Viscous flux and turbulence models linearization for aerodynamic shape optimization for turbomachineries

Texte intégral

(1)Viscous flux and turbulence models linearization for aerodynamic shape optimization for turbomachineries Chi-Tuân Pham. To cite this version: Chi-Tuân Pham. Viscous flux and turbulence models linearization for aerodynamic shape optimization for turbomachineries. Engineering Sciences [physics]. Arts et Métiers ParisTech, 2006. English. �NNT : 2006ENAM0030�. �pastel-00002058�. HAL Id: pastel-00002058 https://pastel.archives-ouvertes.fr/pastel-00002058 Submitted on 5 Jan 2007. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) N° d’ordre : 2006-30. ÉCOLE DOCTORALE 432. École Nationale Supérieure d’Arts et Métiers Centre de Paris. THÈSE présentée pour obtenir le titre de. DOCTEUR de. L’ÉCOLE NATIONALE SUPÉRIEURE D’ARTS ET MÉTIERS Spécialité : Mécanique par. Chi-Tuân PHAM. __________________ LINÉARISATION DU FLUX VISQUEUX DES ÉQUATIONS DE NAVIER-STOKES ET DE MODÈLES DE TURBULENCE POUR L'OPTIMISATION AÉRODYNAMIQUE EN TURBOMACHINES. __________________. soutenue le 25 septembre 2006 devant le jury composé de. MM.. C. J.-A. C. A. M. J.. BASDEVANT DÉSIDÉRI FAVRE LERAT MASMOUDI PETER. Professeur, Université Paris 13, Paris Directeur de recherche, INRIA, Sophia-Antipolis Ingénieur, Snecma, Moissy Cramayel Professeur, ENSAM, Paris Professeur, Université Paul Sabatier, Toulouse Ingénieur, ONERA, Châtillon. Président Rapporteur Directeur de thèse Rapporteur. __________________________________ L’ENSAM est un Grand Établissement dépendant du Ministère de l’Éducation Nationale, composé de huit centres : AIX-EN-PROVENCE ANGERS BORDEAUX CHÂLONS-EN-CHAMPAGNE CLUNY LILLE METZ PARIS.

(3)

(4)

(5) "!#$%'&)(*+-,.*,$/'010'2),3.042)5067.08950:;=< >@?BA1@C60')2.DEF.G-,.*,H.0JIK0'!#A19 *, 9(*,+LM(. 0N!OLNP$,.A1*.DQ.06@!#RC6 DRL#S950UT@L#DQ,.9V8L'3!#)(G,)2)5L#9.DQ.08*(@.XWY,.*572)5L'(9V6L'+!# [Z]\$T$?^>XW_E`%1a 950cb d *.DQ.*2.9Y*5L#e!fZghi5*!FjU50'(*9.L# k^%# A#AlYjm592)Kn!O *)2.*.L#o!OLFPHCpT$Wqn.ejm50'(9.L# d 2)V6L')( C69!#&)(n 2*%'srH!#t[Z L#0# *,JjUT$?^;sne 0'(YV8L'4T$uvA#L#9( d7w !#NC60')2.DEOn^!#tDNZg75 E2)2.L'. X!'0'(-9.L# ,)V6L# AlKb d G9.0'(`_$*.DQ.*2.9.`jm50'(9.L#oW@S 0Euc.n6ke*5rx)(*(*.L#^!#Y[Zy?^THCpW$jn7!fZg75 2)2).A#*,@!#Y!O I7. 2).*q%'&)(*-.0zA192.L# 9.HAl5L#$*5L'(H(*)(2)50'(*. 9(,)2.S *,)(H2)50'2).0108+S{*,)!'2.950:!OLmDQ,.DQ5 *F. SqA#*,.A1950z!#SF(*5L#*.010'2)Kb d Zg!O*)((*-DQ)(Hp|r}($*.DQ.*2.9.DQ.08*(-_tjU50'(*9.L# d 2)V8L')(3k~.*.nf 0#I7,.0#9.L#-\$T@?^>@WRni!#-DNZg75 .0'2!O*,KnO!fZg)75 G(LtDNZg IKL# 9.GLOEDQ5DQ.08*(X5A#Al5L#0'(.A# L'(A192.L# 9&.*.DQ.08X!'0'(SR!#.0#9&.* IK0'+!O*5 *3Al.0'!'06G9)(GA#%1(*)(X2.L'2.S9)(X!#H*,)!'2.950m.X!#A#*,.A1950m!#+S-(*5L#*.010'2)Kb1jm.*2. ,.I89.DQ.08XAl5L#9)(2)50#019(*(0'2))(G(2.9.08|/1V6L')(GV8LcZ fRA#L4DNZgA#Al5*.G.0J( DRL#S950N08L#DQ,.9V6L'H. ,.*5p!O601DF9V6L'Kb jm)(G( 0'2)&.*)(Y*.DQ.*2.9.DQ.06*($7508@_Fjm50'(9.L# d 0OW@08*5 0'qP,)(9!#,.[n'P$ *)2.*.L#X!#+>@)2*%'.*2%' _$[Zy;T@>@;=W .`jU50'(9.L#^jm5%1DQ)!Qjz(DQ5L'!O[n7ke*5rx)(*(*.L#^!#[Zy@0# 7.*( *,Gk L#iCOh19.n7Al5L#o75 L#I7,H2)HDQ,.DQ5 *+.0N06XV8L'+A#Al5*.L#X.XAl5L#Y[Z 06*,.*.@V6LcZ 9(G508GAi5*,3_-2)H [b d +*.DQ.*2.9Rjm50'(9.L#$`SL'!# w (!#.06n1ke*5rx)(*(*.L#X!#+[ZyX0# 7.*( *,Rk9(qOn'!#HDNZg75 Gr[ [Z %'50#0'.L#Q!#{A#*,)(9!#.-DQ50 L#.-jU50'(*9.L#Q`%#9(**5A#%'t<)p*Kn~ 0#I7,.0#9.L#{C60')2.DEOne!fZg75 -A#9( A1@L L#7b jm50:)K `!#Q%'&)(*-0cZgL# 3A1(qhl5L#o.0[Zy,.R(0'(H[Zg9!#Q*)2*%#0#9V6L'{!#-0'5DRh#*.LO 0#I7,s 0#9.L#*(+\$T@?o>XW!#)(@L#0# *,)($jmT$?^;njUT$?`Clnl?û~CpW.$?^Y>X;X!OLUP+CpT@Wqn1

(6) .@WX;G!OLmPGW@W$kv. !fZ 0#I7,.0#9.L#*(qC60')2.DEOb d -9)(H*.DQ.*2.9F92.^!'0'(H9.L#HIK95h1 *,Kb. 0'(+ 0#I7,.0#9.L#*(+5063.LL#0*9 A192.L# 9&.*.DQ.08t DFAi508QAi.0'!'08Q2).*J%'&)(Kb d ZyspA# DQ4DQ)(E( 0'2)&.*)(-*.DQ.*2.9.DQ.08*(4_:C6*,s A#%10' w L#IKL#h#L#Lz!OLUP,.A1*.DQ.08H!fZyWY,.*5p!O601DF9V6L'qWXA#A# 9V6L',)3!#3[Z]\$T@?^>@WV8L#[n1*5L 5L#*(X*&)( I7.08 DQ.06n#H2)50'(2.*,X!#)(o%'.L#*)(o.069&.*)(_DNZg9!#.Y_DQG(5 o!#X( L1950'(oA1r}59(o 0'sp92h#9)( (L#!#)(@2)50O/'IKL#950'(3!#+L#hi5DE2*%# 0')(bfjm.*2.,.I89.DQ.063_E()(@2)5 9&.IKL')(!#R[Z L#0# *,q

(7) 9)( w 950#0'.$.$uf950'.^( 950UAi5L#X9.L#*(9!#)(@Al50'2.L'. 9)((L#X2). 0'($Ai5 08*($!#+L#hi5DE2*%# 0')(b d *.DQ.*2.9Y,.I89.DQ.08`P0#9.'P)(2Ai5L#e(*)( 2)50#019(*(0'2))(^.e(*50FsOAl.9(*.0Q,.*56!Op01DF9V6L' sO*.0'3 0'(cV6L'R,.9!U9.n#*5L'(X!#.LOJ!#[Z L#0# *,RWX;b )K 1$.LFAl5L#e2)506*sp*995IK92.9.~s !#,.7.95A#Al,G_@[Z]\$T$?^>XW's]*HnL#0-0'5DV8L#O%106*. Ai.L#.*G.0'2)5*950#IK*.DFA'(^DQ)(^)(*A# *(n1sB[Z 0'!#5p2. 9G5LFS@r[*5L'2*%'G2)5DFDQ ZgOA#LF[ZgA#Ai.9.Â1.

(8) 9A1(*(*,Kb#k DFc9)(Y0'5DRh#*.LOJ 0#I7,.0#9.L#*(XV6L#c508YA#LJDNZg9!#.@_@!#5DFA#*.s .GV8L' $*.DQ. 2.9Kn R75L'!O9(+2%19.L#*.L'(*.DQ.08R*.DQ.*2.9.RCp,.h1(9.0@. hcnlIK0'!zI75L#*5L.$/'0z2)50#019((*.L#H!#)( .08 9)(!# @SFhi.* lnV8L#~DNZgF*5L 5L#*(X DFA#*)((950#0',3A1@S-A#9!O *,KnSFA#*,)2.9(950z!#3(*)(@!OSI 0'5K(92)(.`(HI7.08 9)(*(*$(0'(`,.I89Kb6jm.*2.lL'(*(*lLOEL#*)(oA192. A106*(Y!OLEDQ5p!OL#9@!fZy5A# DF9(950 )7)2@V8L#19Y)K i+,.*,YL#0QA#S9( n89 Ai. oI75L#*5L d L# 9.0{jz)7.L#.o[Zy,.*.0'.1A#*,)(.08nK/1!#&.9$L Ai5K(*Kn'k (*2~>$L'!fb d H*.DQ.*2.9-L'(*("*5L'(G9)(G 0#I7,.0#9.L#*($V6L#cDNZy508A#Al5*,39.L#*(@2)50#019(*(0'2))( (*2.9.06|/1V8L')(n.0JA192.L# 9. $ 0'2).08$9. HAi5L#X(qDE

(9) 99(*+!#+S-L#h#L#9.0'2)Kn $ 0'2).08H5L1 9. .4`SL'!#mjzDF IK0'50 Ai5L#E9.L#{%1L#*U2)50#019(*(0'2)U!#MS:( DRL#S950 06L#DQ,.9V8L'Kn d 0Oke9.* ^.L# 953Ai5L#R()(+2)50#019(*(0'2))(q.0:DQ,)20#9V6L'E!#)( 'L#9!#)(q.+Ai5L#3DNZg75 3Ai.DF9(3!fZg(*(L#*.RDE 0'( 950M,)2)593!fZ 0#I7,.0#9.L#*(!#,.h#L#$!#+%'&)(*H!#HDE0#9&.*HA# L'(@(*.*. 0'Kb d Zy5L#h# 9-*&)(2). 0'.DQ.063L#0mIK0'!z0'5D3h#*F!fZ 0#I7,.0#9.L#*(HV6L#DNZy506HAl.DF9(!fZy f)2.L'.+2).* %'&)(*F.HV6L' q*.DQ.*2.9F92.^.*5L#*)(H9)(H,)V6L# Al)(Ai5L#Sthl50#0'-%6L#DQ.L#nfS{hl50#0'QDRh#S0'2)Q!# )K "V6L#f{*&.IK0'.06@.G9.L#@!O9(Al50# h# *,Kb d R*.DQ.*2.9QL'(*(~*5L'($9)(@ 0#I7,.0#9.L#*(3C60')2.DE47)2qV6L# Zg~A#LU 9.nfV6L#506Xr[ H)K0'2). DE$%'&)(*Y.eV6L##DNZy508er[ A#*.0'!O*G2)50'(*2.9.0'2)G!#)(e.0 .LOq 0'!OL'(*9.9(bKkDF.LOin 9.0'(e*5L#eA1 92.L# 9&.*.DQ.08_R*.DQ.*2.9.@ w V6L#i0cZg DE9(Y2)5DFA#*,H(*)(%'.L#*)(X /'0JV6L'$DE3%'&)(@A#L#9((*H)K0'2). 9HA# L'(@A#9!#.DQ.08$Al5K(( h#9Kb1jm.*2.",.I89.DQ.08+LOML#*)(Fs]* hi5O(X<$nl\ Fn1>@j Al5L#G9.L#9!# *)2*%#0#9V6L'Kb d $*.DQ.*2.9HL'(*(iPjU<Al5L#Y)75 G,.*,@DQ504A#*.DF9.2%'srn'<(*50t(*L'2)2))(*(*.L#nOT@umAi5L# )75 Y(L# plA#*)(*V8L'$.089&.*.DQ.06X2)@A#*5 .Y.G\HCFAi5L#Y(*)(`2)50'(. 9(Ài5L#`/'0# L#0'$%'&)(*_R22.*&.* 0'!OL'(9."2)5*)2.*.DQ.06b ;=c)(*&)(Y*HV6LcZ L#0J)K "(**, 9(*H(0'(Y(5L'2.9(YDE*,.9.9(n# 0Orx5DE9V8L')(X5LM!ODF 0#9(|r}( b d `9.0'( !#50'2_X*.DQ.*2.9.eke%# A#AiY.*50##. P$9!O9. w S9(*Àl5L#9.L#^9!#_X*,)(*5L'!O**5L#A#*5h#9&.DQ 0Orx5DE9V8L'$ 0'2)5DFA#*,.%'.0'( h#93LJ2)5DFDRL#0N!#)(!#5p2.*508*( b d @*.DQ.*2.9H,.I89.DQ.06@$%#9(S 0'Ps 0#9($. w IK *-5DFDQ. 0mAl5L#@9.L# 5932)5DFDRL#0#92 7Kni9.L#XA#*5rx50'!#32)50#019(*(0'2)q!#)(@*5L1I7)( !#[Z]\$T$?^>XW

(10) .Y9.L#X E22. *,HAi5L#Y*,)(*5L'!O*H9)(A#*5h#9&.DQ)($!ODF 0#9(|r}(@V8L' ZgfA#LJ*.0'2)508*.b uc)(-(*5L#7.0# *(-V6L' {I8*!#.!#t2))(-0#0',))(F!#E%'&)(*{0't(*.9.08-A1(-2){V6LcZ 9(q(*508F(0'(RS 2)5DFA1IK0#9H.9)(hl50'(DQ5DQ.06*(YA1(*(*,)(Y)7)2SRh10'!#H!#!#5p2.*508*(G.04Ai.DE0'.08*D3L#950cb d *.DQ.*2.9Y!#50'2*5L'( 9)(e!#562.*506*(^. (IKS *)(^V6L' ZgOA#L-2)*5 7.^.Â#A#*,)2.9.eAl.0'!'06^2))(^0#0',))( !#U%'&)(*UL#*5L#J!#M!O9(2.L'(*(950'(t(*2.9.08|/1V6L')(J5L I7,.0',.9)(n!#UA1L'(*)(t2 r},Kn!#NA1L'(*)(4!#, .L#0'. 5L !#MA1L'(*)(t!fZgL#*)(EI7.0#*)( ^9)(t0'2.9.0'( e H;=I75E9z5* )pS*.L#{0'5DE0'! *5L'2*%'s=_ *5L#E.QV6L#G2)508*9N.0 *5L#*J2. *2)50'(0'2)e w L#0'5 R`%# h#* B_mSmDQ5p!#)(9N(0'(-A1*. [n^DE9( V6L'.`9.06 d )!O.-V6L'. 9{uc?C:.0BL#hi5DE2*%# 0')(n 2*%1AiLBh1(cT@5 . H<#LOO SMh# h# 95%'&)V6L' D3h#L#S06*Kn!#.A#*E!# *2*%'5 .3!#-[Zy.!0 DFDEI7ee$*,.I75 *Q2)5L#I7.LOL# 9(*.L#3!fZS.]*Ai5L# 9)(eL#hi5DE2*%# 0')(c8uf950'.1sOAl.^.0Q26 *,Kn ZgL#9(eA#*,srx,.*,YL#0QspAi.e2)p C6*YAi5L#e9)( w 5L#*. 9)(" >X5010E[Zg,.*572)5L'(92.9.04_$[Z %6L#DQ5L#(*#A192.L# 9.c6jz%#9."L w 5#h qk`\$P DE(*.nKL'( 0'X_Hh#SIKL')( .Al.L:!O9(2.*.3DF !OL*,)(L+$ e956!O9FV6L#^{Al.L#.*Q!'A#*,F9-2)5*!'I7Q!#-({V6L'.*F!#-h1!H w L#0'%5 qCp50#92 _zS:2)5L#AiNV6L#X%',.9(*(J0'5K({2%'.7.LOin!#.A#*U!#)(EA#*5h#9&.DQ)(t%',)59V8L')(t.0 )P V6L#G0cZ 08*,.*)(*(.084V8L'J9)(Q%1L#*({(Ai,)2.S 9(*)(cCp,.h1(9.&0 3WX 9' mCp.h B!O9(*2.*.E08L#DQ,.92.9.0vIK0'! r[0t!OL{r}5p5LO#.*59(cpufL#( 7np9XIK0'!4DE*.L#G 9.DE0'!4!#@(L'2.9((*)(o 0'(*h#9)(c'\@ 69.) H', 7.* sOAl,. DQ.06*.L#, + %',)592.9.0J_$S!#,)2)5062.950t!#,.*5L#06*e79)(eA# L'( .L#0')(`\@ p9. Y\@ ) R[Zy5*!O* Onp2KZy)(`(*504!'!'On69Grx565L'(*(76<#0 -)59.( Y>X92*%#9 F2)5L#A#9.L#r}5Lt.`DRL'(92.9.0J!'0'([ZgaDQe0 /`0#0t9 DQ5*!qV8L#p(*er[LO/'9o.06*o9)(~*5L#h# 950'( !fZ %',. 92)5A#*&.*)(c7,.9!O 0'o[Zg2)5L'(*92.9.0#0'ÌK*,)2)5[h#*.*50#0' 2KZy)(L#0NL#*H2)5612 6 fV6L'$9)(IK!O9.08*(Yp9.01DQ5[0'5DE0'!#(c1?^DFDE-!#508YSq(h# *,+LJ(*.0'(!# uf9-.+_{SE*,.L#0#950#019(F(*508H!#.7.08L'(+L#0'R0'5L#7. 9F(*Al,)2.S *,eijm.7.D S{!#.0#9&.*FA#A#*.069Q.0 5A# DF9(950t!#r}5DQ)( n7,.I89.DQ.08 .L#0'2 7.0'!#35 [A1!'5 40cnp[Zg,.*56,.S(*92. *,X0cZgHV6LcZg_h#9.0E(Y*.0# n.

(11) .qL'((o*5L'(q9)(q(IKS *)( d L# 9.0 u A#*.DF9.QA#A#*.06.05A# DF9(950 ,.*56,.S(*9V8L'e H. 9 (IKS *$9$A# L'(A#9!#$!#$[Z %#9(*5 *!OLJP+CpT@W d L# 9.0Jj( E.L#G_+[Z c IKL#9(*,e /o570#0J!#.LOO9&.DQ A#A#*.08e.0z5A# DF9(950,.*56,.S(9V6L'KnIK0'!U0# A#Ai5A#%# 9ef`6 eL#*R.0'2.O2.95Ai,)!O9R!#RS{< PB d 2)V6L')(q_NV8L#`[Zy50A#*5DQ.3L#0%'5 50,)2.S *2.!'0'(39{!#,.A1*.DQ.08F5h'(*2.L#3!#E[Zg,.*56!Op01DF9V6L' A#A# 9V6L',)+.X.0O/'0mC6*,sr[0M!#.0#9.GDQ.DRh#*+*)2).0'(*,+!#SQ2(*Kb W~7)2o9)(e0#0',))(n A1DFO9)( !#562.*506*(n2). 0'( 9.0'((508A# L'(~DE*V6L',)(b;=8R@!#, _@2).LORV6L#6506 A1(*(*,XA#*)(*V6L'X( DRL# 0',.DQ.08*59(0'(.0E9,.I7.*.*!E!#XA#%1(*@A1oA#Ai5_HDQ5[n69)(o2DE!#)( !#GA#*5DQ5 p$L# SL#DQ G$L# IKL#i -.`9X2)5L#A#SI7Kn69G7,.95#n89G0')2.`!fZgh#92)5np(3L# IKL'.*@.(*)( 0Orx5DE950'(h#9.0tI8*!#,))("6[ZgL#*3L# SL#DQ w {2)5L'(92.9.0J 06*.Al5S*.L#nODE

(12) 9* *!O 0#9.n IK0'!-h1)K*!fn9(*.L##V8L# 50#IK9.06*Y!#`DRL# A#9)(eDQ5*(e!#A1(*(*e<#*,)!#,.9.2 `<#*)!#!O) H DFA# 92. *.L#n .0'2.O2.95Al,)!O9-p 06*F2.L#D3L#9,)Q!OLzrx5p5$.+!OL"5L#n"2)5DF9V8L'F!#q*,.Ai,. 950.Al5p&.*F_{()(%'.L#*)(b ;="MtL'(*(~2).LOU7)2-V8L# ZgA1(*(*,3A# L'($!#3*.DFA'( 1DF9(*($<#*,)!#,.9V6L'qSF%',)(*!#q08L#DQ,.*5zR!'0'( 9E!#5DE 0'4!#{[Zy5A# DF9(950 !#Frx5DQ)(nspAi.*E.0*,)(*5 L#950B!#E(O(*&.DQ)(R 0', *)(n~5L#I80'( n IK0'!#q758I7.L'(*Knlhi50#0'3A# Ai.9.*q.$V6L#L#EA1I7,q9+DQ.DQ-.0'2!O08H.$A1r}59($9)(@DQ.DQ)( A#*5h#9,.DE9V6L')(b6<h#92)LOFDRL# A#9)(Y(*5h#9V8L'.*( n8!fZghi5*"! X(*|rx#h ln d 5p.h1 FA#L#9( Y<1 r}5L .G.0O/'0 @<1h {A1

(13) 9[ [n#06L#DQ,.92.9.0MA#*,)(*.K08GSq7592. *,3,.DQ,. *Kn1_qS-2)5L#AlH!#H2%'.7.LON(0'( /15 L#*KnLUA#L# "50#I7R_-rx *+.0669q_-0cZ DFAi5*3V6L'.c0'5K( IK9V6L'3!#R( DF n'IK0'!M2)508!O92s *.L#nKDE

(14) 9*G!#GSH(9(.^!OL pL#0#Ixr}LcnKspAi.o.0Q!#5L#h#9G75 *G A#9Y0',.I8950cn7DQ.*2._$*5.C6*.A#% Ai5L#~75K(*.9)2.L#*)(b?e .0O/'0-SGDF9(*( e 9(@V6L#OXA1I7,DQ50Rh#L#*L-Ai.0'!'08 *59(950#IKL')(^0#0',))(n _XS@(*6DFA1%#9*)2)50#08L'Kn8,.I89.DQ.08eIK0'!#758I7.L'(Kn9)(~DQ5p!#&.9)(e!#`L#h#L#9.0'2)D3L# |,)2*%'. 9Kn - S2)50#01

(15) 9o.o7)2GV8L# Zg#A#LQ,)2*%10#I7.!#0'5D3h#*.L'(*)(!O9(*2.L'(*(*950'(bjU.*2.L'((OAl5L#e*)(e*.9)2.L#*)( b ?e0O/'0cn +75L#S9($*.DQ.*2.9.DE-r[DF 9 1DQ)(XA1*.06*($V6L#"DNZy506H(*5L#*.08Lz.$(*L#A#Al5*,3Al.0'!'06 *5L#*)(2))($0#0',))(.@A1($(.L#9.DQ.08H2))(@!#.0#9&.*)(H0#0',))(!#R%'&)(*Kn'DQ50Ur *&.*-L'(*(~Al5L#$*5L'($(*)( 2)50'(*. 9(nO(*)(DRL# A#9)(G*.9)2.L#*)(G!OL4DE08L'(2. n#*5L#*)(Y2))(Y!O9(*2.L'(*(950'(V6L'$[Zy50M3A#LJ,)2%10#I7.YA1( (*.L#9.DQ.06$LN(L .G!#HSq%'&)(*+.Y*5L#@( DFA#9.DQ.08$!fZg)75 @,.*,+DQ50Jr *&.*Kb d ZysOA# DQ.eL#0'q!#.0#9&.*RAi.0'(*,)3Al5L#$DQ)(HDF9(@V6L' +0'RAi.LOMA1(X*5L'(2. *.$92..HL'(*( _ 9.L#*( @AcZ Ghi50#%'5DFDQ 4V6L#c508GAi.DF9(G!fZy,.I87.@.0'2)5*+A# L'(GDQ)(G(*5 *,))(G.2 4)' 8.0'!#( b . .

(16)

(17)

(18)

(19) ! #"$% & ( )+* %,

(20) -%/.%/ 0"1324 56

(21) .789

(22) ;:<=1%>?@A".+B1%".+<C<=1D"AE5FG"1%8 !.. Kb k~5K( 950m!OLNA#*5h#9&.DQKbl\@A# DF9(950M95p29H.GIK95h19+.0U,.*5p!O601DF9V6L'bHb+bHb+b+b Kb Kb k~5K( 950UDE%',.DE9V8L'R!OLJA#*5h#9&.DQKn'0'5950'( b+b+bHb+bHb+b3bHb+bHb+bHb+b+b Kb Kbg jU5p!OL#9)(G!#H2*%1

(23) 90')($!fZy5A# DF9(950z,.*56!Op01DF9V8L'+95629+5LJIK95h19qbHb+b+b Kb Kbg `%1

(24) 90')(X!fZy5A# DF9(950 b+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b Kb Kb I jU,.%'5p!#)(Y%#9,.*2*%#9V6L')(@Al5L#Y[Zy5A# DF9(950m!#rx5DQ)( bHb+b3bHb+bHb+bHb+b+b Kbg <'5D3L#S950z!#)(X,)V6L1950'(G!#HSqDQ,)20#9V6L'3!#)( 'L#9!#)( b+b+bHb+bHb+b3bHb+bHb+bHb+b+b KbgOb ^V8L1950'(@!#HT$69.C6*35 7)( b3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b KbgObg ^V8L1950'(@!#HT$69.C6*35 7)(@DQ57.0#0',))7( N}>XW$THGC Otb+b+bHb+bHb+b3bHb+bHb+bHb+b+b KbgObg ^V8L1950'(@!#HT$69.C6*35 7)(@DQ57.0#0',))7( N}>XW$THGC O!'0'(Y9*.Al&.*+*.S|rtb+b+b KbgOb I jU5p!#&.9)(G!#L#h#L#9.0'2)b+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b KbgORb Q 50'!O 950'(@LOJ DF *)( b+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b KbgORb K >X.S950'(X,.*5p!O601DF9V6L')( bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b Kbg \@A# DF9(950MA1GDQ,.%'5p!#)(X!#IK!O9.06@!O9(*2.*&.*)( bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b KbgOb ;06*56!OL'2.950cbT@5950'(b1P$,.Ai.0'!'0'2))( bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b KbgObg 92.L#"!#HIK!O9.08*(XA1X!O f,.*.0'2))(Y/'0#9)( b+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b KbgObg 92.L#"!#HIK!O9.08*(XA1GSqDQ,.%'5p!#3!#[Zy,)V6L1950N 0',9(*,)Eb3bHb+bHb+bHb+b+b KbgOb I 92.L#"!#HIK!O9.08*(XA1GSqDQ,.%'5p!#3!#[Zy,)V6L1950U! 5 06*3!O9(*2.*&.*Rb+bHb+b+b KbgORb Q ;06*,.*.X.X2)65 T#Y*.S|r^!#)(YDQ,.%'5p!#)(@! 5 08*3.Y 0',9(,)+!O9(*2.*&.*)(b+bHb+b+b KbgORb K P$,. 7,))(@!fZy5*!O*+,.9.7, b+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b Kb I c *.DQ.08H!OLJDQ5p!#&.9+!#HL#h#L#9.0'2)HAi5L#G9)(G,)2)5L#9.DQ.06*(Xp9(*V6L'.LObHb+bHb+bHb+b+b KRb Q 50'2. L'(950Nb+bHb+bHb+b3bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b. U V :<W #".X#1

(25) :6%>?@.. Ob jU,.%'5p!#+!#)(Y75 L#DQ)(G/'0#9( b+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b Ob Kb ".DF 0'595IK9q.Y0'5950'( bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b Ob Kbg <'5D3L#S950F(*.DF|!O9(*2.*&.*`.0R)(A12)Âl5L#~ 08*,.IK950q*.DFA',( +)(A12)!#,)2)5L#A#9,) Obg <~ LON!#H2)5067)2.950cbiCp2%',.DE(X!#,)2).08*,)( b+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b ObgOb ;06*56!OL'2.950Mb3bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b ObgObg Cp2*%',.DEQ!#H>@56 b+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b ObgObg ? p*.0'(*950ULN(*)2)50'!N5*!O*+!fZgA#A#*5p DE950z.0M)(A12)Y N DQ,.%'56!#+jmHC#u O Obg <~ LON!#H!O iL'(950M!O9(*2.*. bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b ObgOb $!O9.08*(@,. L',)($LO42).06*)(X!#)(G2). L#9)( bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b ObgObg $!O9.08*(@,. L',)($LO42).06*)(X!#)(Y 06*.rx2))($!#)(G2). L#9)( b+b3bHb+bHb+bHb+b+b. (H. '. . JI. !K. L !M. ! M $P O K <L $M $M $M $S. $S $P O O K FI. H $K $K $K <L <L $M $S IP 'I 8I .

(26) . Ob I P@9(2.*,.9(950U!OLJDQ5p!#&.9+!#+jU92*%'.l92.L#"!#H[Zy,.A19(*(*.L#G!#32)5L'2*%'+ DF * b I$I Ob I'b 92.L#X!#4[Zy,.A19(*(*.L#E!#M2)5L'2*%'N DF *NAl5L#F9)(Q2)50O/'IKL#950'(4_z!#.LO . *59(YA1*59( b3bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b IQ Ob I'bg 92.L#"!#H[Zy,.A19(*(*.L#@!#H2)5L'2*%'+ DF *+Al5L#YL#0'+2)50O/'IKL#950_qL#0'HA1*5ob IK ORb Q P@9(2.*,.9(950U!OLJDQ5p!#&.9 k ε u~L#0'!#.C6%1DE bHb+bHb+bHb3b+bHb+bHb+b+bHb3bHb+bHb+b+b IL ORb QOb <~ LOJ2)5087)2.|r$bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b IL ORb QObg <~ LOJ!O iL'(|r-b3bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b IM ORb QObg ".DQ+(*5L#*2) bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b IM ORb K 50'!O 950'($LO4 DF *)(b+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b QO ORb KOb k*5 !OSh19V8L'tbHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b QO ORb KObg C66DQ,.9FbHb+b3bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b QO ORb KObg T@50J*, 1sO950 bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b QK ORb KOb I <#*5089&.*R(*508*R(L#h'(*50#9V6L' 50'!O 950U!#A#*)(*(*950cb'ke*5/'"!#HA#*)((950 (9V8L' DFAi5K(*,) bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b QK ORb KORb Q <#*5089&.*R.0808*q(L#h'(*50#9V6L' 50'!O 950m!fZ 0 )2.950vb+b3bHb+bHb+bHb+b+b QK ORb KORb K c *.DQ.08$08L#DQ,.9V6L'3!#)(X2)50'!O 950'(@LOJ DF *)(YAi5L#G9 'LON!O lL'(|r b+b+b QK Ob L 50'!O 950'(@!#H2)2)5*!M.08*+!#5DE 0')( b+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b QFI Ob Lpb P$,s/'0# 950U!#)(Yr}*5089&.*)(X!#2)2)5*! b+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b QFI Ob Lpbg c *.DQ.08*(@08L#DQ,.9V6L')(X!#)(G2)2)5*!#(b(G!fZ L#0N2)2)5*!U_qAl5 06*(G2) 5 x0'2.9!#.08*( Q$K ORb M 92.L#~!#)(YIK!O9.06*( bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b Q$K ORb MOb >X,)(*5 L#950-!#)(~(*p(*&.DQ)(~ 0', *)(e!#)(~DQ,.%'56!#)(^! 5 08*.~ 0',9(,)!O9(2.*&.*)(;Q$K ORb MObg P$,s/'0# 950U!#)(GDE92))( 2)5h#9.0#0')(Xs'2.*+.XA#A#*5p2*%',) b+b3bHb+bHb+bHb+b+b Q$M ORb MObg 92.L#"!#HS-(*.0'( h# *,3!OLJ*,)(9!OLNA1GA#Ai5@LJDE SI7+b+b3bHb+bHb+bHb+b+b K$P ORb S \@L# 9(X!#HAi5K([ *.DQ.08@Al5L#X9H292.L#"!#+!#,. 7,))(X!#$rx50'2.950'(@,.*5p!Op01DF9V8L')( KO ORb SOb \@L# "!#Al5K(*[ *.DQ.08$Al5L#Y9)(G2)50O/'IKL#950'($!fZg,.*5p!O601DF9V6L'3sO*.0' KO ORb SObg \@L# "!#Al5K(*[ *.DQ.08$Al5L#Y9)(G2)50O/'IKL#950'($!fZy,)2)5L#9.DQ.08*(2)50O/'0',)(Hb+b KK Ob ! P 50'2. L'(950Nb+bHb+bHb+b3bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b KK. H %:G6%.!% &9"10B "1% .%2. Ob X> .DE*V6L')(G DF 01 *)(X.X0'5950'( b3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b Obg XW A#A#*5p DE950 µ /'I7,2 b+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b Obg XW A#A#*5p2*%'R!#pAl @2)5L'2%'+DF 0'2) b3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b ObgOb WXA#A#*5p2*%' @2)5L'2%'+DF 0'2) tA#%6p(9V6L' b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b ObgObg ? p*.0'(*950!#{[ZgA#A#*562%' H2)5L'2*%'tDF 0'2) A#%6p(9V6L'4_NSN 0',9(950 !OL 'LO4!O iL'(|r b3bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b ObgObg P$,. l!OL{292.L#i!#GSHr}5DRL#9@!#2 'LOE!O lL'(|rc!'0'(`[ZgA#A#*5)O DE950N!#G=6Ai X2)5L'2%'+DF 0'2) bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b ObgOb I $!O9.08*(@,. L',)($LO42).06*)(X!#)(Y 06*.rx2))(b3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b ObgORb Q P$,. K950NA1GA#Ai5@LN2%1DFAU2)50'(*.K|r bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b ObgORb K c *.DQ.08!#)(G2)50'!O 950'($LO4 DF *)( bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b Ob I uf 0',9(950U!OL 'LOJ!O iL'(|r(0'(@A#A#*5)O DE950U!#pAi @2)5L'2%'+DF 0'2)2 4_ µ /'I7, b3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b Ob I'b ke*.DF9&.*Hrx5D3L#S950 bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b Ob I'bg P$.LOO9&.DQrx5D3L#S950 b+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b ORb Q 50'2. L'(950MA19. 9R(L#YSq 0',9(950U!OL 'LO4!O iL'(|re.G!#H[ZgA#A#*562%' µ /'I72, ORb K uf 0',9(950z!OLJDQ56!#&.9+!#3jM92%'. :bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b ORb KOb >X,)(*5 L#950N!#H[Zy,)V6L1950M!#,s/'0#9(*(08 µ bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b ORb KObg P$,.Ai.0'!'0'2))(X!OLN2)5p E2.9.08$!#Hp9(*2)5K( *,L#h#L#9.08* µ b+bHb+b3bHb+bHb+bHb+b+b.

(27) . . K$Q K$K K$K K$K K<L K<L K$S L6P Lp L L KM M$K M<L M<L M<L .

(28) ObRKObg uf 0',9(950U!OLN2)5pE2.9.08$!#Hp9(*2)5K( *,DQ59,)2.L#S * µ b+bHb+b+bHb3bHb+bHb+b+b ORb KOb I P@9(2.*,.9(950M.X!#,. K950M!#S-7592. *, bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b ORb KORb Q P$,. K950M!#S-950#IKL'.L#$!#DQ,.S0#I7Qb+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b O b L uf 0',9(950z!OLJDQ56!#&.9 k ε !#Hu"L#0'!#.C6%1DE bHb+bHb3b+bHb+bHb+b+bHb3bHb+bHb+b+b Ob Lpb P$,. K950M!#)(G2)5pE2.9.08*($!#p9(*2)5K( *, bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b Ob Lpbg P$,. K950M!OL 'LO4p9(*V8L'.LO b3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b Ob Lpbg P$,. K950M!OLN*.DQ3!#H!O9(*( A1950 b+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b Ob Lpb I P$,. K950M!OLN*.DQ3!#H2)5*)2.950Mh1(G>@.60'59!#({b+b+bHb+bHb+b3bHb+bHb+bHb+b+b Ob LpRb Q P$,. K950M!OLN*.DQ3!#A#*56!OL'2.950 b+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b ObRM w S0 b3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b Y** ,%<% & "1.XE5:

(29) :!F%. ? .C"A:2 :8@<. I'b ; 06*56!OL'2.950cb>X,)(L# *(YA#*,)(.08*,)(bi5DFDQ.08 *)($2)5DFD3L#0'(FbHb+bHb+b3bHb+bHb+bHb+b+b I'bg cL#7&.*3!O *3!#+P,.9,."Ohi5K(*(*3 b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b 'I bgOb ,)5DQ,.9b+b3bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b 'I bgObg 50'!O 950'(@,.*5p!O601DF9V6L')( b3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b 'I bgObg C6 D3L#S950M06L#DQ,.9V8L'R!#H[Zy,)2)5L#9.DQ.08(950#01 * bHb+bHb+b3bHb+bHb+bHb+b+b 'I bgOb I 92.L#"!#)(G(*.0'( h# *,)( b'jU5p!#&.9H!#+jU92*%'. b+b+bHb+bHb+b3bHb+bHb+bHb+b+b 'I bgObRQ 92.L#"!#)(G(*.0'( h# *,)( b'jU5p!#&.9 k ε !#3u"L#0'!#.C6%1DEbHb+b+bHb3bHb+bHb+b+b 'I bgObRK 50'2. L'(950NA19. 9 bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b I'bg WX 9R\$T$?^>@Wj K b+b3bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b 'I bgOb ,)5DQ,.9b+b3bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b 'I bgObg 50'!O 950'(@,.*5p!O601DF9V6L')(X.GDQ)(*L#*)(GspAi,. DQ.089)(bHb+b3bHb+bHb+bHb+b+b 'I bgObg C6 D3L#S950M06L#DQ,.9V8L'R!#H[Zy,)2)5L#9.DQ.08(950#01 * bHb+bHb+b3bHb+bHb+bHb+b+b 'I bgOb I 92.L#"!#)(G(*.0'( h# *,)( b'jU5p!#&.9H!#+jU92*%'. b+b+bHb+bHb+b3bHb+bHb+bHb+b+b 'I bgObRQ 92.L#"!#)(G(*.0'( h# *,)( b'jU5p!#&.9 k ε !#3u"L#0'!#.C6%1DEbHb+b+bHb3bHb+bHb+b+b 'I bgObRK 50'2. L'(950NA19. 9 bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b I'b I 50'2. L'(950Nb+bHb+bHb+b3bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b Y** ,%<% &0= 0= .X%.! :.X"3@ &

(30) ;GFW1%,@ OQ b ;06*56!OL'2.950cb>X,)(L# *(YA#*,)(.08*,)(bi5DFDQ.08 *)($2)5DFD3L#0'(FbHb+bHb+b3bHb+bHb+bHb+b+b OQ bg P@9(* h#L#*.L# w (*(*Hke*)((950 bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b OQ bgOb ,)5DQ,.9b+b3bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b OQ bgObg 50'!O 950'(@,.*5p!O601DF9V6L')( b3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b OQ bgObg C6 D3L#S950M06L#DQ,.9V8L'R!#H[Zy,)2)5L#9.DQ.08(950#01 * bHb+bHb+b3bHb+bHb+bHb+b+b OQ bgOb I 92.L#"!#)(G(*.0'( h# *,)( b+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b OQ bgObRQ 50'2. L'(950NA19. 9 bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b OQ bg >X5L' w (*(*Hk^*)(*(950 bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b OQ bgOb ,)5DQ,.9b+b3bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b OQ bgObg 50'!O 950'(@,.*5p!O601DF9V6L')( b3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b OQ bgObg C6 D3L#S950M06L#DQ,.9V8L'R!#H[Zy,)2)5L#9.DQ.08(950#01 * bHb+bHb+b3bHb+bHb+bHb+b+b OQ bgOb I 92.L#"!#)(G(*.0'( h# *,)( b+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b OQ bgObRQ 50'2. L'(950NA19. 9 bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b OQ b I 50'2. L'(950Nb+bHb+bHb+b3bHb+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b &,.% & E&::F=/ . .

(31) . M$M $M S SK S$Q S$Q S$K S$M S$S !P$P !OP (&H !KP !PFI !PFI !P$K !P$K K!P K K K K K KJ I O $ P $ K $ K. (8H ' $S JIP JIP JIP JIP JIQ JIK !KQ !KQ !KQ !KQ !Q$M !Q$S !KK ( .

(32) I .

(33) . ?. ?.X

(34) W:

(35) ;%>?@.. (= U (G H. Wqb %',)5*&.DQ3!#)(Yrx50'2.950'(Y DFA# 92. *)(QbHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b L Wqbg XW I75 %#DQR!#+T@'4Y*50 b+bHb+bHb+b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b L Wqbg 92.L#~!#H!#,. 7,))(GA1XA1(*(I7H.0NKSh#9)(X2)5DFA#9s#)( b+b+bHb+bHb+b3bHb+bHb+bHb+b+b L. . ?.C" * %,

(36) -%/.%/ 0"1 2 &F

(37) ;.. w b 50'!O 950U!#+2)5067.I7.0'2)R!#[Zg I75 %#DQ3 *,.|r bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b w bg ^8V L1950'($!OLJA#*5h#9&.DQ3!fZy5A# DF9(950U!#rx5DQ)(X)7)2+*5L#*)(G9)(G!#,.Ai.0'!'0'2))( b+b w bgOb T@5950'(b1P$,.Ai.0'!'0'2))(b+bHb3bHb+bHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b w bgObg ^V8L1950'(@!#S-DQ,.%'5p!#+!#[Zy,)V8L1950U 0',9(*,) b+bHb+bHb+b3bHb+bHb+bHb+b+b w bgObg ^V8L1950'(@!#S-DQ,.%'5p!#3! 5 06*JbHb+b+bHb+bHb3bHb+b+bHb+bHb+b3bHb+bHb+bHb+b+b. ( L6Q L6K L$L L$L L6M.

(38)

(39) . .

(40) !#" 13:6B 13:N T TVU ! "HY Z\[:] "_^` TV[Fa e )&B e )&N. $

(41) % '&)('*()+'& ,-( ./0 13244)26517&18:9;4<1>=72(2651?@ 21A ?@?@1C&)1

(42) 1D?E138&)1C&)1

(43) F (2G H&)1 $ IF +) J

(44) ?E1@2 ?@4; 1K&)138

(45) L;( 8&)( ?@)&)J $ 1 kM ε ?@?@1O&)1

(46) #1D?@1

(47) P&)1Q&)13: (2G '&)1 $ E 1D4 JD?@1O2?@4< ; 18&)13R

(48) L;(S P&)( ?@)&)J $ 1 kM ε & ,- D1D2D1

(49) R 13 $

(50) % '&)('*()+'& ,-( ./R44 )2651O&)17:94<1W=2D(26518?@ 21XA ?@)&)J $ 1Q&)18(( $ 1D2D1 $

(51) %F $

(52) % 'b_= µc d PA ?@?@1>&)137 1D?@1

(53) Q&1C4 )&)(2G f&)1 $ IF +) J

(54) ?E1>2D?@4< ; 1@&)1

(55) Q

(56) L;(S O&)( ?@)&)J $ 1 kM ε ?@?@1Q&)13P 1

(57) ?@13P&)1Q4)&)(2G g&)1 $ C 1D4 JD?@1h2 ?@4; 1O&)1

(58) P 3L;(S X&)( ?@)&)J $ 1 kM ε. i 9?K $ 13 <6&j&lk (g&) ?@ 1@mn1+)1D?@4 $ 1Co ∂Ω 13: $ 18 &'&)1 Ωp ∂ &)

(59)

(60) 17&)1 $ K.r2 g 1 $ $ E S $ 1 x q y q z g q g q g 4< D6S1D(Rd &) 1

(61) ; ∇ 4< D6S1D(R6S 1 $ ∇∧ 4< D6S1D(P&) 1

(62) d 1D2D1 ∇· ,x. ,y. ,z.

(63) K Z\1F 13 $ 1

(64) D 1

(65) F1O&)(g a 21>2D 1

(66) &18265 $ 1D(X 4 32 L;(1Ob@41

(67) F '2:6; 1 c 21 >2D 1

(68) &18265 $ 1D(X 4 32 L;(1Ob@ $ (?@182 :6; c 21 >2D 1

(69) &174 13 C 2 :6; 1O&)1 $ $ &)1 i ()51D $ &'&) D4<1D&;&)(Id O2F %&) D C 2 :6; 13P&)(I?@&J $ 1 kM ε C q C q C 21>2D 1

(70) &1 % D1O&)1Q265?E4 $ 6 CD 21 >2D 1

(71) &1 % D1O&)1Q265?E4'4)2651 CD

(72) 21 >2D 1

(73) &174< 21O&)1O4 13 CL &)?C 1O&)1Q& g&)1 α D. 1

(74) F1

(75) (&)13#()+j&)1Q&) D.r?CS D r . 2 g&lk ?@ %F1

(76) ?E1

(77) ; D D. 1

(78) d 18 ; 1D184P( Q&)1O?C 1 e D. 1

(79) d 17 $ 184P( Q&)1O?C 1 E D. 1

(80) d 17 $ 181 $ S 14P( Q&)1O?C 1 E. D 1 F1

(81) (&)(j*()+I2 1

(82) 2G . Fc. D 1 F1

(83) (&)(j*()+I&) ,-( . Fd r . 2 &)1O21

(84) 2G W P1D9 $ &Omr?@)&)J $ 1 kM εp f q f r . 2 g&)184 /mr?@)&)J $ 1 f *()+' ; %L (1D()+j& 21 kM εp *()+' ; %L (1D()+j& 21P D S $ ( O ( $ k ; 1

(85) F.n 21.r J

(86) 18 .r2 g2 ;17&lk &) %21 k G (α) .r2 g2 ; 6 17& k &) %21 k g ( , ) d6&1D(R1 $ S 181D+4 ?@ D1O& $ 181D4<JD171

(87) ; 6 g d6&1D(R1 $ S 1ObE(I 6SX&)1O .r

(88) 1

(89) 21O&) g 1D; 5 $ 4 186 $ 174P( Q&17?C 1 H ?K182D?@4 $ 1+)1 q 62D 182

(90)

(91) 17&1 −1 &)1O4F 18 ?Cd 14< 1. 1

(92) F1

(93) (X (j?CS %218 %&)1D; I r . 2 I :132G . J (α) r . 2 I :132G . J( , ) 2 :6; 1O&)1 ? K D. 1

(94) d 1O2D D %L;(18 (( $ 1D;1 k 2 1 >2D 1

(95) &182D&(2G 8 51D?E %L;(17 (( $ 1D; kc 2 1 >2D 1

(96) &182D&(2G 8 51D?E %L;(1 k F @ ? ?E1O&)13X2

(97) 1 C2D 1

(98) ;P&)1Q2D&)(2G 7 51

(99) ?@ %L (1 k¯ d (1D(X&)18?@ $ d1 $ ` K ? 18&1 " 265 M 132G 1

(100) (P ?C $ 17I 321

(101) 1

(102) ?E1

(103) ;#( 6 1 $$ 1Q&(' 1

(104) 2 1D(R265?@4g D)&)9?@ %L;(1 n! ?K18&18.r2 P2D; 6 ; 1 n" $$ 1Q&(' 1

(105) 2 1D(R&1O46?@J 13R&)18.r?@1 α n µ. ε1. ε2. α. 1. 2. µ V V. k. k.

(106) L p P " . . p Pr. e c c r ! ( P1 , P1 c . . . ). R R Sx Sy Sz (α). q q. . t T . . V v. . q q . 1. . . 2. 3. . w (α) (α) α " . 1. .

(107) . . T u . . 41

(108) F I:6S L;(1 1

(109) ?@1Q&)184)&)(2G g&)(j?@)&)J $ 1 kM ε 132G 1

(110) (X&)1O S % $ 1

(111) #4 ?@ 13PSF6265 ObE(1Q2D1 $$ ( $ 1 41

(112) F j $ 18('41

(113) F '&lk ?K 1O&)1 e & $ ?K18&1 e & $ (( $ 1D; 132G 1

(114) (R*()+I&)1O265 $ 1D( 132G 1

(115) (R*()+I&)1O&) ,<( ' (( $ 1D;1Q&lk 1

(116) ; 5 $ 4 1 2 :6; 18( 1D6F1 $$ 17&1

(117) Pd; 74 .n Pb $ @?@ 17?E $ 1O&)('d O2D & D

(118) L;( P&)1 $ E?@

(119) 2D %L (18&1

(120) #*( %&)13X&) % 2D D %F

(121) 1

(122) ?K18&1 P1D9 $ & ?K18&1 P1D9 $ &#(( $ 1D; 44< P&1

(123) R41

(124) F 6 $ 1

(125) 44< P&1

(126) # 1

(127) ?@4

(128) (1

(129) # $ 13 4 :1

(130) 2 I&)(I 132G 1

(131) (PF(F.n 21 ( S $ 1

(132) X& 1

(133) 2 x q y 1 z 1

(134) 2 1

(135) (X&)1Q2 &)

(136) 1

(137) #&)(I?@ $$ d1O ( .n2 %L;(1 132G 1

(138) (P 1

(139) F1O&lk 1D; %1

(140) ?@1D; 1

(141) ?E4 1

(142) ?E4< D6S(18F %L;(1 132G 1

(143) (R 1

(144) ?@1O (621 1

(145) ?E4< D6S(18& k P(j 1

(146) ?@4

(147) (17 6 $ 1 2 ?E4< ;18 ( S; $ k S+)1 &)(I 132G 1

(148) (P 1

(149) F1 132G 1

(150) (P 1

(151) F1O&)1Q2D6&)x D1

(152) u q v 1 w $ (?@1O&lk (1Q2D1 $$ ( $ 1 2 ?E4< ;18 ( S; $ k S+)1 y &)(I 132G 1

(153) (P 1

(154) F1 &) 132G I&)1O?C $$ d1 mr1

(155) 4 j q k p 132G 1

(156) (P 1

(157) F181 $ S i1 2 ?E4< ;18 ( S; $ k S+)1 &)(I 1

(158) 2 1

(159) (P 1

(160) F1 1

(161) 2 1

(162) (X&)1Q2 &)

(163) 1

(164) #&)(Iz ?@ $$ d18 $ (?@ L;(1 ?CS %21 F2D 1D18&('?C $$ d1 132G 1

(165) (X&)1O S % $ 1

(166) R2 1D 0 13 F 265 ObE(1Q21 $$ ( $ 1 6SXd (26511D&) P&(' 1

(167) 2 1D(X265?@4I D)&)9?@ %L;(1 132G 1

(168) (X265?E4I

(169) )&)9?@ L;(18F(P(18.r; JD17&(I&?C 1. . . .

(170) M Z\1F 13Rd1

(171) 2

(172) L (1

(173) 1

(174) 2G1D(X&1

(175) R4?EJD 1

(176) R&)18.r ?@1 α 2DF 1O&)1 $ $ &)1 i () 51

(177) $ &j&)

(178) 41

(179) & &('d; 82 F %&)

(180) . β 6 44< X&)1

(181) P265 $ 1D(6RF4<

(182) 2D L;(13 γ = γ

(183). 4 % 1D(R&1Q2(2651 $ ?@ 1 δ 6 ) ( j + & Q 1 ) & . . . 4 . . ε ()+j&)1Q& F 4 ' 41 ε˜ &) %F21Ob $ @4 η 1D&1D?@1D;P 1D; 4 L;(1 η. 1

(184) 2G1D(X & : ; λ D 2 ; 1 >2 1D;X&)('*()+'& ,-( .

(185) λ D 2 ; 1 >2 1D;X&)1O 2;F O&)9?E %L;(18?@ $

(186) 2( $ 1

(187) µ D 2 ; 1 >2 1D;X&)1O 2;F O&)9?E %L;(17 (( $ 1D;

(188) µc. @ ? ?@18&1

(189) X2D;

(190) 1 >2 1D;P&)18 % 2D 8&9;?@ L;(18?@ $

(191) 2D( $ 171P( ( $ 1

(192) ; µ ¯ D 2 ; 1

(193) >2 1D;X&)1O 2;F O2

(194) ?@ %L;(17 (( $ 1D; νc 2

(195) 1 C2D 1

(196) ;P&1O ; %2 O2 D?C %L (1F.r?E @mr?@)&)J $ 1Q&)1 i 4 $ M $$ ?C p ν˜ S. % $ 18 3&)( 1O&)1 $ h.r 2G '& k ?E F 1D?@1D;X&)1 " %2651 $ . ξ C ? 17 $ (?@ L;(1O&)('*( &)1 ρ 4 ?@J 18&)1Q2 1

(197) 2 W1

(198) ; 4 %L;(17& 1

(199) 1

(200) σ D 2 F 1

(201) R&)('*()+I&) ,<( . 4<( $ 18?@)&)J $ 1 kM ε σ q σ D 1 . 1D(X&1

(202) X2D; 6 ; 1

(203) R&)(1

(204) Pb $ E % 2D τ D 1 . 1D(X&1 P1D9 $ & τ r . G 2 $ ?E 1

(205) (X&)1O4<1D; 1 φ r . G 2 I&182D 132G W1D; 4 L;(1O&)1

(206) 1D ψ . F 2D ω ¯ ) & C ? 1OF4 % $ Ω c c. . ijk. k. ε˜.

(207) J : R @0BL#hl5*,2.*.L#E)(*qL#0 !O9(*Al5K( |r$DQ,)20#9V8L'J2)5DFA#9s#J!#)( 0',N_UA#*5A#L#9(*.QL#0 ,.*50'srH.0 2)2.*59(*(06 SXV6L108 *,Y!#`DQ5L#7.DQ.08^!fZg 0#I7,.*,Kbuc)(L#hl5*,2.*.L#*(^*,)2).08*(e(*`2)5DFAl5K(*.06^!fZ L#0' (*5L {06* N}5L#Osn!fZ L#0m2)5DFA#*)((*.L#n!fZ L#0'-2%1D3h#*F!#32)5DRh#L'(950.$!fZ L#0'RL#h# 0'Kni!O9(Ai5K(*,)( (L# K08+9QDQ.DQ{ #Kbcuc (A# *F[Zg 3sO*,.9.L#R!#)( 0',KncAl5L#+A19Kn_N DQ.08*.q[Zy.08*,){!OL 2)5DFA#*)(*(*.L# N 'LO A# DE * OsnAl5L#{A19U_.*U, )2.*,M!#.9&.*U9NDQ5*.L#4(0'(t.*NA1(*(*,MA1 9Q!O9(Ai5K( |rA#*5A#L#9(|r N 'LO:(*)2)50'!' * Osb"u"E2)5DFA#*)(*(*.L#-4Ai5L#Hr}50'2.950!fZg2)2.*5

(208) 9*ES4A#*)((950 !fZg*.3!OL 'L#9!#{)K08R(50:.08*,)Q!'0'(3S42*%1D3h#*t!#F2)5D3h#L'(*950cb~u"42%1D3h#*t!#Q2)5D3h#L'(*950 )(F9J(9&.I7J!fZ L#0'4*,2.950 2*%# DF9V6L'MV6L#,.9&.7N[Zy,.0'.IK9J%'.DF9V8L'M!#)(FI8 7beu"mL#h# 0'MmAi5L# rx50'2.950 !fZy.08

(209) 90'.Q9)(Qh#*)(FDQ5*.L#Q.0 !#,.*.0'!'06Q9)(-I8 4h# T#9,)(be?e0O/'0cne[Zg FsOA#L#9(*,4A1-S L#h# 0'+2)506 h#L'R.0JA# L'(@!OL 'LO4(*)2)50'!' *qLJI8 0M!#+V6L108 *,+!#+DQ5L#7.DQ.08b ucF2)5DFA#*)((*.L#3.StL#h# 0'Q(*-2)5DFAi5K(*.083!fZ L#0'F(*L'2)2))(*(950:!fZy,.I7)(nf2)50'( L',)(3!fZ L#0:*5*5 N *5L'$DQ5h# 9 O.Y!fZ L#04(**5 N *5L'@/## OsbOP$)(GL#h1I7)( np!O9(*Al5K(*,)((L# K08[Zg ) DRL#n'(*508DQ506*,)(Y(L# 2*%1V6L'*5L'Kbu"$Ai.r}5DE0'2)!fZ L#0'*5L')(Â#A#*,)2.9,)A1e!#)(r}50'2.950'( A# L'(e5L-DQ5 0'(e2.S(*(9V6L')( *.0'!#.DQ.08`9(*.08*5A#9V6L'KnKLO-!#Y2)5DFA#*)(*(950cnK!#,.h# ^!#h#95p2I7KnAl.*)( IK95h19)(n7A#*5/''!fZg0#IK9)(^.0 (*59Kn8DEI7@LEAi5DFA1I7Kb)b)b$pAlX!#Yrx50'2.950'(n8!#,.Ai.0'!'08Y!#Y[Zy,)2)5L#9.DQ.06.!#GS+I7,)5DQ,.9Kn (*.E!#,)( IK0',+A1@SF(L# *+A1@[ZyspA#*)((950

(210) '.blu"-rx5DQ3!#)($L#h1I7)($)(*X!#,s *.DF 0',)G!#(*5*YV6L'[Zy50Q5h#9.0#0'S$DQ. 9.L#*YK9.L#^!#)(r}50'2.950'(o,.*5p!Op01DF9V8L')(eAi. 0'.08*)( b u"$*)2%'.*2*%'@!#)(r}5DQ)(^,.*5p!O601DF9V6L')(^5A# DE9)(o$*5L#^!fZghi5*!-*.Ai5K(*,(L# 9Y()75 xr[ *Y. [ZysOAl,.9.0'2)!#)(c 0#I7,.0#9.L#*( !#o2)50'2).A#950cbP.A#L#9(~L#0'^*.08 0'!fZg0#0',))(n SG( DRL#S950-08L#DQ,.9V6L' .04DQ,)20#9V8L'3!#)( 'L#9!#)(XRAl.DF9(Y!fZg01 O(*.G!#)(Y,)2)5L#9.DQ.08*(X 08*.0')($)7)2L#0'DQ5p!#,. 9(950N!# 2)5DFA#9sO *,G2.*59(*(06* N},)V8L1950E!OL-Ai5*.089. ! S<L6P ! S$M$P nK,)V8L1950'(^!fZy?^L#9. ! S$M$P ! S$M$Qn ,)V6L1950'(R>@W@THCB! S$M$Q OsbeE(75 xrx *4JA#*5IK*)(*(* 7.DQ.08-,.*,QL# 9(*,{Al5L#3SN2)50'2).A#950 !fZgLO h1I7)(E!#NL#hl5DE2%# 0'U.0 2)5DFA#9,.DQ.084!#)(Q*)2*%#0#9V6L')(t.DFA# 9V8L')(b`P$9( 0#IKL'50'(EV6L1*N,.Ai)( !'0'(-Sm2)508 h#L#950 !#)(F(* D3L#S950'(F06L#DQ,.9V8L')(E_U[Zy5A# DF9(950 !#Erx5DQ)(Q,.*5p!O601DF9V6L')( [Z L'(I7-9qA# L'(L'!O DQ.08 *{2)50'(9(*F_t,. L'.HStV6L1 *,F!fZ L#00'5D3h#*- DF *,F!#qrx5DQ)(A1H!#)( 292.L#9(H!fZg01 O(*ef2).*qDQ,.%'56!#F)(+L'(*(* 0'2.9.0#0'FV6L'qS{(* D3L#S950:06L#DQ,.9V8L'F.0zDQ,)20#9V6L' !#)( 'L#9!#)(biP&)(9qDF 9.Lz!#)(+0#0',))(F! S<L6POnf!O f,.*.08*(+L#*.L#*( 0'5DFDQ.063@92 O(E g$ K^. o0'!#.A#SK*(F K L6Q! 508@2)50'(9!#,.*,+!#)(rx5DQ)(X(*5 9!#)(GA1DQ,.*,))(@.G506X292.L#9,HA1X!O f,s *.0'2))(/'0#9)(9)(HIK!O9.06*(+!#)(rx50'2.950'(3,.*5p!O601DF9V6L')(HA1A#Al53LOzA1DQ&.*)(+!#qrx5DQKn Ai5L#H DQ.06*.HL#0'qDQ,.%'56!#-!fZy5A# DF9(950:A1H!#)(*2).06*KbiX0'q*59(9&.DQ-,.Ai-t,.*,q 0# 9,)qA1 d DQ)(*5"0 g$ MnfV8L#o4A#A# 9V6L',Q.0 ! S$M$MtStDQ,.%'56!#E!OL:2)508*9Q5A# DE`LO,)V6L1950'(+!#-StDQ,s 20#9V6L'{!#))( 'L#9!#)(c~!#&)(R95*(n"9E292.L#`!#)(RIK!O9.08*(q0',)2))(*( *)(-_NL#0'QDQ,.%'5p!#{!fZy5A# DF9(950 95p293Ai5L# .*q*, 9(*,q.0U*,)(*5 K08H!#)($A#*5h#9&.DQ)( 0', *)( ,)V8L1950'(+! 5 08*)(ni,)V6L1950 0',9(*,) A# L#*V8LcZ L#0UIK0'!M0'5DRh#* NxLmDQ5 0'(L#08V8L'R!#+A1DQ&.*)(!#Hrx5DQ OG!#R2| 2.L#9(+!fZg01 O(* N A#*5h#9&.DQQ0'50 0', * Osb"?e0O/'0cncStA#L#9(*(0'2)F!#)(+292.L#S*.L#*(+DQ5p!#.0')(3tAi.DF9( SJ*, 9(950!fZy5A# DF9(950'(F,.*5p!O601DF9V6L')(3IK95h19)(q(L#+9{!#5DE 0'E!#EA1DQ&.*)#( RKO b)( )KLOfnp.0'2)5*$*,)(*.7,)(Y_RSR2)50'2).A#950N!#Grx5DQ)(Y( DFA#9)(n6L# 9(*.08I7,.0',.9.DQ.06GL#0N I75 %#DQ .

(211) !P I7,.0',.9V6L'q2)5DFDQqDF 0# DF9(*.L#H.H!#)(@DQ,.%'56!#)(H!#R*,.IK*)(*(950zAi5L#$2)5DFA#9,.*.nf!OL#06$[Zy5A# DF9( 950cn#S-2)50#019(*(0'2)3!#)(rx50'2.950'(@,.*5p!O601DF9V6L')(X(*L#Y9H!#5DE 0'3!#A1DQ&.*)(b u^Zy5A# DF9(950 !#4rx5DQ)(Q9!O DQ.0'(*950#0'. 9)(t2)5DFA#9s#)(Q 06*,.*)(*(06{[Z 0'!OL'(9M0'JAi.L#E.* *, 9(*,)FL'(*L'. 9.DQ.083A1R2))(HDQ,.%'56!#)(R!fZy5A# DF9(950IK95h19EAl5L#H[Z 0'(*08b"k5L#R2).*Q9(*50cn [Z 08*,.*.G!#)(h#L#*LO4!fZy,.L'!#)( 0'!OL'(9.9(Y(*Xr}5p2 9(*HL 5L#*!fZ %8L#c(L#9)(DQ,.%'56!#)(Y!fZy5A# DF9(950 A1-IK!O9.08beuc.L#-DF9(*t.0 L#6*{0',)2))(*( *t9t!#,.7.95A#Al.DQ.06E!fZ L#0't A#942)5DFAl,.*.0'2) A1 DQ,.9(950I7,)5DQ,.9V8L'{!#)(+rx5DQ)(3(5 9!#)(3.R!#)(3DE SI7)(375 L#DF9V6L')(n"DQ,.%'56!#{!#E!#)(*2).06*Kn ( DRL#S95008L#DQ,.9V6L'Q!#)(+,)2)5L#9.DQ.06*(R.R292.L#o!OLIK!O9.08q!#)(r}50'2.950'(R,.*56!Op01DF9V8L')(3A1 A#Ai5oLOqA1DQ&.*)(`!#r}5DQKbKu"+!#,.*.DF 01950{!#[Zy,)2)5L#9.DQ.08.^!#)( IK!O9.08*(L#*5L#^!#S rx5DQ 0# S9HAl.DQ.G!#H292.L#9.XA1YSqDQ,.%'56!#H!#H!#)(*2).06*HL#0J0'5L#7LN7)2.*.L#X!#A1DQ&.*)( !#@r}5DQ+L'V6L'.f9$DQ56!OL#9H!#$*.DE SI7HAi.DQ.G!fZg(*(*5p2.9.L#0J0'5L#7LJDE SI7H75 L#DF9V6L'Kb1)( 5Ai,.950'(X(*506X.0'2*%1

(212) 90',))(@ *,. 7.DQ.08 L'(V8LcZg_-!#,.*.DF 01950m!fZ L#0M5A# D3L#D 9562[b P+2))(Y*59(@,.Al)( nOS-A# L'(G2)5DFA#9s#+)(G9H292.L#!OLJIK!O9.08!#)(r}50'2.950'($,.*56!Op01DF9V6L')( A1HA#Ai5RLOmA1DQ&.*)(R!#qr}5DQ)( bc?e0: f.ni9)(HSh#9)(3I7,)5DQ,.9V8L')(R.3,.*56!Op01DF9V6L')( !#2))(r}50'2.950'(X(*508Y 9,))(A1Y9)(Y,)V6L1950'(Y!#SRDQ,)20#9V8L'+!#)( 'L#9!#)( np(*lh#9.0NV6L'$9292.L#c!#)( IK!O9.08*(^0',)2))(*( *S@*,)(*5 L#950F!fZ L#0'Y,)V8L1950- 0',9(*,)Y5LQ! 5 08*KnK2KZy)(=_ !O *[Z 067.*(950Q!fZ L#0 (O(*&.DQ- 0', *E!#QIK0'!#Q 9Q!#5063S4DE92){)(HS4DE92) 2)5h#9.0#0'E!#)(3,)V8L1950'(R!#FS DQ,)20#9V6L'@A1À#Al5GLt2*%1DFAN,.*56!Op01DF9V6L'Kbpk Y 9.L#*(np9)(` f.*(op9(*V6L'.LOA N}!#,)2)5 9.DQ.08*(n Ai.*)(RA1qr}*5*.DQ.08nAi.*)(RA1-DQ,.S0#I7Kn ,)2# 'LO6[A#*5/'[n DQ5p!O|/12950'(F!#{SMAi.08*t!OL !OS IKDFDQRA#Al5$!#+A#*)(*(950O!#,.h# .X!OLm!#,.h# @!#+h#95p2I7Kb)b)b O 5L'.06@L#0N*9RA#*,.Ai50'!#,.08!'0'( 9)(3,)2)5L#9.DQ.06*(QL#*5L#R!#)(qL#h1I7)(q!#QL#hl5DE2%# 0'Kb;=o2)50669.06q!#50'2t!#Q2)50'(9!#,.*.q9)(3,)V6L1 950'(E!#JT)p9.C6*35 7)({DQ57.0#0',))( N}>XW$TGC ORAi5L#F9)(Q292.L#9(E!fZg01 O(*N.{!fZ 087.*(*.{SmDE92) 2)5h#9.0#0'Q!#F2))(+,)V6L1950'(+!O9(*2.*,.9(*,))(HA13A#Al53L:2%1DFA,.*56!Op01DF9V6L'FAl5L#H9)(3292.L#9( !#HIK!O9.06*(b W@LM!#,.h#L#@!#)(@0#0',))(R! S$S$POn'!#+0'5D3h#*.LOmL#*.L#*(@508XDF9(@.0 L#p*+2))(X292.L#9()7)23L#0'HDQ5 !#,. 9(950!#. 'L#9!#RA1r[ bf.LOUV8L#L# 9(9.06$L#0'qDQ,.%'5p!#R!O *-!O9(*2.*&.*q508H!#50'2q 0',9(*,R9 h# S04!#2 'LOE!# 'L#9!#XA1r[ (L#`2%12.L#0'$!#)(2). L#9)(!#GDE SI7$A1A#Al5YL{2%1DFAN,.*56!O6 01DF9V6L'Kb6;=9(o506`*.DE*V6L',@V6L'G[Zy5h#*.06950N!#GIK!O9.06*(À#*,)2.9(,. 2)50'!O 950#0',)A1o[Zys'2. L'!# !#S$ 0',9(950cnK9)( 'LO-!fZ 08*.r[2))( r *5069&.*G!#.K08e0'5DFDQ.08`.*Y!#,. 7,)(^s#2.*.DQ.06b7k5L# [Zy,.L'!#t!fZy,)2)5L#9.DQ.08*(-DQ5p!#,. 9(*,)(+A1R9)(R,)V6L1950'(R>@W@THClnfSN 0',9(950s'2.*E!#)(q,)V6L1950'( !O9(*2.*&.*)(`.o!#)(^,)V6L1950'(o!OLQDQ5p!#&.9G!#YL#h#L#9.0'2)@)(^L#0'Ya2%'XsO5*!O 01 *.DQ.08Y*!OL'Kb8k5L# 2).*Q9(50cn"!O f,.*.08*(R0# 7LO!fZgA#A#*5)O DE950'(F508R,.*,{2)50'(9!#,.*,)(q!'0'(+SJ *,.L#*{Ai5L#+9 292.L#"!#HSqDE92) 2)5h#9.0#0'Kb1T@5L'(G.0U!O9( 0#IKL'.*50'(XV6L1* Sq 0',9(950U!OL 'LO469(V8L'.LOJ)(G5DF9(* g$ K!8 9z2)5p E2.9.08M!#mp9(*2)5K( *,zL#h#L#9.06*:.492)56 E2.9.06M!O%L 'LO !#2*%19.L#ML#h#L#9.08M(*506 2)50'(*9!#,.*,)(X2)50'(06*( NxA#A#*5)O DE950z!O * /'I7, GO g$ Pn RK<L n L! 8 9z2)5p E2.9.08M!#mp9(*2)5K( *,zL#h#L#9.06*:.49µ2)56 E2.9.06M!O%L 'LO !#2*%19.L#ML#h#L#9.08M(*506 2)50'(*9!#,.*,)(`2)50'(06*(.(*.L#9(o9)(o*.DQ)(!#$2)5L'2*%'@DF 0'2)@!OL 'LOQ69(*V6L'.LOE(*506`!#,. 7,)( RQ$Mn I8 8 9DQ5p!#&.9+!#HL#h#L#9.0'2)R)(Y 0',9(*, g n gF In gK! n RQ$P!n gK! n g$ M!b u"J!#.LOO9&.DQ{A#A#*5p DE950B)(3(*e*,.A10'!OL'EV6LcZy. 9FAl.L#R.*E2)50'(9!#,.*,)Q2)5DFDQEL#0: *.DQ.08 (0'!'*!fb C60')2.DER.^[Z]\$T$?^>XWv!#,.7.95A#Ai.08!#.A#L#9(oDF|=$ P$PFIqL#0'G2*%1

(213) 90'$!fZy5A# DF9(950t95629@!#rx5DQ)(n Ai5L#oSV6L'. 9XL#0t292.L#l!#XIK!O9.08G)7)2A#A#*5)O DE950 µ /'I7, Q3,.*,G*.*.06Lcbpu"X(L#A#Ai5o 0Orx5 DE9V6L'@!#$2)X i)(`9X95IK92.9.os RS!i!#,.7.95A#Al,HL{P,.A1*.DQ.06G!#C6 DRL#S950NTXL#DQ,.9V6L' !#)(Y,)2)5L#9.DQ.08*($.YWY,.*572)5L'(9V6L'X N}P+CpT@W O`!#[Z]\$T@?^>@WRbO?e0N2)5DFA#9,.DQ.06@!#H2)$)K "2)5062s . .

(214) K L'.[n~C60')2.DENN(*5L#%1 *,Q,.K L'.+9-hl,.0',s/12)E!fZ L#0'Q 0',9(950:A# L'(3A#*,)2.9(*Q!'0'(H9E2!O*Q!#-S A#*,)(*.06*F%'&)(*-.0:2)5087.06950B;<>@?Gbiu^Zy5h )2.|r!#-2).*F,.L'!#F)(H!#F292.L#9.+!#)(IK!O9.08*(R!# rx50'2.950'(R,.*5p!O601DF9V6L')(3!#FDE0#9&.*EA#*,)2.9(*Q.0(F!#.DE0'!'08-(Z o)(H0',)2))(*( *Q!fZyi)2.L'.RS 0',9(950:!OL 'LOMp9(*V8L'.LOm!#)(@,)V6L1950'(H!#RT)p9.C6*35 7)(37)2RDQ5 0'(!fZgA#A#*5p DE950'(b"u" !#,.DE*2*%'4N2)50'(*9(*,E_J(ZgA#A#L#7.-(L#+L#0'E 0',9(950B!OL 'LO69(*V6L'.LO:( DFA#9A NxA#A#*5p DE950 /'I7, q.oA#A#*5p2*%'G!#=6Ai. 2)5L'2*%'GDF 0'2) GOV8L#'5 i*L#0Q2)5p!'I7Y( DFA#9Y.o$Al.DF9(o!fZy5h#*.0# !#YµA# *.DF9&.*)(`9.L#*(`!#GIK!O9.06*(`!fZ L#0t5*!O*X!#YIK0'!#.L#2)5*)2.oDE9(Â1(`s#2.*.DQ.06`9!#.069V8L')( )7)2$9)(K9.L#*(!#$*,srx,.*.0'2))(5h#*.08L')(YA1!O i,.*.0'2))(/'0#9)( bpu~R!#.LOO9&.DQ,.Al$2)50'(9(*_-h10O !#50#0'.Q[ZgA#A#*5p2*%'N!#4=6Ai H2)5L'2%'NDF 0'2) .E_mA#*.0'!O*N.0 2)5DFA#*J*5L#*)(F9)(Q!#,. 7,))(E!'0'( 9. 'LOUp9(*V8L'.LON*5L#H.02)50'(*.K08[Z %8pAi5%'&)(*Rr}5*-!#RDQ56!#&.9-!#qL#h#L#9.0'2)q/'I7,Kbc.Al.0'!'06n [ZgA#A#*5p2*%'+!# µ /'I72, {Ai.L#G.*Al,.01 9(06*H0'5DFDQ.08@Al5L#G2). 0'(XDQ56!#&.9)(X!#L#h#L#9.0'2)Kb . 0'(@L#*.L#*(XV8L#iA#*.0#0'.08$.0N2)5DFA#*H9DQ5p!#&.9H!#L#h#L#9.0'2)+!'0'(Y9.L#*(Y 0',9(950'( n#A1 p9.0#0'.08q_UDQ,. 95*.3S4A#*,)2.9(*950!#F9.L#*(3*,)(L# *( N g n gF In gK! n RQ$Pn gK n g$ M!Osb"?e08p9(I708 V6L'F[Zgh'(*.0'2)E!#E 0',9(950B!OL:DQ56!#&.9{!#QL#h#L#9.0'2){(*5 3*5AAl,.01 9(06*QAi5L#R2). 0'(R2( *)(n[Zy5h )2.|r!#+ 0',9(*.H!#.LOMDQ5p!#&.9)(@!#RL#h#L#9.0'2)FE,.*,3/##,R /'0z!#37,.|/1.HV6L'32KZy)($h#9.0 SE 0',9(950:!#-2))(@DQ5p!#&.9)(H!#RL#h#L#9.0'2)FV8L#Al.DQ.[Zy5h#*.06950!#3IK!O9.06*(HA#*,)2.9(bik DF [Zy.0'(*.DRh#9{!#)(RDQ56!#&.9)(q!#QL#h#L#9.0'2){L# 9(*,)(RA139)(q!#,.A1*.DQ.08*(F!#450'2).A#950!#4C60')2.DEOn !#.LOUDQ5p!#&.9)(H508+,.*,q*.*.06L'(HAl5L#9)(292.L#9(+!fZg01 O(*-.H!#RIK!O9.06*( lL#0zDQ56!#&.9F I7,.h#9V6L' N}jU92*%'. IKO.GL#0JDQ56!#&.9R_-!#.LOJ,)V6L1950'(X!#0'(*Al5 N k ε !#Hu"L#0'!#.C6%1DE g< L Osb )(YLON506Gr[ Y[Zy5h .X!#H!#.LOJA#L#h# 92950'( d bKk~.*.n7P-bKP$L# 950 $b Hb7ke%1DNnp508 h#L#950E*5H!O9(2.*.* DFA# 92. ÎK!O9.080'!F!O9(*2.*.* ! 5 08XDQ.%'56!4rx5X.*5p!O601DF92R(%1AlH5A# DF 950cn?`YY\$jmWCln1$ P$PFI RQ$M!8 D P-b1P$L# 950cnl>X)2).06H< PWY2. p 9)($+\$T$?^>XW 1;=DFA# 92. +C6I7)( d b1k.*.nf$b Hblke%1 rx5+5DFA#9sz<955 4 C6 DRL#S950'(30'!:$!O9.08-5DFA#L#950zr}53C6%1AiF\@A# DF 950cn RQ$Sb KeC6Ai)2.S";(*(L'+ N :5( p(*%'5AMk~5K(*CpW$>Y\$P-RZ P$Q<Osn1_qA1

(215) 9*# `%12.L#0'R!#H2))(G!#.LOJA#L#h# 92950'(X*.A#*.0'!N!#)(G*,)(L# *(X!#)(G2%1A# *)($-. I'b HDE06L'(*2. @)(*G5I80#9(*,+2)5DFDQ+(L# b PH0'(Y9H2%1A# *EKnO9A#*5h#9&.DQHDE%',.DE9V6L'3!fZy5A# DF9(950m!#$r}5DQ)(@,.*56!Op01DF9V8L')(@)( A#*,)(*.06*,+ 0'(fV8L'@Sq(L'2.L#*H!fZ L#0'2*%1

(216) 90'H!fZy5A# DF9(950NIK95h19H5L495p29KbOu"3r}5DRL#S950N!#)( ,)V6L1950'(!#`SXDQ,)20#9V8L'!#)( 'L#9!#)(.0qDQ5p!#,. 9(950q>@W@THCH. !#)(~DQ56!#&.9)( !#`L#h#L#9.0'2)`L# 9(,)( !'0'(q2).*E%'&)(*{)(R.0'(*L# *EA#Ai.9,)Kb \@0!#,)2. -95*(-.0!#,. `[Zy5A# DF9(950BA1RDQ,.%'56!#t!# IK!O9.08*( .".03A192.L# 9.~9)(~!#.LODQ,.%'5p!#)(!O9(*2.*&.*)("V6L'^(*506"SDQ,.%'5p!#o!#e[Zy,)V6L19503 0',9(,) !O9(*2.*&.*:.JSDQ,.%'5p!#! 5 08*:!O9(2.*&.*KnYAl5L#J9)(V8L'. 9)(JL#0292.L#+!#DE92) 2)5h#9.0#0':!# h# S0M!# 'LO4A1YA#Al5XLU2*%1DFAU,.*5p!O601DF9V6L'+!#5 G.*H*, 9(,Kb#X0'h# h# 95IKA#%#9R!#,. 9,) *.S 7XL- *.DQ.08!O#L 'LO-!O iL'(|rl.e!#)(eDQ5p!#&.9)(e!#L#h#L#9.0'2)YAi5L#e9292.L#'!#Y2).*DE92) 2)5h#9.0#0'H*.DF 0'32)H2%1A# *Kb ucR2*%1A# *-F!#,)2. XSE!O9(*2.*,.9(950m!#)(@,)V6L1950'(X>@W@THCtA1GSQDQ,.%'56!#R!#)(G75 L#DQ)(X/'0#9(n .0QA192.L# 9.`9)( 'LOQ2)5087)2.|r".o!O iL'(|rn9)(eDQ5p!#&.9)(o!#YL#h#L#9.0'2)Kn69)(^(Ai,)2.|/12. *,)(o!#G2)50'!O 950'( LO- DF *)(o.o!#Y2)2)5*!fb8?e0E5L#*Kn79)(o,.9,.DQ.08*(!#*,)(*5 L#950{!#)(eDQ,.%'5p!#)(o!#GIK!O9.08`!O9(2.*&.*)( 0'( V8L'q9q292.L#e!#)(H!O i,.*.06*(*.DQ)(H(*508H,.0'50'2),)C( N DF9(H_QA19-292.L#e!#3S{A19-!O iL'( 7 !#HSqDE92) 2)5h#9.0#0'3!#h# S0U!# 'LOtA1XA#Al5@LU2*%1DFAU,.*5p!O601DF9V6L' Osb PH0'($932%1A# *QOn'9)(!O i,.*.06*)(HA#A#*5)O DE950'(+!OL 'LOM!O iL'(|ro.!#)($*.DQ)($!#)(@DQ5p!#&.9)( !#RL#h#L#9.0'2)q!#RjM92%'.X l. k ε !#Ru~L#0'!#.C6%1DEOnc 0'(V6L'+9.L#!#,. K950mA1$A#Ai5 LB2*%1DFA ,.*56!Op01DF9V6L't(508-!#,)2. *)(b P0'(RL#0A#*.DF9.q*.DFA'( n"9 'LO!O iL'(|rX)(-!O i,.*.069, _ /'I7, lb @0'tA#A#*5p DE950 !#tpAi +2)5L'2*%'tDF 0'2) )(F95*(-!fZghl5*!L# 9(*,)KnA#L#9(-50 sOA# µ9V8 L'@Sq2)5DFA#9sp|/12950N!#)(sOA#*)(*(950'(.0J(Zg l0'2%#9(*(06!#2).*A#A#*5)O DE950cn#*5L 5L#*(.

(217) _ µ /'I7, lb#k XS-(L# *Kn'S-!#,. 950m!#)(YDQ56!#&.9)(X!#HL#h#L#9.0'2)3)(Xhi5*!#,)Kb ucX2*%1A# * IHA#*,)(.08*G9)(^*,)(L# *(^!#G!O f,.*.08*)(o 0',9(950'(o!OL 'LOF!O iL'(|ri,.7.06L'. 9.DQ.08 2)5D3h# 0',))(Q_M2). 9E!OLDQ56!#&.9t!#EjU92*%'.+ (L#3!#.LO2(R!fZy,.A#*.L#7""SJL#7&.*J!#,s/'0#9{A1 P,.9,.t!O * Xhi5K(*(*+ t.Y[Zg 93\$T@?o>XW

(218) j KObOP)(YIK!O9.08*(@!#$r}50'2.950'(@,.*56!Op01DF9V8L')(@.Y!#)( (*.0'( h# *,)(@!fZy,)2)5L#9.DQ.08_-SqA1*5c L'(*.06@2))(Y*,)(L# *(XAl5L#G2%1V8L'3 0',9(950cb ?e0O/'0cnf!'0'(9-2%1A# *X QOni!#)(*,)(L# *(+!OLzDQ.DQ-pAl-V6LcZgL2*%1A# *+ IJ(*506$A#*,)(.08*,)(HAi5L# !#.LOF2(e!#`L#hi5DE2*%# 0'Kb6;#(ZgIK ^!#!#.LOF2(e!fZgL#hl)(^9(*59,))(e!#L#h# 0' L#0FP@9(* h#L#*.L# w (*(* ke*)(*(*950M.YL#0'+>X5L' w (*(Hke*)(*(950cb.

(219)