• Aucun résultat trouvé

Characterization of program dependecies by integer programming technique

N/A
N/A
Protected

Academic year: 2021

Partager "Characterization of program dependecies by integer programming technique"

Copied!
22
0
0

Texte intégral

(1)

HAL Id: inria-00074534

https://hal.inria.fr/inria-00074534

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.

Characterization of program dependecies by integer programming technique

Yvon Jégou

To cite this version:

Yvon Jégou. Characterization of program dependecies by integer programming technique. [Research Report] RR-2138, INRIA. 1993. �inria-00074534�

(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 AUTOMATIQUE

Characterization of program dependencies by integer programming techniques

Yvon J´egou

N˚ 2138

Novembre 1993

PROGRAMME 1

Architectures parall`eles, bases de donn´ees, r´eseaux et syst`emes distribu´es

(3)
(4)

, - -. /01#2%

3#46587:9;

<>=

58?

@BADCFEGAIH*JKJMLNOQPRAISDTVUXWYLSZWY[VADL]\^8H*A_H*`X`baL]`XL]\c>d8He\YL]\f>Lf>CGgVg/hL]Li\cVAVhL]\YLjH*[>kL]WR\Yl>\YWaL]JML]\fmUn\DWYADUndo[hL]\

@BAYCpZL]WqPrsq/@tPu

uH*^o^8CGAYWf>LAYLjSYToL]AISDTVLvgw>xVNjyFz{OQ|/C*}FLiJvdVAYLN~F~GyONjz^8H*EGL]\

€+i‚jƒ*„8…*‚G†M‡ˆg>WYL]EGL]A^VADCFEGAIH*JKJMUXgVEWYLSDTVgoUŠ‰G[VLi\S]H*gvdtL/[V\YLjfvUXgWDTVLSDT8H*A_HFS_WDL]AYUX‹HeWYUXCFgKC*Œ6AYL]`HeWYUXCFgV\

dtL]WˆŽL]L]gWYTVL}FH*ADUŠHedV`XL]\C*Œ^VAYCGEFA_H*JM\j’‘>[tSYT0WYLSDTVgVU‰G[VL]\HeAYLS_CGgV\YUf>LiAYLf0WYCKd8LŒˆH*A/WYC>CKL_kV^8L]go\YUX}FL

WDCvd8L[V\DLf#UXgHeg“He[VWYCGJHeWYUSCF^VWDUXJMUX‹]UXgVEWYC>CF`ˆ•”"L\YTVC*Ž:WDT8H*W/WDTVLS_CF\DWCeŒ–\Y[tSYTHWDLSDTVgVU‰G[VLS]Heg

dtLd8He`ŠHeg8S_Lf“d—lKWYTVL‰F[tH*`XUXWˆlvC*ŒWYTVL$UngmŒ˜CFADJH*WDUXCFgWYT8HeWS]Hegd8L$L_kVWYAIHGS_WYLjf6™R[VAHe`XEFCFADUXWYTVJ'WDAIHegV\ˆš

Œ˜CGAYJK\–\DL]WY\/CeŒ›Lj‰F[tH*WYUXCGgV\Heg8fvS_CGgV\YWDAIH*UXg>WY\WYTtH*W’HeAYLLZkmWDAIHGS_WYLfœc>d—lWYToLCF^oWYUXJMUX‹]UXgVES_CFJK^VUX`nLiAcjŒ˜ADCFJ

^VADCFEGAIH*JK\Heg8fv^oAYCVf>[8S_Li\HSYTtH*AIHGS_WYLiAYUX‹H*WDUXCFg#C*ŒBWYTVL\YCG`X[VWYUXCFg#f>CFJ#H*UXgC*Œ–WDTVL\Yl>\YWDL]J•ž/TVLAYLi\Y[V`XW

UX\HAYL]\DWYADUŠSZWYLf"f>CGJHeUngKC*Œ’^tCF\D\YUXdV`XL}FHe`n[oL]\/Œ˜CGALHGSDT}FH*ADUŠHedV`XLH*\ŽL]`X`H*\Hv\YLiWCeŒgVL]ŽŸ^tL]ADWYUXgVL]g>W

S_CGgV\YWDAIHeUng>WD\ž/TVL\Yl>\YWDL]J UX\RAY[VgUXg8SZAYL]JKL]g>WIH*`X`XlvŒ¡AYCFJWYToL,S_CGJM^VUX`XL]Aj/‡ˆWY\H*^V^V`XUS]HeWYUXCFgf>CGJH*UXgKUn\

gVCGW`XUXJMUXWYLf“WYCWDTVLMS_CFJK^V[VW_H*WYUXCGgC*Œf>Li^8L]gtf>L]g8S_UXL]\j‡ˆgŒbHGS_Wc•UXWS]Heg"d8Lv[V\DL_Œ˜[V`L]}GL]AYl>Ž/TVL]ADL#WYTVL

f>LjS_UX\YUXCFg"CeŒWDTVLS_CGJM^VUX`XL]Af>L]^tL]g8f>\CFg"WDTVLMSDT8H*A_HFS_WDL]AYUX‹HeWYUXCFg¢C*Œ/AYL]`H*WDUXCFgV\dtL]WˆŽ’LiL]g£}FHeAYUH*dV`XL]\CeŒ

WDTVL^VADCFEFA_H*J

¤K¥>¦6§Y¨©tƒFªB*†«f>L]^tL]g8f>L]gtS_UXL]\c6UXg>WYLiEFL]A/^VADCFEGAIH*JKJMUXgVEtc¬SZCFgV\DWYAIHeUXg—WD\coCF^VWDUnJKUX‹H*WDUnCGgV\

­®v¯

°b±ˆ²³

¯

°+´–µX±ˆ¶ˆ·_¸

Unit´e de recherche INRIA Rennes

IRISA, Campus universitaire de Beaulieu, 35042 RENNES Cedex (France)

(5)

0 !% +1“2%'! - vQ%2%'$ %

¥m ¥:† r6Li\WDLSDTVgVU‰G[VL]\vf>LM^VADCFEGAIH*JKJHeWYUCGg#\Y[VA`XL]\L]g>WYUXL]AD\v^8Li[V}FL]g>WL]WYADLM[VWDUX`nUX\VhL]L]\vfVH*gV\

`HMSZAIHFSZWVhL]ADUn\_H*WDUnCGg£f>L]\AYLi`ŠHeWYUXCFgo\Lig—WDAYLv`XL]\R}FH*AYUHedV`XL]\L]g>WDUbaLiAYL]\vf>L]\^VADCFEFA_H*JKJML]\jc>L]W^V`X[V\^8H*ADWYUS_[>š

`XUbaL]AYLiJML]g>WfoH*gV\`XLS]He`ŠSZ[V`f>L]\fhL]^tL]g8fVHeg8S_L]\j0H*UX\CGgS_CFgo\YUf6aL]ADLvL]gEhL]g/hL]A_H*`‰G[VLvS_L]\WDLSDTVgVU‰G[VL]\

\DCFg>W/WYADCF^SZC[VWDL][V\YLi\^tCF[oAL]WDAYLUXg>WVhLiEFAVhLiL]\fVHegV\/`XL]\CF[VWDUn`X\/H*[VWDCFJ#H*WYU‰G[VL]\jF|/CG[V\/JMCGg>WYAYCGgV\’‰G[VLS_L

S_C[VW^tL][VWL]WYADLp_[o\YWYUhLv^tH*A`H#‰G[8H*`XUXWVhLvf>L]\ADL]`H*WDUnCGgV\‰G[VU^tL][V}GL]g>WLiWYAYLK^VAYCVf>[oUnWDL]\B|/CGWYADLMH*`XEFCeš

ADUnWDTVJMLWDAIH*go\ˆŒ˜CGAYJMLf>Li\L]gV\DL]JvdV`XL]\fYhL‰G[8H*WDUnCGgV\/L]Wf>LS_CGg—WDAIHeUng>WDL]\L_kVWDAIH*UXWDL]\^8HeA`XLS_CFJK^VUX`H*WYLi[VA

L]Wv^oAYCVf>[VUXWv[VgVLS]HeAIHGS_WVhL]ADUX\IH*WDUXCFg:f>[:f>CFJ#H*UXgVLMf>L#\DCF`X[VWYUXCGgV\,fm[£\Yl>\DWaL]JKLF’qLKAVhL]\D[V`XWIH*W#S_CFg>WDUnLig—W

[VgoLADL]\YWDAYUS_WYUXCGg f>Li\“fmCFJHeUXgVL]\vf>L}FHe`XL][VAY\#f>L]\#}FH*ADUH*dV`XL]\MHeUngo\YU‰G[[Vg L]gV\YLiJvdV`XL“fmLgVCG[V}FLi`n`XL]\

S_CGg>WYAIHeUXg—WDL]\^V`X[V\^8LiAYWYUXgVLig—WDL]\•qL]WH*`XEFCGAYUXWYTVJKL^tL][VWL]WDAYLMH*^o^8L]`jhLvf>LJH*goUbaLiAYLUXg8S_AVhLiJML]g>WIHe`XL^8H*A

`XLS_CGJM^VUX`H*WDL][VA*‘>CGgMf>CFJ#H*UXgVL’fHe^V^V`XUS]H*WDUXCFggL]\DW^8He\`XUnJKUXWVhL’He[\DL][V`6S]H*`S_[V`6f>L]\/fhL]^tL]g8foH*g8S_Li\>‡ˆ`

\DLAVhL]}›aL]`XL[VWDUX`nL/^tH*AYWDCF[VWCœa[M[ogMSYToCFUkfm[MS_CFJK^VUX`ŠHeWYL][oA+fhL]^8Lig8f#f[VgVLS]HeAIHFSZWVhL]ADUn\_H*WDUnCGgf>LRAYL]`HeWYUXCFgV\

L]g>WDAYLf>Li\}FH*ADUH*dV`XL]\j

©t‚¬i§I…¥† fhL]^8Lig8f>L]g8SZL]\c•^VAYCGEFA_H*JMJ#HjWYUXCFgL]g>WYUˆaL]ADLFcV\Dl>\YWaLiJML]\f>LS_CFg>WYA_H*UXg>WYL]\jcVCG^VWYUXJMUX\_H*WYUXCGg

(6)

4 5 K!2/

Heg>l:CF^VWDUXJMUX‹H*WDUXCFgV\^8LiAˆŒ˜CGAYJMLjf:d>l«JMCVf>L]ADg S_CGJM^VUX`XL]AY\#H*ADLd8He\YLfCGg H ^VAYLjS_UX\YL£H*gtH*`Xl>\YUX\MCeŒ

WDTVLJKL]JMCGAYl£HGS]S_L]\D\YL]\UXgV\DUf>LWYToL^VADCFEGAIH*JK\Bž/TVLCF^oWYUXJMUX‹HeWYUXCFgV\$Ž’L"H*ADLUXg—WDL]AYLi\YWYLjfUng:S_C*}GL]A

}GLS_WYCGAYUX‹HeWYUXCFgscj^8HeAIHe`n`XL]`XUX‹HeWYUXCFgsc_WDTVLL_kV^V`XCFUXWIHeWYUXCFgC*Œ6fVH*W_H/AYLi[V\YLFc>fVHeWIH/`XCVS]He`nUXWˆlO WDL]JM^tCFA_H*`>H*\BŽ’Li`n`

He\’\D^8HFS_UHe`VOŸcG`nC>CG^vAYL]CGAIf>L]ADUXgVE8cVfVHeWIHfmUn\DWYADUndo[VWYUXCFgMHeg8fv`XC>CF^MfmUn\DWYADUndo[VWYUXCFg•*P SDT8HeAIHGS_WYL]ADUX‹H*WDUnCGgMCeŒ

WDTVLAYLi`ŠHeWYUXCFgo\/d8L]WˆŽL]L]g0JML]JKCFAYlHFS]S_Li\Y\YLi\UX\/gVL]Lf>LjfKŒ˜CFA/H*`X`6WDTVL]\YL$WYAIHegV\ˆŒ¡CFAYJ#H*WDUnCGgV\

‡ˆgKWYTVL 8AD\YW/EGL]gVL]A_H*WYUXCGgCeŒ–CG^VWYUXJMUX‹]UXgVES_CGJM^VUX`XL]AD\c*WDTVLf>L]^tL]g8f>L]gtS_LMH*g8He`Xl—\DUX\WYLSDTVgoUŠ‰G[VLi\ŽL]AYL

CGAYUXL]g>WYLfWDC*ŽHeAIf>\WYTVLf>LiWYLS_WDUXCFgvC*Œ6}FLjS_WYCGA’S_CVf>L]\jc—Heg8fŽL]ADLd8He\YLfCGgWDTVLS_CFJK^V[VW_H*WYUXCGgC*Œ8\DUXJM^V`XL

ADL]`H*WYUXCGgV\G‡ˆgJKCVf>L]AYgv\Dl>\YWYLiJM\ceWYTVLR`nC>CG^,S_CGg>WYAYCG`V}FH*ADUH*dV`XL]\f>CgoCFW’f>L 8gVLWDTVL/[VgVU‰G[VLf>UXJKL]gV\YUXCGgV\

CeŒmWDTVL\Dl—\DWYL]JK\*™R[VAsEGL]gVL]A_H*`XUX‹]LffmL]^8Lig8f>L]g8SZlWYL]\DWS_CFJK^V[VWYLi\6WYTVLADL]`H*WDUnCGgV\sdtL]WˆŽL]L]gWYTVL}FH*AYUHedV`XL]\

CeŒœHR\Yl>\DWYL]J [Vg8f>L]AH\DL]WCeŒ›S_CFgo\YWYA_H*UXg>WY\j*ž/TVL]\DL}FH*ADUH*dV`XL]\BS]H*gd8L/`XC>CF^S_CFg>WYADCF`ˆcj^VAYCGEFA_H*JŸ\Dl>Jvd8CG`n\jc

S]Heg"AYL]^oAYL]\DL]g>WM\Y[odV\YL]WD\CeŒWDTVLMUXg8fmL_k \D^8HFSZLvC*ŒH*g"H*ADAIHjl>c6CFAS]H*g"ADL]^VAYLi\YL]g>WvCFWDTVL]A}FHe`X[VL]\UXgWYTVL

WDL]\YWj8ž/ToL{He^V^V`XUS]H*WDUXCFgfmCFJHeUXgCeŒ+WDTVLf>L]^tL]g8f>Lig8S_lSDT8HeAIHFSZWYL]ADUn‹jH*WYUXCGgL_kVWYL]gtf>\gVC*Ž WYC

6

}FLSZWYCFADUX‹H*WDUnCGgH*g8fK^8HeAIH*`X`XL]`XUX‹H*WDUXCFg

6

fVH*W_H^tH*AYWDUXWYUXCFgVUXgVE“Œ˜AYCGJ Heg«UnWDL]AIHeWYUXCFg"\D^8HFSZL^8H*ADWYUXWYUXCGgVUXgVE8s™Rg8SZLH*g¢UnWDL]AIHeWYUXCFg"\D^8HFSZLT8H*\

d8LiL]gf>UX\YWDAYUXdV[VWDLf#CGg“H$^8HeAIH*`X`XL]`6\Dl—\DWYL]JcVUXWd8LSZCFJMLi\^tCF\Y\DUXdV`XLWDCMf>Lf>[tS_LH^8HeAYWYUXWDUnCGgVUXgVECeŒ

WYTVLfVH*W_HŽ/TVUSDT#UXJM^VADC*}FL]\`XCVS]He`nUXWˆlvUXgMWDTVLWDAIH*go\ˆŒ˜L]AD\

6

UXWYL]A_H*WYUXCGgv\Y^8HGS_L^8HeAYWDUnWDUXCFgVUXgVERŒ˜ADCFJ H$fVH*W_HfmUn\DWYADUndo[VWYUXCFg•*‡ˆgMWDTVUX\’S]H*\DLFcGWYTVLfVH*W_HH*ADLH*`XAYLHGf>l

f>UX\YWDAYUXdV[VWDLfHGS_AYCG\Y\WDTVLJML]JKCFAYUXL]\j>P\UXg#WYTVLv^VADL]}>UXCF[V\S]H*\DLFc6WYToL`XCVS]H*`XUXWˆlMCeŒ’WYToL,HGS]S_L]\D\YL]\

S]H*g#dtLUXg8S_ADLH*\DLf#d>lHegHFSiS_[VAIHeWYL^tH*AYWDUXWYUXCFgVUXgVEC*ŒBWYTVL$UnWDL]AIHeWYUXCFgK\Y^8HGS_L

6

UXJM^VADC*}—UXgVEfVH*W_HAYLi[V\YLFo”:TVL]gvWDTVL\_H*JKL/L]`XL]JML]g>WCeŒ–H*gMHeAYAIHjlUX\’HFSiS_L]\Y\DLf#J#H*g>lWYUXJKL]\BUngMH

`XC—CG^gVL]\DWc*WDTVLS_CGJM^VUX`XL]A6WYADUXL]\BWYCAYL]\DL‰G[VL]g8SZLWDTVL`nC>CG^gVL]\DW–UXgCFA_f>L]ABWYCdVADUngoEWYToL]\YLHGS]S_L]\D\YL]\

S_`XCF\DL]AUXgMWDUXJMLF>‘>[8SDTH$WYA_H*gV\Œ˜CFADJH*WDUXCFgvCF^oWYUXJMUX‹]L]\WYToLJKL]JMCGAYlTVUXL]AIHeAISDT>lM[VWDUX`nUX\_H*WYUXCGgs

6

UXJM^VADC*}—UXgVEfVH*W_H"`XCVS]H*`XUXWˆl—Bž/ToLCF^VWDUXJMUX‹]L]AMS_CGJM^V[oWYL]\vWDTVL\D[VdV\DL]W#C*ŒWDTVLUXWYL]A_H*WDUnCGg:\Y^tHFS_L

Ž/TVUSDT“SZCFg>WIHeUngo\HFS]S_Li\Y\YLi\WDCvJML]JKCFADl`XCmSiH*WYUXCGgV\/WYT8HeWH*ADL{SZ`nCG\YLWYCvLjHFSDTCFWDTVL]Aj

0H*g>lHe[VWYTVCGAY\T8Hj}GL\YWD[8f>UXLf0WYTVLvf>L]^tL]g8f>Lig8S_lWYL]\DW^oAYCFdo`nLiJc87:9’Heg8zFzocV”"CG`Œ¡LzF~>c;9’HegV”"CF`z$<Gc

”£He`n`HGS_LzFz>cG@B[VEFTt~VN=Y$>\Y[8He`X`nl>cjWYTVLi\YLWDL]\YWD\/Ž’LiAYLLiUnWDTVL]A/H*^V^oAYCjkVUXJH*WDLfWDL]\YWD\’CGA’fVH*W_Hf>L]^tL]g8fmL]g8S_l

CGAYUXL]g>WYLf WYL]\DWY\ž/TVLS_CFJK^V`XL_kVUXWˆlCeŒWYToL“He`XEFCFADUXWYTVJ Ž/H*\MH*g¢UXJM^tCFAYW_H*g>WŒbHGS_WYCGA #CFADLADLS_L]g>WD`nl>c

WDTVL[V\DLC*ŒEFL]gVLiAIH*`RUXg—WDL]EFLiAv^VAYCGEFAIHeJMJKUngoEWDLSDTVgVU‰G[VL]\KT8Hj}FL#dtL]L]g:^VADCF^tCF\DLf6ž/ToL“He^V^V`XUS]H*WDUXCFg

f>CGJHeUng«CeŒWYTVLWYLi\YWUX\MgoC `XCGgVEFL]AK`XUnJKUXWYLf¢WYC«f>L]^tL]g8f>Lig8S_lŸf>L]WDLS_WDUnCGgscHeg8f:LZkmWDL]g8f>\jc/gVC*ŽcWYC

WDTVLCG^VWYUXJKUn‹jH*WYUXCGg"C*ŒHFS]SZL]\Y\DL]\WYC"WDTVLJML]JKCFAYlTVUXL]A_H*AISDT>l>’™R[VAM\DCF`X[VWDUnCGg«d8L]`XCGgVEF\KWYC"WYToUn\K`H*\YW

S]HeWYL]EGCFADl—;9LSiH*[V\DLWDTVLS_CG\YWCeŒ+Heg—lKUXg—WDL]EFLiA^VADCFEFA_H*JKJMUgoEWDLSDTVgVU‰G[VL]\f>L]^tL]g8fm\\YWDAYCGgVEF`XlMCGg#WYTVL

g>[VJvdtL]AC*Œ}FH*ADUH*dV`XL]\jc6WYTVLHe`nEGCFADUnWDTVJM\WDT8H*WTtHj}FLMdtL]L]g«^VADCF^tCF\DLf¢\YC0ŒbH*AWDAYl¢WYCJKUngoUnJKU‹]LWYToUn\

g>[VJvdtL]ACeŒ’}FH*ADUH*dV`XL]\RUng0WYTVL\Yl>\YWDL]J6™R[VA\YCG`X[VWYUXCFg0Un\RgVCFWd8He\YLf0CFg0\Y[8SDT"HMJKUXgVUXJvU‹HeWYUXCFgsc>H*gtf

UXg#JHeg—lMSiH*\YLi\ctgVL]ŽŸHeAYWYU›SZUŠHe`6}FH*ADUŠHedV`XL]\/H*AYL$Ung>WDAYCVf>[8S_Ljf#d8LjS]H*[V\DLWDTVL]UXA^oAYL]\DL]g8S_LMS]HegHFS]S_Li`nLiAIH*WDL

WDTVLSDT8H*A_HFS_WDL]AYUX‹HeWYUXCFg#CeŒ+WDTVL\YCG`n[oWYUXCFgV\j

ž/ToLvgVL_kVW\YLjS_WYUXCFg¢\YTVC*Ž/\$TVC*Ž WYTVLv\Dl—\DWYL]J.Ung>WDL]AIHGS_WY\Ž/UXWYT£H#S_CFJK^VUX`XL]ARŒ˜AYCGJ WYToLMS_CFJK^VUX`nLiA \

^tCFUXg>WC*Œ’}>UXL]Žtž/TVL]g"ŽL,fmL]\IS_ADUXd8LKTVC*Ž WYTVLvLj‰F[tH*WYUXCGgV\Heg8fWDTVLMS_CGgV\YWDAIH*UXg>WY\HeAYLvAYLi^VAYL]\DL]g>WYLf UXg

(7)

\DLS_WYUXCGgMyHeg8f$TVC*Ž"WYTVLi\YLHeAYLWYA_H*gV\ Œ˜CFADJMLf$UXg\YLSZWYUXCFg ¬‘mLS_WYUXCGg H*`X\DCADL]^tCFAYWD\CFgWYToL’L_kVWDAIHFSZWYUXCFg

CeŒ+UXg>Œ¡CFAYJ#H*WDUnCGgŒ¡AYCFJ WYTVL\Yl>\DWYL]J f>[oAYUXgVEWYTVLWDAIHegV\ˆŒ˜CGAYJ#H*WYUXCGgV\

*#% $ *R! !"$!$/( $/

qT8HeAIHGS_WYL]ADUX‹]UXgVEWYTVL’fmL]^8Lig8f>L]g8SZUnLi\’dtL]WˆŽL]L]gWˆŽ’CRJML]JKCFAYl/HFSiS_L]\Y\DL]\/S_CFADAYL]\D^8CGg8f>\BWYCSYTtH*AIHGS_WYLiAYUX‹]UXgVE

WDTVL/\YCG`n[oWYUXCFgC*Œ6H*gUng>WDL]EFL]AB`XUXgVLHeAs\Yl>\DWYL]J Ž/UnWDTS_CGgV\YWDAIH*UXg>WY\j*ž/TVLL‰G[8H*WDUXCFgV\BC*ŒtWYTVL\Yl>\YWDL]JŸLZkm^oAYL]\D\

WDTVLLj‰F[tH*`XUXWYUXL]\vWYTtH*WMJv[o\YWvdtLH*\D\YL]ADWYLfUXg«CFA_f>L]AMWDC HGS]S_L]\D\WYTVL0\IH*JKL#JML]JKCFAYl`XCVS]H*WDUnCGgsBž/TVL

S_CGgV\YWDAIHeUng>WD\v`nUXJKUnWRWYTVL#f>CFJ#H*UXgCeŒWYToLS_CGJM^V[VW_H*WDUnCGgstž/TVLS_CFgo\YWYA_H*UXg>WY\vH*ADLML_kVWYA_HFS_WDLf Œ˜AYCGJ WYTVL

`XC>CF^#H*g8fKWYToL}FHeAYUH*do`nLfmLS_`H*A_H*WYUXCGgV\>‡ˆg#\YCGJMLS]H*\DL]\coWYTVL]l#S]H*gHe`n\DCdtLf>Lf>[tS_LfKŒ˜ADCFJ He\Y\DL]AYWDUnCGgV\

CGAS_CFg8fmUnWDUXCFg8He`6Ungo\YWYAD[8S_WDUnCGgV\

oCFAUXgV\YW_H*g8SZLFc8S_CGgV\YUf>LiAWYToLŒ˜CF`X`XC*Ž/UXgVE^VAYCGEFA_H*J Œ˜A_H*EGJML]g>W

!

"

# $

%'&(

)*,+-

%'&.

)/+0)1

&.

'

,+2

%'&.

/)*3+

4.

4.

PR\H tAY\YW\YWDL]^MUXgvWDTVLCG^VWYUXJMUX‹HeWYUXCFgCeŒsWYTVL]\DL\DL‰G[VL]g>WYUH*`t`XC>CF^V\jcFWDTVLHFS]SZL]\Y\DL]\WDCWYTVLH*ADAIHjl

%

Jv[V\DW

dtLH*gtH*`Xl>‹]Lf6>ž/TVLWDAIH*go\ˆŒ˜CGAYJHeWYUXCFgo\WYT8HeWH*ADL^tCF\D\YUXdV`XLCFgKWYTVL`XC>CF^V\f>Li^8L]gtf 8AY\DW/CFg#WYToL{fmL]^8Lig>š

f>Lig8S_lCFgWYTVL]\DLMHFS]SZL]\Y\DL]\B”"LSZCFgV\DUŠfmL]ATVL]ADLvWYTVLAYLi`ŠHeWYUXCFgo\dtL]WˆŽL]L]g

%'&.

5)*/+

Heg8f

%'&.

/)3+



ž/TVLv\DL]`Œf>L]^tL]g8f>Lig8S_l"CFg

%'&.

)/+

Jv[o\YWH*`X\YC#dtLMS_CFgo\YUf>L]ADLf6•ž/TVLv\Yl>\YWDL]J C*Œ/L‰G[8H*WDUXCFgV\WDT8H*W

Jv[V\DW’dtLSDT8HeAIHFSZWYL]ADUn‹iLf#UX\

7698

:6 ;

23<* / "$"&&'&>=

$89? ;

"$A@ !

=

Heg8fKWYTVLSZCFgV\DWYAIHeUXg—WD\H*ADL

N9B

B ;

" C@

=

N9B

B ;

" C@

=

” TVL]g#CF[VAfmL]^8Lig8f>L]g8SZlSDT8H*A_HFS_WDL]AYUX‹HeWYUXCFgHe`XEFCFADUXWYTVJ UX\H*^V^o`nUXLfKWDCWDTVUX\\Yl>\DWYL]JC*ŒL‰G[8HeWYUXCFgV\

Heg8f"S_CFgo\YWYA_H*UXg>WY\jcsUXWWYADUnLi\WYCSZCFJM^o[VWYLWYTVLMfmCFJHeUXgCeŒ^tCF\D\YUXdV`XLv\YCG`X[VWYUXCFgo\Œ¡CFALHGSDT"}FH*AYUHedV`XLFt‡ˆg

CG[VA/\Yl>\YWDL]JctH*`X`tWYTVL}FHeAYUH*do`nLi\’T8Hj}GLWYTVL\IHeJMLR\YWIHeWY[V\j

ž/ToLtAY\YW•\YWDL]^CeŒ—WDTVL’f>L]^tL]g8fmL]g8S_lvSDT8H*A_HFS_WDL]AYUX‹HeWYUXCFgWYA_H*gV\Œ˜CFADJM\6WDTVL’S_CGgV\YWDAIH*UXg>WY\•Ž/TVUSDT{SZCFg>WIHeUng

JKCFAYL$WYT8HegCFgVL$}FH*AYUHedV`XL]\UXg>WYCvL‰G[8HeWYUXCFgo\HjŒ¡WYL]AWYToLUXg—WDAYCVf>[8SZWYUXCFgCeŒHv\D^8H*ADL}FHeAYUH*do`nLG>ž/T—[o\ctUXg

CG[VAL_k8HeJM^V`XLFc>WDTVLS_CGgV\YWDAIH*UXg>W

B

UX\/WYA_H*gV\ Œ˜CFADJMLfKUXg>WYCvL‰G[8HeWYUXCFg

:?8D

NH*g8fKWDTVLgVL]Ž

\DUnJK^V`XLS_CFgV\DWYA_H*UXg>W

D

NBEojP/Œ˜WDL]AsWDTVUX\sWYA_H*gV\Œ˜CFADJHeWYUXCFgsc_WDTVLADL]JHeUngoUngoES_CGgV\YWDAIHeUng>WD\–Li\Y^VADL]\Y\dtCF[og8f>\

CGg"WYTVLv}FHeAYUH*dV`XL]\j6ž/TVL]l"H*ADLMH*^V^o`nUXLfWDC#WYTVLK}FH*AYUHedV`XL,f>Li\IS_ADUn^oWYUXCFgV\H*g8f"HeAYLvAYLiJMC*}FLjf#Œ˜ADCFJ WYTVL

\Dl—\DWYL]JVPŒ˜WYL]A/WDTVUX\/\YWDL]^scVCG[VA/\Yl>\DWYL]J dtLS_CGJML]\

(8)

76 :?

$? $8

E

$?9? 8 E

9?? D N 8 E

$?? D x 8 E N B

N B

D N B E

D x B E

ž/ToLWDAIHegV\ˆŒ˜CGAYJ#H*WYUXCGgV\’f>L]\_S_AYUXdtLf0Ung H*ADL{He^V^V`XUXLfKWYCWYTVL$L‰G[8H*WDUnCGgV\/Ž/TVUSDTMdtLS_CGJML

76

?

$? 8 E

? D x 6 8 E

? ?

76

8 E

D N ? x 76

8 E N B

N B

D N B E

D x B E

ž/ToL{fmCFJHeUXgADLf>[8S_WDUXCFg#\YWDL]^S_CFJK^V[VWYLi\/gVL]Žd8CG[Vg8f>\Œ˜CFA/LjHFSDT#}FH*AYUHedV`XL/UngKWYTVL\Dl—\DWYL]JVADCFJ

L‰G[8HeWYUXCFg

? D x 6 8

EHeg8fvWDTVLd8CG[Vg8f>\

D x BEjN B

cGgVL]ŽdtCF[Vg8fm\H*AYLS_CGJM^V[oWYLf$Œ˜CGA

D

xH*gtf

N7B

D

x:BEvH*g8f"N9B

BEV6™Rd—}>UXCF[o\Y`Xl—c>WDTVL\YL]WC*Œ\DCF`X[VWYUXCGgV\UX\LiJM^VWˆl>>ž/TVUX\JKLH*gV\/WDT8H*W

WDTVLADLHFf>\CFg

%'&.

/)3+

f>C$gVCFW’HGS]S_L]\D\/WYTVLR\IHeJMLJML]JKCFAYl`XCVS]H*WDUXCFgV\H*\WYTVLRŽ/AYUXWYL]\CFg

%'&.

)/+

WDTVL]lMH*ADLUXg8f>Li^8L]gtf>L]g>Wož/TVLS_CGJM^VUX`XL]AS]HegS_CGg8S_`X[8f>LRWYT8HeW’WDTVLCG[VWYL]A`XC>CF^MS]Hegvd8LAY[ogvUngK^8H*A_H*`X`XL]`ˆ

>\Y[8He`X`nl>cDWYTVL’fmLS_UX\YUXCFg$^VAYCVS_L]\D\BC*Œ8H/S_CFJK^VUX`XL]A8UX\6gVCGWs`XUXJMUXWYLjfWYC/WYToL’SDTVCFUS_LdtL]WˆŽL]L]gvH\YL‰G[VLig—WDUH*`

UXg>WYL]AD^VAYLiWIH*WDUXCFgC*Œ’H`XC—CG^H*g8fH^8H*A_H*`X`XL]`6CFgoLFtž/TVLCF^oWYUXJMUX‹HeWYUXCFgv^VADCVS_L]\Y\$Un\/JKCFADL{SZCFJM^o`nLZkœoCFA

UXgV\DWIH*gtS_LFc6S_CFgo\YUf>L]A/WDTVLŒ˜CG`n`XC*Ž/UXgVE\YUXJK^V`XL/`nC>CG^s

3

$

&.

+0

&

+

4(

ž/ToL{SZCFAYADL]\Y^tCFgtf>UXgVEM\Dl—\DWYL]JUX\

8 ?

N7B

B

8

N.E E N7B

B

‡ˆgKWYTVUX\\Yl>\YWDL]Jc

Heg8f

ADL]^VADL]\YL]g>WRWˆŽ’Cvf>U›LiAYL]g>WCmSiS_[VAYLig8S_L]\C*ŒBWYTVLR\IHeJML/}FH*ADUH*dV`XL

Fž/ToUn\

\Dl—\DWYL]JT8He\\YCG`n[oWYUXCFgV\dV[VWWYTVLf>CFJ#H*UXgC*Œs\DCF`X[VWDUnCGgV\CeŒsLHFSDTM}FHeAYUH*do`nL/UX\UXWD\f>CGJHeUng$C*Œ–f>L tgVUXWYUXCFg

WDTVLUnWDL]AIHeWYUXCFgo\’CeŒ–WYToUn\`XC>CF^MS]HegVgVCFWdtLAD[Vg#UXg8f>L]^tL]g8f>Lig—WD`Xl—>ž/TVUX\UX\’WDTVL 8AD\YW/\DWYL]^#UXgMWDTVLf>LS_UX\YUXCGg

^VADCVS_L]\Y\C*Œ/WYToLMS_CFJK^VUX`nLiARL]^tL]g8fmL]g>W,f>C>L]\gVCGWJMLjH*g#\YL‰G[VLig—WDUH*`ˆs@BH*A_H*`X`XL]`BUng>WDL]AY^VADL]WIHeWYUXCFg"J#Hjl

\DWYUX`X`Vd8L/^tCF\D\YUXdV`XL/UŒ›\DCFJKLAYL]`HeWYUXCFgvS]H*gvdtL/L]g>Œ¡CFAISZLfvdtL]WˆŽL]L]gMWDTVL/UXWYL]A_H*WDUnCGgV\ež/TVL]gscjŒ¡CFAWDTVL/\YLSZCFg8f

\DWYL]^scœŽ’LvS]H*gHFfVf0\YCGJMLS_CFgo\YWYA_H*UXg>WCFg

H*g8f

tž/TVL\YLj‰F[oL]g>WYUH*`B`XC>CF^S_CGg>WIH*UXgV\RWˆŽ’C>Ungtf>\CeŒ

f>Li^8L]gtf>L]g8S_UXL]\vCGgWDTVLMHFSiS_L]\Y\DL]\vWYC

uHe”buLHFfHjŒ¡WYL]A”"ADUXWYLRCFg\YCGJML`XCVS]HeWYUXCFgV\Heg8f”£HGu

¡”"AYUXWYLH¬Œ˜WYLiA{uLHFf/CFg0\YCFJKLCFWYToL]A`nCVS]HeWYUXCFgo\8rœL]W[V\S_CFgo\YUf>L]AWYToL,uRH*” f>L]^tL]g8f>Lig8S_UXL]\B‘>CGJML

L]`XL]JKL]g>W’CeŒ

HeAYLŽ/ADUXWYWYLig“HeW’UXWDL]AIHeWYUXCFg

UXgMWDTVL\DL‰G[VL]g>WYUHe`s`XC>CF^vdtL_Œ˜CFADLd8L]UXgVEAYLjHFf#H*WUXWYL]A_H*WYUXCGg

ž/ToUn\UX\LZkm^oAYL]\D\YLf d—l0WYTVLvS_CFgo\YWYA_H*UXg>W

6‘>C#WYToUn\S_CGgV\YWDAIHeUng>WUX\HGfVf>Lf0WYC#WYToL\Dl—\DWYL]J

Ž/TVUSDT#UX\/gVC*Ž

8 ?

N7B

B

8

N.E E N7B

B

(9)

ž/TVLADL]\Y[V`XWDUngoE,f>CGJHeUngo\sC*ŒB}FH*`X[VL]\+Œ˜CFA

H*gtf

H*ADLgoC*Ž N B B ~H*g8f oN7B

BŸN(E Eo*ž/TVL

uRH*” f>L]^tL]g8fmL]g8S_lUX\^oAYL]\DL]g>WCFgo`nlCFg#H^tH*AYWC*ŒB}FLSZWYCFA

Gž/TVL]\DLADL]\Y[o`nWD\/\YTVC*Ž CFgMŽ/ToUŠSDTK^8H*ADW’CeŒ

WDTVL}FLjS_WYCGAWYToL]AYLUX\Hvf>L]^tL]g8f>L]gtS_lMWDTVLf>CFJ#H*UXgvC*Œ

6cVUXgV\DUŠfmLŽ/ToUŠSDT#\Y[odV\YL]WCeŒ–WYToLUXWYL]A_H*WYUXCGg

\D^8HFS_LKWYTVLi\YLv}FH*ADUH*dV`XL]\H*ADLvŽ/AYUXWYWDL]g“WDTVLMf>CGJH*UXg#C*Œ

H*g8f0UXgŽ/TVUSDT"^8H*ADWWYTVL]l"H*ADLADLHFf

WDTVLf>CGJHeUngC*Œ

sP/WWYTVUX\\DWIHeEFLFcH#^tCF\D\YUXdV`XLMf>LSZUn\DUXCFg"Œ¡CFAWDTVLS_CGJM^VUX`XL]AJHjl0d8LKWYC\D^V`XUnW$WYTVL

UXWYLiAIH*WDUXCFg\Y^8HGS_LvUXgWˆŽ’CKCFAWYToAYL]Lv^8HeAYWD\6ž/TVUX\WYA_H*gV\ Œ˜CFADJHeWYUXCFg#Jv[V\DW/d8Lv}FHe`nUfVHeWYLfŒ˜CGAWYTVLCFWDTVL]A

f>Li^8L]gtf>L]g8S_UXL]\$WYT8HeW/L_kVUn\DW/UXgMWYToL\IHeJML`XC>CF^•

‘m[V^V^tCF\YLWDTVLuHe”Qf>Li^8L]gtf>L]g8S_l#Ž/H*\/WDTVLCFgo`nlvCGgVLUXgMWYToL`XC>CF^•>ž/TVLUnWDL]AIHeWYUXCFgK\Y^8HGS_LS]Heg#d8L

S_[oWUXg>WYCWYTVADL]L\Y[odV\YL]WD\

„"¨ƒ˜‚j¥ B€]¥>‚S_CGg>WIH*UXgVUXgVEvLi`nLiJML]g>WY\/CeŒWYTVLfmCFJHeUXgMC*Œ

dV[oWgVCvL]`XL]JKL]g>WŒ˜AYCGJ WDTVLf>CGJHeUng

C*Œ



„"ƒ*¥>„8ª« –€i¥>‚S_CFg>W_H*UXgVUXgVEvL]`XL]JKL]g>WY\C*Œ/WYTVLvf>CGJH*UXg#C*Œ

do[VWgVC#L]`XL]JML]g>WŒ˜AYCGJ WYToL,f>CGJHeUng

C*Œ



„"ƒ*¥>„8ª#¨ƒ¡‚¥ B€+i¥>‚S_CGg—W_H*UXgVUXgVEWYTVLUXg>WYL]AD\YLSZWYUXCFgCeŒWYTVLWˆŽC,f>CGJHeUngo\

ž/TVL0UnWDL]AIHeWYUXCFgo\Ž/TVUSDT:f>C"gVCGWdtL]`XCFgVE"WDCWDTVLf>CGJHeUngC*Œ

CFAWYC"WDTVLf>CFJ#H*UXg"C*Œ

S]Heg«d8L

He\Y\YCVS_UHeWYLf#Ž/UXWDT“Heg>lv\Y[VdV\DL]W

”"LvTtHj}FLvEFCGWWDTVAYLiL`XC>CF^o\•ž/TVLMŽ/ADUnWDLM\D[VdV\YLiWvUn\$L_kVLS_[VWDLf 8AD\YWB‡ˆW\YToCF[V`fdtLMAY[ogVg8H*do`nLKUXg

^8HeAIHe`n`XL]` ¡gVC\YL]`Œ’f>L]^tL]g8f>Lig8S_l]tP/Œ¡WYL]A/WDTVLŽ/AYUXWYL\Y[odV\YL]WjctWYTVLAYLjHFf eŽ/AYUXWYL\Y[odV\YL]WRUX\/L_kVLS_[VWDLfH*gtf

UX\\DL‰G[VL]g>WYUHe`btž/TVLAYLjHFf#\D[VdV\YLiWUX\WYToL]gLZkmLjS_[VWYLjf"H*g8f#UX\R^8H*A_H*`X`XL]`ˆ>‡ˆgWYTVUX\RL_k8H*JM^o`nLGcVWYToLADLHFf

Ž/ADUnWDL\Y[odV\YL]WRUX\/L]JM^VWˆl>

3

&.

+0

&

+

4(

3 -

&.

+0

&

+

4(

PŒ˜WYL]AWDTVUX\WDAIHegV\ˆŒ˜CGAYJ#H*WYUXCGgscFLjHFSDT`XC>CF^#UX\CF^VWDUXJMUX‹]LfUngtf>L]^tL]g8f>L]g>WD`nl>c6H*g8f“d8CGWYT"H*AYL{Œ˜CF[Vgtf#WYCKd8L

^8HeAIHe`n`XL]`ˆt‡ˆgLHFSDT\Y[VdV\DL]Wc•WYToLvUnWDL]AIHeWYUXCFgo\goL]LfgVCGWdtLvS_CFg>WYUXEG[VCF[V\UXgCFAIfmL]AWYC#EFL]goL]AIHeWYLv\Y[tSYT£H

WDAIH*go\ˆŒ˜CGAYJHeWYUXCFg•/C*ŽL]}GL]AcsSZCFg>WYUXEF[oCF[V\\Y[odV\YL]WD\,HeAYLvLHe\YUXL]AWDC#UnJK^V`XL]JMLig—WdtLS]H*[o\YLMWDTVL]l"f>C#gVCFW

JKCmfmUŒ¡l,f>UXADLS_WY`XlKWYTVLCGAIf>LiA/C*Œ–JKL]JMCGAYlvHFS]SZL]\Y\DL]\6ž/ToL{He`XEFCFADUXWYTVJ UX\/\YUXJM^o`nLiA

‡ˆg$WYTVUX\BL_k8H*JK^V`XLFc]ŽL’TtHj}FL\YTVC*Ž/gWDTVL/EF[oUŠfmL]`XUngoLC*Œ8CG[VAf>L]^tL]g8f>Lig8S_lvH*g8He`nl>\DUn\•\Yl>\YWDL]Jj‡ˆgCFA_f>L]A

WDCMdtLUXg—WDL]EFA_H*WDLf#UXgV\YUf>L$WYTVLvf>LS_UX\DUnCGg#^VAYCVS_L]\D\c•UXW/Jv[V\YW/UXg>WYL]A_HFS_WRŽ/UXWYT#WYTVLCF^oWYUXJMUX‹]UXgVESZCFJM^oUn`XL]Aj

”:ToL]g£H#f>L]^tL]g8f>L]gtS_l£UX\WYC#dtLMH*g8He`nl>‹]Ljf6c6WYToLMS_CFJK^VUX`nLiA\YLig8f>\HK\YLiWCeŒL‰G[8HeWYUXCFgo\{Heg8fHM\DL]WCeŒ

S_CGgV\YWDAIHeUng>WD\’WDCWYTVLR\YCG`n}GL]A’Heg8fWDTVL]g#H*\ >\BŒ¡CFAWDTVLf>CGJHeUngCeŒs\YCF`X[VWDUXCFgV\•Œ˜CGACFgVL/CGAJMCGAYL}FH*ADUŠHedV`XL]\

ž/TVLS_CGJM^VUX`XL]AHeg8H*`Xl>‹]L]\vWDTVL]\DLAYL]\D[V`XWY\MHeg8f«S]H*g¢\YL]g8f gVL]Ž'L‰G[8HeWYUXCFgo\MH*g8f gVL]Ž S_CFgV\DWYA_H*UXg>WY\vWYC

WDTVL#\Yl>\YWDL]JBž/TVUX\UXg—WDL]AIHGS_WYUXCGg£JHjl"S_CGg—WDUXg—[oLM[Vg>WYUX`/WDTVLS_CFJK^VUX`nLiA{fmLS_Uf>L]\KWYT8HeWUXWT8H*\vL]goCF[VEGT

>gVC*Ž/`XLf>EGLCFg#WYTVLf>Li^8L]gtf>L]g8S_l0WYCvJH FL/WDTVLf>LSZUn\DUXCFgs

ž/ToL FLil"^8CGUng>WUXg"WDTVLMUXg>WYL]A_HFS_WDUXCFg£dtL]WˆŽL]L]g«WYToL“SZCFJM^oUn`XL]AHeg8fWYTVLf>Li^8L]gtf>L]g8S_l«\Dl—\DWYL]J.Un\

UXgWDTVLvL_kV^VAYLi\Y\YUXCGgCeŒ’\YCG`n[oWYUXCFgfmCFJHeUXgV\>‡ˆgCF[VAR\YUXJM^o`nLL_k8HeJM^V`XL]\jcVWYToL]\YLvADL]\Y[V`XWD\Ž’LiAYLUng>WDL]AY}FHe`n\

(10)

CeŒUng>WDL]EFL]AD\B”"LvŽ/UX`X`\YLiLWDT8H*W$WYTVUX\Un\$gVCFWWDTVLMCGgV`Xl^tCF\D\YUXdV`XLSDT8HeAIHGS_WYL]ADUX‹H*WDUnCGg£CeŒWYTVLK\YCF`X[VWDUXCFg

f>CGJHeUng

gVLiŽ S_CFgV\DWYA_H*UXg>WY\#UXg—}GCF`X}>UXgVEWˆŽC"CFAMJKCFADLM}FH*ADUH*dV`XL]\MS]Heg H*`X\DC"d8L^oAYCVf>[8S_Ljf6/‡ˆg¢ŒbHFSZWc

WDTVLf>L]^tL]g8f>L]gtS_l SDT8HeAIHFSZWYL]ADUn‹iL]AMADL]^VAYLi\YL]g>WY\KWYTVLK}FH*`X[VLMf>CGJHeUng0C*ŒLHGSYT¢UXg—WDL]AYgtH*`}FH*AYUHedV`XLMH*\Heg

UXg>WYL]AD}FH*`ˆHGSYT«L_kVWDL]AYg8He`}FHeAYUH*dV`XL bH0}FH*AYUHedV`XL >gVC*Ž/g"Œ¡AYCFJ.WYTVLS_CGJM^VUX`XL]A S_CGAYAYLi\Y^tCFg8f>\#WDC Heg

UXg>WYL]ADg8H*`6}FHeAYUH*do`nLG*‡ˆgMWDTVLADL]\YCG`n[oWYUXCFgK^VAYCVS_L]\D\ctH*AYWDU›S_UH*`t}FH*ADUŠHedV`XL]\’S]HegHe`n\DCdtLUXg>WYADCVf>[8S_LfKd>lWYTVL

SDT8HeAIHFSZWYL]ADUn‹iL]Ac>Ž/TVUSDTT8Hj}GL’goCJMLjH*gVUXgVE/CG[VWY\DUŠfmLFjž/TVL/AYL]`HeWYUXCFgV\•d8LiWˆŽ’L]LigvUng>WDL]AYg8He`>}FH*AYUHedV`XL6H*gtf

L_kVWDL]AYg8He`s}FHeAYUH*dV`XL

Un\/f>L tgVLfK[V\YUXgVEWˆŽC,S_CGgV\YW_H*g>WY\

H*g8f

d>lvWYTVLL‰G[8HeWYUXCFg

8

6

WDTVL}FH*`X[VLf>CFJ#H*UXgvC*ŒH*g#L_kVWYLiAYg8He`s}FH*ADUH*dV`XLUX\/\D^8H*AD\YLF

™RgKAYL‰G[VL]\DWŒ˜AYCGJ WYTVLS_CFJK^VUX`nLiAcjWYTVL\Dl—\DWYL]JH*`X\YC^oAYCVf>[8S_Li\/`nUX\DWY\C*ŒsS_CFgV\DWYA_H*UXg>WY\/CFgv\D[VdV\DL]WY\/CeŒ

WDTVL}FHeAYUH*do`nLi\8qCGgV\YUf>LiAWDTVL^VAYL]}>UXCF[o\L_k8H*JK^V`XLŽ/TVL]gWYTVL}FH*`X[VLC*Œ

UX\RgVCFW —goC*Ž/gH*WS_CFJK^VUX`nL

WDUnJKLF

8 ?

N7B

B

N7B

B

ž/ToL–ADL]\Y[o`nWBf>CFJ#H*UXgV\6H*ADL–goC*Ž 7XNjN(E <Fy < xFzGz=_Œ˜CFA

c7x_xVN <FyFx <$< =]Œ˜CFA

H*gtf/7yIxoN <GyGx$<Gz=

Œ˜CGA

>ž/TVL`ŠHeAYEGL}FH*`X[VLi\/C*Œ–WDTVL[V^V^tL]AdtCF[og8f>\/T8Hj}GLdtL]L]gS_CGJM^V[oWYLfŒ˜ADCFJ'WDTVL`ŠHeAYEGL]\YW/ADL]^VAYLi\YL]g>š

W_H*dV`XLUXg>WYL]EGL]A/Œ¡CFAWDTVL}FHeAYUH*dV`XL]\RC*ŒWYToL^VAYCGEFA_H*J bx ?

N]ož/TVL]\DLADL]\Y[V`XWD\{SiH*gVgVCGWdtLLZkm^o`nCGUXWYLf6

ž/TVLS_CFJK^VUX`XL]AsgVLiLf>\WYTVLRAYL]`H*WDUXCFgV\BdtL]WˆŽ’LiL]g#WYTVL/`XC>CF^}FH*ADUŠHedV`XL]\H*g8fWDTVL`XC>CF^dtCF[Vg8fm\UXgCGAIf>L]AWYC

J#HFLHRf>LS_UX\YUXCGgs‘>[tSYTvH*gUXg>Œ˜CGAYJ#H*WYUXCGgS]Hegd8LCFdVW_H*UXgVLfd>lHSZCFgV\DWYAIHeUXg—W•AYL‰G[VLi\YWež/TVLSZCFgV\DWYAIHeUXg—W

ADL‰G[VL]\YW/`XUX\YWD\WˆŽCCFAJKCFADL’}FHeAYUH*dV`XL]\H*g8fWDTVLSDT8HeAIHFSZWYL]ADUn‹jH*WYUXCGgM\Yl>\DWYL]J SZCFJM^o[VWYL]\S_CFgV\DWYA_H*UXg>WY\Ungmš

}GCF`X}>UngoEWDTVL]\YL$}FH*AYUHedV`XL]\>‡ˆg#CF[oAS]H*\DLFctWYCMH$AYL]`H*WDUXCFg#AYL‰G[VLi\YWCGg

H*g8f

c>WYTVL\Dl—\DWYL]J ^oAYCVf>[8S_Li\

WDTVLS_CGgV\YWDAIH*UXg>WY\

x$B

?

6 B xVN <GyFx$< <

?

xVN <FyFx < B x

? B ? N

ž/ToL tAY\YWS_CGgV\YWDAIHeUng>WS_CGJML]\Œ¡AYCFJWYToLUXgVUXWYUH*`6S_CFgo\YWYA_H*UXg>WY\H*g8f#f>C>L]\gVCGWS_CFg>WIHeUXgJv[tSYTKJMCGAYL

UXg>Œ˜CGAYJ#H*WYUXCGgs_ž/TVL/\YLjS_CFg8fAYL]`HeWYUXCFgUX\–JKCFADL^8C*ŽL]AŒ˜[V`VdtLS]He[V\YLRUnWBUXg8f>US]HeWYL]\H^tH*AYWC*Œ8WDTVL/UXWYL]A_H*WYUXCGg

\D^8HFS_LGHFSDTvWYUXJKLHSZCFgV\DWYAIHeUXg—WC*ŒsWYToLŒ˜CFADJ

B

?

dtL]WˆŽ’LiL]gH`XC>CF^v}FHeAYUH*do`nL

Heg8fWYTVLR[V^V^tL]A

dtCF[Vgtf

UX\CGdVWIHeUngoLf6c•WYTVLvUXWYLiAIH*WDUXCFg£f>CGJH*UXgCeŒH“`nC>CG^ S]Heg"d8L#S_[VWHeWWYToLM^tCFUXg>W

•ž/TVL

ADL]\Y[V`XWDUngoEv`nC>CG^MUX\/gVC*Ž

$/

&.

+0

&

+

4(

/,)3

&.

+0

&

+

4(

ž/ToL^oAYL]\DL]g8S_LvCeŒ–\Yl>JvdtCF`X\Ung#WDTVLL‰G[8H*WDUnCGgV\/UX\/gVCFWHeg#L ›LjS_WYUX}FL`XUXJMUXWIHeWYUCGgWDCvWYTVL$AYL]\DCF`X[VWYUXCGg

CeŒ+WDTVL\Yl>\YWDL]J

(11)

(%• %B$ v

ž/TVL/f>L]^tL]g8fmL]g8S_lvH*`XEFCGAYUXWYToJ:JHegVUX^V[V`H*WDL]\8Lj‰F[tH*WYUXCGgV\–Heg8fUXg>WYL]ADg8H*`>}FH*ADUH*dV`XLf>CFJ#H*UXgV\jYPRgUXg—WDL]AYgtH*`

}FHeAYUH*dV`XLvf>CFJ#H*UXg#UX\f>L 8goLf"d>lH#`XC*ŽL]Ad8CG[Vg8f"Heg8fHeg"[V^V^tL]Ad8CG[Vg8f66ž/ToLvUng>WDL]AˆŒbHGS_LvdtL]WˆŽ’LiL]g

WDTVLM\Dl—\DWYL]J Heg8fWDTVLSZCFJM^oUn`XL]AH*\D\YCVS_UH*WDL]\WDTVLvUXg>WYL]ADg8H*`}FHeAYUH*do`nLi\Ž/UXWDTWDTVLvL_kVWYL]ADg8H*`/CGgVL]\d>lH

Jv[V`XWDUn^o`nUS]HeWYUX}FLŒbHGS_WYCGAH*g8f#Hf>UX\Y^V`HGS_L]JMLig—W e>ž/TVL 8AY\DWWYUXJKLH*g#L_kVWYL]ADg8H*`•}FH*ADUŠHedV`XLUX\/JMLiWcGWYTVL

}FHe`n[oL MUX\ VkVLfWYCCFgoLFc WYC‹iL]AYC"H*g8f WYTVLKd8CG[Vg8f>\vH*ADLML_kVWDAIHFSZWYLf Œ˜ADCFJ WYTVLKL‰G[8H*WDUXCFg"CFA$WYTVL

S_CGgV\YWDAIHeUng>WjV”:TVLiAYLWDTVLd8CG[Vg8f>\S]H*gVgoCFW/dtL{SZCFJM^o[VWYLfKWDTVL]lHeAYL VkVLf#WDCdtLWDTVL`ŠHeAYEGL]\YWH*g8fWYTVL

`XC*ŽL]\YW/ADL]^VAYLi\YL]g>WIHedV`XLvUXg—WDL]EFLiAY\UXgKWYTVL`HegVEF[8HeEFLF>ž/ToLUXgVL‰G[8H*WDUXCFgV\C*ŒWˆŽCvCFA/JMCGAYLR}FH*AYUHedV`XL]\HeAYL

WDAIH*go\ˆŒ˜CGAYJMLjf"UXg>WYCL‰G[8HeWYUXCFgo\d>l"WYToLMUXg>WYAYCVf>[tS_WYUXCFg¢C*Œ\D^8H*ADL}FHeAYUH*do`nLi\'VCGAUXgV\DWIH*gtS_LFc! #"%$

B

! #"%$

Un\RWYA_H*gV\Œ˜CFADJMLfKUXg>WYC&! #"%$

6('

8 ! ")$

tž/TVLUXgVUXWYUH*`sfmCFJHeUXgvC*Œ

'

UX\07E+*%=sŽ/TVL]ADL,*“Un\

S_CGJM^V[oWYLfŒ˜ADCFJ-! #"%$

Heg8f ! ")$



ž/ToLL‰G[8H*WDUXCFgV\H*AYL\YWDCFADLfHe\[V\D[8H*`BUXgHegH*ADAIHjl#C*ŒUXg>WYL]EGL]AY\j 9LjS]H*[V\DLvL‰G[8H*WDUXCFgCGA}FH*ADUH*dV`XL

L_k8SDT8HegVEFL]\MHeAYLŒ˜AYL‰G[VLig—WMfm[VAYUXgVEWDTVLSZCFJM^o[VWIHeWYUXCFgsctWDTVL#L‰G[8H*WDUnCGgV\Heg8f"}FHeAYUH*dV`XL]\H*AYL#HFS]SZL]\Y\DLf

WDTVAYCG[VEFT#AYLig—[oJvd8L]ADUXgVEv}FLSZWYCFAD\

qCGgV\YUf>LiA/WYTVLRŒ˜A_H*EFJKL]g>W

3

/.

&.

.

+-

&0.

+213131

4(

4(

ž/TVL$L‰G[8H*WDUnCGgV\H*gtfvWYToLS_CFgo\YWYA_H*UXg>WY\HeAYL

8

.

.

8

N9B

B

B

. B

N9B

B

B

. B

‡ˆg#WYToLf>L]^tL]g8f>Lig8S_l\Dl—\DWYL]JWYToL^VAYCGdV`XL]J'UX\/AYLi^VAYL]\DL]g>WYLfd>lKWYTVLL‰G[8HeWYUXCFgV\Heg8fKWYTVLf>CGJHeUngo\

? . 8 E

. ? 8 E

.

?

?4'

8 E

.

?

?4'

8 E

64'

? 8 E

64'%5? 8 E

.

64'6? 8 E

.

64'7? 8 E

7nNIxoN <FyGx <*z=

7nNIxoN <FyGx <*z=

.

7nNIxoN <FyGx <*z=

.

7nNIxoN <FyGx <*z=

' 7EIxoN <FyGx <<=

' 7EIxoN <FyGx <<=

' 7EIxoN <FyGx <<=

'%5 7EIxoN <FyGx <<=

'6

7EIxoN <FyGx <<=

' 7 7EIxoN <FyGx <<=

(12)

ž/TVL\DL]JHeg—WDUS_\/C*ŒBWYTVL}FH*ADUH*dV`XL]\UXgMWYToL{SDT8HeAIHGS_WYL]ADUX‹H*WDUnCGg\Yl>\DWYL]J H*ADLgoCFW/AYLi`ŠHeWYLfKWDCvWYTVL\YLiJH*gmš

WDUŠSZ\CeŒ’S_CFADAYL]\D^8CGg8f>UXgVE#}FH*ADUŠHedV`XL]\/UXgWYToL^VADCFEGAIH*JFPR`X`–WDTVL}FHeAYUH*dV`XL]\/TtHj}FLWDTVL\_H*JKL\DWIHeWY[V\j oCFA

UXgV\DWIH*gtS_LFcH#}FHeAYUH*dV`XLAYL]^oAYL]\DL]g>WYUXgVE£H#`XC>CF^£S_CGg>WYAYCG`Heg8f"H#}FHeAYUH*dV`XLAYL]^oAYL]\DL]g>WYUXgVE£H#`XC>CF^"dtCF[Vgtf

T8Hj}GLWYToL\IHeJML\DWIHeWY[V\j “CFAYLiC*}FL]Ajc8H*ADWYU›S_UHe`s}FH*ADUH*dV`XL]\ M}FH*ADUŠHedV`XL]\/Ž/UXWYTVCG[VWH*g>lKJMLHegVUXgVEUXg#WYTVL

\DCF[VA_S_L^oAYCFEGAIHeJ S]Heg#d8LUXg>WYADCVf>[8S_Lf0f>[VAYUXgVEvWDTVLS_CGJM^V[oWIH*WDUXCFgvd>lMWDTVL\Yl>\DWYL]J CGA/d—lKWYTVLS_CFJš

^VUX`XL]AjVž/TVLHeAYWDU6S_UH*`s}FHeAYUH*do`nLi\S]HegAYLi^VAYL]\DL]g>WUXg>Œ˜CGAYJHeWYUXCFgWYTtH*WUX\ >gVC*Ž/gKŒ˜ADCFJWYTVLSZCFJM^oUn`XL]ACFA

WDT8H*W/UX\/WYCvdtLS_CFJK^V[VWDLfKd—lvWDTVL\Dl—\DWYL]J

ª•¥¥ªs„+…e¥ª ¡ƒ*¥m…e‚ ¡©"„ª ª ˆ]‚j„…*¥

P [V\D[8H*`•[V\YL$C*Œ–\D[8SDTH*g#H*ADWYU›S_UH*`6}FHeAYUH*do`nLRUX\/UngKWYTVLf>Li^8L]gtf>L]g8S_lf>UX\YWIHeg8S_LSZCFJM^o[VWIHeWYUXCFgsG”:TVLig

H*g8f

AYL]^VADL]\YLig—WRWˆŽ’CUXgV\YW_H*g8SZL]\/C*ŒsWDTVL\_H*JML/`XC>CF^MSZCFg>WYADCF`t}FH*AYUHedV`XL

cGL‰G[8HeWYUXCFg

8

?

S]HegMdtL\Yl>\YWDL]JHeWYUS]H*`X`XlUXg>WYADCmfm[8S_LfKd>lWDTVLS_CFJK^VUX`XL]A*PRgHeg8H*`Xl>\YUX\CeŒsWYTVLf>CGJH*UXgCeŒ6^oAYCVf>[8S_Li\

UXg>Œ˜CGAYJ#H*WYUXCGgCGgWDTVLf>L]^tL]g8f>Lig8S_l bf>UXAYLjS_WYUXCFg•c>^8CG\Y\YUXdV`XLf>UX\YW_H*g8SZL]\

¡©6©«ƒ*¥>©tƒFªs¥>ƒ

9LS]He[V\YLvWDTVL`XC>CF^SZCFg>WYADCF`B}FH*ADUŠHedV`XLT8Hj}GLgVCM\D^8LSZUŠHe`s\DWIH*WD[V\c6S_`He\Y\YUS]He`sUXJM^o`nUS_UXWCGAIf>LiAYUXgVEM\D[8SDTH*\

`XL_kVUS_CFEGAIHe^VTVUSRCFAIfmL]AYUXgVEvCeŒHgoL]\YWRC*ŒUXWYL]A_H*WYUXCGgV\/T8H*\RgVCvUXg>WYL]AD^VAYL]W_H*WDUnCGg#Ung#CG[VA/\Yl>\YWDL]J /C*ŽL]}FLiAc

L‰G[8HeWYUXCFgo\MH*g8f}FHeAYUH*dV`XL]\AYLi^VAYL]\DL]g>WYUXgVE¢\Y[8SDT«UXg>Œ˜CFADJHeWYUXCFgSiH*g£dtL#UXg—WDAYCVf>[8SZLf6BP }FH*ADUH*dV`XLMS]Heg

ADL]^VAYLi\YL]g>WvWYToL,fVHeWYLvH*\D\YCVS_UH*WDLfŽ/UXWYT\DCFJML$^VAYCGEFAIHeJ L]}FLig—Wj6ž/TVL]g"ADL]`H*WDUnCGgV\dtL]WˆŽL]L]g¢WYTVLvfVH*WDL]\

CeŒ+WDTVL]\DLL]}FLig—WD\S]Heg#d8LL]}FHe`n[tH*WYLjf68rœL]W/[V\S_CGgV\YUf>L]ARWYTVLS_`H*\Y\DUS]H*`6`XC>CF^

3

/.

3

&.

.

+

&.

3

.

+)

&(

. 3,+

4(

4(

ž/ToUn\S_CVf>LR\YLSZWYUXCFgKUn\B\DL‰G[VL]g>WYUH*`ˆGž/TVUX\’S]Hegvd8L/L_kV^VADL]\Y\DLfKd>l,fVHeWYUXgVEWYToLL]}GL]g>WY\/oCFAUXgV\DWIH*gtS_LFc

CGgVLMS]H*g"UXg>WYADCVf>[8S_LvWDTVLv}FH*ADUŠHedV`XLHeg8fLj‰F[tH*WYUXCGg

8

!

6 .

Ž/TVUSDT He\Y\DCmSZUŠHeWYL]\WYToLMfVH*WDL

}FHe`n[oL"$Ž/UnWDTMUXWYLiAIH*WDUXCFg

&.

. +  /L]ADLFc

!

UX\/HS_CFgo\YWIHeg>W/Ž/UnWDT

!#%$

O UXgvEFLigVL]AIHe`ˆc>WYTVL —goC*Ž/g

[V^o^8L]ARd8CG[Vg8fKC*ŒWDTVL}FH*AYUHedV`XLS]HegdtL[V\YLjf6

ž/ToLHeAYAIHjl$L]`XL]JML]g>W

.

•Un\BŽ/ADUnWDWYL]gMfm[VAYUXgVEUXWYL]A_H*WDUnCGg .

H*WfVH*WDL&

8 '!

6 . 

ž/TVLv\_H*JKLL]`XL]JKL]g>WUn\$AYLHGf"f>[VAYUXgVE#UXWYLiAIH*WDUXCFg .

H*g8f"fm[VAYUXgVE#UXWYL]A_H*WDUnCGg .

R\Y[8SDT£WDT8H*W

? N

. 8 . ? N

8 .

]ož/TVLfVH*WDL]\

8 !

6 . H*g8f

8

(!

6 . 

‡ˆg#CFA_f>L]ARWYCvH*g8He`nl>\DLWDTVLAYL]`HeWYUXCFgV\/dtL]WˆŽL]L]gWDTVLŽ/AYUXWYLi\H*gtfvWYToLAYLHGf>\/WYCvWDTVL\_H*JML/Li`nLiJML]g>WS]Heg

He^V^8LjH*AcBŽLMUXg>WYADCVf>[8S_L#WYToL}FHeAYUH*do`nLi\

H*g8f

fmL 8gVLf¢d>l"L‰G[8HeWYUXCFgV\)

8 ?

H*gtf

8 ? 

ž/ToLŽ/ToCF`XL\Yl>\YWDL]J UX\

(13)

8 ? N

.

8

.

8

.

8 . ? N

8

! 6

.

8

' ! 6

.

8 ! 6 .

8 ?

8 ? N B

B

N B

B

N B B

N B

.

B

N B

.

B

N B . B

B !

™Rg8SZLvWYTVUX\\Dl—\DWYL]J UX\AYLfm[8S_Lf6c•WYToLv}FH*AYUHedV`XL

Heg8f

H*ADLŒ˜CF[Vgtf#WYCTtHj}FLCFgV`Xl#^8CG\YUXWYUX}GL

}FHe`n[oL]\6ž/ToUn\ADL]\Y[V`XWSiH*g"dtLvUng>WDL]AY^VADL]WYLjf"H*\Œ˜CG`X`nC*Ž/UXgVE

HFS]SZCFAIfmUngoEWDC#WYTVLMfVHeWYLMf>L 8gVUXWYUXCFg tctWYTVL

HeAYAIHjl#L]`XL]JKL]g>WY\H*ADLH*`XŽ/Hjl>\Ž/AYUXWDWYL]gd8LZŒ˜CFADLdtL]UXgVEMADLHFfœ 9LS]He[V\YLKWYTVUX\fVH*WDL,S_CGAYADL]\Y^tCFg8fm\WYCKWYTVL

\DL]JHeg—WDUS_\’CeŒ–WDTVL

`XC>CF^o\c>WYToL]\YLADL]`H*WDUnCGgV\T8Hj}FLRWYCvdtLADL]\Y^tLS_WDLf0Ung#H*g>lv}FH*`XUf`XC>CF^MADL]CFA_f>L]ADUngoE8

9L_Œ˜CGAYLWDAYl>UXgVEMH*g>lK^VAYCGEFAIHeJ WDAIHegV\ˆŒ˜CGAYJ#H*WYUXCGgsc—H`XC>CF^#ADL]CFA_f>L]AYUXgVE#S]H*g0d8L}FHe`XUŠfoH*WYLjfvŒ¡AYCFJ WYTVL

gVLiŽŸfVH*WDL]\H*\D\YCVS_UH*WDLf#WYCWYToLL]}FLig—WD\tqCFgV\DUŠfmL]A/WYTVL$gVL]Ž fVH*WDL

D 8 6 .

H*\Y\DCVS_UH*WYLjf#WYCUXWYL]A_H*WYUXCGg

.

]>”"LRUng>WDAYCVf>[8S_LL‰G[8HeWYUXCFgo\

D 8

6

. c D 8

6

.

c D 8 6 .

WYCAYLi^VAYL]\DL]g>WWYTVLgVL]Ž

fVHeWYL]\/CeŒsWYTVLRŽ/AYUXWYLi\H*g8fADLHFf>\/WDCWYToL\_H*JKL/L]`XL]JML]g>Wj ‰G[8H*WDUXCFgV\ D 8 D

?$D

Heg8f D

8D

? D

L_kV^VADL]\Y\WDTVLAYL]`H*WDUXCFgV\/dtL]WˆŽL]L]gWDTVL]\YLvfVHeWYL]\j8™Rg8S_LWDTVLgVL]Ž\Yl>\YWDL]J UX\/AYLfm[8S_Lf6c D

H*g8f D HeAYL

Œ˜CG[Vg8f#WDCMT8Hj}GLCFgV`XlM^tCF\DUXWYUX}FL}FHe`X[VL]\ož/TVLCFAIfmL]AY\C*ŒWDTVLŽ/AYUXWDL,Heg8fKAYLHGf>\HFS]S_Li\Y\YLi\WDCvWYTVL\IHeJML

L]`XL]JKL]g>WC*Œ6WYToLH*AYA_HjlUX\BWYToL\IHeJMLUXgWDTVL/gVL]Ž foH*WYL/\Dl>\YWYLiJ He\UXgvWYTVL/CGAYUXEFUXg8He`>CFgVL

WYToL/gVL]Ž:fVH*WDL]\

f>L 8gVLH^tCF\D\YUXdV`XLAYL]CGAIf>L]ADUXgVEMCeŒ–WYToL`XC>CF^#L_kVLSZ[VWYUXCFg•

ž/ToUn\/S_CGg8S_`X[V\YUXCGg`XLHGf>\/WYCMSZCmfmLWYA_H*gV\Œ˜CFADJH*WDUXCFgV\j

%•(%• ,%BF v#%

/

ž/TVL$d8H*\DUŠS{\Yl>\YWDL]J WYA_H*gV\ Œ˜CFADJH*WDUXCFgMUX\/WDTVL,SZCFJvdVUXg8HeWYUXCFgvCeŒ+WˆŽCvL‰G[8HeWYUXCFgV\/UXg#CFA_f>L]ARWYCMLi`nUXJKUngtH*WYL

H¢S_CFJKJMCFg¢}FH*ADUŠHedV`XLKŒ˜AYCGJ CFgVLCeŒWYToL]J™[oALZkm^tL]ADUnJKL]g>WY\#\YToC*Ž WYT8HeWMWYToLJKCF\YWvUXg>WYLiAYL]\DWYUXgVE

L‰G[8HeWYUXCFgo\MH*AYLKWYTVCG\YL#Ž/TVUSDT f>Li^8L]gtf«CFg¢WYTVL#JMUXgVUXJ[VJ C*Œ}FHeAYUH*do`nLi\•‡ˆg Heg

$

\Yl>\YWDL]J $

L‰G[8HeWYUXCFgo\c

}FHeAYUH*dV`XL]\ ]c

$ B

c•WYToLM}FH*ADUH*dV`XL]\HeAYLK\Y^V`XUXWUXg>WYCWˆŽC\YLiWY\

H " $*<.&'’CeŒ

$

}FHeAYUH*dV`XL]\Heg8fH<3- /B&'–CeŒ

? $

}FHeAYUH*do`nLi\9l“H\DL‰G[VL]g8SZLvC*Œ`XUngoLH*AS_CGJvdVUXg8H*WDUXCFgV\CeŒWYTVL

L‰G[8HeWYUXCFgo\/WYTVL\Yl>\DWYL]J UX\/WYA_H*gV\ Œ˜CFADJMLfUXgM\Y[tSYTHŽ/HjlvWYT8HeW/LHFSDT#}FH*ADUH*dV`XL/Œ¡AYCFJ WYTVLf>UH*EGCFg8He`8\DL]W

He^V^8LjH*AY\UXgCGgV`XlCFgoLL‰G[8HeWYUXCFg• HFSDT"WDUnJKLWˆŽC\Dl>gVCFg>l>JM\H*ADLMf>UX\IS_C*}GL]AYLjf0OWˆŽ’C#}FHeAYUH*dV`XL]\

Heg8f#H*ADL\Yl>gVCGg—l>JKCF[V\/UŒ’H*gLj‰F[tH*WYUXCGgCeŒ’WYToLŒ˜CFADJ

6

8

S]HegdtL^VADCVf>[8S_Lf“OQCGgVLCeŒ

WDTVL}FHeAYUH*do`nLi\UX\ADL]JMC*}GLfH*\ŽL]`X`–He\WDTVLL‰G[8H*WDUnCGgsVž/ToLdtCF[Vgtf>\C*Œ’WDTVLADL]JMC*}GLf#}FHeAYUH*dV`XL]\HeAYL

ADL]^8CGAYWDLf"CGgWDTVLvCFgVLWYTtH*WUX\ GL]^VWj6P/Œ˜WDL]AWDTVUX\WDAIHegV\ˆŒ˜CGAYJ#H*WYUXCGgscVWˆŽC#L_kVWYL]ADg8H*`}FHeAYUH*do`nLi\{SiH*gd8L

He\Y\YCVS_UHeWYLf#Ž/UXWDTWDTVL\_H*JMLRUXg—WDL]AYgtH*`sCGgVLFož/TVL\YW_H*g8foH*AIf“AYL]^VADL]\YLig—W_H*WDUnCGgC*ŒWDTVL\Yl>\DWYL]J UX\/\YToC*Ž/g

UXg 8EF[oAYLvNF

‘m[8SDT“HADL]^VADL]\YL]g>W_H*WYUXCGgUX\/CFdVW_H*UXgVLfd—l#HvS_`H*\D\YUS]H*`6Li`nUXJKUngtH*WYUXCGg^VADCVS_L]\Y\j

(14)

x1 x2

x3 x4

xn

column subset diagonal subset

•UXEF[oAYLvN

\DWIH*gtfVH*A_f#AYL]^oAYL]\DL]g>WIH*WDUXCFg

%

HGSDTWYUXJMLHgoL]Ž L‰G[8H*WDUXCFgMUX\/UXg>WYADCmfm[8S_Lf#UXg#WYToL\Yl>\YWDL]Jc>CGA/UX\S_AYLHeWYLf“d—lK`XUngoLH*AS_CGJvdVUXg8H*WDUXCFgsc

WDTVUX\’L‰G[8HeWYUXCFgKUX\’E>S]fGšˆAYLf>[tS_Lf

WYTVLRE—S]fKCeŒ–H*`X`8WDTVL/ŒˆHFS_WDCFAY\UX\SZCFJM^o[VWYLfœFPR`n`tWYToL}FHeAYUH*do`nLŒˆHFS_WDCFAY\

Heg8fWDTVLvS_CFgV\DWIHeg—WRŒbHGS_WYCGAH*AYLvf>UX}>Uf>Lf#d>lWDTVLE>S]f66ž/ToLE>S]fGšˆAYLf>[tS_WYUXCFg"S]HegŒbHeUX`sUŒ’WYToL,S_CGgV\YW_H*g>W

ŒbHGS_WYCGABC*ŒVWYTVLL‰G[8HeWYUXCFgSiH*gVgVCGWBd8L/f>UX}>UŠfmLfd>lWYTVLE—S]fœcUXgŽ/ToUŠSDTSiH*\YLGc*WYTVL\Yl>\DWYL]J T8H*\BgVCR\YCF`X[VWDUXCFg

L]JM^VWˆlMfmCFJHeUXgADL]\Y[V`XWD\H*ADLAYLi^8CGAYWYLjf#WYCvWDTVLS_CFJK^VUX`nLiA>qCFgV\DUŠfmL]A/WYTVL$`nC>CG^

&

/2

)+0

&.

+

&

/2

))3/+-

&.

+

4(

ž/TVL$L‰G[8H*WDUnCGgx

6 8 x

6 6

NSiH*gVgVCGW/d8L$E—S]fGšˆAYLjf>[8S_Lfœ8ž/ToUn\/\Dl>\YWYLiJ T8H*\/gVC\YCG`X[VWYUXCFg•

(

P }FH*AYUHedV`XL 0T8He\HMfmCFJHeUXgv\YWYADUf>L

' UŒ’He`n`•UXWY\^tCF\D\YUXdV`XL}FHe`n[oL]\S]H*gdtLŽ/AYUXWYWDL]g 8 ' 6 c

Ž/UXWYT

'

H*gtf

S_CFgo\YWIHeg>WHFSDTWYUXJKLHgVL]ŽL‰G[8H*WDUnCGg#Un\SZAYLHeWYLf6ctLHGSDT}FHeAYUH*do`nLRC*ŒWYToLLj‰F[tH*WYUXCGg

UX\’S_CGgV\YUf>LiAYLf6>ž/ToL/E—S]fCeŒœHe`n`>WDTVL/CFWDTVL]AgVCFgg>[V`X`>ŒbHFSZWYCFAD\C*Œ6WYToL/L‰G[8H*WDUnCGgvUX\+SZCFJM^o[VWYLfœ*ž/TVUX\E—Sif

dtLS_CGJML]\/WDTVLf>CFJ#H*UXg\DWYADUŠfmLC*ŒsWDTVL}FH*AYUHedV`XLF—qCGgV\YUf>LiA/L‰G[8H*WDUnCGg 6

6 6 ! ! 8

Références

Documents relatifs

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

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

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

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

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

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

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

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