Retro-information in Wheeler-Feynman Universe Model: Applications Over an Hypothetical Concept in Quantum Mechanics

(1)

HAL Id: inria-00073155

https://hal.inria.fr/inria-00073155

Submitted on 24 May 2006

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub-

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non,

Retro-information in Wheeler-Feynman Universe Model:

Applications Over an Hypothetical Concept in Quantum Mechanics

Philippe Jacquet, Véronique Joly

To cite this version:

Philippe Jacquet, Véronique Joly. Retro-information in Wheeler-Feynman Universe Model: Appli- cations Over an Hypothetical Concept in Quantum Mechanics. [Research Report] RR-3530, INRIA.

1998. �inria-00073155�

(2)

a p p o r t

d e r e c h e r c h e

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Retro-information in Wheeler-Feynman universe model: Applications over an hypothetical concept in quantum mechanics

Philippe Jacquet et V´eronique Joly

No 3530

TH `EME 1

(3)

(4)

-.. /012(34& 56# . 22/7//0 . 3986%:2%;

//0(

<=>@?@>BAADCFEHGJILKMCLNCLNPO;QLRTSHU>BKVMCWEJSH?BX

Y Z"[\^]$_a`cbedgfh]gikj"lm]n4fhopfqnr[\^]gf

sutrvkwq]n4xey{z|]gtr}v,\

beikzz|vLt~nep]1tr]g}Z"]gtr}Z],k,W` `k6zi,,]gf

mg",, Y2y{f~nhy{"nhZ"]"v,"@{vp}ik{ynqo}v,}]zpnyji,nhj"\\^]g}Z|ik"y}fm0] ¡y{nhtrvppj}]¢nhZ"]

Z£o£zJvknhZ]nhy}i,¤}v,|}]z"nv,¥Dth]nhtrvk¦y"¥§v,tr\^iknhy{v,V¨1©]^iki,opfh]nhZ]6]ªJ]T}'n1vk¥zikti,"v«lpi,}vLj"z"{yvL

fhv,jtr}]¬v,¥tr]nrthv,@y{p¥§v,tr\$inryvLPyFvLtr"]tnhvPji,Lnry¥§oPnhZ"]1"]g®\^]Tikfv,¥}v,\^z"jpnry"^nrZin4}v,j"¯|]

"]try°L]gm¥§thvL\3f~j|}Zi,Z£o£z|v,nhZ"]nhy}i,V}v,|}]z"ng¨

±F²³H´rµ¶ ·,¹¸p¥§vLth\$iknhy{v,Vº}v,\^\j"y{}ginryvLVºVjiknhj\»\^]g}Zi,"y{}gfº½¼DsDb¾zikti,pv«l½ºV¿£Zi,""vL

i«1ºpy{Lnr]L]t¥Ài,}nhv,try{ÁginryvLV¨

ÂÃ½ÄhÅ¦ÆgÇ ÄÈÉ{Å¦Ê@ËÌ

ÍÎVÏ«ÐÑÒÀÓBÔ ÕÖTÔ@ÏT×'Ò ØÙÓDÚØÔBÏ$Û§ÜÝVÛßÞ0à"áÛ§âJã|ÝVäåæèçTÒB×éÀÐqêëÔhà|Ô@Ï«Ð4Ó@Ðqêq×'ì«íPÕÖTÔBÏ«×'Ò ØÙÓuÚØÔ@Ï$åÜãJÝVÞîäHÏÕrÔBØÙïÙïÙ×'ì

ð'ñ'ò'ñ'ñ ó Ò@Õì«êqÐ

Unit´e de recherche INRIA Rocquencourt

(5)

3! #$ + -.. /2( (% %// . 6# . 228^%

/86% 8^%:286%

¼u1\$ik{\^[i,Lnj"]g{j"]Dz|]gj1]Tf½z"try}yzJ]gf2p]u"vLvp}i,ynhdD]\^dg}i,"yLj]uLj|iknhyj"],º

v,jf4ynhtrvppj"yf~vLf{]}vL}]gzpn4Z£o£z|v,nhZ"dnhyj"]p]:thdnhtrvk¦yp¥§vLth\$iknhy{v,V¨ev,j|f4ik|ik{o£fhv,|f ]ªH]np]gf

}v,j"z{i,,]gf¬zi,triLpv«l"ikjpl¡p]6¥Àiv,z|vLj"°,vLytjiknhy]gt1{iz"j"yfrfhi,}]^p]gfv,j"°L]gikj"l¡\6voL]fp]

}gik}j"fj"yVfh]tiky{]n¯i,fhdgf fhj"te}]}v,}]zpnZ£o£z|v,nhZ"dnhyLj],¨

¶

T

´

¸

p¥§vLth\$inryvLVº£nhdgdT}vL\6\:j""y}iknhy{v,Vº"\^dT}iky{j"]1jiknry{j"]Lº"zikti,"v«l£]¼usDbº{v,yp]

¿pZik"v,Vº£¥ÀiL}'nhvLthyfrinhy{v,]nhy{]tf¨

(6)

:$*%/D2

©îZ]]{]t ik|"]go\^i,mp]g°,]{v,zJ]g$i\^v£"]Jvk¥Vj""y{°,]gtrfh]e¯iLf~]T$v,mzikthnhy}{]ey{Lnr]ti,}nhy{v,Ù¦¨Y Zy{f

\^vpp]gpZi,f,y{°,]gtry{fh]nhv¬nhZ"]ef~nri,"i,tr\6vpp]gpZ"y}Zyfy6jfh]y{6\6vfqn¤£j}]Tiktz"Z£opf~y}fg¨2}v,\^z"{]nh]

iL}}]zpnik}]Fvk¥1©¾\6vpp]g{fm"]]T"f$nrZ"]WiLfhfhj"\^zpnryvLnrZin¥§jpnhjth]¡]g°,]gLnfm}v,j" y j"]|}]¡ziLfqn

]g°,]gLnf¨ Y Zy{f$yfPi \^]tr]¡}vLfh]gj"]|}];vk¥"v,{v£}gik{ynqoy"!¬ji,nhj"\$#F]g}Zi,"y}f%!&#(''¨ 4v,p

{vp}i,ynqo^\6]TikfDnhZ|in j"p]gtfhv,\^]¬}v,"ynryvLfunqvz|ikthnhy}{]gf0ynrZi}v,\^\^v,PZy{f~nhvLtho$}vLnhy{j]enhv

y{nh]gtriL}'n1ynrZ"]^¥§jpnhjth]Lº2]g°,]Z"]gWnrZ"]oiktr]^y{fhv,inr]gWynqv;"y{f~nhy{}'n6f~ziL}]^{v£}ginryvLf¨$Y Z"]Tf~]

}v,}]zpnf¯thvLj",Znnrv¬]g°£y{p]g}]0¯£o1¼uy|fqnr]y{Vºksvppv,f*)£o1ik|bvLfh]:y6i¥Ài,\6vLjfzikzJ]t+,-@ºLiktr]0f~nhy{

viL"i«opfZ"vknyfhfhj"]gfg¨ evL¢{vp}ik{ynqoF]ªH]g}'nZi«°L]¯J]] ik|ik{oÁg]gF¯£o.]{/¤i,¡]lpz|]gthy{\^]nh]T

¯£o10¬f~zJ]g}n2_Lº¦¨

b]T}]gLnro¿£Z"v,t&{_g¦º .]""]n~n34-¦º65]gtrfhZ"]gp¥§]789:<;=>i,?5trv°,]gt@BAC½Zi«°,]p]g°,]{v,zJ]gPnhZ"]

}v,}]zpnv,¥eLj|iknhj"\ }vL\^z"jpnh]gtZ"y}Z nriD),]gf1iLp°iknri,,]6¥§trv,\ Lj|iknhj"\ \^]g}Zi,"y{}gf1\^]nrZ"vppvk

{v,Lo,¨mx4]tr]$0]$zthvLz|vf~]6nhvFL]ni;{ynhnh{]$¥§j"thnhZ"]gty{ y\$ikLy|inhy{v, ik| p]gfr}try¯J]Pfhv,\^]^z|v,nh]nry{i,{f

y{ ©îZ"]]g]gt~E"]go£"\$ik\6vpp]guy{vLtr"]tnhvFi,{vF8- EGC-H--¡vL fh\$ik{nhy{\^]Pfh}gik{],¨Pxe]gth]

]m}v,y{ nhZ"]mnh]gth\ vk¥etr]nrthv,@y{p¥§vLth\$inryvL¢nrv¢\^]gi, nhZ"];ik¯y{ynqoWnhv¢nhtikf~¥§]t:y"¥§v,tr\^iknhy{v,fv,7i,

i,th¯ynrtri,tho¢fhziL}]^nhy{\^]P°,]T}'nrv,tT¨I04\6vL"¢fhj}Z °,]T}'nrv,tfºnhZ"vf~]$Z"y}Z zJv,y{Lnnhv ikt¢nrZ"]PziLfqn6iktr]

}]Tiktro^nrZ"]1\^vLf~ne}Zik{]g",y{"$ik|my{¯|]1\$iky{"{omi,pth]Tfhfh]gmynrZ"]1z"tr]gfh]n"vknr],¨

¸ $fhZ"v,thn¤th]nhtrvk¦yp¥§vLth\$iknhy{v,v,j":¯|] zJvLfrf~y{¯"{] nhvnhZ"]e}vLf~n¤vk¥Ji,\^]py{"1fhv,\^] vk¥nrZ"]z"trvppj}'n

¥§vLth\ f~nrinr]gf4z"th]Tf~]gneyFnrZ"]:f~nri,"i,tr\^vpp]@¨©W]:y{"vkn¬"y{fr}jfrfeZv®tr]{]°iknenrZ"]gfh]i,\6]g£

\^]gLnf}v,j{F¯J]6yW\6vpp]gthf~j¯fqnrynrjpnh]Tfvk¥0f~nri,"iktF\^vpp]y{J!¬ji,nhj"\K#F]T}Zik"y}fg¨©W]6y{

i,{fhv:i,¯fhv,{jpnh]go^v,\^yneik{|nrZ"]\^]nri,z"Z£opf~y}i,|z"trv,¯]g\^f0zJvLfrf~y{¯"{o$tri,y{fh]gm¯o$tr]nrthv,@y{p¥§vLth\$inryvLV¨L0n

{]giLfqn¥§v,tnrZ"]1}v,\6¥§vLt~n vk¥VnrZ"]th]Ti,p]gt0]MNJiLfhfhj"\^]¬nhZikn y¥2]°,]gt~nrZ"]{]gfrf0th]nhtrvk¦yp¥§vLth\$iknhy{v,

i,f:]°L]nhj|ik{o zJvLfrf~y{¯"{],ºnhZ]yn^0vLj" }vL}]gth v,"{o °,]tro f~Zv,thn:tik"L]Pnhtik|fq¥§]gtrf?%ÀiknhZv,j"LZ

}gi,fr}iLpy]ªJ]T}'nf}vLj"W¯J]mzJvLfrfhy¯"{]C'¨Iv,t]l"ik\^z"{]$0]m}v,j"y\$i,,y{"]$tri,",]Tfvk¥v,tp]gtf~vL\^]

\^y}trvLfh]g}v,"fg¨¿pj}Z$tri,",]Tf¤v,j"$}]gt~niky{"o6"v,n0f~j O$}]enrv\$i),]4z"triL}'nry{}gik"z"tr]g"y{}nhy{v,$y{mfqnrvp}P)L

]l"}Zik"L]¬\$i,t)L]n

#FvLth]mynh]gth]Tfqnry¡v,j"t:z|vLyn6y{fnhv¢fhZ"v¾nhZ|in:]g°,]g th]Tfqnrthy}'nr]g v,f~Z"vLt~n:°,]tro¢tik,],ºtr]nrthv,

y{p¥§vLth\$inryvL v,j" Zi«°L]¡nrZ"] z|v,nh]nry{i,¬nrv¯thy{"ynh]gth]Tfqnry ¯"tr]giD)LnrZ"trv,j"LZfPy{®y{p¥§vLth\$inryvL

nrZ"]vLtho1i,:}v,\^z"jpnr]t¤fr}y{]}],¨¿pj}Z:¯J]] "n¤v,j"¯J] y:nhZ"] py{th]T}'nu}vLnhy{j|inhy{v,vk¥nrZ"] ik{th]Ti,po

y{\^z|vLt~nikn¯|]g"] nrf]l£zJ]g}nh]Tm¥§trv,\ Lj|iknhj"\}vL\6zjpnh]gtrf&{_gpºNA@¨

¸ ny{¯J]:fhZ"v;y¡nhZ"]zth]Tf~]gLn¬zikzJ]tnrZiny¥utr]nrthv,@y{p¥§vLth\$inryvLm]tr]zJvLfrf~y{¯"{],º"nrZ"];nry\^]

z|ikti,pv«l\^y{,ZnDvp}}j"tu¯J]nq]]gPf~vLj"tr}]eik$"]gf~nhy{inryvLV¨Y Z]4iki,opfhy{fuvk¥Hnhy{\^]ezikti,"v«l]ªH]g}n0y{

i,i,z"z"trv,z"try{iknh]¬\6vpp]gVf~ZvefDnrZin nrZ"]jf~]v,¥2zi,triLpv«l"ik|}v,j"zy{"60vLj"{fhyL"yJ}iknro^y{\6zthv°L]

nrZ"]¬}Z|ik""]g}i,zi,}ynqo:¥§trv,\ nhZ"]4}gi,fh]eynhZ"vLjpn}v,j"z"{y{"1%B¿pZik"v,P}iLf~]''¨Q"vLtD]l"i,\6z]e]4}v,fhy

"]tim¯"y{i,thoF}Zi,""]ynhZ7R7yz"jpnrf}v,""]T}'nr]gFnrv1R7vLjpnhzjpnrfg¨1©W]$iLfhfhj"\^]:if~o£\^\^]nhtry}:}gi,fh]

Z]tr]¥§v,te]Ti,}Zv,jpnrz"jpn4z"trv,¯|ik¯"y{ynqom°L]g}nhv,tyf3SUT=V8W@XYT[Z0Z"]Fy{"z"j"n¬f~]n~nry"my{fe$i,JS*W\XT]VTNZ

Z]y"zjpnef~]n~nhy{"^yf_,ºpynhZTY^`_£¨¤Y Z"]1}i,frfhy{}gikV¿£Zi,""v,}i,zi,}ynqo$v,¥fhj}Z}Zi,""]g½y{f/R]a2b

ynhZ

a

b1c

W9deT\fUgDhji TkdS*W\XYTNZjfUgDhjiSW\XIT[Zl %q_C'

(7)

¸

z"tr]gfh]}]4vk¥Vz|ikti,pv«l"ikJ}vLj"z"{y":0]¬y{½f~Zv nhZikn0nrZ"]}gikziL}ynqo$}ikm¯|]1pvLz"z|]TPj"zmnhv R]a

ynhZ

a c

W V*fUgDh

i T

W\XIT

l %BD'

y{,j"tr]^_1py{fhz"i«opf/a2bFika°,]tfhjfQTV¨

0 0.2 0.4 0.6 0.8 1

0.5 0.6 0.7 p 0.8 0.9 1

yLj"th]^_ub]nrthv,¦}Zi,""]gH}gikziL}ynqo,ºp}i,frfhy{}gikn%À"iLf~Z]g 'ºpv,zz|]T7%Àz"iky{ '

j"t~nrZ"]tr\^v,tr],º£tr]nhtrvk¦y{p¥§v,tr\$inhy{v,}v,j{ik{v y{nh]gth]Tfqnry"6y{\6zthv°L]\^]n y;}vL\6zjpnhy{"º"i,{vk

y{"|º¥§vLt4]l"i,\6z]1nrZ"]¥ÀiL}'nrv,tryÁTinhy{v,;v,¥¤i,£oy{nh]L]t¬vk¥nR7py{,yn4y¢v,"]\:j"nhy{z"y}iknhy{v,¢}vLf~n¬ik|

SRLZ0th]nhtrvk¦\^]\^v,tro$°,vLj"\^]L¨Q.]gv ]1f~ZvZ"v f~j}Z¥Ài,}nhvLthy{Ágiknhy{v,}v,j"¯|]1zthvL,tik\^\^]g½¨

!#"%$'&)(*+,"%(.-#/'&10%$"3214,(576'8:9

;=<,0>6?9

@

A%()0#"%$CB)D$#$)EF5#52=<,0HGFIKJ8:IL!8

@

!,M#-,/#D%N)(?9

;1-O5PG3Q1J,M#6C8R0TS'(U<>!#MT0#"T+'(9

V

21-O5PG3QWJ,M,6C8R0S'()<X"%(0T+#"T<F5PGFIYJ8

(,D%N)(.E,"32=<,0Z5W[W6X/'N#N=+)\(T*]E#"2^\([)8

V

(8)

Y Z"] tf~nfh]g}nhy{v,¢y{nhtrvppj}]Tf4v,p¦vp}gik{ynqoFik| .]{¤y]gjik{ynhy{]gfg¨Y Z"]$f~]T}v,|¢fh]g}'nryvL¢p]Tfq

}thy{¯J]gf Z"vi,Z£o£zJvknhZ]nhy}i,Vi,fho£\6\^]nhtry{}}vLpynhy{v,f}v,j"P{]giLPnrv6tr]nrthv,@y{p¥§vLth\$inryvLm}tr]giknhy{v,Vº

i,7tr]nrthv,¦}Z|ik""]g}gikziL}ynhy{]gf6iktr]ji,nhy]g½¨Y Z"]nhZ"y{trfh]g}'nryvL yf$p]°Lvknr]g nrv¢nrZ"]Fiki,opfhy{f

v,¥z|ikti,pv«l"ikH]ªJ]T}'nC\^y}trvk¦¯"tri,}Z"y{"^j""y{°,]gtrfh]Zo£zJvknrZ"]gfhy{fg¨/0a¥§v,j"thnhZ¡fh]g}nhy{v,Fpyfh}jfrf~]Tf nhZ"]

zJ]tfhz|]T}'nhy{°,]v,¥2tr]nhtrvkë}vL\^z"jpnhy{"|¨

$ $/J#* (#^(V2e(

0e¥ßnh]gt2i z"Z£opf~y}i,]°L]n mynyf½zJvLfrf~y{¯"{]¤nhve}th]Tinr]2nqv nqy{1zikthnhy}{]gfgºgfri«oezi,t~nry{}]_ui,zikthnhy}{]Dpº

ynhZ$]l"i,}'nro6v,zz|vf~ynh]efhz"y{f¨n0î]{ )£"v$]lpz|]gthy{\^]nD}vLf~yf~nrfuy{nhv\^]Ti,fhj"thy{"nhZ]enqvf~z"y{f

fh]z|iktinh]gov,;nqvPf~zy¢"]°£y{}]gf2%Àv,t¬z|vL{i,thy{Á]gtrfP'_ik|¡pºJ]gi,}Z;v,¥nrZ"]\ vLthy{]nh]T;v,Ftr]gfhz|]T}'nry°L]

iklp]gf4i,¬ynhZ;tr]gfhz|]T}'nhy{°,]1i,",{]gfik|

i

¨¬;]gi,}Z;fhz"yFp]g°£y{}]¬nrZ"]1\^]giLf~j"tr]th]Ti,"f

dkW^vLt X3W%Bf~]g] Lj"tr]D'¨Y Z"yf:\6]Ti,fhj"tr]\^]n:fhopfqnr]\ y{fk)£"v nrv¢z"trvppj}]}v,trtr]inhy{v,|f

Zy{}Z;f~]g]\ nrv$}tr]ginr]&MNJ¥Ài,f~nh]t nrZik{yLZLnepyf~nrikn]ªH]g}ng¨DY Zy{f zi,triLpv«l$Zi,f ¯J]]g;z"jpney{

]g°£y{p]g}]4¯o^¼uy{f~nh]gyVº£svppv,f)yJikmbvLfh]e%À¼usDb@'º"ik^inr]t0i,ik{o£Á]T^¯oH.]{]-¦¨©W]p]vknh]

nrZ"]ziky{t0v,¥V\^]gi,fhj"tr]gfu¥§thvL\ nrZ"]¬nq0v6f~z"y{"]°£y{}]gf0¯£o:nrZ"]¬nhj"z"{] SS CZPV

i

S

i

ZZ¨¤©îZ"]gPnhZ]fhz"y{

!

! " " ""

#%$

&%'

f~z"y{;p]°£y}]$_

!

!(

zi,t~nry{}]^_nhtiwq]T}'nhvLtho

)

#%$

&%'

fhz"yFp]g°£y{}]1

*" "

" +

z|ikthnhy}{]1nrtrikwq]g}'nrv,tro

i

y{,j"tr]% 0e;¼usDbaz|iky{t fhopfqnr]\

"]°£y{}]gfiktr]¬i,y{,"]T½º[;G;¤nhZ"]1i,",{]gf, i,-

i

iktr]nhZ"]1frik\^],º]¬vL¯|]gth°L]enhZ|innhZ"]v,"{o^z|vfhfhy{¯"]

\^]Ti,fhj"th]¬nhjz"]Tfeiktr]S dkW V8X3WZuv,t3SX3WDVdkWZDpy{f~nhtry{¯"jpnh]TynrZzthvL¯ik¯"y{{ynqoW/.10p¨

©îZ"]g$nhZ]4f~zy$p]g°y}]TfDi,th] \^y{frik{y{,"]T 2 X3

i c 4c65

º,\^]Ti,fhj"th]nrj"z"{]gfu]TjiknhvHSdkW VPdkW-Z

i,(S*X3WDVX3WZDiktry{fh],¨¤Y Z"]gv,troP]gf~nri,¯"{y{fhZ"]gf0nrZiney{F}i,fh]vk¥zikthnhy}{]gf v,¥fhz"yJW/.10,

7

sut

S Z c

dkW98:

i

S i Z c

X3W

c

sDt

S Z c

X3W;8:

i

S i Z c

dkW

c

i=<

g?>

i S i Z

sut S Z c dkW98:

i

S

i Z c dkW

c sDt S Z c X3W;8:

i

S

i Z c X3W

c i > i S i Z

%À '

Y Z"]ik¯Jv°,]ezthvL¯ik¯"y{{ynqo^pyfqnrthy{¯"jpnryvLPy{f )£"v$nhvth]g°,]gi,|pyf~nriknDy{nh]gtriL}'nhy{v,$¯J]nq]]gmp]g°y}]

_1i,^"j"thy{"^\^]giLf~j"tr]\^]gLnTºpi,fp]gz"y{}nh]T¯£o1.]gVy{ _>L,1-¦¨

(9)

²£¶

²

²£¶

²

Fn 8F 88 E 83 -(:B=69G 8-[;

¶V¶ 0¬fhfhj"\^]vLFnhZ]6}v,nhtiktroPnrZin¬nhZ"]6°,]T}'nhvLt4v,¥Dik{2zJvLfrf~y{¯"{]:i,f~]tf SjZv,¥Dzi,t~nry{}]P_

y{ p]°£y}];_,ºV¥§v,tik{uzJvLfrf~y{¯"{] "ºyf1"v,n1ikªJ]T}'nr]g¯£o¡\^]gi,fhj"tr]\^]n1v, p]g°y}]P"¨$©W]$y{Dz"thv°L]

nrZin4nhZ"yfZ£o£z|v,nhZ"]Tf~yfyfetrv,"$ik|mnrZ£jf4i$pyf~nrikney{nh]ti,}nhy{v,FfhZ"v,j"vp}}jte¯|]nq0]g]Fp]g°y}]$_

i,;p¨

¿£y{}]¡f~z"y{f$v,¥z|ikthnhy}{]_¡i,îf~j"\$f^nrv7"º\^]gi,fhj"tryz|ikthnhy}{]F fhz"y{ v,v,"]¡i,",{];y{f

]Tj"y°i,]gLn0nhv6\^]gi,fhj"tryzikthnhy}{]_¬v,$nrZ"]fhi,\6]ik"L]¬¯"jpn ynrZvLz"zJvLfhynr]¬ik|f~]tTº ;G0¥§vLti, %

sDt

SjZ=d%

i

S jZ c5

c

WL¨uY Z"]tr]¥§vLth]0]1}gikFp]nr]tr\^y"]nrZ"]fh]g}vLv,tp]twqv,y{n4pyfqnrthy{¯"jpnryvL

v,¥nrZ"]ikfh]t °,]T}'nhvLtvk¥zikthnhy}{]^_0wqj|fqne¯£omtr]¥§]gthy{":nhv$yp]nrynqo %B '^

sut -S 8Z c 8: -S

i Z c"!

c sut S 8Z c# 8:

i

S

i Z c X !

Y Z"]&.]{y{"]gji,ynhy{]gf0ikz"z"{y{]gfuvL^nhZ"tr]]4]°,]gnrf%$ º'& i,)(¨ ( p]"v,nh]TfunrZ"]4}vL\^z"]g\^]nri,tho

]g°,]gLnv,¥*(

sut $ 8&

+ sut

$ 8(

d7sut & 8 (

,]njf}v,|f~yp]t¬nhZth]g]:ik,{]gf º i

ik| -kº½]:iLfhfhj"\^]nrZin]°L]n.$)yf S Z c dkW

ºJnhZ"]

]g°,]gLn/& S

i Z c dkW

ik|0( S --Z c dkW

¨n0ezz"o£y{"H.]{Vy]gjik{ynhy{]gf ]fhZ"vLj"{Zi«°L])

sut

S Z c

dkW;8:

i

S i Z c

X3W

1+

sut

S Z c

dkW;8:

i

S-Z

c

X3W

d

d¬sut

sut S

i Z c

dkW;8:

i

S --Z

c

dkW

Zy{}Znhtikfhinh]Tf ynrv

<

g?>

i S X i

0 Z + < g > i S X - 0 Z d >

i S i X -

0 Z

Y Z]¡ik¯Jv°,]y"]Tjik{ynqopv£]gf$vknPZ"vL{¥§v,tPi, y |"ynqovk¥1ik"L];°ik{j"]Tfº¥§v,t$]l"ik\^z"{] c 5 º

i c32

i

ik- c i 2

-

¨Y Z"]tr]¥§vLth]iP"y{f~nri,Ln¬ynh]gtriL}'nryvLvp}g}j"tfe¯J]nq]]g¡p]°£y}]P_i,Fp]°£y}]:

\^]Ti,fhj"th]g\^]nrfg¨2©îZ]m¯JvknrZm\^]giLf~jth]g\6]gnrff~y{\j"nri,"]vLjfho^vp}}j"tgºLnhZ]tr]¬yf0nhZ"]gth]¥§v,tr]¬i"y{f~nri,Ln

]ªJ]T}'neZ"y}Zv£}g}j"tf¥Ài,f~nh]gt nhZi,;y{,Zng¨

²£¶ ² 546 87PE-Pk:9@7\-0n; 8 [-+:G:<< G(-=

¶V¶ fhy{}]^nrZ"]$z"trv,¯i,¯"y{ynqo¡vk¥iknh]gthiknhy{°,]$ik|f~]tfv, ]giL}Zp]g°£y{}]$th]g\^i,y|fW .10Ziknh]g°,]t

nrZ"]ik,{]f~]n~nhy{"$vLnrZ"]v,nhZ"]gtep]°£y}],¨Yv$\$iD),]y"¥§v,tr\^iknhy{v,nhtik|fq¥§]gtrf zJvLfrf~y{¯"{]0]1\:jfqn¬th]go

vLi,Z£o£zJvknhZ]nhy}i,½nqyfqnT¨

> ?

/A@ %'& (2( 6# . 2((3* "1¤2

BDCE FHG/IKJMLNPOQSRTOVU*W.NGTLXW/Y[ZTW.L]\^I_O`aIbGdcDeQ*fVG/I_`gLX`

¸ m_>,£ ©îZ"]g]{]tik2]o£"\$ikynhtrvppj}]gi,v,tryLy|ik,y{nh]gthz"tr]ninryvL1vk¥N!&# ¯iLf~]T1v,nhtikfri,}

nryvLzthy{}y{z"{],¨uY Z"]nrtri,fri,}'nryvLmz"try{}y{z"{]zj"thzJvLfh]iLf0nhvPfhv,{°,]triLpy{iknhy{v,z"thvL¯"{]\$f¨©îZ"]g]{]t

(10)

S

yLj"th]1'Q#¡y{}thv,@¯"tik|}Z"yj""y{°,]gtrfh]gfgº£nhZ]p]giLmziknhZnhy{\^]1y{fi,fhZ"]g

i,7"]o£"\$i,}v,fhy{"]tr]g¢nhZikny{ ik£o7!&# ]lpzJ]try\^]nnhZ]tr]6yfi;fhv,j"t}]6]°L]n i,WizJvk

nr]nhyikfh]nv,¥¤nri,thL]n4]g°,]nf¨@0 nri,thL]n4]g°,]ny{f¬p]nr]tr\6y{"]TF¯£oynrf}v£vLtrpy{iknh]gf y{¨&"v,t

]l"ik\^z"{]Pv,"]}ik}v,|f~yp]t:i¢fhv,j"t}]$v,¥ey{,Znz"ZvknhvLf:v,tv,nhZ"]gt:zi,t~nry{}]Tfi,f]°L]n-º¤i,7i,f

niktr,]nfh]nºi$f~y{\^z"{]fh}th]g];z"jpn4vL;zikthnhy}{]nhtiwq]g}nhvLthoL¨@%§ynhZ¡i6nqv$f~{ynf~opf~nh]\ y;¯J]nq]]g

nrZ"]tr]v,j{;¯J]y{nh]th¥§]tr]|}] Lj"tr]gfevLFnhZ]:fr}tr]]N''¨0 nri,thL]n4]g°,]nz|vf~ynhy{v,

0vLj";¯|]:nhZ"]

}v£v,tpy{inr]gfvk¥zi,t~nry{}]y{\6z|i,}'nevLmnrZ"]fr}tr]]¨

¸ nrZ"]Pnrtri,fri,}'nryvL ynh]gthzth]nrinryvL nhZ"]z"trv,¯i,¯"y{ynqo¢vk¥nrZ"]Pniktr,]n]°L]n

yfLy°L] ¯£onhZ"]

°i,j"]vk¥2nhZ"]¥§vLth ikt$ i«°,]e¥§j}'nryvLZ"yn~nry$z|vf~ynhy{v,

º"i,\^]{o@S

Zº"\:j"nhy{z"y{]g¯£o^nhZ]°i,j"]

v,¥nhZ"]:¯i,}P)£ ikt i«°,]¥§j}'nryvLF¥§thvL\

Z"yn~nhy{"y"ynhyikzJvLfhynryvL º||ik\^]{o -S

Z S

Z i ¨ ¸n

iL}'nf1i,fy¥0nrZ"]$¯i,}P)£ ikt¡ i«°,]:¥§j"}nhy{v, ]g}Z"v£]T¢vLWnrZ"]^¥§jpnrj"th]$zJvLfhynhy{v,Pik|W}v,\^]gf¯iL}P)Fnhv

z|i,f~n zJvLfhynhy{v, }giktrtho£y{"nrZ"]tr]¥§vLth]nrZ"]}vL°Lv,{jpnhy{v,°ik{j"] S

Z i ¨

Y Z"]¯"tik}Zy"¬j""y{°,]gtrfh]uZ£o£z|v,nhZ"]Tf~yfy{fi4°L]tro¬trv,j,Zfhy\^z"{y|}iknhy{v,v,¥"nhZ"]0¥§v,tr ikt£@¯|i,}P)£i,tr

nrtri,fri,}'nryvL¢Z£o£z|v,nhZ"]Tf~yfZ"y}Z i,frf~j"\^]TfnhZ"]Pfrik\^])£yv,¥]g}Z"v¥§trv,\ nrZ"]^¥§jpnhjth]¨1v,t1]giL}Z

zJvLfhynhy{v,

nrZ"]tr];y{f^iWz"thvL¯ik¯y{ynqoeT]S

Z1¥§vLt6nhZ"];zi,t~nry{}]nhvZ"ynPynPik| iWz"thvL¯ik¯y{ynqo S Znhv

zJ]tfhy{f~nv,ynT¨u©îynrZ;z"thvL¯ik¯y{ynqo W+X S Zº|nhZ"]1zi,t~nry{}]trv,{{f¯iL}P)$nhv$y{"ynhyik½]g°,]n4¿H¨

©îZ"]g:trv,{{y"¯iL}P)nhvynfy"ynhyik£zJvLfhynryvLnrZ"]f~opf~nh]g\Zi,f"v\^]\^v,tro1vk¥|nhZ"]i,}nhji,pf~]TLj]}]

v,¥½]°,]gnrfu¯J]nq]]gm¿$ik|^z|vf~ynhy{v,

ºZy{}ZPiL}'nhj|ik{o^fqnik^vL^nhZ"]4¥§jpnhjth]¬vk¥¿H¨ ¸n0yfDi,fDy¥fhziL}]

nry\^]j""y{°,]gtrfh]4¯"tik|}Z"]gf0v,;¿$v,i:"]gi,$nhy{\6]ziknhZikmth]nhti,}'nfDvL¿(- 2GH¨ ¸¥2nhZ"]

z|ikthnhy}{]1thvL{¯i,}P)pffh]°L]tikHnhy{\^]gfgº"nrZ"]FnrZ"]tr]1y{¯|]:f~]g°,]tikV"]gi,nry\^]z|inhZ|fºJikFfhzi,}]@nhy{\^]

j"y°L]tf~]:y{¤z"trvp}]]T¢vL¡nrZ"] tfqnz|inhZWnhy{\^]^Z"]tr]nrZ"]^zikthnhy}{]^pv£]gf"v,ntrv,{¯i,}P)H¨:Y Zy{f

{y{°,]nhy{\^]1zinrZy{{½¯|]}gik{]TmnrZ"]1zJ]tf~yfqnr]n nhy{\^]1zinrZV¨D¿£]] Lj"tr]:¥§vLteik;y{{jfqnrtriknhy{v,

Y Z"]Dz|]gtrfhy{f~nh]g}]¤zthvL¯ik¯"y{{ynqoev,¥£i Ly°L]1fh]nev,¥£zJvLfhynhy{v,Zi,fV]lpz"tr]gfrf~y{v, S6Z c

T]S

!

Z S! Z

! ¨

(11)

Y Z"]$zthvL¯ik¯"y{{ynqoFnrZin1nrZ"]$zJ]tf~yfqnr]nnhy{\^]PzinrZ}v,nri,y|fnhZ"]$]g°,]n

nhZ"]^zi,t~nry{}]$ZynfnhZ"]

niktr,]n iknez|vf~ynhy{v,

1Zi,fnrZ"]ji,"triknhy}4]l£zth]TfhfhyvL

T=S

Z S Z

NS Z %,j'

0}g}v,tpy{"$nrv¯iLf~y}ji,nhj"\ \^]g}Zi,"y}jiknrynqoHT=S Z jS

ZfhZ"v,j{¢¯|]:z"thvLz|vLt~nryvLiknhvnhZ"]

frjiktr]1vk¥u i«°,]¥§j"}'nryvL¢ik\^z"{ynhjp] @S Z i

vLt4ynrf¬]gj"y{°ik{]ng¨Y Z"]LvL¯ik2z|]gtrfhy{f~nh]g}]z"thvL¯i

¯y{ynqomy{f NS ZDi,mnhZ"]1LvL¯ik½trv,{¯|i,}P)^z"trv,¯i,¯"y{ynqoeW\X NS Z¨n.oP°£ythnhj"]1v,¥nrZ"]}vLf~]gth°iknhy{v,mv,¥

nrZ"]v v,¥0nrZ"]$fhji,th]T¡ i«°,]:¥§j"}nhy{v,nhZ"]$j}vLpynhy{v,i,¤thvL{¯i,}P);z"trv,¯|ik¯"y{ynqo ¢fhZ"v,j{W"vkn

"]zJ]:v,nhZ"]nri,thL]npy{fhzJvLfhynryvLy{nrZ"]D¥§j"nhj"tr],¨©]}gik{LnrZ"yfthj"{]0nhZ"]9M =83P V88 ¨

² 7p¤ Y Z]tr]yfui,tr]giknnh]\^zpninryvL:nrvy{p]gnhy¥§oy{:nrZ"]eji,"triknhy}0]lpz"th]Tfhfhy{v,f/%, '[T=S Zik|

S Z¬nrvF¯|]$tr]gfhz|]T}'nry°L]{o¡z"trv,zJv,thnhy{v,i,nrv @S Zik|¢ynrf}v,wqjLinr] S Zv,tik£o¡]Tj"y°i,]gLnTºVy¥

vL"]nr]\^zJv,tiktry{o¥§v,tr,]nfnrZ"]:zthvL¯"]g\$f¬i,¯|vLjpn}v,\^z"{]lF£j"\¯J]tfg¨4p]gt4nrZ"y{fzJ]tf~zJ]g}nhy{°,]:nhZ"]

fhj"zJ]trz|vf~ynhy{v,mvk¥½nqvtrv,{¯iL}P)6fhopfqnr]\$f}v,j{$¯J]iki,vL,j"vLjfnhv:nhZ]¬fhj"z|]gthzJvLfhynhy{v,Pv,¥Vnq0v:i«°L]

¥§j}'nryvLfy{!&# ¨|Y Z"]gfh]ynh]gth]Tfqnry^}v,fhyp]tinryvLf0i,th]"v,nezikthnvk¥2nhZ"]1z"tr]gfh]nzi,z|]gtg¨

¸ nhZ]]l"ik\^z"{]v,¥4nrZ"]¡f~vLj"t}]F¿7v,¥¬{yLZLn^nrZ"]¡pyf~z"i,}]\^]n^vk¥nhZ"]Ffr}tr]]g v,j"}Z|ik"L]

nrZ"]ynh]gt~¥§]gth]g}] ,jth]ik nhZ"]gth]¥§v,tr]¡nhZ]¢¥§j"|}'nhy{v, S

Z¯jpnynhZv,jpn¡}Zi,",y{" nrZ"]WLvL¯ik

zJ]tfhy{f~nh]g}]z"trv,¯i,¯"y{ynqo

T=S

!

Z S! Z ! ¨

©îynhZF¼us0b fhopfqnr]\$fp]Tfh}thy{¯|]TyFfh]g}'nryvL;:]1f~Z"vLj"mvL¯pnri,y

S

S S ZPV

i

S

i

Z*Z

c SdkWDVdkWZ

c S S S ZV i

S

i

Z*Z

c

S*X3W V8X3WZ

c 0 > i i X

0

%BD'

S S -S8ZPV

i

S

i

Z*Z c SdkWDVX3WZ

c S SS 8ZV i

S

i

Z*Z c S*X3W VPdkWZ

c 0 < g >i i X

0

%À '

Z]tr] $v,j{¯|]nrZ"]1j"}v,"ynryvL"ikz|]gtrfhy{f~nh]g}]v,¥nhZ]1¼usDbfho£f~nh]g\;¨

BDC "I f OVQ'W=Q%OJU f LQ^W fgOU W.` I_OLfVG U*`'c/JMJ;I fgO LN"eI O`gLX` f I_W.NPI

04$ynr]tr]gf~nhy{"1}i,fh]yf¤Z"]^nrZ"]ezJ]tf~yf~nh]|}]yfui,fho£\6\^]nhtry{},¨L"vLtu]l"i,\6z]]e}vLj"{6y{\$ik,y{"]ei,

Z£o£zJvknhZ]nhy}i,½¼usDbafho£f~nh]g\ Z"]gth]¬nhZ"]1zJ]tfhy{f~nh]g}]1pyfqnrthy{¯"jpnryvLvLf~nriknh]f~j¯f~]n

S Z

c

dkW

v,j{i,}nhji,{o °iktro y¥§j"}nhy{v, vk¥f~]n~nry"f^v,zikthnhy}{]FW"]°£y{}],¨ "vLt$]l"ik\^z"{]v,"]F}vLj"

y{\$ikLy"]:ik¡¼us0b fhopfqnr]\ }tr]ginr]gFy{¢i,"y{fhvknrthvLz"y}}vLpynhy{v,f¬f~j}Z¡nhZikn¼ S S Z*Z4c 5

¥§v,tf~vL\^]

¨

©]iLfhfhj"\^]$nhZ|in6nhZ"]gth]P]lpy{f~n6ikn]Ti,f~nnqv¢fh]n~nry¡z|vf~ynhy{v,|fºufh]nhnhy{"¢¢i, fh]n~nry _,ºvL

"]°£y{}]:fhj}ZnhZ"]¥§vL{vy{"^Z"v,"fg¨

Y Z"]1zJ]tf~yfqnr]}]vk¥¤fqninh]1fhj"¯fh]n -S8Z c dkW

yFfh]n~nryP"ºpyf SdkW-Z

nhZ"]1zJ]tfhy{f~nh]g}]vk¥¤f~nrinr]1f~j"¯|f~]n S Z c dkW

y{Ff~]n~nhy{";_,ºpyf SEdkWZ

SdkW-Z 4

c SEdkWZ¨

(12)

,]n

S*X3W-Zik|

S*X3W-Z tr]gfhz|]T}'nry°L]{o;"]"v,nh]gf4nhZ]:zJ]tf~yf~nh]|}]v,¥0f~nrinr]:fhj"¯fh]n

S Z c

X3W

Z];f~]n~nhy{"Pi,th]tr]gfhz|]T}'nhy{°,]goP^i,_,¨

¬j"]0nhv¬nhZ"]z|]gtrfhyfqnr]}]0}vLfh]tr°«iknhy{v,1trj"{]0]DZi«°L]

SEdkWZ8d S*X3W-Z

c

SEdkWZd SX3WZ

c

|º

Z]tr] $yf nrZ"]1,{v,¯i,Hz|]gtrfhy{f~nh]g}]1v,¥nrZ"]1¼usDbfhopfqnr]\;¨uY Z"]tr]]lpyfqnf S<TDV_ CZik|(SUT-V_9Zf~j|}Z

nrZin

7 S5 Z c

T

S*W-Z

c _ V

%A'

i,

7 -S5 Z c T

-S*W-Z c _9kl

%4 '

i, T d _ c T d _ c

W1ikT 4c

T ¨ ¸ n4}v,\^]TfnhZikn

sDt S Z c dkW £f~]n~nhy{"P

c T %> '

sDt

S Z c

dkW £f~]n~nhy{"F_

c T %~_g '

%~_,_C'

Y Z]tr]¥§v,tr]yp¥§vLth\$iknhy{v,nhtikf~¥§]tf iktr]zJvLfrfhy¯"{]¥§thvL\3p]g°y}]:nrv^"]°£y{}]^_,¨

BDC:B "I f OVQLW=Q%OJU f LQ^W `aQ^ZTONPI

OVI f OVQNGTU*WTW/I NPU e.U N L f c

¸ nrZ"]fh]gj"]@º]}i,2i,}'nry°L]1p]°£y}],ºnhZ"]:p]°£y}]1v,;zi,t~nry{}]$_Lºik|;zi,frf~y{°,]1p]g°£y{}],ºpnrZ"]p]g°y}]

vLz|ikthnhy}{]1"¨

©]}i,;¯"j"y{{;nrZ"]p]g°y}]Tf4fhj}ZnhZiknenhZ]pyªJ]gth]g}]1v,¥¤fhziL}]@nhy{\^]vp}iknhy{v,;¯J]nq]]¡iL}'nry°L]

i,Pz|i,frf~y{°,]4"]°£y{}]gf }i,P¯J]i,£o^i,th¯ynrtri,tho6°,]T}'nhvLtg¨ ¸ mz|ikthnhy}j"ikt0nhZ"]\^]giLf~j"tr]\^]gLn ikf~]n~nry"

vLmi,}nhy{°,]p]°£y}]¬}v,j"$vp}}j"tfDy{PnrZ"]4¥§j"nhj"tr]¬Zy{]4\^]giLf~jth]g\6]gn0v,mzi,frf~y{°,]¬p]°£y}]0wqjfqn vp}}j"trf

ik¥ßnh]gt:fhv,j"t}]$]g°,]n3º¤f~]g] ,jth],¡¥§v,t:i,7y{{jf~nhtinhy{v,¨¡Y Z"]tr]¥§vLth]mi,7i,fho£\6\^]nhtry{}$¼DsDb zi,yt

fhopfqnr]\3}gik¯|]i^fhv,j"t}]v,¥2tr]nhtrvk¦y{p¥§v,tr\$inhy{v,¨

¿£y{}]DnrZ"]i,",{]Dfh]nhnhy{"4vLi,}nhy{°,]0"]°£y{}]0}giki,nr]trinr]u¯|]nq0]g]nq0ve°i,j"]Tfº]DZ|i«°,]D}th]Tinh]T

i6¯"y{i,thoPtr]nrthv,@y{p¥§vLth\$inryvLmfhv,j"t}]L¨ ¬f~y{"P¿£Zi,""vLmnrZ"]vLthoLº£nhZ"]}gikziL}ynqoPvk¥2nhZ"]1tr]nrthv,¦}Zi,""]g

a2b=S

ZzJ]t¼usDbaz|iky{tZ"]nhZ]1z"thvLz|vLt~nryvLmv,¥ik,{]gfinzJvLfhynryvLF:yf

yf,y{°,]gm¯£o

a b S Z c

S

T9dS*W\X

ZTCZ X

S<TZ X`S*W\X Z

SUT8Z

ynhZ

S! Z c X !

fUgDh i ! d1S*W X

!

ZjfUgDh i S*W X

!

Z¨Y Z"]DvLzpnhy{\$ik°«i,j]Dyf2Ly°L]1¯£o

Ic

ynhZ

c

S<T

_

T

_

Z

¨

©îynhZ jiLf~yëf~o£\^\^]nhtry} F¼usDb f~opf~nh]\$fgº4Z"]g T c

i

XT Wi, T c

i

dT;ynhZ

T 8d T W,¨ ¸ nhZ"yfe}iLf~]Lº£nhZ"]\$ilpy{\j"\}i,zi,}ynqo1a2bzJ]t4¼usDb ziky{ty{V¯J]

a

b!

S"T9d#TZ

i

0Qf<g h,0

l %~_TD'

(13)

!

! " " " " " " " " " " " " " "

#%$

&%'

zi,frfhy°L]p]g°£y{}]

!

!(

)

#%$

&%'

i,}'nry°L]1p]°£y}]

*" "

" +

*

ziLfqn

¥§jpnhj"tr]

y{p¥§vLth\$inryvLPnrtri,fq¥§]gt°,]T}'nhvLt

yLj"th] ,C 0e;Z£ozJvknrZ"]nry{}gik½tr]nrthv,@y{p¥§v,tr\$inryvLmf~opf~nh]g\ ¯"j"y{{;vL¼DsDbf~opf~nh]g\

1¤22 . 1*P( . 1*$7/0% . A@

TCE LWTU OVc OVU*N IbU W3fVG/I f LXJIeTU OVUTQ

i, T ¨

¬"]1}v,fhy{"]t\R¢¼DsDbaziky{tf0v,¥z|ikthnhy}{]gfgºtr]gfhzJ]g}'nry°L]{omfhv,j"t}]TPv,YR fhy\:j"nrik]v,j|f¬]g°,]gLnf

º

i

ji,nhynqo

"!$#

i

'& R¤º"0]1fri«o^nhZiknnhZ"]1vLtriL}{]i,fh0]gtyfk_ ¨

²£¶ ² )(+* 8 88Ga 3787 CP kk:G:]GM PG-

< 1

+

& R

c-,

.

,"/0 1

R243

T ,

5 _ ,

5

%~_g '

6 ¶ ¶ Àp ³ * 81R87:9<;/- 88Ga=I-J-:G:n)8-87D P +

'&

R 873 >C

@?M N8 -:G: E;BA/ 88GaDCE;+ R

EP7E>C8D;7 - 8)< X7 )8:<

V < 8+MN=7-8: 8Ga&M G-H<nG -JF?M -N8 -: :G:L -8;

¶V¶ ¬f~y{"6nhZ]i,fho\^zpnrvknry{}]gf~nhy{\$inr]v°L]t ¯"y{"v,\^yikH¥ÀiL}'nhvLtrf

1 R

R 3 THG _

GJI

W

K

0EL R S*W X Z SNM S

VT]V_DZZ

V %~_8,j'

ynhZ%M S VT]V_DZ

c

PORQ

Q

5 PORQ

5 Q

(14)

sut

& R I W

K

0EL R nS*W\X LZ

W

W\X

0

SNM S$nVTDV_ CZ*Z

sut

R I W

K 0 L R nS*W\X LZ

W

0

0 X W

SPM SnVTV _9Z*Z

4¥u}vLj"tf~]nhZ]¯"y{iktroPv,ti,}]Ly°L]gf try{fh]nhv^nrZ"]1¥§v,{{vy"^zi,triLpv«l½¨ ev,nhZ"y{"Pz"tr]°L]nrfi6¥ÀiLfqn

i,jfh}thjz"j"{v,jfv,zJ]tinrv,tZ"vºkik¥ßnh]gt¤th]Ti,py{"enrZ"] v,ti,}]ikfh0]gt2vL:z|i,frf~y{°,]p]°£y}]gfy{""vi,

Zy{f ¯J]gf~n nhv$}vLLnrtriLpy}'n0ynev,mnhZ"]iL}'nry°L]p]g°£y{}]gfg¨Y2v:nhZ"yf ]yn0vLj"{mthjm¥ÀiLfqn]v,j"LZPnhv^ziLfhf

nrZ"]v v,¥ fhyfqnr]tzikthnhy}{]gf1i,}Zik"L]nrZ"]Pfh]n~nryLfv, iL}'nhy{°,]^p]g°y}]Tf¯|]¥§v,tr]^\6]Ti,fhj"tr]\^]nrf

vp}g}j"tT¨ ¸¥nhZ"]1vLtriL}{]1fhi,y{ ºpnrZ"]nhZ]v,zJ]tinrv,tf~]nrfei,2f~]n~nhy{"feinezJvLfhynryvLJW,º"y¥nhZ"]i,f~]t

i,fk_ ºnrZ"]nhZ]1v,zJ]tinhvLtf~]nrffh]n~nryLfinezJvLfhynhy{v,

5

ºpy{¯JvknrZF}i,fh]1}vLLnrtriLpy}'nhy{":nhZ"]1vLtriL}{]

Y Z"yfi,z"zi,th]gLn½j"|}v,|f~yfqnr]}o4y{,¯|]D}gik{]TikGHGH=M 7 ?f~y{}]nhZ"]uvLz|]gtriknhvLt

f~nhtry{°,]gf}v,nhti,py}'nry¬iz"tr]gpy}'nryvLV¨Y Z] }v,fh]gj"]g}] fhZ"v,j"¯J]ei&)£y:vk¥Jz"trv,¯i,¯"y{ynqo1y£°,]gtrfhy{v,

i,;"]g]g"fenhvm¯J]}giktr]¥§j"{o;ik|ik{oÁg]g½¨eY2v$nrZ"y{f4]¡0]\$iD),]gfejf~]:vk¥¤\^y{}thv,@¯tri,}Z"y{"^j""y{°,]tfh]

Z£o£zJvknhZ]gfhy{fg¨¬Y2vfhy\^z"{y¥§o;nhZ"]6iki,opfhy{f40]6i,frf~j"\^]nhZikn¬Z"]g¢v,]¼usDb ziky{tthvL{¯i,}P)pfgº|i,2nhZ"]

RW¼usDbazi,ytf trv,{¯iL}P)6nhv£v¨

²£¶ ² #@6 ¶ g«"¶ $ ¶ MN' 'G:G -L .8GN -:<.<nG P-

U g P1 CM[:BGaV < 8= =H- CH-& M 78-8: [S$LZ. S SLZ6dNSLZZ -P7[SLZ . S [S$LZ6d

[SLZZ@;^<nG SLZ

c

,0

, T , _ ,

[SLZ

c

,0

, T ,

_ ,

%~_TD'

¶V¶ ©îZ"]

c 2

ynhZ

2 Rik{ik"L]zJvLfhynryvLf¤v,^i,}nhy{°,]p]g°y}]i,th]fh]n¤y^zJvLfhynryvL_

}v,trth]Tf~zJv,|py1nhv^zJ]tf~yfqnr]}]¬zthvL¯ik¯"y{{ynqo SWZu¥§v,tnhZ]¼DsDb ynrZi,f~]t_1ik S5 Z¥§vLt nhZ"]

¼DsDbaziky{tf ynrZ;i,fh0]gte"¨uY Z"]gth]¥§v,tr]¬nrZ"]1zJ]tf~yfqnr]}]z"thvL¯ik¯y{ynqomvk¥nhZ"]fh]nev,¥]g°,]n c 2

y{{¯J]

, S -S*WZZ

, S S5 Z*Z ,

2 & RWnrZ"]i,",{]gfei,th]1fh]n4y{FzJvLfhynryvL

º£nhZ"]1]g°,]gLnzJ]tf~yf~nh]|}]z"trv,¯i,¯"y{ynqoP¯|]T}vL\6]Tf

, S S*WZZ

,

S S5 Z*Z

, ¨

Y Z"]gth]¥§v,tr]nrZ"]:zJ]tfhy{f~nh]g}]:vk¥unrZ"]6fh]nvk¥0]°,]gnrf}v,trtr]gfhz|vLpy{"$nhvnhZ]:vLtriL}{]ikfh]t4]Tjik

nrv¡;y{f

[SLZ1ikWnhZ]Pz|]gtrfhyfqnr]}]6v,¥0nrZ"]m}v,\^z"{]\^]nri,thoWf~]nvk¥ ]°,]gnrf}v,trth]Tf~zJv,"y"nhv

nrZ"]ik|f~]t1_yf [SLZ'¨0Y Z"]1zJ]tf~yf~nh]|}]1vk¥nhZ]1Z"v,{]1v,ti,}]f~opf~nh]g\3yf3S [SLZLd [SLZZ

i,mnhZ"]p] "ynhy{°,]i,f~]tfz"trv,¯i,¯"y{ynqoPiktr]Ly°L]¯oikz"zy}iknhy{v,mv,¥yp]gLnrynqo7%, ''¨

6 ¶ ¶ Àp ³ 4 8II --: '7 -< 8 R 7 9<;3 E;3 8` )8:<YG

P -U g P1 CM[:BGa`- < =%C <nG 6=7MN' 'G:G ;1- 8 <n8 < 8 ^ E; ()8:<

V < 8= = <nG W M[ P'G:BGD;

(15)

¶V¶ ¬f~y{"nhZ]ei,fho\^zpnrvknry{}]gf~nhy{\$inr]v°L]tnhZ]¯"yv,\^y{i,p]lpz"tr]gfrf~y{v,|f+%~_8, ''ºkynD}vL\6]TfnhZikn¤nhZ"]

"y{f~nhtry¯jpnhy{v,vk¥ .-R¡y{ffhZiktrzmiktrv,j ¡Z"]g1R¡y{}th]Ti,fh]gfg¨0vL\6z|iktry"nhZ"]tr]gfhz|]T}'nhy{°,]¬0]gyLZn

v,¥ [S$LZik| [SLZ1Z"] Rnr]"fnhv¡y{ ynqoLº] |7iF}trynry{}gik0°«i,j]

fhj}ZnhZikn:Z"]g

`^ nrZ"]^p] ynry°L]:z"trv,¯|ik¯"y{ynqo;vk¥DZ|i«°y{"PvLtriL}{]f¬i,fh0]gt4]gji,nrvºQ;GZ"]D R¤º

nr]fnrvW¯J]z"th]gz|vLp]gtri,Ln6Z"] R y{}tr]giLf~]Tfº¤ik|7Z"]g PnrZ"]z"thvL¯ik¯y{ynqo v,¥4Zi«°£y

Z 0 S

Z 0 c W,¨

² 7p¤ ¸ ¥y|fqnr]gi,Wvk¥ikW}v,nhtiktry{v,jf4v,zJ]tinhvLt¬]6Zi«°,]^imÁg]gi,vLjf4vLz|]gtriknhvLt¬Z"y}ZWf~nhtry{°,]gf

nrvWZ|i«°,]Pz"tr]g"y{}nhy{v, tr]gi,y{Á]T Ziknh]°L]t:nhZ"]z"tr]gpy}'nryvL yf ;G;ik{ i«o£f:f~ynr}Z]gf:nhZ"];ik,{]Pnhv

zth]Tpy{}nh]TPzJvLfhynryvLV¨ ¸ mnrZ"yf}i,fh]enrZ"]ziky{t vk¥°«i,j]gfvk¥+S<TDV_ CZ0ik(S<T V _98Z0i,th]f~ynr}Z]gynhZ"]

v,t"fgº£ynnrj"th|f v,jpn nhZ|innhZ]zthvL¯ik¯"y{{ynry]Tf vk¥2vLtriL}{]i,fh0]gt0]TLj|ikHnhv$6v,t1_¯JvknrZmnr]nhvYW/.10p¨

º T c W ."º T c

0?."º c W .0,1Á]Tik{v,jf

}v,j"zy{"^v, ,jth]6ik}vLnhtiktryvLjf0}v,j"zy{"^v,Lj"th]1¨

100 80

60 40

20 0.04

0.03

0.02

0.01

0

yLj"tr]1%,¬triL}{]i,f~]t ynhZ;Á]Tik{v,jf}v,j"zy{"

(16)

100 80

60 40

20 0.35

0.3

0.25

0.2

0.15

0.1

0.05

0

y{,j"tr]1%,¬ti,}{]ikfh0]gt ynrZ;}v,nhtiktry{v,jf}vLj"z"{y"

TC "I f OVQNGTU W.W/I NPU e.U N L f c LfVG Y%I W/I OVU eTU OVUTQDU NPQ^Z/e LXW/Y

¬]mj""]lpz|]T}'nh]T ¯£o¦z"thvppj|}'n:v,¥enhZ]zth]g°y{v,j|f:i,ik{opf~yfyf:nhZikn^z|ikti,pv«l"ik0}v,jz"y{"}ik°,]gtho

fhy{,"y|}i,nh{o¬y{\^z"thv°L]nhZ"]}i,zi,}ynqo¯|vLj"1v,¥"th]nhtrvkë}Zik"]@¨4vLz"z"y{"¬}Z|ik""]gL}gikziL}ynqo}v,fhy{f~nrf

y{nhv6ynrthvppj}y6i6zi,triLpv«l"ik|}v,j"zy{"6¯|]nq0]g]mz|i,frf~y{°,]iki,}nhy{°,]p]°£y}]gfg¨¤Yv6¯J]zth]T}yf~]0]

iLfhfhj"\^]nrZinnrZ"]^th]Tf~j"n¬v,¥0\^]giLf~jth]g\6]gn¬ziLfhfhy°L]:p]g°£y{}]gfiktr]z"trv°£y{"]g;nrviL}'nhy{°,]^p]g°y}] C:i

tr]{yik¯"{]1}Zik"]@¨

5

VW

%Àyn¬\6]TikfnrZinnrZ"] @nhZ;py{,ynevk¥ & y{f

!#

i

ºpy¥]1tr]¥§]tnrv$¼usDbfhz"ynh]gth\^y{"v,{v,Lo ''¨

¸ p¥§vLth\$iknhy{v,FnrZ"]vLtho;ikW¿£Zik"v,FnrZ"]vLth]g\ ikz"z"{onhvth]nhtrvkë}Zik"]i,Fy{¢ik¯fh]|}]v,¥Dzi

ti,"v«lpi,J}v,j"zy{"6nhZ"]}Z|ik""]gV}i,zi,}ynqo?a2b

y{f

a b

R c

5

S T d SW\X

ZGT Z X

S<T

Z X`S*W\X Z

SUT Z

%~_g '