• Aucun résultat trouvé

Discrete Approximations of the Hamilton-Jacobi Equation for an Optimal Control Problem of a Differential-Algebraic System

N/A
N/A
Protected

Academic year: 2021

Partager "Discrete Approximations of the Hamilton-Jacobi Equation for an Optimal Control Problem of a Differential-Algebraic System"

Copied!
26
0
0

Texte intégral

(1)

HAL Id: inria-00072322

https://hal.inria.fr/inria-00072322

Submitted on 23 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.

Discrete Approximations of the Hamilton-Jacobi Equation for an Optimal Control Problem of a

Differential-Algebraic System

J. Frederic Bonnans, Philippe Chartier, Hasnaa Zidani

To cite this version:

J. Frederic Bonnans, Philippe Chartier, Hasnaa Zidani. Discrete Approximations of the Hamilton- Jacobi Equation for an Optimal Control Problem of a Differential-Algebraic System. [Research Report]

RR-4265, INRIA. 2001. �inria-00072322�

(2)

ISSN 0249-6399 ISRN INRIA/RR--4265--FR+ENG

a p p o r t

d e r e c h e r c h e

THÈME 4

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Discrete approximations of the Hamilton-Jacobi equation for an optimal control problem of a

differential-algebraic system

J. Frédéric Bonnans — Philippe Chartier — Housnaa Zidani

N° 4265

Septembre 2001

(3)
(4)

Unité de recherche INRIA Rocquencourt

Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay Cedex (France)

Téléphone : +33 1 39 63 55 11 — Télécopie : +33 1 39 63 53 30

12$3!4%567%+% 8:9<;= >7 .6%?')%4@ >+!7

BAC

DEGFGHIKJ7ILHNMPORQ*SUT7TGVUT7WNXRY[Z\7M^]PM^_7_`ba*\GVUHcNMP`LHedfY[g!Sih7WTGViVkjMPJ7VUT7Mml

n>oqp4r0st*uwvyxzr${q|~}1?x€L‚ƒs.€…„†?xr0x~‡ˆ}‰ˆxz€…‚

Š s‡ˆ‹y‡Œˆpr0s‡.€Lr0„q|s4Ž†s‡

[?€‰‘’s4“vK”–•—˜.—

™}‰„)„š€LŒ Š s?s&oqs?&o)s›‚UœtK…žLŸRuwvys„†ˆsr$ q?s$‰¡L¡q¢u£…6„)}…¤…s‡

¥§¦¨©4ª1«q¬…©…­ n>o)xz‡.„š}‰„Us4 Š x~‡ˆ4{)‡ˆ‡ˆs‡?oqs‚y{qr0s4?xz}‰|C?s‡ˆ€…|z{†ˆxz€…‚!€‰®?oqs¯°}…r*xz|ˆ€…‚q±m²K}…4€… qx±m³s||zr}‰‚

sN´K{)}1?x€L‚µ}L‡ˆ‡ˆ€†x~}1?s Š=¶ x·?o€…„†?xr}…|¸€L‚L?ˆ€L|G„q?€… q|zs4r oqs4‚µ?oqs§‡Œ?}‰ˆss´K{)}‰ˆxz€…‚µx~‡€‰®}…|¤Ls4 q&}‰x~

Š x·¹is4?s4‚Kˆx~}‰|>’‹y„Us

ȼ

s Š x~‡ˆ4{)‡?‡0 €µ‚y{qr0s4?x~4}‰|‡?&oqsr*sN‡ n>o)s!¼š?‡Œfˆs Š {)4s‡*ˆ€µ?oqs½‡Œ?}‰‚ Š }‰ Š

®¾&}‰r0s €Lˆ¿iÀ o)x|zs?oqs6‡ˆs4€…‚ Š½Š €KsN‡°‚)€‰–‡ˆ{q„q„U€L‡ˆs6}…‚y‹!¿y‚q€ |zs Š ¤Ls€‰®G?oqs6²K}…4€… qx~}‰‚b€…®Gˆoqs Š }1&}

º

s§€L †?}…x‚Á‡Œ€Lr*s!s4?ˆ€Ls‡Œˆxzr}1?s‡À7}…‚ ŠŠ x~‡ˆ„q|z}e‹,‚y{qr0s4?xz}‰|ˆsN‡Œ{)|·&‡€… q?}‰xz‚qs Š €…‚k}R‡Œxzr0„q|s!ˆsN‡’

„)ˆ€L q|sr

ÂbÃKÄiÅ?Æ$Ç ª1Ȩ…­ —“„†ˆxzr}‰|…4€…‚Kˆ?€…|PÀ Š x¹is4?s4‚Kˆx~}‰|±m}…|¤Ls4 q&}‰x~‡Œ‹†‡Œˆs4rƒÀN¯°}‰r0xz|·?€…‚†±É²K}…€L qx±m³s4|z|zr0}…‚°sN´L{š}1±

?x€L‚BÀ Š ‹y‚)}…r*x~„q?€…¤L?}…r*r0xz‚q¤)Ày}‰„)„qˆ€eŽ†xzr}1ˆxz€…‚‡ˆ&o)s4r0s‡Ày¼)‚qxˆs Š x¹is4?s4‚)4s‡À†ÊKx~‡?€L‡ˆx’‹f‡Œ€L|{†?x€L‚)‡

˸̾ÍÎBÌÐÏщÒÓԆÓKՌÖ<×NÑ1Ø&ÙNՌ×<Ú.ÎÛ4ܒÝÞeߒàeܒÛ<Þeá¾âŒÑKã1á^ä&àeܒß<ÓCåšæä&çéè~êyã1á^ߒëeߒáìçéÜÓÒiÛ<àNà1ä&àeíÉîçéàNá^çïäNÓðáŒÓ

ñ

̾ÍÎBÌÐÏхòCä&æ.óeÞeíBëeß[Òiߌä&ÞeèéçéߒޖÚ<×<Ö&ôõ.Îߒàeàeߒíã)ÎÏÍ7òCåÓeåšæä&çéè~êqÔ)öeçéèéçéóeó‰ß<ÓòCöeä&áìâ^çéߒámîçéàeáìçïäNÓðá

÷7øù

ó1ä&á¾âPߒæ.ߒà4âëeßúä?âPö

ù

æä?â^çéÝ4ÞeߒíˆÑ1ûàeçüߒá^í^çâù ëKýþá^è

ù

ä&àeíŒÑeÿ†ä‰Û<á^ä?âPÛ<çéáìß[úÏ7ԚúþÑûã)ÎܒçéߒàeܒߒíˆÑ1ÒCÔØ&×NÑ

ô×<ÖØ.þá^è

ù

ä&àeíŒÑeã1á^ä&àeܒßхä&àNë̾ÍÎBÌÐÏ ¾ÎBÛ4܌Ý4ÞeߒàeܒÛ<Þeá¾âˆÑ…ã1á^ä&àeܒß<ÓCåšæä&çéèÛ<Þeí^à1ä<äNӅçéëeä&àeç·îçéàeáìçïäNÓðzá

(5)

"$4%&f')(6+ĵ=/!2/37+% 9 $:$!9

!4%4 #9’/ AC #%@>+7'q9<;> .6 .%

¨ ­ ˜s*}…Œ?xz4|s Š xz‡?{qˆs§|~}b‡ˆ€…|z{†ˆxz€…‚5‚y{qrˆx~´K{qs Š s!|´K{)}‰ˆxz€…‚ Š s¯°}‰r0xz|·?€…‚†±É²K}…€L qx±

³s||zr}‰‚}…‡?‡Œ€†4s>{q‚„q?€… q|zp4r0s Š s[4€…r0r}‰‚ Š sG€L„†ˆxzr}‰|zs…À4´K{)}…‚ Š |´K{)}‰ˆxz€…‚s‡Œ Š s7’‹y„Us¸}‰|z¤ q?xz4€‰±

Š x·¹is4?s4‚Kˆxzs4|

€…{š‡ Š x~‡?{†?€…‚)‡ Š s4{qŽR‡ˆ&or}…‡‚y{qrˆx~´K{qs‡

s$„q?s4r0xzs4‡Œs6 Š {qx–}…{R4} Š ˆs*‡’&}‰‚†±

Š }‰ Š ÀB}‰|z€…&‡´L{)s|s‡ˆs€L‚ Š ‚qsf‡Œ{)„q„š€K‡Œs}…{){q‚)sf€…‚)‚)}‰x~‡ˆ‡?}‰‚šs Š Š ˆxzÊs‡ Š sN‡ Š €…‚)‚4sN‡ €…{)‡

€L †ˆs‚q€…‚š‡ Š s‡s‡Œˆxzr0}‰ˆxz€…‚)‡ Š sˆ?s4{)À†s4°„q?€ Š {qxz‡ˆ€…‚š‡ Š s‡°N‡Œ{q|?}‰?‡>‚y{qr4?x~´L{)s‡‡ˆ{q{q‚b„)ˆ€L q|pr0s

?s‡Œ°‡Œxzr0„q|zs

! Ç ©N¨ Å ¬" ¨Á­ ˜€…r0r}‰‚ Š s!€…„†?xr}…|sLÀ7‡ˆ‹†‡’?p4r0sƒ}‰|z¤4 )ˆx~€…±Š x¹is4?s4‚Kˆxzs4|PÀ#N´L{š}1ˆxz€…‚ Š s¯“}‰r0xz|·?€…‚†±

²K}…4€… qx±É³s||zr}‰‚BÀ„q?€…¤L?}…r*r}‰ˆxz€…‚ Š ‹y‚)}…r*x~´K{qs…À‡?&or0}L‡ Š }…„q„q?€eŽyxzr}1?x€L‚BÀ Š x·¹4?s4‚)4s‡¼)‚)xsN‡4À

‡ˆ€…|z{†?x€L‚)‡ Š sÊyxz‡?€K‡Œx

(6)

¥

!4353

¦76

Ã

¬…©98 "^«q¨N¨;:<¬L«†©;:

Ç>=@?¸ˆxzr}‰?‹ftABR…ŸqÀ†v†s€L‚

Š

}…ˆ‹tCA

LŸ†À†žLŸB½¡

D E

679/!¸

n>o)xz‡„)}‰„Us4x~‡ Š s4ʅ€…ˆs Š ˆ€$ˆoqs Š x~‡ˆ4{)‡ˆ‡ˆxz€…‚f€…®B‚K{)r*sˆx~4}…|šr0s4ˆoq€ Š ‡¸®¾€…>‡Œ€L|Êyxz‚q¤6}…‚f€…„qˆxzr0}…|U4€…‚Kˆ?€…|

„)ˆ€L q|sr €‰®} Š x¹is4?s4‚Kˆx~}‰|±m}…|¤Ls4 q&}‰x~ Š ‹y‚)}…r0xzƒ‡ˆ‹y‡Œˆsr vy„Us4x·¼š}‰|z|‹LÀ s Š xz‡?{)‡?‡*ˆo)sr0s4ˆoq€ Š ‡

®¾€L€Lr*„){†ˆxz‚q¤ƒˆo)sÊe}…|{)s6®¾{)‚)<?x€L‚BÀ š}…‡ˆs Š €…‚=ˆoqs Š x~‡??sˆxGF}‰ˆxz€…‚,€‰®ˆoqsf}L‡ˆ‡ˆ€†x~}1?s Š ¯“}‰r0xz|·?€…‚†±

²K}…4€… qx±É³s||zr}‰‚8s´K{)}‰ˆxz€…‚IH^‡ŒssRs ¤ ³s4|z|zr0}…‚KJ2MLPÀ–³>}‰?|sN‡NJéMLPO vy{)&o r0s4ˆoq€ Š ‡Àxz‚»ˆo)s,}…‡ˆs

€…®“€L„†ˆxzr}‰|°4€…‚Kˆ?€…|>„q?€… q|zs4r €‰®} Š x·¹is4?s4‚K?xz}…| Š ‹y‚)}‰r0x~‡ˆ‹†‡’?s4rƒÀ>}‰?s Š xz‡?{)‡?‡ˆs Š x‚ ³>}‰ Š x}‰‚ Š

˜}…„q{F;F4€‰±É•“€…|~sˆ?}QJz¢…ÀSR„q„Us4‚ Š x·Ž5 y‹TB

VU

}‰|~€…‚)sLmÀ[˜}…r0x|z|x}‰‚ Š U

}‰|~€L‚qsWJtLPÀ

U

}‰|~€…‚)sNJYXZLPÀG}‰‚ Š

™€…{q‹§}…‚ Š n€L{qˆxz‚QJAL

[ɂ„q?xz‚)xz„q|zs…ÀL‡ˆ{)&o0„q?€… q|zs4r‡[}‰‚0 Usˆs Š {)4s Š ˆ€?oqs°‡Œ?}‰‚ Š }‰ Š ®¾&}‰r0s €Lˆ¿€…®U€L„†ˆxzr}‰|)4€…‚Kˆ?€…|

€…®$}‰‚»€L Š x‚)}…ˆ‹ Š x¹Usˆs‚L?xz}…|“sN´K{)}1?x€L‚ n>oqs,xŠ s}5x~‡f?€ks4ŽK??}L<!ˆoqs,}‰|z¤…s4 )?}…xzƒÊ1}‰?x~}‰ q|zsb®¾?€…r

?oqs*ˆxzr0s Š s4?xÊ1}‰ˆxzʅs‡“€‰®ˆoqsf}…|¤Ls4 q&}‰x~$4€…‚)‡Œˆ&}‰xz‚KÀCx s ÀBˆ€ƒsŽ†„q?s‡?‡“ˆoqs}‰|z¤…s q&}‰x~Ê1}‰?xz}… q|zs*}L‡–}

®¾{)‚)<?x€L‚€…®‡Œ?}‰ˆs}‰‚ Š 4€…‚Kˆ?€…|PÀ†}‰‚ Š €‰®7‡Œ€Lr0s–€…®?oqs4xz Š sˆxzÊ1}1ˆxzʅsN‡

¯°€ sʅs4NÀšˆoqx~‡4}…‚q‚q€‰}‰| }e‹†‡“ šs Š €L‚qs n>oqs0r}‰xz‚R?s}L‡Œ€L‚bxz‡“?o)}1NÀB€‰®Ð?s4‚BÀi?oqs Š ‹K‚š}‰r0xz‡–xz‡

}eÊ1}…x|~}‰ q|zs…ÀU q{†‚q€…–x?‡ Š sˆxzÊ1}1?xÊLs‡ n>oqx~‡–xz‡–xz‚ Š ss Š ?oqs*r0}…x‚=ˆsN}…‡ˆ€…‚ƒ®¾€L°?oqs Š s‡ˆx¤L‚½€‰®‡Œ„Us4x·¼š

‚y{qr0sˆx~4}…|‡?&oqs4r0sN‡®¾€L–xz‚Kˆs¤…&}1ˆxz€…‚b€…® Š x¹is4?s4‚Kˆx~}‰|±m}…|¤Ls4 q&}‰x~ Š ‹y‚)}…r*x~*‡Œ‹†‡Œˆs4rƒÀB‡ˆs4s6s ¤ ¯°}…x?s4

s4°}‰| J\L

[ɂ!ˆo)}‰>}…‡ˆs…Àyx>r}e‹0 Us–s4¹UsN<?xÊLs°?€ Š x~‡??sˆxGF4s“ˆo)s“„q?€… )|srx‚ƒ} }e‹*ˆo)}‰x~‡>€Loqs4?s4‚K xˆo

?oqs“‡ˆ„qxzˆx€…®CˆoqsN‡Œs‡ˆ„šsNx~}‰|zx]Fs Š ‚y{qr0s4?xz}‰|i‡ˆ&o)s4r0s‡ÀLs4Žqs4„q€‰®4€…{q&‡ˆs.®¾€…¸ˆoqs“®ì}…¸ˆoš}1>€…‚qs°}…xr‡

‚)€‰>ˆ€o)}eÊLs“o)x¤Lo€L Š s4.}…{q&}…4‹…À†‡Œxz‚)4s“?oqsÊ1}‰|z{qs–®¾{q‚)ˆxz€…‚ƒxz‡x‚ƒ¤…s‚qs4&}‰|i‚q€… Š x·¹is4?s4‚K?xz}… q|s

[ɂ0?oqxz‡¸„)}‰„Us4 s.xz‚Kˆ?€ Š {)s“‡Œ{)&o}r0s4ˆoq€ Š ÀK€… †&}‰xz‚0s4?ˆ€LGs‡Œˆxzr0}‰ˆsN‡4ÀK€…r0„)}…ˆs xˆo0?oqsxŠ s}

€…®?s Š {)ˆxz€…‚§ˆ€*ˆoqs‡Œ?}‰‚ Š }‰ Š ‡ˆx·?{)}1?x€L‚BÀ†}‰‚ Š!Š x~‡ˆ4{)‡ˆ‡‚y{qr0s4?x~4}‰|i?s‡ˆ{q|?‡®¾€…> U€‰ˆor0s?oq€ Š ‡€…‚!}

‡ˆxzr*„)|ssŽq}…r*„)|s

n>oqsƒ„)}…„šs0xz‡*€…?¤L}…‚qxGF4s Š }L‡6®¾€…|z|€ ‡ vysˆxz€…‚8½„q?s‡ˆs4‚K&‡$?oqsƒ„q?€… q|zs4r }‰‚ Š ?oqs!r}…x‚ oy‹L±

„U€‰?oqs‡ˆs‡ n>oqsf€L‚Kˆxz‚K{)€…{)‡–„q?€… q|zs4rxz‡„q?s‡ˆs4‚K?s Š x‚5‡ˆs<?x€L‚Q2)À oqxz|sf‡ˆsˆxz€…‚,tƒxz‡ Š sʅ€…ˆs Š ˆ€

?oqs–‚K{)r*sˆx~4}…|C}‰‚)}…|‹†‡ˆxz‡¸€‰®?oqs‡’&}1ˆs–s´K{)}‰ˆxz€…‚

s€… †&}‰xz‚fs4?ˆ€LsN‡’?xr}‰ˆs‡Àyx‚‡ŒsN<?x€L‚Ÿ®¾€…ˆoqs

Š xz‡??s?sˆxzr0sf€…„†?xr}…|4€…‚Kˆ?€…|[„)ˆ€L q|srƒÀ}…‚ Š x‚Á‡ŒsN<ˆxz€…‚žb®¾€…?oqsf®¾{)||z‹ Š xz‡??s?x]Fs Š „q?€… q|zs4r

{qr0s4?xz}‰|C?s‡ˆ{q|?‡.}‰?s–„qˆsN‡Œs‚Kˆs Š xz‚ƒ‡ˆsˆxz€…‚NX

^ _

@:Á ! #+% a`cb 7 .%44!A£ ./!%<

˜€L‚)‡ˆxŠ sˆoqs®¾€L||z€ x‚)¤ Š x·¹is4?s4‚Kˆx~}‰|±É}‰|z¤…s4 )?}…xz Š ‹y‚)}‰r0x~–‡ˆ‹†‡’?s4rƒÀ

dee

feeg h

ij,klnm o pqkijklnmsrtZjklnmrnuVklnmmvl.wyx"r

z j o {|ki j klnmm l.wyx"r

i j k1xCm}o5~€

H’¢ZO

¯°s4?s

~

‡’&}‰‚ Š ‡[®¾€L¸?oqs°xz‚qxˆx~}‰|C€L‚ Š xˆxz€…‚®¾€L¸?oqs–‡Œ?}‰ˆs“Êe}…ˆx~}‰ )|sH쀅 Š x¹Usˆs‚L?xz}…|šÊ1}…ˆx~}‰ q|zsZO

ijklnm.

‚„ƒGÀ oqxz|s

t j klnm…

‚S†fxz‡“4}‰|z|zs Š ˆoqs6}‰|z¤…s4 )?}…xz–Ê1}‰?xz}… q|zs‡ so)}eÊLs Š s4‚q€…ˆs Š z

j‰ˆ

oŠ{|k~|m

—“ )‡ŒsˆÊLs

(7)

?o)}1

s–{)‡ˆs?oqs“‚)€‰?}‰ˆxz€…‚

kij,rt;j m

®¾€L¸?oqs–‡ˆ€…|z{†?x€L‚f€‰® HŒ¢ZO¸x‚!€…

Š

s4¸ˆ€6‡Œˆ?s‡?‡€…‚?oqs

Š

s4„Us4‚

Š

s‚)s

€…®

ij }‰‚

Š

tZj

xˆof?s‡ˆ„šsN<G?€ˆoqs°x‚qxˆx~}‰|U€L‚

Š

xˆxz€…‚

~

n>oqs

Š

s4„Us4‚

Š

s‚)s°€‰®

ij s

t;j

xˆo?s‡ˆ„Us<

?€f?oqs*4€…‚Kˆ?€…|Ê1}‰?xz}… q|s

uVklnm$

‚& x~‡°{q‚

Š

s4&‡’?€y€

Š

}‰‚

Š

r6{)‡Œ– Us64|sN}‰“®¾€…|z|€

xz‚q¤?oqs*‡ˆsˆˆxz‚q¤§€…®

?oqs„q?€… q|zs4r

˜€L‚)‡ŒxŠ s>ˆoqs®¾€L||z€ x‚)¤6xz‚†¼)‚qxˆs$oq€…?x]F€…‚!€…„†?xr}‰|B4€…‚Kˆ?€…|i„q?€… )|sr ?

'

k~|m}o (*),+

-./021 354

687 ki

j

klnmrt

j

klnmrnuVk~€rnlnmm9:<;>=?l

®¾€L

~N

‚ ƒ 

H^O

¯°s4?sA@CBED Š s4‚q€…ˆsN‡ˆoqs!‡Œs4€‰®}‰|z|[€L‚L?x‚y{q€L{)‡}…‚ Š „qxsNs xz‡ˆs Š x¹Usˆs‚L?xz}… q|zs0®¾{q‚)<?x€L‚)‡€…® F

xrHG

F

xˆo§xr}‰¤Ls°xz‚§}‚)€…‚qsr*„q’‹04€…r0„)}L<‡ˆ{q )‡ˆs%@ €‰®€‚ & À 7

xz‡}®¾{)‚)<?x€L‚f®¾?€…r ‚ ƒJI ‚ †I ‚ & x‚Kˆ€

‚À}…‚ ŠLK x~‡.}0„š€K‡Œxˆxzʅs€L‚)‡Œ?}‰‚K

º

s}…‡?‡Œ{)r*s–?o)}1.?oqs®¾{q‚)ˆxz€…‚)‡

7 À p Àq}…‚ Š {

‡ˆ}‰ˆx~‡’®¾‹fˆoqs®¾€L||z€ x‚)¤6oy‹y„š€…ˆoqsN‡ŒsN‡?

¯¢=±Bn>oqs®¾{q‚)<?x€L‚

7 ˆ

‚„ƒ I ‚„† I ‚ &NM ‚5xz‡G4€…‚Kˆxz‚y{q€…{š‡4À1}‰‚ Š ‡?}1ˆx~‡Œ¼)s‡ˆo)s®¾€L||z€ xz‚q¤°sN‡’?xr}1?s?

O7

ki|rt"ru mQP

7

kiRrtSRru m O,TVUCW

k O i!PQiR

OYXZO

t[PTtR

O

msr O7

kirtrnu7m O\T^]_W

r

®¾€…‡ˆ€…r0s U W r ] W w x

Àq}…‚ Š ®¾€…}‰|z|

i|ri

R 

‚„ƒ

r trt

R 

‚S†

r uN

@

¯“±n>oqs®¾{q‚)<?x€L‚

p ˆ

‚„ƒ I ‚„† I ‚

&`M

‚„ƒ»x~‡0€‰®“4|z}L‡ˆ‡badc‰À}‰‚ Š ‡?}1ˆx~‡Œ¼)s‡$ˆoqs®¾€L||z€ x‚)¤

s‡Œˆxzr}1ˆs?

O

pqki|rt"ru mQPTpqki,RrtRrnu7m O,T5Ue

k O ifPQiR

O>XgO

tPTtR

O

mr

O

pqkirtrnu7m OTV]he

r

®¾€…‡ˆ€…r0s

U e r ] e w x

Àq}‰‚ Š ®¾€…}…||

i|rni R 

‚„ƒ

r t"rt R 

‚S†

r uN

@

¯ 2k±n>oqs–®¾{q‚)ˆxz€…‚

{ ˆ

‚„ƒ M ‚S†0x~‡

xz„)‡?&oqx·F€L‚L?x‚y{q€L{)‡À xˆob4€…‚)‡Œ?}…‚L

Uji

w x

¯t8n>oqslk I k!r0}‰ˆ?x·Ž

{ R

ki"mpnmki|rt"ru m

x~‡xz‚yʅs4ˆˆxz q|zs*®¾€…$}…||

ki|rt"ru m  ‚ I ‚„† I @*À}…‚ Š,¶ s

o)}eʅs? oooF

{Rki"m+p m ki|rtrnu7mqp

: c ooo T ] r

r

kqs%i

c

rts%iSuMm  ‚ ƒ I ‚ ƒ r O

{RRki"mskvs%i

c

rts%iSuZm

OwT ] i

xEx

O

s%i

c

OyO

s%iSu Or

r

st  ‚ † r O

pnmzmki|rt"ru mkqst"rtst m

O{T ] e

mzm

O

st Ou 

®¾€…‡ˆ€…r0s„š€K‡Œxˆxzʅs4€…‚)‡Œ?}…‚L&‡

] À ] i

xEx

}‰‚ Š ] e

mzm

}‰‚ Š ®¾€Ls4ÊLs4?‹

ki|rt"ru m 

‚„ƒ I ‚„† I @

¯°‹K„U€‰?oqs‡ˆs‡!¯¢ƒ?€k¯ 25}…ˆsb‚)}‰ˆ{q&}‰|.s4Žyˆs4‚š‡Œxz€…‚)‡f€‰®ˆoq€K‡Œs½4|z}L‡ˆ‡ˆx~4}‰|z|z‹{)‡ˆs Š oqs4‚»‡Œˆ{ Š ‹yx‚q¤

?oqs¯°}…r*xz|ˆ€…‚q±m²K}…4€… qx±m³s||zr}‰‚ H쯓²L³…O°s´K{)}‰ˆxz€…‚½®¾€L–ˆoqs0Ê1}‰|z{qs6®¾{q‚)<?x€L‚=€…®}‰‚=€…„†?xr}…|74€…‚Kˆ?€…|

„)ˆ€L q|sr ˜€…r0„q{qˆxz‚q¤f?oqs$?xr0s Š s4?xzÊe}‰ˆxzʅs€…®Gˆoqs0}‰|z¤…s q&}‰x~€…‚š‡’??}…x‚K“}…|€L‚q¤§}??}‰‘’sˆ€…?‹…À s

€L †?}…x‚ o)}‰xz‡.}‰|z|s Š ?oqs%! }|| T&"sn"

xo~

~ l {|ki

j

klnmm o { R ki

j

klnmm+pqki

j

klnmrt

j

klnmsruqklnmms

(8)

n>oš}‰‚q¿†‡ˆ€–oy‹K„U€‰?oqs‡ˆx~‡¯°t)À1?oqs>xr0„q|zx~x®¾{)‚)<?x€L‚$?oqs4€Lˆsr›xr0„q|zxsN‡ˆo)}‰ Hì}1G|zs}L‡’7|€†}‰|z|‹O

s>4}…‚

s4Žyˆ&}…<°ˆoqs*}‰|z¤…s4 )?}…xzÊ1}‰?x~}‰ q|zs

tZjklnm

®¾?€…r ˆoqx~‡“s´K{)}1?x€L‚b€…NÀšsN´K{qxÊ1}…|s‚L?|‹LÀ)?o)}1

s*4}…‚b€… †&}‰xz‚

h

tZj,klnm  K‹

Š

x·¹is4?s4‚Kˆx~}1?x‚)¤}‡ŒsN€L‚

Š

ˆxzr0s n>oqxz‡–¿yxz‚

Š

€…®}‰|z¤…s q&}‰x~<±

Š

x·¹is4?s4‚K?xz}…|‡Œ‹†‡Œˆsr xz‡‡?}‰x

Š

ˆ€

 Us€…®7xz‚ Š s4Žb

…U

€…°ˆoqs6‡ˆ}…¿…s€‰®[‡ˆxr0„q|zx~x’‹…À s$‡ˆo)}‰|z|‡ˆ{q„q„U€L‡ˆsxz‚bˆoqx~‡„š}‰„Us4?o)}1°ˆoqsˆss4Ž†xz‡Œ?‡}

4€…‚Kˆxz‚y{q€…{š‡Œ|z‹ Š x·¹is4?s4‚Kˆx~}‰ )|s}‰‚ Š

xz„)‡?&oqx·F“4€…‚Kˆxz‚y{q€…{)‡¸®¾{q‚)ˆxz€…‚ ®¾?€…r ‚„ƒ I ‚ &

xz‚L?€‚S†6‡Œ{š&o

?o)}1.®¾€L}‰|z|

ki|ru m@

‚qƒ I ‚ & À

to ki|ru m

xz‡.ˆoqs 0,>/0" >‡ˆ€…|z{†ˆxz€…‚€‰®ˆo)soqxŠ)Š s4‚b€L‚)‡Œˆ&}‰xz‚LZ?

x o { R

ki"m+pqkirtrnu7ms

H2O

[m®iˆo)s.®¾{q‚)ˆxz€…‚

ki|ru m

4}…‚* Us°4€…r0„q{†?s Š ‚y{qr0s4?xz}‰|z|‹LÀ1ˆo)s4‚ s4}‰‚0s|xzr0x‚)}‰ˆs.?oqs°}…|¤Ls4 q&}‰x~

Ê1}…ˆx~}‰ q|zs“}…‚ Š ?s Š {)s“ˆoqs–„q?€… q|zs4r ?€$?oqs€…„†?xr}…|i4€…‚Kˆ?€…|U€‰®}‰‚§€L Š x‚)}…ˆ‹ Š x¹is4?s4‚Kˆx~}‰|is´K{)}‰ˆxz€…‚

¯°€ sʅsÀ7x*€…®Ðˆs4‚ €†44{q?‡$ˆoš}1

p

}‰‚ Š {

}‰?s!}eÊ1}‰xz|z}… q|zs…À7 q{†‚q€…6?oqs4xz Š s4?xÊ1}‰ˆxzʅs‡ [mxz‡0‡Œˆxz||

„U€L‡?‡ˆx q|zsf?oqs4‚kˆ€=x‚Kˆs¤…&}1?s§‚y{qr0s4?xz}‰|z|‹=ˆo)s‡Œ?}‰ˆs§sN´K{)}1?x€L‚ n>o)s!r}‰xz‚k4€…‚Kˆ?x ){†ˆxz€…‚€…®ˆo)xz‡

„š}‰„Us4§x~‡§ˆ€Á‡Œ?}‰ˆsR}k‚y{qr0s4?xz}‰|“‡?&oqsr*s½®¾€…ƒ‡Œ€L|Êyxz‚q¤µˆoqsµ¯°²K³2s´K{)}1?x€L‚ }…‡?‡ˆ€y4xz}‰ˆs ŠÁ¶ xˆo ˆoqs

€L„†ˆxzr}‰|B4€…‚Kˆ?€…|i„q?€… q|zs4r

_

/!9!Aw$k ! 60/!$/! !7+ƒ%

v†x‚)4sƒ€…{q0oy‹y„š€…ˆoqsN‡ŒsN‡*}…||z€ ?€,s4Ž†„qˆsN‡ˆ‡6?oqsb}‰|z¤…s4 )?}…xz§Êe}…ˆx~}‰ )|s

tklnm }…‡0}

xz„)‡ˆ&o)x·F§®¾{q‚š<ˆxz€…‚

ki|klnmruqklnmnm

Àqxx~‡.€…‚yÊLs4‚qxzs4‚K>ˆ€ Š s‚q€‰?sˆoqsŒˆs Š {)4s Š–Š ‹K‚š}‰r0xz‡.}‰‚ Š ?{q‚q‚qxz‚q¤f€K‡’}L‡

ki|ru m ˆo pqki|r kirnu7msru m ki|ru m ˆo 7

ki|r kirnu7msru m

H¾tCO

º

s4}…‚§®¾€Lˆr6{q|~}1ˆs–?oqs€L‚L?x‚y{q€L{)‡€…„†?xr}…|B€…‚K?ˆ€L|C„qˆ€L q|zs4r }L‡®¾€…|z|€ ‡;?

'

k~|m}o (*),+

-./ 021 3 4

6 kijklnmrnuVklnmm$9 :<; =

?l

®¾€…

~W

‚ ƒ r

H^ŸO

o)s4?s

i j klnm

x~‡.‡ˆ€…|z{†ˆxz€…‚€‰®ˆoqs€L Š xz‚)}…ˆ‹ Š x¹is4?s4‚Kˆx~}‰|CsN´L{š}1ˆxz€…‚

h

ij,klnm o

kijklnmsruqklnmnm l@wyxr

ij,k1xCmSo ~€

HìžO

v†x‚)4s–ˆoqs Š ‹y‚)}…r0xz‡}…‚ Š ˆ{q‚)‚qx‚)¤04€L‡Œ>®¾{q‚)<?x€L‚)‡.}‰?s

xz„)‡ˆ&o)x·F}…‚ Š  š€L{q‚ Š s Š Àqxxz‡ s4|z|C¿y‚q€ ‚

?o)}17?oqs.‡’&}1ˆs>sN´L{š}1ˆxz€…‚6o)}…‡G}“{q‚qx~´K{qs‡ˆ€…|z{†ˆxz€…‚6x‚6ˆoqs‡ˆ„)}Ls€‰®U}… )‡ˆ€…|z{†ˆs|‹4€…‚Kˆxz‚y{q€…{)‡®¾{q‚š<ˆxz€…‚š‡4À

}…‚ Š ˆo)}‰?oqsÊ1}‰|z{qs–®¾{q‚)<?x€L‚!x~‡¼)‚qxˆs}…‚ Š ¯…|Š s44€…‚Kˆxz‚y{q€…{š‡}L‡ˆs4|z|~‡ˆoqs‚qs4ŽK.|zs4r0r}

s

U 6

 Us Š s4¼)‚qs Š  y‹

U 6 ˆo

k~

R

rnu7m P k~Vru m

~ R PQ~

~R! o ~SuN

@"

«%$&('*) ! ,+M'(0" .0,N-0,| t|.-/sQ|S|0@'G 15- 0"! P!

1

o32

K w U4

1 o ;

576 K98

U4



H1XO

(9)

)

!" WP! n

U

wyx 0S|

w x

s0"!9!"&0 &''

~

& | ~ R

P&

O~ R P ~ OT

0SP!

''] S‰!'y|M

O'

k~|mP

'

k~ RPm O T5UO

~ PQ~ R O 

H\O

/ &P! &t|M0 P! @0, ' #'y| SP!N&"s " 1!-

˜€L‚)‡ŒxŠ s>ˆoqs¯“}‰r0x|ˆ€L‚†±É²L}L€… )x·±É³s4|z|r}‰‚ H쯰²K³…Os´K{)}‰ˆxz€…‚

-S./

K

k~|mP

k~Vru m j

k~|mP k~€rnu7m o x r

~W

‚ ƒ r

HAO

¯°s4?s

jo

~ c

r!7r"

~

ƒ$#

}…‚ Š

Š s4‚q€…ˆsN‡ˆoqsxz‚q‚qs„q?€ Š {)<.xz‚ ‚„ƒ

U

€…G€L‚KÊLs4‚qxzs4‚šs…À s?s}‰|z|yoqs4?s[?oqs Š s¼)‚)x·?x€L‚6€…®)Êyxz‡?€K‡Œx’‹‡Œ€L|{†?x€L‚BÀ‰‡ˆs4s˜?}…‚ Š }‰|z|y}‰‚ Š xz€…‚)‡

JéŸZL

< = :¾©Z:Ç= $ &''& "1"0"0 „0,|1& & ‚qƒ %''] z|9 +Z&( &'0,T*),+.- 0

+& ./



adc

k

‚„ƒ

m

0}!" ''] S‰!'y|M

kxm /P

~ c

'G;&'V;%0,K"…+ P

/0}P!

0

-./

K

k~

c

mP

k~

c

ru m1!j

/

k~

c

mP k~

c

rnu7m

T

x

k

xx

m

/P

~u

'G;&'V%>%0,K"…+ P / 0@!"

0

-./

K

k~ u&mP

k~ uru m1!j

/

k~ u&mP k~urnu7m32 x

«†ª54 $&(' /sT(0‰P! -&0, | z|&| s |76„! 98 "1"0,( + & |

':;) 0

-<-0>=$&s'] ?A@B(- P!.P! +&&'0" 0,J' P! %0,"/0" -&0,| z| |90,"s%'C &>>0"&0

+ZMsD‰'(0,1&Q !" $#*=K /0" -

E F

/ƒ >7$%%<A

sG{)‡ q?xsG)‹ Š x~‡?{)‡?‡ €‡’&}‰‚ Š }‰ Š ¼)&‡’ˆ±P€L Š s4‡?&oqsr*sN‡®¾€…G‡Œ€L|Êyxz‚q¤“ˆoqs.‡Œ?}1?s>s´K{)}1?x€L‚ [ɂ*s}L&o

€…®š?oqs‡ˆs°‡?&oqs4r0sN‡4À…ˆoqs°4€…‚Kˆ?€…|†Ê1}…ˆx~}‰ q|zs.x~‡[‡Œ{)„q„š€K‡Œs Š ˆ€ Us°€L‚)‡Œ?}‰‚K Š {)ˆxz‚q¤ˆo)s.ˆxzr0s°‡’?s4„IH

wyx

v†x‚)4s s64€…‚)‡ˆxŠ s4°€L‚qs6‡Œˆs„½r0s?oq€ Š ‡4Àix“x~‡“‡ˆ{KJfxzs4‚K–ˆ€‡’&}1ˆsˆoqs6®¾€…?r${q|~}0®¾€L–4€…r0„q{†?x‚q¤§ˆoqs

‡Œ?}‰ˆs$}‰®Ðˆs°?oqs¼)&‡Œ–‡Œˆs4„ vy€šÀš|zs–{)‡¼)Ž

u 6 

@BED*}‰‚ Š }…‚bx‚)x·?xz}…|4€…‚ Š xˆxz€…‚

~Q

‚„ƒ n>o)s €

‡?&oqsr*sN‡.}‰?s

iMLj o ~ X H

pqk~€rtNL

j

ru

6 m

x o { R

k~|mpqk~€rtNLj ru

6 m

HŒ¢¡O

€L‚§?oqs€…‚)s–oš}‰‚

Š

Àš}‰‚

Š i L

j o ~ X H

pqk~€rt L

j

ru

6 m

x o {|kiML

j m P {|k~7m

H΢ɢZO

(10)

€L‚½?oqs0€‰ˆo)s4o)}‰‚

Š

n>oqs*¼)&‡’‡?&oqs4r0s*xz‡–€‰®sŽ†„q|zxz4x·–’‹y„šs

oqxz|zs6?oqs0‡ŒsN€…‚

Š

€…‚)s6x~‡€‰®¸xzr0„q|zxz4x·

’‹y„Us

[ɂbsN}…&oƒ€‰®7ˆo)s‡ˆs‡ˆ&oqsr0s‡À)€…‚)so)}…‡>?€§‡ˆ€…|zʅs}f‡ˆ‹y‡Œˆsr €…®7‚)€…‚q|zx‚)s}‰.sN´K{)}1?x€L‚)‡ [ɂb„q&}…ˆx~s…À

?oqx~‡ x|z|Cr0s}…‚{š‡Œxz‚q¤}*Êe}…ˆx~}‰‚K.€‰®

s ˆ€…‚#‡.r0s4ˆoq€ Š Àqxz‚ oqx~&o§?oqs²L}L€L qxz}…‚§r}e‹f Us}‰„q„)ˆ€eŽ†x±

r}‰ˆs Š {)‡ˆx‚)¤6¼š‚qx·?s‡ Š x·¹is4?s4‚)4s‡ n>oqs®¾{q‚)ˆxz€…‚)‡ Š s4¼)‚qxz‚q¤0ˆo)s–sN´K{)}1?x€L‚)‡ˆ€0 Us‡Œ€L|ÊLs Š Àyoq€ s4ÊLs4NÀ

oš}eʅs“ˆ€0 šs4€…r0„q{†?s Š!¶ x·?ob}6¤L€y€ Š }…{q&}…4‹ n>oqxz‡r0}…¿…sN‡}…‚!sN‡ˆ‡ˆs4‚K?xz}…| Š x·¹is4?s4‚)4s šs4 ss4‚ˆoqs

 €$‡?&oqs4r0sN‡?ˆoqs“¼)&‡’‚qs4s Š ‡}„q?s4xz‡ˆss4Ê1}…|{)}‰ˆxz€…‚€…®

p

}‰‚ Š { RÀ o)s4?s}…‡[ˆoqs‡ˆs€L‚ Š ‚qss Š ‡€…‚q|z‹

?€!sÊ1}‰|z{)}1?s

p

}…‚ Š {

[ɂR€…ˆoqs €… Š ‡Àšx®€L‚q|z‹

{

x~‡}eÊe}…x|~}‰ )|s*}‰‚ Š ‚q€‰x·&‡ Š s4?xÊ1}‰ˆxzʅs…ÀU?oqs4‚=ˆoqs

‡ˆs4€…‚ Š ‡?&oqs4r0s4}…‚! Usxr0„q|zs4r0s‚L?s Š À oqs4?s}L‡¸?oqs¼)&‡’°}‰‚q‚)€‰

:ìª1¨4©0¨¬ à à [ɂ!ˆoqs¼)&‡Œ°‡ˆ&oqsr0s so)}eʅs“ˆoš}1

i L

j

o5~

X H

pqk~€r k~€rnu

6

mru

6

ms

HŒ¢NO

ÃyÇ ª Ã

&('

6V

u 6  ‚ &

r~

4 

‚„ƒŠ- +& T& | &"}|

o k~€rnu

6 m

- !" &'0,Q+

{Rk~|m+pqk~€r

ru

6 m o5x

V&'' H

25x

0}P! n ns‰0,"/0" &'0,T*) - - n +& 0 !" 0,|1&"

~

M

kiMLj rtNLj mr

P!

~

P! 0,"/0" &'0,Q+

k 2;x m

& 6S>!,8"1"0"&0 S0,1& -

n; )Gn>oqs„q?€y€‰®x~‡.|~}…‡?‡ˆxz}‰|C}‰‚ Š ?oqs4?s®¾€Lˆs–€…r0xŒˆs Š

¬ Ç= È ¨N¬ Ã Ã º

s‚q€ ˆ{q?‚ˆ€*ˆoqs‡Œˆ{ Š ‹§€…®ˆo)s‡ŒsN€…‚ Š ‡?&oqs4r0s

ÃyÇ ª à & :^¨4© ÃC= ¬ à « = È = : à ¨¨ Ç © à ¨ Ç "©;:Ç>= 6V

u 6  ‚ & &|

~ 

‚„ƒ

- +& Q& | &"s}|

o k~Vru

6 m

P! &'(0,1&T+

{ Rk~|m+pqk~€r

ru

6 m o5x

) !" n s$H

6 w x 01

wŠx

& |"!

w x

0.''q | | > +

~

s0"!NP!7&''

x 8 H 8 H 6

P!

.Ms )# $ -!"M 0,>/0" &'(0,1&

kiML

j

rtNL

j m

NP! &%

k~€r('

u m I % k r()

u m -

n; )Gn>oqs„q?€y€‰®®¾€L||z€ ‡>|z€L‡ˆs4|z‹ˆo)sxŠ sN}…‡>€…®¯°}…x?s4.s4}‰| J\ML ˜€…‚š‡ŒxŠ s4>?oqs‡ˆ‹y‡Œˆsr

i|k+*>m o ~ X H

pqk~€rtk*>mru

6 m X H

k+* P 2Mmpqk~€r

ru

6 m

x o {|ki|k+*>mnmP {k~|m



H΢;2O

U

€…

*9o 2

À€HŒ¢;2COxz‡.sN´K{qxÊ1}…|s‚L>?€NH’¢…¢MO<À o)x|zs®¾€…

*9oŠx

À)x·o)}L‡>ˆo)s€… yÊyx€L{)‡.‡Œ€L|{qˆxz€…‚

ioŠ~

}‰‚ Š

t o •“x·¹is4?s4‚K?xz}‰ˆxz‚q¤ x·?oƒˆsN‡Œ„Us?€

* À s–¤Ls

h

i o H p m

k~Vrt"ru

6 m h t X H

pqk~Vr

rnu

6 m

x o { R

ki"m+p

m

k~€rt"ru

6 m h t X { R

ki"m+pqk~€r

ru

6 m

H΢4tCO

(11)

€ À Š

{qs§ˆ€µ¯t)ÀGx0xz‡6s}L‡Œxz|‹5‡ˆs4s‚5ˆo)}‰

{ R

ki"m+pnmk~Vrt"ru

6 m

xz‡6x‚yÊLs4ˆˆxz q|s§®¾€…

i

x‚%

k~Vr 'u m xˆo

ock ] ] i

x>x m :

c–}…‚

Š

ˆo)}‰

r i  %

k~Vr

mr

r t  ‚ † r O

k{,Rki"m+pSmk~€rt"ru

6

mnm : c O,T

] 

º

xˆo)x‚ %

k~€r 'u m

À€H’¢tCOx~‡.s´K{qxzÊ1}‰|zs4‚K>ˆ€0ˆo)s Š x·¹is4?s4‚K?xz}…|B‡Œ‹†‡Œˆs4r

h

i o

H

k~€ri|rtCmpqk~€r

ru

6 m

h

t o PQk{

R

ki"mp

m

k~€rtrnu

6

mm : c { R

kimpqk~Vr

rnu

6 m r

o)s4?s

k~Vri|rt m

xz‡“ˆo)s*„)ˆ€…‘’s<?x€L‚

P pnmk~€rtrnu

6

mkP{ Rki"m+pnmk~Vrt"ru

6

mnm : c { Rki"m

}‰‚ ŠR¶ x·?o=xz‚qxˆx~}‰|

4€…‚ Š x·?x€L‚)‡

i|kxCmSo5~

}‰‚ Š

t"kx mqo

n>oqx~‡‡ˆ‹†‡’?s4r o)}L‡.}*{q‚qx~´L{)s‡Œ€L|{†?x€L‚ o)xz&ob‡?}1ˆx~‡Œ¼)s‡

O

i|k+*>mPQ~

O o oooo 3

6 h

i|k Cm?

oooo T * H k 2 X

UeS] Uji

m

]he

r

O

t"k+*>mP

O T ] O{ R

k~7m+pqk~Vr

rnu

6 m

6 X

3 c

6 { RRk~

X

lskik*>mPQ~|mmsk1pqk~€r

ru

6

msri|k+*>mP ~7m?l

O

T ] ] i

xEx ]heO

i|k+*>mPQ~

Or

}…‚ Š ˆoy{)‡.?s4r}‰xz‚)‡xz‚%

k~Vr('

u m I % k~Vr )u m

®¾€…

* T 2

„q?€1ÊyxŠ s Š H 8 H 6 oqs4?s

H 6 o (*)

k 2 X U e] Ui

m

]he

r !

] ] i

xEx ]he

k 2 X

UeS] Uji

m

]he

# 

[ɂ5€L

Š

s4?€½„q?€1ʅs{q‚qx~´K{qs4‚)s‡?‡4À

s§€L‚)‡Œx

Š

s$}‰‚q€…ˆoqs$‡ˆ€…|z{†ˆxz€…‚

kirtm x‚ %

k~Vr 'u m I % k r()

u m

€…®

H΢ɢMO

?xˆxz‚q¤

s%ioi PQi

À

st otP t

}‰‚

Š

sp o pqk~Vrt,rnu

6

mP pqk~€rtrnu

6 m À

s–ˆoqs‚oš}eʅs

x o {|ki"mP {ki"m

o { R

ki"m$s%i X % i

kiri,mskvs%i|rts%i"m

o H { Rki"mp m k~€rtrnu

6

m$st

X H { Rki"m

% e

k~Vrt"rtCmkvst"rtst m X % i

ki|ri"mkqsi|rzsi"msr

o)s4?s

% i

ki|ri"mkqsi|rzsi"mao 3 c

6 k 2PQlnm1{

RR

ki

X

l2s%imskvs%i|rts%i"m?l

}…‚ Š % e

k~Vrt"rtmskvst"rtstCmao 3 c

6 k 2PQlnm+p mtm k~Vrt

X

l2st"ru

6

mkqst"rtst m?ls

(12)

[m.®¾€L||z€

‡ˆo)}‰

stocktP {RPki"mp m k~€rtrnu

6

mm

:

c

{,Rki"m

% e

k~€rtrtmskvstrzstCm X H % i

ki|ri"mkqsprzsp mS

º

s€L‚)‡ˆs´K{qs4‚K?|‹¤Ls.ˆo)ss‡Œˆxzr0}‰ˆs

O

st

OwT ] kU i ] e

mtm

X H 6 U ue ] i

xEx m O

st Ou

T ] kU i ] e

mtm

X H 6 U ue ] i

xEx m ! O

st O

€ À)„q?€1ÊyxŠ s Š !!x~‡°‡ˆ{KJfxzs4‚K?|‹ƒ‡Œr}…||PÀq?oqs64€…‚)‡Œ?}…‚L

] k Ui ] e

mzm

X U ue ] i

xEx

m

!ƒx~‡°‡ˆr0}…||zs4ˆo)}…‚

2

}…‚ Š§¶ s‚qsNs‡?‡?}‰?x|z‹0o)}eʅs

st o x

n>oqs®ì}….ˆo)}‰

sio x

®¾€…|z|z€ ‡.‡’??}…x¤LoLˆ®¾€… }… Š |‹

ÃyÇ ª à &$ V& u 6  ‚ & z|‰& |

x 8 H 8 H

6

P! @0,1&

~ M i Lj

|

~ M t L

j

HŒ¢NŸO

P!

~

!" 0,>/0" &'0,5

k 2 2Mm

':&Q %

k~Vr ' m I % k k~Vru

6

msr$)

m

& 06S>! 98

"1"0"&0 S0,1& -

n; )–xÊLs4‚

~

}‰‚

Š

~

xz‚W‚qƒ[Àq|s4

k*>m}o *,~

X k 2P *>m

~

}‰‚

Š

4€…‚)‡ˆx

Š

s4ˆoqs‡ˆ‹†‡’?s4r

i o

k+*>m X H

pqk

k+*>mrtrnu

6 m

x o {kim P {|k

k*>mm

r

HŒ¢žO

o)€L‡ˆs=‡ˆ€…|z{†ˆxz€…‚ xz‡

kiML

j

rtL

j m

®¾€…

* o 2

}‰‚

Š

kiML

j

rtL

j m

®¾€…

* o x

R°‡xz‚ „q?s4Êyxz€…{)‡§ˆo)s4€…?s4rƒÀ

Š

x·¹is4?s4‚Kˆx~}1?x€L‚

xˆoƒ?s‡ˆ„šsN<>ˆ€

*

|zs}

Š

‡ˆ€

h

i oKk~ P

~7m

X H p x k

rt"ru

6

mk~ P

~ m X H pSm&k

rt"ru

6 m h

t

x o cL

k{

R

ki"m PQ{

Rk m X H { R kimp

x k rt"ru

6

mm|k~ P

~7m X { R

ki"m+pnmk

rt"ru

6 m h

t

xˆoƒxz‚qxˆx~}‰|4€…‚ Š xˆxz€…‚š‡

ik1xCm„o i

j

}‰‚ Š

t"kxCm„o tNL

j

x·?oqxz‚ƒˆoqs‡ˆs

o

. 6

c

% k

k*>mr

msr

„)ˆsÊKxz€…{š‡‡ˆ‹†‡’?s4r x~‡.sN´L{)xÊ1}‰|zs4‚K>ˆ€0?oqs Š x¹Usˆs‚Kˆx~}‰|Cs´K{)}‰ˆxz€…‚

h

i o k~ P

~7m

X H p x k

rtrnu

6

msk~ P

~ m X H pnmk

rtrnu

6 m h

t

h

t o P k{ Rki"m+p m k rt"ru

6

mnm

: c c

L

kP{ Rki"mP { Rk m X H { Rki"m+p

x k rtrnu

6

mmk~lP

~|m

xˆo0?oqs°‡?}‰r0s.xz‚qx·?xz}…|š4€…‚ Š xˆxz€…‚š‡¸}…‡[ šs4®¾€…?s [m¸o)}…‡¸}{q‚qx~´K{qs°‡ˆ€…|z{†ˆxz€…‚*®¾€…

* 8

*

o)xz&of‡?}1?xz‡Œ¼)s‡

O

i|k+*>mP

k+*>m OT

H

]he T

Références

Documents relatifs

Il y a dans la moelle osseuse (Figure 5) un compartiment extra vascu- laire contenant des cellules souches très minoritaires ayant chacune un potentiel de différenciation

Abbreviations used: DMEM, Dulbecco’s modified Eagle’s medium; ERK, extracellular-signal-regulated kinase; GFP, green fluorescent protein; GST, glutathione S-transferase;

To test whether the vesicular pool of Atat1 promotes the acetyl- ation of -tubulin in MTs, we isolated subcellular fractions from newborn mouse cortices and then assessed

Néanmoins, la dualité des acides (Lewis et Bronsted) est un système dispendieux, dont le recyclage est une opération complexe et par conséquent difficilement applicable à

Cette mutation familiale du gène MME est une substitution d’une base guanine par une base adenine sur le chromosome 3q25.2, ce qui induit un remplacement d’un acide aminé cystéine

En ouvrant cette page avec Netscape composer, vous verrez que le cadre prévu pour accueillir le panoramique a une taille déterminée, choisie par les concepteurs des hyperpaysages

Chaque séance durera deux heures, mais dans la seconde, seule la première heure sera consacrée à l'expérimentation décrite ici ; durant la seconde, les élèves travailleront sur

A time-varying respiratory elastance model is developed with a negative elastic component (E demand ), to describe the driving pressure generated during a patient initiated