• Aucun résultat trouvé

A Sparse knapsack algo-tech-cuit and its synthesis

N/A
N/A
Protected

Academic year: 2021

Partager "A Sparse knapsack algo-tech-cuit and its synthesis"

Copied!
20
0
0

Texte intégral

(1)

HAL Id: inria-00074411

https://hal.inria.fr/inria-00074411

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- lished 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.

A Sparse knapsack algo-tech-cuit and its synthesis

Rumen Andonov, Sanjay Rajopadhye

To cite this version:

Rumen Andonov, Sanjay Rajopadhye. A Sparse knapsack algo-tech-cuit and its synthesis. [Research Report] RR-2260, INRIA. 1994. �inria-00074411�

(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

A Sparse Knapsack Algo-tech-cuit and its Synthesis

Rumen Andonov, Sanjay Rajopadhye

N˚ 2260

Mai 1994

PROGRAMME 1

Architectures paralle`les, bases de donne´es, re´seaux et syste`mes distribue´s

(3)
(4)

)*+(($,

-+.0/21436573809!3:9<;>=4?@A!3CBA<DE-7A!B9!FAC8GHDI1=J=

KLNMPOQLSR,TUTUVW#X YZL\[^]<_a`NV,[b`Nc<LdV,efRgL\RghihkjV%hiVleJm4noRQepVleq4Vrq4MQs<sutV%V,eJmLvtVlepV,R,c<w

V%`xepyvep`jV%TUV,eq4_ze{`NLN_an<cutV,e

KLNMQ|{V`xY#K0}

~ZR,f<fMQLd`q4VLNV,[S]<V%L\[^]vV2s€‚PQƒQ„X …*Rg_0W%†P†g‡X WƒˆfoRgOQVle

‰UŠI‹JŒ,,Ž<QŒ‘“’”Vuepyvep`NVT+Rg`d_z[%R,hihiy•q4V%LN_a–‘VRgs—_iTUf<LdM,–‘V,qRghiOPMQLd_i`N]vT™˜š[RghihaV,q›`d]<Ve{fRgL\epVœRghaOQMQ

LN_a`N]<T7ž Ÿ¡MQL`N]vV#OQV%svV%LSR,h!¢‚sRgfedRQ[S¢fvLNMQnvhiV%T“£]<_z[S]U]RPe:nV%`N`dV%LR%–‘V%L\RgOQV•[%RQe{V#fV%LpŸ¡MPLNT+R,s[JV

`N]R,s`d]<Vxep`\RgsqvRgLSq ˜šq4V%soepVQžIq‚y4sR,TU_z[0f<LNMPOQL\RgTUTU_as<OœRghiOPMQLd_i`N]vT*¤I¥:]<V#q‚V%LN_a–QR,`N_aMQs_zenRPepV,q

MQs¦`NL\RgsešŸ¡MQLdT+Rg`d_iMQs¦M,Ÿ#`d]<V+ep`\RgsqvRgLSq¦LNV,[bc<LNLdV%s[JV,e_is‚`NMR*ep`NLdV,RgT§Ÿ¡c<s[J`d_iMQsoRghf<LdMQOQL\RgT+ebm

Rgsq¨[%Rgsvs<MQ`—nV*RQ[S]<_aV%–‘V,q*n4y©`d]<V+cepcoRghœepfRP[JV%¡`N_iTªVUT+Rgfvf<_is<O*`dV,[S]<s<_z«‘c<V,enV,[%RgcoepV+`N]<V

q4V%fV%sq‚V%s[J_aV,eRgLdVep`\Rg`d_z[%R,hihiy+c<svf<LNV,q‚_z[J`\Rgn<haV‘¤¬<c<LN`d]<V%LdTUMQLdVe{c[S]*RUe{fRgL\epV—RghaOQMPLN_i`d]<T™Ÿ¡MQL

`N]<VOPV%s<V%L\Rgh0¢‚sRgfedRQ[S¢*f<LNMPn<hiVT­]RPe›s<MP`›nV%Vs”f<LdMQfM‘e{V,q”_as*`N]<V—hi_a`NV%L\Rg`NcvLNV‘m!`dM+`N]<V—nV,ep`

MgŸIMPc<L:¢‚s<M,£hiV,q‚OQV‘¤I’”VR,hze{M_iTªf<hiV%T—V%s‘`I`N]<V•epfR,LSepV•RghiOPMQLd_i`N]vT®MPs+R›ha_is<V,R,LRQepy‚s[S]<LNMPs<MQcoe

RgLdLSR%y£_i`d]—[JMQse{`SR,s4`uep_i¯VTUV%TUMPLNy#MPsV,RP[^]—K0°±˜²_k¤³V‘¤amQR#£uRl–‘VbŸ¡LNMQs‚`0R,LNLSR%yf<LdM‚[JV,edepMQLbžS¤0¥:]<V

RghaOQMQLd_i`d]<T™[Rgs+LNc<s+MPs7R,s4yªs4c<T—nV%L0MgŸf<LNM‚[bV,eNe{MQLSexRgsoq´]oRQeMQf<`d_iT+R,hµ`d_iTUVœepfV%Vlq4c<fC¤0¥:]<V

epV,[bMQsq7˜¡nRQ[S¢‚`NLSRP[^¢‚_isvO4žIf<]RPepV#M,ŸI`N]<Vq‚y4sR,TU_z[:fvLNMQOPLSR,TUTU_isvO›_¶e0Rghze{MTUM‚q4_¸·V,q—epM`d]Rg`_a`

[%Rgs+nVfV%LpŸ¡MPLNTUV,qU_as+epfR,LSe{V%hiy Rgsoq´_as RˆTUVTUMQLdyVJ¹´[J_iVs4`0T+R,s<s<V%L¤

º¼»>½

¾š¿{À%Á

½

¾:Â4Ãi¿{Ä¡Å^Æ

Ç%È,É,ÉQÊb˲̡ÍdΛÏ%Ð#Ì¡Ñ,ÍÒgË¡ÍpÓPÔ²Ñ>Õ!Ê%Êb˚Î%Ö×ÓPØS̲ÍdÎ#ÙCÍ{Ú²ÍdØS˚ԲÑ>Û<˲ÊbÜJËkØSÝßÞáàbâPØ^ÓPÎ#Ï%Ðx̲Ñ,ÍuãoÚ¡É,˲ÖäÌå ÙçæÉ,˲ÊdèšÍdÔéÌ

êçæêCæëZìzêCÊQí,îbîbïJëbðpí

ñ ØSÓPÎlÊbÓ,ÊSò,óHÖ×Ë¡Ö×ÚkØgíôiËIìiÊbÓxõ×ÍdØNòJÍHôaË¡ÊJݨÕ!Í{Ó%Ì¡Í{ËHÊSô Õ!ÊbÝZÉ,È,̲Í{ËöÇgԚÖ×Í{ÓPÔšÍØ^ÓPÎZ÷<ÍdÔ²Ñ,Ó,Êbõ×ÊJÜbÐ%âÇ%Ê^øùØ,â,åµÈ,õ×ÜØ^ˡָØbð

ñšñ ËkØ{èéÊbÉPØJÎ%Ñ%ÐbÍdóHÖ×Ë¡Ö×ÚkØgíôaËIìiÉPØS˲ָ̡ØSõ×õ×ÐÚ¡ÈgÉ,ÉPÊJˡ̲ÍdÎ#Ï%МêHÇ,җú˚ØSÓ%ÌCêCÊPí,û•ü¡Û4ý¼þgÿbëJð

(5)

'´©) ´( › ›,$,($´

‹

ZMQcoe:TUMQs‚`NLdMQse[JMQTUTªV%s‘`0qtV%Ld_i–‘V%Le{y<e{`<tV%T+R,`N_¶« c<VTV%s‚`Ic<s RghiOPMQLd_i`N]vTUV#R,T±tV%

hi_aMQLvtV¨˜šR,f<fV%htV ! #"#$&%('*),+.-/$0-&12žUfMQcvL7hiV*fvLNMQnvhšjV%TUV OtV%sutV%LSR,hq‚c2edRQ[J\jRgkq4M‘e*R%–‘V,[*q‚V,e

fV%LpŸ¡MPLNT+R,s[JV,eTUV%_ahihiVc<LNVe(V%s*TªMgy‘Vs<s<V«‘c<Vh43×R,hiOQMPLN_a`N]<TUV•ep`SR,sq<R,LSq*fRgL#fvLNMQOPLSR,TUT+Rg`d_iMPs

q4y‚sRgTU_¶« cvV‘¤650V%`N`dV©qtV%LN_a–QR,`N_aMQsCm« cv_#LNV%fMùepV epc<L+c<s<V*`dLSRPq4c[J`d_iMQs6q4V,e V,«‘cR,`N_iMPseLvtt V,[Jc<Ld

LNV%s‚`NVle#ep`\Rgsq<R,LSq*–‘V%LSec<s*h¶Rgs<OùRgOQVŸ¡MQso[J`N_aMQs<s<Vhq4Vha_ze{`NV,ebmµs<VfV%cv`ZŸkRg_aLNVR,f<fV%h0R,c<w*`NV,[S]<

s<_z«‘c<V,e[bhzRQedep_¶« c<Vleq4VUfvLNMQ|{V,[b`N_iMPs¨epfR,`N_zR,hiVUV``NV%TUfMPLNV%hahiV—[%R,LhiV,erq:tV%fV%sq<R,s[JV,esvV7e{MQs‚`

fRQer[JMQsvs4c<Vleep`\Rg`d_z«‘c<V%TUV%s‚`%¤87xs”`dV%hRghiOPMQLd_i`N]vTUV—[JLNVc<w7fMQcvLhiV—f<LdMQn<hkjV%TUVq‚c¦eNRP[7jR q4M‘e

OtV%sutV%LSR,hHs93äRgf<foRgLSR;:<i`xfRQerjRs<MQ`dLNV[bMQs<sR;:<zedeNRgso[JVq<R,seZh¶Rˆha_i`N`vtV%LSR,`Nc<LdV‘¤=xMQce_iTUfvh%tV%T—VJs‚`NMPse

Rgcedep_[JV%`œRghaOQMPLN_i`d]<TUV>epc<L#cvs*L<tV,e{V,Rgc*ha_isutV,R,_iLdVRPepy‚s[S]<LNMPs<V+˜²c<s*LvtV,epVlRgc¨jRŸ¡LNMPs4`\e#q>3³MPsq4V,eSž

q<RgsoeZhiV,«‘c<V%hö[^]oRQ«‘c<V#f<LdM‚[JV,eNe{V%c<L tV%htVTUV%s‚`SRg_aLNVxq4_¶epfM‘e{V—q>3³cvs<VT±tV%TUMP_iLNVxq‚V›`\Rg_ahihiVx·w4Vù¤>50V%`

RghaOQMQLd_i`d]<TUV[bLNV%c<w+Ÿ¡MQs[b`N_iMPs<s<V—R%–‘V,[c<s*svMQT—n<LNV>« c<Vhz[JMPs« cvVq4V—f<LNM‚[bV,eNe{V%c<LSe#V%`œM@? LNV—c<s

ACB -D-FE#1

B

MQf<`d_iT+R,hš¤HGCR”e{V,[JMPsq4V+f<]RPepV©˜¡hiVULdV%`NMPc<L—RgLdLN_kjV%LNVQž•q4V+hzR7f<LdMQOPLSRgTªT+Rg`d_iMQsq4y4soRg

TU_z«‘c<VxV,ep` tV%OùRghiVTUV%s‚`(TªM‚q4_· tVœfµMPc<LœeI3³VwtV,[bc<`NV%LR,ceNe{_q4VT+R,s<_kjVLNV[JLdV%ce{V#V%`+tV,[JMPs<MQTªV#V%s

T±tV%TUMP_iLdV‘¤

(6)

B A B=A A A A

´:7'"”x0$%U

¥:]<V#¢‚sRgfoeNRQ[S¢Uf<LdMQn<haV%T _zeRrR[JhzRPeNe{_z[Qm,#Kš[JMPTUf<haV%`NVx[JMPTnv_isR,`NMQLd_zR,hµMPf<`N_aTU_i¯lRg`N_aMQsf<LdMQn<

hiV%T £_i`d]T+R,s4y>Rgf<fvhi_z[Rg`N_aMQseZcƒQ†‚m‚…*¥†Q„km‚RgsqU[Rgs—nµVxŸ¡MQLNT—c<h¶Rg`NVlqRQeŸ¡MQhahiM,£xeI£:VœRgLNV

OQ_a–‘V%srR ¢‚sRgfoeNRQ[S¢M,Ÿ [%R,fRQ[J_a`{ygmP_is‚`NMx£]<_z[S]£:V:T´Rlyxf<c<` `py‚fV,e!MgŸ MPn<|{V,[J`SebmgVlRQ[S]MQn<|{Vl[J`

MgŸ`{y4fVH]oRQeR

B $ " '²m"!$#šmvRgsq R&% -&% @) '¡m(')#šm ˜*')#km!$#{m+ Rgsq,ZR,LNVrRghah!fM‘e{_i`N_a–‘VZ_as4`dV%OQVLSe^ž\¤

-ZV%`dV%LNTU_as<V./#šmC`N]<V—s‚c<TnV%LxMgŸ0¡²`d]”`{y‚fµVMPn<|{V,[J`\e•`dM7nVª[^]<MùepV%s epM RPe›`NM+T+R,w4_aTU_i¯V#`N]<V

`NMP`SRghCfvLNMg·o`Z£_a`N]<MPc<`ZVw<[JVV,q4_isvO›`d]<Vr[%RgfoRQ[J_a`pyùm4_š¤V‘¤im

T+R,w132

4

#6587

!#9./#:;2

4

#65+7

')#<./#>=?@./#BA±„ˆ_as4`dV%OQVL@DC2W"@S$@FE/E/E/@GIH ˜dWgž

}kŸJ._ze!LNVlep`NLd_z[J`dV,qZ`dMZnVRLK %9=#$–‘V,[J`dMQL˜²_š¤V‘¤imbV,RQ[S]MQn<|{V,[b`I[%RgsnV[S]<M‘e{V%srRg`ITUM‘e{`!MPs[JVQž

£:V#]oRl–‘Vœ`N]<V£:Vhih!¢‚s<M,£s „NMùW[%RPepV‘¤0¥:]vV›¢‚sR,feNRP[^¢UfvLNMQnvhiV%T [Rgs+nVe{MQha–‘V,qUepVl« c<Vs4`d_zRghahiy

_is:Or˜*&%žx`N_iTªV‘m!R,sq*`N]<_¶e•OP_i–‘V,ex_i`rR

B=A -&1E#"

B

"6"="#+ %  [JMQTUfvhiV%w‚_i`{yIQPSR$Tl†ep_as[JV_a`#_ze

fMQhiy‚s<MPTU_zR,h‘£¤³L%¤`%¤PRZfR,LSRgTªV%`NV%L˜²£]v_z[S]_i`\epV%h¸ŸdmgT´RlyœOQLNM,£¨V%w4fMPs<V%s‚`N_zR,hihay#£_i`d]_is<f<cv`e{_i¯%VQž\¤

’”V>ep`Ncoq4y q4y4soRgTU_¶[•fvLNMQOPLSR,TUTU_isvO&VU:Vh9WNTPmZcƒP†šm<MQsvVMgŸ0`d]<Ve{`SRgsoq<RgL\q*Rgf<f<LdM‘RP[^]<Vle

`NMepMQha–4_as<O*`N]v_ze›fvLNMQnvhiV%T*¤ ¥:]<V RghaOQMPLN_i`d]<T§£:MQLd¢<e_as©`{£:M f<]RQe{V,eJmRŸ¡MQLd£R,LSq©f<]RPepVUŸ¡MQL

[%Rgh¶[Jc<h¶Rg`N_as<OU`d]<V

B

$F" 'MgŸu`N]<V—MQfv`N_iT´Rgh0e{MQhicv`N_iMPsCmIRgsq`N]<V%sömHR+nRQ[S¢‚`NLSRP[^¢‚_isvOUf<]RPepVU`d]Rg`

cepVleH`N]<_¶e`NMr[JMQsoep`NLdc[J``d]<VxepMPhic<`d_iMPs–‘V,[b`NMQLm.<¤¥:]vVLNV,[JcvLNLNVs[JV:Vl« cR,`N_aMQsŸ¡MQL`d]<V Ÿ¡MPLN£uRgLSq

f<]RPepV_ze:OP_i–‘V%s+nV%hiM,£¤

XY ˜[Z<ž\C±T+R,w<˜ XY] 7g˜^Zož_@*! Y\`aXY ˜[ZLba' Y žNž ˜k ž

¥:]<VVl« cR,`N_aMQs*_zexq4VJ·os<V,q´Ÿ¡MPLRghah„&cdZ,=@\„ecgf,=*m!R,sq7`N]<VrnMQc<sqvRgLNy[bMQsq4_a`N_aMQse

RgLdV‘m Xih

˜[Z<žC X"Y

˜k„ žC“„7R,sq XY

˜[Z<žLCjbk £]<VslZac „$m£V+RgLdV_as4`dV%LNV,e{`NV,q*_is*·sq‚_is<O

X 2

˜*%žS¤¥:]<VULNVl[Jc<LNLdV%s[JVŸ¡MQLr`N]<V´„NM‘W+¢‚sRgfedRQ[S¢”fvLNMQnvhiV%T§_zeMQs<hay©R ephi_aOQ]‚`TUM‚q‚_· [%R,`N_aMQs

˜še{V%V#`N]vVe{c<ned[JLN_af<`ZM,Ÿ`d]<VrepV,[bMQsq RgLNOPc<TUV%s‚`Jž_

XY ˜[Z<ž\C±T+R,w<˜ XY] 7g˜^Zož_@*! Y\`aX

YG] 7

˜^ZLba' Y žNž ˜ ž

Y#e[JMQTªfRgLdV,qU`NM—n<LSR,s[^]Rgsq+nMQc<sq©˜kRgs<MP`N]<VL[JhzRPeNe{_z[#`NV,[S]<s<_¶« cvV#`NMªepMPhi–‘V`N]<Vf<LdMQn<

hiV%T žSm<_i`x_zexMgŸ¡`NVs©R,LNOQcvV,qa³…*¥†P„H`d]Rg`rq4y‚sRgTª_z[#f<LNMPOQL\RgTUTU_as<Oª[%Rgh¶[Jc<hzR,`NV,e`N]vVŸ¡c<s[J`d_iMQs

X Y

˜[Z<žœRg` (CfMQ_is‚`SeR,sq”`N]‚ce 6%

A

fR%y<e`N]<V—£:MPLSe{`[%RPepV—f<LN_¶[JV‘mDOr˜*&lž\mC£]<V%LNVlRQe#`N]<V

R%–‘V%LSR,OQV[%RPepV*fV%LpŸ¡MPLNT+R,s[JV MgŸnvLSRgso[^]ßR,sq nMPc<sq2R,hiOQMPLN_a`N]<T+e_ze—MgŸ¡`NVs T—c[S] nV%`d`NV%L¤

ZM,£:V%–‘VL%mZMPLNM,£_i`d¯Rgsoqon‚R,]<s<_pVn8T%‡"!]R%–‘V#OP_i–‘V%s+Rq‚y4sR,TU_z[f<LdMQOQL\RgTUTª_is<OrRghaOQMPLN_i`d]<T

Ÿ¡MQLU`d]<V*„M‘W*f<LdMQn<haV%T £]<_z[S] ]RPeUTc[S]©nV%`d`NV%L+R%–‘V%L\RgOPV*[%RPepV*fV%LpŸ¡MPLNT+R,s[JV‘¤ß¥CM¦q<R,`NV‘m

epc[S] Rgs*_aTUf<LNM,–‘V,q—RghaOQMPLN_i`d]<T ]RQes<MP`ZnV%V%sq4V%–‘V%haMQfV,qŸ¡MQLx`N]vV -q8-&$ ‚¢4sR,feNRP[^¢+f<LdMQn<

hiV%T¤U}šs©`N]v_ze›foRgfV%L%m£V+epyvep`dV%T+R,`N_z[Rghihay q4V%LN_a–‘VUe{c[S]¦Rgs¦R,hiOPMQLN_a`N]<TmRgsoq”`N]<Vs¦RQq<q‚LNV,ede

_i`\e›_iTªf<hiV%T—V%s‚`SR,`N_iMPs*MQs Rgs¨Rgf<fvhi_z[Rg`N_aMQs¨epfV,[b_· [fvLNM‚[JV,edepMPLUR,LNLSR%y‘¤G!_i¢‘VU`d]<V,ZMQLdM,£_i`N¯

n‚Rg]vs<_R,hiOQMPLN_a`N]<T*mCMPc<L_aTUf<LNM,–‘V,q*R,hiOPMQLN_a`N]<T§R,hze{M*cepV,e`N]<V—ŸkRQ[J``N]oRg``N]vVU[JMùep`Ÿ¡c<s[J`d_iMQs

_zeTUMQs<MP`NMPs<_z[^X ]<V%s[bVMQs<V+s<V%Vlq<e›`dM*[%R,hz[Jc<h¶Rg`dVU_i`MQsvhiy Rg`—[JV%Ld`SR,_is /$&%('4%/D

B

"#%9'

A

¤*¥:]<V

[JMQs‚`NLd_in<cv`N_iMPse:MgŸ`N]vV›foRgfV%LœRgLNVre{c<TUT+R,LN_i¯V,qRPe(Ÿ¡MQhahiM,£xe

(7)

B

YZs+_iTªf<LNM,–‘V,qR,hiOQMPLN_a`N]<T&˜k[%RghahiV,q—`N]<VrepfoRgLSe{VrRghiOPMQLd_i`N]vT7žHŸ¡MPL`N]<VOQVs<V%LSR,hC¢4soRgfedRQ[S¢

f<LdMQn<haV%T®£]v_z[S]]RPe:nV%`N`dV%LRl–‘VLSRgOPV[%RPepV#fV%L{Ÿ¡MQLNT´Rgs[JVx`N]oRgsU`d]<Vep`\RgsqvRgLSq*˜kq4V%se{VQž

q4y‚sRgTª_z[Zf<LdMQOPLSRgTªTU_is<O>RghaOQMQLd_i`d]<T*¤

n‘yvep`dV%T+Rg`d_z[q4V%Ld_i–PRg`d_iMPs7MgŸ`d]<Ve{fRgL\epV—RghaOQMPLN_i`d]<T n4y+`dLSRgsoe韡MQLdT+Rg`d_iMPs7MgŸ`d]<VLdV,[Jc<Ld

LNVs[JVMgŸu`N]<Vªep`\RgsqvRgLSqq4y‚sRgTª_z[›fvLNMQOPLSR,TUTU_isvOŸ¡MQLdTc<h¶Rg`d_iMQs _is‚`NM+R+e{`NLNVlRgT­Ÿ¡c<s[b

`N_aMQsR,hHfvLNMQOPLSR,T*¤

…7M‚q4_¸· [%Rg`d_iMPs©MgŸx`d]<VUR,hiOPMQLN_a`N]<T&Ÿ¡MQLnM‘MQ¢‚¢‘V%V%fv_is<O _is4Ÿ¡MPLNT+R,`N_iMPs©e{M7`d]Rg`r`N]<V—nRQ[S¢‚

`NL\RQ[S¢4_as<Of<]RPepVr[%Rgs´Rghze{MnV#fV%L{Ÿ¡MQLNTªV,qepfR,LSe{V%hiy—_isªR›–‘V%LdyTUV%TUMPLNyVJ¹´[J_iVs4`IT+Rgsv

s<V%L>˜²nV,[%R,cepVrMgŸuepfRP[JVha_iTU_a`SR,`N_iMPseJm<£Vq4Mªs<MQ`q‚_zeN[bceNe`N]<_¶eZ]<V%LdV‘¤x¥:]<V_as4`dV%LNVlep`NVlq

LNVlRQq4V%LI_ze!LdVJŸ¡V%LdLNV,q#`NM ³Yœ~Z†,‡Qn8kmQR%–PRg_ahzRgnvhiVŸ¡MQLRgs<MPs4y‚TUMPceµŸ¡`NfŸ¡LNMQT 4ž\¤

}šTUf<haV%TUVbs4`\Rg`N_aMQs MgŸx`N]vVUe{fRgL\epV+R,hiOQMPLN_a`N]<T§MQs¦R+hi_as<V,RgLrRPepy‚s[^]vLNMQsvMQcerRgLNL\R%y”£_a`N]

[JMPsep`\Rgs‚`:e{_i¯%VTUV%TUMPLNy#MPsV,RQ[S]—K0° ˜²_k¤³V‘¤am,R#£R%–‘VJŸ¡LNMPs4`RgLdLSR%yfvLNM‚[JV,edepMPLYSPœ~P ¡ž

n‚yUf<LNM,–‚_is<OnMPc<sq<eZMPs7`d]<Vrep_i¯V#MgŸ0haM‚[%RghCnvc? V%LTUV%TUMPLNy_asUV,RQ[S]+f<LNM‚[bV,eNe{MQL%¤

¥:]<V*LdV%T+R,_isq4VLM,Ÿ`N]vV*fRgfV%L _zeMPLNO‘R,s<_i¯V,q RPeŸ¡MQhihaM,£xedn‘V,[*©OP_i–‘V,eUR,s _as4`dc<_i`d_i–‘V

V%w‚f<hzR,sRg`d_iMQs—MgŸ `d]<VZMQLdM,£_i`N¯ n‚R,]<s<_„M‘Wx¢4sR,feNRP[^¢>RghaOQMQLd_i`d]<T*¤I¥:]<V%sCm8n‘Vl[

f<LNVlepV%s‚`SeH`d]<V

Ÿ¡MQLdT+Rgh q4V%Ld_i–PRg`d_iMPsM,ŸI`N]<Ve{fRgL\epVR,hiOPMQLN_a`N]<T Ÿ¡MQL`N]<VxOQVs<V%LSR,h!¢‚sRgfoeNRQ[S¢—f<LNMPn<hiV%T ˜¡nV,[%RgcoepV

MgŸçepfRP[JVhi_aTU_i`\Rg`N_aMQse!£VMQs<hay`dLNV,R,``N]<V:Ÿ¡MPLN£uRgLSqf<]RPepVQž\¤)n‘V,[:‡e{]<M,£xe]<M,£ `N]vVxRghiOPMQLd_i`N]vT

[%Rgs*nV_aTUf<hiVTV%s‚`NVqMPsR£R%–‘VJŸ¡LdMQs‚`#R,LNLSR%y f<LNM‚[JVleNepMPL%m!£]vV%LNVrV,RQ[S]K0° ]RPeZMQsvhiyU·s<_a`NV

TUV%TUMPLNy‘¤ ¬H_isR,hihay‘m n‘V,[,W”OQ_a–‘V,eMQc<L [JMPs[Jhicoep_iMPse—Rgsqßq4V,ed[JLN_anµVleˆMPfµVs f<LdMQn<haV%T+eb¤ ’V

[JMQso[Jhicq‚V›`d]<_ze:_as4`dLNM‚q4co[J`N_aMQs+£_i`d]7Rn<Ld_iVJŸe{c<LN–‘V%yù¤

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

…*Rgs‚yRgc<`d]<MQL\e›]R%–‘V_as4–‘V,e{`N_aO‘Rg`dV,qfoRgLSR,hihaV%hx˜šq4V%soepVQžxq‚y4sR,TU_z[f<LNMPOQL\RgTUTU_as<O+R,hiOQMPLN_a`N]<T+e

Ÿ¡MQLU`d]<V+¢4soRgfedRQ[S¢ fvLNMQnvhiV%T*¤¨…7M‘e{`£MQLd¢ ]oRQeU[JMPs[JV%s‚`NL\Rg`dV,q©MQs `d]<V*„M‘W7fvLNMQnvhiV%T ˜¼Ÿ¡MPL

V%wvRgTUf<haV‘m¬oVLi²ž\m#Rgsoq RPq<q4LNVleNepVle7q4_?!VLNV%s‚`UTUM‚q4VhzeM,ŸfR,LSRghahiV%hœT+RQ[S]<_isvV,eéX K(~xY#…*ebm

q4_ze{`NLd_in<c<`dV,q±TUV%TUMPLNy©T+RP[^]v_is<V,ebm:hi_as<V,R,L7R,LNL\RlyveJmxTUV,e{]<V,eUR,sq fV%LpŸ¡Vl[J`+ep]‚c1ªV,eJ¤“¥:]<VLNV

]RQe+R,hzepM¦nV%V%s6epMPTUV7£MQLd¢ MQsß`N]vV*OQV%s<VLSRghœ¢4sR,feNRP[^¢±fvLNMQnvhiV%T*muRghih•q4V,Rgha_is<O £_i`N]±`d]<V

q4V%se{V—q4y‚sRgTU_¶[#f<LNMPOQLSR,TUTU_as<OUR,hiOPMQLN_a`N]<T ³Y#~x†g‡ùR4m5 5pR‘†P„<mC¥CV%s†Q„iš¤r¬<MQL#`d]<_zebm!`N]<VnV,e{`

fV%LpŸ¡MPLNT+R,s[JV:_¶eçMPn<`SR,_is<Vlqn4yMQcvL0epyvep`dMQhi_¶[:R,hiOQMP²`dV,[S]<š[bc<_i` ³Y#~x†g‡ùRC˜kepV%VLNVJŸ¡VLNV%s[bV,e!`N]<VLNV%_as

Ÿ¡MQLœR[bMQTUf<haV%`NVxq‚_zeN[bceNe{_iMQs žS¤

¥:]<VnoRQep_¶[ _¶q4V,R 7#ƒQ†/<M,ŸI`N]<Vxe{fRgL\epVR,hiOQMPLN_a`N]<T _ze0R« cR,LN`dV%L[JV%s‚`Nc<Ldy›MPhzq!m‘n<cv`:e{V%V%T+e

`NM]R%–‘V#nV%VsUcepVlq´MPs<hiyŸ¡MQL`d]<V„M‘Wf<LNMPn<hiV%TmQ`NM`d]<V#nV,ep`M,ŸMPc<L¢‚s<M,£hiV,q4OPV‘¤DxMQLNM,£_a`N¯

Rgsq n‚R,]<s<_#OP_i–‘V*e{V,«‘c<V%s‚`N_zR,h#R,hiOPMQLN_a`N]<T´eˆŸ¡MQLU`d]<V„NMùW*¢4sR,feNRP[^¢ Rgsq±LNVhzRg`dV,q fvLNMQnvhiV%T+e

cep_as<O—`N]<_¶e _¶q4V,R&Vn8T2i0˜ n‘V,[W‚¤QW ž0 n8T‡šmR,sq G!VV›V`#R,hš¤<_iTªf<hiV%T—Vbs4`0_i`MPs Rˆ]‚y4fV%L\[Jc<nV

cep_as<O*R q4_i–‚_zq‚V—Rgsq©[bMQs«‘c<V%Lrep`dLSR,`NV%OPy G>n8n3šmI£]<_z[S]*`SR,¢‘V,e54˜&7678

`

:9Jžx`N_aTUVMQs;8

(8)

B A B=A A A A

f<LNM‚[bV,eNe{MQLSebm‘RgsoqcepV,e*4r˜*&%žCe{`NMQL\RgOPV_is`d]<V:£MQL\ep`[%RQe{V%¤ 50]<VsV%`IR,hš¤,f<LNV,e{V%s‚`IR f<_afV%hi_as<V,q

hi_as<V,RgLuRgLdLSR%yU£]<_¶[^]UcoepV,e Or˜*&%ž0e{`NMQL\RgOPV‘m Or˜ lžMQs7VlRQ[S]UMgŸ™f<LNM‚[JVleNepMPLSe5pR‘†P<m 5…*†Qk¤

¥:]<V%yª[JhzR,_iT `d]Rg``d]<V#nRP[^¢‚`NL\RQ[S¢4_as<O`SRg¢‘Vle 4r˜*7ž0`N_aTUV‘mQnvc<`q4MsvMQ`OQ_a–‘VRgs´RghiOPMQLd_i`N]vT™`NM

epc<noep`SR,s4`d_zR,`NV`N]<_¶e[JhzR,_iT*¤

’”V TUV%s‚`N_iMPs¦`N]R,`UMQc<LªTUM‚q4V%hxMgŸ>[JMPTUf<c<`\Rg`N_aMQs¨_ze£:V,R,¢‘V%LpX Rgs±RPepy‚s[S]<LNMPs<MQceULd_is<O

MgŸ8f<LdM‚[JV,edepMQL\eJmI£]<V%LNV—V,RP[^]*f<LdM‚[JV,edepMQL]RPe#MQs<hayR[bMQse{`SRgs‚`TUV%TUMPLNy ˜²M,Ÿxep_a¯%VžSmIRgsq

£:V>RQ[S]<_iV%–‘Vœ`N]<VMPf<`N_aT+RghC£MQLSe{`Nk[%RQe{VfV%LpŸ¡MPLNT+R,s[JV‘m<sR,TUV%hay3Or˜

2

žS¤ 7xs<hi_a¢‘VepMPTUVM,Ÿ0`N]<V

`N]<VMQLNV`N_z[Rgh!£MQLd¢!m£:V>q4MsvMQ`œRg`N`dV%TUf<``dMnvLN_isvO`d]<VLdc<s<s<_as<O`d_iTUV•q4M,£s7`NM—fMQhay4s<MPTU_zR,h

Rg`0`N]vVV%w4fV%soepVMgŸçRgsUVw4fMQsvV%s4`d_zR,h4s‚c<T—nµVLHM,ŸCf<LdM‚[JV,eNe{MQL\eZ˜²V–‘V%s£_i`d]`N]<VxLSR,f<_zq—RQq4–PR,s[JV,e

_is G>n‚}0`NV,[S]<s<MPhiMPOQy‘m‚£:V#Ÿ¡V%V%h `N]R,``N]<_¶e _¶e:`NM‘M—V%w4fV%soep_i–‘VPžS¤

´("”$($ U 7©*0$%U ß( + —$%0

’”Vœs<M,£ f<LdV,epVs4`uRgs+_is‚`Nc<_a`N_a–‘VV%w4fvhzRgsoRg`N_aMQsUM,Ÿ`d]<VZMPLNM,£_i`d¯% n‚Rg]<sv_CepfoRgLSe{VrRghiOPMQLd_i`N]vT®Ÿ¡MQL

`N]<Vœ„NMùW›¢‚sR,feNRP[^¢—f<LNMPn<hiVT*¤I}ésª`N]<V#LdV,[Jc<LdLNV%so[JV˜

žSm X"Y

˜[Z<žLNV%f<LdV,epVs4`\eá`d]<V#MPf<`N_aT+Rghf<LdMg·`

`N]R,`[%R,s*nµV—RP[^]v_iV%–‘V,qUce{_is<OªMQs<hay`d]<VMQn<|{Vl[J`SeWDE/E/E/fm Rgsoq £_a`N]*R+[%R,fRQ[b_i`{yUMgŸZ¤#}²Ÿ£:V

RQq<q—TUMQLdVx[%RgfRP[J_i`{y+˜¡_š¤³Vù¤im‘RPeDZ_is[bLNV,RPepV,eSžSm4£V#[RgsUMPs<hiy %+ B

$F"@-`N]vVZ`dMQ`SR,h!f<LdMg·`m<R,sqU£:V

`N]‚ce:]R%–‘V#`d]<V#Ÿ¡MQhihaM,£_is<OMPnepV%Ld–PRg`N_aMQsC¤

Žv>)8- 1=/I'4%"

X Y

˜^Z<ž %A + "="'4"=% /D( %9,/$0-F

A

%9 %9Z

ZM,£m4R,s4y—TUMPs<MQ`dMQs<_¶[ Ÿ¡c<s[J`d_iMPs]RPeRSe{`NV%f‚£_ze{Ve{]RgfV—˜še{V%V#¬I_iOUW,žSmvRgsqU]<V%so[JV‘m‘MQs<V

[%Rgsq4V%`dV%LNTU_as<Vx_i`Se:–PR,hic<VŸ¡MQLœRgs‚y Zm<_¸Ÿ0£:V¢‚s<M,£2_i`\e:–QR,hic<VleZR,`Z`d]<Ve{`SRgLd`ZM,Ÿ0V,RP[^]ep`NVfC¤}š`

T+R%y`N]<VLNVJŸ¡MPLNV#nV#LdV%f<LNVlepV%s‚`NV,qª[JMQTUfvhiV%`dV%hiyn‚y+RepV%`m#MgŸ

B

#%$ A

˜š[%R,hihaV,qU[JLd_i`N_¶[%RghfMQ_as4`\e^ž

! @#"—˜$ !ž*kmQOQ_a–4_as<O`N]<Vr[JM‘MPLSq4_asRg`dV,e£]<V%LNV_a`x[^]R,s<OQVleJmRgsoq`N]vV›svV%£ –PR,hic<V‘¤

¥:]<VrepfR,LSepV>RghaOQMQLd_i`d]<T™_ze:noRQepVlqMQs `{£:M¢‘V%y—MQne{V%LN–PR,`N_iMPse

Žv&%(')*"—˜$ !ž %

A + "="'4"=% /+ 1=/I'4%" '*)8- , "#$

B " A

%('4% @- %9' - -&$

A

p! =E&'

'*)8-- 1=/I'4%"L! ` "˜. ba'•ž %A

A " + "="'4"=%/

}šs ŸkRP[J`%mC_i`_¶e›e{_iTUfvhiy+`N]<VŸ¡c<s[b`N_iMPsCm/"˜. öž ep]<_¸Ÿ¡`NV,q*`NM+`N]vVLd_iOQ]‚`n4yI' R,sq”c<fn‚y&! ˜še{V%V

¬H_iOr‘žS¤0Y#e0R›LdV,epcvhi`%m‘_a`0[%Rgs´Rghze{MnVxLNV%f<LdV,epVs4`dV,qˆn‚yRrepV%`m01

M,ŸCfR,_iL\eJ¤2/1

_¶e([bMQse{`NLNco[J`NV,q

Ÿ¡LNMPT3n4y e{_iTUf<hayURPq<q4_as<OU`N]vV›foRg_iL V'@*!$C`dMUV,RQ[S]+V%hiVTUV%s‚`:R,sq7n‚y_as[Jhacq4_isvO,V'@*!$RQe

Rgs RQqvq4_i`d_iMQsoRghIV%hiV%TªV%s4`_is+`N]<Vre{V%`/

1

C(4V'@*!$.52674! ` '@#"—˜$ !ž ` !$,8+! @#"˜. !ž*:9;<5

Žv7=>')/"—˜$ !ž =E@?r˜$ !ž #$0- ' % " + "="'4"=%/A 1$=/&' %"

A '*)8- ')8-0 1$,/I'% "CB˜$ !ž\C

T+Rgwv˜$"—˜$ !žG@D?r˜. öždž %A

A " + "="' ",%/

ñFE Ö×ÓrØ^ÓPÎ#Ç%Ì¡ÊJË¡Í{ËHÉPÊJÖäÓ%ÌHÊbÈ,ÌC̲ÑPØSÌHÌ¡Ñ,Ö×ÚIԚÊJÈ,õ¸Î#ÏPÍHG ÊJˡڡÍ(Ì¡ÑPØ^ÓÌ¡Ñ,Í(Ú¡ÍJIJÈ,Í{Ó%Ì²ÖØ^õØSõ×ÜbÊJË¡Ö×Ì¡Ñ,ÝLKE Ç,þ,ÿNM¡íCêCÊJÌ¡Í

Ñ,Ê#G!Í{òJÍ{Ëdâ%̲ÑPØSÌC̲Ñ,ÍØNòbÍpËkØSÜJÍÏPÍ{ÑQØNòÖ×ÊJË Ö×ÚCÍ$O,ÉQÍdԚ̡ÍNÎ̲ÊÏPÍÏQÍ{̡̲Í{ËÏPÍdÔpØSÈ,Ú²Í0ÊSôÚ¡ÉQØSˡڲÖ×ÌzÐí

(9)

B

"—˜$ !ž

"—˜$ !ž

¬H_iOPc<LNV—W0Y2TUMPs<MQ`dMQs<_¶[ZŸ¡c<s[J`d_iMQs "—˜[Z<ž0[%R,s7nVrq4V,ed[JLN_anµVlq´n‚y+Re{V%`MgŸ \[JLN_a`N_¶[%Rgh fµMP_is‚`SeJ4¤

¬H_iO

_ahihacep`dLSRg`dV,e›`d]<_zebm£]<V%LdV"—˜$ !žœRgsq ?r˜$ !žrRgLdV+ep]<M,£s¨_is©`d]<_is¦hi_as<V,e—˜²`N]vV%_iL>[JLN_a`N_z[Rgh

fMQ_is‚`SeR,LNV[b_iLS[bhiV,eR,sq+eN«‘cRgLdV,eJm‚LNV,e{fV,[J`N_a–‘V%hiyžS¤I¥:]<VœT+RgwM,ŸI`N]<V#`{£M›Ÿ¡c<s[b`N_iMPse(_¶e:e{_iTUf<hay

`N]<V NMQcv`NV%LV%s4–‘VhiMQfVRPeep]<M,£s+n4y`d]<_z[S¢hi_as<V‘¤/B”˜. !ž_zeRgh¶epMTªMQs<MP`NMQsv_z[Qm‚Rgsoq´_a`Se[JLN_a`N_z[Rgh

fMQ_is‚`SeR,LNV+V%_a`N]<V%Lr`N]<V´[J_iL\[JhiV,e#MPL—eN«‘cRgLdV,eU˜²_k¤³V‘¤amHMQsvhiy [JLN_a`N_z[Rgh0fMQ_is‚`SeM,Ÿ#MPs<V+MgŸœ`N]<Vª`p£M

ð

ð

ð

ð

¬H_iOPc<LNV>$ "˜^Z<ž:_¶e TUMPs<MQ`dMQs<_¶[˜kep]<M,£sq4MP`N`NVlqµžGmCe{M+RgLdV"˜. ba'#ž²Xße{]<_Ÿ¡`dV,q`dMU`N]vVLN_aOQ]‚`

˜šq<RPep]<VlqµžRPe £V%hihöRQe\! ` "—˜$ b '•ž¡Xße{]<_Ÿ¡`dV,qULN_iOP]4` ,E•c<f ˜še{MQhi_¶qµžS¤

(10)

B A B=A A A A

"˜$ !ž

?r˜. öž

B”˜. !ž C T+Rgw˜."˜$ !ž_@D?r˜$ !žNž

"˜. öž

¬H_iOPc<LNV

,B”˜$ !ž\C±T+R,w˜$"—˜$ !žG@D?r˜. öždž_¶eRghze{MTªMQs<MP`NMQsv_z[

Ÿ¡c<s[J`d_iMPse^ž\¤ ZMQ`dVR,hze{M`d]Rg`œepMPTUV#MgŸ`N]vV[bLN_i`d_z[%R,h!fMQ_as4`\e›˜¡MgŸ "˜. öžRPe:£:V%hahCRPe+?r˜$ !ždž:T+R%y

s<MQ`xR,f<fV,RgL>˜šep]vMg£s _isUOPLSR%yž:_asB˜$ !žS¤

ZV%s[JVr£:V—]R%–‘V`N]<V—R,hiOPMQLN_a`N]<T&OP_i–‘V%s*nV%haM,£¤xc<LV%w‚f<h¶RgsR,`N_iMPs”]oRQe›nV%Vs*nRQe{V,q”MQs

`N]R,`MgŸpxMQLNM,£_a`N¯rRgsq3n‚R,]<s<_˜še{V%V V n8T7˜ n‘V,[P¤(W4¤QW‘žŸ¡MQLœRQq<q‚_i`N_aMQsR,hIq4V%`\Rg_ih¶e^ž\¤

WP¤ 7)C(4V' 7q@*!87 .5

‚¤ Ÿ¡MQLSf C߁)EFE/EG*m<[JMPsep`dLNc[b` Y

RPeuŸ¡MPhihaMg£xeq

˜šR‘ž G!V%` 1 C YG] 7 6 4' Y @*! Y .5H6 4! ` ' Y @ X ` ! Y -8+! @ X 9; Y] 7 ` ' Y = 5

˜¡`N]<_¶e:_zeR—epc<fV%L\epV%`M,Ÿ0`N]<Vr[JLd_i`d_z[%R,hµfMP_is‚`SeMgŸ Y žS¤

˜¡n!ž 50MPsep`dLNc[J` Y n4yrLNV%TUM,–‚_is<OœRghah<[bLN_i`d_z[%R,h4fMP_is‚`Se @ X 9;/1‘`d]Rg`RgLdV E#"#+ %9='C-FE

n‚y+RgsvMQ`N]vV%L%m<_k¤³V‘¤am _¸Ÿ 16@ X 1Q/9;/18 01(=L Rgsq X 1 A X ¤

¤ ZM,£

X 2

˜*%ž[%Rgs nV›VlRQep_ahiy—MQn<`\Rg_as<V,q´Ÿ¡LdMQT 2 ¤

$ r($´ E(* — $(

YZhi`d]<MQcvOQ]©`d]<VnoRQep_¶[_zq‚V,RUnµV]<_isq`N]<V+R,nMg–‘VªRghaOQMPLN_i`d]<T§_ze›M,–‘V%LrR « cR,LN`dV%Lr[JV%s‚`Nc<Ldy*MQhzq

7œƒQ†/šm‚_i`]RPe s<MP`nV%V%s Rgf<fvhi_iVlq´`dM`N]<VOPV%s<V%L\RghC¢‚sRgfedRQ[S¢Uf<LdMQn<haV%T*m‘`NM`d]<VnµVlep`MgŸáMQc<L

¢4svMg£haV,q4OPV‘¤I}é`C_¶eC[JhiVlRgLC`N]oRg`~ V%T´RgLN¢veHW

RgLdVep`d_ihahQ–PRgha_zq!mPRQeC_ihahice{`NLSR,`NV,q#_as¥IRgnvhiV,eWRgsqr4¤

(11)

B

f W  ‡ W ƒ T † WQW W

WJ‡

W „ „ „ „ T T T T T Wb‡ WJ‡ Wb‡ WJ‡ WJ‡

 „ „ „ W%ƒ ,‡ g‡ g‡

„ „ „ † † WiT WT ,‡ g‡ W

‡ „ „ „ † † ,‡ g‡ ,‡ g‡



¥HR,n<hiVW"Rghac<V,e›M,Ÿ X"Y ˜^Z<ž#Ÿ¡MQL—R*ep_aTUf<haVOQV%s<VLSRgh¢‚sR,feNRP[^¢f<LNMPn<hiVTl C ‡vm\ C§WJ‡vm

')# C W$@N‡+@Sƒ$@W%„$m!$#BC T @$@\†$@S,‡+ep]<M,£s<_as<O—`N]<VTUMPs<MQ`dMQs<_¶[J_i`{y‘¤

fW VW‚mTF ¸W%„‚miWJ‡"

 ‡vmi 4maW%ƒ ¸W%4mäg‡"

‡vmi ƒ4mä† 4miWƒ W„4maWT/ W4mׁ,‡ WJ‡vmׁ"W

‡ ‡vmi ƒ4mä† 4miWƒ W„4mäg‡ Wb‡<m



¥HR,n<hiV>$0¥:]<VfR,_iLSece{V,qU`NM—LNV%f<LdV,epVs4``N]<VV%wvRgTUfvhiVxMgŸ¥IRgn<haV—WQ¤

ZM,£:V%–‘VL%m,`N]<Vf<LdV,epVs[JVMgŸ XY MQs—`N]<VLd_iOQ]‚`]R,sqUe{_zq4VM,Ÿ˜k žIf<LdV,[Jhicoq4V,eRZsoRg_i–‘VVw4`dV%sep_aMQsCm

ep_as[JVs<M,£m Y q4V%fV%sq<e˜²LdV,[Jc<L\ep_i–‘VhiyžMPs _a`SepVhŸd¤“¥:]<V%LdVJŸ¡MQLdV”£V”s<VV,q `dM¨q4V%–‘V%haMQfßRgs

RghaOQMQLd_i`d]<T®`d]Rg`u[JMQsoep`NLdc[J`\e(_i` %9=/ $0-&+.-q ' 6•coep_isvO`N]vV#fRgLd`N_¶Rghihay—[JMQTªf<c<`NVlq Y ¤0¬<MQL`N]<_¶e

LNV,RPepMPsCm‘£:V:LdV%f<LdV,epV%s‚`C`N]vV(Ÿ¡c<s[b`N_iMPs—RQeRxep`dLNV,R,T M,ŸfRg_aLSeHL\Rg`d]<V%L`d]Rgs>R#epV%`¤¬<c<Ld`N]<V%LdTUMQLdV‘m

£:V—T+Rg_as4`\Rg_as7`{£:M RQq‚_i`N_aMQsR,h0_is‚–QR,LN_¶Rgs‚`SeZ_as”MPc<LLNV%f<LdV,epVs4`\Rg`N_aMQs #`d]<V—fRg_aLSeRgLdVUe{MQLN`dV,q*_is

_is[bLNV,RPep_isvOUMQL\q4V%L#M,Ÿ£:V_iOQ]‚`Sebm$Zm0˜šR,sq7]<V%so[JV—Rgh¶epMU`d]<V—RQedepM‚[J_¶Rg`NVlq!m

X

3×eSžGmIRgsoq `d]<VZ83×e#R,LNV

nMQc<sq‚V,q7n4y ,m<`N]<V¢‚sRgfedRQ[S¢+[%R,fRQ[J_a`{y‘¤

G!V%`m!Ÿ¡MQL f C WDE/E/E_ mnVU`d]<VªepV,«‘c<V%s[bV,e#`N]R,`LNVf<LNV,e{V%s‚` XY ˜^Z<žS¤’VUs<M,£ epyvep

`NV%T´Rg`N_¶[%Rghahiy¦q‚V%LN_a–‘V*R”Ÿ¡c<s[J`d_iMPsRgh#fvLNMQOPLSR,T `N]R,`MPfV%LSR,`NV,eUMQs6epVl« c<Vs[JV,eM,ŸfR,_iL\eURgsq

[%Rgh¶[Jc<h¶Rg`NVle Ÿ¡LNMQT ‚¤’”VªcepV—`N]<VŸ¡MQhahiM,£_isvO7s<MP`SRg`d_iMPs”Ÿ¡MQLr£LN_i`d_is<O e{c[^]f<LdMQ

OQL\RgT+eq:e{V,« cvV%s[JV,eR,LNV>q4V%hi_aTU_i`dV%qn‚yUn<LSRP[JV,e˜še{M<m—q‚V%s<MQ`dV,e`N]<VV%TUfv`pyªepVl« c<Vs[JVQž_m

q4V%s<MP`NV,exR—epV,«‘c<V%s[bV#£]<M‘e{V.)8-F#E›_¶e:`N]<VV%haV%TUV%s‚` mRgsq+£]<M‘e{V '4#%(!˜¡_š¤³Vù¤im4`d]<VLNV,e{`MgŸ0`d]<V

epV,«‘c<V%so[JVQžI_ze0`N]<Ve{V,«‘c<V%s[JVùm+m‘`N]<VœV%hiV%TªV%s4`\eçM,ŸIMQc<Lxe{V,«‘c<V%s[JVleá_asU`N]v_ze(foRgfV%LR,LNV#foRg_iL\e:MgŸ

_is‚`NV%OPV%LSebm ˜²£:VcoepVn<L\RQ[S¢‘V%`Se Ÿ¡MPL[JMPsep`dLNc[J`d_is<OªfRg_aLSe^ž\¤¬<c<s[J`d_iMPsRgf<f<ha_z[%R,`N_aMQs*ce{V,e

(12)

B A B=A A A A

fRgLdV%s‚`N]<V,e{V,eZ˜¡V%O<m _ze:`d]<V#LdV,epc<ha`:M,Ÿ0R,f<f<hiy‚_isvO`N]vV•Ÿ¡cvs[J`N_aMQs `NM`d]<V#`{£:M

RgLdOQc<TUVs4`\eRgsqµ¤C’VUq4Vb·s<VŸ¡c<s[J`d_iMQsoe›V,«‘cRg`d_iMPsRghahiy‘mCce{_is<O epVfRgL\Rg`NVªV,« coRg`N_aMQse#Ÿ¡MQL

q4_ ? V%LdV%s‚`fRg`d`NV%LdseZMgŸ`d]<V_as<f<c<`\emµŸ¡MPL#V%wvRgTUf<haV‘m4`d]<V›Ÿ¡MPhihaMg£_as<OªepfV,[J_¸·V,e`N]<VrnµV]R%–4_aMQL#M,Ÿ

`N]<V#Ÿ¡c<s[J`d_iMQsöm<£]<V%s+V%_i`d]<V%LMgŸ0_a`Se:_isvf<c<`Se:_¶e:`N]<VV%Tªf<`{y—epV,«‘c<V%s[bV

xc<LUq‚V%LN_a–QR,`N_aMQs¦_zenRQe{V,q MQs¨`N]<V+Ÿ¡MQhahiM,£_is<Oe{V%LN_aV,eMgŸhaV%TUTªRg`SR‚m£]<_z[S]©Ÿ¡MQhahiM,£ q4_aLNV,[J`dhiy

Ÿ¡LNMPT­~V%T+R,LN¢veZW

m `N]<V>q4_zed[JceNe{_iMPs7_is `N]<Vf<LdV%–‚_iMQcoeZe{V,[J`N_aMQsCmR,sq7`N]vV_is‚–PRgLd_zRgs‚`Se:M,ŸMQc<L

LNV%fvLNV,e{V%s4`\Rg`d_iMQsö¤

©Ž ' XY ˜[Z<ž %A

$0-

B

$D-

A

-q'C-FE:K/ ')8-

A

- 1=-q=/I- ')8-q ! Y ` XY ˜[Z&b ' Y ž %A

$0-

B

$D-

A

-q'C-FEeK/ 2 &% )8-0$0-

! " # $

! " % & '(*)

+ ) !' ' , -

©Ž% '"˜. !ž =E&?r˜$ !ž #$0- + "="'4"=% / 1=/I'4%"

A

$D-

B

$0-

A

-' -FE K/ =E !.

$0-

ACB

-F/I'4% @-D7 '*)8-q B˜$ !žlC T+Rgw˜."˜. öž_@D?r˜$ !žNž %A

$0-

B

$D-

A

-q'C-FEdK/ ©‹IŠI‹

/

!0

 "

!. E-[p -FE A "("%

A21

3. . . 4

$5 . ) 4 3. . !.

+ 2 .65 ) 3. . 4 !.

+ 2 7 . ) 8 " . 93 .

ZMQ`dV`N]oRg`x_is7`d]<Vh¶RQe{`#[Jh¶Rgce{VR,nµM,–‘V‘m`N]vV›]vV,RQq7M,Ÿ0nMQ`N]e{V,«‘c<V%s[JVle _¶eZ[JMPsepcvTUV,q+Rgsq

Re{_is<OPhiVMQcv`Nf<c<`xV%haV%TUV%s‚`0_ze:f<LdM‚q4c[JV,q ¤¥:]<_zeV%se{c<LNVle:`N]R,`Z`d]<VMPc<`Nf<cv`Zf<LdM‚q4c[JVlqn‚yU`N]<V

+_¶e

A ' $&%/I'6_is[bLNV,RPep_isvO*_is©_a`SeSZ”–PR,hic<V,ebm:RŸkRP[J``N]oRg`—£_ihihnVcoepVJŸ¡c<hhzR,`NV%L¤©¥:]‚ceJm

`N]<VxŸ¡c<s[J`d_iMQs:rRQ[S]<_iV%–‘Vleá`d]<VV,«‘c<_i–PRghaV%s‚`(M,Ÿ)nù`NV%f 4˜kR ž0M,Ÿ0`N]<V•epfR,LSepV>„NMùWR,hiOQMPLN_a`N]<T*¤

ZM,£mRghahH`d]Rg`x_zehiVJŸ¡`_¶e `dMULNVTUM,–‘VZ`d]<Vq4MPTU_isoRg`NVlq´VhiV%TUVs4`\eJ¤0~V,[%RghahC`N]R,`#RfR,_iL Z 1^@ X 1Q

q4MQTª_isR,`NV,eZ@

X

_? Z<1D= Z X 1 A X

mC_š¤³Vù¤im_i`x]RQeepT´RghihaV%Lr˜²MQLœV,« coRgh²žu£:V%_aOQ]‚`#n<c<`#h¶RgLdOQV%L

˜²MPLV,« coRgh²ž0fvLNMg·o`%¤ U:V,[Rgce{V#`N]<VrMQc<`df<c<`xMgŸ; _ze:_asMPLSq4VLZM,Ÿ0_is[bLNV,RPep_isvO£:V%_aOQ]‚`SeJm‚`N]<V

q4MQTª_isR,`NMQLª˜²_¸ŸœRgs‚yµžM,ŸR,s VhiV%TUVs4`#T—ce{`›nV+MQsvVM,Ÿ#_a`Se

B

$0-FE-F/I-

ADA

"#$

A

%9 ')8-

A

- 1=-q=/I-\¤

ZV%s[bV#£:V#]oRl–‘V`d]<V#Ÿ¡MQhihaM,£_is<Ov¤

<>=

?

 >)8- ""% %9

B

$F"D #$ #+ /D"#+

B

1#' - A Y $F"#+

Y]

7

A@ +3 B3 C ! : D

% )8-&$D-

(13)

B

@ + :+ 8 7

@ + :+ 8 27 2 (A+ ,8 2 ) @ +3

!+ ) @ + :+ ,8 2

ZMP`NV0`N]oRg` :M‚[%[bc<LSeHMPs`d]<VLN_aOQ]‚`C]Rgsqe{_zq4Vùm‘epM#`d]<V:fvLNMQOPLSR,T q4VJ·os<V,eC`N]<VuepV,«‘c<V%s[bV

LNV,[bc<LSe{_i–‘V%hay‘¤C¬<c<LN`d]<V%LdTUMQLdV‘mQ`N]vV#e{`NLNco[J`Nc<LdVZM,ŸI`N]<Vxf<LdMQOQL\RgT“_zeR›e{`SR,sq<RgL\qUMQs<V#`d]Rg`0M‚[%[bc<LSe

_isUh¶Rg¯%yŸ¡cvs[J`N_aMQsR,h!h¶Rgs<OPcRgOPV,e³YH’ Tlƒ4m‚¬H’ Tlƒšm‚RgsqU_¶eáM,Ÿ¡`NV%sªcepV,q—`NMT´Rgs<_af<c<hzR,`NVx_is4·os<_i`dV

epV,«‘c<V%so[JV,e˜²£_a`N]<MPc<`C]R%–‚_is<O`dMV%–PRghicoRg`NV0`d]<V%T7ž\¤C¥:]<V·sR,h‚epMQhac<`N_aMQsrMgŸv`N]<Vx˜¼Ÿ¡MPLN£uRgLSq#f<]oRQepV

MgŸ`N]<VPžOQVs<V%LSR,hC¢4soRgfedRQ[S¢f<LdMQn<haV%T“_ze(MPn<`SR,_is<VlqªŸ¡LdMQT 84m‘£_i`d]U`N]vV›_as<_i`d_zR,hi_i¯lRg`N_aMQs`d]Rg`

$,› U ‘:U+ ::) ®7x(—

}š`#_ze#£:VhihI¢4s<M,£s ›R,] T%‡`N]R,`R+e{`NLNVlRgT Ÿ¡cvs[J`N_aMQsR,hf<LdMQOQL\RgT§[%R,s”nV_aTUf<hiVTUVJs‚`NVlqURQe

Rs<V%`{£MQLN¢ªMgŸf<LNM‚[bV,eNe{V,eJm [JMQTªTc<sv_z[bRg`N_as<ORPepy‚s[S]<LNMPs<MQce{hiy+`N]vLNMQcvOQ]7·<Ÿ¡MUnvc? V%LSeb¤ nùc[^] R

s<V%`{£:MPLN¢[%Rgs*nV—epyvep`dV%T+R,`N_z[RghihayU[bMQse{`NLNco[J`NV,q7noRQepVlq7MQs<hay7MQs*`d]<V

A

' #/I'4%/ A

'4$I1 /I'41$D-MgŸ

`N]<Vrf<LNMPOQL\RgT*¤¬<MPLZV%wvRgTªf<hiV‘m‘`d]<Vf<LdM‚[JV,edepMQLœ`N]R,`Z_aTUf<hiVTV%s‚`SeMPc<LZfvLNMQOPLSR,T­`NMª[JMPTUf<c<`dV

Ÿ¡LNMPT _¶e:[JMPsep`dLNc[J`dV,q—RQe១MPhihaMg£xeb¤xc<L0MQc<`df<c<`:_¶e(`d]<VZLdV,epcvhi`0MgŸR,f<f<hiy‚_isvO›`d]<V

Ÿ¡c<s[J`d_iMPs7@ +3 *˜²£_i`d]¦R7ed[%Rgh¶RgLrfRgL\RgTUV%`dV%L%mI„‘ž#`NM `N]<VªMQc<`df<c<`M,ŸœR Uc<s<_a`%¤ ¥:]<V

hzR,`N`NVL`SRg¢‘Vle:`p£MR,LNOQcvTUV%s‚`SeJm‚MQs<VM,Ÿ0£]<_z[S]U_¶e:`N]<V_isvf<c<`e{V,«‘c<V%s[JVùm<Rgsoq´`d]<VMQ`d]<V%L_ze:`d]<V

MQc<`df<c<`0MgŸçRgsC2#c<s<_a`%¤¥:]<V_is<fvc<`MgŸ `d]<_ze_zeC_i`\epV%h¸Ÿ `N]<VMQc<`df<c<`epV,«‘c<V%so[JV ˜²£_a`N]

`N]<VœfRg_aL R,`:_i`\e]<V,RQqžS¤\ZV%so[JVZ£VZsvV%V,q—RR•Ÿ¡VV,q4nRP[^¢rhiM‘MQf+£]<_¶[^]ª[JMPsep_¶ep`Se0MgŸçR•·<Ÿ¡M

n<c? V%Lm<_is<_a`N_zR,hi_a¯%V,q£_i`N] -˜kepV%Vr¬H_aO‡4žS¤

G!M‘MP¢4_as<ORg`r`N]<V+q‚VJ·s<_a`N_iMPse#MgŸœ`N]<VlepV—`N]<LdV%VˆŸ¡cvs[J`N_aMQsebm£:VªepV%Vª`N]R,`>@ +3 7[Rgs©nV

_iTUfvhiV%TUVbs‚`NV,qUce{_is<O R7e{_iTUfvhiVd`N]<LdV,ep]vMQhzq LNVOQ_ze{`NV%Lœ£]<_z[S]”_¶e#_is<_a`N_zR,hi_a¯%V,qU`NM„4¤U}²Ÿu`N]<V X

–PRghicvV›MPsU`N]vV›_as<f<c<`fRg_aL:_¶e(OQLdV,Rg`dV%L`N]oRgs+`N]<Vœ`N]<LdV,ep]<MPhzq!m‚_i`_ze(foRQeNe{V,qU`N]<LdMQc<OP]©˜¡c<f q<Rg`d_is<O

`N]<Vr`N]<LdV,ep]vMQhzq7LdV%OQ_¶ep`dV%L`NM X žSmMQ`d]<V%LN£_¶epVr_i`x_zex[JMQse{c<TUV,qU£_a`N]<MPc<`#f<LdM‚q4c[J_as<O+Rgs MQc<`df<c<`

˜²£VxeNR%y`d]Rg`_a`H_¶e 'C-&$D-FE"#1#'¼ž\¤0¥:]<V cvs<_i`I_zee{`NL\Rg_iOP]4`{Ÿ¡MQLd£RgL\q!m‚Rgsq_¶eH_iTªf<hiV%T—Vbs4`dV,q

£_i`d]”`{£:M[JMQTªfRgL\Rg`NMPLSe˜²`d]<VªepV,[JMPsq*MQs<VU_¶e#cepV,q*`NM[JMQTªfRgLdV X –PRghac<V,e#_is [%RQe{V`d]<VZ 3äe

RgLdVV,«‘cR,h²žS¤ 2U_ze#_iTªf<hiV%T—Vbs4`dV,qUep_aTUf<hayn‚y*RUfR,_iL#M,ŸxRPq<q4V%L\eJmIRgsqR+[JMQTªfRgL\Rg`NMPL

Ÿ¡MQLxOQV%svV%LSR,`N_isvO—Rgs dV%sq+MgŸáepV,«‘c<V%s[bV`SR,O7˜¡s<MQ`xe{]<M,£s7_is+`d]<V#·OQc<LdVQžS¤

ZM,£mQ`dM_iTUf<haV%T—V%s‘`C`N]<VLdV,[Jc<LdLNV%so[JV#˜k žSm‘£Vs<V%V,q “epc[S]f<LdM‚[JV,eNe{MQL\eJm<[bMQs<s<Vl[J`NV,q_is—R

hi_as<V,RgLxR,LNL\Rly˜²_ŸIŸ¡V%£V%L:f<LdM‚[JV,edepMQL\e#RgLdVrRl–PR,_ihzR,n<hiVùm4`N]vVR,hiOPMQLN_a`N]<T [%Rgs+nV_aTUf<hiVTV%s‘`dV,qn‚y

[JMQs‚·OQc<Ld_is<O`d]<V%TERPeRZLN_as<OR,sqcep_as<O#T—c<hi`d_if<haVHfoRQeNe{V,e^ž\¤0°0RQ[S]f<LdM‚[JV,eNe{MQL_¶e[JMPs<s<V,[J`dV,q#`NM

`N]<Vs<Vw4``d]<LNMPc<OQ]Rgs "#1#'

B 1 ' K1 -0$^mR,sq]RPeZRhiM‚[Rgh!Ÿ¡V%V,q‚nRQ[S¢nvc? V%L#q‚V,eN[JLd_inV,qUR,nMg–‘Vù¤

}š`r[%Rgs nµV´ep]<M,£s¦`N]R,`e{c[^]Rs<V%`{£MQLN¢*M,Ÿxf<LNM‚[bV,eNe{MQLSe_¶eR

B

#$D'4% (6 /D"#$&$0-F/I'_aTUf<haV%

TUV%s‚`SR,`N_iMPs©MgŸ•`N]<V+OQ_a–‘V%s¦f<LNMPOQL\RgTX _Ÿx`N]vVfvLNMQOPLSR,T `NVLNTU_asRg`dV,eJmI`N]<V%s¨`N]<V+s<V`p£MQLd¢©MgŸ

f<LNM‚[bV,eNe{V,eR,hzepM+`dV%LNTU_asRg`dV,exRgsq*f<LNM‚q‚c[JV,e`N]<V—edRgTUV–PRghac<V,eb¤YZhihMQc<LrRgLdOQc<TªV%s4`\eZ_is*`d]<V

f<LNV–4_aMQceepV,[J`d_iMPs+q4V,R,hi`0£_i`d]UfRgLd`N_¶RghC[bMQLNLdV,[J`ds<V,eNeM,Ÿ`d]<VZfvLNMQOPLSR,T*m<R,sq£:Vœs<V%V,q`NMf<LdM,–‘V

`N]R,`#`N]vV›fvLNMQOPLSR,T­MgŸ(¥:]<V%MQLdV%T&Wrq4M‘V,eZ`dV%LNTª_isR,`NV‘¤¥çMªep]<M,£E`N]v_ze:£:Vs<VV,q`dMf<LdM,–‘V›MPs<V

[JLNco[J_zR,hoŸkRP[J`%m‘sR,TUV%hay›`d]Rg`_i`0_zeHŸ¡LdV%VZM,Ÿq4V,RPq4hiM‚[S¢+˜²nV,[%R,cepVxMgŸI`d]<VxLNV,[JcvLSep_a–‘VsRg`dc<LNVxMgŸI`d]<V

(14)

B A B=A A A A

ÿ

xc<`Nfvc<`#¬}p¬

G!M‚[Rgh¬}{¬

K FM

…7V%LdOQV ¬H_ahi`NVL

¬H_iOPc<LNV‡8\-x_iLNVl[J`]RgL\q4£R,LNV_iTªf<hiV%TªVJs‚`SR,`N_iMPsM,Ÿ`d]<Vf<LNMPOQL\RgT MgŸ¥:]vV%MQLdV%T&WQ¤

f<LNMPOQL\RgT*m<`d]<_ze:_¶eZR—q4_ze{`N_as[J`:fMùeNep_an<_iha_i`{yžS¤’V£_ihahCe{]<M,£2`N]<_¶e n‚yUf<LdM,–4_as<O—RˆhaM,£:V%LnMQcvsq

MQs+`N]vVe{_i¯%VM,Ÿ`d]<Vn<c? V%LSeb¤

Y epVl[JMQsq_iTUfMPLN`SR,s4`IRPepfV,[J`_zeC`N]<VTUV%TUMPLNyLNVl« c<_aLNV%TªV%s4`mS_š¤³Vù¤im%`N]vVep_a¯%V:M,Ÿ`N]vV:n<c? V%L\eJ¤

¬<MQL0R#e{MgŸ¡`{£R,LNV_aTUf<hiVTV%s‚`SR,`N_aMQs#MPsURZOPV%s<V%L\Rgh<fvc<LNfM‘e{VZT´RQ[S]<_is<Vùm%`N]<_¶eç_¶eHs<MQ`RZha_iTU_a`SR,`N_iMPsC¤

ZM,£:V%–‘VL%m4MPc<Lx`SRgLdOQV%`x_zexR—q4V,q4_¶[%Rg`dV,q G>n }(f<LdM‚[JV,eNe{MQLmCRgsq7_a`nV,[JMQTªV,e[JLNco[J_zR,hC`NM—f<LNM,–‘V

`N]R,`Z`d]<Vn<c? V%L\eZR,LNVnMPc<sq4V,qUŸ¡LNMPT­R,nMg–‘Vù¤:¥:]<VŸ¡MQhahiM,£_is<O`d]<V%MPLNV%T R,sep£V%LSe`N]vV,epV`{£:M

f<LNMPn<hiVT+e១MPL`N]<V#Ÿ¡V%V,q‚nRQ[S¢nvc? V%L%¤

<>=

?

 %' + ' % +.-C- 2 /I-

B

'' '*)8- -q=E2 '*)8- =1 + KI-&$ " -D(-&+.-'

A

%9' )8-."@/D

1=-&1 - " ' )8-Sf( ' ) B $ ";/I-

ADA

"#$%

A

KD"#1=E-FE $F"#+ KD";-K/L' Y ,E $ "#+ KI-D"% K/<

? ?

 G!V`%m0Rg`—R,s4y_isoep`SR,s4`m(`d]<VUhaM‚[%Rghn<c ?!VL—[JMQs‚`SR,_is©V%haV%TUV%s‚`Se Zi7@ X 7 šm EFE/E/Z9@ X Q*m

`d]<Vn<c ?!VL›haV%s<OP`N]7_¶eZ`N]‚cek¤YZh¶epM<m hiV%`x`N]<V–PR,hic<Vr_is*`N]vV`N]<LdV,ep]<MPhzq7LdV%OQ_¶ep`NVLZM,Ÿ:`d]<V

@ +3#c<s<_a`0nµV X 1

m<RgsoqhiV%` Z@

X

µnVx`N]<Vx–PRghac<VRg`0`d]<VZ]vV,RQqM,ŸC`d]<V#_isvf<c<`epV,«‘c<V%so[JV‘¤

ZM,£m‚£:V]R%–‘V`N]<V#Ÿ¡MQhahiM,£_isvOŸ¡MQc<Lx[%RPepV,eb¤

WP¤ e{V%hiVl[J`Se!`d]<V:haM‚[%Rgh‚–PRghicvV‘m8Zi7/@ X 7 šm,£]<_z[S]_¶e(˜kR ž·hi`dV%LNVlq•MPc<`%mPMQL˜²n!ž fRQedepV,q

`d]<LNMPc<OQ] n4y @ + µ¤

‚¤ œepV%haV,[J`SeC`N]vVZ_as<f<c<`–PR,hic<V‘mZ@

X

kmQ£]<_z[S]_ze˜šR žC·ha`NV%LdV,qMQcv`%m‘MQLx˜²n žCfRQedepV,q

`d]<LNMPc<OQ] n4y @ + µ¤

(15)

B

}šs [%RQe{V+WQ¤×R‚mpZi7/@ X 7 _¶e›q‚V%hiV%`dV,q´Ÿ¡LdMQT `N]<VŸ¡LNMPs4`#M,Ÿ`d]<Vn<c? V%LmHR,sq*`N]<Vªep_a¯%VM,Ÿ`N]vV

haM‚[%RghIn<c? V%Lœq4V,[JLdV,RQe{V,e:n‚y*WQ¤}šs*[%RPepV—WQ¤nCmBZi7/@

X

7 C_¶eZq4VhiV%`dV,qˆŸ¡LNMPT™`N]vV›Ÿ¡LNMPs4`M,Ÿ0`N]vV

n<c ?!VL%m RgsqaZi7 ` ' Y @ X 7 ` ! Y C_zef<h¶RQ[JV,q+R,`Z`d]<VV%soq!mepMU`d]<Vn<c? V%Lœep_a¯%VLNV%T+R,_ise

}šs [%RQe{Vr4¤×R—Rgh¶epMvm<_i`LNVT+Rg_ase`N]<VreNR,TUV˜¡`N]<V_isvf<c<`–PRghac<V‘m Z@ X C_¶eep_aTUf<hiy—q‚V%hiV%`dV,qµž\¤

¬H_asRghahiy‘m _is[%RPepVª4¤³n_i`œ_is[JLdV,RQe{V,e#n4y W+˜GZ@ X _¶e•fvhzRQ[bV,q*Rg``N]vVV%soq7MgŸ`d]<V—n<c? V%L%m

£_a`N]<MPc<`x[^]oRgs<OP_is<Or`N]<VZŸ¡LdMQs‚`Jž\¤’”Vxs<M,£2[bMQse{_zq4V%L[%RPepVWP¤×R`dMep]vMg£6R›haM,£:V%L0nMQc<soq!m

R,sq7‚¤³n7`dM—ep]<M,£ER,s7c<fvfµVLnµMPc<sq!¤

ZM,£m<`d]<V#ŸkRQ[J``d]Rg``d]<V–QR,hic<V_as`d]<V#`d]<LNV,e{]<MQh¶qLdV%OQ_¶ep`NVL:_ze X 1TUV,Rgsoe(`N]oRg`x`N]<V%LdV#_ze

RfRg_aLZ<19@

X

1Vkm<_is+`N]vV›haM‚[%RghCnvc? V%L˜¡£]<_z[S]U]RPe nV%VsfoRQeNe{V,q`d]<LNMPc<OQ]e{MQTUVœ`N_iTªVZ_as

`d]<VfRQe{`#%žS¤}šs[%RPepV+WQ¤äR4m X 7 ` ! Y = X 10˜²n‚y*q4Vb·s<_i`d_iMPs7MgŸnV%_as<OU·hi`dV%LNV,q+MQc<`bžSmCR,sq

`d]4ce#`d]<VfoRg_iL Z<19@ X 1V0_zeœR

A 1 /D/I- ADA

"#$ZM,ŸZi7q@ X 7 ZV%so[JV‘m!£]<Vs<V%–‘V%Lx`N]<V—n<c? V%Lre{_i¯%V

q4Vl[JLNV,RPepV,ebmµ`d]<V%LdV›_¶eZR,`ZhaV,RQe{`ZMPs<VMP`N]<VLZ–PRghac<V_is `N]<VhiM‚[RghIn<c? V%Lx`N]R,`#]RQes<MP`#y‘V%`

nV%V%s[JMQsoepc<TUVlq!¤

ZM,£m4Ÿ¡MPL#[%RPepVr4¤nCm<£:Vœ]R%–‘V›`d]<V#Ÿ¡MQhahiM,£_is<O—[bMQse{`NLSR,_is‚`Seq

Zi7 ` ' Y Z

Z A Z 7 `

¥:]<V·LSe{`#[bMQse{`NLSR,_is‚`_ze:nV,[%R,cepV Z@ X C_ze:`d]<V£_is<s<VL%m<£]<_ahiV`N]<Vre{V,[JMQsoq´_¶e nV,[Rgce{V

`d]<VMQc<`df<c<`xepVl« c<Vs[JV#_¶e:TUMQs<MP`NMPs<_z[#R,sqU`N]<VLNVR,LNV 8b¨W#V%hiVTUV%s‚`SeHnV%`{£:VV%sIZi7/@

X

7

R,sq Z@ X xV%s[JV‘m c ' Y ¤ nù_is[JV—`N]vVnvc? V%L_ze_is<_a`N_zR,hi_a¯%V,q7£_i`d]¦`N]<V+e{_is<OPhiV%`dMQsCm

„$@S„išm<_i`\e:hiV%svOQ`N]+_¶e 6%

A

nµMPc<sq4Vlq´Ÿ¡LNMPT RgnM,–‘Vn4y ' Y ¤

50MPs[JV%Lds<_is<O*`d]<V+e{_i¯%VUM,Ÿ`N]vVUMQc<`df<c<`—n<c? V%Lm(MPnepV%Ld–‘VU`N]oRg`—`N]<VUfvLNM‚[JV,edepMPLSe—RgLNV [JMPs<

s<V,[J`dV,q ha_is<VlRgLNhay‘m:MPs<hiy¦`N]vLNMQcvOQ]ß`N]<V,e{V*n<c? V%L\eJ¤E¥:]<_¶eTUV,R,seˆ`d]Rg`ª`N]<VM,£ M,Ÿ>q<Rg`\R_¶e

c<s<_¶q4_iLdV,[J`N_aMQsR,hš¤ ZM,£m _¸ŸRgsUMPc<`Nfvc<`n<c? V%L_zeHŸ¡c<hihkm‘`N]<V#fvLNM‚[JV,edepMPL_zeHŸ¡MQL\[JV,q`dM£R,_i`¤\ZM,£

V%–‘V%Lm £Vr[%Rgs+e{]<M,£ n‚y+e{_iTUf<haV_isq‚c[J`N_aMQsU`d]Rg`_a`Se0MQc<`df<c<`xn<c? V%L:£_ahih V%–‘V%s‚`NcR,hihiyrnV,[JMQTªV

s<MQsv¼Ÿ¡c<hah˜šRPeNepcvTU_is<O `N]R,``N]<V+]<Mùep`_¶e[JMQs‚`N_as4c<MPcephay©[bMQse{c<TU_isvO*q<R,`SRŸ¡LNMPT`N]vVUMQc<`df<c<`

n<c? V%L#M,Ÿ`N]<VrhzRQe{`ZfvLNM‚[JV,edepMPLJžS¤œ¥:]<VfvLNM‚[JV,edepMPL›_¶e `d]4coe _¶q4hiVMQsvhiyUŸ¡MQLRnMQc<soq4V,q*s4c<T—nV%L

MgŸe{`NV%febm<R,sqU`N]<V%LdVZ_¶es<MfM‘edep_an<_iha_i`{yMgŸq4VlRQq4haM‚[^¢ ¤¥:]<VœMQc<`df<c<`:nvc? V%Le{_i¯%Vœ[%Rgsvs<MQ`xR?!Vl[J`

`N]<Vr[JMPLNLdV,[J`NsvV,eNe0MgŸ`N]<V_iTªf<hiV%T—V%s‘`\Rg`N_aMQsCmPn<c<`MQsvhiy—`N]<VrepfV%Vlq ˜¡hzR,`NV%s[byµž\¤}šsUf<L\RQ[J`d_z[JV#`d]<V

ep_a¯%V [%Rgs¦nV*q4V`NV%LdTU_is<Vlq n‚y©V%w‚`NV%soep_i–‘Vªep_aTcvhzRg`d_iMPsC¤ xc<Lf<LdV%hi_aTU_isoRgLNy*LdV,epcvhi`Se_asq4_¶[%Rg`dV

`N]R,`#R–‘V%LdyUe{T+Rghahµs‚c<T—nV%L#˜¡`p£MMQLx`N]<LdV%V#LdV%OQ_¶ep`NVLSe^ž0_¶e:cepcoRghihay+epc‚¹+[J_aV%s‚`%¤

" &"$ $ )(*) . ) $+ $! #" $*/%$

¬<LNMQT ¥:]<VMQLNVTE4mQ£V0s<M,£©]R%–‘V0Rhi_isvV,RgLIRPepy‚s[^]vLNMQsvMQceR,LNL\Rly£]<MùepVTUV%TUMPLNy_ze!nMPc<sq4V,q

n4y '&(')m `d]<VhzR,LNOPV,ep`0fM‘edep_invhiVx£:V%_aOQ]‚`%m‘R#f<LdMQn<haV%T fR,LSR,TUV%`NVL%¤DU:Vl[%Rgce{VMgŸö`N]<_¶eJmQMPc<LepMQhac<

`N_aMQs_zeIs<MQ`0[bMQTUf<haV%`NVhiyTUM‚q4cvhzRgL{X±_¸Ÿ'&(')_is[bLNV,RPepV,ebmQ_i`I£_ihah‘nµVsvV,[JV,edeNRgLdy`dM#LNV,q‚V,ep_aOQs`d]<V

ñ

êçÊbÌ¡Í̲ÑPØSÌCÖ×Ó,Ö×ָ̡Ø^õäõ×Ð%â+*-,/. Ø^ÓPÎZÌ¡Ñ,Íõ×Ê,Ô{ØSõ‘ÏgÈ10ùÍpËIÖ×ÚCÖ×Ó,Ö×ָ̡ØSõ×Ö32{ÍdÎ2GCÖ×Ì¡Ñ K FM

(16)

B A B=A A A A

f<LNM‚[bV,eNe{MQL%¤\xMg£V%–‘V%Lmg£Vx[%Rgs—cepVx`N]vV#R,f<f<LNMùRQ[S]`d]Rg`£RPeáfvLNV%–‚_iMPcephayce{V,q>Ÿ¡MPLq4V%LN_a–4_as<OR

f<c<LdVxepyvep`NMPhi_¶[RgLNL\R%y›Ÿ¡MQL0`d]<Vxq4V%se{V¢4soRgfedRQ[S¢f<LdMQn<haV%TjYœ~C’߆g‡iš¤}kŸ £V:]R%–‘Vf<LdM‚[JV,eNe{MQL\e

£_i`d]n<c ?!VL:e{fRQ[bVZŸ¡MQLMQs<hay7fRg_aLSeJm‚£:Vœep_aTUf<hiyr[JMPs4·OPc<LNV<')#6f<]‚yvep_z[Rgh<f<LdM‚[JV,edepMQL\e:`NM

ep_aTc<h¶Rg`dV:MQsvV›fvLNM‚[JV,edepMPL%¤ n‘_is[bV#R,hih`N]<V ')#!–PRghac<V,e:R,LNV#¢‚s<M,£sU£]<Vs7Rf<LNMPn<hiVT®_¶eáhaM‘RPq4V,q!m

£:Vu[%RgsªRgh¶epMrq4V%`dV%LNTU_as<V˜¡M@?+ha_is<VQžöRZŸ¡V%£¦n<_i`\eHMgŸö[JMPs4·OPc<LSR,`N_iMPsU_is‚Ÿ¡MQLNT´Rg`N_aMQsr£]<_z[S]_as4Ÿ¡MQLdT+e

`N]<VrK0° £]<V%`d]<V%L_a`_ze:`NM—fR,LN`N_¶[J_ifoRg`NV•RQ[J`d_i–‘V%hayM,Ÿep_aTUf<hiy—[bMQs‚`NLN_an<c<`dV#_i`\e TUVTUMQLdyU˜²_a`x[%Rgs

nVV,RPep_ahiyep]vMg£s `N]R,``{£:M n<_i`\e›R,LNVUVs<MQc<OP]”Ÿ¡MQhahiM,£_isvO7`N]vVha_is<V,e#M,Ÿ ³Y#~C’߆g‡i¡žS¤3n‘c[S]

Rgs RgLdLSR%y*£_i`d] 8Uf<LdM‚[JV,eNe{MQL\eJm[bMQs4·OPc<LNVlq”_is‚`NM RULN_as<O<mI[%R,s¦epMPhi–‘V—Rgs‚y*f<LdMQn<haV%T­_asep`\Rgs[JV

_is±˜¡s<MQ`dV+`N]R,``d]<_ze_ze`N]vV£MQL\ep`—[%RPepV+LNV,e{c<hi`bž

W8 2

4

#6587

9')#6 ¨fRQedepV,eb¤¦¥:]<V+£:MPLSep`—[RQepV

LNc<svs<_is<O`d_iTUVx_ze:`d]<V%slOr˜

2

ž\m<£][J_a]_¶e:MQf<`d_iT+R,hš¤

´#,"”0$U”

}šs `d]<_zefoRgfV%L%m£:V+]R%–‘VUce{V,q¦epMQTªV–‘VLNyMQhzq©_¶q4V,RQe`NMq‚V%LN_a–‘V+R”e{fRgL\epVRghiOPMQLd_i`N]vT Ÿ¡MQL

`N]<V•q4y4soRgTU_¶[:f<LNMPOQLSR,TUTU_as<O#`NVl[^]<sv_z«‘c<V Ÿ¡MPLe{MQhi–‚_isvO`N]vV#OQV%svV%LSR,h!¢‚sRgfedRQ[S¢fvLNMQnvhiV%T*¤I¥:]<V

nRQe{_z[_¶q4V,R_¶eZ`N]<VŸkRQ[J``d]Rg`#`d]<V—[JMùep`ZŸ¡c<so[J`N_aMQs*_zexTUMQs<MP`NMPs<_z[& 7#ƒQ†/kmCRgsq7_a`epc‚¹+[JVleZ`NM

[%Rgh¶[Jc<h¶Rg`NVª_i`MQsvhiy¦R,`U[JVLN`SR,_is /$&%(' %/D

B

"#%9'

A

m0_š¤V‘¤imfMP_is‚`Se£]<V%LNV+`d]<VUŸ¡c<s[J`d_iMQs¨[S]RgsvOQV,e

–PRghicvV‘¤LU:Vl[%Rgce{VMgŸu`N]<_¶eJm!`d]<VˆŸ¡cvs[J`N_aMQs[%R,s”nVLdV%f<LNVlepV%s‚`NV,q RQerepV,«‘c<V%s[bV,e M,ŸfR,_iL\eJ¤¥:]<V

epV,«‘c<V%so[JV,e:R,LNV‘m<MPs+`N]<VrR%–‘V%LSR,OQV‘m<T—c[S]Ue{]<MQLd`NV%L`d]Rgs `N]<V¢‚sRgfoeNRQ[S¢+[%R,fRQ[b_i`{y‘m<R,sqU`N]<_¶e:_ze

`N]<Vr¢‘V%yU`dM`d]<V_aTUf<LNM,–‘V%T—V%s‚`0MgŸ0`d]<VR%–‘V%L\RgOQVrLNc<svs<_is<O—`N_aTUV‘¤pZMQLdM,£_i`N¯>Rgsq n Rg]<s<_I]R%–‘V

f<LNVlepV%s‚`NV,qV%w‚`NV%soep_i–‘VVTUf<_iLd_z[%R,h<qvRg`SR`dM—epc<fvfµMPLN``d]<_zeŸkRQ[J`0Ÿ¡MQL`N]vVepfR,LSe{V„NMùWR,hiOQMPLN_a`N]<T*m

Rgsq7MPc<L#f<LdV%hi_aTU_isoRgLNyªep_aTcvhzRg`d_iMPse:[JMPs4·LdT­`N]oRg`#`d]<_ze_ze#R,hze{MU`NLdc<V›Ÿ¡MPL#`N]<VrOQV%svV%LSR,hHf<LdMQn<

hiV%T¤YZhze{MsvMQ`NV—`N]oRg`rep_as[JV`N]vVf<LNMPn<hiV%T _ze #Kß[JMQTªf<hiV%`dV‘m`N]<V % "#$

A

'/D

A

-Z`d_iTUVr_ze#e{`N_ihah

V%w‚fµMPs<V%s‚`N_¶Rgh˜¡fRg`d]<MQhaMQOP_z[%R,hHV%wvRgTªf<hiV,e0[%R,s+nµVrV,RQe{_ihayU[JMPsep`dLNc[b`NV,qI50]‚– Q„¡žS¤0YZs R,sRghay4`d_z[

ep`dcq4yUM,Ÿ0`N]<VrR%–‘V%L\RgOQV•[%RQe{V[JMPTUf<hiVw4_a`pyr_ze:`d]<Vrepc<n<|{V,[b`:MgŸáMQc<LxMQs<OPMQ_as<O£MQLd¢!¤

YZs<MQ`d]<V%Lx[JMPs4`dLN_an<c<`N_aMQsUM,Ÿ0`N]vV#fRgfV%Lx_ze:`d]<Vrepyvep`dV%T+Rg`d_z[xq4V%Ld_i–PRg`d_iMQs+M,Ÿ`d]<VrRghiOPMQLd_i`N]vT+e

n4y*`dLSR,se韡MPLNTU_as<O+`N]<VUMPLN_aOQ_isoRgh:LdV,[Jc<LdLNV%so[JVV,«‘cRg`d_iMQs _is‚`NM ep`dLNV,R,T Ÿ¡c<so[J`N_aMQsR,h:f<LdMQOQL\RgT+eb¤

xc<L q4V%LN_a–PRg`N_aMQsß_ze+RghaTUM‘e{`+TUV,[S]Rgs<_¶[%RghkmRgsoq f<LNM,–‚_zq4VleR¦f<LNM‘M,Ÿ—MgŸª[JMPLNLdV,[J`NsvV,eNeUMgŸ>`N]<V

q4V%Ld_i–‘V,qf<LNMPOQL\RgT+eb¤

¬H_isR,hihay‘m:£:V*]oRl–‘Ve{]<M,£s ]vMg£ `N]<Ve{`NLdV,RgT Ÿ¡c<so[J`N_aMQsR,h#f<LNMPOQL\RgT+eU`N]oRg`+£:Vq4VLN_i–‘Vlq

[JMQcvhzq”nV+_iTUfvhiV%TUVbs‚`NV,q7MPs R7£uR%–‘VJŸ¡LNMPs4`>RgLNL\R%y©f<LNM‚[bV,eNe{MQL%muRgs¨RQe{y4s[S]<LdMQs<MPceˆfvLNM‚[JV,edepMPL

RgLdLSR%y‘m0£]<V%LNV V,RQ[S]¨K0° ]RQe·w‚V,q TUVTMPLNy‘mI_isq4VfµVsq4V%s‚`MgŸfvLNMQnvhiV%TfoRgLSR,TUV%`dV%LSeb¤¦}és

epc[S]¦R,s R,LNL\Rlyùmf<LNMPn<hiV%T´e•£_a`N]©h¶RgLdOQV%LfR,LSR,TUV%`NVLSeep_a¯%V,eR,LNV ep_aTUf<hay*epMPhi–‘V,qn4y RQq<q‚_is<O

TUMQLdVf<LNM‚[bV,eNe{MQLSebm4MPL:LNVcep_as<O`N]<VedRgTUVxR,LNL\Rly_asT—c<ha`N_ifvhiV:foRQeNe{V,eJ¤0}šs—MQL\q4V%L:`dMrq4M`d]<_ze0£:V

f<LNM,–‘V`N]oRg`#`d]<VhaV%s<OQ`d]eZM,Ÿ0`N]<Vnvc? V%LSeZ_as*R,LS[S]<_i`dV,[J`NcvLNV#_¶e#Rgha£R%y<enMQc<soq4V,q!¤¥:]<_¶e L\Rg_¶epV,e

Rgs+_is‚`NVLNV,e{`N_isvOMQfV%s «‘c<V,e{`N_iMPsC¤0}š`:_¶e:£:V%hahµ¢‚s<M,£s+`N]R,`Zh¶Rg¯%yªep`dLNV,R,T®Ÿ¡c<s[b`N_iMPsRgh f<LNMPOQL\RgT+e

³¬H’ Tlƒkm:[JMPLNLdV,epfMQsoq±RghiTªM‘ep`TªV,[^]oRgs<_¶[%Rghahiy7`dM©s<V%`{£MQLN¢veMgŸ•f<LNM‚[JVleNepVle[JMPTUT—c<s<_z[Rg`N_as<O

`N]<LdMQc<OP]·<Ÿ¡M>[^]R,s<s<V%h¶eRg] T‡šm‘`N]vV,epVœRgLdV#s<MQ`LNV,R,hi_¶ep`N_¶[:nV,[%RgcoepV#`d]<VZfvLNMQnvhiV%T M,ŸIf<LNM,–‚_is<O

nMQc<sqve MPsnvc? V%LhiV%svOQ`N]oe:_ze(cvsq4V,[J_¶q<RgnvhiV ’©RPqg‡k¤H’V›£V%LNVœepco[%[JV,ede韡c<hC_asUf<LNM,–‚_is<Or`N]<V

Références

Documents relatifs

Unite´ de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unite´ de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP

Unite´ de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unite´ de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP

Unite´ de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unite´ de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP

Unite´ de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unite´ de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP

Unite´ de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unite´ de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP

Unite´ de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unite´ de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP

Unite´ de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unite´ de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP

Unite´ de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unite´ de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP