• No results found

Feedback control methodologies for nonlinear systems

N/A
N/A
Protected

Academic year: 2020

Share "Feedback control methodologies for nonlinear systems"

Copied!
28
0
0

Loading.... (view fulltext now)

Full text

(1)

56768:9;9+<=9;>+?A@B6DCE6CF>HGJIDKA@DGJILMB6CE6D81GJIDNDOQP

79;ISR9;>1TVUA>!W19&OX9&GJ>HY"Z\[=I]5^Y"[_9;I^RQ[a`bYc7UAdceDfDRHGJRQ[_UAI

g

9;eGJ>"Rdh9;ISR UJTjiGJRZD9;d\GJRQ[kY;O

l UA>"RZ7mGJ>Un<o[_IGp5ARHGJR9Eq'IS[=rs9;>HOt[_RQu

W Gv<=9+[_wAZ@

l

7xSyvzA{s|

}~€ƒ‚&„&…†n‚A‡!ˆ ISfDd‰/9;>1UJTjY+UAdheDfDR+GJRQ[_UAIGŠ<dh9;RZDUDLDOZGŠrA9‰9;9;IeD>"UAeU^OX9&L[_IRZD9'<a[=R"9;>HGJRfD>9ER"ULS9&Ot[_wAI

GJILOQuSI^RZD9&O‹[=Œ;9T9;9&LS‰GsYNMY+UAISR>Un<ŽO, ZD9;IRZD9EeS<kGJISR [kO1dhUDLS9+<_9&L‰^u\IDUAIS<a[_ID9&GJ>‘LSuSIGJd[kY;O;6:’“R,[ŽO'IDUAR:[_dhdh9;”

Ls[ŽGnR9+<_u•Y"<_9&GJ>&@SZDUJ19;rA9;>&@s ZS[kYZc[kOR"ZD9!‰/9&OQR1dh9;RZDUDLTUs>mGwJ[_rA9;I\eD>UA‰S<_9;dM–SRZS[kO:d—GŠu˜LS9;e/9;IL\UAI\RZD9 IGJRfD>"9

UJT‘R"ZD9IDUAIS<a[=ID9&Gn>Q[_RQ[_9&O;@ RZD9MO‹[=Œ;9UnT‘RZD9MOXu™OQR"9;dM@ ZD9;RZD9;>cRZD9MGJdhUAfDISRUJT‘Y+UAISR>Un<,fOX9&LšUA>hRQ[_dh9ID9;9&LS9&L

TUA>RZD9\dh9;RZDUDL›[ŽOGY+UAIY+9;>I@:GJILšUARZD9;>TœGAY+R"UA>HO;6’tIRZS[kOeGJe/9;>˜GY+UAdceD>9;ZD9;IOt[_rA9MY+UAdheGn>Q[kOQUAIOQRfLSu

UJT `rA9\dh9;RZDUDLDOTVUA>RZD9OQu^ISRZD9&Ot[kOUJT IDUAIS<a[_ID9&GJ>Y+UAI^R">UJ<mOQuDOQR9;d—O‘[kOhY;GJ>>Q[_9&L]UAfDR&6MC,ZD9e9;>QTVUA>d—GnIY+9—UJT

RZD9Edh9;RZDUDLDO:UAI•OX9;rA9;>HGŠ<R9&OQR1eD>Us‰S<=9;d\O GJ>9EOQRfLs[_9&L@GJILOXUAdh9>9&Y+UAdhdh9;ILDGnRQ[_UAIO1GJ>9d—GALS9GAO:RU ZS[kYZ

T9;9&LS‰GAY"NMY+UAISR>UJ<dh9;R"ZDU™Lc[kO'‰9&OQR R"UhfOQ9EfDILS9;>rvGJ>Q[_UAfOY+UAILs[_RQ[_UAIO;6

žtŸ ƒ¡£¢¤V¥Q¢V¥¦¤V§t ¨¦"¢¢V©&ª&ªJ«+¤V¬V¥Q­¡£®ªv¦"¤V¬¯;°¦ ±4²±4³´µ^²¶Š·¹¸Eº4·»¼4¤“¦"®;¬´µS²¶&·µS½¿¾+À+ÁHÂX;+ÄQÓÅtÍÂ"½H½;Ʀ"®&­¡£®ªv¦"¤V¬¯;°

´jµS²¶&·¼4¤“¦®;¬µS½¿¾+À+ÁHÂX;+ÀQÓÅtÍÂ+ÁH¾+ÁÇ_´4´j¶ŠÈ·SŸÉ

Ê ¥tÃkË ¦X¡ÍÌ_Îb¢V§Q¯J¥Q¥“Ì£¥Q¤“Ï4¥Q«+¢QЮ&§Q¢V©sÐ¥Q­&©

ÑQ¥tÃkË ¦X¡ÍÌ_Îb¬V¤“¦"®vÏ4§Q«+®;¬V¤V«Ì_ÐË,¦"¬V AЮ&§Q¢V©AÐ¥Q­&©

(2)

C1ZD9EUAeDRQ[_d—GŠ<TV9;9&LS‰GAY"N—Y+UAISR>UJ<UJTjG<a[_ID9&GJ>!OQuDOQR9;dÞ[kO GOQfD‰DßQ9&Y+R1 ZS[kYZZGsO1‰9;9;I9+àDR9;IOt[_rA9+<_uMOQRfLs[_9&L

á

OQ9;99A6âw6ã

Ô;ä

GJILRZD9>9+TV9;>9;IY+9&O'RZD9;>9+[_IåH6'’VTmR"ZD9Y+U^OQR,TfDIY+RQ[_UAIGv<[ŽOæsfGALS>HGJRQ[kY‘[=IRZD9OQRHGJR"9GJILY+UAI^R">UJ<“@

GJIL19hGAOOQfDdh9TVfS<a<,OQRHGnR9N^IDUJ1<_9&LSwA9A@FRZD9;IçRZD9hUseDRQ[_d—GŠ<mY+UAISR>UJ<4[kOGc<a[_ID9&GJ>hOQRHGJR"9TV9;9&LS‰GAY"N<kGŠè ZD9;>"9

RZD9—Y+UAISR>UJ<wSGŠ[_IOGn>9hUA‰DRHGv[=ID9&L]‰Su›OXUJ<_rA[_IDwçGMLs[aé9;>9;ISRQ[kGŠ<VêvGŠ<_wA9;‰D>HGŠ[kYW:[kY;Y;GJRX[,9&æsfGJRQ[_UAI6C1ZD9OQfY;Y+9&OOUJT

RZS[kOE<a[_ID9&GJ>hæsfGALS>HGJRQ[kY>"9;wAfS<kGJRUA> á‹ë4ì

WåeD>UA‰S<_9;dí[ŽOLSfD9—R"URZD9•OXfY;Y+9&OOtTVfS<,LS9;rA9+<_UAeDdh9;ISRUJTm>"UA‰DfOQRGnIL

9+î•Y"[_9;I^REGŠ<_wAUA>Q[_RZDd\O:TUs>!OQUJ<_rs[=IDw\RZD9W:[kY;Y;GJRX[j9&æsfGJRQ[_UAI6B'UJ19;rA9;>&@s[aTRZD9EeS<kGJI^R'[kO LS9&OY+>Q[_‰/9&L‰^u\IDUAIS<a[_ID9&GJ>

LSu^IGJd˜[ŽY;Oƒ@RZD9;IšRZD9—UseDRQ[_d—GŠ<,OXRHGJR9TV9;9&LS‰GAY"Nç<kGŠï[kOwn[=rs9;Iç[_IšR9;>d—OUJT RZD9OQUJ<_fDRQ[_UAIšRURZD9—BGJd[a<_RUAID”

ð

GAY+UA‰S[_”“8:9+<a<=d\GJI á B

ð

8'å9&æsfGJRQ[_UAI¹ãñx

ä

6C1ZD9B

ð

8ò9&æsfGJRQ[_UAIMeD>"Uvrs[kLS9&O1RZD9OQUJ<_fDRQ[_UAIMR"UR"ZD9UAeDRQ[_d—Gv<FY+UsI^R>"UJ<

eD>UA‰S<_9;dóTUs> wA9;ID9;>HGŠ<IDUAIS<a[_ID9&GJ>OQuDOQR9;d—Oƒ–ZDUJ19;rA9;>&@S[_R'[kO'[=IdhU^OQREY;GAOQ9&O,[_dheUSOOt[_‰S<_9hRU—OQUn<=rs9˜GnIGŠ<_u^RQ[kY;GŠ<a<_uA6

C1ZS[kOZGsO<_9&LcRUd\GJI^udh9;R"ZDU™LDO:‰9+[_IDwheD>"UAeU^OX9&L[_IRZD91<a[_R9;>HGJRfD>"9 TVUA> GŠuDORUGJeDeD>UŠà^[_d—GnR9+<_uUs‰DRHGŠ[_I—R"ZD9

OQUJ<_fDRQ[_UAIRU\RZD9B ð 8ô9&æAfGJRX[=UsIõGAO'19+<o<GAO'UA‰DRHGŠ[_IçG\OQfD‰UAeDRX[=d\GŠ<TV9;9&LS‰GAY"NõY+UAISR>Un<bTVUA>wA9;ID9;>HGŠ<IDUAIS<a[_ID9&GJ>

LSu^IGJd˜[ŽY;Gv<jdhUDLS9+<kO;6

ö ID9heU^O"Ot[_‰S[o<a[_RQu[kORUY+UAIOQR>fY+RRZD9hY+UAISR>UJ<GAOGhe/UJm9;>OX9;>Q[_9&O;@9+[_RZD9;>E‰^uOQ9;eGJ>HGnRQ[_IDwUAfDR!R"ZD9IDUsID”

<o[_ID9&GJ>X[=RX[=9&O‘[_IõR"ZD9OQuDOQR9;d÷[_ISRUGeUJ19;>‘OX9;>Q[_9&O;@Us> ‰^u\[_ISR>UDLSfY"[_IDwMGhR9;dceUA>HGn>u—rJGJ>Q[kGJ‰S<_9hGJIL9+àDeGJILs[_IDw

GJ>UAfDIL›[_R&6õC,ZD9;I¹RZD9c`>HOQRT9;÷R9;>"d—O[_IšRZD9•OX9;>Q[_9&OTUs>RZD9—Y+UsI^R>"UJ<,GJ>"9TUsfDILç‰SuçrvGn>Q[_UAfOR9&YZDIS[kæsfD9&O;6

C1ZS[kO'[ŽLS9&Gc[kO‰GAOX9&LUAIçY+UAIOt[kLS9;>Q[_IDwRZD9OQuDOQR9;døGAOGhe/9;>RfD>‰GnRQ[_UAIMUJTmG˜<a[_ID9&GJ>OQuDOQR9;d@D1[_RZRZD9Y+UsI^R>"UJ<

‰9+[_IDw•GnI9+à™R9;IO‹[=UsIUJTRZD9<a[_ID9&GJ>EY+UAI^R">UJ< á RZD9 `>+OQR1R9;>d*UJT4RZD9!e/UJm9;> OQ9;>X[=9&O,[kO1UA‰DRHGv[=ID9&L\‰SuOQUJ<_rA[_IDwhR"ZD9

W:[kY;Y;GJRQ[9&æAfGJRX[=UsI\TUA>1RZD9OQUJ<_fDRQ[_UAIUJTRZD9<a[_ID9&GJ>Q[_Œ;9&LOQuDOQR9;dåH6:C1ZD9&OQ9ERQu^e/9&O1UJTdc9;RZDU™LDOGJ>9ELS9&OY+>Q[_‰/9&L[_I

ã£ùD@Sú@|D@Dz

ä

6

ˆ IDUAR"ZD9;>˜GneDeD>U^GAY"Zç[kOR"ZD>UAfDwAZOQfY;Y+9&OOt[_rA9MGneDeD>UŠà^[_d—GJRX[=UsI@ ZD9;>9MGJI][_R9;>HGJRX[=rs9eD>U™Y+9&O"OE[kOfOX9&LšRU

`ILçGMOQ9&æsfD9;IY+9hUJT GJeDeD>UŠàS[=d\GJRQ[_UAIOGneDeD>U^GAY"ZS[_IDwRZD9—OQUJ<_fDRQ[_UAI]UJTmRZD9\B ð 8%9&æsfGJRQ[_UAI6hC,ZS[ŽO‘[kOLSUAID9h‰Su

OQUJ<_rA[_IDwçGMOX9&æAfD9;IY+9\UJTmws9;ID9;>HGŠ<a[_Œ;9&LB!GJd˜[o<_RUsID”

ð

GAY+UA‰S[_”“8:9+<a<=d\GJI áû B

ð

8 å9&æAfGnRQ[_UAIO;@GnIL[kOLs[kOY+fO"OQ9&L[_I

ãay^@^ü

ä

[_IMGwA9;ID9;>HGŠ<Y+UAISR9+àDR&6

ˆ

dhUA>9EY+UAIY+>9;R"9!R9&Y"ZDIS[kæAfD9TVUA>:`ILs[_IDwhRZD9ELS9&Ot[_>9&LMOXUJ<_fDRQ[_UAI\[kOmLS9&O"Y+>Q[_‰9&L\[_I

ã£{D@

Ô&ýJä

@S ZD9;>"9G

û

GŠ<_9;>Ns[_IeD>U™Y+9&LSfD>"9E[kO1fOQ9&LpRU`ILMGISfDdh9;>Q[kY;GŠ<OQUJ<_fDRQ[_UAIRURZD9

û

B ð 8þ9&æsfGJRQ[_UAI6

ö RZD9;>!dc9;RZDU™LDO,[_IY"<_fLS9hRZD9OQRHGnR9;”“LS9;e9;ILS9;ISRW:[kY;Y;GJRQ[9&æAfGnRQ[_UAI

á

5 g W'ÿ1åH@D'ZS[ŽY"Z[kOEGJI9+àDR9;IOt[_UAIUJT

RZD9‘Wm[ŽY;Y;GnRQ[9&æsfGJRQ[_UAIRUIDUAIS<a[=ID9&Gn>‘OQuDOQR9;d\O!ã

ÔAÔ

@

Ô

x^@

Ô

ù

ä

6C1ZD9Y+US9+î•Y"[_9;ISRHO:[_IRZD95

g

W ÿ GJ>"9 TVfDIY+RQ[_UAIO1UJT

RZD9‘OXRHGJR91[_IOQR"9&GAL\UJT‰/9+[=IDw\Y+UAIOQRHGJISR”VrJGŠ<_fD9&LGAO4[_IRZD9'<a[=ID9&Gn>!Y;GAOQ9A6C,ZS[ŽO,d—GJNA9&OÛRZD9!9&æsfGJRQ[_UAIdfY"Z—dcUA>9

Ls[oîY+fS<=RRU—OQUn<=rs9A6 ˆ <kOQU@ [_IRZD9IDUAIS<a[_ID9&GJ>Y;GAOQ9ERZD9>9&OQfS<_RQ[_IDwMY+UAISR>Un<b[kOUAIS<_uMOQfD‰/UAeDRQ[_d—GŠ<“6C1ZD9;>9[kO!GŠ<kOQU

G—Y+UAISR>Un<dh9;RZDUDL‰GAOQ9&LUsIõ>"9;eD>9&OQ9;ISRQ[_IDw—RZD9hY+fD>rs9UJTRZD9hOQuDOQR9;d£O OQUJ<_fDRQ[_UAIçGAOG˜<o[_ID9&GJ>EUse9;>HGJR"UA>‘GnIL

RZD9;I[_ISrA9;>RQ[_IDw[_RãÔ ú ä @DGJILMGnI9+à™eS<_UA>HGnRQ[_UAIMUJT4RZD9fOQ9EUnTjID9;fD>HGv<ID9;RHO1RU\OQUJ<_rA9ERZD9B ð 8ò9&æsfGJRQ[_UAIšãÔ | ä6

ö e9;ID” <_U^Use•Y+UAISR>Un<ŽO4Y;GJIhGŠ<kOQU‰9:TVUAfDIL‰^uG rJGJ>Q[_9;RQuUJTbLs[aé9;>9;ISRdh9;RZDUDLDO;6ZS[a<_9 UAe/9;ID”<_U^UAehY+UAISR>Un<ŽO

GJ>9Mws9;ID9;>HGŠ<a<_u IDUAR\fOQ9+TVfS<!TVUA>\eD>HGAY+RQ[kY;GŠ<GJeDeS<a[kY;GJRQ[_UAIO;@'[_Rh[kO\e/U^OOt[_‰S<_9çRUç9+àDR9;ILþRZD9;d [_I^RUY"<_U^OQ9&LS”<_USUAe

Y+UAI^R">UJ<kO;6C,ZS[ŽOY;GnI‰9 LSUAID911[_RZGJIE[_ISR9;>e/UJ<kGJRQ[_UAIhUJrA9;>R"ZD9mOQRHGnR9mOQeGsY+9mGAO4LS9&OY+>Q[_‰9&L[=Iã

Ô

z

ä

@;TVUA>49+à GJdceS<=9A6

C1ZD91UAe9;ID”<_USUAehY+UAI^R">UJ<™Y;GJI‰9:TVUAfDILE‰SuOQUn<=rs[_IDwG1RQ1UA”VeUJ[_ISR‰/UAfDILDGJ>uErJGŠ<_fD9

á

C:8åeD>"UA‰S<_9;dM@A ZS[kY"Z[ŽO

UA‰DRHGŠ[_ID9&LcTV>UAd÷RZD9ID9&Y+9&OOGJ>ucUAeDRQ[_d—GŠ<a[_RQu•Y+UAILs[_RQ[_UAIOƒ6’tR,Y;GnI—‰/9OQUJ<_rA9&L\‰Su—Ls[kOY+>9;RQ[_Œ+[_IDw•GnIL\RZD9;I•OXUJ<_rA[_IDw

9+à GAY+RX<=ušãÔ z ä @/UA>9+<ŽOX9‰SuMUsID9UJTmOQ9;rs9;>HGŠ<4[=R"9;>HGJRQ[_rA9dh9;RZDUDLDO

á

æAfGsOt[a<o[_ID9&GJ>X[=Œ&GnRQ[_UAI@4wA>HGALs[_9;ISR!dh9;R"ZDU™LDO;@9;R+YJ6aå

GAO:[_I¹ã

Ô

yn@

Ô

üS@

Ô

{D@Dx

ý

@/x

Ô+ä

6

’“R:[kOmGv<ŽOXUE[_dheUs>RHGJISRRUIDUAR9 R"ZGJRmLs[aé9;>9;ISRmdc9;RZDU™LDO:GJ>9EGJeDeS<a[kY;GJ‰S<_9RULs[aé9;>9;ISRmeD>"UA‰S<_9;d—O;615AUAdc9!UJT

RZD9dh9;R"ZDU™LDO'RZGJR 191[a<o<4[_I^rs9&OQRQ[_w^GJR9[_I›LS9;R+GŠ[a<ÛY;GJI‰9fOQ9&LUAIõGdcUA>9EwA9;ID9;>HGv<jeD>Us‰S<=9;dóRZGJIRZD9UsID9

m9'1[a<o<Y+UAIOt[kLS9;>&@sTUs>9+àGJdheS<_9A@S1[_RZ•GIDUAIS<a[_ID9&GJ>1TVfDIY+RQ[_UAIUJTRZD9!Y+UAISR>Un<ÜGAOۏm9+<a<GAO:RZD9!OQRHGnR9A6C1ZD9;>9!GJ>"9

GŠ<kOQU—dc9;RZDU™LDO'ZS[ŽY"ZçGJ>9LS9&Ot[_wAID9&LõTUA>'UARZD9;>EOQe9&Y"[a`bYeD>Us‰S<=9;d\O;@OQfY"ZõGAO'RZD9‰S[a<a[_ID9&GJ>hOQuDOQR9;d

á

(3)

[=ISrAUJ<_rA9&L›[_I¹R"ZD9h9&æAfGnRQ[_UAI@GAOELs[kOY+fOOQ9&L][_Iòã£xSyA@xAü

ä

6

ˆ

dh9;RZDUDLçLS9&GŠ<a[_IDwõUsIS<=u]1[_RZ¹OQuDOQR9;d—O ZD9;>9hR"ZD9

I^fDd‰9;>UJTjOXRHGJR9GJILY+UsI^R>"UJ<rvGJ>Q[kGJ‰S<_9&OEGJ>"9ERZD9OGJdh9[kO1eD>"9&OQ9;I^R"9&L\[_I¹ã£xs{

ä

6

’“IRZS[kOeGJe/9;>—GçY+UAdceD>9;ZD9;IOt[_rA9MY+UAdheGn>Q[kOQUAI OQRfLSušUJT `rs9—UJTRZD9dh9;RZDUDLDOhLS9&OY+>Q[_‰/9&L GJ‰/Uvrs9—1[a<a<

‰9\e9;>QTVUA>dh9&L]UAI¹OX9;rA9;>HGŠ<1R9&OQReD>"UA‰S<_9;d—O;6ç9\1[a<a<!LS>HGŠ OQUAdc9—Y+UAIY"<_fOt[_UAIOhGAORUM'ZS[ŽY"Zšdh9;RZDUDLDOwn[=rs9

RZD9‰/9&OQRE>9&OQfS<_RHO,TUs>!Y+9;>RHGŠ[_IRQu^e/9&O UnTjeD>Us‰S<=9;d\O;@GJILMGv<ŽOXU•Y+UAIO‹[ŽLS9;>EUsRZD9;> T“GAY+RUs>HO1OQfYZçGAO,RZD99+à^[_‰S[a<a[=RQu

UJTRZD9dc9;RZDU™LDOEGnILRZD9Ls[oîY+fS<=RQuçGJILpRQ[_dh9[=ISrAUJ<_rA9&Lp[_IRZD9+[_> [_dheS<_9;dh9;ISRHGJRX[=UsI¹GJILfOX9A6‘C,ZD9eGJe/9;>[ŽO

UA>w^GJIS[_Œ;9&LhGsOTVUJ<a<_UvO;6C1ZD91eD>UA‰S<_9;d OQR+GJR9;dh9;ISR[kOwJ[_rA9;I[_I5A9&Y+RQ[_UAI\xD6C1ZD91dh9;R"ZDU™LDO4RUE‰/9 Y+UAIOt[kLS9;>9&L1[a<a<

‰9LS9&OY+>Q[_‰/9&L\[_Iç5A9&Y+RQ[_UAIMù 6’tIeGJ>RQ[kY+fS<kGJ>&@Ü5A9&Y+RQ[_UAIMùD6£ùLS9&OY+>Q[_‰9&O'RZD9OQfY;Y+9&OO‹[=rs9GJeDeD>UŠà^[_d—GnRQ[_UAI—dc9;RZDU™L6

89&Y;GnfOQ9RZD9;>9M GAOcGJI 9;>>"UA>[_IòUAID9MUJTR"ZD9TVUA>dfS<kGAO[_IòRZD9MUA>X[=wn[=IGv<‘eGJe/9;>&@1RZS[kOOQ9&Y+RQ[_UAIòY+UAISRHGŠ[_IO—G

LS9;RHGŠ[a<_9&LõLS9;>X[=rJGJRQ[_UAIUJTRZD9Edh9;RZDUDL6C1ZD9e9;>QTVUA>d\GJIY+9EUJTRZD9dh9;R"ZDU™LDO1UsITVUAfD>19+à GJdceS<=9&OEGn>9Ls[kOY+fOOQ9&L

[=I]5A9&Y+RQ[_UAIMú/@GJIL\UJrA9;>HGŠ<a<Y+UAIY"<_fOt[_UAIOEGJ>"9EwJ[_rA9;I[_Iç5A9&Y+RX[=UsIõ|D6

‡„&Ø~! #"%$'&‚;…D‚(")$*"×/‚

7UAIOt[kLS9;>EGIDUAIS<a[_ID9&GJ>‘OXu™OQR"9;d*UJTRZD9ERQu^e/9

+

á-,

å

.

á

á-,

åå

á

á/,

åå

á

ý

å

1032

á

Ô

å

 ZD9;>9

.

á

å[kOEGcIDUAIS<a[_ID9&GJ>ETVfDIY+RQ[_UAIUJTRZD9OQRHGJR9

*46587:9; @ *<

58=>9@?

[ŽOR"ZD9Y+UAISR>UJ<“@GJIL [kO!G

Y+UAIOQRHGJISR”VrJGŠ<_fD9&LBADCFE\d\GJR>Q[aà6 ˆ <kOQUY+UAIOt[kLS9;>‘GcY+U^OQR1TVfDIY+RQ[_UAIGŠ<

G

á

H0I2 å

KJ*L

0 M

1NPOQ

NP9 1RS

,

1[_RZ—G'wJ[_rA9;I—Y+UAIOQR+GJI^R"”VrvGŠ<_fD9&LTAUCVA÷OQuSdhdh9;R">Q[kY1eU^O‹[=RX[=rs9!OQ9;d[_”“LS9+`IS[_R9d—GJR>Q[aà

O

GJILG@EC@EhOQuSdhdh9;R">Q[kY

eU^Ot[_RQ[_rA9MLS9+`IS[_R9d\GJR>Q[aà

9

6MC1ZD9\UAeDRQ[_d—GŠ< Y+UAISR>UJ<eD>Us‰S<=9;dí[kORU`ILGOQRHGJR"9T9;9&LS‰GsYN¹Y+UsI^R>"UJ<

)W

á

å

 ZS[kYZd[_IS[=d˜[=Œ;9&ORZD9Y+U^OQR,TUA> GŠ<a<e/U^OOt[_‰S<_9[_IS[=RX[ŽGv<mY+UAILs[_RQ[_UAIO

H0

6

X UA>RZD9Ot[_dheS<_9;>h<a[_ID9&GJ>\eD>UA‰S<_9;dM@'ZD9;>9

.

á

å

YZ0

@RZD9UseDRQ[_d—GŠ<TV9;9&LS‰GAY"N Y+UsI^R>"UJ<[kOwJ[_rA9;I‰Su

W

á

å

\[9])^

N`_ @'1[_RZ

_

‰9+[_IDwRZD9çOQUJ<_fDRQ[_UAIòRUšRZD9d—GJR>X[oàWm[ŽY;Y;GnRQ[9&æAfGnRQ[_UAI

_ 0Q: N0 _ [

_

9 ])^

N _

KOD

ý 6—C1ZD9cRZD9;UA>Q[_9&OTUs>ERZS[kOE<a[_ID9&GJ>hæsfGALS>HGJRQ[kY>"9;wAfS<kGJRUA> á‹ë4ì

WåEeD>UA‰S<_9;díZG&rs9h‰9;9;I

9&OQRHGJ‰S<a[kOQZD9&L TUs>h‰UAR"Z RZD9p`IS[=R"9õGJIL [=IS`IS[_R9çLs[_dh9;IOt[_UAIGv<eD>UA‰S<_9;d—O

á

OQ9;9M9A6âw61ã£ù

ý

@mù

ÔHä

åH6’“IòGALDLs[_RQ[_UAI@

OQRHGJ‰S<_9hGJIL>UA‰DfOQREGŠ<_wAUA>X[=R"ZDd—O'TUs>‘OQUn<=rs[_IDwRZD9hW:[kY;Y;GJRQ[9&æsfGJRQ[_UAIZGŠrA9Gv<=>"9&GALSuM‰/9;9;I›LS9;rs9+<=Use9&LšGJILMGJ>"9

m9+<a<jLSUDY+fDdh9;ISR9&L\[_Id—GJISu—eS<kGAY+9&O,[_IMRZD9<o[_R9;>+GJRfD>9GJIL•[_IMR9+àDR‰USUANDO;6

X

UA> R"ZD9EIDUAIS<a[=ID9&Gn>Y;GAOQ9A@SRZD9UseDRQ[_d—GŠ<T9;9&LS‰GsYNMY+UAISR>Un<b[kO'N^IDUJ IR"U‰/9UJTRZD9TVUA>d

W á

å

[

Ô

x

9 ])^

Na)b

á

å

2

 ZD9;>9R"ZD9TfDIY+RQ[_UAI

a

[ŽO,RZD9OQUn<=fDRX[=UsIMRURZD9BGJd[a<_RUAID”

ð

GsY+UA‰S[_”“89+<a<kd\GJIç9&æsfGJRQ[_UAI

a N

b

á

å

.

á

å

[

Ô

ú

a N

b

á

å

9

])^

N a b

á

å

c N Od

ý1e

á

xSå

C1ZD9õB ð 8Þ9&æAfGnRQ[_UAI[_RHOQ9+<aTE[kOcrA9;>uLs[oîY+fS<=R\RU¹OXUJ<_rA9MGJIGŠ<_uSRQ[kY;GŠ<a<=u TUs>—GJISu¹‰DfDRhR"ZD9õOt[_dheS<_9&OQR\eD>UA‰S<_9;d—O;@

ZDUv19;rA9;>Š6C1ZSfO9+éUA>R+O4ZG&rs9 ‰9;9;I\d—GALS9 R"UEI^fDdh9;>X[ŽY;Gv<o<_uGJeDeD>UŠàS[=d\GJR91RZD9!OQUn<=fDRX[=UsI—UJTRZD9B ð 8š9&æsfGJRQ[_UAI@

(4)

‰9;9;IMeD>"UAeU^OX9&L\[_IMRZD9<a[_R9;>HGnRfD>9A6

f ‡gh"i"DÙ4~…†3jlkØFׂ&„ŠØm on8"S‚3pØÜÙFØm ŽØ)qÝr"D€ts“Ø„vupØ×P kݜ×w"^…„x&my€ƒ‚(")$ç€

f ‡Õ ‡Ø1z{"D„&m"D„JÝr"D€h}||„ŠØ1}Ý~$…D‚&Ý_ØF×

ö ID9RQuSe9UJTdh9;RZDUDLUJTUA‰DRHGv[=IS[_IDwMGJIGJeDeD>UŠàS[=d\GJR9OXUJ<_fDRQ[_UAIMRU\RZD9B ð 8 9&æAfGJRX[=UsI á xSå[kO ‰SufOt[_IDw GeUJ19;>—OQ9;>Q[_9&OcRU¹GJeDeD>"U&àS[_d—GJR9 a á å+6 C1ZS[kO[kOhLSUsID9M‰Su û GJ>>HGJ>+LGJILšUARZD9;>HO[=I%ã£ùS@ú@| ä 6ò7UAIO‹[ŽLS9;> RZD9h>9;eD>9&OX9;I^RHGnRQ[_UAI a á å L 3€ 0 a  á åH@'ZD9;>9h9&GAY"Z a  á å ‚ á 3ƒ

?Šå+6 ˆ <kOQUõOQ9;eGn>HGJR9RZD9hIDUAIS<a[_ID9&GJ>

TfDIY+RQ[_UAI . á å4[_I^R"UheUJ19;>HO:UJT GAO . á å KZ0 L 3€ ? .  á å1[_RZ .  á å K á  åH6:5AfD‰OQRX[=R"fDRQ[_IDw—RZD9&OX9

9+à™eGJIO‹[=UsIO1[_ISRUhRZD9B ð 8þ9&æsfGJRQ[_UAI>9&OQfS<_RHO,[=I

„ L … †€ 0 á a  å N bm‡ „ 0ˆ L … †€ ? .  á å ‡ [ Ô ú „ L … 3€ 0 á a  å N bw‡ 9 ])^ N „ L … 3€ 0 á a  å b ‡ ‰HN!Ot ý1e 8uOQ9;eGJ>+GJRQ[_IDw—UsfDRm‰SueUJ19;>HO:UJT 19EUA‰DRHGv[=IMGcOQ9;>Q[_9&O UnTj9&æsfGJRQ[_UAIO < á a)0 å N b Z0T[ Ô ú á a%0 å N b 9 ])^ N á a%0 å b‰1N!O ý á ùSå á a ^ å Nb 0[ Ô ú á a ^ å Nb 9 ])^ N á a%0 å b@[ Ô ú á a)0 å Nb 9 ])^ N á a ^ å b á a%0 å Nb . ? á å ý á úDå á a  å N b 0[ Ô ú  … ? € 0@Š á a ? å N b 9 ])^ N á a  ]H? å b3‹o  ])^ … ? € 0Š á a ? å N b . 3ƒ ^Œ]H? á å ‹ ý 2 á |Så  ZD9;>9{Ž x 2 ù 2 ú 2 ereree ÿæsfGJRQ[_UAI á ùSå!Y;GJI‰/9—OQUJ<_rA9&L1[_RZ a 0 á å

 N _

@'ZD9;>9RZD9hOQu^dcdh9;R>Q[kYe/U^Ot[_RQ[_rA9—LS9+`IS[_R9hd\GJR>Q[aà _ OXUJ<_rA9&ORZD9hW:[kY;Y;GJRQ[9&æsfGJRQ[_UAI _ Z0‘ N0 _ [ _ 9 ])^ N _ ‘O’ ý 6EC1ZS[kOwJ[_rA9&ORZD9hOQRHGJILDGn>HL\<a[_ID9&GJ> Y+UAI^R">UJ<“6ÿæsfGJRQ[_UAIO á ú åÛGnIL á |SåY;GJI‰9OXUJ<_rA9&L\TVUA> a  @1Ž Ô 2 x 2 ù ere#e @J‰Su\d—GJNs[=IDw a  GhO"Y;GŠ<kGJ>1eUJ<_uSIDUAd[kGŠ< Y+UAI^R+GŠ[_IS[=IDwhGŠ<a<eU^OO‹[=‰S<_9EY+UAd‰S[_IGJRQ[_UAIO:UJTbeD>"U™LSfY+RHOÛUJTRZD9 OQRHGJR"9m9+<_9;dh9;ISRHO:1[_RZ—GRUARHGv<™UA>+LS9;>UJT!Ž x @™GnIL

RZD9;IMOQfD‰OQRQ[_RfDRX[=IDwc[_R1[_I^R"UhRZD9E9&æsfGJRQ[_UAIMGJILOQUn<=rs[_IDwTVUA> RZD9EY+U^9+îY"[=9;ISRHO;61C1ZS[kO Y;GJI‰/9LSUAID9TVUA> GAO1d\GJI^u

R9;>d—OEGAOLS9&Ot[_>9&L@4‰DfDR[_I¹wA9;ID9;>+GŠ<RZS[kOæsfS[kYNs<_uçwA9;RHOrA9;>"u›Y+UsdheS<a[ŽY;GnR9&L@49&OQe9&Y"[kGŠ<a<_uçTVUA>EeD>Us‰S<=9;d\OE1[_RZ¹G <ŽGn>wA9hISfDd‰9;>UnT'OXRHGJR9rvGn>Q[kGJ‰S<_9&O;6 ˆ OG\ GŠuMUJT!GŠrAUJ[kLs[_IDwMRZS[kO;@ û GJ>>HGJ>+LeD>UAe/U^OQ9&OGdh9;RZDUDLUJT1`ILs[_IDw á a ^ å b dhUs>9Ot[_dheS<_uA@'ZS[ŽY"ZM>"9&OQfS<_RHO1[_IGrs9;>u—9&GsOQu—dc9;RZDU™LpUJT`ILs[_IDwMGhæsfGALS>HGJRX[ŽYRQuSe9Y+UAI^R">UJ<jãñù ä 6 ’“IOQR9&GsLEUJTfOt[_IDwRZD9e/UJ<_u^IDUsd[kGŠ<>9;eD>9&OQ9;ISRHGJRX[=UsI@&19d\G&uEY+UAIOt[kLS9;> á

ú å GsO[kO4GJILEfOQ9:RZD9mOXfD‰OQRQ[_RfDRQ[_UAI

(5)

å

[9 ])^

N

ã

_ [ ZN0 [ _

9

])^

N

å

]H^

_ .

?

å

ä-e

zSå

’VT

.

?

á

å

ý

á

RZGJR[kO;@F[aT!RZD9;>9GJ>9cIDUõæsfGALS>HGJRQ[kYcR9;>d—O¿åH@RZD9;I

á

úDå1[kOOQUJ<_rA9&L]R>Q[_rs[kGŠ<a<=uš‰Su

a

^

ý 6

ÿæsfGJRQ[_UAI

á

|SåÛTUA>Ž

x˜1[a<o<RZD9;I‰/9UJTRZD9TVUA>d

á

a

?

å

Nb Z0T[

Ô

ú

á

a

?

å

Nb

9

])^

N

á

a%0

å

b@[

Ô

ú

á

a%0

å

Nb

9

])^

N

á

a

?

å

á

a)0

å

Nb .

K

á

å

ý1e

C1ZS[kO'[ŽO'9+àGAY+RQ<_uMRZD9OGJdh9TVUA>døGAO á úDå9+àY+9;eDRERZGJR IDUJ

a

?

[kO,[_IõR"ZD9eS<kGAY+9UJT

a

^

GJIL

.

K

[ŽO,[_IRZD9eS<kGAY+9

UJT

.

?

6hC1ZSfOERZD9\OQUJ<_fDRQ[_UAI[kOGnIGŠ<_UAwAUAfORUR"ZGJREUJT

á

úDåH@1[_RZ

á

a

?

å

b“[

x

á

N0

[

_

9 ])^

N

å

])^

_

.

K

á

åH@

>9&OQfS<_RQ[_IDwh[_IGT9;9&LS‰GsYNMY+UAISR>Un<ÜUnTjRZD9TVUA>d

á

å

[9 ])^

N

ã

_

[

á

N

0

[

_

9

])^

N

å

]H^

_

.

K

á

å

ä-e

’VT

.

K

ý

GAO19+<a<“@DRZD9;I\RZD9 >9&OXfS<=RX[=IDw\Y+UAI^R">UJ<1[a<a<‰9ERZD9!O"GJdh99+à Y+9;eDR:TVUA>

.

P

[_IRZD9 eS<kGAY+9EUnT

.

K

64’“I\UARZD9;>

mUs>HLDO;@DRZD9RQmUs”VR9;>d*Y+UAISR>UJ<jLS9&O"Y+>Q[_‰9&L‰Su û GJ>>HGn>HLc[kO1TVUAfDILfOt[_IDw—R"ZD9E<_UJm9&OXR”VUA>HLS9;> IDUsIDŒ;9;>U

.



R9;>"dM@

 ZGJR9;rA9;>'RZGJR1d—GŠu—‰/9A6

C1ZS[kOdc9;RZDU™L]ZGAOOQUAdc9<a[=d˜[=R+GJRQ[_UAIO;6’“R[kOIDUARe/U^OOt[_‰S<_9MRUp[_IY+>9&GAOQ9\RZD9GAY;Y+fD>HGAY+uçUnT,R"ZD9•GJeDeD>"U&àD”

[=d\GJRQ[_UAI‰Su GALDLs[_IDwçdcUA>9R9;>d\OR"UõR"ZD9eUJ19;>˜OX9;>Q[_9&O1[_RZDUAfDRhR"ZD9R9&Ls[_UAfOeD>UDY+9&OOUJTEOQUJ<_rA[_IDw]TUs>R"ZD9

eUJ<_uSIDUAd[kGŠ<UJTRZD9hGJeDeD>UAeD>X[ŽGnR9UA>+LS9;>&6ö IS<_uMRZD9`>HOQRR‹1UR9;>d\O UJTRZD9hOQ9;>Q[_9&OY;GJIM‰/9TUAfDILp‰^ud\GJR>Q[aà

Y;GŠ<kY+fS<ŽGnRQ[_UAIO!GsOmLS9&O"Y+>Q[_‰9&LGJ‰UJrA9A6

ˆ

<kOQU@DRZD9ERQ1UA”VR9;>"d Y+UAISR>UJ<UAIS<_u•Y+UsIOt[kLS9;>HO UsID9!UA>+LS9;> UJTIDUAIS<a[_ID9&GJ>Q[_RQuA@

GAO!OXZDUv'I[_I á zSå: ZD9;>9UAIS<_u

.

?

[kOfOQ9&L@/[_wAIDUs>Q[_IDwMGJI^uZS[_wAZD9;>EUs>HLS9;>!eGn>RHO'UJT

.

6!’œTmG\eD>UA‰S<_9;døZGAO'‰UAR"Z

æAfGALS>+GJRQ[kYGJILçY+fD‰S[kYIDUAIS<a[_ID9&GJ>Q[_RQ[_9&O;@4TVUA>9+à GndheS<_9A@RZD9;IçR"ZD9˜Y+fD‰S[kYceGJ>RUJTmR"ZD9˜OXu™OQR"9;d 1[a<a<m‰/9[_wAIDUA>9&L6

89&Y;GnfOQ9UJT4RZS[kO1eD>UAe/9;>RQuh[_R!OQ9;9;d\O1>9&GAOQUsIGJ‰S<_9ERUUAIS<_ufOQ9ERZS[kO1dh9;RZDUDL\UAIeD>Us‰S<=9;d\O 1[_RZUsID9EUA>HLS9;> UJT

IDUAIS<a[=ID9&Gn>Q[_R‹u

á

 ZD9;RZD9;>RZS[kO4UA>+LS9;>4[ŽO:æAfGsLS>HGJRQ[kYJ@^Y+fD‰S[kYJ@sUA>ZS[_wAZD9;>;åH6C1ZD9 dc9;RZDU™LLSUS9&OZGŠrA9:RZD9!GALSrJGJI^R+GJwA9

RZGJR1[_R1[kO'rA9;>u\9&GAOQu\RU[=dceS<=9;dc9;I^R&@GJIL•[=R+O Y;GŠ<kY+fS<kGJRQ[_UAIOEY;GJI‰/9LSUAID9rA9;>uæAfS[kY"NA<_uA6

f

‡

‡ˆ&b‚;…D‚("•—–t"˜|"/×ÜÙh"/ׂš™\݆A†J…D‚&ݛ”œ4څD‚&ݎØ×

C1ZS[kOdh9;RZDUDLMGŠ<kOQU\>9&OQfS<_RHO,[_I›G˜TV9;9&LS‰GAYNMY+UsI^R>"UJ<[_IeUJ19;>‘OQ9;>X[=9&O,TVUA>dM@DR"ZDUAfDwAZ[_RELSU^9&OEOXUhRZD>UAfDwsZ

GhLs[aéÜ9;>"9;I^R eD>"U™Y+9&OOƒ6’“IOQR"9&GAL\UJTOQUJ<_rA[_IDw\RZD9B

ð

8þ9&æAfGJRX[=UsI\[=R+OQ9+<aTX@/RZD9EeUJ19;> OQ9;>Q[_9&O'9+à™eGJIO‹[=UsI[kO GJeDeS<a[_9&L

RURZD9h>9+<kGJR"9&LçOQRHGJR"9;”“LS9;e9;ILS9;ISRW:[kY;Y;GJRQ[19&æAfGnRQ[_UAI á 5

g

W ÿ,åH6C1ZD95

g

W ÿôdh9;RZDUDL[kOLs[kOY+fOOX9&L[_I¹LS9;RHGv[o<

‰^u]7<_UAfDRQ[_9;>&@ g =5AUAfDŒ&GGJILi>HGAY+9;N[_I ã

Ô

ù

ä

@bGnILRZD9fOQ9UJTmR"ZD9e/UJm9;>OX9;>Q[_9&OTVUA>!R"ZS[ŽO9&æAfGnRQ[_UAI[ŽO‘T>"UAd

ç9;>IS<a[ÛGnIL7U^UsNõã

ÔsÔHä

6

C1ZD9[kLS9&G‰9;ZS[_ILçR"ZD9hdh9;RZDUDL[kORUeGJ>HGŠ<a<_9+<mR"ZD9hfOQ9hUJT1RZD9—W:[kY;Y;GJRX[m9&æsfGJRQ[_UAITVUA>E<a[_ID9&GJ>eD>UA‰S<_9;d—O

‰^u>9;'>Q[_RQ[_IDwRZD9MIDUAIS<a[_ID9&GJ>pTfDIY+RQ[_UAIòUJT

[_I

á

Ô

åGsO

.

á

å



á

å

6 l UAR9MR"ZGJRhRZD9YZDUJ[kY+9çUnT

[ŽO

IDUAREfDIS[kæAfD9A@4GJILLs[oé9;>9;ISRY"ZDUJ[kY+9&OE1[a<a<m>9&OXfS<=R[_I¹Ls[aé9;>9;ISRY+UAISR>UJ<kO;6þ[_RZ

.

>9;'>Q[_RR9;I[_IçRZS[kO G&uR"ZD9

OQRHGJR9;”“LS9;e/9;ILS9;I^REW:[kY;Y;GJRQ[9&æsfGJRQ[_UAI\[kO UnTjRZD9TVUA>d

_

á

å

á

å

‰ N

á

å

_

á

å

[

_

á

å

9 ])^

N

_

á

å

žOŸ

ý

2

á

yAå

GJILRZD9EUseDRQ[_d—GŠ<T9;9&LS‰GsYNMY+UAISR>Un<b[kO'wJ[_rA9;I‰Su

á

å

[9 ])^

N

_

á

å

e

á üSå

ç9MIDUAR"9MRZGJRcRZD9õW:[kY;Y;GJRX[OQUn<=fDRX[=UsI

_

á

å[ŽO\OQRHGnR9;”“LS9;e9;ILS9;ISRMGJILš[kO\IDUAR\GAOh9&GsOQu¹R"Uç`ILþGAOTVUA>hR"ZD9

Y+UAIOQRHGJISR!Y+US9+î•Y"[_9;I^REY;GAOQ9A@ 9+à Y+9;eDR'TUs>,O‹[=dceS<=9eD>Us‰S<=9;d\O 1[_RZY+9;>RHGŠ[_IMOQR">fY+RfD>9&O;6,ö ID9eD>UAe/U^OQ9&Lpdh9;RZDUDL

(6)

ç9>9; >Q[_R9 [_IR9;>d—O'UJT,G\Y+UAIOQR+GJI^R'eGJ>REGJILG—OQR+GJR9;”“LS9;e9;ILS9;ISReGn>R‘GsO å 0 c †¡ å  ZD9;>9  

[kO!GcR9;dhe/UA>HGJ>ucrvGJ>Q[kGJ‰S<_9fOQ9&L•TUA>'RZD99+àDeGJIOt[_UAIRZGJR 1[a<a<‰9OX9;R RU

Ô

<kGJR"9;>&6o]9ID9+àDR  >Q[_R9

_ GAO Ge/Uv19;>!OX9;>Q[_9&O:[_I   < _ á h2—  å _ á 匢£ € 0¤ _ £ á 匢£ € 0¥ Z _ £-£ á 匢£ € 0   ? x erere L … †€ 0   i¦  á å 2 á {Så  ZD9;>9 _ [kO!OQuSdhdh9;R">Q[kYJ@bGJILOQUh9&GAY"Z ¦  [kOOQuSdhdh9;R>Q[kYGAO119+<a<œ65AfD‰OXRQ[_RfDRQ[_IDwRZD9&OQ99+à™eGJIO‹[=UsIO1[_ISRU—R"ZD9

OQRHGJR9;”“LS9;e/9;ILS9;I^REW:[kY;Y;GJRQ[9&æsfGJRQ[_UAI á yAå+@^19`IL

„ L … †€ 0    ¦  ‡ á Z0¤‰ 3¡T á åå M

N0 6 †¡T N

á å R „ L … †€ 0    ¦  ‡ [ „ L … 3€ 0   1¦  ‡ 9 ])^ N „ L … 3€ 0   1¦  ‡ žO ý1e

l UJ ‰Suhd—GnRHYZS[_IDwR9;>d\O4[_I^rsUJ<_rA[_IDwhRZD9EOGJdc9 eUJ19;>HOUnT

  19UA‰DRHGŠ[_I\RZD9'TUJ<a<_UJ1[_IDwhOQ9;RUJT49&æAfGJRX[=UsIOR"ZGJR Y;GJI‰9fOQ9&LRU\LS9;R9;>d[_ID9 ¦  ¦ 0ŒZ0¤žZN0 ¦ 0[ ¦ 0 9 ])^ N ¦ 0¤‰O ý á Ԋý å ¦ ^ M Z0[ 9 ]H^ N ¦ 0 R M N0 [ ¦ 0 9 ])^ N R ¦ ^ ¦ 0¡T§‰¡T N ¦ 0 ý á ÔsÔ å ¦  M 0 [ 9 ])^ N ¦ 0 R M N 0 [ ¦ 0 9 ]H^ N R ¦  ¦  ])^ ¡T§‰¡T N ¦  ])^ [  ])^ … ? € ^ M ¦ ? 9 ])^ N ¦  ])? R ý1e á Ô xSå ÿæsfGJRQ[_UAI á Ô&ý å[kO1R"ZD9OQRHGJILDGJ>+LW:[kY;Y;GJRQ[9&æsfGJRQ[_UAIpTUA>1RZD9<a[_ID9&GJ>eGJ>R 0 6ÿæsfGJRQ[_UAIO á ÔAÔ åGJIL á Ô x™åjd\G&u

‰9—OQUn<=rs9&L@‰DfDRGAO1[_RZRZD9hB ð 8%eUJ19;>OQ9;>Q[_9&O9+à™eGJIO‹[=UsI[_REd—GŠuM‰9hG\R9&Ls[_UAfOeD>UDY+9&OO'[aT,R"ZD9TVfDIY+RQ[_UAI

¡T

á

å[kOY+UAdheS<a[kY;GJR9&L6 B'Uv19;rA9;>Š@S[_IõOQUAdc9OQe9&Y"[kGŠ<mY;GAOX9&O;@S[_R [kO'9&GAOt[_9;>RUhUA‰DRHGv[=IZS[_wAZD9;>"”VUA>HLS9;>E>9&OQfS<_RHO,TVUA>

RZD9h5 g W ÿ 9+à™eGJIO‹[=UsI6 X Us> 9+à GndheS<_9A@/[=IRZD9Y;GAOQ9RZGJR RZD9IDUAIS<a[_ID9&GJ>TVfDIY+RQ[_UAI

. á å[_I á Ô åÛ[ŽOEæsfGALS>HGnRQ[kY [=I @SRZD9TfDIY+RX[=UsI ¡T á å1[a<a<‰9<a[_ID9&GJ>'[=I @DGJILTV>UAd á ÔsÔ åRZD9 ¦ ^ R"9;>d÷1[a<o<4‰9EUJTUs>HLS9;>  ZS[kYZ1[a<a< eD>U™LSfY+9hGJIUA>HLS9;>

? Y+UAISR>Un<œ@GJILOQU—UsI61’“IõY+UsdheGJ>Q[kOQUAIRUcRZD9B ð 8ô9+à™eGJIO‹[=UsI@D[_RE>9&æsfS[_>9&O R"ZD9UA>HLS9;>

K R"9;>d a ^ RU—Us‰DRHGŠ[_IçGJIUA>HLS9;> ? Y+UAISR>UJ<“–/RZ^fO'[_R[kOID9&Y+9&OOGn>uMRUY+UAIOt[kLS9;>GcdfYZ<kGJ>wA9;>EISfDd‰9;>EUJT eU^OO‹[=‰S<_9hY+UAd‰S[_IGJRQ[_UAIO'UJTRZD9OQRHGJR"9!rJGJ>Q[kGJ‰S<_9&O'[_I 6

C1ZD9\5 g W ÿþdh9;RZDUDL[kOdfY"ZM9&GAOt[_9;>ERUY+UAIOt[kLS9;>TVUA>EG—Y+9;>R+GŠ[_IõY"<kGAOOUJTIDUsIS<o[_ID9&GJ>X[=RQuT“GAY+RUA>Q[_Œ&GJRX[=UsIO;@

OQe9&Y"[a`bY;GŠ<a<_uA@RZDU^OQ9cTUs>'ZS[ŽY"Z ¡ ZGAORZD9MO"GJdh9cTfDIY+RQ[_UAIUnT [_IGv<o< UJT[_RHO9+<_9;dh9;I^R+O;@mGnILOQU¹Y;GJIš‰9  >Q[_RR9;I—GsO ¡T á å c¨ á å ¡T”© ,[=R"Z—GEY+UAIOQRHGnI^R”VrJGŠ<_fD9&Lhd\GJR>Q[aà ¡”© 64’“IhRZS[kO:Y;GAOQ9A@A‰SuLS9+`IS[_IDw ¦  á å ¨  á å á ¦  å © @S ZD9;>9 á ¦  å © [kO!GcY+UAIOQRHGJISR1d—GJR>X[oà@D19EUA‰DRHGv[=I\TV>UAd á Ô xSå á ¦  å © M Z0[ 9 ])^ N ¦ 0 R M N0 [ ¦ 0 9 ])^ N R á ¦  å © á ¦  ])^ å

© ¡T © ‰¡TN©

(7)

UJT5

g

W ÿ eD>UA‰S<_9;d—O Y;GJI‰/9OQUJ<_rA9&L\RUhGAO:d—GnI^uhR"9;>d—O:UJTRZD9Ee/UJm9;> OQ9;>X[=9&O'GAO1LS9&Ot[_>9&L6 ö IY+9GAO:d—GJISu ¦



R9;>d—O1GAO:LS9&Ot[_>9&LZGŠrA91TVUAfDIL@SRZD9Y+UAISR>Un<D[ŽO,UA‰DRHGŠ[_ID9&L\‰Su—OQfD‰OQRQ[_RfDRX[=IDwRZD9;d÷‰GAY"N[_ISRU á {SåjGnIL á üS偏,[=R"Z

 

OX9;RmR"U

Ô

6

C1ZD95

g

W'ÿšdh9;RZDUDL[kOmO‹[=d˜[o<kGJ>,[=Ic[_RHOGsLSrvGJISRHGJwA9&O:GJIL\Ls[ŽO"GALSrvGJISRHGJws9&ORURZD9!RQ1UA”VR9;>"d)B

ð

8dc9;RZDU™L6

C1ZD9;uh‰UsRZ—Y+UAIOt[kOQR1UJTY;GŠ<kY+fS<kGJRQ[_IDwhUAfDR:RZD91`>HOQRÛT9;þR9;>d—OÛUJTGEe/Uv19;>1OQ9;>Q[_9&O;@DGJILhY;GJIc‰UARZ\‰9EY;GŠ<kY+fS<kGJR9&L

rA9;>u—æsfS[kYNs<_uA6mB'UJm9;rs9;>&@DGAO:d—GJISuR"9;>d—O:UJTRZD95 g W'ÿOQ9;>Q[_9&O GAO1LS9&Ot[_>9&LY;GJI—‰/9TUsfDILcTUA>1RZD9EY;GAOQ9E'ZD9;I

¡Tª«¨

á

å

¡”©

@GAOLS9&OY+>Q[_‰9&LòGJ‰/Uvrs9A@'ZS[o<_9RZD9•B ð 8÷GJeDeD>USGAYZGŠ<_ GŠu™OfOQ9&OUAIS<_ušR‹1UR9;>d—O;6çC,ZS[ŽO

GAOOQfDdheDRX[=UsI—UAIcRZD9 TVUA>dïUnT

¡

LSU^9&Oj<a[=d˜[=R'RZD9!eD>"UA‰S<_9;d—OÛTUA>'ZS[ŽY"ZRZD9E5

g

W'ÿGJeDeD>U^GAY"Z[kO:dhU^OQRfOX9+TfS<“@

ߋfOQR GAOÛRZD9EB ð 8òGJeDeD>"U^GAY"Z[kO1dhU^OQR:fOQ9+TVfS<ÜUsIS<=u˜TUA>1eD>Us‰S<=9;d\O,[=R"Z—UAIS<_u\UAID9'<=9;rs9+<ÜUnTIDUAIS<a[_ID9&GJ>Q[_RQuA6mC1ZD9;>"9

[ŽO:GŠ<kOQUERZD9 LS>HGŠ ‰GAY"NERZGJRR"ZD9!5

g

W'ÿçdh9;R"ZDU™L[kOGJeDeD>"U&àS[_d—GJRQ[_IDwERZD9 OQUn<=fDRX[=UsIhUJTRZD9E5

g

W'ÿ @J ZS[kY"Zh1UAfS<kL

eD>U™LSfY+9\UAIS<_uõGOQfD‰UseDRQ[_d—GŠ<mY+UAISR>UJ<9;rA9;I[aT!OQUJ<_rA9&L›9+à GAY+RX<=uA@F ZS[a<_9—RZD9\B

ð

8%dc9;RZDU™Lp[kOGneDeD>UŠà^[_d—GJRX[=IDw

RZD9B ð 8ò9&æAfGnRQ[_UAI[_RHOQ9+<aT6

f

‡

f

‡ˆ&Ú†A†3"D€&€ŠÝr¬w"*­—…) #"D„†jFÝV×}||4„&Ø1}4Ý®$…D‚&Ý_ØF×

’“IOQR9&GsL\UJTjR"ZD9E>9;wAfS<kGJ> B ð 8ò9&æAfGnRQ[_UAI

á

xSåH@SRZD9EOQfY;Y+9&OO‹[=rs9

û

Gv<=9;>"NA[_IõGneDeD>UŠà^[_d—GJRX[=UsI

á

5

û

ˆ ådh9;RZDUDL

áT>"UAd 8:9&GJ>HL@5^GJ>X[ŽLs[kOGJIL§ç9;I[_Iïã£{S@

Ô&ýnä

åfOQ9&OcRZD9Mws9;ID9;>HGŠ<a[_Œ;9&LBGJd[a<_RUAID”

ð

GAY+UA‰S[_”“8:9+<o<d—GJI áû B

ð

8 å

9&æAfGJRX[=UsI68:9&Y;GJfOQ9hRZD9;>"9E[kOGJI9;>>UA>[_IRZD9eGJe/9;>E‰^u89&Gn>HL9;R‘GŠ<“6hãÔ&ýŠä UAIMeGJws9˜z ý xD@/m9>9&LS9;>Q[_rA9hR"ZD9

eD>UAeUSOQ9&Ldh9;R"ZDU™L\ZD9;>9A6,7UAIOt[kLS9;>RZD9Y+U^OQR1TVfDIY+RQ[_UAIGŠ<

a

á

0

–

å

G

á

0

2

å

J*L

0

á

N

N

9

å

S

,

 ZD9;>9

á-,

åOGJRQ[kOt`9&OÛRZD9 IDUAIS<a[_ID9&GJ> LSu^IGnd[kY;O

dK.

á

å

á

åH@J1[_RZ\Y+UAI^R">UJ<

á

åjGJIL[_IS[_RQ[kGŠ<Y+UAILs[_RQ[_UAI

10

6 g [aé9;>9;ISRQ[kGJRQ[_IDw

a

GŠ<_UAIDwhRZD9EeGnRZMUJT4RZD9OQuDOQR9;dÞ<_9&GALDO'RUhRZD9

û

B ð 8ò9&æAfGnRQ[_UAI@

¯° GP ã

a¤2

ä1±Y²³

a

³

10´

N

á

.

á

0

å

á

0 åå

‰ N

0

O 0

N

á

0

å

9

á

0

å

ýHe

á

Ô

ùSå

C1ZS[kO ‰/9&Y+UAdh9&O'RZD9EIDUA>d—Gv<FB

ð

8ò9&æsfGJRQ[_UAIp[aTjRZD9TUs>dfS<ŽGTVUA> RZD9Y+UsI^R>"UJ<“@

á

10

å

[

Ô

x

9

])^

N

³

a

³

0

á

10

å

2

á

Ô

úDå

[ŽO'fOQ9&L•[=I á

Ô

ùSå+6’“IOXR9&GAL@GeD>"U™Y+9&OO,[kO!OX9;R fDeRU—OQUn<=rs9 á

Ô

ùSåGJIL á

Ô

úDåRUAwA9;RZD9;>,[=IGJI\[_R9;>HGJRX[=rs9EeD>U™Y+9&O"O;6

ç9:`>HOQRY"ZDU^U^OX9,GnI[_IS[_RQ[kGŠ<Y+UAI^R">UJ<ATVfDIY+RQ[_UAI ¶µ 0¥·

á

å

á

TVUA>49+à GJdceS<=9A@sRZD9:<a[=ID9&Gn>UAeDRQ[_d—Gv< Y+UAISR>Un<å+6jC,ZD9;I

m9EfOX9RZD9

û

B ð 8þ9&æsfGJRQ[_UAI

á

1[_RZRZD9ErJGJ>Q[kGJ‰S<_9

10

IDUJ Y"ZGJIDwA9&L\RU

åRU`IL‘¸º¹w»¼-½

¸

b

‰SuOQUJ<_rA[_IDw

„

³

a

µ

0¥·

³

‡

N

M

.

á

å

µ

0¥·

á

å

R

‰ N OQ

á

µ

0¥·

å

N 9

µ

0¾·

ý1e

ç9<_9;R!RZD9EID9+àDREY+UAI^R">UJ<[_IMRZD9OQ9&æsfD9;IY+9‰/9

µ

^

·

á

å

[

Ô

x

9 ])^

N

³

a

µ

0¥·

³

á

å

e

ç9EeD>UDY+9;9&LRUhfOX9RZS[kO1RU˜`IL

a

µ

^

·

GJIL

µ

?

·

(8)

ˆ GŠ<_9;>Ns[_I¹dc9;RZDU™L]Y;GJI¹‰/9—fOX9&LçRUGJeDeD>UŠàS[=d\GJR9hRZD9 B ð 8ï9&æsfGJRQ[_UAIOQUMR"ZGJR[_R˜Y;GnI¹‰/9•OQUn<=rs9&L

I^fDdh9;>X[ŽY;Gv<o<_uA61CULSUER"ZS[ŽOƒ@A19 YZDUSU^OQ9 GEOQ9;RUJT

‰GsOt[kOFTfDIY+RQ[_UAIOÀ¿†Á

ÂÃ

€

^

GJILLS9+`ID9 RZD9 ¦

?

[_IDID9;>1eD>U™LSfY+R

GAO Ä

.%2ŨwÆ! JIÇ .

á å ¨ á å S P2  ZD9;>9 5

[kO\GJI^uY+UAdheGsY+R˜OXfD‰OQ9;RhUJTERZD9>9;wJ[_UAIþUJT‘GJR"R>HGAY+RQ[_UAIGAOOXU™Y"[kGJR9&L 1[_RZRZD9NSIDUJ I OQRHGJ‰S[a<a[_Œ+[_IDw

Y+UAI^R">UJ< wµ 0¥· á åH6C1ZD9 û GŠ<_9;>NA[_IGJeDeD>UŠà^[_d—GnRQ[_UAIUJT a µÈ · [kO wJ[_rA9;I‰^u a µÈ · à á å à … € ^1É µÈ · Á á å 2  ZD9;>9R"ZD9Y+U^9+î•Y"[_9;ISRHO É µÊÈ · OGJRX[ŽO‹Tu\RZD9E19&GJNcTUA>"d*UJT á Ô ùSå < Ä ¯° G¶ ã à … € ^)É µÈ · Á Ë2 µÈ · à ä 2 Á  Æ` ý á Ô |Så TUA>Ž Ô 2 ere#e 2¥ 6jC,ZD9E[_IS[_RQ[kGŠ<ÛY+UsI^R>"UJ<TVfDIY+RQ[_UAI µ 0¥· à TUs> á Ô

|SåÛ[ŽOY"ZDU^OQ9;I@GJIL\RZD9E<kGJR"9;> [_R9;>HGnR9&O GJ>9TUsfDIL

GAO:TVUJ<a<=UJ!Oƒ6ÿæsfGJRQ[_UAI á Ô |SåwJ[_rA9&O 9&æAfGnRQ[_UAIO R"U˜OXUJ<_rA9ETVUA>1RZD9 fDIDN^IDUJ IO É µÊÈ · @3Ì Ô 2 x 2 ere#e 2— < à … € ^%É µÊÈ · Ä ² ³ Á ³ ´ N M . µÈ · à R 2 Á  Æh Ä HN¶OQ á µÊÈ · à å N9 µÈ · à 2 Á  Æ` ý á Ô zSå TUA>Ž Ô 2 e#ere 2¥ 6C1ZD9EID9+àDR‘Y+UAISR>Un<ÜfDeLDGJR9E‰/9&Y+UAdh9&O µÊȃ ^ · à 8[ Ô x 9 ])^ N à … € ^ É µÈ · ²P³ Á ³ t´ e á Ô yAå X >UAd á Ô z™åÜGJIL á

Ô yAåRZD91eD>UDY+9&OOY;GJI‰91 >X[=R"R9;IhGAOGnI[_R9;>+GJRQ[_rA91d—GJR>X[oàeD>"UA‰S<_9;dM@A1[_RZRZD91ID9&Y+9&OO"GJ>u

[=IDID9;>\eD>UDLSfY+RHO\Y;GŠ<kY+fS<ŽGnR9&Lþ‰9+TVUA>9;ZGJIL6c]91[a<o<EfOQ9RZD9IDUARHGJRX[=UsI‘Í µÈ · à M É µÈ · ^ 2 erere 2 É µÈ · à R N @ZÎ Ã á å á Á ^ á å 2 erere 2 Á à á åå N @1GJILš<_9;RvÏtÎ Ã

LS9;IDUAR"9RZD9 ð GsY+UA‰S[kGJI UJTÎ

Ã

6 ˆ <kOQU@:TVUA>hGJI^uš>9&GŠ<_”VrJGŠ<_fD9&LTVfDIY+RQ[_UAI

(9)

X >UAd RZD9YZDUSOQ9;I\[_IS[=RX[ŽGv<[=R"9;>HGJR9 µ OXUJ<_rA9 É µ 0¥· à æå32  ZD9;>9 Ÿ Û à Û á GnIL å‚[ Û Ü [ Û ß 6 û [_rA9;IRZD9 áç åtRZh[_R9;>+GJR9A@/RZD9 áç Ô åtRZ\[_R9;>HGJR9[kO RZD9OQUJ<_fDRQ[_UAI RUhRZD9E9&æsfGJRQ[_UAI É µÊȃ ^ · à æå32  ZD9;>9 U Û à [ ^ ? à ? € ^ É µÈ · ? Û áßwá ? GJIL å[ Û Ü [ ^ P M à ? € ^ É µÊÈ · ? Û á!ßwá ? R Í µÈ · à 6 á l UAR9R"ZD9 ^ P [_IR"ZD99+àDeD>9&OOt[_UAI TUA> å

@D ZS[kYZ GAO:[_IY+UA>>9&Y+RX<=u >Q[_RR9;IGAO

^ ? [_IRZD9EUA>X[=wn[=IGv<jeGJe/9;>ã Ô&ýŠä 6aå ˆ R 9&GAY"ZMOQR9;e çoè ý @DRZD9Y+UsI^R>"UJ< [ŽO'wJ[_rA9;I‰^u µÊȃ ^ · à é[ Ô x 9 ])^ N ϚΠN Ã Í µÈ · à e C1ZD9OQfY;Y+9&O"Ot[_rA9 û

GŠ<_9;>NA[_IGJeDeD>UŠà^[_d—GnRQ[_UAIdh9;RZDUDL\[kO1dhUs>9ERQ[_dh9;” [_I^R"9;IOt[_rA9RZGJIRZD9`>HOXR RQmUdh9;R"ZD”

U™LDOLs[kOY+fOOQ9&L6C1ZD9—GsY+RfGŠ<[_R9;>+GJRQ[_UAIšeD>U™Y+9&O"O[kOTœGAOXR&@‰DfDRRZD9hRX[=dc9—ID9;9&LS9&LšRUY;GŠ<kY+fS<kGJR9\RZD9h[_ISR9;wA>HGv<ŽO [=I á Ô üSåmGJIL á Ô {™åmY;GJI‰9hOt[_wAIS[a`bY;GJISR&6EC1ZD9dh9;RZDUDLZGAO'RZD9hGALSrJGJI^R+GJwA9R"ZGJR1[_R[kOEGJeDeS<a[ŽY;Gn‰S<=9\RU—G˜<kGJ>wA9;> Y"<ŽGsOOEUJT eD>Us‰S<=9;d\O;@1[_RZDUsfDRRZD9h>"9&OQR>Q[kY+RQ[_UAIO‘[=dceU^OQ9&L]‰SuõR"ZD9`>HOQRERQ1U—dc9;RZDU™LDOƒ6—B'Uv19;rA9;>Š@/[=RZGAOER"ZD9 Ls[ŽO"GALSrvGJISRHGJws9A@‰/9+[_IDw›GnIM[_R9;>+GJRQ[_rA9hdh9;R"ZDU™L@4RZGJR[_R[ŽOLS9;e9;ILS9;ISRhUAIRZD9—Y"ZDU^OQ9;I›[=IS[_RQ[kGŠ<1[_R9;>HGnR9 µ 0¥· 6c’VT RZS[kO1[kO1IDUAR'm9+<a<jY"ZDU^OQ9;I@ RZD9;IRZD9Edh9;RZDUDLd\G&u\Y+UAI^rs9;>wA9ErA9;>u\Ot<_Uv,<=uA@/UA>1d—GŠu\9;rA9;IIDUAR!Y+UAISrA9;>ws9‘GJRGŠ<a<œ6

f ‡ê‡ÖŠ×‚("™„3|4Øw _…D‚&ݎØ× Ø%s”ëìíØb~ #")$ï&bØw Vڂ&Ý_ØF×܀

ˆ rs9;>uõLs[aé9;>9;ISRGJeDeD>USGAYZRU\`ILs[_IDwçGcTV9;9&LS‰GAYNçY+UAISR>Un<[kOEfOX9&L[_I¹RZD9>9;d\GŠ[_IS[=IDwRQ1U—dc9;RZDU™LDO RUh‰9Ls[kOY+fO"OQ9&LID9+à™R&6:C1ZD9&OQ9Edh9;RZDUDLDO'fOQ9ER9&Y"ZDIS[ŽæsfD9&O'TVUA>:`ILs[=IDwGJIUAe9;ID” <_USUAeõY+UAISR>Un<bTVUA>1RZD9OQu™OXR9;d 1[_RZMGhY"ZDU^OQ9;I\[_IS[_RQ[kGŠ<ÛY+UsILs[=RX[=UsI H0 6:C1ZS[kO1[kO1>9;e/9&GJR9&L•TUA>1d—GnI^uhrJGŠ<_fD9&O UnT H0

6 ˆ R 9&GAY"ZeUJ[_ISR&@DRZD9[_IS[_RQ[kGŠ<

Y+UAI^R">UJ< wµ b ¼ · á-, ý åR"ZGJR[kO4TVUAfDIL˜[kOmY+UsIOt[kLS9;>9&LhR"ZD9‘Y+UAISR>Un<rvGŠ<_fD9EGJR H0 6C,ZD9;I—GJIc[=ISR9;>e/UJ<kGJRQ[_UAIc[kOmLSUsID9

Uvrs9;>˜Gv<o< RZD9&OX9h[_IS[_RQ[kGŠ<EeUJ[_ISRHORUTUA>"d GY"<_U^OQ9&LS”<_USUAe

á

T9;9&LS‰GAY"N/åY+UsI^R>"UJ<

á

åH6C1ZD9UAe/9;ID”<_U^UAe Y+UsI^R>"UJ<

[ŽO,TVUAfDIL‰^uOQUJ<_rs[=IDwR"ZD9BGJd[a<_RUAIS[kGJIçOQuDOQR9;d GJ>X[ŽO‹[=IDwcTV>UAd*RZD9ID9&Y+9&OOGJ>"uUAeDRQ[_d—GŠ<a[_RQuMY+UAILs[_RQ[_UAIOã Ô @ Ô y ä wJ[_rA9;IM‰Su + . á å [ ^ ? 9 ]H^ N)ð ð [. N b á å ð [ x O á

x ý å

1[_RZ[_IS[_RQ[kGŠ<Y+UAILs[_RQ[_UAI á ý å ñH0 GJIL `IGŠ<‘Y+UAILs[_RQ[_UAIþ<a[_dòôó L ð á-, å ý

6 X >UAd RZS[kO;@1R"ZD9MUAe/9;ID”<=USUAe

Y+UAI^R">UJ<[kO!Y;GŠ<kY+fS<kGJR9&LGAO á-, å [ Ô x 9 ])^ N ð á-, å e ’“IR"ZD9rA9;>HO‹[=UsIEUJT™R"ZS[ŽOFdh9;RZDUDLLS9&O"Y+>Q[_‰9&L‰^u’“R"U!GJIL5^Y"ZD>US9;R9;>ã Ô z ä @&RZS[kOFeD>UA‰S<_9;dô[ŽO4OQUJ<_rA9&LEGsO/TUn<o<_UJ!O;6 X

[=>+OQR RZD9'`IGŠ<RQ[_dh9[kO Y"ZGJIDwA9&LcTV>UAdÞ[_IS`IS[_RQuRUhGhYZDUSOQ9;I\`IS[_R9@õ@DRZD9;IR"ZD9ER‹1UA”Ve/UJ[_I^R1‰/UAfDILDGJ>u\rvGŠ<_fD9

á

C8åeD>UA‰S<_9;d [kO Ls[kOY+>9;RQ[_Œ;9&LI^fDdc9;>Q[kY;GŠ<a<=uTVUA>

,

4

ãý

2

õ ä 6C1ZD9Ls[kOY+>"9;R9C:8ïeD>UA‰S<_9;d*[kO1wn[=rs9;IM‰Su

(10)

 ZD9;>9{E Ô 2 erere 2¥«[ Ô @DGJIL [ŽOGeD>9&O"Y+>Q[_‰9&LI^fDd‰/9;> UJTLs[ŽO"Y+>9;RQ[_Œ&GJRQ[_UAIp[=ISR9;>rJGŠ<kO;@OQUhRZGJR ¡ õ ä 6 B 9;>9 10 [kO RZD9Y"ZDU^OQ9;Ip[_IS[=RX[ŽGv<ÛY+UAILs[_RQ[_UAI@GJIL ð à ý 6 ë 9;RRQ[_IDwù á ^ 2 ere#e 2¥ à ])^ 2 ð ^ 2 ere 2 ð à ])^

åmGJIL\>"9; >Q[_RQ[_IDw á x

Ô åGAO ú á ù å „ ^ ö ò á ? [‰ ?(])^ å [ ^ ? á . á ? å ž. á ?ø])^ åå ^ ? 9 ])^ Nwð ? ^ ö ò á ð ? ƒ ^ [ ð ? å ^ ? . N b á ? å á ð ? ð ? ƒ ^ å x O ? ‡ ? € ^¾ûýüýüýüýûà ])^ ý á xsxSå >9&OQfS<_RHO'[_IõG\xIA á D[ Ô åmLs[_dh9;IOt[_UAIGŠ<mOQuDOQR9;dóUJTIDUAIS<a[_ID9&GJ>9&æsfGJRQ[_UAIO á  ZD9;>9QAó[kORZD9I^fDd‰9;>UJTmOQR+GJR9 rvGJ>Q[kGJ‰S<_9&O+å1 ZS[kY"ZõY;GJI‰9OXUJ<_rA9&L\fOt[_IDw l 9; RUsIP£O1dh9;RZDUDL6C1ZD9 l 9; RUsIP£O1dh9;RZDUDLc[_R9;>HGJR"9[ŽO ù ƒ ù3þ [ ãÙÏ ú á ù3þ"å ä N ú á ù†þ¿å 2

 ZD9;>9{Ï ú [ŽO'RZD9 ð GsY+UA‰S[kGJIMUJT ú GnIL\ZGAO1RZD9TVUJ<a<_Uv,[=IDwOQR>"fY+RfD>9 <

Ï ú „ Í ÿ [ N ‡ e C1ZD9!d\GJR>Q[aà

[ŽO:‰S<_UDYN<_UJ19;>‰S[_”“Ls[kGJwAUAIGv<FGnILRZD9d—GJR>Q[kY+9&OÍ GJIL ÿ GJ>9 ‰S<_UDYN\Ls[ŽGnwAUAIGŠ<“@^Gv<o<1[_RZc‰S<=UDY"N

Ot[_Œ;9{A6C1ZD9ErJGŠ<_fD9&OUJTRZD9E‰S<_U™Y"N™OGJ>9GsOTVUJ<a<_UJ!O

á

fOt[_IDw

Û

;

GsO GJIBADCBA [kLS9;I^RX[=RQud—GnR>Q[aàbå

< ?øû? Ô ¡ , Û ; [ Ô x .ºb á ? å 2 ? ƒ ^Œû? [ Ô ¡ , Û ; [ Ô x .ºb á ? å 2 Í ?øû? Ô x 9 ])^ N¤2 ÿ ?øû? Ô x . N b(b á ? å á ð ? ð ? ƒ ^ å x O e ç9çZGŠrA9¹Y;GJ>">Q[_9&LòUAfDRRZD9ç>"9&æAfS[_>9&L [_I^R9;>"eUJ<kGJRQ[_UAIOƒ@ETVUJ<a<_Uv,[=IDwþ’“RUòGJIL%5^Y"ZD>US9;R9;>£OY"ZDUJ[kY+9A@,[=R"Z

û >9;9;IP£OÜTVfDIY+RQ[_UAIO4UJTDR‹uSe9¤¯ á

h2 å ¢ [ ¢GJILGYZDUn[ŽY+91UJT ù e yTVUA>RZD9:9+à™e/UAID9;I^RŠ6jC,ZD9mY"<_U^OQ9&LS”<_USUAe Y+UAI^R">UJ<[kO RZD9;Iwn[=rs9;IM‰Su á å … Ȁ ^ Ð È ¯ á h2 á H0 å È å 2  ZD9;>96¿ Ð È Â GJ>9MR"ZD9õY+US9+î•Y"[_9;I^RHO\UnT‘RZD9p[_I^R9;>"eUJ<kGJRQ[_UAI GJILU¿ á 10 å È Â GJ>9MR"ZD9 [_IS[_RQ[kGŠ<eUJ[_ISRHOcfOQ9&LþRU [=ISR9;>e/UJ<kGJR9Uvrs9;>hRZD9>9;wJ[_UAI 5

6 C1ZD9õY+US9+î•Y"[_9;ISRHO—Gn>9MYZDUSOQ9;I OQUçRZGnRhRZD9MY+UAISR>UJ<1`RHO˜9+à GAY+RX<=uGJRhR"ZD9

[=ISR9;>e/UJ<kGJRQ[_UAIeUJ[_ISRHO;@OQUhRZGJR áá 10 å å … Ȁ ^ Ð È ¯ áQá 10 å †2 á 10 å È å á/, ý 2 á H0 å å TUA>GŠ<a<Ì Ô 2 erere 2 Þ6B'9;>9 á/, ý 2 á H0 å

åE[kO\RZD9UAe9;ID”<_USUAe Y+UAI^R">UJ< TVUA>c[=IS[_RQ[kGŠ<hY+UAILs[_RQ[_UAI

(11)

ÒÔÕ Û ¯ 0 å ^ 2 0 å ^ å ÖºÖÖ Û ¯ 0 å ^ 2 0 å å 6 6 6 6 6 6 6 6 6 Û ¯ áá H0 å 2 á 10 å ^ å ÖºÖÖ Û ¯ áá 10 å 2 á 10 å å ×ÙØ Ú ÒÔÕ Ð ^ 6 6 6 Ð ×ÙØ Ú ÒÔÕ ý 2 0 å ^ å 6 6 6 á-, ý 2 á 10 å å ×ÙØ Ú 2  ZD9;>9 Û [kOGJI[kLS9;ISRQ[_R‹ud—GnR>Q[aàUJTLs[_dh9;IOt[_UAIš@JRZD9 ISfDd‰9;>UnTÜY+UAISR>UJ<DrvGn>Q[kGJ‰S<_9&O;6 l UAR9 RZGnRRZD9'rvGŠ<_fD9&O UAIRZD9Ls[kGJwsUAIGŠ<GJ>9GŠ<a<Œ;9;>"UTUs> RZD9Y"ZDU^OQ9;ITVfDIY+RQ[_UAI*¯h6 C1ZD9EfOQ9UnTRZD9[_I^R"9;>eUJ<kGJRX[=UsIMd—GJNs9&OR"ZS[ŽO'dh9;RZDUDL\rA9;>ucRQ[_dh9;”“Y+UAIOQfDd[_IDw@/wJ[_rA9;IRZGJR1RZD9EUAe/9;ID”<=USUAe Y+UAI^R">UJ<mdfOQR‰/9\TUAfDIL]TVUA>d—GJISuçLs[aéÜ9;>"9;I^R[_IS[_RQ[kGŠ<‘OXRHGJR9&O;6çC,ZS[ŽO[ŽO˜9&OQe9&Y"[kGŠ<a<_u R>"fD9hTVUA>eD>UA‰S<_9;d—O,[=R"Z <ŽGn>wA9;>hISfDd‰9;>HOcUJT‘OQR+GJR9rvGn>Q[kGJ‰S<_9&O;– RZS[kO˜[_IY+>9&GAOQ9&OcRZD9RQ[_dh9ID9;9&LS9&L‰UsRZ‰^ud\GJNA[_IDwçR"ZD9MLs[ŽO"Y+>9;RQ[_Œ;9&L

C8 eD>Us‰S<=9;d dfY"Zc<ŽGn>wA9;>!GJILc‰Su[_IY+>9&GAOt[_IDw\RZD9!ISfDd‰9;>1UJT[_ISR9;>e/UJ<kGJRQ[_UAIeUn[=ISRHO1ID9;9&LS9&LLSfD9!R"UR"ZD9

<ŽGn>wA9;>Ls[_dh9;IOt[_UAI6:’“R4[kOIDUsRjGrA9;>"uY+UAdheS<a[kY;GJR9&LceD>UDY+9&OO;@JZDUJ19;rA9;>&@AGJILGŠ<a<UJTRZD919+à™e/9;IOt[_rA9EY+UAdheDfDRHGJRX[=UsI

[ŽOcLSUAID9UJé”<a[=ID9A@ OXUõR"ZD9MGAY+RfGŠ<!Y+UAISR>UJ<1UJT!RZD9MOXu™OQR"9;d Y;GnI OQRQ[a<a<!‰9LSUAID9rA9;>u¹æsfS[kYNs<_uA6 C1ZD9;>9MGn>9—IDU

>9&OQR>Q[kY+RQ[_UAIOUAIRZD9RQu^e/9&OEUJTeD>Us‰S<=9;díRZGJRY;GJI‰/9—OQUJ<_rA9&L6hC1ZD9eD>UDY+9&OOUJT[_IY+>9&GAOt[_IDwRZD9hGAY;Y+fD>HGAY+uUJT

RZD9Y+UAISR>UJ<‰Su•GALDLs[_IDw\dhUA>9[_ISR9;>e/UJ<kGJRQ[_UAIeUJ[_ISRHO:[kOGŠ<kOQU—OQR>+GŠ[_wAZ^RXTUA>",Gn>HL6

f

‡b‡ÖŠ×‚("™„3|4Øw _…D‚&ݎØ× Ø%s!Ö+‚("D„&…D‚&Ý#¬w"÷&bØw Vڂ&Ý_ØF×܀

ˆ O‘[=I]RZD9heD>9;rs[_UAfOEdh9;R"ZDU™L@FRZS[kOER9&Y"ZDIS[kæAfD9GŠ<kOQUMfOX9&O[_I^R"9;>eUJ<kGJRX[=UsI¹UJrA9;>EGISfDd‰9;>UnTmUAe/9;ID”<=USUAe

Y+UAI^R">UJ<OQUJ<_fDRQ[_UAIO;@ ‰DfDRmR"ZD9Edh9;RZDUDL\UJTUA‰DRHGv[=IS[_IDw\RZD9&OQ9EOQUJ<_fDRQ[_UAIO,[kO Ls[aéÜ9;>"9;I^R&6ے“IRZS[kO1dh9;R"ZDU™L@DeD>"UAeU^OX9&L

‰^u—iGJ>"N^d—GnI—GJILEGJRŒã£x

ý

@^x

ԃä

@ARZD9EBGJd[a<_RUAIS[kGJIMOQuDOQR9;dÞ[kO1OQUJ<_rA9&LcIDUAR GAOUAID9'<kGJ>wA9ELs[kOY+>9;RQ[_Œ;9&LC8

eD>UA‰S<_9;d wn[=rs9;IM‰Su á xsxSåH@A‰DfDRRZD>UsfDwAZMGJI\[_R9;>HGJRX[=UsIeD>U™Y+9&O"O1<_9&GALs[_IDw\RUhRZD9LS9&Ot[_>9&LY+UAISR>Un<œ6

ç9GJw^GŠ[_IYZDUSU^OQ9G`IGv<RQ[_dh9@õ@GnIL\1[_RZ[_R!LS9+`ID9hGLs[kOQRHGJIY+9TVfDIY+RQ[_UAI ú á õ 2 ð 0 å ( á õ– 0 2 ð 0 å ? ð á õ– 0 2 ð 0 å ? á õ– 0 å ? e B 9;>9 á P2 ð å N [kO4fOQ9&LER"U‘Ot[_dheS<a[aTVuIDUsRHGJRQ[_UAI@AGJIL á õ– (0 å[kO4RZD91OQUJ<_fDRQ[_UAIhGJR4RQ[_dh9oõUnTRZD9mBGJd[a<_RUAIS[kGJI OQu™OXR9;d á x ý å OQRHGn>RQ[_IDwMGJR (0 á GnIL á õ– 1032 ð 0 å!GnIL ð á õ– 102 ð 0 å!GJ>9RZD9hOQRHGJR"9˜GnILçY+U^OQRHGnR9eGJ>"RHOUJTmR"ZS[ŽO OQUJ<_fDRQ[_UAIåH6 ú

[kO1Gdh9&GAOQfD>"9;dh9;I^R1UJTZDUJ Y"<_U^OQ9ERUŒ;9;>URZD9‘OXu™OQR"9;d ,[o<a<‰9GnRmRX[=dc9”õ@SwJ[_rA9;IGrvGŠ<_fD9EUJT

ð 0 6 C1Z^fO:RZD9UAe/9;ID”<=USUAeMY+UAISR>Un<D[ŽOÛTVUAfDIL\‰Su˜OXUJ<_rA[_IDw[_IST ¼ ú á õ 2 ð 0 åRU`ILcRZD9!rJGŠ<_fD9EUJT ð 0  ZS[kY"Zd[_IS[_d[_Œ;9&O ú á GJILhOXULS>Q[_rA9&ORZD9OQu™OXR9;dèY"<_U^OQ9&OQR:RUEŒ;9;>UGnRRQ[_dh9õEåH6C1ZD9'd[_IS[=d˜[=Œ&GnRQ[_UAIh[kO1LSUAID9 ‰SuG û GJfO"OQ” l 9;'RUAI dh9;RZDUDL61ö ID9OQR+GJ>RHO:1[_RZGhYZDUSOQ9;I ð µ 0¥· 0

@GJILc[_R9;>HGnR9&O GAO:TVUJ<a<_UJ!O <

M ð µ ƒ ^ · 0 R N M ð µ —· 0 R N [ M Ï ú á ð µ · 0 å R N M Ï ? ú á ð µ · 0 å R ])^ 2 á xsùSå  ZD9;>9{Ï ú GJILBÏ ? ú Gn>9ERZD9EwA>HGsLs[=9;ISR!GJILB 9&O"Ot[kGJIUJT ú 1[_RZ>9&OXe9&Y+RRU ð 0 GJILMGn>9EwJ[_rA9;I‰Su Ï ú á õ 2 ð µ · 0 å ²T³ ³ ð 0 á õ 2 ð µ —· 0 å ´ N á õ 2 ð µ —· 0 å 2 Ï ? ú á õ 2 ð µ · 0 å ²T³ ³ ð 0 á õ 2 ð µ —· 0 å ´ N ²T³ ³ ð 0 á õ 2 ð µ —· 0 å ´ N á õ 2 ð µ · 0 å ³ ? ³ ð ? 0 á õ 2 ð µ —· 0 å e X UA>!GOQfSîY"[=9;ISRQ<_uõY"<_U^OX9[=IS[_RQ[kGŠ<[_R9;>+GJR9A@SRZD9ER9;>d ³ ? ä ³ ð ? 0

[kO GsOOQfDdh9&L\rA9;>"u•OQd\GŠ<a<œ@OQU[_R [kO:[_wAIDUs>9&L6mC,ZS[ŽO

(12)

M

ð

µ

ƒ

^

·

0

R

N

M

ð

µ

—·

0

R

N

[ N

³

³

ð

0

³

N

³

ð

0

³

³

ð

0

‡

])^

e

C1ZS[kO[_R9;>HGJRX[=UsIçeD>UDY+9&OOE>9&æsfS[_>9&OE‰/UARZ GnIL

³

ä

³

ð

0

GnRERZD9`IGŠ<RQ[_dh9õ6hC1ZD9rvGŠ<_fD9\UJT Y;GJI‰9

TUAfDILOt[_dheS<_u‰SuOQUJ<_rs[_IDwRZD9 BGJd[a<_RUAIS[kGJI—OQuDOQR9;d

á

x ý åTVUA> GJ>HLR"U@õ@AOQRHGJ>"RQ[_IDw TV>UAd%RZD9:[_IS[=RX[ŽGv<ÜY+UAILs[_RQ[_UAI

(0@

á

1032

ð

0

å

N

6C1ZD9EeGJ>RQ[kGŠ<LS9;>Q[_rvGJRX[=rs9&O Y;GJI\‰9TVUAfDILc[_I—RZD9TVUJ<a<_UJ1[_IDw GŠuA64’VTR"ZD9‘BGJd[a<_RUAIS[kGJIOQu™OXR9;d

[ŽO

Q

°

á å+@^,[=R"Z

(0

á

10I2

ð

0

å

N

@SRZD9;ILs[oé9;>9;ISRQ[kGJRQ[_IDw\1[_RZ>9&OQe/9&Y+R!R"U

ð

0

eD>U™LSfY+9&O

!

"

#

#

ò

¸%$

¸

¼

M

°

¸'&

¸$

á

å

R

¸$

¸

¼

¸%$

¸

¼

á

ý

å

„

ý

Û

‡

e

ˆ LŠßQUJ[_IS[_IDw—RZS[kO:RURZD9EB!Gnd[a<=R"UAIS[kGJIMOQuDOQR9;d÷>9&OQfS<_RHOÛ[_IMGxIA

á

A

Ô

åjLs[_dh9;IOt[_UAIGŠ<OQuDOQR9;dÞUJTö g ÿO:RU‰9

OQUJ<_rA9&LUsIçã

ý

2

õ

ä

6

’“IçRZD9cdh9;RZDUDLUJT,iGJ>"N^d—GnI›GnILEGnRŒhRZD9hd˜[=IS[_d[_Œ&GJRX[=UsI¹UJT ú

á

õ

2

ð

0

å Uvrs9;>

ð

0

[ŽOGAY+RfGŠ<a<_u¹Y;GJ>">Q[_9&L

UAfDRTUs>‘G\OQ9&æsfD9;IY+9hUJTmRX[=dc9rJGŠ<_fD9&O@õô[_IY+>9&GAOt[_IDwMR"Uv GJ>+L\[_IS`IS[_R‹uA6C1ZS[kO>9&OQfS<_RHO'[_I¹GOX9&æAfD9;IY+9hUnTrvGŠ<_fD9&O

TUA>

ð

0

 ZS[kYZY+UAISrA9;>wA9EUAIR"ZD9`IGŠ<rvGv<=fD9hGAO,RZD9`IS[_R9;”VRQ[_dh9eD>UA‰S<_9;d—O'wA9;R!Y"<_U^OQ9;>RURZD9GAY+RfGŠ<[_IS`IS[_R9;”

RQ[_dh9eD>UA‰S<_9;dM6!C,ZD9OQUJ<_fDRQ[_UAIUJTR"ZD9BGJd[a<_RUAIS[kGJIçOQuDOQR9;dówA9;ID9;>HGJR9&Lp‰^uR"ZD9`IGv<

ð

0

[_IRZD9OQ9&æAfD9;IY+9˜[ŽO

RZD9;IçfOQ9&L]RUUA‰DRHGv[=I]RZD9—LS9&Ot[_>9&LšY+UAISR>UJ< á-,

åH6hC1ZS[kOeD>UDY+9&OO[kO[_dhe/UA>RHGnI^RE‰/9&Y;GJfOQ9\rvGŠ<_fD9&OUJT

ð

0

9&GJ>Q<_u

[=IR"ZD9MOQ9&æAfD9;IY+9d\G&u]IDUAR‰9rA9;>u]wAU^UDL@GJILšd\G&uçY;GJfOX9RZD9•OXu™OQR"9;d R"Uõ‰S<_UJ÷fDeš[aTVõÞ[kOhY"ZDU^OQ9;IRUSU

<ŽGn>wA9A65AR+GJ>RQ[_IDw1[_RZ GçOQd\GŠ<a<Àõ*GJIL][_IY+>9&GsOt[_IDwç[_RTV>UAd RZD9;>9\ZD9+<_eOhR"U›GŠrAUn[ŽL]RZS[kO;6š’“R[kOhGŠ<kOQU]fOQ9+TfS<

[=IOQZDUJ1[_IDwMR"ZGJRRZD9crvGŠ<_fD9&OUJT

ð

0

 ZS[kY"Z Gn>9TUAfDILšGAY+RfGv<o<_u¹Gn>9—Y+UAISrA9;>wJ[_IDwGAOõ

= (

6C1ZD9\C8

dh9;RZDUDLçLS9&OY+>Q[_‰9&L][_Iþ5A9&Y+RQ[_UAIùD6ÍúMLSUS9&OIDUsREID9;9&LçRU‰9—OXUJ<_rA9&LTVUA>GOQ9&æAfD9;IY+9\UJT1`IGŠ<RQ[_dh9&Oƒ@‰/9&Y;GJfOQ9

RZD9;>9E[kO1IDU\RZD>9&GnRmUnTjRZD9eD>UA‰S<_9;dó‰S<=UJ1[_IDw\fDe6mB'UJ19;rA9;>&@s[_R!Y+UAfS<kL‰9fOX9+TfS< áRZDUAfDwAZRQ[_dh9;”“Y+UsIOQfDd[_IDwDå

RULSURZS[kO:RUd\GJNA9EY+9;>RHGŠ[_I\RZGJRoõþZGAO:IDUAR‰/9;9;IMYZDUSOQ9;I—R"U^UOQd—GŠ<a<RUwn[=rs9‘GwAU^UDL\GJeDeD>UŠà^[_d—GnRQ[_UAI—UnTÜR"ZD9

[=IS`IS[_R9;”VRX[=dc9heD>UA‰S<_9;dM6

C1ZD9[_IS[_RQ[kGŠ<ErvGŠ<_fD9UJT

ð

0

Y;GnI ‰9MY"ZDU^OQ9;I T>"UAd RZD9<a[_ID9&GJ>æAfGALS>+GJRQ[kY>9;wsfS<ŽGnRUA>heD>Us‰S<=9;d6 C1ZGJR[kO;@

ð

µ

0¾·

0

x

_

H0 'ZD9;>9

_

[kORZD9hOQUJ<_fDRQ[_UAIçRU\RZD9hGŠ<_wA9;‰D>HGv[ŽYW:[kY;Y;GJRX[m9&æsfGJRQ[_UAI6 X UA>‘OXfD‰OQ9&æAfD9;ISRrJGŠ<_fD9&OEUJToõ

[=I]RZD9—OQ9&æsfD9;IY+9hRZD9heD>"9;rA[_UAfO‘`IGŠ<[_R9;>HGJR9hY;GJI‰/9hfOQ9&LçGAOR"ZD9ID9; [_IS[=RX[ŽGv<[_R9;>HGJR"9A6C1ZD9˜[=ISR9;>e/UJ<kGJRQ[_UAI

UJTmRZD9UAe/9;ID”<_U^UAeY+UAISR>UJ<kOEY;GJI]‰9—Y;GJ>">Q[_9&LMUsfDR[=I]RZD9—OGJdc9 GŠuMGAOELS9&OY+>X[=‰/9&L[_IçR"ZD9heD>9;rs[=UsfOOQ9&Y+RQ[_UAI@

fOt[_IDw—RZD9OXe9&Y"[a`9&L

û

>"9;9;IP£O:TVfDIY+RQ[_UAIO ,[=R"Z)

ù

e

y^6

ˆ O:1[_RZRZD9eD>9;rs[_UAfO1dh9;RZDUDL@DRZD9'[_I^R"9;>eUJ<kGJRX[=UsId—GJNA9&O:RZD9EY;GŠ<kY+fS<kGJRQ[_UAIMUnTRZS[kO:TV9;9&LS‰GAYN\Y+UAI^R">UJ<ÜG

rA9;>uhRQ[_dh9;”“Y+UsIOQfDd[_IDwheD>UDY+9&OO;6B'Uv19;rA9;>Š@ARZD9'[_R9;>HGJRQ[_rA9dh9;RZDUDLcUJT`ILs[=IDwcRZD9!Use9;ID”<_U^UseMY+UAI^R">UJ<bOQZDUAfS<kL

‰9OXUAdh9; ZGJR:T“GAOQR9;>1RZGnIRZD9Ls[kOY+>9;RQ[_Œ;9&LC8%eD>UA‰S<_9;døGAO1RZD9EeD>Us‰S<=9;døLs[_dh9;IOt[_UAIp[=IY+>"9&GAOQ9&O;6:’“R!Y;GnI

GŠ<kOQUh‰9E>"9+`ID9&L‰Su•GALDLs[_IDwhdcUA>9[_I^R"9;>eUJ<kGJRX[=UsIeUJ[_ISRHO1[_IRZD9O"GJdh9,GŠu—GsO1RZD9eD>9;rA[_UAfO'dh9;RZDUDL6C1ZD9;>"9

[ŽO,IDUOQR>X[ŽY+R:<a[_d[_R UAI\RZD9R‹uSe9&O:UJTeD>Us‰S<=9;d RU ZS[kY"Z\[_R,Y;GnI—‰/9‘GJeDeS<a[_9&L@/‰DfDR,GsO,[=R"Z—RZD95 û

ˆ

dh9;R"ZDU™L\UJT

5A9&Y+RQ[_UAIõùD6ñùD@SRZD9e/9;>QTUs>d—GJIY+9EUJTRZS[kO'dh9;RZDUDLMLS9;e9;ILDO'[_IGJI9&OOQ9;ISRQ[kGŠ< GŠu—UsIRZD9YZDUn[ŽY+9UJTRZD9[_IS[_RQ[kGŠ<

[=R"9;>HGJR9A6

ꁇ}||! ݆J…D‚&Ý_ØFׂ;Øcë"™€ƒ‚T„ŠØb~ r"%$ç€

’“IçRZS[kOEOQ9&Y+RX[=UsIç19,[o<a<mY+UAdceGJ>9RZD9e9;>QTVUA>d\GJIY+9hUJTRZD9`rA9cdh9;RZDUDLDOELs[ŽO"Y+fOOQ9&L[_IçRZD9eD>9;rs[_UAfO

OQ9&Y+RQ[_UAIhUAIhOQ9;rs9;>HGŠ<R9&OQR49+àGJdheS<_9&O;6`ç911[a<a<ÜY+UsIOt[kLS9;>RZD9+[_>mY+UsI^R>"UJ< GnfDRZDUA>Q[_RQu

á

[“6Í9A6Ž@JRZD9 GJ‰S[a<o[_RQuhRUELS>Q[_rA9 R"ZD9

OQRHGJR9&O,RUhŒ;9;>UDå+@DRZD9GndhUAfDISR UJTY+UAI^R">UJ<fOQ9&L@/RZD9EUJrA9;>HGv<o<Y+U^OQR UJTR"ZD9Edh9;RZDUDLDO;@bGnILRZD9Y+UAdheDfDRHGJRX[=UsIGŠ<

(13)

RQ[_dh9GJILšUAeO U^GJRQ[_IDw\eUJ[_ISR!Use9;>HGJRX[=UsIO+åmfOX9&L6 ˆ <o<Y+UAdheDfDR+GJRQ[_UAIO119;>9LSUAID9fOt[_IDwMY+UDLS9&O '>Q[_RR9;I[_I

i

ˆ

C

ë

ˆ

8@S[_dheS<_9;dh9;ISR9&LUAIGh5AfDIq1<_R>+Gh|D6

’“Ic[=dceS<=9;dc9;I^RQ[_IDwh’tRUGJILp5^YZD>"U^9;R9;>º£OC8òeD>UA‰S<_9;d÷dh9;RZDUDL@AR"ZD91[_R9;>HGJRQ[_UAIceD>U™Y+9&O"O GAO4>"fDIhfDI^RX[o<

ú

+* Ԋý

]-,

6C,ZD9iGJ>NSd—GJIGJILEGJRŒ[_R9;>HGJRQ[_rA9Edc9;RZDU™L\ GAO'Y+fDR UJéç ZD9;I

È

á

õå

[.

È

])^

á

õEå

/* Ô&ý

]-,

@

TUA>19&GAY"Ztõ@GJIL

á

õ

å

[

á

õ

])^

å

/* Ô&ý

]-,

[_IMRZD9EOQ9&æsfD9;IY+9UJT!õòrJGŠ<_fD9&O;6mC,ZD9EeGJ>RQ[kY+fS<kGJ>!OQ9&æsfD9;IY+9EUJT!õ

rvGŠ<_fD9&O:fOQ9&LrvGJ>X[=9&O:GJdhUAIDwER"ZD9mR"9&OQReD>UA‰S<_9;d—O;@SGAOLSUERZD9!Ls[kOY+>"9;RQ[_Œ&GJRQ[_UAI[_ISR9;>rvGv<

¡

,

GnIL`IGŠ<RQ[_dh9¤õ fOX9&L

[=IRZD9C8ïeD>Us‰S<=9;dódh9;RZDUDL6 ˆ IDUARZD9;>eGJ>HGJdh9;R"9;> RZGJRrvGJ>X[=9&O,[kORZD9>"9;wJ[_UAI

5

UJrA9;>' ZS[kYZRZD9c5

û

ˆ

dh9;RZDUDL[_ISR9;wA>HGJR"9&OGJIL]RZD9C8*GJIL]’“R9;>HGnRQ[_rA9hdh9;RZDUDLDO[_I^R9;>"eUJ<kGJR9

á

RZD9hISfDd‰/9;>UJT1[=ISR9;>e/UJ<kGJRQ[_UAI

eUJ[_ISRHO fOX9&LrvGn>Q[_9&O GAO119+<a<VåH6

ꁇ Õ ‡›}…w$6| r" Õ

C1ZD9 `>+OQR19+à GJdceS<=9[kO LS9&O"Y+>Q[_‰9&L‰Su7<_UAfDRX[=9;>Š@ g =5AUAfDŒ&GD@DGJIL\iM>+GAY+9;N[=IçãñùAx

ä

@DGJIL—Y+UsI^RHGv[=IO:RQ1UOQR+GJR9

rvGJ>Q[kGJ‰S<_9&OEGJILpRQmUhY+UAISR>Un<ÜrJGJ>Q[kGJ‰S<_9&O;6C1ZD9OQuDOQR9;d@D ZS[kYZZGAOY+fD‰S[ŽYIDUAIS<a[_ID9&GJ>Q[_RQ[_9&O‘[=I9&GAY"ZM9&æsfGJRQ[_UAI@ [ŽO

wJ[_rA9;IM‰Su 0

^

?1

0

^

[6

K

^

ž

?

^

c

?

^

?

?21

0

Ô ý

ý Ô

1

0

^

?1

e

ç9TœGsY+RUA> RZD9EIDUsIS<o[_ID9&GJ>TVfDIY+RQ[_UAI

.

á

å

K

á

å

‰^u

.

á

å

0

Ô

?

^

Ô

Ô

?

^

[

Ô

1

0

^

?

1

TUA>\RZD9š5

g

W ÿ÷dc9;RZDU™L6

X

UA>\RZD9eD>UA‰S<_9;dM@'m9fOQ9&LþRZD9[_IS[_RQ[kGŠ<˜Y+UsILs[=RX[=UsI

10c

á

Ô

2

Ô

å

N

6èC,ZD9›Y+USOQR

TfDIY+RQ[_UAIGv<jRU‰/9d[_IS[_d[_Œ;9&L[kO

G

á

10I2 å

J*L

0

„

1N

0

^

?

ý

ý

^

?

1

Q

N

0

Ô ý

ý Ô

1

‡

S

,

e

X UA>hR"ZD9õC:8oødc9;RZDU™L@1UsfD>•Y;GŠ<kY+fS<kGJRQ[_UAIOpfOQ9&L

¡

,

ý1e£ý

|çGJILR"ZD9`IGŠ<!RX[=dc9Fõ

|

e

xA|D6 X UA>hR"ZD9

[=R"9;>HGJRQ[_rA9dh9;RZDUDL@DRZD9OX9&æAfD9;IY+9UJT`õ rvGv<=fD9&O GAO'OQRHGJ>R"9&L—GJRZõ

0 ÔIe£ý

GnIL\[_IY+>9&GAOQ9&Lp‰^u9&æsfGŠ<a<_uõOQeGsY+9&L

RQ[_dh9[=ISR9;>rJGŠ<kOEUJT

¡

õ

ý1e

xA| 6‘C,ZD9>9;wJ[_UAI

58

ã

[

Ô

2

Ô;ä C ã

[

Ô

2

Ô;ä @GJIL

ԊýAý

Ô&ý

C

Ô&ý

>9;wAfS<kGJ>X<=uçOQeGsY+9&L

[=ISR9;>e/UJ<kGJRQ[_UAIeUJ[_ISRHO 19;>9EfOX9&L6

X [=wsfD>9

Ô

OQZDUJ!O

(3

TUs>RZD9`rA9TV9;9&LS‰GAY"N Y+UAI^R">UJ<kOLS9&OY+>Q[_‰9&L%9&Gn>Q<a[=9;>Š@GJIL GŠ<kOQU TUs>RZD9UAe9;ID”

<=USUAeçY+UAISR>UJ<FTUAfDILpfOt[_IDwRZD9hLs[kOY+>9;RQ[_Œ;9&LRQ1UheUn[=ISR‰UAfDILDGJ>"uMrvGv<=fD9eD>Us‰S<=9;d GneDeD>U^GAY"ZTVUA>RZD9E[_IS[_RQ[kGŠ<

Y+UAILs[_RQ[_UAI

10

6 ˆ <a<UJTRZD9&OQ9>9&OQfS<_RHOEGn>99+à™R>"9;dh9+<_uõY"<_U^OQ9RU\9&GAY"ZõUsRZD9;>&@/1[_RZRZD9hC8è‰GsOQ9&Ldh9;RZDUDL

e9;>QTVUA>d[_IDwOt<a[=wsZ^RQ<_uh‰/9;RR9;>&@AGnILRZD9E5

û

ˆ

dh9;RZDUDLe/9;>QTUs>d[_IDwOt<a[_wAZSRQ<_uh1UA>HOQ9A64C1ZD9 IDUA>"d—O4UJTbR"ZD9,Y+UsI^R>"UJ<

GJ>9—OQZDUJ I›[=I

X

[_wAfD>9—x•TUs>GŠ<a<`rs9hdh9;RZDUDLDO;6C1ZD9;>9GJ>9hUsIS<=uçOQd\GŠ<a<,Ls[aé9;>9;IY+9&O‰9;RQ19;9;IçdhUSOQRUJT

RZD9dh9;R"ZDU™LDO;@ 1[_RZMRZD9Y"<_9&GJ>!9+àY+9;eDRQ[_UAI‰9+[_IDwRZD9h5

û

ˆ dc9;RZDU™L@/ ZS[kY"ZM>9&æsfS[_>9&O ID9&Gn>Q<_uR‹,[ŽY+9GAO1dfY"Z

Y+UAI^R">UJ<[_IS[=RX[ŽGv<o<_uA6

C1ZD9hRQ[_dh9—GnILUAeOE>"9&æAfS[_>9&L›TUs>E9&GAYZ›T9;9&LS‰GAY"NçY+UAISR>UJ<“@Gv<=UsIDw1[_RZ¹9&GsYZUJT RZD9+[_>rJGŠ<_fD9&OTUA>ER"ZD9

Y+U^OQR:TfDIY+RX[=UsIGŠ< G

á

10I2

åH@SGJ>9'<o[kOQR"9&Lc[=ICGn‰S<=9 Ô 6jCFUhY+UAdheGJ>"9A@^R"ZD9EUAe9;ID”<_USUAeõY+UAISR>Un<ÜY+U^OQR:[kO1ú6=yv{AzA|D@AGnIL

RZD9 <a[_ID9&GJ> Y+UAISR>UJ<

á

 ZS[kYZGŠ<kOQUhOQfY;Y+9;9&LDOÛ[_IMLS>Q[_rA[_IDwRZD9eD>UA‰S<_9;d÷RUŒ;9;>U[_IRZS[kO9+àGJdheS<_9JåY+U^OQR[kO:ú6ayJü

Ô&ý

6

C1ZD9!Y+U^OQR+OGJ>9!GŠ<a<rA9;>uO‹[=d˜[o<kGJ> á 9+àY+9;eDR 5 û

ˆ

å+@JrvGJ>us[_IDw‰^uUAIS<_uhGJ‰UsfDR

ý

6£|54 GJdcUAIDwRZD9;d\OQ9+<_rA9&O;@^GnRGJ‰UAfDR

|64ï<_9&OORZGJIR"ZD9E<a[_ID9&GJ>Y+UAISR>UJ<“61C1ZD9Y+UAdceDfDRHGJRQ[_UAIGŠ<4RQ[_dh9ETVUA>!C:8èGJIL’tR9;>&@ [=ISrAUJ<_rs[_IDwRZD9OQUJ<_fDRQ[_UAI

(14)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0

0.5

1

1.5

Time

Norm(x)

HJB

SDRE

SGA

TPBV

Iterative

Open−Loop

X [_wAfD>9

Ô

< 7:UAdheGJ>Q[kOQUsIUJTjR"ZD9EIDUA>d—O1UnTTV9;9&LS‰GAY"NMY+UAI^R">UJ<a<_9&LR>HGnߋ9&Y+R"UA>Q[_9&OÛ[=Iÿ4àGJdheS<_9

Ô

6

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0

1

2

3

4

5

6

Time

Norm(u)

HJB

SDRE

SGA

TPBV

Iterative

Open−Loop

X [_wAfD>9x < 7:UAdheGJ>Q[kOQUsIUJTjR"ZD9EIDUA>d—O1UnTTV9;9&LS‰GAY"N•Y+UAISR>Un<ŽOm[=Iÿ4àGJdheS<_9

Ô

6

UJTjd\GJI^u\UAe/9;ID” <=USUAeeD>UA‰S<_9;d—O;@ [kO dfY"Z\<ŽGn>wA9;> RZGnIRZGJR UJTB

ð

8òGJIL5

g

W ÿ'6C1ZD9c5 û

ˆ

Y+UAdheDfDRHGJRX[=UsIGŠ<

RQ[_dh9[ŽO'[_I‰9;RQ19;9;IRZD9&OQ99+àDR>9;dh9&O;@/‰DfDR[kOEOQRQ[a<a<dfYZ<_9&OORZGJIRZD9[_I^R9;>"eUJ<kGJRQ[_UAIdh9;R"ZDU™LDO;6EB'UJm9;rs9;>&@

RZD9!9+àDe9;IO‹[=rs9Y+UAdheDfDR+GJRQ[_UAIOUnT5

û

ˆ @^C:8 GJILc’“R9;> GJ>9GŠ<a<FLSUsID9!UJé”<a[_ID9A@OQURZD9;u—Y+UsfS<ŽLc‰9E>"fDI•GJwSGŠ[_I

rA9;>uæsfS[ŽY"Ns<=u1[_RZhGLs[aéÜ9;>"9;I^R

H0

[aTÜOQUELS9&Ot[_>9&L6 X UA>4RZS[kO4eD>UA‰S<_9;dïRZD9‰/9&OQRY"ZDUJ[kY+9mUnTbdh9;RZDUDLSUJ<_UAwAuGneDe9&GJ>HO

(15)

7¤q%C:[_dh9 OX9&YJ6aå X <=UseO 7USOQR

B

ð

8

ý

6

Ô

| ú

e

y

Ô

C

Ô&ý P

ú6ñzA{AüA|

5

g

W'ÿ

ý

6£x

Ô

ú

e

üA{C

Ô&ý

P ú6ñzA{AxA{

5 û

ˆ Ô

6£|Ax

ÔIe zA{C

Ô&ý87 Ô yS6£|Aù

ý

{

CZ8 úsú^üD6Íú^z

ÔIe zAxC

Ô&ý

^

0

ú6ñzAü

ý

{

’tR9;> {™y&ú6£üA{ x

e

xAüC

Ô&ý89

ú6ñzSyvzAü

CGn‰S<=9 Ô <l fDdh9;>Q[kY;GŠ<jY+UsdheGJ>Q[kOQUAIUJTTV9;9&LS‰GAY"NMY+UAI^R">UJ<dh9;RZDUDLSUJ<_UAwJ[_9&O,[=Iÿ4àGJdheS<_9 Ô 6

RUM‰/9•B

ð

8ïUs>h5

g

W ÿ

<

R"ZD9;u›GsYZS[_9;rA9\>9&OQfS<_RHOrs[=>"RfGŠ<a<_u GAOwAUSU™LçGsOGJISuUARZD9;>dh9;RZDUDL@GJILçLSUçOQUM,[=R"Z

d[_IS[=d\GŠ<ÛY+UsdheDfDRHGJRQ[_UAI6

ꁇ ‡›}…w$6| r"

C1ZD9—OQ9&Y+UAIL]9+àGJdheS<_9—19—Y"ZDU^OQ9cRUR9&OQRERZD9\rvGn>Q[_UAfOTV9;9&LS‰GAY"N›Y+UsI^R>"UJ<dh9;RZDUDLDO[kOT>"UAd iGJ>NSd—GJI

GJIL:EGJRŒã£x

ýJä

6E’“REZGAORQ1UOQRHGJR9rvGJ>X[ŽGn‰S<=9&OGJILUAID9hY+UAISR>Un<jrJGJ>Q[kGJ‰S<_9A@GJILZGAOEGY+fD‰S[kYcIDUAIS<a[_ID9&GJ>Q[_RQuM[_I

RZD9OQuDOQR9;dM@D'ZS[ŽY"Z[kOLS9+`ID9&L‰Su 0

^

?21

0

?

K

^

1

0

ý

Ô

1

e

C1ZD9ETVfDIY+RQ[_UAI

.

á

å4[ŽO'>9; >X[=R"R9;IMGAO

.

á

å

0

ý Ô

?

^

ý

1

0

^

?21

TUA>1RZD95 g W'ÿdh9;RZDUDL6C1ZD9[_IS[_RQ[kGŠ<Y+UAILs[_RQ[_UAI[kO

0

á

Ô

2

ý å

N

GnIL\RZD9Y+U^OQR:TVfDIY+RQ[_UAIGŠ<RU‰/9d[_IS[_d[_Œ;9&L

[ŽO

G

á

10I2 å

J L

0

„

N

0

^

?

ý

ý

^

?

1

Q

Ô

x

?

‡

S

,

e

X UA> R"ZS[ŽO,9+à GJdceS<=9A@ [_IMRZD9CZ8 dc9;RZDU™L\19EfOQ9&L

¡

,

ýHe£ý

|GJILtõ

y

e

|

ý

6 X UA>'RZD9[_R9;>HGJRQ[_rA9Edc9;RZDU™L@

õ

0d ÔIe£ý

GnIL

¡

õ

ý1e

|D6C1ZD9MOGJdh9c>9;wJ[_UAI

5

ã

[

Ô

2

Ô;ä C ã

[

Ô

2

Ô;ä

GAO‘[_I ÿ4àGJdheS<_9

Ô

 GAOfOQ9&L@,[=R"Z

Ô&ýAý

Ô&ý C Ô&ý [_I^R"9;>eUJ<kGJRX[=UsIMeUn[=ISRHO;6

X [=wsfD>9hùhLS9;eS[kY+RHOERZD9OQRHGJR"9

^

GnIL X [_wAfD>"9úLs[ŽOXeS<ŽGŠuDORZD9Y+UsI^R>"UJ< TUs>‘GŠ<a<4`rA9Y+UsI^R>"UJ<dh9;RZDUDLDO;6

C1ZD9h5 û

ˆ

dh9;RZDUDL[_R9;>+GJRQ[_UAIO'ID9;rA9;>‘GsY+RfGŠ<a<_uõY+UAISrA9;>wA9&LpRU—G˜`IGŠ<jY+UAISR>Un<œ–/RZD9UAID9OQZDUJ IZD9;>9 á  ZS[kY"Z

LSU^9&O'TVUA>HY+9RZD9OQu™OXR9;døRU\Œ;9;>UDå:[ŽOR+GJNA9;IõGvTR9;>EGJI[_R9;>HGJRX[=UsIõISfDd‰9;>ER>"fDIY;GJRQ[_UAI6’“RY;GJI‰/9˜OX9;9;I[_IõR"ZD9

`wAfD>9&O'RZGJRRZD9E[_ISR9;>eUn<ŽGnRQ[_UAIdh9;RZDUDLDOELS>Q[_rA9RZD9OQRHGJR"9&O RUcŒ;9;>U•O‹<o[_wAZSRQ<_uMdcUA>9O‹<=UJ1<_uRZGJIMR"ZD9h5 g W ÿ

GJILMB ð 8þdh9;RZDUDLDO;@D‰DfDRRZD95 g W ÿþGJILMB ð 8òdh9;R"ZDU™LDO1>"9&æAfS[_>9dhUA>9Y+UAISR>Un<ÜR"U˜GsYZS[_9;rA9RZS[kO;6

CGJ‰S<_9MxY+UAI^R+GŠ[_IOR"ZD9hRQ[_dh9GJIL*UseO>"9&æAfS[_>9&LšGJILšY+U^OQRETVUA>9&GAYZY+UAISR>UJ<dc9;RZDU™L6CUçY+UAdheGn>9A@

RZD9hUAe/9;ID”<=USUAe Y+UAISR>Un<mY+U^OQR[kO

Ô

6£|AzAxnú6 X UA>R"ZS[ŽO9+à GndheS<_9—RZD9˜<o[_ID9&GJ>\Y+UAI^R">UJ<4TœGŠ[a<kORUM‰D>X[=IDwRZD9OQu™OXR9;d

RUŒ;9;>U6C,ZD9˜Y+USOQRHOGJ>9hOt[_d[a<kGJ>

á

Gnw^GŠ[_I1[_RZRZD99+à Y+9;eDRQ[_UAIšUJT 5

û

ˆ åH@/‰DfDRIDUsR‘GAOEY"<_U^OX9—GAO,TUA>ÿjà GndheS<_9

Ô

6C,ZD9;uõrJGJ>u‰^uGJ‰UAfDR|54 GJdhUAIDwRZD9;d\OQ9+<_rA9&O;@GnILõGn>99+éÜ9&Y+RX[=rs9h ZD9;IçRZD9<a[_ID9&GJ>hY+UAISR>UJ<4TœGv[o<kO;6hC,ZD9

(16)

0

1

2

3

4

5

6

7

8

9

10

−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time

State x

1

HJB

SDRE

SGA

TPBV

Iterative

Open−Loop

X [_wAfD>9ù < 7UAdheGJ>X[ŽOXUAIUJT4T9;9&LS‰GAY"NMY+UAISR>UJ<a<_9&LMOXRHGJR9&O

^

[_Iÿ4àGJdheS<_9xD6

0

1

2

3

4

5

6

7

8

9

10

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

Time

Control u

HJB

SDRE

SGA

TPBV

Iterative

Open−Loop

X

[_wAfD>"9Eú

<

7UAdceGJ>Q[kOQUAI\UJT4T9;9&LS‰GAY"NMY+UAISR>UJ<kO:[_Iÿ4àGJdheS<_9xD6

References

Related documents

In Figure 3 we plot the 0-day patch rate for all high-, and medium-risk vulnerabilities Microsoft released a patch for in the period from January 2002 to December 2007.. The

In particular, the Italian Association of Medical Oncology (AIOM) guidelines include the personal history of triple-negative BC (TNBC) patients diagnosed ≤60 years and the

The delimcc library was the first direct implementation of delimited control in a typed, mainstream, mature language – it captures only the needed prefix of the current

Furthermore, the mecha- nisms involved were investigated by correlating the effect of carnitine excretion with markers of proximal tubular dam- age and by studying the effect of

For this purpose, first, the indicators for patent valuation and prioritization were taken from the literature and aggregated and finalized based on opinions of

Information Technology (IT) as a structural factor and instrument transforms architect of organizations, business processes and communication, and is increasingly

Proces kontinuiranog upravljanja promjenama koji donosi utjecaj na organizacijsku strukturu poduzeća, razvoj operativnih sposobnosti organizacije, sustav upravljanja ljudskim

To explore the tissue specificity of the genetic effects on DNA methylation, we examined whether the meQTLs detected in EAGLE lung tissue data could be replicated in TCGA breast ( n