ K ¼ ; $9 y¥‚ ¼ V¹ K ¼ ;

 

… #g   #W   #O #W  { 

#3 #

!

¯8©

‡zInA0L_ZX^uA0LONTAWRA>[ ZuLREHQFGB\A>LInA(A>GjZXGib ;LOQcB\A } $9 y ‚ ¼ V¹ K ¼ ;C–  w y ‚ ¼ V¹ K ¼  • }¨r–  } º ¼ ¹VK ¼ w y • ¼ ¹VK ¼   A(IKt`a]NiZ«A(LOWREHAQXG InA-EHG N] Z†qF› A-LONTY_NTA>QFGPVA(LOGNiA?LONT[HZXAPVLrd\AfQFe˜PREMdTLOWVEMqFA(PVAJPREHWVQXQ˜G QXLjPRNTQXQ‡*IKLRP5NTALRN]PRZuA>LrY(QFGTGiQ—b˜¡SgQFWVZubTLVA(LOWcA>Wrd\NiQFQž[UphI GTQXPRS?S?ZXEHZX[H[[ „ JEHP>›‹ImA·Y†ZXG¶ZX[MI‹Z†phPg‘]Gib ZquZX[HaiA—‡™QFW    LON]ZuLgPOZuLREHP‘]A(PgLRNTA’Y>QFG8LOGTEUaTEULp Y(QXGTbTEULREHQFG 2› ™=t\k »‚ k ‚ „ kšxWVQFS LRNTEHPKA eidiWRA(PVPREUQFG‰›\EULKEHPKZu[HPRQcA>bTEUqXA(G8L~LRN]ZuL;IKNTA>G DFAfLOP~PVSgZu[H[HA>W‹ImAoSjaTPL~L_Zu^XAjZ#Y(QFWVWRA>PRd\QFGTbTEUGTDF[Up-PVSgZu[H[HA>W h›CZ?PVEULRa]ZuLOEUQFGLON]Z«L~EUP Y(QXS?S#QFGBTaiLsEUP;GTQXL*ZX[UImZ†phPsGiA(Y(A>PRPRZXWVpXk Ž;NTAGTA e˜LcEUPRPVaTAEHPrLONTAbTAf‘]GTEMLOEHQXG QX‡KLONiAJbTA(WVEUquZuLREUqFAuk np ZuG]ZX[HQXDXp LOQ’LONiA Y†ZuPRAJQX‡;‡™aiGTY>LREHQFGTP5QX‡KWRA(ZX[nquZXWVE ZXBT[UA(P>›InAJbTA>‘TGTAJLONTAgbTA(WVEUquZuLOEMqFA?QX‡sZ—‡™aTGTYfLOEUQFG  œ¹8„ QX‡ZŠY>QFS?di[HAfegquZXWREHZXBT[HAŒZXP(¸  œ¹8„z•  ƒV¹ K_„  ƒV¹ Kzy ¬ ¹8„•  œV¹ K „ U [ H E S  œV¹ K „2} [HEHS } »‚ k ‚ „ ¬¹   K   ¹• ¹VK ? G QXWRbTA>Wo‡™QFW0LONiAgbTA>WREUquZuLREUqXA   ƒ¹8„ LOQ—SgZu^XA#PRA(GiPRAX›LRNTAg[UEHS#EUL~SjaTPVLoAfe˜EUPVLŠZuGTb SjaTPL‹B\A~EUGTbTA(d\A(GibTA(G8L;QX‡ NiQžI|¬ ¹|—  ›`LONTZuL‹EUP(›hEHGTbTA>dCA>GTbTA>G`L‹QX‡LONTA*bTEHWVA(YfLOEHQXG EHG§IKNTEHY_N§LONTA—dCQXEHG8L V¹ K QFG¥LRNTA·Y>QFS?di[HAfe§di[ ZXGTA…EHPcB\A(EUGTD ZXdidTWRQ8ZuY_NTA(b‰k|Ž;NTEUP ZXPVdCA>Y>L#bTEHb GiQXLŠAfe˜EUPVLcEHG LRNTA-Y†ZXPVAQX‡sLONTAbTA>WREMqXZ«LOEUqXAJQX‡*Z’‡™aTGTYfLOEHQXG QX‡*Z WVA†ZX[ quZXWREHZXBT[UAX›iPVEHGTY>ArLRNTAdCQXEHG8L ‚v K QFG-LONiAoWVA†ZX[ Z«e˜EUP;Y†ZXG—QFGT[UpgBCArZXdidTWRQ8ZuY_NTA(b·ZX[HQFGiD QXLRNTA(WKWRA(ZX[ quZX[UaTA(PKQFGLONiAoZžeiEUP(k ŽQ-bTA>S?QXGTPVLRWOZuLRA5LONTAŠEUS?d\QFWL_ZXGTY>AoQu‡šLRNTEHPŒZXPRd\A(YfL†›‰InAŠY(QFGTPVEHbTA>WZgY(QXaTG8LOA(W ¡ AfeiZXS#dT[UAX›uLRN]ZuLEHP>›FZs‡™aiGTY>LREHQFGr‡™QFWIKNTEHY_N5LRNTAmbiA(WREMquZuLOEMqFAšEHPˆGTQXLdTWRQFd\A(WV[UpbTAf‘]GTA>b‰k Ž;NTEUPK‡™aiGTY>LREHQFG-EHP‹LRNTAY(QFS#dT[UAfeY>QFG Ÿ aTDFZuLOAu¸ |}  œ¹8„2} ¹ ]WRQFS!LONTAbTA>EU‡™GTEMLOEUQFGJQX‡ˆLONTAbTA>WREMqXZ«LOEUqXA0ImAN]Z†qFAu¸ ¬ vg• E …¬ =   ƒV¹ Kf„2} [HEUS  ¹ Ky ¬ ¹`„z• ¹ K } H [ U E S ¬¹   K   K    K ¬ vjy EH>¬ = ? ‡zInAY_NTQhQFPRALONTArZXdidTWRQ8ZuY_N·ZX[UQFGTDjLRNTA[HEHGiAŒbTA>LRA(WVS?EUGTA(b-B8p = } = Kz y 2™v?• ‚v Kf„2– ¬…¬ v= } LONiA(G-LONTAbTA>WREUquZuLREUqXAŒIKEH[H[CL_ZX^uALRNTA0‡™QFWRS E E   ƒV¹ K „2} {s• } {K• „ w {ny E {my w ?





¯F¯ 

 "!$#%! ;Ž NTEUPŒ[ ZXPL~A e˜dTWRA>PRPREUQFG QFB8qhEHQFaTPV[Up—bTA(d\A(GibTP0QFG·LRNTAjd]ZuLRN&QX‡šZXdTdiWRQ8ZXY_N ¬ ¹k—  › LONTZuL5EUP(›ˆLONTA#qXZu[HaTAcQX‡‹LRNTAgPV[HQFd\A#QX‡‹LONiA?[UEHGTA ›ˆLONTA>WRA>‡™QXWRAŽ ]²šh²f± «³‰Ž  X²v( ¹ 3(² o/ (+Ž;.² -  OŽƒk Ž;NTAdCQXPRPREUBT[HA0biA(d\A(GTbTA>GTY(AoQX‡ LONTAWRZuLOEUQc¬  ¬ QFGLRNTArZXdTdTWVQ8ZXY_NLOQ EHG8LRWRQhbTaTY(A>PcZXGTQXLRNTA(W5GTQXLOEUQFG‰›LRN]ZuLŠQX‡5‰³ /\³X´ +Ž  & ƒŽ ¹8«.„k 5 Y ¹ ‡™aiGTY>LREHQFG  œ¹8„ EUPjY†ZX[U[HA>¹Vb K ³‰/\³X´ +Ž  &mEHGLONiArbiQFSgZuEHG QX‡ˆLONTA v =8¡dT[HZXGTAŒEM‡ ¸  œ¹8„ EHP;bTAf‘]GTA>b·EHG ·›˜LON]ZuLKEUP(›]EML;EHP;PVEHGTDF[UAf¡»qXZu[HaTA>€b œTZXGib  EUP~bTE A>WRA>G`LRE ZXBi[HArEHG —›CLONTZuLŒEUP(›xLONTAjbiA(WREMquZuLOEMqFA   œ¹8„ Afe˜EUPVLOPŒZXGTb’EUP ‘]Giœ¹8EULO„ Auk b / (+/ ‰³ /\³X´ PRA Y(QXGTbTEULREHQFGiPJZXWVA’GTQXL-S#A>L(›KLRNTA’‡™aTGTYfLOEUQFG EHPgY†ZX[U[HA( ‡™aTGTYfLOEUQFG¶Y†ZXG|BCA GTQFGh¡ ZXG]Zu[Up`LOEUY’EHG|ZXG|A(G8LOEUWRA bTQFS?ZXEUG QFW-ZuL…EHPVQF[ ZuLRA(b d\QFEHG8LRP QFG§LONTA ¹ dT[HZXGTAXk Ž;NiA·d\QFEHG8LOPcIKNTA>WRA’Z ‡™aTGTYfLOEHQXG EHP#GTQFGh¡ ZXG]Zu[Up`LOEUY-ZXWRA…Y†ZX[U[HA>b  / ‰1h´M³X±  Ž»² fk Ž;NTA(WVAŒZXWVA*EUS?d\QFWL_ZXG8L=Y>QFGTPRA>t`aTA(GTY>A(P;QX‡CLONTA*ZXG]Zu[Up`LOEUY(EULp5QX‡Z‡™aTGTYfLOEHQXG  œ¹8„ ¸   ƒ¹8„ EHP;Y>QFG8LOEUGhaiQFaTP  LONiEHP;EHP;^`GTQIKG·ZXP;LONTAolmQFaTWVPOZuLKLRNTA(QFWVA(S „ œ]ZuGTb  œ¹8„ N]ZXPKY(QFG8LREHG`aTQFaTPKbTA>WREMqXZ«LOEUqXA(PKQX‡zZX[H[CQFWRbiA(WRP>k @ ADFEMqFArZj‡™A>I¨AfeiZXS#dT[HA>PsQu‡ZXGTZX[Up`LOEUY0ZXGTb…GTQFGh¡ ZXG]Zu[Up`LOEUY~‡™aTGTYfLOEHQXGTP(¸ Ž;NTAc‡™aTGTYfLOEHQXG  œ¹8„0} ¹ F › IKNTA(WVƒA D EUPoZ-d\QFPREMLOEUqXAŠEHG8LOA>DFA(W>› EHPrZXG]ZX[Mp`LOEHYcZuGTbPVQ ZXWVAJZX[U[šPVEHS#dT[HAc‡™aTGTYfLOEUQFGTP5Y>QFG8L_ZXEUGTEHGiD—EML†›zA e˜Y(A(d˜LcEU‡;EML5EUP5EHG LONTA?bTA(GiQFS?EUG]ZuLRQFW(F › B\A(Y†ZuaTPRA~LRNTA(GgEULnY†ZXGgquZXGiEHPRN?‡™QFW ¹o}¨ Y†ZXaTPVEHGTD5dTWRQFBi[HA(S#WP œhEHG#‡œZXY>L  œ¹8„2} Q{ 5X¹ EHPKZuG]ZX[Up`LREHYŒAfqFA(Wp`IKNTA(WVAjAfe˜Y(A>diLs‡™QFW ¹j}| ›TIKNTEHY_N…EHPKZŠPVEHGTDFai[ ZXWVEULpFk Ž;NTA…‡™aTGTY>LREHQFG  EHP?ZGiQFG˜¡ ZuG]ZX[Up`LREHY‡™aTGTYfLOEHQXG ZXGib PRQ ZXWRA—ZX[H[;PVEHS#dT[HA ‡™aTGTYfLOEUQFGTP;Y(QXG`LOZXEHƒGi¹FEH„…GTDŠ} EML†¹k=]QFW‹EUGTPVLOZXGTY>AX›TLONiAŒ‡™aTGTY>LREHQFG  ƒ¹8„2}7 :A 9 ¹LREHQFG ›TBCA>Y†ZXaiPRAX¸  œ¹8„2}7 :A 9 ¹WRAf‡™QFWRA  œ¹8„ EHP=GTQuLšZXG]ZX[MphLREHYukˆ@¶N]Z«L2bTQ˜A>P EUL‹S?A(ZXGJLOQŠN]Z†qXAoZj‡™aTGiY>LOEUQFG[HEU^XA 7 :A 9 ¹PRPREUQFG…Y(A(WL_ZXEUGT[Up#[UA†ZXbTP‹LRQcZ S?ZXdTdTEUGTDT›iPVEHGTY>A  ƒ¹8„2 } €} z v R = „‰y E   v R = „–  v R = „z}|v R  ™v R = „=}€ BTaiLmLONTEUP‹SgZudTdTEHGiD5EHPmGTQXLKZo‡™aiGTY>LREHQFGEUGgLONTA~aTPRa]Zu[‰PRA>GTPRAu›TLON]ZuL‹EHP(›˜EULmY†ZXGTGiQXL;B\A bTE A>WRA(G8LRE ZuLRA(b‰›TAfLOYuk JEUL‹EHPKZcGTQFG˜¡ZXG]ZX[MphLREHYs‡™aTGTY>LREHQFG k ]QFWKZXG-ZXG]Zu[Up`LOEUY~‡™aTGTYfLOEHQXG  = E  = ›hLRNTAAfe˜EHPLOA(GiY(AQX‡ LONiA#biA(WREMquZuLOEMqFAj[UA†ZXbTPŒLRQLONTAЇ™QF[Uƒ[HQ¹8IK„2EH} GTD? |WRA>} [ ZuzLREH QFv GTR P~„CBCy AfLImA>™A(v GR LR„ NTAcd]ZXWLOE Zu[zbTA>WREUquZ«¡ LOEMqFA>PsQu‡LRNTAWRA†Zu[ ZXGTb…EHS?ZXDFEHGTZXWVp#d]ZXWLOP>¸  }v = R = }”• v »‚ k ‚ „ 































































`¯ ½ Ž;NTA>PRA#ZXWRAŠY(ZX[H[UA(b’LRNTA2³‰1‚&  »²O*#³‰/2/ ±O²f´M³‰Ž  (+/ fkoŽQdiWRQqFAŠLONiEHPŒPL_ZuLRA(S#A(G8L InAŠWRA([Mp…QFG’LONTA5bTA>‘]GiEULOEUQFG’QX‡=LRNTAŠbTA>WREUquZuLREUqXAX›CIKNiEHY_N’‡™QFW~ZXG ZXG]ZX[Mp`LOEHY‡™aTGTYfLOEUQFG SjaTPLsAfe˜EHPL†¸ ¬   œ¹8„2} [UEHS »‚ k ‚ „   K ¬ ¹ Ž;NTEUGT^`EHGTD QX‡  ƒ¹F„ EUG LOA(WVS?PQu‡jEULRPWRA(ZX[0ZXGTb|EHS?ZXDFEUG]ZXWp¥dTZXWVLRP(› ™v R = „ ZuGTb  ™v R = „ WVA(PRd\A(YfLOEMqFA([MpF›TIKNTEUY_N…ZXWRA0B\QXLONJ‡™aiGTY>LREHQFGTP;Qu‡ v ZXGTbq=\›˜InArY(ZXGIKWREMLOAŒLONiA bTE A>WRA(G8LRE ZX[]QX‡  ƒ¹F„ EUG#LRA(WRS#PšQX‡ LRNTA*dTZXWVLRE ZX[TbiA(WREMquZuLOEMqFA(P2IKEULRN?WVA(PVdCA>Y>LmLRQ v ZuGTb =\¸ ¬  } v ¬ vŠy = ¬…= } v y E v ¬ vcy = y E = …¬ = } v y E v ¬ vŠy • E = y = E …¬ = }  ¬ vcy   E …¬ = IKNTA>WRAŠLONTAŠ[HZXPVL~A(t`a]ZuLREHQFG PVA(WVqXA(PrZXPŒLRNTAŠbTA>‘TGTEULREHQFG’Qu‡  ZXGTb   k@¶EULON’LRNTA(PVA bTAf‘]GTEULREHQFGiP‹LONTAbTA>WREUquZuLREUqXAŒL_ZX^uA(PKLONTA0‡™QFWVS ¬=   ƒ¹VK_„š} [UEHS ¬ vŠy E   5   „ …     K ¬ vcy EH¬…= Ž;NTA*bTA(WVEUquZuLOEMqFAsSjaTPL‹B\A~EHGibTA(d\A(GTbiA(G8L‹QX‡LRNTA*ZXdTdTWVQ8ZXY_NJQX‡¬ v R >¬ = —  IKNiEHY_N Y†ZuG—QFGi[UpJB\ArZXY_NTEUA>qFA>b—‡™QFW  }   ›]QFW>¸  y E  } • E  y  = = v v ™=t`a]ZuLOEUGTDoLRNTA~WVA†ZX[CZXGTbgEHS?ZXDFEHGTZXWVp5d]ZXWVLRPmQX‡  ZuGTb  InAŒQFBiLOZXEHGcLONiA0l‹ZXaTY_N8p8¡ › ™2txk ƒ‚ k ‚ „ ksŽZX^`EHGTDJY>WRQFPVP¡¢bTA(WVEUqu ZuLOEMqFA>P~QX‡=LRNTA(PVAjWRA>[ ZuLREHQFGTP 7 EHA(S?ZXGTG—WRA>[ ZuLREHQFGTP> ZXGTb—ZXbTbiEHGTDjLRNTA(SdTWVQ˜biaTY(A>P*ZuGTQXLONiA(WKPRAfL*Qu‡zWVA([ Z«LOEHQXGTP(¸ w  = } w=  R w  = } • w  – w  y w=  }€ v v w v w w w v  w  } w = R w=  } • w = – w  y w=  }€ ° k © »  ‚ 8„ vw v v v w w w ]aTGTYfLOEHQXGTPˆLRN]ZuLˆPOZ«LOEHP‡ p0LONTEUPY>QFGTbTEMLOEUQFG‰›žY†ZX[U[HA>b  ZXdT[HZXY(A  PˆA(t`a]Z«LOEHQXG‰›XZuWRAšWRA>‡™A>WRWVA(b LOQ#ZXP i³XX± *k(+/  &fk Ž;NTA5NTZXWRS#QFGTEUYŒ‡™aTGTY>LREHQFGiP~ZXdidCA(ZXWs‡™WVA(t`aTA>G`LR[Up-EUG—A>thaTZuLOEUQFGTPsWRA([HZuLOA>b—LRQ?PVA>q8¡ A(WRZX[=dTN8phPREUY†ZX[šdTNTA>GTQFS#A(G]Zi›ˆPRaiY_N ZXPrA([UA(Y>LRWRQFPL_ZuLREHYj‘]A>[HbTPrdTWVQ˜bTaiY(A(bB8p A([HA>Y>LRWREM¡ Y†Zu[ Y_N]ZXWVDFA(P>›TLONTA*LOA(S#d\A(WOZ«LOaTWVA~‘]A([UbEHGZuGEHPRQuLOWRQXdTEHYKLONTA>WRS?ZX[ Y>QFGTbTaiY>LOQXW‹aTGTbTA>W PVLRA†ZXb˜p0NTA†Z«L TQžI›žLONiAšdiWRA(PVPRaTWVAš‘TA([Hb0‡™QFWEUGTY(QXS?dTWVA(PVPREHBi[HA[UEHt`aTEHb ]QI EHGrZ;d\QFWRQFaiP S#A(bTEUaTS—k Ž;NTA5lma]ZXY_N8p8¡ 7 EHA(S?ZXGTG…WRA>[ ZuLREHQFGiP‹N]Z†qFArY(A>WVL_ZuEHG-EHS#dCQXWVL_ZuG`LmEHS#dT[HEUY†ZuLREHQFGiP(¸  

… #g   #W   #O #W  { 

#3 #

!  































































































































































¯:



 "!$#%!

LRNTA ™v R = „XR  ™v R = „ ‡™aTGTYfLOEHQXGTP  QX‡ LOA>G Y†ZX[U[HA>b‘]A>[HbTP „ ZXWVAgbTAfLOA(WVS?EUGTA(b B`p LRNTABCQFaiGTb]ZXWpJquZX[HaTA>PWœ EM‡‹QFGTA#‘]A([Ub EHPr^`GTQIKG‰›LONiAgY(QXG Ÿ aTD8ZuLRA#‘TA([Hb  ‡™WRQXS &QFW ’‡™WVQFS C„ EUP bTAfLOA>WRS#EHGTA>b…aid…LRQ?ZcY(QXGTPVLOZXG8L*Qu‡zEUG`LRA(DFWRZuLOEUQFG€œ ZŠY(QXS?dT[UAfeZXG]ZX[MphLREHY~‡™aiGTY>LREHQFG…EHP;bTAfLOA>WRS#EHGTA>b…B8pLRNTABCQFaiGTb]ZXWpJquZX[HaTA>PWœ ZXG8pc[UEHGTA(ZXW2Y(QFSjBiEHG]ZuLREHQFGŠQu‡‰LONTAKLInQo‘]A>[HbTP ™v R = O„ R   v R = „ QX‡ ZXG?ZXG]ZX[Mp`LOEHY ‡™aTGiY>LOEUQFG·EUP~Z#N]ZXWVS?QFGiEHY‡™aTGTY>LREHQFG  B\A(Y(ZXaTPRAoEUL*Y(QFWVWRA>PRd\QFGTbTP~LRQgSjai[ULOEUdT[HE ¡ Y(ZuLOEUQFG-QX‡LRNTAQFWREUDFEHGTZX[\‡™aiGTY>LREHQFG  œ¹8„ B`pZ#Y>QFS?di[HAfeJG`aTSjB\A(W „ k ]WRQFS LRNTA(PVA InA Y†ZXG€ZX[UPRQ bTA(WVEUqXA LRNTA&‡™QF[H[UQžIKEUGTD DFA>GTA(WRZX[0PVLOZuLOA>S?A>G8LOP(k ? ‡  H(œ¹8O„ R  œ¹8„ ZXWRALInQ~ZuG]ZX[Up`LREHYz‡™aTGiY>LOEUQFGTPEUGZKbiQFSgZuEHG ·›LRNTA(GrPRQKEHP‰LRNTA‡™aTGTYfLOEUQFG  œ¹8„ DFEUqXw A(G…B`p\¸  ƒ¹8„ }  H>ƒ¹F„ˆy  œ¹8„  ƒ¹8„ }  H>ƒ¹F„  œ¹8w „ { R w Afe˜Y(A>diLšIKNTA(WVA  ƒ¹8„2}¨  } { R_‚F„  ƒ¹8„ } œ¹8„  ƒ¹8„ }  H>  ƒ¹8„V„ w EHGLONiAnPRZXS?AšbTQFS?ZXEUG —k nprZXGTZX[HQFDupŒLOQKLONTAnY†ZXPVAnQu‡T‡™aTGTYfLOEHQXGTPQu‡TWRA(ZX[8quZXWREHZXBT[HA>P(› LONiA‡™QX[H[HQIKEUGTDjWRai[HA(PKZu[HPRQ#ZXdidT[Up?LOQcLONTAbTE A>WRA(G8LRE ZuLREHQFGJQu‡ZXGTZX[Up`LOEUYŒ‡™aTGTYfLOEHQXGTP(¸ b  ƒ¹F„š} b  H>ƒ¹8„  œ¹8„ y  H(œ¹8„ b  ƒ¹F„  œ¹8„2}  H(œ¹8„  ƒ¹8„ – b¹ b¹ b¹ w w w b  ƒ¹F„š} b  H>  ƒ¹8„V„ b  ƒ¹F„  œ¹8„2}  Hf  œ¹8„R„ – b¹ bw w b¹ w w zEHGTZX[H[MpF›˜ZXG—EUS?d\QFWL_ZXG8L‹EUS?di[HEHY(ZuLOEUQFGgQu‡LRNTAol‹ZXaTY_N8p8¡ 7 EHA(S?ZXGTG…WRA>[ ZuLREHQFGiP‹EHP  »‚ k°© {ž„ ¹ }¨ G§QFWRbTA>WŠLOQ dTWRQqFA-LONiEHP(›2InA—B\A(DFEUG B`p A e˜dTWRA>PRPREUGTDLRNTA-qXZuWRE ZuBT[HA>P v ZXGTb = EUG LO? A>WRS#PKQX‡ ¹ ZXGTb ¹ ¸ v-} ‚{ ƒ¹*y ¹`X„ R = } ‚ { E œ¹r• ¹F„ ‡™WRQXS IKNTEUY_N…InAoQXBiL_ZXEUG‡™QFW‹LONTAd]ZuWVLOEHZX[ biA(WREMquZuLOEMqFA(P‹IKEMLON…WRA>PRd\A(Y>LsLOQ v ZXGTqb =C¸ }v v¹ ¹ y v¹ ¹ } ¹ y ¹





















!



































!







¯

… #g   #W   #O #W  { 

#3 #

!

 



¹ ¹ E • E = } = ¹ y = ¹ } ¹ ¹ *PVEHGTDŠLRNTA(PVAoA eidiWRA(PVPREUQFGTPsEHGLONTAol‹ZXaiY_N`p8¡ 7 EUA(S?ZXGTG…WRA([HZuLOEUQFGTPmInA‘]GTb‰¸  }v = – ¹ y ¹ } E ¹ • E ¹  }= • v – E ¹ • E ¹ } • ¹ • ¹ – E ¹ y E ¹ } ¹ • ¹ Y bibTEHGTDŠLRNTA0LImQ#A(t`a]ZuLREHQFGiPsQXG…LRNTA0‡œZXW;WREUDFN8L;QX‡zLRNTArZXB\QžqXA[HEHGiA(P‹InArDXA>L†¸ ¹  Šy E  „‰y ¹  Šy E  „} ¹  jy E  „• ¹  Šy E  „ IKNTEUY_N—PVEHS#dT[HEM‘]A(PmLRQŠLONTA0‡™QF[U[HQIKEHGTD5WRA(PVaT[UL(¸  }¹ • ¹ – ¹ }| ZXPobTA(PVEHWRA>b‰k Y Y>QFGTPRA>t`A(aTGTY>A-QX‡‹LONiEHPrWRA(PVaT[UL5EHPLON]Z«LjZ—‡™aiGTY>LREHQFG LON]ZuLoY(QXG`LOZXEHGiP Afe˜dT[UEHY>EULO[Mp ¹ Y†ZuGTGTQXLsB\AoZuG]ZX[Up`LREHYX›iZj‡œZXY>LKInArNTZqXA5Zu[HWRA(ZXbipgS?A>G`LREHQFGiA(b‰k ŽQoEH[U[HaTPLOWOZ«LOA‹NTQI LRNTA(PVA*Y>QFGTY>A(diLRPnInQFWR^x›`ImA*Y(QFGTPVEHbTA>W=LONTAK‡™QF[H[UQIKEHGTDŒPVEHS#dT[HA AfeiZXS#dT[UAX¸=DFEMqFA(G-LONiA‘TA([Hb  v R = „z} Y(QFP ™vC„ A G  InA·ImQXaT[Hb¥[HEH^uA…LRQ ^`GTQIIKN8LONTA>WJQFW#GTQXLgEUL#EHP#N]ZXWVS?QFGiEHYX›mZXGTb EM‡ŒEMLgEUP(›mIKN]Z«L EHP#Y(QXG Ÿ aTD8ZuLRA…‘TA([Hb  ™v R = „ ZXGTb¥IKNTZuLgEUP?Y>QFS#dT[HA e§ZXG]ZX[Mp`LOEHY‡™aTGiY>LOEUQFG  ƒ¹8„} ™v R = „2y E  ™v R = „ ŽQZXGTPImA>W?LRNTA…‘TWRPVL#t`aTA>PVLOEUQFG¥InA…Y†ZX[UY(aT[HZuLOAJLRNTA—PVA(Y>QFGTb d]ZXWLOEHZX[]bTA(WVEUquZuLREUqFA>PnQu‡ LONiA~DFEMqFA(G#‘]A([UbgZuGTbgY_NTA>Y_^gEM‡ LONiA(EHW2PVaTS qXZuGTEHPVNTA(PšQFWšGTQXL†¸ w  } • Y(QFP ™vC„ A G  R w=  }€y Y(QXP ™vC„ A G  vw w LONiAšPVaTS QX‡˜IKNTEHY_NrqXZuGTEHPVNTA(P>›«IKNTEUY_N5S#A†ZXGiP LRN]ZuL ™v R = „ EUPZKN]ZXWVS?QXGTEHYz‡™aiGTY>LREHQFG‰k @AgGTA e˜LoLOWp&LOQ·biA>LOA>WRS#EHGTAcLONiAgY(QXG Ÿ aTD8ZuLRA#‘TA([Hb  ™v R = „ k]WVQFS LONTAgl‹ZXaTY_N8p8¡ 7 A(EHS?ZXGTGWVA([HZuLOEUQFGTPmInAoQXBiL_ZXEUG‰¸  }v ”• = } Y>QFP  vC„ A G  –  ™v R = „} 9 Y>QFP  vC„ A G  ; b v-} A G  9 PVEHG  vC„ˆy§J¦ Hf = g„ ;  }= v } • PREHG ™vC„ A G  –   v R = „z} 9 • PREUG ™vC„ A G  ; b = } PVEHG  vC„ 9 A G  y¦ w  vCg„ ; 

















































































































































¯ 

 "!$#%! KI NTA>WRA ¦VH( = „ ZXGTb ¦ w ™vC„ ZXWRA*Y(QFGTPL_ZXG8LRP‹QX‡ EHG8LRA(DFWRZuLOEUQFG‰›`dTWRQhbTaTY>A(bgLRNTA~‘]WVPVLn‡™WRQFS LONiAŒEHGTbiA>‘]GTEMLOAŒEUG8LOA(DXWOZX[\QqFA(W;b v ›˜LONiA0PRA(Y>QFGTb‡™WRQXS LRNTAŒEUGTbTA>‘TGTEULRAŒEHG8LOA>DFWOZu[CQqFA>W b =\knŽ;NiArLInQJbTE A>WRA(G8LsAfe˜dTWVA(PVPREHQXGTP*‡™QFW  ™v R = „ QFG`BiLOZXEHGiA(b—‡™WVQFSLRNTArLInQgEUG8LOAf¡ x DFWRZuLOEUQFGTP‹SjaiPVLsBCAA>thaTZX[»›TPVQ A G  ¦VH( = „} PVEHG  vC„V¦ w ™vC„ IKNTEUY_N·Y†ZuG·QFGT[Mp-BCArPOZ«LOEHP‘]A(b—EU‡ˆLONTAfp—ZXWRArBCQuLON…A(t`a]ZX[ LOQcLONTAoPOZXS#AY(QFGiPVL_ZuG`L ¦ › B\A(Y†ZuaTPRAsLONTAK‘]WRPLmEUP2Afe˜Y([UaTPREMqFA([Mp?Z‡™aTGiY>LOEUQFG#QX‡ =ŠZXGib?LONiA*PVA(Y(QXGTbJEHP2A eiY>[HaTPVEUqXA([Up Zj‡™aTGTYfLOEHQXG…Qu‡ =\k=Ž;NTEHPKY>QFGTY([UaTPREUQFG-DFEUqXA(P  ™v R = „} PVEHG ™vC„ A G  y ¦ ZXGTb¥ImA’IKEU[H[;L_ZX^uA·LONiA’Y(QFGiPVL_ZuG`L ‡™QFWgPVEHS#dT[HEUY(EULpXk¶Ž;NTA(G LONiA·Y(QXS?dT[UAfe ‡™aTGTYfLOEUQFG  ƒ¹8„ SjaiPVLsBCA0DXEUqFA>G—B8p ¦}   ƒ¹F„š } z v R = „‰y E   v R = „z} 9 Y(QFP ™vC„y EPVEHG ™vCc„ ; A G  } A G  } A   3j$&$&QFSc¡ dT[UAfe’‡™aiGTY>LREHQFGTP }  ƒ¹F„ kjŽ;NTA>PRAcS?ZXdT¹ dTEUGTDFP~LOZX^XAcaTPŒ‡™ WVQFS ZgquZX[UaTAŠQX‡ ¹ LRQ-Z quZX[HaiA*QX‡ LRNTWRQFaiDFN  œ¹8„ k Y qFA>WVp?PREUS?dT[UAX›hZX[US?QFPL2LOWREMqhE ZX[TY(ZXPRA~EHP2LONTAsSgZudTdTEHGiD dTWVQ˜bTaiY(A(b…B8pLONTA0‡™aTGiY>LOEUQFG |}€£`¹~y§J¤ R 2£ R𤠏5Y>QFGTPVLOZXG8LOP IKNTEUY_N‰›Afe˜dTWVA(PRPVEHGTD EUG’LOA(WVS?P0Qu‡nEMLOPŒWVA†ZX[ZXGTb&EHS?ZXDFEUG]ZXWp-d]ZXWVLRP } #y E x› Y†ZuG—B\A0IKWREULVLOA>G—ZuP(¸ |} jy E  } ƒ£ y E £ „>™vŠy ZE = „ y€ƒ¤ zy E ¤ „ – ™v R = „} œ£ Rv?• £ Z= „y§¤ VR  ™v R = „=} ƒ£ = y £ vC„y¥¤ IKNTA>WRA‹InA;N]Z†qFAsZX[HPVQŒPRA>d]ZXWRZuLOA>bcLRNTA‹Y>QFGTPVLOZXG8LOP £ ZXGTb ¤ EHG8LOQŒWVA†ZX[iZXGTbcEHS?ZXDFEUG]ZXWp d]ZXWLOP>kŽ;NTEHPzWRA(diWRA(PVA(G8LOPnZ~PVNTEU‡ L=Qu‡\LRNTA‹QFWVEHDFEUG5B8p •*¤ ZuGTb#Z~WRQXLOZuLOEUQFGŠZXGibŠPRY†Zu[HEHGiD QX‡LONTAoQFWREUDFEHG]Zu[ PRAfLŒQX‡quZX[HaTA>P*Qu‡ v ZXGib =\k “˜d\A(Y>EU‘]Y(ZX[H[MpF›]EU‡ImAobTA>‘TGTAoLRNTA5ZuGTDF[HA LONiWRQFaTDXN } L_ZuG G2H  ££  – £ m} ¼ £ ¼ Y(QFP  „XR £ } ¼ £ ¼ PREHG  „ LONiA…QXWREHDXEHG]ZX[šquZX[HaTA>PcQX‡ v R = ZXWRA-WVQXL_ZuLRA(b§B8p LONTA…ZXGTDX[HA ZXGTb§PRY(ZX[HA>b¥B8p LONiA ‡œZXYfLOQFWc¼ £ ¼¾k;Ž;N`aTP>› EM‡zLONiAoquZX[HaiA(PsQX‡ v R =-bTA>PRY>WREHB\AjZ#Y(aTWqFAoQFG—LRNTA ¹ di[ ZXGTAu›]LONTEUP 





































¯ Y(aiWVqFAoIKEH[H[B\A5PVNTEU‡ LRA(b‰›\WRQuL_ZuLRA(b’ZuGTb’PRY(ZX[HA>b·LONiWRQFaTDXN—LONiA5S?ZXdTdTEUGTD?EUS?di[HEHA>b-B`p LONiA‡™aiGTY>LREHQFG  œ¹8„ ›]BTa˜L  Ž i³O,]²  ´ ´€/ (+Ž& i³‰/ h²fk ? L0EHPsQX‡ LRA(G&aTPVA>‡™aT[ƒ›C‡™WRQXS Z#dTWOZuY>LOEUY†ZX[ˆd\QFEHG8L*QX‡=qhEHA>I›\LOQgqhEUA>I”LONTAoSgZudTdTEHGiD ‡™WRQXS LRNTA’QFdidCQFPVEULRA—d\A(WVPRd\A(Y>LREUqXAXk Ž;NTA&Y>A(G8LOWRZX[~EUbTA†Z EHP?LRQ Y(QXGTPREUbTA(WgZ PRAfLQX‡ Y(QXS?dT[UEHY(ZuLOA>b&Y(aTWqFA(PoQFG LONTA ¹ ¡¢dT[ ZXGiAcIKNiEHY_NLRNTWRQXaTDFN  ƒ¹F„ DFAfLOPS?ZXdTd\A(b LOQ…Z PRAfL~Qu‡qFA>WVp…PREUS?dT[UA0Y(aTWqFA>PŒQFG—LRNTA ¡di[ ZXGTAuknŽ;N`aTP>›CInAoIKEU[H[‰d\QFPRALONiAot`aTA>PVLOEUQFG ZXPj‡™QF[U[HQIKP(¸ EMqFA>G LONTAJ‡™aTGiY>LOEUQFG  ›=IKN]ZuLc^`EHGib§Qu‡*Y>aTWVqXA(P#EHG LRNTA dT[ ZXGiA dTWVQ˜bTaiY(AsPRQFS#A*PVEHS#dT[HA;Y>aTWVqXA(P‹EUG#LRNTA ƒ¹F „ di[ ZXGTA Ž;NTEUPnEUP2BCA>Y†ZXaTPVA*LRNTA*aiPRA>¹ ‡™ai[HGTA>PRP QX‡TLRNTAmS?ZXdTdiEHGTD*Y(QFGTY>A(diLz[HEUA(PˆEHG5PVEHS#dT[HEM‡ phEHGTD‹LRNTA‹Y(aiWVqFA>P=ZXGTb5PRN]ZXd\A(PzQX‡]EHG8LRA(WRA>PVL(k Y G5A>qFA>GcS?QFWVAnbiE N#Y(aT[MLzt`aTA>PVLREHQFGjEUP(¸ 0EUqFA>GŠZ~PVA>LQu‡xY(QFS#dT[HEUY†ZuLRA(brY(aTWqFA>P=QFG5LONiA ¹LONidTA [HZXGTdTAu[ ›xZuIKGTNTA ZuL~@ ‡™aTA‹GiIKY>LOEU[HEU[hQFGGTQX L2ƒZ«¹8LR„ LOA>Y†S?ZXG—d˜LSgLOZuQrd—ZXbTLONibiA(WRS4A(PVPQFLOG8NTLOEUQgP=t`Z?aTPRA(AfPL~LOEHQuQX‡=G#PRbiEUS?EHWRdTA>Y>[UALR[UpFY(aT›XBTWqFaiA(L=P~LOQFNiG A ‡œZXS#EH [UE ZXWVEULp0InAsIKEU[H[TbTAfqFA>[HQFd#IKEULONcLONiAsS?ZXdTdiEHGTDFP=Qu‡‰PRAfqFA>WOZX[\Y(QFS#S#QFGЇ™aTGTY>LREHQFGiP DFQhA(PsZŠ[HQFGiDjI‹Z†pLOQImZXWRb…PRaiDFDFA(PLOEUGTDgZuG—ZuGTPVInA(WKLOQ#EUL;EUG-SgZXG8pgPREULRa]ZuLREHQFGTP>k Ž;NTAjPVEHS#dT[HA>PVLsPRAfLŒQX‡=Y>aTWVqXA(P0QFG…LONTA ¡¢dT[ ZXGiArY>QFWRWVA(PVdCQFGib·LOQ ’} Y>QFGTPVLOZXG8L LRNTA(PVAŠZXWVAoPLOWOZuEHDFN8LsqFA(WLOEUY†ZX[ˆ[HEUGTA(P>›\IKEMLON -ZuPRPRaiS?EUGTDJZXG8p-quZX[HaiAoB\A>LInA(A>G ZX GTb oy ˜ „ ›]ZuGTb…LRQ } Y>QFGTPVLOZXG8L  LONTA>PRArZXWVArPLOWRZXEHDFN8LKNTQXWREZ\>QFG8L_ZX[ [HEHGiA(P(›˜IKEULO• N ˜  ZXPVPRaTS#EHGTDrZXG8pjquZX[UaTA‹B\A>LInA(A>G ZXGTb k ŒLRNTA(W=PVEHS#dT[HAmPRA>LRPnQu‡ Y>aTWVqXA(PšQFG LONiA dT[ ZXGiA~ZXWVA*LRNTQFPRAsLON]Z«LmY>QF• WRWV˜ A(PRd\QFGTbJoy LRQj˜ Z„ ‘ie˜A(b-ZXWVDFaTS#A(G8L ·ZXGTb?qXZuWRE ZuBT[HA S?ZXDFGTEMLOaTbTA ?QX‡ ›XIKNiEHY_N#ZXWRAnWOZ†phP=A(S?ZXG]ZuLREHGTDs‡™WRQFS”LONiA‹QFWREUDFEHG5ZuL‘ie˜A>b?ZuGTDF[HA  IKEULRN—LONiA Z«e˜EUP(›xQFWKLONTQFPVArLRN]ZuL*Y(QFWVWRA>PRd\QFGTb·LRQJZŠ‘ie˜A(b&S?ZXDFGTEMLOaTbTA  ZuGTb quZXWREHZXBT[UAoZuWRDFaT S#A(G8L  QX‡ ›xIKNTEHY_N ZXWVA5Y>EHWRY>[HaT[HZXWsZXWRY>P~Y>A(G8LOA>WRA(b ZuL*LONTAoQFWREUDFEHG ZuL;‘ie˜A>b·WOZubTEHaTP   LRNTArZXWRY>P*ZuWRA0‡™aT[H[ Y(EHWVY([UA(P‹‡™QFW   µ ‚  „ k @ AEU[H[HaiPVLOWRZuLOA*LONTA>PRArEHbTA(ZXP‹IKEULRN…PVA>qXA(WOZu[ˆA eiZXS?di[HA(P>k ]¸Œ@A#Y>QFGTPVEHbTA>WŒLONTAcS?ZXdTdTEUGTDJQX‡šLONTA ¹ ¡¢dT[ ZuGTAjLOQLONiA ¡di[ ZXGTA LONiWRQFaTDXN…LRNTAAfe˜dCQXGTA(G8LOEHZX[ ‡™aTGiY>LOEUQFG‰¸ |} A  } A Y(QFP  = „y EUA PVEHG  = „=– ™v R = „=} A Y>QFP  = „XR   v R = „=} A PVEHG  = „ ? G&LONTAŠPVdTEHWVEUL0biEHPRY>aTPRPVA(b ZXBCQqXAX›‰InA#Y>QFGTPVEHbTA>WIKNTZuLY(aTWqFA>PoEUG’LONTA ¹ dT[ ZuGTAjDFAfL S?ZXdTd\A(b LRQ·qFA>WVLOEUY†ZX[š[HEUGTA(P ™v R = „r} ‚K QFWoNTQFWVEZ\(QXG`LOZX[2[HEUGTA(P   v R = „o}  K QFG LONiA di[ ZXGTAukŠ]QFW~qXA(WVLREHY(ZX[=[HEUGTA(P0QFG&LRNTA dT[ ZuGTA(P0LONiA#Y>QFWRWVA(PVdCQFGibTEHGTD-Y>aTWVqXA(P QFGLONiA ¹ dT[ ZuGTAZXWRA0DXEUqFA>G—B8p\¸ ™v R = „=} A Y(QFP  = „} ‚K – v-} [HG  KO„• [HG  Y(QXP  = „R„ ‡™QFW ‚K   R Y>QFP  = „  r– •  ‚ µ =Jµ  ‚ – v-} [HG  • ‚K „z• [UG • Y(QFP  = „V„ ‡™QFW ‚K µ  R Y>QFP  = „ µ r–  ‚ µ =Jµ © ‚  3

z"#g!



















  



















½ 

 "!$#%! ˜“ EUS?EU[ ZXWV[UpF›u‡™QFW‹NTQFWVEZ\>QFG8L_ZX[\[HEUGTA(P‹QXGgLONTA dT[ ZuGTA(PmLRNTA0Y(QXWRWRA>PRd\QFGTbTEUGTDŠY(aiWVqFA>PKQFG LONiA ¹ dT[HZXGTAZXWVArDXEUqFA>G—B8p\¸  ™v R = „=} A ˆPREHG  = „=}  K – v…} [UG   Kf„z• [HG  PVEHG  = „V„ ‡™QF’W 9  K  $ R PREUG  = „  r–  µ =Jµ €; – v…} [UG •  Kf„=• [HG  • PREUG  = „R„ ‡™QF’W 9  K µ $ R PREUG  = „ µ r–  µ =?µ ‚ €; Ž;NTA>PRArSgZXdidTEHGTDXPKZXWRA0EU[H[HaiPVLOWRZuLOA>bEHG…zEUDTk ‚ k ¯Tk @ A·Y†ZXG A eTZuS?EUGTA…LRNTA’S?ZXdTdTEUGTD diWRQhbTaTY(A>b B8p¥LRNTA’POZuS?A…‡™aTGTY>LREHQFG aTPREUGTD d\QF[ ZXWmY(QhQFWRbTEUG]ZuLRA(P;EHGLRNTA dT[ ZXGiAX¸ |} A  – [HG  0„=}€¹5– [HG   „y E  }¶vŠy ZE = – [UG   „2} v R  } = N = EHGZ ? G LRNTEHPrY†ZXPVAX›Y>aTWVqXA(PjbiA(PRY>WREUBCA>b B8p Z…Y(QFGiPVL_ZuG`LoquZX[HaTA#QX‡ v } ‚ v K IKEULR– WOZuGTDFAQX‡ˆqXZu[HaTA>P;PRd]ZXGiGTEHGTD ‚  ›iSgZXdLRQ#Y>EHWVY([HA>P;QX‡Y(QFGTPL_ZXG8L*WOZXbiEHaTP  } A  ¸ 9 v-}¶‚ v KJR  =Jµ ‚ €; — 9  } A  R   µ ‚ €; “˜EUS?EU[ ZXWV[UpF›Y>aTWVqXA(PŠbTA>PRY>WREHB\A(b B8pY(QFGiPVL_ZuG`L5qXZu[HaTA?QX ‡ = } = K ZXGTb v LOZX^`EHGTD·ZX[H[ WRA(ZX[xqXZu[HaTA>P • ˜ µ v µ ˜ ›hSgZud?LOQoPVLRWOZXEUDFN8Lm[UEHGTA>P  WOZ†phP „ A>SgZuG]ZuLOEUGTD‡™WRQFS LONiA QFWVEHDFEUGZuLsY(QFGiPVL_ZuG`L*ZXGiDF[HAZXGiDF[HA&LRQŠLONTA  ZžeiEUP(¸ 9 • ˜ µ v µ ˜R = } = K‘; — 9  &µ ˜R  } = K.; Ž;NTEUPŒZXG]Zu[UphPREUPsQu‡LONTAoSgZudTdTEHGiDFP*diWRQhbTaTY(A>b’B8p-LONTAr‡™aTGTY>LREHQFG } Afe˜d ƒ¹F„ EHGibTEM¡ Y†Z«LOA(PnLON]ZuLmA>qXA(WVp?PVLRWREUdJQX‡‰IKEUbiLON ‚  EHƒG =?ZuGTb • ˜ µ v µ ˜ QFG ¹ ¡dT[HZXGTA*SgZXdiP QFG8LOQ#A(G8LREHWRA ¡dT[HZXGTAXkzŽ;NTEHPKEHP‹LRWRaTA0‡™QFW;LRNTASgZXdidTEHGTDŠaiPREHGiD#Y(ZuLOWVA(PVE ZXG…QFWKdCQX[ ZXW Y(QhQFWVbTEHG]Z«LOA(P;EUGLONTA dT[HZXGTAXk ‰¸n@A5GTA ehL~Y>QFGTPREUbTA(WsLONTArS?ZXdTdTEUGTDcQX‡LONiAoEUG`qXA(WVPRAo‡™aiGTY>LREHQFG…QX‡ LONiA;Afe˜dCQXGTA(G8LOEHZX[»›XG]ZXS#A([UprLONiA‹G]ZuLRaTWOZX[i[HQFD8ZuWREULRNTSIKNTEUY_NcIKEU[H[hdTWRQqXAKLRQ0BCAmSjaTY_N LOWVEHY_^`EHA>W(kˆ@ AKA(S#dT[UQžp5dCQX[ ZXWY>Q˜QXWRbTEUG]ZuLOA>P‡™QFW ¹ ›8IKNTEUY_N‰›hZXP=ImAsN]Z†qFAsPRA>A(G#A†ZXWV[HEHA>W(› IKEULRNLONTAaTPVAoQX‡ ™=aT[HA>W  P;‡™QFWRSjai[ ZjS?ZX^XAŒLRNTEHGTDXP;PREHS#dT[UA(W(k } [UG ƒ¹F„n} [HG  uA „=} [UG   „y E  – ™v R = „=} [HG   „2} [HG  º v w y = w O„ R   v R = „=}  } LOZXG G2H v=  “˜EUGTY(A’LRNTEHPJEUPgLONiA EUG8qFA(WVPRA S?ZXdTdTEUGTD QX‡LONiA&Afe˜dCQXGTA(G8LOEHZX[»›KInA Y(ZXG¶SgZu^XA’LONiA Y(QXWRWRA>PRd\QFGTbTA>GTY(A ™v  R =  ‚œ   R    „ ›xZuGTb—‡™WVQFSLONiEHP;QFBiLOZXEHG-LONiA S?ZXdTdTEUGTDoB8p?WRAfqFA(WVPREUGTD5IKN]ZuLnImA*‡™QFaTGTbg‡™QXWšLRNTA~S?ZXdTdTEUGTD |} A  k=Ž;NTEUPnPVEHS#dT[HA ZXWVDFaTS#A(G8LKDFEUqXA(P;LONiA‡™QX[H[HQIKEUGTDjS?ZXdTdTEUGTDFP(¸ 9  }  KVR   е ‚  ; — 9 ™v R = „} ‚Km} [HG   KfX„ R   ™v R = „ µ ‚  ; 





  



3

½{

z"#g!

y

 

v



3π/2 π π/2 0

u

0

x −π/2

y

    

v

   

2π 3π/2 π

0

y

u

0

π/2

  

x v

  

3π/2 π π/2 0 −π/2

y

u

0

x

!"#$% & '

v

("#$% & '

3π/2 π π/2 0

zEUDFaTWRA ‚ k ¯T¸

−π/2

0

u

   y 

nsu‰p y `3agf_j:†

x



*)ƒeVpLp3f}j:†ohJlyVŠ p$^_eJj:nbch Š p3^}eJj:nbgm:d%hQ`:†Qm r)eVdgbcnXagf}eJj>hJdpxhQ^_eVdrsh‰hJd%„Lf_j3eVbcnXaf_jbgm:n p ^_eJjLnJ 3



 

½‚



 "!$#%!

}  KJR  jµ ˜ ;— 9 •˜ µ ™v R = „ µ ˜R  ™v R = „=}  K;}  Ks; LONTZuLŠEHP>›=Y(EUWRY([UA(PoQX‡sWOZXbTEUaTP  K QXG LONTA ¹ dT[HZXGTA?SgZXdLOQ&PVLRWOZXEUDFN8LjqFA>WVLREHY†Zu[m[HEUGTA(P ™v R = „} ‚Km} [UG   Kf„ QXGoLONiA dT[HZXGTA2QX‡iNTA(EUDFN8L ‚  ›«IKNTEU[HA=WRZphPzZuLZXG5ZuDF[HA  K LRQ LONiA v Z«e˜EHPšQFG#LONTA ¹ dT[ ZuGTA*S?ZXdcLOQoPVLOWRZXEHDXN`LnNTQFWVEZ\>QFG8L_ZX[x[HEUGTA(P  ™v R = „=}  K‹}  K QFG LRNTA di[ ZXGTAuk’Ž;NTEUP5EHPjZX[H[=InA([H[mZXGTb GTEUY(A#IKNTA(G ·[UEHA(PIKEULRNTEHG ZXG EHG8LRA(WVquZX[ QX‡ ‚  ›\ZXPKImA5ZXPRPVaTS?A>b’PRQ#‡œZXW(›xBTa˜L~[UA†ZXbTP;LRQgbT}E N?Y>aT[ULREHA>PsEM‡zLRNTAoWRZXGTDFArQX‡qXZu[HaTA>P QX‡  EHPGTQuL-PRd\A(Y(EM‘]A(b k @ A&N]Zub|PVA(A>G¨B\A>‡™QFWVA’LON]ZuL…ZuPJ‡œZXWJLONTA&biA>‘]GTEMLOEUQFG QX‡ LONiA—Y>QFS?di[HAfe G`aTSjB\A(W ¹ EHPcY>QFGTY(A>WRGTA>b‰›‹EMLOP#ZXWRDXaTS?A>G8L &Y(ZXG Y_N]ZuGTDFA…B`p ‚  EUP0ZXG8p&EHG8LRA(DFA>W IKEULRNTQFaiLrZuG`p·dTWRQXBT[HA>S—k*QImAfqFA>W(› IKNTA(G ImAŠImZXG8L0LOQL_ZX^uA LO NiA0[HQFD8ZuWREULRNTS QX‡ „ ¹ ›iLONiEHPKZXSjBiEHDFaTEMLp#EHGLONTAZuWRDFaTS#A(G8LKdTWVQ˜biaTY(A>PsbiE N#Y(aT[MLOEUA(P‹EUG bTAfLOA(WVS?EUGTEHGiD…B\QXLRNLONiA?S?ZXDFGTEMLOaTbiA?ZuGTb LRNTAJZuWRDFaTS#A(G8LrQX‡;[UG œ¹8„ k ? G LONTA#Y†ZXPVA QX‡;LRNTASgZudTdTEHGiD·dTWVQ˜bTaiY(A(b B8p [UG LONTEUPjEHP5Z’bTEHPRZXPVLRA(W(¸#bTA>dCA>GTbTEHGiD&QFG LONiAcquZX[UaTAŠQX‡ ›InA?Y(ZXG A(GTb aTd Sg} ZXdidTEHGTƒ¹8DJ„ LRNTAcA(G8LOEUWRA ¹ dT[ ZuGTAŠQFG8LOQ…ZXG8p&PLOWREUd QX‡šIKEHbiLRN ‚  QXG LRNTA’Z«e˜EUPrEUG’LONTA dT[HZXGTAukŠŽ;NTEHPrZXSjBiEHDFaTEMLpF›‰WVA>‡™A>WRWRA>bLRQ—ZuP AVSjai[ULOEMquZX[HaTA>bTGTA>PR‘P Ci›]EHPsPRQFS#A>LRNTEHGTD#LOQ#BCA5Z†qFQFEUbTA(b&Z«LŒZX[U[Y(QFPLOP>› EU‡LONTA‡™aTGTYfLOEUQFG [HG ƒ¹8„ EHPKLOQJN]Z†qXAjdTWRQXdCA>W~S#A†ZXGTEUGTDTksŽQ?LONTEUP*A>GTb‰› InAjbTAf‘]GTA5LInQGTA>I”GiQXLOEUQFGTP(¸ 4(±V‰³ / & ,2(  /2Ž ;ZXGib 4(±V‰³ / & ’&O13Ž fk Y   rEHPKZŠPREUGTDFaT[HZXWREMLp#QX‡ZЇ™aTGTYfLOEUQFGIKNTEHY_N…PRa CA(WVP;‡™WRQFSS5aT[M¡ LOEMquZX[HaTA>bTGTA>PRP(k •sQXLKZX[U[ PVEHGTDFai[ ZXWVEULOEUA(PšZXWVA0BTWOZXGiY_N…d\QFEUG`LRP(›˜BTaiLsZjBTWRZXGTY_N-dCQXEHG8L‹EUP GTA>Y(A(PVPOZXWVEH[MpjZŒPVEHGTDFai[ ZXWVEULpFk]QFWzA eiZXS?di[HAX› ¹5}¨ EHP=Z~PVEHGTDXaT[ ZXWVEULprQX‡]LRNTAm‡™aTGTYfLOEUQFG  œ¹8„2} Q{ 5X¹ BTa˜LKEHP‹GTQuLsZjBTWOZXGiY_N—d\QFEHG8LmBCA>Y†ZXaTPVA0LONTEUP‹‡™aTGTY>LREHQFGbiQ˜A>P;GTQXL;PVa A>W ‡™WRQXS SjaT[MLOEMqXZu[HaTA>bTGTA(PVP(k ? G LONiA…Y(ZXPRA-QX‡sLONiA…GTZuLOaTWRZX[;[HQXD8ZXWREMLONTS…›zIKNTEUY_N bTQ˜A>P PRa A>W~‡™WRQFSS5aT[ULREUquZX[HaiA(bTGTA>PRP>›\LRNTA5d\QFEHG8L ¹g}” EUPŒZ?BiWOZXGTY_N&d\QFEUG`L*B\A(Y†ZuaTPRAŠZ«L LONiEHP;d\QFEHG8L;LONiArbiA(WREMquZuLOEMqFA0QX‡ˆLONTA0‡™aTGiY>LOEUQFG b [HG œ¹8„2} { b¹ ¹ bTQhA(PoGTQXLoAfe˜EHPL  EMLrbTQ˜A>P5GTQuLjN]Z†qFAJZ…InA([H[2bTAf‘]GTA>b qXZu[HaTA „ [k “˜EHS#EH[HZXWR[MpF› InAJY(ZXG ZXWVDFaTA5LRN]ZuL0LONiAŠdCQFEUG8L v¹ — ˜ EUP0ZJBTWOZuGTY_N dCQFEUG8LŒ‡™QFW~LRNTAŠG]ZuLRaTWOZX[[HQFDFZXWREMLONTS…› B\A(Y†ZuaTPRA [UG  ¹{  } • [UG ƒ¹F„ PRQrLONTA*BCA>N]Z†qhEHQFWšQX‡‰LRNTEHP2‡™aTGTYfLOEHQXG?‡™QFW J{ 5X¹8„ — ˜ EHP2LONTA*POZXS#A~ZuPšLRNTA~B\A(N]Z†qhEHQXW QX‡‰LRNTA~‡™aTGiY>LOEUQFG?‡™QXW ›hQFGT[MpcIKEULONgZ5S#EHG`aTPšPREHDXG‰k maiLnImA~N]Z†qFA0ZX[UWRA(ZXbip#A(P ¡ L_ZuBT[HEUPRNTA>b5LON]Z«LIKNTA(GŠ|¹ LR— NTAm quZXWREHZXBT[UAmZXdidCA(ZXWREUGTD~EUG5LONTEUPz‡™aTGTYfLOEUQFGjDFQhA(PzLRQ\(A>WRQ0LONiA ‡™aTGTYfLOEUQFG—EUP;GTQFG˜¡ZXG]ZX[Mp`LOEHYuk=Ž;NTA(WVA>‡™QFWVAX›xImArN]Z†qFArA(PL_ZXBi[HEHPVNTA(b-LONTZuLKLONTA0‡™aTGTYfLOEUQFG [HG ƒ¹8„ N]ZuPKLInQgBiWOZXGTY_N…d\QFEHG8LOP>x› \(A>WRQ?ZXGTb ˜ k Y    gEHPrZ—Y>aiLjQX‡nLONTA?Y(QFS#dT[UAfe dT[HZXGTAŠIKNTEHY_N Ÿ QFEHGTP0LInQ’BTWRZXGTY_N d\QFEHG8LOP>¸0ImA#EHS?ZXDFEUGTA5LONTZuLIKEULON LONiA#NiA([Hd QX‡‹Z-dTZXEHW0QX‡mSgZ«LONTA>SgZuLREHY(ZX[zPVY(EHPVPRQFWVP 9



























X½ © InAo[UEULOA>WOZX[U[Up#Y(a˜L*LRNTAY(QFS#dT[HA e-dT[HZXGTArZX[HQXGTDcZ#[UEHGTA0PVQ#LRN]ZuLsEULKEUPKGTQXL*ZX[H[UQImA>b-LRQ Y(WVQFPRP‡™WVQFS”QFGTA‹PVEHbTAmQX‡xLONTA‹[UEHGTA2LOQŒLRNTA‹QXLRNTA(W>k ? GŠLONiA‹Y†ZXPVA‹QX‡xLONiA‹[HQFDFZXWREMLONTS QFGiA d\QFPRPVEHBT[UA0Y(aiLKInQFaT[Hb…B\AoZu[HQFGTDŠLRNTA v Z«e˜EHP;‡™QFWVS v…}€ LRQ vv— ˜ k2Ž;NTEUPsY_NiQFEHY>A WRA>PVLRWREHYfLOP0LONiA?ZuWRDFaTS#A(G8L EHG’LRNTAcWOZXGiDFAcQX‡nquZX[UaTA(P'9 ›‰IKNTA>WRAcImAcEUSgZXDXEHGTA LONTZuLšQFGTAKPREUbTA*Qu‡CLRNTA*Y>aiLnEHP2ZXY>Y(A(PVPREUBT[HA  Ÿ aTPL‹ZuBCQqFAKLONiA R ‚ v ˆ„Z«e˜EHP „ IKNTEU[HA‹LRNTA*QuLONTA>W EHP0GiQXL  Ÿ aTPLoB\A([UQI LONiA v Z«e˜EHP „ kcŽ;NTA#A CA(Y>LrQX‡nLONTEUP0EHP0LONTZuLEULA>[HS#EHG]ZuLRA(P0ZuG`p ZXSjBiEHDFaTEMLpgEUGLONTA0quZX[HaiA(P‹LONTZuLKLONTA0‡™aTGTYfLOEUQFG-[HG œ¹8„ EHPKZX[U[HQInA(bLOQŠL_Zu^XA  Ž;NTA(WVAKZXWRAšS?ZXG8poQuLONTA>WdCQXPRPREUBT[HAšY_NTQFEUY(A>Pz‡™QFWZ~BTWOZuGTY_NŠY(aiL(k ? G5‡œZuY>L†›FZXG8po[UEHGTA Ÿ QFEUGTEHGTD;LRNTAnd\QFEUG`LRP  ZXGTb ˜ EHPˆZs[HA(DXEULOEUSgZ«LOAzY_NiQFEHY>AX›FZuP[UQFGTD*ZXPEMLˆbTQ˜A>PGiQXLzY>WRQFPVP EULRPRA>[U‡ ›ˆBCA>Y†ZXaTPVAJLONTA>G Z·d\QFWVLREHQFG QX‡‹LRNTAJY>QFS?di[HAfe di[ ZXGTAcInQFaT[Hb BCA?Y(QFS#dT[HAfLOA>[Up Y(a˜LOQ  EML5Y>QFaT[Hb GTQXLjB\AJWVA†ZXY_NTA>b ‡™WRQFS LRNTAJWRA>PVLŠQu‡‹LONTAgdT[ ZXGiA „ ›IKNTEHY_N EUP5GTQuL ZX[U[HQImA>b‰k ™šZuY_N#PVaTY_NcY_NTQFEUY(A‹QX‡xBiWOZXGTY_NŠY>aiL=WVA(PVLRWREUY>LOPLONTA‹WRZXGTDFAnQX‡]LONiA;ZXWRDXaTS?A>G8L QX‡ ¹ LOQrQFGTAsPRAfLmQX‡CquZX[HaTA>PnPVd]ZXGTGiEHGTD5ZXG?EUG8LOA(WquZX[xQX‡ ‚  k=]QFW2AfeiZXS#dT[HAu›hEM‡CInA~NTZXb Y_NTQFPVA(GLONiAŒdCQXPREULREUqXA =?Z«e˜EHP‹ZuPmLONTA~BTWOZXGiY_NY(aiL(›iLONTAŒZX[H[UQžInA(b?qXZu[HaTA>PmQX‡ oInQFaT[Ub B\AoEUG—LONiA5EHG8LRA(WVquZX[ 9 5F$‚ R ½ 5F‚F„ ›]EU‡ImAoN]ZXb·Y_NiQFPRA>G’LONTAoGTA(D8Z«LOEUqXA v ZžeiEUP~ZuP*LONiA BTWRZXGTY_N…Y(aiL(›iLONTAŒquZX[UaTA(P;Qu‡ 5InQFaT[Ub-BCAŒEUGJLONTAEUG`LRA(WqXZu"[ 9 "R © ˆ„ ›iAfLOYXk2Ž;NTA>WRArZXWVA ZX[UPRQ…S?QFWVA?Y>QFS#dT[HEUY†ZuLRA(b dCQXPRPREUBT[HA#Y_NTQFEUY(A>P(›z‡™QFW0IKNTEUY_N LONiAgWOZuGTDFA#QX‡ …SgZ†p B\A bTE A>WRA(G8LŒ‡™QXW~A†ZuY_N quZX[UaTA5Qu‡=LONTAjWRZXbTEUaTP h› BTaiLŒEUL~ZX[UImZ†p˜P0PVd]ZXGTPŒZXG&EHG8LOA>WVquZX[ˆQX‡ ‚  ‡™@¶QFW‹EULRquN ZX[ULOaTNTA0A·QX‡EHG8˜LOkWVQ˜bTaiY>LOEUQFG¥IKEMLON¥BTWOZXGiY_N|d\QFEUG`LgZXGTb¥LONTA&ZuPRPRQhY(EHZuLOA>b BTWRZXGTY_N Y(a˜LOP(›*ImA&N]Z†qXA LRNTA(WVA>‡™QFWVA&SgZXGTZXDFA(b LRQ A([HEUS?EUG]ZuLRA…LRNTA&dTWRQXBT[HA>S QX‡oSjaT[MLOEUquZX[ ¡ aTA>bTGTA(PVP5‡™QFWLONTA#G]ZuLRaTWOZu[š[UQFD8ZXWVEULRNTS—k#Ž;NTEUP5ZXdidTWRQ8ZuY_N Y†ZuG BCA?ZXdTdi[HEHA>b LRQ·ZuG`p ‡™aTGTYfLOEUQFG LRN]ZuLrPRa A>WRP‡™WRQFS S5aT[ULREUquZX[HaiA(bTGTA>PRP>kk “hQ…‡œZXW0InA?NTZqXA?S#A>LrQFGi[Up&QFGiA ‡™aTGTYfLOEUQFGTP=LON]Z«LnPVa CA(WRPš‡™WRQFS LONTEUPšdiWRQFBT[UA(S…›8QXLONiA(W2LON]ZXGcLONiA*G]Z«LOaTWRZX[][HQFDFZXWREMLONTS…› IKNTEUY_N?EU"P D WVQ˜QuL2QX‡ ¹ k Y YfLOa]ZX[U[UpX›FLONTA>PRA;LImQr‡™aTGTYfLOEHQXGTP2ZXWRAKWVA([ Z«LOA(b ›8BCA>Y†ZXaTPVA~ZuP bTEUPRY(aiPRPRA>bBCAf‡™QFWRAu›˜QXGTA*Y(ZXGJaTPVA*LRNTA~[UQFD8ZXWVEULONiS LOQobTA>‘TGTA*LRNTA~d\QImA>W ¹ IKNTA>WRA £ EHP*Z?WVA†ZX[ G`aTSjB\A(W>›\IKNiEHY_N’EUP*EUbTA(G8LOEM‘]A(b…IKEULRN—LONi|A D WVQ˜QuL†k‹Ž;N`aTP>› ‡™QFW;LONTAodTaTW ¡ d\QFPRA>PjQX‡‹LRNTAgdTWVA(PVA(G8LcbTEHPVY(aTPVPREUQFG‰›zLRNTAgQFGi[Up&LOWVaT[Up Sjai[ULOEMquZX[HaTA>b&‡™aTGTY>LREHQFG LON]Z«L SjaTPLKBCAŒ‘˜eiA>b—B8pJLRNTA0EHG8LRWRQhbTaTY>LREHQFGQu‡BiWOZXGTY_N…Y(a˜LOPKEHPmLRNTA0G]ZuLRaTWOZu[‰[HQFDFZXWREMLONTS…› IKNTEUY_N—QhY(Y(ZXPREUQFG]ZX[U[Up?[HaTWV^hP;EUGLONTAbTAf‘]GTEULREHQFG-QX‡QXLRNTA(W‹‡™aTGiY>LOEUQFGTP>k •*QXLREHY>AsLRN]ZuL2LONTAsEHG8LRWRQhbTaTY>LREHQFG#QX‡‰ZrBTWRZXGTY_NJY>aiLšLON]ZuLšWVA(PVLRWREUY>LOPšLONTAKquZX[HaiA(P2QX‡ LONiAjZXWVDFaTS#A(G8L~LRQ  Jµ ‚  EUP~A>thaiEUquZX[HA>G8L*LRQ?L_Zu^hEUGTD?LRNTAjdTWVEHGTY>EHd]Zu[‰qXZu[HaTArQX‡ LONiAoZuWRDFaTS#A(G8L(k Y PŠZuGTQXLONiA(W5EU[H[UaTPVLRWOZuLREUqFAcA eTZuS?dT[UAgQX‡mLONTAJGiA(A(b LRQ’EHG8LRWRQhbTaTY(A?BTWOZuGTY_N Y(aiLRP Y(QXGTPREUbTA(W;LONiA‡™aiGTY>LREHQFG‰¸ ® [HG ƒ¹0• V¹ Kf„ Ž;NTEUP‹‡™aTGTY>LREHQFG-EUP;QX‡ LOA>G…aiPRA(b…LOQŠPVEHS#dT[HEM‡ p#LRNTAbTA(PVY(WVEHdiLREHQFG-QX‡ˆWOZubTE ZX[CQFW;Y(EUWRY>aTSc¡ ‡™A(WVA(G8LOEHZX[ ]QI ‡™WRQFS4ZgPVQFaTWVY(A  IKEULON…LONTA y PREHDXG „ QXW~ZgPVEHGT^  IKEULON…LONTA • PVEHDFG „ PREMLOa]Z«LOA(b’ZuL ¹?} ¹VK k~Ž;NTAjY>QFSjBTEUG]ZuLREHQFG…QX‡LRNTA5LInQJY_NTQFEUY(A(P~QX‡=PREUDFGTP>› Y(A>G8LOA(WVA(b 3

z"#g!















½u¯



 "!$#%!

  

y

z θ

r1

r2

r θ1



θ2 0

a

x

z EUDFaTWRA ‚ k¾½˜¸ d.eJjLr%mƒr)`:blZhJdbgm:nl `LjLrsbgfihQj  y  ^_j  y  q^}j  y . ZuL;LInQ?biE CA(WRA>G8L*d\QFEUG`LRP ¹j}|£ ZXGTb ¹5} •~£ ›]EHP;Y(ZX[H[UA(bLONiArPVQFaTWVY(Af¡¢PREUGT^Jd]ZXEUW(¸  œ¹8„2}  H>œ¹8„ y  ƒ¹8„2} [UG ƒ¹*y¥£h„z• [UG ƒ¹• £h„2} [HG   H „y E   H•  „  w w w IKNTA>WRA  Hg} ¼ ¹jy£ ¼ R  HJ} Y WRD 9 ¹Šy £ ; ZuGTb  w } ¼ ¹?•¨£ ¼ R  w } Y WVD 9 ¹J•€£; › IKEULRN LRNTAgPVQFaTWVY(A?ZuL ¹·} •*£  bTA>GTQXLOA>b B8p&LONTA#‡™aTGTYfLOEHQXG  H>ƒ¹8„V„ ZXGibLONiA?PVEHGT^ ZuL ¹} y0£¥ bTA(GiQXLOA>b§B8p LONTA?‡™aTGTY>LREHQFG  w ƒ¹F„R„ k ™qhEHbiA(G8LO[MpF›‡™QFWrLONTEUPo‡™aTGTYfLOEUQFG InAgGTA>A(b LRQ—EUG`LRWRQhbTaTY>A?BTWRZXGTY_NY(aiLRP(›B\A(Y(ZXaTPRA#LONTA>WRA?ZXWRA?ZuLr[HA(ZXPVLrLInQ·BTWRZXGTY_N d\QFEHG8LOP>› ¹Š} ®£ ›xIKNTA>WRALONTA‡™aTGTYfLOEHQXG—EUPsGiQFG˜¡ ZuG]ZX[Up`LREHYXk2ŽˆQgPVA(ALONTEUP(›]ImArGTQXLREHY>A LONTZuL*‡™QXW*Z#Y([UQFPRA>b’d]ZuLRN—LONTZuL~A>GTY(EUWRY>[HA(PsA(EMLONTA>W*B\QXLRN·QFWsGTA(EMLONTA>W*Qu‡ ¹c} y£ ZuGTb ¹oZXPc} ZuLo•~LO£ NTLOANTB\A0A(t`DXa]EHGTZXG8GTLREUGTEULDTp ›z LR N]HˆZu• LŠEU P(w ›=„ EML_LŠZubT^XA(QhPKA(PŠLONiGTA0QXPOLjZXEHS#GTY>AŒWRquA†ZuZXPR[HaTAJAŒB8Zup L;Z·LONT‡œA0ZXYfA>LOGTQFb…W5QXQX‡‡ LRNTA0d]A>qXZuA(LRGN LONiQFaTDFN A†ZuY_N¥QX‡KLRNTA-ZXGTDF[UA(P  H ZXGTb  w EHGTY>WRA(ZXPRAB8p ‚  kŽ;N`aTP>›mPRaiY_N ‚ Z&d]ZuLRN InQFaT[Hb GTQXL[UA†ZXb LOQ-Sjai[ULOEMquZX[HaTA>bTGTA>PRP(kc]QFWZ-Y([UQFPRA>bdTZuLON LON]Z«LA(GTY>EHWRY>[HA>PrQXGT[Up QFGTA*QX‡ QFW LONiA~t`a]ZXG8LOEMLp   EHGTY>WRA(ZXPRA>PmB8p ZuLnLONTAsA(GibJQX‡ LONiA0d]ZuLO¹oN}¨WVA(£ [HZuLOEMqF¹jA~LR}”Qj•~EULR£PmquZX[HaTAŒZuL‹LONiAŒBC A>DFH\EH• GiGTEHw GT„ DikŽ;NTA(PVA0‡œZXY>LRPK‚ ZXWRAŒA>PVLOZXBT[HEUPRNTA>b B8p EUGTPRd\A(YfLOEHGiD&zEHDik ‚ kª½˜k ŒGTAJt`aTA>PVLOEUQFG InAGTA(A>b LRQ&ZXGTPImA>WŠEHPrIKNTA>LRNTA(WŠLONiA ‡™aTGTYfLOEUQFG&N]ZXP0ZuG`p·QXLONiA(WŒBTWRZXGTY_N d\QFEHG8LOP>k 0GiAjdCQXPRPREUBT[HA5Y†ZXGTbiEHb]ZuLRAjEHP v¹ — ˜ › BTaiLKLRNTA0‡™aTGTY>LREHQFG-EUPKZXY>LRa]ZX[H[Mp?InA([U[bTA>‘TGTA(b—EHGLONTEUP;[HEUS?EML†¸  œ¹8„2} [HG ƒ¹*y¥£h„z• [HG ƒ¹• £h„2} [HG  ¹sy¥£ — [UG {„=}¨ ‡™QFW ¹|— ˜ ¹• £  Ž;NTA#QXLONiA(WrdCQFPVPREUBT[HAŠY(ZXGTbTEUb]ZuLOAu› ¹—} ›ZX[UPRQ-bTQhA(PrGTQXLrdTWRA>PRA>G`LjZXG8p dTWRQXBT[HA>S—› B\A(Y†ZuaTPRAu¸  œ8„=} [UG ƒ£h„• [UG •*£h„š} [HG  £ } [HG  •o{„=} [HG  A  „2} E  •*£  







F½ ½ Ž;N`aTP5LRNTAgQFGi[Up BTWRZXGTY_N d\QFEHG8LOPoZXWVA ¹ }®£ k Y GTQuLONTA>WoImZp LOQ—PRA>AgLONTEUPoEUPrLRQ A>quZX[Ua]ZuLRAŒLONTAbTA>WREUquZuLREUqXA0QX‡LRNTA0‡™aTGTYfLOEHQXG‰›iIKNTEUY_N·EHP>¸ { • {   ƒ¹F„š} ¹~y§£ ¹• £ IKNTEUY_N EHPŠInA([U[sbiA>‘]GTA>b A>qXA(WphIKNiA(WRA&A e˜Y(A(d˜Lg‡™QFW ¹¥} ®£ k¶lmQFGTPVA(t`aTA(G8LR[UpF›;InA GTA>A(b&Z#BTWOZXGiY_N’Y(aiL Ÿ QFEUGTEHGTDŠLRNTAod\QFEUG`LRP ¹c}”®£ k Y G8p…PRaTY_N&d]Z«LON—IKEU[H[‰biQT› ZuGTb EULŒbTQ˜A>P0GTQXL0NTZqXA#LRQd]ZXPVPŒLONTWVQFaTDFN q¹ — ˜ k Y dCQXPRPREUBT[HA5Y_NTQFEHY>Aj‡™QFWZJBTWRZXGTY_N Y(a˜L*EUP;PRNTQIKG—EHG…zEHDik ‚ kª½˜k 3

z"#g!



y

0

v



x

0

u

EHDFaTWVA ‚ k i¸ )ƒeVpLp3f_jL†hJl€yVŠ p3^}eJj:nbch Š p3^_eJj:nbgm:d%hQ`:†Qm   y  y w   ‰¸=@ AY>QFGTPREUbTA(WKGTA ehLŒZŠPREUS?di[HAŒd\QImA>W*QX‡ ¹ ›]LONiArPVt`a]ZXWRAuk sPREUGTD Y†ZuWVLOA>PREHZXG-Y(QhQFWRbTEUG]ZuLRA(P(›TInAN]Z†qFAu¸ |}€¹ w – ™v R = „ y E  ™v R = „} ™v w • = w „y E ƒ‚«v = „ Ž;NTA;[HZXPVLzAfe˜dTWRA>PRPVEHQFGcDFEMqFA(P>›X‡™QFWˆLONTA;Y>aTWVqXA(P=QFGjLRNTA ¹ dT[ ZuGTAnLRN]ZuLS?ZXd5LRQŒqFA>WVLOEUY†ZX[ [HEUGTA(P ™v R = „} ‚K „ QFW‹LRQcNTQFWRE \(QFG8LOZX[‰[HEUGTA(P   ™v R = „=}  Kf„ QFG-LONTA dT[HZXGTAX¸ vxwn• = wn} ‚KVR = } ‚« v K IKNTEUY_NZXWRAsN8phdCA>WRB\QF[ ZXP>›iZuPmEH[U[HaTPLOWRZuLOA>b#EUGJzEUDTk ‚ Mk ikxWVQFS LONiEHPšSgZXdidTEHGTD0InAŒPRA>A LONTZuL2N]ZX[M‡CQu‡\LRNTA ¹ dT[ ZXGiA;SgZXdiP=QFG8LOQ0LONTA;A>G8LOEHWVA dT[ ZuGTAX›8B\A(Y(ZXaTPRAKEM‡\InAKWRA>PVLOWVEHYfL LONiA#quZX[UaTA(PQX‡ ¹ LRQ v ­  QFW0LRQz= ­  ›ImA#PVLREH[H[zY†ZXGQFBiL_ZuEHG ZX[H[LONTA#dCQXPRPREUBT[HA quZX[HaiA(PsQX‡  ZXGTb xk “˜EHS#EH[HZXW;ZXWVDFaTS#A(G8LOP*ZXdTdT[MpLOQ?PRaTB˜¡¢WRA>DFEHQFGiP*QX‡zLONTA ¹ dT[HZXGTAX› IKNTEUY_N’LONTWVQFaTDFN }  ƒ¹F„;} ¹ w ZXWVA AVEUG xZuLRA(xb CgLRQJY(QqXA(WŒSjaiY_N&[ ZXWVDFA(WsWRA>DFEHQFGiP QFGLONiA di[ ZXGTAuk2]QFW;EHGTPL_ZXGiY(AX›TLRNTAWRA>DFEHQFG-A>GTY([UQFPRA>b—B8pLONiArPVt`a]ZXWRA ¹ ¸  v gR  =    

½‰



 "!$#%!          vB                                                                                                                                     2l 2                                                                                                                         Au C D 0  2

y

   

c

                  

d 0

b l a

x

zEUDFaTWRA k ˜¸ y )ƒ eVpLp3f}j:†hJlea ‰`LeVdgn dgn)†QfihQj0hQj0bgmLn yVŠ p$^_eJj:n bchbgm:n Š p3^}eJj:n bgmLdghQ`:†Qm w EHbiA(G8LOEM‘]A(b-B8pLONTAY>QFWRGTA>WRPsZuL ¹ ¸ ™v R = „ £ ¸  cR_8O„ R ¤ ¸  cR œO„ R ¦ ¸ ƒ R ƒ„XR ¸ œR_8„ QFGrLONTA ¹ dT[HZXGTAX›«IKNTEHY_No[HEUA(P A(G8LOEUWRA>[UpQFGrLONTA2‘]WRPLt`a]ZXbiWOZXG8L  aTdTd\A(WˆWREUDFN8Lt`a]ZuWVLOA>W dT[HZXGTA „ ›TDFAfLOPKSgZudTdCA>bLOQcLONTAWRA>DFEHQXGEHbTA>G`LREU‘]A>b—B8pJLRNTAdCQXEHG8LOP ¸  R  „ ¸   Jw R_FO„ R ¸ ƒ$ R ‚  w O„ R ¸ •  Jw R_8O„ R 4¸ œ R_8„ IKEULRN LONTA&Y>QFWRWVA(PVdCQFGibTA(GTY>A £ — RO¤ — kRO¦ — ER — —k Ž;NiEHPWRA>DFEHQXG AfehLRA(GTbTP~QžqXA(WsLONTAr‘]WRPL*LInQJt`a]ZXbTWRZXG8LOP*QX‡LONiA dT[ ZuGTA aTdTd\A(W*N]ZX[M‡dT[HZXGTA k ‡ InALRNTEHGi^?QX‡ˆLONiA0PRt`a]ZXWVArQXGJLONTA ¹ dT[ ZuGTA0ZXP;Y>QžqX A(WVEHGTDŠLONiA0 A(G8LOEUWRAŒ‘]WVPVLKt`a]ZXbTWR„ ZXG8? L dT [HZX— GTAXk ˜ „ › LONiA(G EMLOPEHS?ZXDFAŠQFG LONiA dT[ ZuGTAŠIKEH[H[=Y>QqFA(WrLONTA#A(G8LREHWRA#aTdTd\A(WrN]ZX[M‡ Y GTQuLONTA>WKImZ†pLOQcPRA>ArLRNTEHP;EUP‹LOQ#aTPRAd\QF[ ZuW‹Y(QhQFWRbiEHG]ZuLRA(P>¸ |}€¹ w –  A>E  }  w A>E  –  }  w R  }€‚  PRQ  µ  —   µ ‚  ›\LON]Z«LŒEHP>›CLRNTAjWOZuGTDFAjQX‡=quZX[UaTA(Ps‡™WRQFS \(A>WRQJLRQ  EHG#LONTAŒZXWRDFaiS?A>G`LnQX‡ ¹ EUPnS?ZXdTd\A(bgLRQŠZoWRZXGTDFA*QX‡quZX[HaiA(Pn‡™WVQFS \(A>WRQ5LRQ ‚  EUGgLONiA ZXWVDFaTS#A(G8LKQX‡ k ¸ Y PrZXGTQXLRNTA(WrAfeiZXS#dT[HAjInA#AfeiZXS#EHGTAŠLONiA#EUG8qFA(WVPRA?QX‡nLRNTA#dTWRA ¡ qhEHQFaiPr‡™aTGiY>LOEUQFG‰›ˆLON]ZuLoEHP>›LRNTAgPVthaTZXWRAJWVQ˜QuL†k *PVEHGTD—Y†ZXWLOA>PRE ZuG Y(QhQFWVbTEHG]Z«LOA(P>›InA N]Z†qFAu¸ |}¨¹ – ~wm}€¹j–  xw2•  w „y E ‚   } vcy ZE = – v-}  xw2•  w O„ R = }‚   ]QFW2LONTA*Y(aTWqFA(P;QXG?LONiA ¹ dT[HZXGTAsLON]ZuLnS?ZXd?LRQ5PVLRWOZXEUDFN8LnqXA(WLOEHY(ZX[\[HEHGiA(P  ™v R = „} ‚K „ QFWnPVLRWOZXEUDFN8L‹NTQFWVZE \>QFG8L_ZX[\[HEUGTA(P   ™v R = „}  K „ QXGJLONTA dT[ ZuGTAX›`ImAŒIKEU[H[\N]Z†qFAu¸ = = w J} ‚K —  } — xwK • ¯ }¶v ‚ ‚K  Kw    y‚ 

l

l













"!

#!

&

  







#!





!

$%!



3

½

z"#g!



y



v

0

zEUDFaTWVA ‚ k ˜¸ 



x

)ƒeVpLp3f}j:†{hJl

u



0

   y 

yJŠ p3^_eJj:nbch Š p3^_eJj:nbgm:dghQ`:†Qm

yL

}  K — } ‚ = K — ¯ =  w Kw •  Kw }|v IKNTEUY_N ZXWVA#dTZXWOZXB\QF[HZXP(› ZXPEU[H[HaiPVLOWRZuLOA>b&EHGzEHDik ‚ k ˜k ? G LONTEUPY†ZXPVAX›LRNTAcA(G8LOEUWRA ¹ dT[HZXGTASgZudTP*QXG`LRQ?NTZX[U‡zQX‡zLRNTA dT[HZXGTAu›\PVEHGTY>ArLRNTAqXZu[HaTA>PsQu‡ ‚K ZXGib  K ZXdTd\A†ZuW PRt`a]ZuWRA(b EHG LONTA#‘]G]ZX[2A(t`a]Z«LOEHQXGTP(›ˆPRQ…LON]ZuLrLInQ—quZX[HaiA(PrQX‡;QFdTd\QFPVEULOAcPVEHDFG Y(QFWVWRA ¡ PRd\QFGTbLOQ—LRH NTAgPRZXS#A?Y>aTWVqXAXk·Ž;NiEHP5EUP0IKN]ZuL5InAgInQFaT[Ub Afe˜d\A(YfL†›=DFEMqFA(G LON]Z«L5LONiA ‡™aTGTYfLOEUQFG ¹ w EHPjLRNTA-EHG8qFA>WRPVA·QX‡sLONTA‡™aTGiY>LOEUQFG ¹ w k Ž;NTEHPcEHPcZ&LOWVQFaTBT[UEHGTD’‡œZuY>L†› NTQInA>qFA>W(›TB\A(Y(ZXaTPVAsInA~ZuWRAsGTQXLšPRaTWVA~Z«LšIKNiEHY_N#QX‡ LRNTAsLInQ5NTZX[UqXA(P2QX‡ LRNTA dT[ ZXH GiA InAsIKEU[H[iA>GTbgaid‰kŽ;NTEUPšNTZXPmZuY>LOaTZX[H[MpoLRQobTQ0IKEMLONcLONTA;‡œZXYfLšLRN]ZuL2LONiAK‡™aiGTY>LREHQFG ¹ w EHPrSjaT[MLOEMqXZu[HaTA>b  EULrEHG8qFQX[UqFA>PŠZ—GiQFG˜¡EUG8LOA(DXA(WrdCQInA(W(›2ZuGTb NTA>GTY(AgLRNTAg[UQFD8ZXWVEULRNTS [HaiWR^`P0PRQFS#A>IKNiA(WRAcEUG’EULRPŒbTA>‘TGTEULREHQFG „ koŽˆQ-PRA>AjLONTEUP0S?QFWVAjY([UA†ZXWV[UpX›CInA#aiPRAcdCQX[ ZXW Y(QhQFWVbTEHG]Z«LOA(P>¸  |}€¹ H w – CA  }  H w A w  w –  }  H w R  } y "R }€ R({ ‚ PRQcLONiA(WRArZXWVAŒLImQ#d\QFPRPVEHBT[UA0Y_NTQFEHY>A(P;‡™QFW‹LRNTA0qXZu[HaTA>PsQu‡ ›iDFEUqhEHGiDŠWREHPVAŒLOQŠLONiALInQ d\QFPRPVEHBT[UArS?ZXdTdiEHGTDFP>k ? G—LRA(WVS?PsQX‡=WVA†ZX[ G`aTSjB\A(WVP(›xLONTEUP*Y>QFWRWVA(PRd\QFGTbiP*LOQ#LONTA‡œZXYfL LONTZuLnLRNTAsWRQhQXLšQX‡ v w EUP ®Œv k ? GgQXWRbTA>WnLOQrWRA>S?QqXA*LONiA~ZXS5BTEHDFaiEULpF›FInA~GiA(A(bJZXD8ZXEUG LOQ EHG8LRWRQhbTaTY(A…BTWRZXGTY_N Y>aiLOP>Bk ™qhEHbTA>G`LR[UpX›mLONTA-BTWRZXGTY_N d\QFEUG`LRPcEHG LONTEUP?Y(ZXPRA—ZXWVA ZXD8ZuEHG ¹…}  ZuGTb z¹ — ˜ ›B\A(Y(ZXaTPRA#QX‡šLONTAcEUG`qXQF[UqXA(S#A(G8LrQX‡šLONTAŠ[UQFD8ZXWVEULONiS EUG LONiAŠbTA>‘]GiEULOEUQFG’QX‡ ¹ IKEULRN £ ¸ WRA(ZX[»k Y G`p·dTWRQXdCA>WŒBTWOZuGTY_N Y(aiL Ÿ QFEUGTEHGiD?LONiA(PRAjLInQ d\QFEHG8LOPsWRA>S?QqXA(P~LRNTA5ZuSjBTEHDXaTEULp-ZuGTb·WVA(GTbTA>WRP~LRNTAo‡™aiGTY>LREHQFG—PREHGiDF[HA ¡¢quZX[HaiA(b‰k;]QFW AfeiZXS#dT[UAX›˜LRNTA0PVLOZXGTb]ZuWRbY_NTQFEUY(A0QX‡LRNTA0d\QFPREMLOEUqXA v Z«e˜EHP;ZuPmLONTA0BiWOZXGTY_N-Y>aiL‹IKEULRN S?ZX dTdT&EUGTµ DoLR‚ Q5LONTA>A~thaiaTEUdTqud\ZXA([HA>W‹G8N]LrZuLR[U‡Q…LRNTA#Y_NT&QFEHµ Y>A QFW}!g8­ „ ›ˆ[HA(ZXQXbT‡P0LRLONTQ-A LONTA#dT[ A(ZuG8GTLR‰A EHWRœhA LONT¹ AŒdTPR[ ZXZXS#GiAA Y_NTQFEUY(A~‡™QXW‹ZjBTWRZXGTY_NY(a˜L‹IKEULRN œ ‚  cµ  ¯ § A>t`aTEU8quZX„ [UA(G8LmLRQj LONTAŒY_NiQFEHY>A }”{ž„ › [HA(ZXbTPjLRQ’LONTA-A(G8LREHWRA ¹ dT[HZXGTAJS?ZXdTdTEUGTD’LOQ’LRNTA-[HQInA(WŠN]ZX[M‡    µ ‚  QXW  |8„ Qu‡LRNTA dT[ ZXGiAXk 















 















½



 "!$#%! 

‰¸2]QFWKZXGTQuLONTA>WsA eiZXS?di[HAŒInArY>QFGTPVEHbTA>WKLRNTA0‡™aTGTYfLOEHQXG

  

|}  œ¹8„2} ¹{ ZXGTb—ZXPV^gIKN]ZuLsEHP‹LRNTAEHS?ZXDFA*QX‡ZcY(EUWRY>[HAŒQFG-LONiA ¹ dT[HZXGTAŒLONiWRQFaTDXN…LRNTA0SgZudTdTEHGiD B8p  ƒ¹8„ QFG·LRNTA dT[ ZuGTAXkKŽ;NTAoA(t`a]ZuLREHQFG·‡™QXW~Z#Y(EHWVY([UArQXG·LONTA ¹ dT[HZXGTAIKEULON—EULRP Y(A>G8LOA(W*ZuL  v‚KJR = K „ ZuGTb—WRZXbTEUaTP gEUP(¸  vJ• v‚Kf„ w y€ = • = K „ w }  w – £\ v w y = w „y§¤Ovcy¥¦ = y j}¨ »‚ k°© ‚F„ IKNTA>WRALONTAd]ZXWRZXS#A>LOA>WRP 2£ R_J¤ R_Q¦ R ZuWRAWRA>[ ZuLRA(bLOQ ‚v KJR = KVR #B`p H ¸ £Š}  { w R ¤K} • ‚« ‚v w K R ¦K} • ‚  = w K R j} v wK  y w = Kw • { *PVEHGTDŠLRNTA0‡™QF[H[UQžIKEUGTDjWVA([ Z«LOEHQXGTP(¸ v-} ¹~y ‚ ¹ R = } ¹‚• E ¹ R2vxwzy = wn}¨¹ ¹ ZXGTb-LONiA‡œZuY>L;LONTZuL €} Šy E  } Q{ 5X¹o– |} ?• E  } Q{ 5 ¹ ›TLRNTA(WVA>‡™QFWVA ¹*y ¹ R  } • E } ¹0E• ¹ R xwzy  w‹} |} { y } } ‚ ‚X¹ ¹ ‚ ‚ ¹¹ ¹¹ InAo‘]GTb…LON]Z«LsLRNTAjZuBCQqFArA(t`a]Z«LOEHQXG…‡™QFW*ZcY(EHWVY([UArQXG…LRNTA ¹ dT[ ZXGiArEUP;LOWOZuGTPV‡™QFWVS?A>b LOQ £~y¥¤ g• ¦  y \  w y  w „2}¨ »‚ k°©F© „ IKNTEUY_NJN]ZXPnAfeiZXY>LR[UpcLONiA~POZuS?AK‡™aTGTYfLOEHQXG]ZX[]‡™QFWRS EUG?LONiA*quZXWREHZXBT[UA(P  ZXGTb cZuPnLONiA A(t`a]Z«LOEHQXGg‡™QFWnLRNTAŒY>EHWRY>[HA*QFGgLONiA ¹ dT[ ZXGiAX$› ™2txk »‚ kª© ‚X„ ›hEHGgLRA(WRS#PmQu‡LONTA~quZXWVE ZXBi[HA(P vS?ZXZXdTGTd\b A(=\bkLOQ#xWVZcQFS4Y(EHWVLOY(NT[UAŒEUP~QFImG-AŠLONTY>AQFGTY>[HaTdTbT[HZXAjGTAXLRN]k ZuLŒLRNTAŠQFWVEHDFEUG]ZX[ Y(EUWRY([UA5QFG’LRNTA ¹ dT[ ZuGTA5EUP Y WRA([HZuLOA>b-SgZXdidTEHGTDŠEUP‹LON]Z«L*DXEUqFA>G-B`pLRNTA0‡™aTGTYfLOEHQXG ƒ¹• £h„ |}  œ¹8„2} ƒ¹• ¤f„









      !"#$ % &" '  (   #)  (+*,.-0/,-012"2 3 " ' !"4

  #5 6 (78-9:-;:-=@?BA (=@C =D? EF 6=@GHD I=J? " > "C HD 6#KC L6 40 & HJ : 60 6 " M G #)  6GN  5? "O=D?AP ( (?AP 6?.LQR S !"TH@HD":U=D? E 6HJ :=@"T?VC8 W 6 6?  6#X( ? L =@HDYZC8 (0 C HD=D (A\[ 9]_^%;6]a`cb.78deEHWRY>[HA0LOQ?ZcY(EHWVY([UAXkšŽQ#PRA>AoLONiEHP(›TInA5d\A(W‡™QFWRS LONTA‡™QF[H[UQIKEHGTD Y_N]ZXGiDFA(PsQX‡ˆqXZuWRE ZuBT[HA>P(¸ ¹  }¨¹r• ¤ ¸sPRNTEM‡ LKQFWREUDFEHGgB`p…B ¹   } ¹ {  ¸5S?ZXdTP;Y>EHWVY([HA>P‹LOQ#Y(EUWRY([UA(P |}x¹   y¶{ ¸o[UEHGTA(ZXW‹PRY(ZX[HEUGTD#B`p R PRNTEM‡ LKQFWREUDFEHGJB8p • { IKNTEUY_N’dTWRQqXA(PŒLONTZuL~LRNTA5S?ZXdTdTEUGTDgB8p ”} ƒ¹o•¥£h‘„ 5Tœ¹o•§¤f„ EUPŒZX[UPRQJZ#SgZudTdTEHGiD QX‡ ZY(EUWRY>[HAKLOQoZoY(EUWRY>[HAX›`PVEHGTY>A*LONiA*QFGi[UpcWRA>[ ZuLREHQFGŠLRN]ZuLnEHG8qFQF[MqFA>P‹ZSgZXdidTEHGTDrEHP2LONiA PRA>Y(QFGib Y_N]ZXGTDXAgQX‡nqXZuWRE ZuBT[HA>WP œLRNTA#QXLONTA>WrLInQ·S#A(WVA([Mp PRNTEM‡ LoQXWrPVY†ZX[UA#LRNTA#Y(aTWqFA IKEULRNTQFaiL‹Y_N]ZXGTDFEUGTDjEMLOP‹PVN]ZXd\AXk Y [U[\LRN]ZuL;WVA(S?ZXEHGTPšLOQŠbTQŠEUPn‘]Gib-LRNTA~quZX[UaTAŒQX‡ LONiA PRY(ZX[HEUGTDŠd]ZXWRZXS#A>LOA>W k npWRA>t`aTEHWVEHGTD5LRN]ZuL;LRNTAŒ‘]G]ZX[A e˜dTWRA>PRPREUQFG…EHP‹A>thaTZX[‰LOQŠLONiA QFWVEHDFEUG]ZX[\QFGTAX›TInA‘]GTb‰¸ € } \¹  y¶{Œ} ¹ {  y¶{Œ} ¹• { ¤ y¶{Œ} ¹r¹r•• £¤ – }|¤m• £ IKNTEUY_N¥Y>QFS?di[HA>LRA(P5LRNTA…ZXWRDXaTS?A>G8L†k Y DFA>GTA(WRZX[HE \†ZuLREHQFGQX‡sLONTEUPjEHPjLRNTASgZudTdTEHGiD dTWVQ˜bTaiY(A(b…B8pLONTAPVQu¡Y(ZX[H[UA(b QF BiEHaTP;‡™aTG8LOEUQFG  PVA(EA ”=WRQFBT[UA(S „ k 3

z"#g!





                                                                                                                                                 zEUDFaTWRA ‚ k ˜¸ )ƒeVpLp3f_j:†hJlbgmLnqagmLeJ„:nX„–dgn)†QfihQj bgm:dghQ`L†Qm    y   W y w  b

c

0

a

l



x

                                                                                                              v

y

B

A C

0

u

1 l2



hQj bgmLnšyJŠ p3^_eJj:nšbch bgm:n Š p$^_eJj:n

~Z†qhEHGTDŠPLOaTbiEHA(bB\QXLRNJLONTAŒS?ZXdTdiEHGTDoQX‡ LONTA~‡™aiGTY>LREHQFG ZXGTbJLRNTA~‡™aTGTYfLOEUQFG ›¹ w ImA5Y†ZXG’Y>QFGTPVEHbTA>W*LONiA5S?ZXdTdTEUGTD?diWRQhbTaTY(A>b’B8p—LRNTA5Y>QFS#J{ 5XdC¹ QFPVEULREHQFG-QX‡LRNTAoLInQ x ‡™aTGTYfLOEUQFGTP(›TLRN]ZuLKEUP‹LONTA0‡™aTGTYfLOEUQFG‰¸ { |}  œ¹8„2} ¹w Y P…ZXG¶A eiA>WRY>EHPRAu›ŒY(QXGTPREUbTA(WLONiA WVA(DFEUQFG QFG LONiA ¹ dT[HZXGTA&PRNiQžIKG€EHG¶zEUDTk ‚ k i› Y(QXGTPREUPVLOEUGTDcQX‡ˆLONTA0A>G`LREHWVAraidTdCA>WKN]ZX[U‡ˆdT[HZXGTA0A eiY>A(diLs‡™QFWKZŠPRA>S?EUY(EUWRY([UAŒQX‡WOZXbiEHaTP  



 "!$#%!  Y(A>G8LOA(WVA(bgZuL=LONTAKQFWVEHDFEUG‰k Ž;NTAKSgZudTdTEHGiD0QX‡CLRNTEHP=B8pjLRNTA;‡™aTGTYfLOEHQXG {Q5X¹ dTWRQhbTaTY>A(PšZ PRA>S?EUY(EUWRY([UA;Y(A>G`LRA(WVA(b-ZuL2LONiA*QFWVEHDFEUG‰›FIKEULRN?WRZXbTEUaTP Q{ 5  ›hIKEMLONcLONTAsd\QFEHG8LnZuLnEHGi‘]GiEULp S?ZXdTdTEUGTD#LRQ?LRNTAoQXWREHDXEHG-QX‡LRNTA5Y>EHWRY>[HAuk;Ž;NTAo‡™aTGiY>LOEUQFG ¹ w dTWRQhbTaTY>A(P~Z#‡™aT[U[ˆY>EHWVY([HA Y(A>G8LOA(WVA(b&Z«L*LRNTAoQXWREHDXEHG‰›hIKEULON…WOZubTEHaTP knŽ;NTA5GiA>LsWRA>PRaT[ML*‡™WVQFSZXdTdi[UphEHGTDcLONiA LInQ?S?ZXdTdTEUGTDFP;EUP;PRNTQIKG·EUG…zEHDTk ‚ k Q{ PR5 A( Arw ZX[UPR'Q ”=WRQFBi[HA(S „ k ‰¸@ArGiAfehLsPVLOaibipJLONiArS?ZXdTdiEHGTDŠEUS?dT[UEHA>bgB8p…Zj‡™aTGTY>LREHQFGJIKNiEHY_N EUqXQF[UqXA(PKB\QXLON-d\QžInA(WVP~ZuGTb—EUG8qFA(WVPRArdCQInA(WVP*QX‡ ¹ ¸  ƒ¹8„2}¨¹Xwzy { ¹w ™ze˜dTWRA>PRPREUGTDJLONiA5Y(QXS?dT[UAfe-quZXWVE ZXBT[UA ¹ EHG—LRA(WVS?P*QX‡=EULRP*WVA†ZX[ZXb’EUSgZuDFEHG]ZuWVpJdTZXWVLRP ¹o}|vcy EZ=#[HA†ZubTP;LOQT¸ { = y E ‚«v = {s• { =  ƒ¹F„š} ™vxwš• = wO„ {my ™v w y w „ w v w y w „w ZXGTb PVA>LRLREHGTD…ZXPaTPVa]ZX[LRNTAj‡™aTGTYfLOEHQXG  A>thaTZX[LOQ = E  = InA ‘]GTb-‡™QFW‹LRNTAWRA†Zu[ ZXGTb-EHS?ZXDFEUG]ZXWVp#d]ZuWVLOƒPK¹8QX„ ‡ ¸ } ™v R „ˆy ™v R „ { = R   v R = „=}€‚«v = {K• { = ™v R = „} ™vxwš• = w_„ {my ™v w y w „ w ™v w y w „ w Y PrZXG&EU[H[UaTPVLRWOZuLREHQFG—QX‡2LONTAcS?ZXdTdTEUGTDJdTWVQ˜bTaiY(A(b B8p  œ¹8„ ›‰InAcY(QFGTPVEHbTA>WrZJY(aTWqFA QFGLONiA ¹ dT[ ZuGTA0bTA(PVY(WVEHB\A(b…B`pLRNTAd]ZXWRZXS?AfLOWVEHY~‡™QFWVS—¸ v „2} uA Y(QFP  „XR =  „=} «A PVEHG  „OR •  µ ‹µ  »‚ k°©X¯ „ IKNTA>WRA  R_£ ZuWRA0WRA(ZX[ d\QFPVEULOEMqFAŒY>QFGTPL_ZXG8LO6P œTLONTEUP;Y(aTWqFAEHPmEH[H[UaTPVLRWOZuLRA(b?EHG-zEUDTk ‚ k { k Ž;NTEUPsY>aTWVqXAoEUP;SgZudTdCA>bLONTWVQFaTDFN  ƒ¹F„ LRQ#ZcY>aTWVqXAoQXG…LRNTA dT[ ZXGiA0DFEUqXA(G-B8pC¸ {  „ }  w A w Y(QXP »‚ „  {ny  A    {    „ }  w A w PREUG »‚ „ {;• »‚ k°©8½ „  A   IKNTEUY_N—EUPKZX[HPVQ#EU[H[UaTPVLRWOZuLRA(bJEUG—EHDTk ‚ k { k C¸ Y P0QFaiW~‘]G]ZX[AfeiZXS#dT[HArImAŠIKEU[H[ Y(QFGiPREHbiA(WŒLONiAjSgZudTdTEHGiDFP~EUSc¡ dT[UEHA(b…B8p—LRNTA5N8phd\A(WRB\QF[UEHYrZXGTb·LRWREUDFQFGTQFS#A>LRWREUYŒ‡™aTGTY>LREHQFGiP(›xIKNTEHY_N&ZuWRArY([HQXPRA([Mp-WRA ¡ [ Z«LOA(b k @A&BCA>DFEHG B8p A eiZXS?EUGTEHGiD LONTA&S?ZXdTdiEHGTD EUS?di[HEHA>b B8p LRNTA N8p˜d\A(WVBCQX[HEHY Y(QXPREHGiAX¸ A  y A G  } A  Y(QFP  = „ y EPREUG  = „V„ y A G  Y>QFP  = „• EPVEHG  = „R„ |} Y>QFPRN œ¹8„ } ‚ ‚ ‚ = > Y F Q R P N ( Y X Q P =  = R P U E T G N R P H E – ™v R „} ™vC„  O„ R  v R „=}  vC„ G  = „ 



  





















































  





3

{

z"#g!

1

Mapping under f(z)=z^2+1/z^2 In[8]:= ParametricPlot@82 Exp@t ^ 2  5D Cos@tD, 2 Exp@t ^ 2  5D Sin@tD[ ZuLREHQFGTP>›TaTPVEHGTDcLONTArdTWVQFdCA>WVLREHA(PKQX‡LONTALOWVEHDFQXGTQFS#A>LOWVEHY0ZuGTb N8phdCA>WRB\QF[HEUY0PREHGiAoZuGTb-Y(QFPVEHGTA0‡™aTGTYfLOEUQFGTP(›TInA0‘]GTb v w y = w } PREUG wž  „y Y(QFP w«C„=} { Y>QFPRN w   „ PVEHGTN w   „ IKNTEUY_N EHP0LRNTA?A>t`a]ZuLOEUQFG ‡™QFWrZXGA>[H[UEHdTPVAjIKEULON AfehLRA(GTb ‚u£&}‚ Y(QXPRN   „ QFG LONTA v Z«e˜EHPsZXGib ‚X¤K} ‚ ¼ PVEHGTN   „ ¼hQFG-LONi0A =ZžeiEUP(›\ZXPKEH[U[HaTPLOWRZuLOA>b…EUG·EHDTk ‚ k {F{ k “˜A>LVLOEHGiD  }  K ¸nY(QFGTPL_ZXG8L(›CInA5PRA>AoLRN]ZuL*Y(QFGi‡™QhY†Zu[ˆA>[H[UEHdTPVA(PsQFG—LRNTA ¹ dT[ ZXGiArIKEMLON-‡™Q˜Y>EZ«L ¹o}®c{ DFAfLKSgZXdidCA>b…LRQ#PLOWRZXEHDFN8LKNTQXWRZE \>QFG8L_ZX[ [HEHGiA(P‹QFG-LONiA di[ ZXGTAu k “˜EHS#EH[HZXWR[MpF› vPREUG w • Y>QFP = w } Y(QFPVN w   „z• PVEHGTN w   „=} { w  C„ w   „ IKNTEUY_N’EHPKLONTAoA(t`a]ZuLREHQFG—QX‡2ZgN8phd\A(WRB\QF[HZ#IKEULRN·[UA(GTDXLRN·PVY†ZX[UA(P ‚u£g} ‚ ¼ PREUG   „ ¼hQFG LONiA v Z«e˜EHPjZuGTb ‚X¤g} ‚ ¼ Y(QFP  C„ ¼CQFG LONišA = Z«e˜EHP(›ZXPjEH[U[HaTPLOWRZuLOA>bEUG zEHDik ‚ k {F{ k “˜AfLRLOEUGTD ’} ‚K ¸;Y>QFGTPL_ZXG8L†›CImAjPVA(A5LRN]ZuL~Y(QFGi‡™QhY†Zu[N8phdCA>WRB\QF[ ZuAoQFG—LONTA ¹ dT[ ZXGiA IKEULRN·‡™QhY(EˆZuL ¹#} ®c{ DXA>L*SgZXdidCA>b·LOQJPLOWRZXEHDFN8LsqFA>WVLOEUY†ZX[ˆ[HEUGTA(PsQFG·LRNTA dTG2[HZXH GTAXk Ž;NTAKEHS?ZXDFA>PQX‡CA([U[HEHdiPRA(PZXGTbcN8p˜d\A(WVBCQX[ ZXA;QFGŠLRNTA ¹ dT[HZXGTA‹LRNTWRQFaiDFN |} PREUG œ¹8„ LOQgNTQFWRE \(QFG8LOZX[zZuGTb’qFA>WVLOEUY†ZX[[HEUGTA(P>› WRA>PRd\A(YfLOEUqXA([MpF›‰QFG’LRNTA dT[ ZXGiA5EHP*EH[U[HaTPLOWOZ«LOA(b EHG…zEUDTk ‚ k {ž‚ k Ž;NTEHPKA eTZuS?dT[UAbTA(PVA(WVqXA(PŒY>[HQFPVA(W;PVY(WRa˜LOEHG8pX›\B\A(Y(ZXaTPVArInA5ZuWRAWRA(ZX[H[MpJEHG8LRA(WRA>PVLRA(b EHG…QFBiLOZXEHGiEHGTDŠLONiArquZX[UaTA(PsQX‡ ‡™WVQFS ¹ ›\BTaiLsImAobTA(WVEUqFA>b—LRNTAoWVA([HZuLOEUQFGTPKBCAfLImA>A(G v‡™aTGTZuYfGTLOb EUQFG= QuB8‡ p DFkgQXEHGTŽ;D&NTEHEUPrG SgLRNTZ†p&A…EHNTG8ZqFqXA>AgWRPRNTA…EUbTbTbTEUWRA>A(G YfLOdTEUQFWVQFG‰BT›2[HLOA>N]S?ZuP0L#IKEUP(EM›šLON B`p SjAaTe˜[ULRdTEUWRquA>ZXPR[UPRaTEUA(GTbTD GiA(¹ PRP>ZX›P#PVQZ InAoA eTZuS?EUGTAŒ LONTAA eidiWRA(PVPREUQFG·QX‡ EHGJ LRA(WVS?PKQX‡ ¹ EUG-S?QFWVA0bTA>LOZXEH[ƒ¸ G ¹5} PREUG  Œ„=} A • ‚ E A – A  •§‚ E ¹Œ• A G  }¨r– 







3



z"#g!

A  } E ¹s® “ {s• ¹ w } E ¹~® “ ¹ w • { IKNTA>WRA5InAjN]Z†qFA5aTPRA>b’LONTAoPRQF[UaiLOEUQFG—Qu‡LONTAoPRA>Y(QFGTbh¡QFWVbTA(WŒd\QF[Mp˜GiQFS?EHZX[‰A>thaTZuLOEUQFG LOQcQFB˜L_ZXEUGJLONTA[ ZuPVLKAfe˜WVdCA>PRPREUQFG‰k=@¶EULRNLONTEUP(›iInAoQXBiL_ZXEUGJLONTAA eidi[HEHY>EUL;A e˜dTWRA>PRPREUQFG QX‡ ZXPsZj‡™aTGTY>LREHQFG-QX‡ ¹ ¸ |} { E [HG E ¹~® “ ¹ w • { }  y { E [HG ¹~® “ ¹r• { “ ¹*y|{ ‚ ‡™WRQXS IKNTEUY_N§InA—Y>QFGTY>[HaTbTALRN]ZuLŠInA—bTQ GTA>A(b LOQ&ImQXWRWVp§ZuBCQFa˜LcBTWOZXGiY_N¥d\QFEHG8LRP ZXGTb&BiWOZXGTY_N&Y>aiLOPŒ‡™QXW*LONiEHP~PVEULRa]ZuLOEUQFG‰k “˜dCA>Y(EM‘]Y†ZX[U[UpX›\LRNTA(WVAŠZXWRAoLImQPVthaTZXWRAŠWVQ˜QXL ‡™aTGTYfLOEUQFGTPšEHG8qFQF[MqFA>bZXP2ImA>[H[\ZXP2LONTA*[HQFD8ZuWREULRNTS ‡™aiGTY>LREHQFG‰›hZX[U[]QX‡ IKNiEHY_NJEUG`LRWRQhbTaTY>A BTWRZXGTY_N dCQXEHG8LOP>k Ž;NiAJLImQ PRt`a]ZuWRA-WRQhQXLOPoEHS#dT[Up LRN]ZuLjLRNTAJd\QFEHG8LOP ¹ } ®Š{ ZXWVA BTWRZXGTY_Njd\QFEHG8LRP(kzŽ;NiAmBTWRZXGTY_Njd\QFEHG8LRPQX‡iLONTAn[HQFD8ZuWREULRNTS¨Y>QFWRWVA(PVdCQFGib5LOQsLONTAšqXZu[HaTA>P \(A>WRQ§ZXGTb EUGi‘]GTEMLpFk np EHGTPVdCA>Y>LOEUQFG‰›;InA&PRA(A&LRN]ZuLJLRNTA&Afe˜dTWVA(PRPVEHQFG¶aTGibTA(WLONiA [HQXD8ZXWREMLONTS!ZXB\QqFArEHP;GTAfqFA>W \>A(WRQi›]BCA>Y†ZXaTPVAX¸ ¹*® “ ¹ w • {*}¨r– ¹Xwm}¨¹Xwš• { IKNTEUY_N#Y(ZXGTGTQuL=BCA;PRZuLOEUPV‘]A>bj‡™QFW=ZXG8poqXZu[HaTA‹Qu‡ ¹ k ŒGjLONTA;QXLRNTA(WzN]ZXGTb‰›F‡™QXW |¹ — ˜ InAoN]Z†qXAX¸ H {  ¹*® “ ¹ w • {*}¨¹*® ¹ {K• ¹ w  w }¨¹~®¥¹  {K• ‚X{¹ w @y IJIJI  IKNTA>WRA?InAgNTZqXAJaTPVA(b LRNTAgBTEUGTQFS#E ZX[Afe˜d]ZXGiPREHQXG LOQ—DFA>LrLONTA#[ ZuPVLoWRA(PVaT[UL(kJ@¶EULRN LONiArdi[HaTP;PVEHDFG‰›TLRNTA[ ZXPL;Afe˜dTWVA(PVPREHQXG·B\A(Y(QXS?A>P ¹~y§¹  {K• ‚X{¹ w y IJIJI  ‚X¹ ‡™QFW 0¹ — ˜ IKNTEU[HAŒIKEULRNLONTAS#EHG`aTP;PREUDFG‰›TEMLKBCA>Y(QFS#A(P ¹• ¹  {K• ‚X{¹ w y@IJIJI  ‚u{ ¹ ‡™QFW ¹|— ˜ Ž;N`aTP(›‹LRNTA—quZX[UaTA(PŠIKNTA>WRA·LRNTA—ZXWRDFaiS?A>G`L#QX‡~LONTA…[HQFDFZXWREMLONTS BCA>Y(QFS#A('P \(A>WRQ QXW EHG˜‘]GTEULp—ZXWVAjB\QXLON ZXdidTWRQ8ZuY_NTA(b’‡™QFW š¹ — ˜ k ? G QuLONTA>W*InQFWRbTP>›‰LONTAjLInQBTWRZXGTY_N d\QFEHG8LOP‡™QFWJLRNTA [HQFD8ZuWREULRNTS ZXWRA B\QXLON€ZuL ¹ — ˜ k ]WVQFS LONiEHP…ZXG]ZX[MphPREHP>›*InA Y(QXGTY([UaTbTA?LRN]ZuLrLONTA#BTWRZXGTY_N Y>aiL5InAgGTA>A(b ‡™QXWrLRNTEHP0‡™aTGTYfLOEUQFG SjaiPVLoDFQ—LRNTWRQFaiDFN LONiA d\QFEUG`LRP ¹ } ®c{ ZXPInA([H[ZuP-LRNTWRQXaTDFN¶LONTA dCQXEHG8L ¹ — ˜ k Y dCQXPRPREUBT[HA Y_NTQFEUY(A-‡™QFWcZ BTWOZXGiY_N Y(a˜LgEUP#PVNTQIKG EUG zEUDTk ‚ k {ž‚ ¸-EULcY>QFGTPREUPVLRP?QX‡*LImQd]ZXWLOP(› •dT[H˜ZXGTA0µ ZXWVv AŒLO 4NTAŒ•oqX{ A(WZXLOGTEHY(b ZX[‰yŠ[UEH{ GTA> P v µ oy ˜ kgk=Ž;Ž;NTNTA#AA(EHS?G8LOZXEUWRDFA A>P0QXdT‡m[ ZuLRNTGTA(A0PVEHAgP‹[HS?EUGTZXA(dTP0d\LRA(Q…b-LRQFNTGJA LR Q  LONiAŠPVLOWVEHd’Qu‡šquZX[UaTA(P~AfehLOA>GTbTEHGi-D…}¨QqX® A(WŒLO5FNi‚ AŠA(G8LOEUWRAjWRZXGTDFAj¹ Qu‡—ZXGTb&NTZqhEUGTDJIKEHbiLRN ‚LONi ArQFdiG WRA(LOY>NTA(A bTEU GTD?Z«e˜ZXEHG]PZX[MQFp˜G PVEHLOP;NTQXA ‡ˆ LONiArdT[HS?ZXGTZXAXdTk?diEHŽ;GTNTDŠEHPrQX‡ˆEHPLONidTAWVA(‡™aiY>EHGTPRY>A>LR[Up’EHQFG-IKNTPREUZuG LoInA#Afe˜dCA>Y>Lo‡™WRQFS ƒ¹F„  

















 "!$#%!

 !#" $&%('*) QFGTPVEHbTA>W‹Z5PVA(WREUA(P‹A e˜d]ZXGTPVEHQFGJQu‡‡™aTF GTY>LREHQFGiPmQX‡ Y>QFS?di[HAfecquZXEUWOZXBi[HA(P>›iZuGTb aTPVA ZXPJLONTA—LOA(WVS?PgEHG LONiA’PRA>WREHA>P ƒ¹• V¹ Kf„ IKEULRBN D Z GTQFGh¡GTA>D8ZuLOEMqFA’EUG8LOA(DXA(W(› ZXPVPRaTS#EHGTDLRN]ZuLImAgZXWRAcEUG`LRA(WVA(PVLRA(bEHG LONTAcB\A(N]Z†qhEHQFWQX‡nLONTAЇ™aTGiY>LOEUQFG GTA†ZXWLONiA d\QFEHG8L ¹VK QFGLONTAY(QXS?dT[UAfe-di[ ZXGTAu¸ F  œ¹8„2} £ FTƒ¹• V¹ K „ »‚ k :¯ „ F xK Ž;NTEUPJEHP#LONTA’d\QImA>WJPRA>WREUA(PJA eidTZXGTPREUQFG QX‡  œ¹8„ ZuLJZ WRAf‡™A(WRA>GTY(A&d\QFEUG`L V¹ K k np ZXG]Zu[HQFDXp—LOQ-IKN]ZuLInAgbTEUPRY(aiPRPRA>b ‡™QFW0d\QImA>WoPVA(WREUA(PrAfe˜d]ZXGiPREHQXGTPoQu‡m‡™aTGTYfLOEUQFGTPQX‡ WRA(ZX[8quZXWREHZXBT[HA>P(›«ZXGTboaTPREUGTDsQFaTW ^`GTQIK[HA(biDFAmQX‡iY(QFG8qXA(WRDXA(GTY>A‹Y(WVEULOA>WREHZi›ImAšY(QFGiY([HaibTA LONTZuLn‡™QX[H[HQIKEUGTDPVL_Z«LOA(S#A(G8LRPmSjaTPLmNiQF[Hb#‡™QFW=LONTA*dCQInA(WmPVA(WVEHA(PnQFG?LRNTA~WVEHDFN8L¡N]ZXGib PREUbTAQX‡ ™2txk »‚ k°:¯ „ ¸ EU‡ˆEMLKY(QFG8qFA>WRDFA>P*‡™QFW WRDFA>Ps‡™QXW ¹ w œ EU‡ˆEMLKbTEUqXA(WRDXA(PK‡™QFW ¹ ZuGTb§¼ ¹ • ¹VK ¼  ¼ ¹ • ¹VK ¼8LRNTA(G—EUL;bTEMqFA>WRDFA>Ps‡™QFW ¹ k









!

















  









X© ŽˆQ Ÿ aTPVLREU‡ p-LONiA(PRA5PVL_Z«LOA(S#A(G8LRP(› InAjY†ZuG·LONTEUGT^-QX‡=LONiA5Y(QXG`qXA(WVDFA(GTY>AcQX‡=LONTAoPRA>WREHA>P EHG…ZXBiPRQF[UaiLOAŒLRA(WRS#PsZXGTb-PREUGTY(A¼ ¹r• ¹VK ¼`EUPsZcWVA†ZX[t`a]ZuG`LREULp\¸ ¼ ¹0• ¹VK ¼ } º ™v?• v‚Kf„ w y¨ = • = K_„ w InAY†ZXG§ZXdTdi[Up LONTAJLRA(PVLRPjImA-[UA†ZXWVGTA(b ‡™QFWoLONTAY>QFG8qFA(WVDFA(GiY(A…QX‡sWRA†Zu[mPRA>WREUA(P(k ? G d]ZXWLOEUY(aT[HZXWjLONTA—Y(QFS#d]ZXWVEHPVQFG§LRA(PL†›™=txk { kª½ „ ›mEHP#aTPVA>‡™aT[sEHG§A(PL_ZXBT[UEHPVNTEHGTD LONiA LInQŠPVL_Z«LOA(S#A(G8LRP;S?A>G`LREHQFGiA(b‰kŽ;NiA(PRA0[UA†ZXbgaTPmLOQoLONTAŒbiA>‘]GTEMLOEUQFGJQX‡LRNTAj±V³: 1 E( &)(+/ X²f± h²O/ &_²f¸EMLšEHP2LONTAsPRS?ZX[H[UA(PLnY>EHWVY([HAKQX‡ WOZXbiEHaTP  ¼ ¼«LRN]ZuLnA(GTY>[HQFPVA(PmZX[H[ d\QFEHG8LOPnZXWVQFaTGTb ¹VK ‡™QFW2IKNTEHY_NJPVA(WVEHA(PnY(QFG8qXA(WRDXA(P(k ? GgLRNT} A~[U¹mEHS#•—EUV¹L K  — ˜ LONTAsPRA>WREHA>P Y(QXG`qXA(WVDFA(P0AfqFA(Wp`IKNTA(WVA#QXG·LONTAoY(QFS#dT[UAfe—dT[ ZuGT‰A œ\EHG·LRNTA5[UEHS#EUL  }” LONTAoPRA>WREHA>P bTEMqFA(WVDFA(PKAfqFA(Wp`IKNTA(WVAjQFG-LONTAY(QXS?dT[UAfeJdT[ ZXGiAXk Y PšZXGcAfeiZXS#dT[UAX›8[HAfL2aTP2Y(QFGiPREHbiA(WLONiAsBiEHGTQFS#E Zu[hA e˜d]ZXGTPVEHQFG#EHG8qFQX[UqhEHGTDZ0Y>QFSc¡ dT[UAfe-G`aTSjB\A(W ¹ ¸ ƒ£~y¥¹8„ 0}¨£ my x£ G2H ¹*y ˆ #‚ •  {ž„ £ G w_¹Xwy ˆ #• {ž© „(  #•§‚F„ £ G  ¹  @y IJIJI ZXGTb ZXPV^—IKN]Z«LEHP~LRNTAŠWOZXbiEHaTPŒQu‡nY>QFG8qFA>WRDFA>GTY(A?QX‡2LONTEUPŒPRA>WREHA>PZXWRQXaTGTb&LONTAŠd\QFEUG`L V¹ Km}¨ k ŒA>‘TGTEHGTD }€:¹ 5X£ ›]InArQXBiL_ZXEUG‰¸ ƒ£Œy¥¹8„ }€£ {ny y ˆ # ‚ •  {ž„ w y ˆ #• {ž© „>  #• ‚F„ zy IJIJI »‚ k ¯ „ @A5LONTA>G ZXdTdT[Mp…LRNTAjWRZuLOEUQgLOA>PVL†€› ™2txk { k¾½ „ ›CLRQbTA>LRA(WVS?EUGTAoLRNTAjWOZubTEHaTP~QX‡2Y(QFGh¡ qFA>WRDFA>GTY(AoQX‡ˆLONTEUP;PRA(WVEHA>P(k2Ž;NTArWOZuLREHQŠQX‡ˆLONTA  D y|{ž„ LOQŠLRNToA D LRA(WVSEHP ˆ #• {ž„ I:D IIh #• D „ F H ˆ #• {ž„ I:I:Ih D #•¶ D • {ž„R„ F G2H } ?D • D  y¶{  y¶{ž„  ZXGTbLONiAšWRZuLOEUQ‹LOA>PVLˆWRA>thaiEHWRA>PLON]ZuL LRNTEHP[HZXPVL A eidiWRA(PVPREUQFG5B\A=BCQXaTGTbTA>b5B8pZKdCQFPVEULREUqFA G`aTSjB\A(WKPRS?ZX[U[HA(WnLON]ZXG-aTGiEULpJ‡™QFWKZu[H[ D  ›]BTaiL #D • D — { D — ˜ – y¶{ [HA(Z†q˜EUGTD#ZXP‹LONiArY>QFGTbTEMLOEUQFGJ‡™QFW;LONTAY>QFG8qFA(WVDFA(GiY(A5Qu‡LRNTAPRA(WVEHA>P ¼ ‰¼8µ {*– ¼ ¹ ¼hµ ¼ £ ¼ IKNTEUY_N—DFEMqFA>PKLRNTAWOZXbiEHaTP;QX‡Y(QXG`qXA(WVDFA(GTY>AjQX‡ˆLONTAPVA(WREUA(PsZXWVQFaTGTb V¹ K‹}| k ]QFWsLRNTA5d\QImA>WŒPRA>WREUA(P~WVA(dTWVA(PVA(G8L_ZuLREHQFG&Qu‡2Z?‡™aTGTYfLOEUQFG  œ¹8„ ›CZXP*DFEUqXA(G’EU’G ™=txk k°¯: ›CZXPRPVaTS?EUGTD?LRN]ZuL*EUL*Y(QFG8qXA(WRDXA(GTY>A(PrZXBTPVQF[HaiLRA([Mp…ZXGTb’aTGiEU‡™QFWVS?[MpJEHGiPREHbiAoLONiA bT»‚ EUPR^ „ ¼ ¹•V¹ K ¼sµ j›;LONiA·‡™QF[H[UQIKEHGTD PVLOZuLOA>S?A>G8LOPZXWVA—LRWRaTA  PRQFS#A—‡™QXWgQFB8qhEHQFaiP WRA(ZXPRQXGTP „ ¸ L

"       … !  #g

!































































!





















 





























!

!







































 "!$#%!



˜EUGTY(A œ¹• ¹VKf„ F EHP;Y>QFG8LOEUGhaiQFaTP(›  œ¹8„ EHPKZX[UPRQŠY>QFG8LOEHG`aTQXaTP(k Ž;NTAd\QImA>W*PVA(WREUA(PKWRA>dTWRA>PRA>G`LOZuLOEUQFG—ZXBCQXaiL ¹VK EUP;aTGTEHt`aTAEUGTPREUbTAŒLONTAbTEUPR^xk @AŒY†ZuGJbTE CA(WVA(G8LOEHZuLOA~ZXGTbJEUG8LOA(DXWOZuLRA*LONiAŒPRA>WREHA>PmLOA>WRS!B8p?LRA(WRS!EHGiPREHbiA*LONiA bTEUPR^x›˜LRQŠQFBiLOZXEHGZjGiA>I€Y(QFG8qFA>WRDFA>G8L*PVA(WVEHA(P>›TPREUGTY(A*LONTA0WVA(PRai[ULOEUGTDjPVA(WREUA(P;N]ZuP LRNTAPOZXS#A0WOZuLREHQŠQX‡ˆLONiA  D y|{ž„ LRQ#LRNToA D LOA>WRSZXP;LRNTAQFWREUDFEHG]Zu[CPVA(WREUA(P>k ]QFW   ›hLONTA0d\QImA>W;PRA>WREHA>P;WRA>dTWRA>PRA(G8LRP~ZXG ‰³ /\³X´ +Ž &n‡™aiGTY>LREHQFG‰›˜IKNTEHY_NEUP EUGi‘]GTEMLOA([Mpg biE CA(WRA>G8LOE ZuBT[HA~IKEMLONTEUGLONTAbTEUPR^JQX‡Y(QXG`qXA(WVDFA(GTY>AXk lmQFG8qXA(WRPVA([MpF› A>qXA(WVp·‡™aTGTY>LREHQFG&NTZXPZJaTGTEUthaiAŠdCQInA(W0PRA>WREUA(P0WRA>dTWRA>PRA>G`LOZuLOEUQFG ZXB\QFaiL V¹ K IKNiA(G-EULmEHP;ZXGTZX[Up`LOEUY~EUG-ZjbTEHPV^?QX‡ˆWRZXbTEHaiP ”ZXWRQFaiGTbEUL(›TZXGTb-ZuG`p S#A>LRNTQ˜b-QX‡QFBiLOZXEHGiEHGTDjLRNTEHP;PVA(WREUA(PKEHPKZuY(Y(A>diL_ZuBT[HAuk @ A…dTWVA(PRA>G8LJGTA e˜L#LInQ PRd\A(Y>EU‘]Y…d\QžInA(W#PRA>WREUA(PcAfe˜d]ZXGiPREHQXGTPgQX‡s‡™aTGTYfLOEUQFGTPcQX‡ Y(QXS?dT[UAfeŠquZXWVE ZXBi[HA(P>›8^`GTQIKGZXP2LONTAsŽzZ†ph[HQXWmZXGib#LRNTA  ZXaiWRA(G8LmPRA(WVEHA>PnA eidTZXGTPREUQFGTP>k Ž;NTA5‘TWRPVLWVA>‡™A>WRP~LRQZ?‡™aTGTYfLOEUQFG·LONTZuL0EHP~ZXG]ZX[Mp`LOEHYrEHG’ZgbTEHPV^·ZuWRQFaTGib&Zgd\QFEHG8L V¹ K › LONiAŠPRA(Y>QFGTb&LOQ-Z#‡™aTGTY>LREHQFG’IKNiEHY_N EHP*GTQXLZXGTZX[Up`LOEUY5EUG·LONTAŠGiA(EHDXNhB\QFWVNTQ˜Qhb’QX‡ V¹ K › BTaiL~EHPsZXG]Zu[Up`LOEUYrEUG’Z#Y(EHWVY(aT[HZXWsZXGTG`aT[UaTPŒZXWVQFaTGTb V¹ K k mQXLRN·PRA>WREUA(PŒZuWRA5A ehLOWRA>S?A>[Up aTPVA>‡™aT[KEHG§WRA>dTWRA>PRA>G`LREHGTD ‡™aTGTYfLOEHQXGTPcQX‡ŒY>QFS?di[HAfe qXZuWRE ZuBT[HA>PcZXGTb§EHG aTPREUGTD LONTQFPVA WRA>dTWRA>PRA>G`LOZuLOEUQFGTPK‡™QFW;dTWRZXY>LREHY†Zu[ZXdTdT[UEHY(ZuLOEUQFGTP(›hPRaiY_N’ZXPKA>quZX[Ua]ZuLREHGTDŠEUG`LRA(DFWRZX[HP>k @ AŠbiEHPRY>aTPRPŒ‘TWRPVL0LRNTAjŽZ†p˜[UQFWŒPVA(WREUA(P0A eidTZXGTPREUQFG‰kŽ;NTEUP0Y†ZXG&B\AŠZXYfLOa]ZX[U[Up…bTA ¡ WREMqFA>b¶‡™QXWZ ‡™aTGTY>LREHQFG  ƒ¹8„ IKNTEUY_N€EUPZXG]Zu[Up`LOEUY·A>qXA(WphIKNiA(WRAQFG|ZXGTb¶EHGiPREHbiA&Z PREUS?di[HA;Y([UQFPRA>bgY>QFG8LOQFaTW ›hB8p#ZXdidT[UphEHGiDLRNTA~l m›3™2txk k°¯X¯ GTQXLRAsLRN]ZuLšEHGcLONiA ‡™QF[U[HQIKEHGTDrdTWVQ˜QX‡ InA0N]Z†qFA0WVA(dT[HZXY(A>b-LRNTA~quZXWVE ZXBT? [UA~QX‡ˆEUG`LRA(ƒ‚DFWRZuLO„KEUQF GgB8p?LONTA0Pp˜S5BCQF[ gZuGTbImArN]Z†qFArY†ZX[U[HA>bJLONTAd\QFEHG8L;IKNTA>WRALONTA0‡™aTGTYfLOEUQFG-EHP;A>quZX[Ua]ZuLRA(b-PREUS?dT[Mp ¹F„ ¸   „ {E  „ b } {E  œ¹8„ } ‚   • ¹8„ ‚  {K•  GG   „( • ¹VKf„ b } ‚ { E    •  ¹V„ K „ {ny ¹•• V¹¹VKK y ¹r•• V¹¹VKK w @y IJIJI b }  ƒV¹ K_„y¨ƒ¹• V¹ K „   œV¹ Kf„y ‚ {  ƒ¹• V¹ Kf„ w    œV¹ K „@y IJIJI IKNTA>WRA‹EUG5LONTAmGTAfehLV¡»LOQu¡¢[ ZXPLzPLOA>djImA‹NTZqXA;aTPRA>bjLONTAmDFA(QFS#A>LRWREUYnPVA(WREUA(PPVaTS#SgZuLREHQFG { } {ny y wy  y IJIJI {K• ¼ ¼PVA(A#Y_N]¼ ZXdiLRA(W ¼ { ›¼ ™=t\k ¼C{ µ k¾‰½ „R„ ›‰IK¼ EMLON } ¼Cµƒ¹j¼ • V¹ Kf‘„ 5T¼¾›‰ZX• GTb’V¹ Kf‡™„ QFW~IKLRNTNTEUY_AŠN[ ZuEUPVPL0quPZXLO[UA(EHb·d&‡™InQXAW N]Z†qF} AraT¹oPVA(• b—V¹ LRKNTAo5 l ? •¥ V¹ ‡™QFK W;LONTA{ŠbT– A>WREUqu¹5Zu•LREUqXV¹ A(K P;QX‡  ƒ¹F•¥„ ‚› V¹ ™=K txk ƒ‚ k ¯`½ „ k “





































































L



"       … !  #g

!

x¸ “˜aTdTd\QFPRAInAImZXG8LsLOQcY†ZX[UY(aT[HZuLOA*LONTAd\QžInA(WsPRA>WREUA(PKQX‡  ƒ¹8„2} PVEHG G2H ƒ¹8„ ZXB\QFaiLsLONTA5dCQFEUG8L ks@Ao‘TWRPVLŒGTQXLOEUY(ALON]Z«L~LONiEHPK‡™aTGTY>LREHQFG—EHP~ZXG]ZX[MphLREHYEHG·Z bTEUPR^·Qu‡nGiQFG˜¡c\>A(WVQV¹ WOK*ZXbT}”EUaT P0ZXWVQFaTGTb’LRNTAŠd\QFEHG8L0QX‡šEUG`LRA(WVA(PVL(koŽ;NiA(WRAf‡™QFWRAu› EULŒPVNTQFaT[Ub N]Z†qFAŽZ†ph[HQFWoPRA(WVEHA>PjAfe˜d]ZXGiPREHQXG ZXWRQFaiGTb LONiEHP5d\QFEUG`L(k sQžInA>qXA(W>›nEML5EUP5S#A(PRPpLRQ LOWpJLOQcL_Zu^XAbTA(WVEUquZuLREUqFA>PKQX‡zLRNTAEHG8qFA>WRPRArPREUGTA0‡™aTGTYfLOEHQXG‰›]PRQcImArWRA>PRQFWLKLOQ#ZcLRWREUY_^\¸ PREUGTY(AZuG`pgI‹Z†pQX‡ˆQFB˜L_ZXEUGTEHGTDoLONTA0d\QImA>WsPVA(WVEHA(P;A e˜d]ZXGTPVEHQFG-EHPKZuY(Y(A>diL_ZuBT[HAŒ‡™QFW‹ZXG ZXG]Zu[Up`LOEUY‡™aiGTY>LREHQFG‰›TInA5Y(ZX[H[‰LRNTA5QXWREHDXEHG]ZX[\‡™aTGTYfLOEHQXG ZXGTb—AfeiZXS#EHGTAEULRPKEHG8qFA>WRPRAu› IKNTEUY_N—EUP;PREHS#dT[Mp?LRNTAPREHGiA‡™aiGTY>LREHQFG‰¸ b¹ |} PREUG G2H ƒ¹F„š– ¹5} PREHG  Œ„=– b } Y(QFP  0„=} º {K• PREUG w  Œ„=} “ {K• ¹ w ‡™WRQXS IKNTEUY_N…InAoY(ZXG…bTA(WVEUqFA0LRNTA0‡™QF[H[UQžIKEUGTDjWVA([ Z«LOEHQXG‰¸ b } { } 9 {ny€•*¹Xwfg„ ; G2H w b ¹ “ {K• ¹ w ZXGTb EHG¥LRNTA’[HZXPVL?Afe˜dTWVA(PRPVEHQFG InA&WRA>Y(QFDXGTZE \>A—LONiA—‡œZXS#EH[UE ZXWjBiEHGTQFS#E Zu[KZXPgEUG ™=txk »‚ k°¯ „ ZXIKGTEUb…LON EHG8£cLRA(}”DFWR{ ZuR LOA>b-} LRA(•~WV¹Sw R B8p} LOA(•rWVSQ{ 5F[H‚ A(›TZXIKbTP‹NTEHLRY_QTN‰¸ ›TIKNiA(G·A e˜d]ZXGTbTA>b·EUG…d\QImA>WRPsQX‡ •*¹ w „ © ½ ¹y@IJIJI |}¨¹sy { ¹  y ¯ ¹ y  {X{ž‚ •*QuLOAmLRN]ZuLzInA;Y†ZuGcZXdTdT[MpoEUG8LOA(DXWOZuLREHQFGrLOA(WVS B8poLOA(WVS LRQ~LONiA‹PRA>WREHA>PzInA;QFBiL_ZuEHGo‡™QXW b 5 b ¹ B\A(Y(ZXaTPRAnLONTA‹BiEHGTQFS#E Zu[FPRA>WREHA>PzY>QFG8qFA(WVDFA(P=aiGTEU‡™QFWVS?[MpŒ‡™QFWK¼ ‰¼ } ¼ •j¹ w ¼hµ { › Z&Y(QFGibTEULREHQFG LRN]ZuLcEHP5Y(A(WL_ZXEUGT[Up POZuLREHP‘]A(b ‡™QFW ¹ EHG LRNTA-GTA(EUDFN`BCQFWVNTQhQ˜b QX‡ \>A(WRQik —QFWVA(QqFA>W(›;LONiA·Y(QXGTPVLOZXG8LQX‡0EUG`LRA(DFWRZuLOEUQFG IKNTEHY_N ZudTdCA(ZXWRP#IKNTA(G InA·EUG8LOA(DXWOZuLRA LONiAŒPRA>WREHA>Pm‡™QFWnb {5 b ¹ EHGJQXWRbTA>WmLOQjQXBiL_ZXEUG?LRNTAŒPRA>WREUA(Pm‡™QFW ›hY†ZXGgBCAŒbiA>LOA>WRS#EHGTA>b B8p&QFBTPVA(Wq˜EUGTDLON]Z«L0‡™WRQFS LONTAŠbTAf‘]GTEMLOEHQXG&QX‡ ImAcN]Z†qFA ¹-} – }  › ZuGTb NTA>GTY(ALONTAY>QFGTPVLOZXG8LsQX‡EUG`LRA(DFWRZuLOEUQFGJSjaiPVLsBCoA \>A(WRQik Y GTQuLONTA>WŒEHS#dCQXWVL_ZuG`LKd\QImA>WŒPRA>WREUA(P~A e˜d]ZXGTPVEHQFG&EUPsLRNTA  ZXaTWVA(G8LŒPVA(WVEHA(P>k0lmQFGh¡ PREUbTA(WcZ’‡™aTGiY>LOEUQFG  œ¹8„ IKNTEHY_N EHPcZuG]ZX[Up`LREHYgQXG¥Z&Y>EHWRY>aT[ ZuWŠZXGTG`aT[UaTPjIKEULRN§QXaiLOA>W WOZubTEHaTVP  H QFG LRNTA#Y(EHWVY(aT[HZXW0Y(QXG`LRQFaTW H ›ZXGTb EUGTGTA>WrWRZXbTEUaTVP  w QFG LONTA#Y(EUWRY>aT[ ZXW Y(QXG`LRQFaTW w ›iB\QXLON?Y(A>G`LRA(WVA(b…ZuL ¹VK k@ AsIKEH[H[xA>S?dT[UQpŠLONTAs‡™QF[H[UQžIKEUGTDEHG8LOA>DFWOZu[HPšQFG LONiArY>QFG8LOQFaiWRP H ZuGTb w ›TL_ZX^uA(G—ZXPKaTPRa]Zu[EHGLONTAY>QFaTG8LOA>W¡Y>[HQhY_^8IKEHPRArPRA>GTPRAu¸    „ b  • ¹8„ R } ‰{ R ‚ @A?GTQuLOEHY>AjLON]Z«LoEM‡nInA Ÿ QXEHG&LONTAŠLInQ·Y>EHWRY>aT[ ZuW0Y(QFG8LOQXaTWRPrB8p&LImQ—[HEHGiAŠPRA(DXS?A>G`LRP LOWRZ†qFA(WVPRA>bEHGcLONTA*QFdTd\QFPREMLOAKbTEHWVA(YfLOEHQXG‰›hZXPnEU[H[UaTPVLRWOZuLRA(b#EHG?zEHDTk ‚ k { i›8LONTAK‡™aTGTYfLOEUQFG   

























‰



 "!$#%!



y

ρ

C2

2

ρ

1

z0

C1 x

0

zEUDFaTWRA ‚ k { i¸

 fid.r)`L^_eVd eJjLj‰`L^_`3a eVdghQ`Lj3„'bgm:npxhQf_jp3^_eJjLnJ~$lZhJd  bgm:n„Ln)d%f VeVbgfihQjhJl bgmLneJ`:d%nXj+bacn)d.finXa"nsup3eJjLagfihQj‚

œLONi A(¹8WR„ Af‡™EUQFP#WRAjZXG]InZXAŠ[MphY†LRZuEHYGAfZuqFdTA(dTWp`[Up…IKNTLONiA(A#WVA’l EHG¥ ZX‡™GTQFb§W~LOQFNiG EHPŒLOPVNTEUA…LOaTWRZuA>LOPREUaTQF[MG‰LOkEHGiDG’Y>LO[HNiQFAŠPVA([Hb§EHS#Y(EUQFLKG8IKLOQXNTaTA>W(WR›;AŠZuLOGTNib A LInQj[HEUGTA;PRA>DFS?A>G8LOPm[UEHA;QFG#LOQFd?QX‡‰? A(ZXY_NJQXLRNTA(W>›˜NiA(GTY>A*LONiA(? EHWšY(QXG`LRWREUBTaiLOEUQFGTP2Y†ZuGTY(A>[ QFaiL(›TImAQFB˜L_ZXEUG‰¸   „   „  { b  ƒ¹F„n} {  • »‚ k ¯ „ ‚  E  • ¹8„ ‚  E  • ¹8„ b ? GLRNTA#[ ZXPLAfe˜dTWRA>PRPVEHQFG‰›zA†ZXY_NY(QFG8LOQXaTWoEUP0LOWOZ†qXA(WRPVA(b EUG LRNTA#Y(QFaTG8LRA(W¡¢Y([UQ˜Y_^8IKEHPVA PRA>GTPRA#ZXGib LRNTAŠEHG8LRA(DFWRZuLOEUQFG’QqFA>W w N]ZuPZXG&QqFA(WRZX[H[zS?EUGhaiPŒPREUDFG&BCA>Y†ZXaiPRAŠLON]Z«L d]ZXWLjImZXPŠLOWOZ†qXA(WRPVA(b§EHG LRNTAY([UQ˜Y_^8IKEHPVAbTEHWVA(YfLOEHQXG EHG LRNTA Ÿ QFEHGiA(b Y(QXG`LRQFaTW>k@A bTA(ZX[TIKEULRN#LRNTA;LImQoEHG8LOA>DFWOZX[UPLON]Z«LmZudTdCA(ZXW2QFGcLONTAKWREUDFN8LV¡¢N]ZXGTbcPREUbTAKQX‡ LRNTAsZXB\QžqXA A(t`a]Z«LOEHQXG…PVA(d]ZuWOZuLRA([UpXk2Ž;NTAr‘TWRPVLsEUG`LRA(DFWRZX[‰Y(ZXG-BCA0IKWREMLRLRA(G—ZXP(¸   „ {E  „ b } {E Hš} »‚ k ¯ „ G   ‚   • ¹8„ ‚  {K• G   „> • V¹ Kf„ b ZXGTb…PREUGTY(A0‡™QFW ¹ EHGLRNTArZXGTG`aT[HaiP*ZuGTb ?QFG-LONTA H Y(QXG`LRQFaTW;InAoN]Z†qXA ¹r• V¹ K µ { • ¹VK InAoY(ZXG…ZXdTdT[MpJLONTADFA>QFS#A>LOWVEHYŒPVA(WVEHA(PKA eidTZXGTPREUQFG-LOQ#QFBiL_ZuEHG { E    „ {my ¹r• V¹ K y ¹• V¹ K w y IJIJI b »‚ kª½ 8„ H=} ‚   • ¹VK_„ • ¹VK • ¹VK 



































































































L

"       … !  #g

!



]QFW‹LONiArPVA(Y>QFGTb·EUG8LOA(DXWOZX[ InAN]Z†qFAu¸ }w • ‚ { E    • „¹8„ b } ‚ { E  {K• GG     „(œ„ ¹r• ¹VKf„ b »‚ kª½ {ž„   ZXGTb…PREUGTY(A0‡™QFW ¹ EHGLRNTArZXGTG`aT[HaiP*ZuGTb ?QFG-LONTA w Y(QXG`LRQFaTW;InAoN]Z†qXA • V¹ K µ { ¹r• ¹VK InAoY(ZXG…ZXdTdT[MpJLONTADFA>QFS#A>LOWVEHYŒPVA(WVEHA(PKA eidTZXGTPREUQFG-LOQ#QFBiL_ZuEHG }w ‚ { E  œ¹r •  ¹V„ K_„ {my ¹r•• ¹VV¹ KK y ¹•• V¹¹VKK w y IJIJI b »‚ kª½ ‚F„ lmQFSjBiEHGTEUGTDjLONTA>PRALImQ#WRA>PRaT[MLOP>›TImAoZXWRWVEUqXAZuL;LONTADFA>GTA(WRZX[Afe˜dTWVA(PVPREHQXG   „ F   ƒ¹F„š} { ƒ   ¹ • ¹ V f K „ »‚ kª½X© „ ‚EF G  • ¹VK „ F H b IKEULRN Z Y([UQFPRA>b”Y(QFG8LOQXaTW’LON]Z«L [HEHA>P·A>G`LREHWVA([Up€IKEULRNTEHG¨LRNTA Y(EUWRY>aT[ ZXW’ZXGTG`aT[HaiP B\QFaTGTbTA>b¶B`p§LONiA&Y(EHWVY(aT[HZXW#Y(QFG8LOQXaTWRP H ZXGib w ›sZXPJY†ZuG|B\A’A(ZXPREU[Up Ÿ aTPVLREU‘]A>b B8p Y(QFG8LRQFaTW#bTA>‡™QFWVSgZ«LOEHQXG‰k Ž;NTA—A e˜dTWRA>PRPREUQFG EUG ™=txk ƒ‚ kª½X© „ EHPŠ^`GTQIKG ZXPcLONiA  ZXaTWVA(G8L-dCQInA(W-PRA>WREUA(PAfe˜d]ZuGTPREUQFG|ZXGTb¶Y(QFG8LOZXEHGTP 4O(+Ž / ² 8‰³ Ž  X²&‰³ / ,2(  Ž X² ,2( m²f± ( ƒ¹• V¹ K „ F k x¸=ŽQ#EH[U[HaTPLOWOZ«LOA*LRNTA(PVAoY>QFGTY>A(diLRPsInAoY>QFGTPVEHbTA>W‹LONTA0‡™aTGTYfLOEUQFG { { y {  œ¹8„2} } ƒ¹• {ž„>ƒ¹• ‚F„ {K• ¹ ¹0•§‚ ZXGTb ZuPR^—IKNTZuL0EHP*EULRP~d\QžInA(W0PVA(WVEHA(P0A e˜d]ZXGTPVEHQFG ZXWVQFaTGTb ¹g}  k0ŽˆQ-ZXGTPImA>WŒLONTEUP t`aTA(PLOEUQFG‰›TInArGiA(A(b-LOQcPVA(d]ZXWRZuLOA0LRNTA0Y(QFS#dT[UAfedi[ ZXGTA~EHGLONTWVA(A0WVA(DFEUQFGTP;EHGJIKNiEHY_N InAoY(ZXG-A†ZXPVEH[UpgbTA>LRA(WVS?EUGTAŒLONTArZXGTZX[Up`LOEUY(EMLpJQX‡ˆLONTA0‡™aTGiY>LOEUQFG‰k=Ž;NTA>PRAoZXWRAu¸ WRA>DFEHQXG ? ¸ ¼ ¹ ¼˜µ { ›iIKNTA>WRArBCQXLRN {Q5T{K• ¹F„ ZuGTb {J5Tƒ¹0•§‚F„ ZXWVArZXG]ZX[MphLREHYDFEHQXG ?.? ¸ { µ ¼ ¹ ¼hµ ‚ ›iIKNiEHY_N…A(GTY>[HQFPVA(P*ZcPVEHGTDXaT[ ZXWVEULp?QX‡ Q{ 5T{;• ¹F„ œ WVA(DFEUQFG ?.?‘? ¸ ‚ µ¼ ¹ ¼ª›CIKNTEUY_N&A(GTY>[HQFPVA(P0Z?PREHGiDFaT[ ZuWREULp-Qu‡2BCQXLRN Q{ 5T {*•¥¹8„ ZuGTb QX‡ Q{ 5Tœ¹•§‚X„ k ? GJA(ZXY_NWRA>DFEHQFG ›hInAŒY†ZuGbTA>LRA(WRS#EHGiA*PVA(d]ZXWRZuLOA>[Up#LONTA*Afe˜d]ZXGiPREHQXGQX‡‰LONiA~LImQj‡™WRZXYf¡ LOEUQFGTPgLRN]ZuL…ZXdidCA(ZXWEHG  œ¹8„ ›sLON]Z«L-EHP(› {Q5T {Š•”¹8„ ZXGTb {Q5Tœ¹•”‚F„ k Ž;NTA’‘]WRPL ‡™WOZuY>LOEUQFG‰› Q{ 5T {=• ¹8„ ›˜EHPnZXG]ZX[Mp`LOEHYsEHG?WRA>DFEHQFG ? ›˜PVQ5InAŒAfe˜d\A(Y>L;Z5ŽzZ†ph[HQXWnA eidTZXGTPREUQFG ‡™QFW0EML0IKNTEHY_N EHP0A(ZXPREU[Up’QXBiL_ZXEUGTA(b ‡™WRQXS LONiA#DXA(QFS#A>LRWREHYŠPVA(WVEHA(P>›PVEHGTY>AcEHG&LONTEUP0WRA ¡ DFEUQFG¼ ¹ ¼hµ { k 7 A(DFEUQFGTP ?‘? ZXGTb ?.?‘? Y†ZuGJBCA~Y(QFGTPVEHbTA>WRA>b-ZXP‹Y(EUWRY>aT[ ZXWnZXGTG`aT[UE\IKNiEHY_N 

































































 

















!

















  









 "!$#%!



y

II

0

I

1

2

x

III

zEUyDF aTWR A  ‚ k {  ˜y ¸   u: eJyt{ p3^in hJeVl dghQeX`L‡jL^i„hJdy eJjL„  eJbgm:`:ndgnXrsje˜‡™aid][HZuGTGTA>PRPREUPŠQFGQX‡KSgLONiZ†p A B\A#biA>LOA>WRS#EHGTA>b B8p SjaTY_NPREUS?dT[UA(WŒS#A>LRNTQhbTP0LON]ZXGB8p N]Z†q˜EUGTD-LOQ…A>quZX[HaTZuLOAŠLONiA EHG8LRA(DFWRZX[HPIKNTEUY_NgZudTdCA(ZXW=EHGŠLRNTAKDFA(GTA>WOZX[]A e˜dTWRA>PRPREUQFGgQu€‡ ™=txk »‚ kª½X© „ œ8LONTEUPI‹ZXP2LONiA Y†ZuPRA~EUG#LRNTAsAfeiZXS#dT[HAsQX‡Z  ZXaTWRA>G8LmPVA(WREUA(PšAfe˜d]ZXGiPREHQXGgLON]Z«LšInA~biEHPRY>aTPRPVA(b-ZXB\QqFAuk 





y

zk

z1

C

zEUDFaTWRA ‚ k { ˜¸

x

0

 ] ^}^_`Lacbcd%eVbgf_hQj0hJl rshQjGTY([UQFPRA>b B8p ZuGTb ƒ¹F„ N]ZuP PREUS?di[HAcWRQhQXLOPoZuL ¹&}¹ R } { RWU U}U R D¥EUGLONiEHPrWRA(DXEHQFG‰k Y PREUS?di[HAcWRQhQXLrQX‡ ƒ¹F„ ZuL S?A(ZXGTPsLON]ZuL*LONTAo‡™aTGTY>LREHQFG—qXZuGTEHPVNTA(P0Z«L*LRNTEHPsqXZu[HaTAoQX‡ BTaiL0EMLOPK‘]WRPL bTA>WR¹gEUqu} ZuLREU¹ qXA5bTQhA(PŒGiQXL  PRA(AcZu[HPRšQ ”2WVQFBT[UA(S {8„ {k •*A(ZXW*LRNTAjWRQhQXLRP*In¹AŠY†ZXG&A eidTZXGTb LONiA‡™aiGTY>LREHQFG ƒ¹8„ EUGŽzZ†ph[HQFWKPVA(WREUA(PsZXP>¸ œ¹8„=}  œ¹ „>ƒ¹• ¹ „y IJIJI 





















: #g…    #O

E



!$#





! 



{



RP EUGTY(A ƒ¹ „o} ›ˆIKNTA(WVAgLONiA?bTQuLOP5WVA(dTWVA(PVA(G8LŠNTEUDFNTA(WrQFWVbTA(WrLOA(WVS?PrEHG ƒ¹c• ¹ „ IKNTEUY_N?quZXGTEUPRN#SjaTY_Nc‡œZXPVLRA(W2LON]ZXGcLONiAs‘]WVPVLšQFWVbTA(W2LOA>WRS ZXP ¹0— ¹ kŽ;NTA~EUG8LOA(DXWOZX[ QX‡ˆLONTAWRZuLOEUQ  ƒ¹8„.5 ƒ¹8„ QqFA>W;LONTAY(QXG`LRQFaTW EHP‹LRNTA(G…DFEMqFA(G…B8p\¸ F  F  œ¹8„  ƒ¹F„  ƒ¹ „  b b E o ¹ } 5 ¹ ¨ } ‚   œ¹ „ H H  H F ƒ¹F„   ƒ¹ „(ƒ¹0• ¹ „ kª½u¯ „ »  ‚ IKNTA>WRAŒLONiA~‘]G]ZX[CWRA>PRaT[ML‹Y(QXS?A>Pm‡™WRQFS!d\A(WV‡™QXWRS#EHGTDrY(QFG8LRQFaTW‹bTAf‡™QFWRS?ZuLREHQFGgZXP‹EHGibTEM¡ Y†Z«LOA(b-EUGzEHDik ‚ k { ŠZXGTbaTPVEHGTDjLRNTA0PRS?ZX[U[CY>EHWRY>aT[ ZuWmd]ZuLRNTP‹IKEULRNWOZXbiEHExLOA(GibTEHGTDjLRQ \(A>WRQ~ZXWRQFaiGTboA(ZXY_N5PVEHS#dT[HA=WVQ˜QuLQu‡iLONiAšbiA(GTQFS#EHGTZuLOQFW>›‡™QFWIKNTEHY_NrLONTAšWRA>PRaT[MLQu2 ‡ ™=txk k»‚ ª© „ ZXdTdT[UEHA>P("k ™qhEHbTA>G8LO[UpX›TEHGJLRNTEHPmY†ZXPVALRNTA0WRA>PREUbTaTA(PKZ«L ¹5}¨¹  } { RVUVUVUOR D „ Y(QXS?A0QFa˜LsLRQcBCA  œ¹ .„ 5  ƒ¹ „ ›iIKNiEHY_N…EHP;A†ZuPREH[MpJAfqXZu[Ha]ZuLRA(b‰k Y DFA>GTA(WRZX[HE \†ZuLREHQFGQX‡iLONTEUPWVA(PRai[ULEHP LONTAnY†ZX[UY(aT[HZuLOEUQFGQX‡TLONiAmY(QXG`LRWREUBTaiLOEUQFG‡™WRQFS Zjd\QF[HA*QX‡ QFWRbiA(W ZuL ¹o}¨V¹ K ›iLRN]ZuL;EUP(›iZ5WRQhQXL;QX‡ QXWRbTA>W EUGgLONiAŒbTA(GiQFS?EUG]ZuLRQFW(k ? G-LONTEUP;Y†ZXPVAX›]LONTA0‡™aTGiY>LOEUQFG-QX‡EHG8LOA>WRA(PLsY†ZXG…BCA0IKWVEULRLRA(G-EHG-DFA>GTA(WRZX[‰‡™QFWVSZXP>¸ W¤ G H V¤ G2H V¤ G  œ¹8„2} y y IJIJIy  2 G H œ¹r• V¹ Kf„ œ¹r• V¹ K_„ œ¹r• V¹ Kf„ y§¤)Ky§¤VH(œ¹r• ¹VKf„y@IJIJI LONTZuL=EHP>›FEULN]ZXP2Z  ZXaTWVA(G8L2Afe˜d]ZXGiPREHQXG#PL_ZXWLOEUGTD~IKEULRNjLONTA‹LRA(WVS QX‡\QFWVbTA(W • k@A bTAf‘]GTAoZcGiA>I‡™aTGiY>LOEUQFG ƒ¹8„ B8pSjaT[MLOEUdT[UphEHGiD  ƒ¹F„ IKEMLONLONiA‡œZuY>LOQXW ƒ¹• V¹ Kf„ ¸ ƒ¹8„ } œ¹r• V¹ Kf„  ƒ¹8„ } W¤ G y§V¤ G H(ƒ¹• V¹ K „y IJIJIžy¥W¤ G2H(ƒ¹0• V¹ Kf„ G2H y¥)¤ K«ƒ¹0• V¹ Kf„ @y IJIJI IKNTEUY_N EUPŒZJŽZ†p˜[UQFWŒPVA(WREUA(P0A eidTZXGTPREUQFG’‡™QFW~LRNTAj‡™aTGTYfLOEUQFG ƒ¹8„ ›PREUGTY(AŠEMLŒY(QXG`LOZXEHGiP GTQrGTA(DFZuLOEMqFAKdCQInA(WVPnQX‡ ƒ¹2•-¹VKf„ ›8LONiA(WRAf‡™QFWRA;LRNTA*Y>Q˜OA N#Y(EHA>G8LnQu‡ LONiAKLRA(WVS QX‡‰QXWRbTA>W •QX‡ { EHP2LONiA*bTA>EHWRGEMqX‡™Z«WVQFLOEUG8qXL†A*¸ Qu‡ LONiA*PRZXS?AsQFWVbTA(WšA>quZX[Ua]ZuLOA>bJZuL ¹o}¨V¹ K ›`IKEULONgZ‡œZuY>LOQXW Q{ 5T • {ž„  G2H { W¤ G2H2}  • {ž„  h¹ G2H ƒ¹8„    QFW>›TA(t`aTEMqXZu[HA(G8LR[UpF›˜‡™QFWKZ#d\QF[UAŒQX‡QFWRbTA>W LONiArWVA(PVEHbTaTA0LOZX^XA>PsLRNTA0‡™QFWRS…¸ A 7 >PREUbTaTA*ZuL V¹ Kf„=}¨W¤ G2H2}  • { {ž„  `¹ G2G2H H Vƒ¹• V¹ Kf„  œ¹8„R„ »‚ kª½F½ „   @¶EULRNŠLONTEUPWRA>PRaT[ML†›8ImAKY(ZXGcDFA(GTA>WOZX[UZE \>A‹LONTA;WVA(PREUbTaTA;LONiA(QFWVA(S LRQoZuG`pjGhaiSjBCA>"W DQX‡ PREUGTDFaT[HZXWREMLOEUA(P ZuL ¹5}¨¹  }”{ RVUVUWUWR D „ IKEULRNTEHGLONiA‹Y(QFG8LRQFaTW ›XA(ZXY_NŠPREUGTDFaT[HZXWREMLp 













 









































!





































































!























!





 "!$#%! ‚ \B A(EHGiDjZod\QF[UAsQu‡ ZXWRBiEULOWRZXWVpcQXWRbTA>W  BTaiL/ (+Ž\ZXG?A(PVPRA(G8LRE ZX[CPREHGiDFaT[ ZuWREULpX›8BCA>Y†ZXaiPRAŒEUG LONTZuLKY†ZXPVArInAY†ZXGiGTQXLsA>quZX[Ua]ZuLOAŒLRNTAWRA>PREHbiaTA „ ¸ F   œ¹8„ b ¹j}¨‚  E  7 A(PREUbTaTA>PšEUG 5„ ª k ‰ „ ½ »  ‚ H



F H  Ž;NTA(PVAŒWRA>PRaT[MLOPnZXWRAKA e˜LRA(WVS?A>[UpcaTPVA>‡™aT[xEHG#A>quZX[Ua]ZuLREHGTDB\QXLON#Y(QFS#dT[UAfecEUG`LRA(DFWRZX[HP ZXP‹InA([U[ ZXP;EHG8LOA>DFWOZu[HP;QX‡ˆWRA(ZX[‰‡™aTGTYfLOEUQFGTP(k ? G-‡œZXYfL†›iLRNTA>pY(ZXG…BCA0aTPVA(b…LOQŠA>quZX[Ua]ZuLRA S?ZXG8p’WRA(ZX[zEUG8LOA(DXWOZX[UPŒB8p&Y([UA>qFA>WR[Mp’S?ZXGTEHdiaT[ ZuLREHGTDcLONiAŠAfe˜dTWRA>PRPVEHQFGTPLONTZuLZXdTd\A†ZuW EHGjLRNTAKEHG8LOA>DFWOZuGTb‰"k “hEHGTY>A‹LONTEUP=ZXPRPVA(WLOEHQXG#Y(ZXGTGTQuL2BCAKbTA>PRY(WVEHB\A(bcEHGcDFA>GTA(WRZX[iLRA(WRS#P(› InAoEU[H[HaiPVLOWRZuLOA*EULKB8pPVA>qFA>WOZX[ WVA(dTWVA(PRA>G8L_ZuLREUqFAoAfeiZXS#dT[HA>P(k ]¸@ArY>QFGTPVEHbTA>WKLRNTA0‡™QF[H[UQIKEHGTDjWVA†ZX[EUG8LOA(DXWOZX[ƒ¸ »‚ kª½ „ } K v w {y¶{ b v IKNTEUY_N¶InA’IKEH[U[*AfquZX[Ha]Z«LOA’ZuPQFGTA’d]ZuWVLQX‡oZ Y>QFS#dT[HA e EUG`LRA(DFWRZX[~QqXA(W-Z Y([UQFPRA>b Y(QXG`LRQFaTW IKNTEUY_N·EUP;PRNTQIKG·EUG-zEHDik ‚ k { i¸ y  y -}  ¹ w {y|{ b ¹ Y PšEHP2Afq˜EUbTA(G8Ln‡™WRQFS EHDTk ‚ k { i›8LONTAsWRA(ZX[xEHG8LOA>DFWOZX[ 5Y(QFWVWRA(PVdCQXGTbTPnLRQrLRNTA~EUG8LOA(DXWOZX[ ZX[UQFGTDKLONTAnd]ZXWVLQX‡TLRNTAmY>QFG8LOQFaiW AfehLOA>GTbTEUGTD~‡™WRQXS v-}¨ LOQ vv — ˜ kˆŽ;NTA‹QuLONTA>W LInQ?d]ZuWVLOPKQX‡LONTAY>QFG8LOQFaTW>›xZX[HQXGTDjLONTArGTA>D8ZuLOEMqFAWRA(ZX[Z«e˜EUP  qv — • ˜ LOQ v-}¨F„ ZXGTbJZX[HQFGiDrLRNTAŒPRA>S?EUY(EUWRY([UAKQX‡WOZubTEHaTP Y(A>G`LRA(WVA(b-ZuLnLONTA*QFWREUDFEHG‰›`DFEMqFAsWREUPRA*LRQ5LONiA Y(QXG`LRWREUBTaiLOEUQFGTPšbTA(GiQXLOA>b-ZXP  ZuGTb  WRA>PRd\A(Y>LREUqXA([UpXk2]WRQFS LRNTAŒWRA>PREUbTaTA*LRNTA(QXWRA(S 



 



  







































y

IR

i 

zEHDFaiWRA ‚ k { i¸ 



I’

0

I

R

hQjb ‡™WRQFS ™=txk »‚ k¾½u¯ „ IKEULRN  œ¹8„·} { ZuGTb ƒ›T¹8LO„2NT}|ZuLK¹ EHP>w ›]y EUL;{ EUk P‹mLONTaiAL;POLRZuNTS?A0A0EHG8‡™LOQFA>W DFWOZuGTb-ZX[HQXGT›]D5IKNTLONiEHY_A0N…WRA†[HA(ZuZX[bTZ«P‹e˜LOEHP‹Qi¸ EUP;ZXGAfqFA(G-‡™aTGTYfLOEUQFGQX‡ v vv— •Kv { b  •svC„š}  } G K { b v- } K •KvC„ w y¶{ v w y|{ —QFWVA(QqFA>W(›šLONTA-EHG8LRA(DFWRZX[  QqXA(WŠLONTA-[HZXWRDFAgPRA(S#EHY>EHWVY([HA?IKEULON WRZXbTEHaiP  — ˜ quZXGTEUPRNTA>P(›zB\A(Y(ZXaTPVA?LONiAgEHG8LRA(DFWRZXGTb DFQ˜A>PrLR[Q \>A(WVQ·‡œZXPVLRA(WLON]ZuG Q{ 5 jkJŽQ Ÿ aTPVLREU‡ p LONiEHP‹Y>[ ZXEUS—›8InA0GTQXLOAŒLRN]ZuL‹InA0Y†ZuGJIKWREULRA~LONiAŒqXZuWRE ZuBT[HAsQX‡ˆEHG8LOA>DFWOZ«LOEHQXG ¹ ZXGTbLONiA bTE A>WRG8LOEHZX[ b ¹ QqFA(WKLONiArPVA(S#EHY>EHWRY>[HA~ZXP(¸ ¹o} ŒA R   ·– b ¹o} ŒEHA Rb  ZXGTb-IKEULRNLONTA>PRAX›]LRNTAEHG8LOA>DFWOZX[  EHGLRNTA[HEHS#EUL  — ˜ L_ZX^uA(PKLONTA0‡™QFWVS—¸ [ UEHS  ‰„2}  [HEHS K   w A w { y¶{ E ŒA b  }  [HEUS  E K  A w A y  H b  }€ PREUGTY(A;LRNTA;EHG8LOA>DFWOZu[TQqFA(W ŒDFEMqFA>PnZŒ‘]GiEULOA‹quZX[UaTAXk ~Z†qhEHGTDA>PVL_ZuBT[HEUPRNTA>bcLRN]ZuL  } ZXGTb ‡™QFW  ›`ImAsY(QXGTY([UaTbTA*LRN]ZuL2LONiAsquZX[UaTA*Qu‡ LONiA*QFWVEHDFEUG]ZX[TEUG8LOA(DXWOZX[ EHP q—  — ˜ } K v w {y|{ b v}  ‚ ZWRA(PVaT[UL=InAsN]ZXb#QFBiL_ZuEHGTA>b?EUG#Y_NTZXdiLOA>W { L› ™2txk  { kª© „ ›8aTPVEHGTDoZXG#EHGTPVdTEHWVA(bcY_N]ZXGiDFA QX‡ŠquZXWVE ZXBT[UA(P6œjNTA(WVA LONiA POZXS#A WVA(PVaT[UL—I‹ZXP·bTA(WVEUqFA>b B8p¨PVEHS#dT[Up|ZXdidT[UphEHGiD¥LONiA WRA>PREUbTaTA0LONTA>QFWRA>S—k mA>‡™QXWRA’InA diWRQhY(A(A>b ImA&‡™aTWLONTA>WJAfeiZXS#dT[HA>P(›sImA’IKEU[H[sDFA(GTA>WOZX[UZE \>A·IKN]ZuLInA ‡™QFaTGib·ZXB\QqFAr‡™QFW;LONTAB\A(N]Z†qhEHQFWsQX‡ˆLONTArEHG8LRA(DFWRZX[  QqFA>WŒZcPRA(S#EHY>EHWVY([HA~QX‡WRZXbTEHaiP  Y(A>G`LRA(WVA(b?ZuLLONiA‹QFWREUDFEHG kzlmQXGTPREUbTA(WLRNTA‹Y†ZuPRA‹IKNTA>WRA‹LONiA;EHG8LOA>DFWOZXGibjEHPzLRNTA‹WRZuLOEUQ QX‡ˆLImQ#d\QF[UphGTQFS#E Zu[HPmQu‡zbTA>DFWRA>A ZXGib h›TWRA>PRd\A(YfLOEUqXA([MpC¸ } :£ ¤)KzKy¥y§£ ¤WHH vŠvcy§y¥£¤ w v v w w y@y I:I:III«I«y§y¥¤£ Rv v  b v w : #g…    #O

E



!$#







! 



























































!























X¯ 

 "!$#%! ZXGTbInAšIKEU[H[uLRWVpŒLRQ*AfquZX[Ha]Z«LOALONiEHPEHG8LRA(DFWRZX[FB8p0LOaTWVGTEHGiDsEML EHG8LOQsZ;Y(QXS?dT[UAfeEUG8LOA(DXWOZX[ QqFA>WKZ5Y(QFG8LRQFaTW QFGTA*d]ZXWVL‹QX‡IKNTEHY_NY(ZXGJB\AŒEHbiA(G8LOEM‘]A(bZuPmLONTA~WRA†Zu[CEUG`LRA(DFWRZX[ \¸ £ Kzy§£ HV¹~y§£ w ¹ w y I:I:Ižy¥£ ¹  b ¹ : X¤ Kzy¥W¤ HV¹*y¥¤ ¹ w @ y I:II«y§¤ _¹ w A>LsaTPsZXPVPRaTS#ArLRN]ZuL;LRNTAY(QFG8LOQXaTW Y(QFG8L_ZuEHGTPsZXG…ZXWVYrQu‡WOZubTEHaTP  Y(A>G`LRA(WVA(b’Z«L LONiAsQXWREHDXEHG‰›«IKNTEHY_N#Y(QFG8LRWREHBiaiLOA>P  LOQŒLRNTA;qXZu[HaTA;QX‡\LONiA;Y(QFG8LOQXaTW2EHG8LOA>DFWOZX[ƒk Y [HQFGiD LONiEHPKZXWVYX›TLONiArEUG8LOA(DXWOZuLREHQFGJquZXWVE ZXBT[UA ¹ ZXGTb-LONTAbTE A>WRA(G8LRE ZX[Cb ¹ LOZX^XA0LONiA‡™QXWRS…¸ ¹5} ŒA R  H   w IKNTEUY_N‰›TIKNTA(G—PRaTBiPVLOEMLOaiLRA(b…EHGLONiArY>QFS#dT[HA eEHG8LRA(DFWRZX[»›˜[HA†ZubTP;LOQT¸ £ Kzy¥£ H ŒŒAA y¥£ w   w A A w @y IJIJIžy§£    A A  E ŒA b : -} )¤ Ky§V¤ H y¥¤ w w w @y IJIJI†y¥¤  ŽZX^`EHGTDcY(QXS?S#QFG‡œZXY>LRQFWRP  A ZuGTb   A  ‡™WVQFSLONiArG`aTS#A(WRZuLOQXWKZXGTb-LONTAbTA ¡ GTQFS#EHGTZuLOQFWrZXGib ^XA(A>dTEHGiD&QFGT[Up LRNTAJbTQFS#EHGTZXG8LoLRA(WRS#P  BCA>Y†ZXaiPRAA>qXA(G8LOaTZX[H[MpInA IKEH[U[ [UA>L  — ˜ „ InA5ZXWVWREMqFAZuL(¸ A G  H EUb  } £¤   G  H #• { y¶{ A • A …} £ ¤   G  H IKNTA>WRAKEHGŠQFWVbTA(WLRQQFBiL_ZuE˜LONiAs[HZXPVLAfe˜dTWRA>PRPVEHQFGcImAKSjaiPVLšZXPVPRaTS#A‹LON]Z«L ;• y’{ }  k0Ž2phdTEHY(k2ZX][H[MQFpFW‹›CLOInNiAjEHP‹ImLOZXQcG8N]L0ZuLOdTNTdCEUP~A>G‰EHG8›]LRImA(ADFWRGTZXA>[ˆA(LRb…QLODFQcEUqXN]AŠZ†qFZ?A quZXGTEUPRNTEUGTDJY>QFG8LOWREUBTaiLREHQFG·IKNiA(G — ˜ #• y|{ •r{Œ– j­ 5y ‚ PRQ;LRN]ZuL LONTA‡œZuY>LOQXW  G  H S?ZX^uA(PLONTA=quZX[UaTAQX‡  LRA(GTbLOQ \(A>WRQTkˆŽ;NTA2Y(QXGTY([UaTPREUQFG ‡™WRQXS LRNTEHP=ZuG]ZX[UphPVEHPEUPzLON]Z«L†›FIKNTA>GcLRNTA;EHG8LRA(DFWRZXGTbcEHP=ZŒWRZuLOEUQŒQX‡xLInQrd\QF[Mp˜GiQFS?EHZX[HP>› Ž ]²k(«.± h²fƒ ± ( Ž ]²,2(«´ +/ (+* œ³X´  / Ž ]²>hO² / (+*  /\‰³ Žg(«|± *…1 OŽ4f²j´M³X± h²f…± 4 ·‰³ Ž;´H²R³ OŽ Ž (qŽ i³‰/–Ž ]²š(«.± h²fk ± ( …Ž ]²,2(«´ +/ (+* œ³X´  / Ž ]²>/213*g²f±V‰³ Žg(«±  Žc( ‰1T³X±V‰³ /2Ž²_>² Ž i³‰Ž k q—  ‰¸ Y PsZŠPRA>Y(QFGTb—AfeiZXS#dT[HAu›iInAoY>QFGTPREUbTA(WsZŠPREUS?EU[ ZXWnWRA(ZX[‰EHG8LRA(DFWRZX[»› ‡™QFWŒIKNTEUY_N Z-PVEHS#dT[HA5Y_N]ZXGTDFAcQX‡šquZXWREHZXBT[UA(P~InQFaT[Ub GiQXL0ImQXWR^xkŠŽ;NTAcWRA>PREHbiaTAŠLONTA ¡ QFWVA(S…›‰NTQImAfqFA>W(› Y†ZXG PLOEH[U[B\AŠZXdidT[HEUA(b’IKEULRN&A(t`a]ZX[zA†ZXPVAXkrŽ;NTAcWRA†Zu[zEHG8LRA(DFWRZX[InA ImZXG8LsLRQ?AfquZX[Ha]Z«LOA0EHP>¸ } K v={y¶{ b v »‚ kª½ „ IKNTEUY_N‰›\ZXP*EUGLONTArdTWRAfqhEHQFaTPsAfeiZXS#dT[UAX›TInAoLOaiWRG…EHG8LOQ?Z#Y>QFS#dT[HA e-EHG8LOA>DFWOZu[QžqXA(W*Z Y([UQFPRA>b—Y>QFG8LOQFaiW H ›]PRNTQIKG…EHG…zEHDik ‚ k ‚X ¸ y y …}  ¹  {y¶{ b ¹ 





































 

 



 



































 

















































  

















: #g…    #O

E



!$#







! 





y

y Path 2

Path 1 IR z2



I’

z1

z3

z0

IR

0

I’

z1 x

R

I

0

R

I

x

z EUDFaT.~LWRlZA hJd‚ kn ‚XVe J¸^_`LeVbgf_j: †{hƒbgpxmLhQnagdgagnXfiw3eJ^_^‚nf_jDFWOZu[ -LON]ZuL0InAŠI‹ZuG`L0LRQ A>quZX[Ua] ZuLRAXkŽ;vNTA>} WRA ZXWVA~Lv InQŠ— S?˜ QFWVA~„ d]ZuWVLOPnLOQjLONiAŒY(QFG8LRQFaTW(›˜QFGTA0Zu[HQFGTDoLONTAŒGiA(D8ZuLREUqXA WRA(ZX[Z«e˜EHPŒ[UA†ZXbTEUGTDcLOQgLRNTAjEHG8LRA(DFWRZX[  ›‰ZXGTb·QFGTAŠZX[UQFGTD#LONTAjPVA(S#EHY>EHWRY>[HAQX‡2WRZXbTEHaiP Y(A>G8LOA(WVA(b§ZuLrLONTAgQFWREUDFEHG‰›ˆ[HA(ZXbTEUGTD…LRQ·LONiAgEHG8LRA(DFWRZX[  k…@ A?GTQXLREHY(A#LON]Z«L5LONiA EHG8LRA(DFWRZXGTb5EUPˆZXG5AfqFA(Go‡™aTGTY>LREHQFGoaTGTbTA>W vv — •Kv ›FPRQsLONTAšEHG8LRA(DFWRZX[`QFGrLRNTAmGiA(D8ZuLREUqXA WRA(ZX[xZ«e˜EHP  ‡™WRQFS qv — • ˜ LRQ v-}¨8„ EUP=LONTAKPOZuS?AsZXP x›8LON]ZuL2EUP(›`EHGŠLRNTAKGTQXL_Z«LOEHQXG QX‡KEHDTk ‚ k ‚X ›  } xk-@ AgY†ZXG Zu[HPRQ·ZXWRDXaTAX›z‡™QXWrLRNTAJPOZuS?A#WRA(ZXPRQFGiPŠZXP5EUG LONiA dTWVA>qhEHQFaiPsA eiZXS?di[HAX›˜LON]ZuL q—  ‡™QFW  — ˜ ›iLRNTA(WVA>‡™QFWVA y  y  [UEH S K  ‰„=}‚ }‚  E  7 A(PVEHbTaTA>PnEUG HV„ ]QFWzLRNTA;WRA>PREHbiaTA(P>›`InAKaTPRA;LRNTA;Afe˜dTWVA(PRPVEHQFG#QX‡ ™=t\k »‚ kª½u¯ „ PVEHGTY>A‹LONTA;biA(GTQFS#EHGTZuLOQFW N]ZXPˆQFGT[MpPREUS?dT[UA=WRQhQXLOPˆEHGiPREHbiA2LRNTAmY>QFG8LOQFaiW ZuGTboLRNTAnG`aTS#A(WRZuLOQXW EHP;ƒ¹8PVEH„2S#}|dT[U¹ p? yJaTGT{ EMLpF›TIKNTEUY_N…‡™QXW;A†ZXY_N—WRA(PVEHbTaiAr[UA†ZXbiP‹LOQT¸ H { R ‡™QFW ¹  } •r{Œ– ¹ } A w H   R }¨RVUVUWUWR ¹ ~‡LONiQFPRArWRA>PREHbiaTA(PsLONTAoQFGTA(PKIKEULRN }  R({ R $‚ R ©cZXWVArIKEMLONTEUG H k —QFWRA>QqFA(W>›CInA GTQXLRA0‡™WRQFS!LONTArZXB\QqFAWRA>[ ZuLREHQFGTP‹LRN]ZuL ¹  } •o{~– ¹ } • ¹ { – ¹{ } • ¹ IKNTEUY_N—[UA†ZXbTP;LRQcLRNTA0‡™QF[H[UQIKEHGTDjWVA(PVaT[UL;‡™QFW‹LRNTAQFWREUDFEHGTZX[CEUG8LOA(DXWOZX[ƒ¸ ‚ }¨‚  E •r{ A   y A    y A   y A    











 





























  





























































 "!$#%!



ZXGTb…aTPVEHGTDŠLONiALRWREUDFQFGTQFS#A>LRWREUY~WRA>[ ZuLREHQFGiP Y(QFP    } • Y>QFP    R PREUG    } PREHG    Y(QFP  ½   } • Y>QFP  ©   R PREUG  ½   } PREHG  ©   InA5ZXWVWREMqFAZuL;LRNTA0‘]G]ZX[WVA(PRai[UL } ¯  PVEHG    y PREHG  ©    } ¯  PREHG    y Y(QXP     A>LcaTPjLRWVp LOQ&A>quZX[Ua]ZuLRAgLONTAPRZXS#AJEHG8LOA>DFWOZu[nIKEULRN LONTAaiPRAQX‡sY(QXG`LRQFaTW w ¸ Y PŒ‡™QXW*LONiAŠdTWRAfq˜EUQFaTPŒdTZuLON‰›CLONTAŠd]ZuWVL0QFG’LRNTA v Z«e˜EHP  ‡™WRQXS v }  LOQ v — ˜ „ DFEMqFA(P#LONTA—bTA(PVEHWVA(b EUG`LRA(DFWRZX[ x›mIKNTEH[UA…LRNTA·dTZuLON Zu[HQFGTD LONiA·Y(EUWRY>aT[ ZXW#ZXWVY·DFEMqFA>P Z quZXGiEHPRNiEHGTDY(QFG8LOWVEHBTa˜LOEHQXG B8p LONTA—POZXS#A’ZXWVDFaTS#A(G8LOPgZXPgB\A>‡™QXWRAX› —  ‡™QXW  k*]QFWsLRNTAj[HZXPVL*d]ZXWLŒQX‡=LRNTEHPsY(QFG8LRQFaTW(›‰ZX[HQFGiD#LRNTAj[HEUGTAoZuLŒZuG&ZXGTDF[UA ¯ WRA>[ —ZuLREUqX˜ A5LOQLONiA v Z«e˜EHP>›ImAcY†ZuG IKWVEULRAjLONTAŠquZXWREHZXBT[UA ¹ ZXGTb&LONTAcbTE A>WRA>G`LRE ZX[b 5 ¹ ZXP>¸ ¹o} «A   R b ¹5} A   b  IKNTEUY_N—[UA†ZXbTP;LRQcLRNTA0‡™QF[H[UQIKEHGTDjY>QFG8LOWVEHBTaiLREHQFG ¸ { b  } • A   b uA   „2} • A    } K uA  {   K   „  y¶{  y|{ @ALRNTA(WVA>‡™QFWVAN]Z†qFA‡™QFW‹LONTAA>G`LREHWVArY>QFG8LOQFaiW(¸ y  y  [UEH S K   „=} {;• A  >„=}‚  E  7 A(PVEHbTaiA(PšEHG w „ ZXGTb PVEHGTY>AgLONiAJQFGT[MpPVEHGTDXaT[ ZXWVEULp&IKEMLONTEUG EHP5ZuL A e˜d E ›aTPREUGTD’LONiA WRA>[ ZuLREHQFGiP5ImA-A>PVL_ZuBT[HEUPRNTA>b¥ZuBCQqFAJ‡™QXWjLONTAJquw ZX[UaTAQX‡KV¹ LOKgNT}A-WVA(PREUbT aT A>P(5 ›2„ ImA‘]GTb LONiA ‘]G]Zu[ ZXGTPVInA(W>›  {;• A   „2}¨‚  E •o{ A   – } •  ¯ E {s• A  A   QFW>›]Zu‡ LOA>WKaTPREUGT'D ™2ai[HA(W  P;‡™QFWVSjaT[HZ5‡™QFW‹LONTAY>QFS?di[HAfeJAfe˜d\QFGTA(G8LRE ZX[UP(› }”•  ¯ E A G   { • A   } =PREUG  } ¯  PREHG  y Y(QFP    IKNTEUY_NEHPmEUbTA(G8LREHY†Zu[\LRQ5LONTA~dTWRAfq˜EUQFaTP;ZuGTPVInA(W‹‡™WVQFS Y(QFG8LOQXaTW H ›iZXP‹EULnPRNiQFaT[HbB\AXk









































 















































































: #g…    #O

E 



!$#



! 





¸ Y PV[HEHDXN`LR[Up S?QFWVA—Y>QFS#dT[HEUY†ZuLRA(b PREMLOa]ZuLREHQFG¥ZXWVEHPRA>P#IKNiA(G LONiA EHG8LRA(DFWRZXGTb N]ZuPdCQF[UA(P?QFG LONTA·WRA†Zu[ŒZ«e˜EHP>›sZXPg‡™QFW?AfeiZXS#dT[HA—EHG LRNTA&Y†ZXPVA’QX‡LONiA EHG8LRA(DFWRZX[ } K v  {• { b v »‚ kª½ „ IKEULRNŠIKNTEHY_NŠInAsbiA†ZX[TEUGŠLONTA;PRZXS?A‹‡œZuPRNTEUQFGcZXP=B\A>‡™QFWVAX›FLONTZuL2EHP>›8B`p5LOaTWVGTEHGTD0EML=EHG8LRQ ZjY(QXS?dT[UAfegEHG8LOA>DFWOZu[ QqFA>WKZjY([HQXPRA(b-Y>QFG8LOQFaTW>›]Zjd]ZXWL;QX‡ IKNTEUY_N…Y(ZXG-BCA~EHbTA>G`LREU‘]A>b ZXPLRNTAKbTA(PVEHWRA>b?WVA†ZX[iEHG8LOA>DFWOZX[ƒkŽ‹InQ5d\QFPVPREHBi[HA‹Y>QFG8LOQFaTW2Y_NTQXEHY(A>PšZXWRA;PVNTQIKGgEHGcEHDTk k k G?LONTAs‡™QF[H[UQžIKEUGTDŒInAŒY(QFGiY(A(G8LRWOZuLRAŒQFG?LRNTA*‘TWRPVLmY_NTQFEUY(AX›hIKNTEHY_N?ImAsIKEH[H[xY(ZX[H[ Y(‚ QX‚˜G`{ LRQFaT? W H ¸ y  y cy y }  ¹  {• { b ¹ •*QXLRA‹LON]Z«L=EHGcZXbibTEULREHQFG5LRQŒLONTA;aiPRa]ZX[iY(QFG8LOWVEHBTa˜LOEHQXGTPz‡™WRQXS LRNTA;dCQXPREULREUqXA‹WRA(ZX[TZ«e˜EUP

  





















y

y

Path 1

Path 2 IR

Ib 

I’



z1

z1

z3

Ia 1

0

IR

I’

z2

R

I

Ib

x

Ia 0

1

R

I

x

z EUDFaT.~LWRlZA hJd‚ kbg‚˜m:{ n¸ n VeJ^_`L eVhƒbgfipxhQj>hQaghJagfil w3bg^_mLnnrshQdgnXj<eJbc^‚hQ`:f_jQXQFWRWRWRWVA>PRPRd\d\QFQFGTGTbTbTP5P‹LRLRQ—Q LRNT AJZXGTbTb-A>PRZuEHWVP‹A(bEHGgEULRG8NTLOA(AŒDXdTWOWVZXA>[ qhEHQX„ aT›zPm‡™WVLQFInS QŠLOAfNieiAgZXS#GTdTA>D8[HA>ZuP LOEMqF A?WRA†Zu[m›TZ«Zue˜GTEUb P ‡™ WRQXS LRNTAJPRA>S?EUY(EUWRY([UAgY>A(G8LOA>WRA(b¥ZuLoLONTAQFWVEHDFEUGIKEMLON WRZXbTEHaiP   IKNTEUY_N‰} ›=‡™QF„ W5LONiA POZuS?AcWRA(ZXPRQXGTPjZXPEUG LRNTA?diWRA>qhEUQFaTPrAfeiZXS#dT[HA>PrquZXGTEUPRNTA>Pr‡™QXW  — ˜ „ ›ImAgZX[HPVQ N]Z†qFAŒLInQŠS#QFWRAsY(QFG8LRWREHBiaiLOEUQFGTPn‡™WVQFS LONTA*LONTAŒPVA(S#EHY>EHWRY>[HA>PšIKEMLONgquZXGTEUPRNTEUGTD5WRZXbTEUE»› Y(A>G8LOA(WVA(bZ«L v}¨®Š{ k=Ž;NTA(PVA~Y>QFG8LOWREUBTaiLREHQFGTPšZXWVAKWRA(t`aTEUWRA>bgEHG#QFWVbTA(W2LOQoZ†qFQFEUb?LONiA PREUGTDFaT[HZXWREMLOEUA(PQX‡ LONTAsEHG8LOA>DFWOZuGTbJZuL ¹5}¨®Š{ k=Ž;NTEHPšPREMLOa]Z«LOEHQXG#EUPšZXG]ZX[UQFDFQFaTP=LRQoLONiA AfeiZXS#dT[UAŒImArN]ZXb-bTEUPRY(aiPRPRA>b’EHG-Y_N]ZudiLOA>W { ›i‡™QFW‹LONiArEUG8LOA(DXWOZX[ { bv K v w • {  











  













 "!$#%!

 

IKNTA>WRA’InA’N]ZXb¶ZXWVDFaTA>b LON]ZuLJZXdTdTWVQ8ZXY_NTEUGTD LRNTA’WRQhQXL?QX‡0LONiA’bTA(GiQFS?EUG]ZuLRQFWgZ«L v-Z~In} A([H{ [˜PVbTphA>S#‘TGTS?A(bcAfLOquWREUZXY†[HZXaT[UAš[Upo‡™QF‡™WzWRQFLRS!NTA;ZXEHB\G8LOQA>qFDFA0WOZuZX[GibJImBCA;A>N][HQZuI¶b#Y(EHPnZX[HWR[UA>A(thb5aiLREHNTWRA>EHPbZXEHdTG?dTQFWVWRQ8bTZXA>Y_WnNjLRL_QjZu^hdTEUWRGTQhDŒbTaTLONiY>AA dTWVEHGTY>EHd]ZX[‰quZX[UaTAQX‡zLRNTArEHG8LOA>DFWOZX[ „ kšŽ;NTEH PsEHPsdTWVA(Y(EUPRA>[UpIKN]ZuLsLONiArLInQgPVA(S#EHY(EUWRY>[HA(P IKEULRN qXZuGTEHPVNTEHGTD WRZXbTEHEm[HA†Zub LRQT¸-]QFWjLONiA…PVA(S#EHY>EHWRY>[HAJY>A(G8LOA>WRA>b ZuL v¨} yŠ{ InA N]Z†qFAu¸ 9 ¸ A 

yjW{ ; ¹ } {ny R | – { b ¹ } •  A { EHA ‹b  } H ¹  • {

K {ny „ • {  ZXGTb…PREUS?EU[ ZXWV[UpX›`‡™QXW‹LONTA PRA>S?EUY(EUWRY([UA~Y>A(G8LOA>WRA(b’ZuL v- } •r{ ImAN]Z†qFAu¸ )9 •rW{ ; ¸ ¹ }”•o{ny A R  ¶”– } G2H ¹  {• { b ¹ } • K   •o{my »A{ „ š• { ¢EHA b  PRQgEHG—LRNTAj[UEHS#EUL —  R š} 2£ R_¤ LONTAoEHG8LOA>DFWOZX[UP …ZXGib  ZXWVA5A>quZX[Ua]ZuLRA(b·EUG·LONiA dTWVEHGTY>EHd]ZX[\quZX[HaTA0PVA(GTPVAX¸ } [U EH S K K HcG v  { • { b vŠy H v  { • { b v { bv  } [UEHS K G G2HcG { b vŠy G2K H @AŠY†ZXG&A eidTZXGTb&LONTAŠ biA(GTQFS#EHGTZuLOQFv WV P~• EUG·{ LONTAŠEUG8LOA(DXWOZXGTbiv PŒ QX• ‡ { ZXGTb ;IKEMLON’LONiA aTPVAoQX‡ˆLONiArBiEHGTQFS#E Zu[CA eidTZXGTPREUQFG‰¸=‡™QFW‹LRNTAdCQF[UA0ZuL ¹o}yj{ InAN]Z†qFA ¹  } {ny A „  } {ny A y IJIJI`– ¹  • {*} A IKNTEU[HAŒ‡™QFW‹LRNTAdCQF[UA0ZuL ¹o} •o{ InAoNTZqXA ¹  } •r{ny A „  }  {s• A „  }”{K• ¢A y IJIJI`– ¹  • {~} • A IKNTA>WRA’InA’N]Z†qFA>A>DF[HA>Y>LRA(b NTEUDFNTA(W?QFWRbiA(WgLRA(WRS#P(›KPVEHGTY>A·ImA ZuWRA·EUG8LOA(WVA(PLOA(b¶EUG LONiAŠ[HEHS#EUL — $ R K} 2£ R_¤ k5@¶NTA>G LRNTA(PVA#A e˜d]ZXGTPVEHQFGTPrZXWVAŠPRaTBiPVLOEMLOaiLRA(b EHG&LONiA EHG8LRA(DFWRZX[HP ZXGTb _›˜ImA‘]GTb‰¸ [HEH S K  „2} • E  { R [HEH S K  „=} • E  •o{ LONTZuLšEHP(›8LRNTAsLInQ5Y>QFG8LOWVEHBTaiLREHQFGiP‡™WRQFS LRNTAsEHGi‘]GiEULOA>PREUSgZX[˜PRA>S?EUY(EHWVY([UA(P=Y(A>G8LOA(WVA(bZ«L v·LONi}”A‘T®cG]{ZX[Y(WRZXA>GTPRY>aTA([ML†[ˆ¸ A†ZXY_N’QuLONTA>W(k ”=aiLRLREHGTDgZX[H[‰LRNTA(PVAjWRA>PRaT[MLOPKLOQFDXA>LONiA(W(›xInAjZXWVWREUqXA5Z«L y  y [U EH S K  „y [UEH S K  „y  [HEU S K   „=}‚ }‚  E  7 A(PREUbTaTA>PnEUG H„ 



















































































































































































: #g…    #O

E



!$#





! 



 

} ‚  E { A  y A  wzy A    B\A(Y†ZuaTPRArLONTAQFGT[MpWRA>PREUbTaTA(PsA(GiY([HQXPRA(b—B8p…LRNTAA(G8LOEUWRArY(QFG8LRQFaTW ZXWRA0LONiArPVEHS#dT[HA d\QF[HA>PKZuL G`LREULREHA(P>¸ Y(QFP  ¯  } • Y(QFP  © ¯   R PVEHG  ¯  } PREHG  © ¯   R A  wm} E InAoDFAfL;‡™QFW‹LONiAquZX[UaTA0QX‡ x¸ } •  {ny “ ‚F„ »‚ k 8„ LJEUPgEHGiPVLOWVaTY>LREUqXA—LOQ IKWREMLOA—LRNTA·A e˜dTWRA>PRPREUQFGTPg‡™QXW ZXGib jEUG Z biE CA(WRA>G8L ‡™QFWVSg? ZuL(¸ [HEUS K  „=}¨‚  E  ‚    •r{ž„> 7 A(PREUbTaTAsZuL ¹5} {ž„ [HEU S K  „š}€‚  E  ‚    •o{ž„> 7 A(PVEHbTaTAsZuL ¹o} •r{ž„ Ž;NTA>PRA~A e˜dTWRA>PRPREUQFGTPnY†ZXG?BCAKWOZ«LOEHQXG]ZX[HE \(A>bcZXP=‡™QF[H[UQžIKP>¸Ž;NiA~EHG8LRA(DFWRZX[TQqFA>W‹ZY(EHWVY(a˜¡ [ ZuWnZuWRYsQX‡ quZXGTEUPRNTEUGTDrWOZXbTEUaTP2Y(A>G`LRA(WVA(b-ZuL ¹5}€V¹ K IKNTA>WRA*LRNTA~EUG8LOA(DXWOZXGTb  œ¹8„ N]ZuP ZPREUS?dT[UAjd\QF[HAu›EHP0A(t`a]Zu[LOQ ‚  EzLREHS#A(PŒLRNTAЇ™WOZXYfLOEHQXG&QX‡nLRNTA#ZXWRYŠEUG aTGTEULRP0QX‡ ‚  LOEUS?A>P;LONTAoWRA(PVEHbTaiAoQX‡zLONTAr‡™aTGTY>LREHQFG—ZuLsLONTAoPREUS?d\AdCQF[U‰A œ\ZXG—AfehLOWRZ#‡œZXYfLOQFWsQX‡ •r{ ZXY>Y(QFS#d]ZXGTEUA(PsLONTAjWVA(PVEHbTaTArIKNTA(G&LRNTAŠZXWVY5EHPsLOWRZqXA(WVPRA(b EUG·LONTAoY([UQ˜Y_^8IKEHPVAjPRA>GTPRAuk Ž;NTEUP5EHP5ZXY>LRa]ZX[U[Up Z·DFA>GTA(WRZX[mWVA(PVaT[ULoLON]ZuL5Y†ZXG B\AgPL_ZuLRA(b ZXPo‡™QF[H[UQžIKP>¸#lmQFGTPVEHbTA>W Zg‡™aTGTYfLOEUQFG  ƒ¹F„ ZXG]ZX[Mp`LOEHYoQFG ZXGTG`aT[UaTP0Y(A>G8LOA(WVA(bZuL V¹ K ›‰IKEMLON&ZJPVEHS#dT[HAodCQX[HAjZ«L ¹o}¨¹VK œiLONiA(G [HEU S K    ƒ¹F„ b ¹5}‚  E  ‚    7 A>PREUbTaTAsZuL ¹5}€V¹ Kf„ »‚ k {ž„ IKNTA>WRA 9 V¹ Ks; EHPKZŠY(EUWRY(ai[ ZXW;ZuWRYQX‡WOZXbTEUaTP *ZuGTb…ZXGTDFaT[HZXW‹IKEHb˜LON ›TIKNTEUY_N—[UEHA(P A(G8LREHWRA>[Up?IKEULONiEHGLONTArZXGiGhai[HaTPKY(A>G8LOA(WVA(b·ZuL V¹ K ¸ ¹]  „n}|V¹ Ky RA R  K   Kzy 









































































 















 "!$#%!  ˆŽ QdTWVQqFA-LONTEUP#PL_ZuLRA(S#A(G8L†›šImA…GTQXLRA‘]WRPL#LRN]ZuL#PREUGTY(A  œ¹8„ EHP#ZXG]Zu[Up`LOEUYJQFG¥ZXG ZXGTG`aT[UaTPnZXWRQFaiGTb ImA*Y†ZXG#aTPVA~EULRP ˆZuaTWRA>G`LnPRA>WREUA(PšAfe˜d]ZXGTPVEHQFG?EHGŠLONiA*GTA>EHDFN`B\QFW¡ NTQhQ˜b-QX‡ V¹ K ZXPRPVaTS?V¹ KEUGTDŠLON]Z«LKEULKY(QXG`qXA(WVDFA(P*aTGTEU‡™WVQFS#[Up#EHGLONiAoZuGTG`aT[HaTP>¸ F  œ¹8„2} s¤ FTƒ¹• V¹ Kf„ F G “˜EUGTY(ALONTAr‡™aTY>LREHQFG…N]ZXP~Z#PVEHS#dT[HAd\QF[HArZuL V¹ K › ¤ }” ‡™QXW

•Œ‚ IKNTEHY_N’[UA†ZXbiP LOQi¸  E VA F A F Ob  }  ƒ¹8„ `¹j} s¤ F s¤ F F F G F G2H   IKNTA>WRALONTAEHG8LRA(DFWRZX[ F EHP;bTAf‘]GTA(b·ZXP(¸  A F H b  F HE Fo}  ZXGTb…A>quZX[Ua]ZuLREHQFGJQu‡zLONiEHP;DFEMqFA(P>¸ ‡™QF"W D } •r{ — G2H=} E ‡™QF"W D ­  — Fr} F H D y|{ { RA F H  • A F H   »‚ k ‚F„ L LONiAnLOA>WRS#PˆIKEMLO0N D } •o{ quZXGTEHPVN‰›FZuGTb5QFGi[Up0LONiAnLOA>WRS D } •r{ ? G5LRNTAn[UEHS#EU

PRaiWVqhEUqXA(P(›x[UA†ZXbT—EUGTDj LOQ  œ¹8„ b ¹j} E W¤ G2H=} E  7 A(PREUbTaTAsZuL ¹o}€V¹ Kf„  IKNTEUY_N—dTWVQqFA(PKLONiArbiA(PREUWRA>b—‡™QFWVSjaT[ Z˜› ™=txk ƒ‚ k {ž„ k •*QXLRA‹LON]Z«L=EU‡ LRNTEHP‡™QXWRSjaT[HZ*PVEHS#dT[UprWRA>bTaTY>A(P=LOQŒLRNTA;WRA>PREHbiaTA‹LONTA>QFWRA>S—k @AŠA(S#dTN]ZXPVZE \(Au› NTQ}¨ImAf‚ qF A(W>›ˆLRN]ZuL0LRNTAj‡™QFWRS5aT[ ZJQX‡ ™=txk »‚ k {ž„ O³ ,:,\´ »² …Žc(  *,\´H² ,2(«´H² o(+/]´ u›`IKNTA>WRA†ZuPnLONiA~WRA>PREUbTaTAKLONTA>QFWRA>S!EUPšquZX[UEHbЇ™QFWnZod\QF[HAKQX‡ZXG8pcQFWRbTA>W(k=ŽˆQ PRA>A~IKNTA>WRA~LRNTEHPšY(QFS#A(Pš‡™WRQFS…›8ImA*QFPRA>WVqXA~LON]Z«Lm‡™QFWnZXGJZuWRBTEMLOWOZuWVpŠquZX[HaiA*QX‡ }€‚  LONiAjAfe˜dTWVA(PRPVEHQFG EUG ™=t\k ƒ‚ k ‚F„ quZXGiEHPRNiA(P0QFGT[Mp-‡™QFW D ­  › IKNiA(WRA(ZXPŒ‡™QFW } ‚  EUL;quZXGiEHPRNiA(PKEHbTA>G8LOEHY(ZX[H[Mpc‡™QFWKZXG8pJquZX[HaiA0QX‡D›TBCA>Y†ZXaiPRArQX‡LRNTAEHbTA>G8LOEULp A w F H } { IKNTEUY_N&EHP0ZgbiEHWRA>Y>L0Y>QFGTPVA(t`aTA(GiY(A#QX‡2LONT…A ™=aT[UA(W~‡™QXWRSjaT[HZik~Ž;N`aTP>›‡™QFW } ‚  InA Y†ZuG¥Z QFWVb LOQ&N]Z†qXA-LRA(WVS?P5IKEMLON›D”µ •r{ EHG LRNTA  ZXaTWRA>G8LcAfe˜d]ZXGTPVEHQFG ›2IKNiEHY_N EHS#dT[UEHA(P*ZJd\QF[HAjQu‡nQXWRbTA>WŒNTEHDXNTA(W~LRN]ZXG aTGTEMLpF›‰PVEHGTY>AjLONTAŠEUG8LOA(DXWOZX[UP F dTWRQhbTaTY>A(b B8pŠLONTA>PRAsLOA(WVS?P2IKEH[U[iquZXGTEUPRN?ZXGTb?InAKIKEH[H[]B\AK[HAf‡ LšIKEMLONcLONTAKquZX[HaiAsQu‡ LONiA*WVA(PREUbTaTAuk 



 











 



 



 















































































 





























{ @ AŒZX[HPVQ5GTQXLRA*LRN]ZuL‹EM‡‰LONiAŒY(EUWRY(ai[ ZXWnZXWRY*EHP2LOWRZqXA(WVPRA(b…EHG#LONTA~Y([HQhY_^8IKEHPVA~PRA>GTPRAu› LONiA·ZXGiDF[HA &EHGTY>WRA(ZXPRA>P(›‹LONiA(WRAf‡™QFWRA   ›nIKNTA>WRA†ZuPgEU‡*EUL#EUPcLRWOZ†qFA>WRPVA(b EHG LONiA Y(QXaTG8LOA(W ¡Y>[HQhY_^`IKEUPRAsPRA>GTPRAu› µ  IKNTEHY_N#dTWRQhbTaTY>A(P2LONTA •r{ž„ ‡œZXYfLOQFW‡œZXYfLOQFW2S#A(G˜¡ LOEUQFGTA>b A†ZXWV[HEUA(W(k-Ž;NTA?‡™QFWRSjai[ Z-QX‡™=t\k »‚ k {ž„ ZX[U[HQIKPoaiP5LOQ’PV^`EHd PVEHS#dT[HAcd\QF[HA>P LONTZuL‹N]ZudTdCA>GJLOQo[HEHAsQFGgLRNTA~dTZuLONQX‡‰EHG8LOA>DFWOZuLREHQFG ›`IKNiEHY_NEHPšA(t`aTEMquZX[HA>G`LnLOQjAfquZX[Ha˜¡ ZuLREHGTDrEHG8LOA>DFWOZu[HP2B8p?LOZX^`EHGTDLONTA>EHWšdTWREUGTY(EUd]ZX[TquZX[UaTAX›˜ZXPnZX[HWVA†ZXbipcS#A(G8LREHQFGTA>bgEUG?LONiA AfeiZXS#dT[UAZXBCQqXAXk Y GTQuLONTA>WˆqXA(WVpraTPVA>‡™aT[hDFA>GTA(WRZX[8Y(WVEULOA>WREUQFG0‡™QFWIKNTA(G5LRNTAšEHG8LOA>DFWOZX[UPQqFA(WˆY(EUWRY>aT[ ZXW ZXWVY(PKQX‡EHGi‘]GiEULOA0WRZXbTEUaTP‹quZXGTEHPVN-EHP(¸    ‰¸nlmQFGTPREUbTA(W;LRNTAEHG8LOA>DFWOZX[ A   ƒ¹F„ b ¹ …} »‚ k F© „ IKNTA>WRA EHP2ZWRA†Zu[»›8d\QFPREMLOEUqXA;Y(QFGiPVL_ZuG`L(› EHPšZ0Y(EHWVY(aT[HZXW2ZXWVY;QX‡‰WRZXbTEHaiP €Y(A>G8LOA(WVA(b ZuL;LRNTAQFWREUDFEHG-ZXGib…[MphEHGTDŠQFG-LONiAraidTdCA>W¡¢N]ZX[U‡ˆY>QFS?di[HAfedT[ ZXGiAX›iLRN]ZuLKEHP>› ¸ ¹o} ŒA R   H   w  ZXGTb-LONiA‡™aiGTY>LREHQFG  œ¹8„ EHP;B\QFaTGTbTA>b—QXG › ¼  ƒ¹8„ ¼ R  ¸F‘]GiEULOA LONiA(G LONTA…EHG8LOA>DFWOZu[  QqFA>W#LRNTA-Y(EUWRY(ai[ ZXWcZXWVYEHPcB\QFaTGTbTA>b ZuGTb§‡™QXW  —  EUL quZXGTEUPRNTA>P(k Ž;NTEUPŠPVL_Z«LOA(S#A(G8LŠY(ZXG BCAdiWRQqFA>b¥ZuPj‡™QF[H[UQžIKP>¸?QXG LONTAY>EHWRY>aT[ ZuWjZXWVYX›=AfehLRA(GTbTEUGTD ‡™WRQXS  H LRQ  w InAoNTZqXAX¸ ¹5} ŒA R b ¹5} ŒEUA ZXGTb-LONiAoZuBTPRQF[UaiLOAŒquZX[UaTA0QX‡ˆLONTAEUG`LRA(DFWRZX[‰QqFA>WsLRNTEHPKZuWRY0L_ZX^uA(P;LONiA‡™QXWRS…¸ ¼  ¼ } A    ƒ¹F„ E ŒA b  A    ƒ¹8„ E ŒA b  IKNTA>WRAgLRNTA?[HZXPVLoWRA>[ ZuLREHQFG EHPbTA>WREMqFA(b ‡™WVQFS LONiA?LOWVE ZXGiDF[HAŠEUGTA(t`a]ZX[UEULpXk maiL…¼ EV¼ } ¼ Afe˜d  E TvC„ ¼ } ¼ A e˜d  E  „ ¼ } { ZXGTbz= }  PREUG   „ ›iIKNTEUY_N—[UA†ZXbLRQT¸ ¼  ¼   A G   b  Y PVPRaTS#A  Hs}   R  }  › IKNTEUY_N&EHP*Y(QqFA>WRP0LONTA5A(G8LOEUWRAjWRZXGTDFAjQu‡šZX[H[UQžInA(b—qXZu[HaTA>P ‡™QFWLONTA?PREMLOa]ZuLREHQFG&w InAZXWVA?Y>QFGTPREUbTA(WVEHGTDi›LONiA(G PVEHGTY>A#LRNTAgEUG`LRA(DFWRZXGTbEHGLRNTAg[HZXPVL : #g…    #O

E



!$#





!























































  



















 















 











 "!$#%! ‚ Afe˜dTWVA(PVPREHQXGjEHPZsPphS?S#A>LRWREHY=‡™aTGiY>LOEUQFG5Qu‡;IKEULONoWRA>PRd\A(Y>LLOQ 5F‚ ›žInAmY†ZuG5A>quZX[Ua]ZuLRA EULKQXGT[UpgEHGJLONiArWRZXGTDFA   5F‚ ZXGTb-SjaT[MLOEUdT[Up#EULKB8p-ZЇœZXYfLOQFW;QX‡ ‚ ¸ PREHG  …•  „=} PVEHG   „=– K  A G   b  }‚ K  w A G   b  BTaiLsEUG-LRNTEHP;WRZXGTDFAŒInArN]Z†qFAX¸    ‚ ¸5PVEHG   „ ­ ‚   IKNTEUY_NjY†ZXGoBCAnA†ZXPVEH[MpPRNTQIKGjB8p5Z*DFWRZXdTNTEUY†ZX[`ZXWVDFaTS#A(G8L†›XZXGTboEU‡iInA‹WVA(dT[HZXY(AšPREUG   „ EHGŠLRNTA*EUG8LOA(DXWOZXGTb#B8p ‚  5  InA*IKEU[H[˜DFA>LmZXG#aTdTd\A(W2BCQXaTGTbc‡™QFW=LONTAsQFWREUDFEHGTZX[hquZX[UaTAX¸    ‚ ¸ • PREHG   „ • ‚   – K  w A G   ™b K  w A G   w 8b @¶EULRN…ZX[H[\LONTEUPKInAQFBiLOZXEHG‰¸ ¼  ¼ €‚   K  w A G   w  b  Ž;NTA‡™QF[H[UQIKEHGTDoY_N]ZXGTDFArQX‡ˆquZXWREHZXBT[HA>P }  ‚  IKNTA>G·EHGiPRA(WLOA>b—EUG-LRNTAEHG8LOA>DFWOZu[‰DFEUqXA(P>¸ ¼  ¼   K   A G b }   {s• A G   „ ]WRQFS!LONTEUP;WRA>PRaT[ML†›TInArQXBiL_ZXEUG-EHGLONTA[UEHS#EULnQX‡  — ˜  — ˜ – ¼  ¼  IKNTEUY_N PRNTQIKPrLON]ZuLrLONiAgEHG8LRA(DFWRZX[  EHPrBCQXaTGTbTA>b PREUGTY(A  EHP‘]GTEULRAgZuGTb EUGLONiA [HEUS?EML  —  EML*quZXGiEHPRNiA(P(k •*QXLRAoLRN]ZuL XQFWRb]ZuG  P  A>S?S?ZcY†ZXG’B\AjZudTdT[HEUA(b…‡™QFW ZoWVA†ZX[ƒ› / ² 8‰³ Ž X²=Y>QFGTPL_ZXG8LKZXPšImA>[H[ƒ›hQXGT[UpŠLRNTA(GgLRNTA~dTZuLONJQu‡EHG8LOA>DFWOZ«LOEHQXG?SjaiPVLn[HEHA QFGLONiA#Z´ ( m²f±nN]ZX[M‡zQX‡ˆLONiArY>QFS#dT[HA edT[HZXGTA  LRN]ZuLKEUP(2› = |8„ k ˆ¸sŽˆQEH[H[UaTPVLRWOZuLRA0LONTAŠaTPVA>‡™aT[UGTA(PVP0QX‡XQFWVb]ZXG  P A(S#SgZ˜›\InAŠY(QFGh¡ PREUbTA(WrLONTA#‡™QF[H[UQIKEHGTD-AfeiZXS#dT[UAgQX‡KZ—WRA†Zu[nEUG`LRA(DFWRZX[=IKNTEHY_N Y†ZXG B\AgAfquZX[Ha]Z«LOA(b B`p Y(QXG`LRQFaTWKEHG8LRA(DFWRZuLOEUQFG‰¸ } G Y>v QFw P •  Tv£Cw „ b v »‚ k X¯ „ 

































  

&

















F© IKEULRN £‚R WRA(ZX[‰d\QFPREMLOEUqXAŒY(QXGTPVLOZXG8LOP(knzEUWRPVL(›iGTQuLOAŒLONTZuL;ImAY(ZXG—WVA>IKWVEULOAŒLRNTEHP;EUG8LOAf¡ DFWRZX[‰EHGLRA(WRS#P;QX‡LImQ#QXLONiA(W;EHG8LRA(DFWRZX[HP>¸ G } ‚{ G A  v w y • A £ w  b v-} ‚{ Hy ‚{ w A G  b v A  b v R } H=} w G vw • £w G v • £ w w ZXGTb Y(ZXG BCAjY>QFGTPVEHbTA>WRA(bZXP0d]ZuWVLOP~QX‡mY>QFG8LOQFaiW0EHG8LOA>DFWOZX[UP~QFG’LRNTAŠY(QXS?dT[UAfe dT[HZXGTA·HXIKR NTw EUY_N€PRZuLOEUPV‡ p§LONTA Y>QFGTbTEMLOEHQXGTPJQX‡ XQFWVb]ZXG  P A(S#SgZ ‡™QFW?LONTA&Y>QFG8LOQFaTWVP PRNiQžIKG·EHG—zEHDTk ‚ k ‚F‚ kmxQXW H ›]ImAodCA>WV‡™QFWVSLONiAoEUG`LRA(DFWRZuLOEUQFG-QFG’ZcY(QXG`LRQFaTWsPR^`EHdh¡ : #g…    #O

E



!$#





























!



























y

 IR+



I’a



y I 2



a

R

0

~

I’a

Ia

I

Ia 0

a

I1

x

~

R x

z hJEUd.DF„LaTeJWRj A  a ‚ kn‚FX‚ to¸ toe hQj[HQFPVEHGTDŠB8p—Z#PVA(S#EHY>EHWRY>[HA [UphEUGTD0QFGŠLONToA 1J,:,]²f±zN]Zu[U‡\QX‡\LONTA;Y>QFS?di[HAfejdT[ ZuGTAX›8B\A(Y(ZXaTPRAsEHGjLRNTEHP=Y(ZXPRA;LRNTAKAfe˜dCQ«¡ GTA>G`LRE ZX[ˆEHG…LONTAoEHG8LOA>DFWOZuGTb·EUG`qXQF[UqXA(P~LRNTA5WVA†ZX[ˆY(QXGTPVLOZXG8L   PRQ?LON]ZuLXQFWVb]ZXG  P A(S#SgZrEHPšPOZuLREHP‘]A(bJ‡™QFW =J­  ‡™QFW2LONiAŒEHG8LOA>DFWOZu[  k=Ž;NTEUPmY>QFG8LOQFaTWmEHG8LOA>DFWOZuLREHQFG [HA(ZXbTP‹LRQT¸ Hy [HEUS K  „y [UEHS K   „y  [HEUS K   „=}¨r– H=} • [HEUS K  „z• [HEUS K   „      IKNTA>WRAŠLONTAŠEUG8LOA(DXWOZX[  QFG&LONiAŠaTdTd\A(WN]ZX[M‡ndi[ ZXGTA5EHPŒA>[HEHS#EHGTZuLOA>b’B8p XQFWVb]ZXG  P A(S#SgZ˜kŽ;NTArQXLONTA>W‹LImQ?EHG8LOA>DFWOZu[HP;ZuL;LRNTAPREUGTDFaT[HZXWREMLOEHA>PmQFG-LONiA v Z«e˜EHP;DFEMqFAu¸ [HEH S K  „2} • ‚{ ƒ‚  E „> 7 A(PVEHbTaTAKZ«L ¹5} •*£h„2} ‚X £ E A G  [HEH S K   „2}”• ‚{ ƒ‚  E „( 7 A(PVEHbTaiAKZuL ¹j}€y£h„2} • ‚X £ E A  ]QFW w ›iInArd\A(W‡™QFWRS LONiA0EHG8LOA>DFWOZuLREHQFGgQFG-ZŠY(QFG8LOQXaTW;PR^`EHdidTEHGTDŠQqXA(W‹LONiA0dCQF[UA(P;Z«L v§} ®r£ QFG LONTA?WRA(ZX[2Z«e˜EHPoZXGTbY([HQXPREHGiD…B8pZ-PRA(S#EHY>EHWVY([HAŠQXGLONiA—Z´ ( m²f±ŒNTZX[U‡nQX‡ 





















































 











X¯ 

 "!$#%! LONiA#Y>QFS#dT[HA e&dT[HZXGTAX› EUG QXWRbTA>WLRQ—PRZuLOEUPV‡ p XQFWRb]ZuG  P A(S#SgZg‡™QXW{=  ‡™QFW0LONiA EHG8LRA(DFWRZX[ ›B\A(Y†ZuaTPRAcEHG’LRNTEHP~Y†ZXPVAcLRNTAŠAfe˜d\QFGTA>G`LRE ZX[zEHG’LONiAŠEHG8LOA>DFWOZX[EHG8qFQX[UqFA>P LONiArWVA†ZX[Y>QF‚GTG PL_ZXG8L • µ  k=Ž;NTEHPKY>QFG8LOQFaTWKEUG`LRA(DFWRZuLOEUQFG[HA(ZXbTP‹LRQT¸ w y [HEUS K  „y [UEH S K   „y  [HEU S K  2G „=}¨r– w } • [HEUS K  „z• [HEUS K   „ IKNTA>WRA?LRNTAgEUG8LOA(DXWOZX[ ‚G QXGLONiAg[HQInA(WrN]ZX[M‡mdT[HZXGTA#EHPA([UEHS#EHG]Z«LOA(b B8p XQFWVb]ZXG  P A(S#SgZ˜kŽ;NTArQXLONTA>W‹LImQ?EHG8LOA>DFWOZu[HP;ZuL;LRNTAPREUGTDFaT[HZXWREMLOEHA>PmQFG-LONiA v Z«e˜EHP;DFEMqFAu¸ [HEH S K  „2} ‚{ »‚  E „( 7 A>PREUbTaTAKZuL ¹5} •*£˜„š} • ‚X £ E A G  [UEH S K   „2} ‚{ ƒ‚  E „( 7 A(PVEHbTaiAKZuL ¹j}€y£h„2} ‚X £ E A  ? G’B\QXLON·Y†ZXPVA(P(›CLONTAoEHG8LOA>DFWOZX[UP~ZuWRQFaTGib—LONiAjPREUGTDFaT[HZXWREMLOEHA>PKZuL v&} ®r£ InA(WRA5A>quZX[M¡ a]ZuLRA(b&EUG’LONTAjaiPRa]ZX[I‹Z†pF›aiPREHGiDJLONTAŠWVA(PRai[ULOP*ImAŠbTEUPRY>aTPRPVA(bZXBCQqXAj‡™QFW~PV^hEUdTdTEUGTD PREUS?di[HAgd\QF[UA(P(k Ž;NTEUPŠEHPjA>thaiEUquZX[HA>G8LjLOQ A>quZX[Ua]ZuLREHGTD·LRNTAEHG8LRA(DFWRZX[HP ZXGTb EUG LONiA5dTWVEHGTY>EHd]ZX[quZX[UaTAoPVA(GTPVAXk •*QXLRAoLONTZuL*‡™QXW ZuGTb  LRNTA5PVA(S#EHY(EUWRY>H[HAQX‡=WRZXbTw EHaiP —  EHPzLRWOZ†qFA>WRPVA(b#EHGjLONiA;Y([HQhY_^8IKEHPVA‹PRA>GTPRAu›hIKNTEU[HAm‡™QXW ZXGTb  LONTA;PVA(S#EHY>EHWRY>[HA

EHP‹LRWOZ†qFA>WRPVA(b’EUGJLONTAY(QXaTG8LOA(W ¡Y>[HQhY_^`IKEUPRArPRA>GTPRAuk lmQFSjBTEUGTEHGiDjLONTAWRA>PRaT[MLOP;InAoQFB˜L_ZXEUGJ‡™QFW‹LONTA0quZX[UaTA0QX‡ˆLONTAQFWVEHDFEUG]ZX[ EUG8LOA(DXWOZX[ƒ¸ } ‚{ 9 H‰y w ;C} • ‚{ †[U EH S K  „ y [HEUS K   „y [UEH S K  „y [HEH S K   „ } • £ PREUG x£h„ ¸ Y PˆZ;‘TG]ZX[8AfeiZXS#dT[UAzImAšY(QXGTPREUbTA(W ZXGrEHG8LRA(DFWRZuLOEUQFG~LONTZuL WRA>thaiEHWRA>P Z’WRA>Y>LOZXGTDFaT[HZXWjWRZuLONTA>W5LONTZXG§Z’PRA(S#EHY>EHWVY(aT[HZXWoY>QFG8LOQFaiW(k ? G8LRA(DFWRZX[HPjQu‡sLRN]ZuLjLphd\A ZXdTd\A†ZuWmIKNTA(GLRNTAŒEHG8LRA(DFWRZXGTbJEUG`qXQF[UqXA(P‹LRWREHDXQFGTQFS#A>LRWREHY;‡™aTGiY>LOEUQFGTP>k 0aiWmAfeiZXS#dT[UA Y(QXGTPREUPVLOPKQXLKLRNTA0‡™QF[H[UQžIKEUGTD5WVA†ZX[EUG8LOA(DXWOZX[ƒ¸ PVEHG  ]vC„ b v-} ? S A  b v } ? ’S 9 ; K‹} »‚ k 8½ „ PREUGTN  vC„ PREHGiN ™vC„ G G @ArGiQXLOEUY(AŒLONTZuLK‡™WRQFS!LONTAbTAf‘]GTEULREHQFGQu‡zLONiArN8phd\A(WRB\QF[UEHY~‡™aTGiY>LOEUQFGTP>› PREHGiN ™vC„2} A • ‚ A G – PVEHGTN  vcy¥‚  E „z} A w  • ‚ A G G w  } PVEHGTN ™vC„ PRQ InA…Y(ZXG§aTPRALONiA…Y>QFG8LOQFaiW#PVNTQIKG EUG¥EHDTk ‚ k ‚ ©&‡™QXWjLONTA-A>quZX[Ua]ZuLREHQFG QX‡sLONiA EHG8LRA(DFWRZX[ ¥EHG ™=txk »‚ k 8½ „ BCA>Y†ZXaTPVA Zu[HQFGTDLONTA’LInQ¥NiQFWRE \(QFG8L_Zu[~d]ZXWLOPQX‡rLONiA Y(QXG`LRQFaTWKLONTArbTA>GTQFS#EHG]ZuLRQFWRPKEUG…LRNTAoEUG8LOA(DXWOZXGTbiP~ZXWVArLRNTA5PRZXS#AXk;]QFW;LONiAod]ZuWVLsQX‡ 





























































































  





















!











 







: #g…    #O

E



!$#







! 





y I’

2π Ib

I’R

Ia 0 

zEUDFaTWRA ‚ k ‚ ©i¸3

f_jQFG8LOWVEHBTaiLREHQFG ZX[HQFGiD-LRNTAŠqFA>WVLOEUY†ZX[=dTZuLON ¹…}  y = R0 = ‚  LONiArEUG8LOA(DXWOZXGTb-B\A(Y>QFS?A>P(¸ A    } ‚ A G   A   – ‚  A   • A G 2G  „ A   A  • A G w ‚G  „ [ HEUS  ‰„2}  [UEHS A {  K w  A ‚ EH•A G A G A w ‚ G  bx= }¨ PREUGTY(AŠLRNTAcEHG8LOA>DFWOZuLREHQFG·QžqXA(EW =·DFEMqFA>PoZJ‘]GiEULOAjquZX[UaTA  LRNTAcEHG8LOA>DFWOZuGTb EHPŒ‘]GTEMLOAŠEUG S?ZXDFGTEMLOaTbTA „ k|“˜EHS#EH[HZXWR[MpJ‡™QFW  ZX[UQFGTDJLONiAjqFA(WLOEUY†ZX[dTZuLON ¹}•  y E = R~‚  ­ =J­  InAr‘]Gib ‚A G  A  G  A ‚ G } A  A ‚ G A G    A G   A G –   •  „  w  •  „ [ HEUS   „=}  [HEHS • A {  K w  A G ‚ wEHA G    A • G A G  xb = }¨ B\A(Y†ZuaTPRArZXD8ZuEHGgLRNTAEHG8LOA>DFWOZuLREHQFGgQžqXA(W =?DFEUqXA(PKZj‘]GTEMLOA~quZX[UaTAXk2]WRQXS!LRNTA0WRA>PREHbiaTA LONiA(QFWVA(SInAoNTZqXAX¸ y  y  [UEHS   „y  [HEUS   „y [HEUS K  „y [UEH S K  „2} • A G w  y [HEH S K  „y [HEU S K  „š}€‚  E  7 A(PREUbTaTAKZuL ¹o}  E „ 



 









































































































































 "!$#%!



LONiA·PREUGTDFaT[HZXWREMLp ZuL ¹ }  EKB\A(EUGTDLRNTA·QFGi[Up QFGTA—EHGTPVEHbTA-LONiA’Y([UQFPRA>b Y(QXG`LRQFaTW>› ZXGTb…PREUGTY(ALONiArd\QF[UA(PsZuL ¹j}R  E R ‚  E‰ZXWVAPREHS#dT[UA0dCQF[UA(P  PVA(A0”=WRQFBT[UA(S {X{ž„ ›TInA QFBiLOZXEHG ¸ [HEUS K  „š} •r{ž„  E  7 A(PREUbTaTA*ZuL ¹o}¨8„=} •  E [HEU S K  „=} •r{ž„  E  7 A(PREUbTaTAsZuL ¹5}¨‚  E „=} •  EHA G w    7 A>PREHbiaTAsZuL ¹j}  E „=}”• A G   IKNTEUY_N‰›TIKNTA(G…PRaiBTPVLREULOa˜LOA(b…EHGJLRNTAdTWRAfqhEHQFaTP;A>t`a]ZuLOEUQFG-DFEUqXAŒ‡™QFW‹LONiAŒqXZu[HaTA0QX‡ˆLONiA QFWVEHDFEUG]ZX[\WRA†Zu[EHG8LOA>DFWOZX[ S 9 ;C}  {K• PVEHGTN {  ˆ„ Km} ? [



















J



 {





’!



=/ #.&%('0" 1 { kLRsNTPRAcEHGiPRDoA(WVLOEHNiA>PA~ŽIKZNiphEHY_[UQFN WnbiPVA(A>WV‘]EHGTA(PnA>PrAfe˜LRNTd]AcZXGiAfPRe˜EHQXd\GTQFPmGTA(‡™QFG8WšLRE AfZXe˜[2d QX ‡ E vC„ ZuGTbgA eiEZd =· = EUPŒ„ ›˜LOPVN]NTZ«QLoI DXLOEUqFN]A>Z«G L ¹…} vJy B8pq™=txk ƒ‚ k { „ k ‚ kLR”=EHWRQFQGTqXP;AcQuLR‡ NTAcZXWRGTA>[ b…ZuLRE EHQFGTDFP*EMqFBCA(G…AfLImEHzG A>A(™=G t`P(LOk NTAŠN8k phdCA>WRZXB\GTQFb [HEUYcZXk GT© b&k LOWVEHDFQXGTQFS#A>LOWVEHY‡™aTGTY ¡ ¹ ¹ »‚ ‚F‚F„ »‚ ‚ „ ©ik np ‡™QF[U[HQIKEHGiDJLONTA?POZXS#AcPVLOA>dTPŠZXPLONiQFPRA#LON]ZuLo[HA>bLR’Q ™=txk ƒ‚ k°© „ ›ˆdTWVQžqXA LRNTAS?QFWVA0DFA(GiA(WOZu[WRA(PVaT[UL ™=txk »‚ k°© „ k ¯TkszEUGTb-LONTAoSgZXdidTEHGTDcQX‡zLONTArY(aTWqFAjbiA(PRY>WREUBCA>b’EHG…d]ZXWRZXS?AfLOWVEHY0‡™QFWRSB8[p ™=txk ƒ‚ kª©u¯ „ ›iLRNTWRQXaTDFNLONTA0‡™aTGiY>LOEUQFG  œ¹8„2}¨¹*y { ¹ ½˜ks]WRQXS4LRNTAjdTWVQ˜Qu‡=LON]ZuL*LONTAo‡™aTGTY>LREHQFG  ƒ¹8„K} Q{ 5u¹ SgZXdiPŒZgY>EHWRY>[HAoEHG·LRNTA ¹ dT[HZXGTAu› ™=t\k ƒ‚ k°© ‚F„ ›CLOQ-ZY(EUWRY([UAjEHG’LRNTA dT[HZXGTAu› ™2txk ƒ‚ k°©F© „ › bTA>LRA(WRS#EHGiA LRNTAŒWOZubTEHaTP‹ZXGTbJLONiAŒdCQXPREULREHQFG?QX‡ LONTA~Y(A(G8LRA(W;QX‡ LONiAŒY(EUWRY([UA~QFGJLRNTA dT[ ZXGiA EUGrLRA(WRS#PzQu‡iLONiAmWOZubTEHaTaP ZXGTbrLONTAndCQXPREULREHQFG  ‚v KJR = K „ QX‡]Qu‡iLONiAmY(A>G8LOA(WzQX‡TLONiA Y>EHWRY>[HA0QFGLRNTA ¹ dT[HZXGTAukUknlmQFS#S?A>G8LKQFGIKN]ZuLsN]ZXdTd\A(GiP*EM‡  v wK y = Kw „=}  w k ikKŽ;NTA0‡™aTGiY>LOEUQFG  ƒ¹8„2} £`¹~y¥¤ ZXGib LRNTA-SgZudTdTEHGiD’EULŠdiWRQhbTaTY(A>P#ZXWRA¦fG]¹*ZuS?y A>b¥Z«‡ LOA(W QF BTEHaiP(k “˜NiQžI LON]Z«L LRNTEHP‡™aTGiY>LOEUQFGcSgZudTP=Y(EUWRY([UA(PzLRQY(EHWVY([UA(P2ZXGTb#[HEUGTA(PLOQ[HEUGTA(P>k Y [UPRQPRNiQžI¥LON]Z«L LRNTAY(QFSjBiEHG]ZuLREHQFGgQX‡LInQgPVaTY_N—‡™aiGTY>LREHQFGTP>›iLONTZuLsEHP(¸  |} £ w ¹  y¥¤ w R ¹  } £ HV¹*y§W¤ H ¦w¹ y w J¦ H ¹~y xH EUPŠZXGTQXLRNTA(W QF BTEUaTP5‡™G`aTY>LREHQFG œn‘]GTb LRNTAJAfe˜dT[UEHY>EULjA e˜dTWRA>PRPREUQFG ‡™QFW ZuPŠZ QX BTEHaTPЇ™aTGiY>LOEUQFG§EHG LOA(WVS?PcQX‡*LONTA…d]ZXWRZXS#A>LOA>WRPŠLONTZuL#A(G8LOA>WgEHG LRNTA…LInQ ‡™aTGiY>LOEUQFGTP;QX‡LONTAY>QFSjBTEUG]ZuLOEUQFG‰k ˜k “˜NiQžI¨Afe˜dT[UEHY(EMLO[Mp?LRN]ZuL;LONiA‡™aiGTY>LREHQFG { |}  ƒ¹F„š} ¹w S?ZXdTP0LONiA#WVA(DFEUQFG QFG LONTA ¹ di[ ZXGTAcPVNTQIKG EHGzEUDTk ‚ k LRQ…LRNTAc‡™aT[H[Y>EHWVY([HA QFGJLRNTA dT[ ZXGiA~Y(A>G8LOA(WVA(b—ZuLmLRNTAŒQFWVEHDFEUG‰›`B8pg‘]GTbiEHGTD5LRNTAŒEUSgZXDXA(PmQu‡ˆZo‡™A>I WVA(dTWVA(PRA>G8L_ZuLREUqFArd\QFEHG8LOPKQFGLRNTABCQFaiGTb]ZXWpQX‡ˆLONTA ¹ ¡¢dT[ ZXGiArWVA(DFEUQFG‰k





























 "!$#%!

 

ik;@A ZuWRA EHG8LOA>WRA>PVLOA>b¨EUG|LRNTA SgZXdidTEHGTD QX‡oLONTA ¹ dT[ ZXGiA LRQ§LRNTA dT[ ZXGiA LRNTWRQFaiDFN |} PVEHG G2H œ¹8„ IKNTEUY_NJI‹ZuP‹bTEHPVY(aTPVPRA>b—EUG?LONiA~LOA e˜L(kšxQXWšLRNTEHPnSgZXdidTEHGTDrLOQjB\AŒS#A†ZXGiEHGTDX‡™ai[»› InAgSjaiPVLjEUG8LOWRQhbTaTY>AJZ…BTWOZXGiY_N Y(aiLoIKNTEHY_N EHGTY>[HaTbTA>PoLRNTAgd\QFEHG8LRP ¹&}4®Š{ ZXGib ˜ k=lmQFGTPREUbTA(W;LRNTA0BTWOZuGTY_N-Y(aiLKY>QFGTPREUPVLREHGTDŠQX‡ LRNTA v Z«e˜EUPm‡™WRQFS •r{ LRQ › LRN]ZuL0EUP(› µ k PŒLONTEUPZXG ZXdTdiWRQFdTWVE ZuLRAjBTWRZXGTY_N Y(aiL0‡™QXW LRoy NT˜ A~‡™aTGTYfLOEUQFGJQX•r‡ EU{ G`LR A(WVA(v PVL oy@¶˜ N]ZuLm? EHPnLRNTAŒEUSgZXDXA*QX‡LRNTAŒBTWRZXGTY_N-Y(a˜L;QFGJLONiA di[ ZXGTAu›]ZXGTbJIKNTZuLKEHP‹LRNTA0WRA>DFEHQFGQu‡ˆLRNTA dT[HZXGTAŒLRQjIKNTEHY_NLONiA0A(G8LOEUWRA ¹ dT[HZXGTA0EUP;SgZXdidCA>b ŒQhA(P;LONTEUP;WRA>DFEHQFGNTZqXArLRNTAPOZXS#ArZXWRA(ZcZXP;LONTAWRA>DFEHQXG Y>QFWRWVA(PRd\QFGTbiEHGTDŠLOQcLONiArBiWOZXGTY_N…Y(a˜L*PVNTQIKG·EUG—EHDTk ‚ k {ž‚ ik ™quZX[HaTZuLOA;LONiAsWVA†ZX[xEUG`LRA(DFWRZX[TEUkG ™=txk »‚ kª½ „ ›8aTPREUGTDLONTAsY(QFG8LRQFaTW w [HZXBCA>[HA>b ”ZuLON ‚ EUGzEUDTk ‚ k ‚˜{ ›iZXGTbJS?ZX^uAŒPRaTWVA~pFQXaDFA>L‹LRNTAŒPRZXS?A*WRA>PRaT[MLKZXPmEUv G ™=txk IKƒ‚ EMkMLON8„ quk ZXGT”EHPVZ†NTp EHGiZuDŠLVLOWOA>ZXG`bTLREUEHE‰QFGY(A>G8LOQ·LOA(LRWVA(NTb&AJZ«EHG8L LRA(DFWRZuLOEUQFZXGTGiPjb·ZuZu[HL QFGTD…LONTA A?eid LImE Q&PV¯ A(S#k EHY(EUWRY>[HA(P ¹5} { ¹o}  5 „ { k*dTlm[HQFZXGiGTPRA5EHbiZXA(GTWb’ZKN]‡™aTZuGTP0YfZuLOL*EHQX[HG A†ZuPVƒLŒ¹8QX„ GTIKAjNTWREUY_QhNjQXL~EHPZuZXL G]ZX[Mp`LOEHY2Af¸qFA(Wp`IKNTA(WVAsQX{k G5“˜LONiNTQžAšI”Y(QXLRS?N]ZudTLŒ[UAfEMe ‡ EML;EHPsZŠPREUS?dT[UAŒWRQhQXL(›iLON]Z«LKEHP(›iEU‡ˆLONTA0‡™aTGT¹?Yf} LOEUQFV¹ G-K Y†ZXG-ƒB\V¹ AK „;IK} WVEULV LOA(G—ZXP ƒ¹8„=} ƒ¹• V¹ Kf„ H>ƒ¹FO„ R H(œV¹ K „ }€ LRNTA(G’LRNTAo‡™aTGiY>LOEUQFG  œ¹8„;}!J{ 5 ƒ¹8„ N]ZXPŒZ?PREHS#dT[UArd\QF[UAjZuL ¹g} V¹ K k*@¶N]Z«L EUPmLONTA0WVA([HZuLOEUQFGJQX‡ H>ƒ¹8„ LRQ œ¹8„ GTA(ZXW V¹ K “˜NiQžI|LONTZuLKEU‡LRNTA0WRQhQXL;QX‡ ƒ¹F„ EUP;QX‡zQXWRbTA>W ›TLRN]ZuLKEUP(›TEM‡LRNTA0‡™aTGTY>LREHQFG-Y(ZXG—B\AŒIKWREMLRLRA(G—ZXP ƒ¹F„š} ƒ¹• V¹ Kf„ Œœ¹8O„ R ~œV¹ Kf„ }¨ LRNTA(G LONiAg‡™aTGTYfLOEHQXG  ƒ¹8„Š} Q{ 5 ƒ¹8„ N]ZXPcZ’d\QF[HA?QX‡KQFWVbTA(W ZuL ¹} V¹ K k @¶N]Z«L*EUP‹LONTAWVA([ Z«LOEHQXGJQX‡ Œƒ¹8„ LRQ œ¹8„ GTA†ZuW V¹ K {F{ kszEUGTb…ZX[H[\LONTAd\QF[HA>P;QX‡ˆLONTA0‡™QF[U[HQIKEHGTDo‡™aTGTY>LREHQFGiP  H>ƒ¹8„2} PVEHGTN { ƒ¹8„ R  w œ¹8„2} L_ZXGiN{ ƒ¹8„ R   œ¹8„2} PREUG { ƒ¹F„ R   ƒ¹8„2} LOZXG { ƒ¹F„ ZXGib PRNTQI LON]ZuL?LONTAfp ZXWVA&ZX[U[sPVEHS#dT[HA—dCQX[HA(P  sEHG8L†¸ aTPVA’LONTA’WVA(PVaT[ULRPJQX‡ ”=WRQXBT[HA>S ›‰ZXP~LRNTA>p’ZXdTdT[Mp—LRQgLONiAŠGTA(EUDFN`BCQFWVNTQhQ˜b’Qu‡=LONTAjbiA(GTQFS#EHGTZuLOQFW WVQ˜QXLRP „ k { {ž‚ k ”=WRQµ qXA XZuQXGTWRb]b ZXGLONT P A·EHG8A(S#LOA>S?DFWOZ—ZuLR‡™EHQFQFWjG LOd]NiZuALON EHG8LOA>DFWO[UphZXEH[nGibTD A>‘TQFGGTA(LRb§NTA&EHG [HQ™=IntxA(k WJƒN]‚ ZuMk X©[U‡„ QX‡IKLOEUNiLRN A Y>QFS?di[H Afe ¹ di[ ZXGTAu›iLONTZuLsEHP(› ¹5}  Afe˜d  E  X„ R   |‚  k