• Aucun résultat trouvé

Polynomial energy decay rate and strong stability of Kirchhoff plates with non-compact resolvent

N/A
N/A
Protected

Academic year: 2021

Partager "Polynomial energy decay rate and strong stability of Kirchhoff plates with non-compact resolvent"

Copied!
16
0
0

Texte intégral

(1)

HAL Id: hal-00129704

https://hal.archives-ouvertes.fr/hal-00129704

Preprint submitted on 8 Feb 2007

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.

Polynomial energy decay rate and strong stability of Kirchhoff plates with non-compact resolvent

Bopeng Rao, Ali Wehbe

To cite this version:

Bopeng Rao, Ali Wehbe. Polynomial energy decay rate and strong stability of Kirchhoff plates with non-compact resolvent. 2004. �hal-00129704�

(2)

+*-,./0$1 1"243 #657 18 :9;<=>3?+@7#A==

BCEDGFHJI:KMLON"PQEH;R?LMSUTWVYX<ZBX[

\^]&_`badcJef`Egihj(kmlonprqtsvuxwykzWu{ky|} q:|wm~J€b‚ƒ<|?|/j(w„pE…u{kUj†~‡wm~J|z;du{ˆdlWdqtkypduM|/lW|/}‰nfˆŠ€E|Œ‹Œpdˆ

}†pfw„|0/f}ŽwU~;|j(qfwm~=jdu{sJwkydl;j‘<’+km}‹~“~J•”–zWu—pfw„|/jŽ|Œ˜s;pfwkydlJj/™š@flJj|Œ˜/s;|l)wu{ˆb‚ ƒ<|E…bw‰pfkml

wU~;|tj/wy}dlon?j(w„pE…kmu{k›wˆ?kmlœwU~;|^pE…/j|/lW‹|•:‹ŒdqOzJp“‹wlG|/jŒj•t}†|/jdu{d|l)wO‘twm~J|:kmlbžŸl)k›w‰|/j(kmqpfu

z;|/}pfw„d}/™

 ¢¡o£¤¥ ad¦ _Eg<§ TU¨©ŒªJª;Cf«"DJSmQd¬Fb­®bDGCESU¯°HJCE±:TmQfS²RvF©Q²¯M¨ŒQd¬Ff®d­•¬¨†C“HJIŽ­•¬ŒQf³JTUSUT´¬•¯f®/HJC“Hvµ„©CE±:D;Q“©(¬HJFb­­/¶

\·¹¸‡_º ]W» ¡ ef`:eE¼cJ__b½y¾$e“cv`b½¥)¿ _fgŽÀEÁ“ÂÄÃEÅ ® ÀEÁ B Å“Æ ® ÁoÆ B Á“Æ ® ÁoÆ B ÁoÇ

È ÉÊtË&Ì@Í^ÎÐÏ?ÑË&ÒbÍ=ÊÔÓ+Ê?Î4ÕÖÓ+ÒbÊ8Ì@×MØ&Ï¢Ù(Ë&Ø

ÚÛHܬªJTm­:D;QfDGF¨ÝFЭ‘¬†Þ;RJ¯¬ªJFr­‘¬Qf³;T´SUT´¬•¯ŠCfß"QЬ†ª;T´HÜFbSUQ“­•¬Tm©DJSmQf¬†F?ݎT´¬†ªàRv¯°H;Qf±:Tm©bQfS

³)C“ÞJH;RJQE¨†¯Šß›FbFbRv³)QE©Œáœ©/C“Ho¬†¨CESm­/¶âF/¬ã!ä7åæ [

³GF?Q–³GCEÞJH;RJFbRçCEDGFHÜ­‘F¬ÝŽT´¬ªç­†±:CoCE¬†ª

³)C“ÞJH;RJQE¨†¯‡èé©/C“H;­‘Tm­‘¬†TUHJIêCfß"Q©/SmQf±:DGFbRçD;QE¨‘¬èëf®MQfH;RÜQЍTU±:±:FbRœD)Qf¨†¬è

P

­†Þ;©ŒªÜ¬†ª;Qf¬

è0ëì è

Pí.îfïoð

¶–ñ;CESUSUCdݎT´H;I^¬†ª;F¬ªJFC“¨†¯êCfߎSUTUHJFbQE¨+FSmQE­‘¬†Tm©T—¬•¯E®0¬†ª;Fò°TU³J¨Qf¬†TUCEHêCfßOQ¢¬†ªJTUH

FSmQE­‘¬†Tm©ODJSmQd¬†FTm­IEC“ÞJòEFb¨†H;FbR:³°¯^¬ªJF"SUTUHJFbQE¨­†¯v­•¬F±ôó

õööööö

÷öööööø

ùEúmú ûêüWý=ùfúmúþý

[ ù í Å T´Hÿã?åæ

ù í ù

í Å CEH!è ë æ

ý=ù"þ Mû

P

ùþ

í Å C“Hÿè

P

æ

ý=ù

þ Žû [ ù

û–ü

ùfúmú

þ [

ùfú

[

û

í Å CEHÿè

P

åæ

ݎªJF¨F í P [

RJFHJCE¬†Fb­"¬†ªJF^Þ;HJT´¬+HJCE¨±^QfS&òEF©(¬CE¨b® í P [

¬ªJF:ÞJHJT´¬"¬ŒQfHJI“FHo¬

òEF©(¬†C“¨®0QEH;RÐݎªJFb¨†F

ü

Å QEH;R Å

à QE¨†F=DJª°¯v­‘Tm©QES ©CEH;­‘¬QEH“¬Œ­/¶! ªJFt³GCEÞJH;R;Qf¨¯

"$#&%')(+*(+,(.-/.0/1)2/34142/6578()2:9/;78()*=<>,/@?A878%19//CBED%*A>/34'+*(F9/6GIH8,*':JK7C')()/,3:-/MLN()347C')OPH8,3)QBERFBF3+,/

0S9/$%9/$TVU@/'417C3)()/'WBPX>R8YCZ8[SLN()347C'+OPH8,34Q]\:/-/$^PB_3478%1/C`babTV;c78*d&e3)7CHNfM*=34;7`,TV')()347C'+OQ`gh3

i \:?@5!LPBj\:H8dd=/QC/lk678dd&Bj0HFHC;m[>nCoEBP?M;c/3)*=178%!DM%E*A>/34')*(VpqH8gr/$*=3+,(BjJK`sl`rstejuCuvYCnCwCXEBjr/$*=3),(B

GI/$O78%H8%I`:axTV;c78*d&eb78d* y/$2NOj/WfMp>782HNH`gh3

(3)

P [õöö

÷ööø P ù í Ã P [ [ ù

P

[ û [ P [ ù

[[ û [ [ [ ù

[P

[ ù í [

P û [

[ [ ù

P

[ þ P [ [ ù [[ û [ ù

[

P

Ã

ÚÛH¬†ªJF©bQE­†FCfß@­•¬ŒQd¬†Tm©ß›FFRv³;Q“©Œá°­Äó

í

ù ú ® í ù ú

®J¬†ªJF=­•¬ŒQf³JTUSUT´¬•¯tCEß&­†¯v­•¬F±

E

µ

Ã

ÝQ“­ÝFbSUS­•¬Þ;RvTUFbR³°¯ RJT—«WF¨FHo¬OQEDJDJ¨C“QE©Œª;Fb­ ­†FFÇ®À®

Å ®

P

®

®ÃEÁ QEH;R

¬†ªJF¨F/ߛFb¨†FbH;©/F­<ݎªJFb¨†FbTUH

¶&ÚÛH^¬ªJTm­<ÝCE¨áG®oÝFÄ©CEH;­†TmRvF¨<¬†ªJF©Q“­‘FCfß RJ¯oH)Qf±:Tm©QES;³GCEÞJH;R;Qf¨¯

©/C“H“¬¨†C“Sm­ ®

K

ݎªJTm©ŒªQE¨†FÄIETUòEFbH³°¯:¬ªJFߛCESUSUCdݎTUHJI+TUHo¬†FI“¨QESG­†¯v­•¬F±ÿó

ú û ù ú

þ

í Å CEH!è

P

æ

ú ûêù ú þ

í Å

CEH!è

P

æ Á

ªJFЩ/C“H;©/FbDv¬:CfßRv¯°H;Qf±:Tm©QES©CEHo¬†¨CESª;Q“­³)FbFHÜTUH“¬¨†CvRvÞ)©/FbR³°¯¬†ªJF¢QEÞv¬†C“±^Qd¬†Tm©TUQEH;­+TUH

¬†ªJF;H;T—¬FtRJT´±:FbH;­†T´C“H;QfS ©QE­†F ­†FFñJ¨ŒQfH;©TU­

¶=ÚÛH–¬†ªJFTUH;H;T—¬F=RvTU±:FbH;­‘TUC“H;QfS©bQE­†Ff®W¬†ª;F

Rv¯°H;Qf±:Tm©bQfSJ©/C“Ho¬†¨CESm­ ߛCE¨±¹D;QE¨‘¬ŸCEßT´H)RvTU¨†F©(¬ŸRJQf±:D;T´H;Iı:F©Œª;QfH;TU­†±^­ DJ¨†C“D)Co­‘FRt³o¯KŽÞ;­­†FSUS

Ã

MCdÝ SUF¬

ù

³GF"Q=­†±:C°Cf¬ª ­†CESUÞv¬†TUC“H:Cfß$­†¯v­•¬F±

E µ Á

¶&VŠFRJF;HJFĬªJF"QE­­‘Cv©/TmQf¬†FbR

FHJFb¨†I“¯ ³o¯

í

à "!

[

ú

þü$#&%=ù ú #[ ('

þ

"! )

ùK*' þ

"+-, #.#

[

þ/#0#

[ '

è1 2

ݎªJF¨FÄߛCE¨M­†±:C°Cf¬†ª ߛÞJH;©/¬†TUCEH)­

ù

43J®vÝF"ª;Q²òEFÄDJÞv¬"ó

)

›ù 53

í [ ù

[P [63

[P þ [ ù [[

[63

[[ þ

[ ù

[P [63

[[ þ [ ù [[

[63

[

P þ Ã

[ ù

P

[

[73

P

[

ªJFH¢Q­‘¬†¨ŒQfTUIEªo¬‘ß›C“¨†ÝQf¨ŒR:©/C“±:DJÞv¬ŒQd¬†TUC“H^IETUòEF­ ­†FF8

Å QEH;R9

6 ó

'

'- í û

-+ , #.#

[

þ/#0#

[

þ;:

::: ù ú

::::[ ' è=<

Å Æ

ªJF¨F/ߛC“¨†F ­‘¯v­‘¬†F±

µ Á

TU­=RvTm­†­†TUD;Qd¬TUòEFTUHЬªJF ­†FH;­†F:¬ª;Qd¬=¬†ªJF^FbHJF¨IE¯êTm­"HJC“HJTUHvµ

©/¨FbQ“­‘TUHJI;¶>¢C“¨†FbCdòEF¨b®oRJFHJCE¬†TUHJIt³o¯8?

í

›ù

ùfú

P

¬†ª;F­‘¬Qf¬†FÄCfß&­‘¯v­‘¬†F±

E µ Á

®vÝF

©QEH ߛC“¨†±tÞJSmQd¬Fެ†ª;F"DJ¨†C“³JSUF±iQ“­ŽQfH?Fò“CESUÞv¬†TUC“H;Qf¨¯F@“Þ)Qd¬†TUC“HÐó

? ú þBA

? í Å ? Å í

?Gë CED

ݎªJF¨F

A

TU­Q:±^QFvTU±^QfSW±:C“HJCf¬CEHJF"C“D)Fb¨Qf¬†CE¨TUHÐQfHÐQfD;DJ¨†C“DJ¨TUQf¬†F"ZMTUSU³GF¨†¬OFHJFb¨†I“¯­†D;Q“©/F

D¢¶ÚÛHr¬ªJFCEHJF:RvTU±:FH)­‘TUCEH)QfS©bQE­†FGà 2 ®ÝFª;Q²òEF­‘ª;CdݎHЬ†ª)Qd¬"F6@oÞ;Qf¬†TUCEH ¶H

ª;Q“­H;CEH

ÞJHJT´ß›CE¨±ôFH;F¨IE¯ÐRvF©Q²¯¢¨ŒQd¬†FE¶JI°CÝF=¬ÞJ¨Hr¬C F­•¬ŒQf³JSUTm­‘ªÐ¬†ªJFDGCESU¯°HJCE±:TmQfSFHJFb¨†I“¯ÐRvFb©bQ²¯

¨Qf¬†F<ߛCE¨ ¬†ªJF­‘±:C°CE¬†ª"TUHJT´¬†TmQfS“RJQd¬ŒQv¶6 ª;F¨FQf¨F­†Fò“F¨ŒQfSoQfDJDJ¨C“Q“©ŒªJFb­Qf³GCEÞv¬ ¬†ªJFD)C“SU¯oH;CE±:TmQfS

FHJFb¨†I“¯¢RvFb©bQ²¯¨ŒQd¬Ff¶VŠFt¨F/ߛFb¨O¬C$

à ߛC“¨ÝQ²ò“F+F6@oÞ;Qf¬†TUCEH¢ÝŽT´¬†ª–SUC°©bQfS T´Ho¬F¨HrRJQf±:D;T´H;IJ®

Æ ß›CE¨QE³;­‘¬†¨ŒQE©(¬<­†¯v­•¬F±^­@³°¯­‘Fb±:TUIE¨CEÞJDtQfDJDJ¨C“Q“©ŒªJFb­®0

À ߛCE¨ªo¯°³J¨TmRJ­@­†¯°­‘¬†Fb±^­ŸQfH)RKÃ

(4)

ÚÛHœ¬ªJTm­=ÝCE¨áG®@ÝFݎTUS´SQERJQEDv¬tQ–HJC“HJSUT´H;FbQf¨"±:F¬†ªJCvRT´Ho¬¨†CvRvÞ;©FbRŠTUH

À& ¬CЬªJF?S´TUHJFQf¨

F6@oÞ;Qf¬†TUCEH ¶H

QEH;R^F­•¬ŒQf³JSUTm­†ª=¬ªJFÄFHJFb¨†I“¯tRvF©Q²¯t¨Qf¬†FÄQE­

ߛCE¨¬†ª;F­†±:CoCE¬†ª^TUHJT´¬TUQESJRJQd¬ŒQ

TUH

A

¶l ª;F±:F¬†ªJCvR TU­RvTU¨Fb©(¬ŽQfH)R^IETUò“Fb­@¬ªJFCEDv¬TU±^QfSWRvFb©bQ²¯:¨Qf¬†FOTUH¬†ªJFÞJH;RJF¨S´¯°TUHJI

©/C“H“¬FF°¬¶

VêF )¨­‘¬ŽFb­‘¬Qf³;S´Tm­†ª:¬†ª;FߛCESUSUCdݎT´H;I+D)C“SU¯oH;CE±:TmQfS)FHJFb¨†I“¯^RvFb©bQ²¯^¨Qf¬†Ftó

¡o¥ a ¡ g jŒj(svq|wU~;pfw

è0ë

íYï

pflG€ èë<ì è

PŽí-ï

Ã

~;|/}|"|“kUj/w›j

ÅpdlG€ ë æ [

jŒs;‹Œ~wU~;pfwm‚;zGsJw‰wykml°n í û ë ‚&ƒ<|Ž~Jpf²|

< Å C¢è ë pdlG€

"!

$#

P C¢è

P

~J|l?/f}?pfl;ˆ¢j(q:bEwU~kml)k›wykypfuŽ€“pfw„p ?)ë9C

A

‚=wU~;|/}†|¢|%“kUj/wpŠ‹Œdl;j/w‰pfl)w'&

Åç€E|)(

zJ|lG€fkmlonfl;u{ˆ–fl+* ? ë

*-,'.0/21j(s;‹~wm~Jpfwwm~J|?|lG|}nfˆ • wU~;|^j(ˆ²j/w„|/q4365f™798~Jpdj p

zJfu{ˆdlGfq=kypfu&€“|Œ‹pfˆ^}†pEw‰|

< Å

Ã:&

&

þB

;!

Å Ç

VêFŽH;FF°¬<©/C“H;­‘TmRvFb¨¬ªJFM­‘¬†¨CEHJI"­‘¬Qf³;T´SUT´¬•¯f¶ OCf¬TU©F¬†ª;Qf¬@¬†ªJFލFb­†CESUòEFbHo¬ å

þEA # PŸTm­&HJCE¬

©/C“±:D;QE©/¬ÄTUHЬªJFFHJFb¨†I“¯¢­‘D;Q“©/FD¢¶ ª;F¨F/ߛCE¨Ff®¬ªJF:©/SmQE­­†TU©+±:F/¬†ª;C°R;­Ä­†Þ;©ŒªêQE­âQ“­†QES´SUF=<­

TUHoòdQE¨†TmQfH)©/FMDJ¨TUH;©/TUDJSUFÓà CE¨¬ªJF+­‘DGFb©/¬†¨ŒQfSRvF©/CE±:DGC“­†T´¬†TUCEH¬ªJFC“¨†¯CfßI

µ OQfI“¯oµ„ñ;CETmQE­ 2

RvCEH><¬ÝCE¨áTUH¬ª;Qd¬©QE­†Ff¶àVŠF¢ª;Q²ò“F±:FbF/¬^­†CE±:F¬†F©ŒªJHJTm©QESRJT0?^©ÞJS´¬†TUFb­=¬†CÞ)­‘F¢±:C“¨†F

IEFbHJF¨ŒQfS0©¨†T´¬†Fb¨†TmQT´H Á QEH;R=

Cfß@­‘¬†¨CEHJI:­‘¬Qf³;T´SUT´¬•¯Cfß@

ë

µÛ­†F±:TUIE¨CEÞJD:TUH¬†ª;F+Qf³;­†FH;©F"Cfß

©/C“±:D;QE©/¬†HJF­†­&CEß)¬ªJFM¨Fb­†CESUòEFbH“¬b¶M ªJFߛC“S´SUCdݎTUHJIM¨Fb­†ÞJS´¬@Tm­ŸQ©/CEH)­‘F@“Þ;FH;©FŽCfß ªJFC“¨†Fb±

QfH;R ¬ªJF+©/C“H“¬¨Q“©(¬T´C“H^Cfß ¬†ªJF+­†F±:TUI“¨†C“ÞJDBA ú/

¡o¥ a ¡ gDCFEf}pdl;ˆ¢s°j(s;pfu@kml;k›wkypdu€“pfw„p ?GëGC D ‚wm~J||/lW|/}nEˆ •:wm~J|^j(ˆ²j(w„|q

365f™7G8pdj(ˆdqMzw‰Ewyky‹Œpdumuxˆ€E|Œ‹}†|Œp²j|/jw‰Hb|}†

SUTU±

úI

KJ

í Å

ªJF?¨†F­‘Þ;S—¬Cfß ªJFC“¨†Fb±

à Tm­tCEDJ¬†TU±^QfSTUH¬ªJF¢­‘FbH;­‘F¬ª;Qd¬¬†ª;F¢FHJFb¨†I“¯B ª;Q“­

HJC¢ÞJHJT´ß›C“¨†±ÿRJFb©Q²¯r¨Qf¬†FTUHr¬ªJF:IEFbHJF¨ŒQfS@©Q“­‘FE¶>¢CE¨FCdò“F¨b®Þ;­‘TUHJI¢Q?­†D)F©(¬†¨ŒQfSQfDJDJ¨C“Q“©Œª®

ÝF?©QEHœDJ¨CdòEF:¬ª;Qd¬t¬†ª;F ¨Fb­†ÞJS´¬Cfß ªJFC“¨†Fb±

Tm­+CEDJ¬†TU±^QfS<ߛCE¨=¬†ªJFCEHJFµ„RJT´±:FbH;­†T´C“H;QfS

DJ¨CE³JSUF± ­‘FbF à 2

L M ×OفÙGNPOŠÍØ$×MÎÐÊ?×MØ$Ø ÍRQO¢Ì@ÍTSÐÙb×OÕVU

ªJ¨CEÞ;IEªJC“Þv¬¬†ªJTm­:D;QED)Fb¨®ŽÝFrQE­­†ÞJ±:F¬†ª;Qf¬ è

í è ë2W è P

CEß+©/SmQE­­X@ZYr­†Þ;©ŒªÜ¬†ª;Qf¬

è ë2[ è P íYîfïoð

¶&VŠF ;¨­‘¬MRvF)HJF¬†ªJFߛC“SUS´CdݎTUHJI+­†D;Q“©/Fb­Äó

\

í^]

[ è P * * [_ í

-+-,

#.#

[ ' è

` í ù C P ã ó ù í Å CEH¢è0ë01 * ù *

[a

í

"!

›ù

[

þœü9#&%=ùG#

[

('

(5)

í ù C [ ã ó ù í ù

í Å CEH?è0ë

1 * ù * [ í

! )

›ù

ùK*'

ñJC“¨MQfSUS

›ù 53

C Y ã [ ã

®;SUF/¬ŽÞ;­¨Fb©bQfSUSĨ†FbFH <­ß›CE¨±=Þ;SUQ ­†FF8

Å

ó

"!

ý [ ù 3 ' í

! ) ›ù

53

*'

û

-+

ý=ùþ Žû

P ù 3

' è þ

-+

ý=ù

:

þ Žû [ ù

3 ' è Ã

MCdÝ SUF¬

ù

³GFQ­†±:CoCE¬†ªr­†CESUÞv¬TUCEH?Cf߬†ªJF­‘¯v­‘¬†Fb±

E

µ à >¢ÞJS´¬†TUDJSU¯°TUHJI

E

³°¯ÐQ

ߛÞJH;©/¬†TUCEHKC8QfH;R Þ;­†T´H;IĨFFbH <­ß›CE¨±=ÞJSmQ Ã

E

®;ÝFI“F/¬ó

"!

yùfúmú

þü.%=ùfúmú % ('

þ ! )

›ù

(' þ

"+-,

' è þ

-+-, ' è þ

-+-,

ùfú

' è í Å

à Ã

ªJFH ÝFœRvF)HJFЬ†ªJFSUTUHJFQf¨?CEDGF¨ŒQd¬CE¨Œ­ !%

[

C

®R@ C `G`

® C

\G`

QEH;R P

C \

³°¯

ù

í

ù

C

a a í

_ C \ C `

@ ù

a a í

›ù

a ù

KC `

P

í _ C \ C

[ ù

í

ù _ ù

C

B¯–ò°TU¨‘¬ÞJFCfßMâQ&F°µ >¢TUSUIE¨ŒQf± <­¬ªJFC“¨†Fb± ­†FF9Æ

®$ÝF­†FF¬†ª)Qd¬! +® @7Tm­¬†ª;F©QEHJCEHJTm©bQfS

Tm­‘C“±:CE¨DJªJTm­‘± ߛ¨CE±C“Ho¬†C" ¨Fb­†DGFb©(¬TUòEFSU¯E®oߛ¨CE± ` CEHo¬CB` ª)QfHJáv­¬CEI°CE³GCESUFbòP<­

F±t³)FRJRvTUHJIo­ ­‘FbF

®)ÝF©Œª;Fb©Œá^FQE­†T´SU¯t¬†ª)Qd¬

® P

®P

[

Qf¨F"©/CEHo¬T´H°ÞJC“Þ;­CEDGF¨ŒQd¬CE¨Œ­Ÿß›C“¨

¬†ªJF+©CE¨¨†F­‘DGCEH)RvTUHJI+¬CEDGCESUCEI“T´F­/¶

LO­­‘Þ;±:F ¬ª;Qd¬"

ù þ P

þ [

3/C ` ®¬†ªJFbH‡ÝFЩQEH‡ß›CE¨±=ÞJSmQf¬†F^¬ªJF¢òdQf¨TmQd¬†TUC“H;QfS

F6@oÞ;Qf¬†TUCEH à à Q“­Äó

ù úmú þ

@R#

P

ù"þ P

[ ù ú þ !P

í Å T´H `

VêFRvF7;HJF=¬†ªJF=FHJFb¨†I“¯?­†D;Q“©/F D í ` \ \®FH;RJCdÝFR?ݎT—¬ª¢¬†ª;F=Þ;­†Þ;QES TUHJHJFb¨

DJ¨C°RJÞ;©(¬"ó

?M#?

%$

í "!

3&#3

þü.%

3 % #3

(' þ

"! )

#

ùK*' þ

"+ , +

#

#

P*' è 1

? í

43K

P

#?

í #ù

#3 '#

# P

CGD

à Á

MF7Fo¬MÝF"TUHo¬†¨C°RJÞ;©/F¬†ªJF"SUTUHJFQf¨ÞJH°³)C“ÞJH;RvFRC“D)Fb¨Qf¬†CE¨

A

QE­ß›C“SUS´CdÝM­Oó

A í

43K

P)(

C D ó 3JCQEH;R

ù"þ P

[

3JC ` 1 Ã 2

(6)

A ? í û 3

@ # P

ùþ P

[ 3 þ !P

û 3

þ

û 3 þ

? C

A Ã Æ

>¢CE¨FCdò“F¨b®°RJFHJCE¬†TUHJIt³o¯8?

í

ùfú

P

(

¬†ªJF+­‘¬Qf¬†FCfß ¬†ªJF"­†¯°­‘¬†Fb±

µ Ã

®vÝF"©bQfH

ߛCE¨±=Þ;SUQf¬†FO¬†ªJF+­†¯v­•¬F±7Q“­QfH?Fò“CESUÞv¬†TUC“H;Qf¨¯F@“Þ)Qd¬†TUC“HÐó

?

úWþ A ? í Å ? Å í ? ë CGD

Ã

ڄ¬MTm­FQE­†¯¬†CDJ¨CdòEFO¬†ª;Qf¬

A

Tm­Q=±^Q&FvT´±^QESJ±:CEH;Cf¬†C“HJFÄCEDGF¨ŒQd¬†C“¨TUH¬†ªJF"FbHJF¨IE¯:­†D;QE©F Dж

ªJFH

A

IEFbHJF¨ŒQd¬Fb­@Q @ëO­†F±:TUIE¨CEÞJD / Cfß©/CEHo¬¨Q“©(¬†TUC“H;­C“H¬ªJFŽFH;F¨IE¯­†D;QE©F D ­‘FbF

Æ

a ¥<¥ _½›`b½ ¥)¿ Cg  ? í

›ù 53x

P C

A [

‚wm~J|lЃ<|~Jpdd|

ù C

[ ã

ì

à Ç

a ¥0¥ g ÄTUòEFH ?Gë

í

›ù ë 53ëP

ëP

ë C

A

®WÝF­‘C“SUòEF¬†ªJF+F@oÞ;Qd¬T´C“H

A ? í

?Gëd¶] ªJTm­

±:FbQEH;­¬†ª;Qf¬

õööö

÷öööø 3 í ûŽù

ë

ù"þ P

[ 3 þ !

í @ 3 ë

3

í

ëj

û

3 í ë Ã

I°TUH;©/FT@ Tm­¬†ªJF+©bQfHJC“HJTm©ÄTU­†CE±:C“¨†D;ªJTm­‘± ߛ¨†C“± ` CEHo¬C ` QEH;R ­†TUH;©/F 3 ë C `®;¬†ªJFbH¢FSUTU±:T—µ

H;Qd¬TUHJI83J®

QEH;R

TUH Ã

®JÝF )H;R ¬†ª;Qf¬

ù

­Qd¬†Tm­(;Fb­Oó

ùþ

P ë û ù ë

þ ë

û–ù

ë í @ 3 ë þ [ ù ë TUH

à 
O­†TUHJIĨFFbH <­OߛC“¨†±tÞJSmQ Ã

®ÝFtT´Ho¬F¨DJ¨†F¬F@“Þ)Qd¬†TUC“H à À

TUHo¬†C ¬†ªJFtߛC“S´SUCdݎTUHJIòdQf¨TmQdµ

¬†TUCEH)QfSF6@oÞ;Qf¬†TUCEHró

! ý [

ù"þüý 3bë

û

3ë

' þ

-+ ,

ý=ùþ Mû

P

ù"þ

ë û ù ë

' è

û + ,

ý=ù

þ

[ ù

û ë

û ù

ë

û [ ù ë

[

þÐü 3ë

:

' è í Å C

à Å

ڄ¬Žß›CESUSUCdÝM­Ÿ¬ª;Qd¬

õööö

÷öööø ý [ ù í 3bë

ûêüý

3ë C ] [ ã

ý=ù"þ Žû

P ù í

û! ë û ù ë

C ] [ è P

ý=ù

þ Žû [ ù

í ë

ûêù

ë

$ûŠü 3 ë

þ [ ù ë

[ C # P è P Ã

jE

ªJFH0®¬†ª)QfHJáv­¬†C¬†ª;F:FSUSUT´DJ¬†Tm©Ä¬†ªJFbCE¨¯ ­†FFK

Á

®$ÝF:RvFRvÞ;©/Ft¬ª;Qd¬

ù C

[ ã ªJF

DJ¨CoCEß Tm­¬†ª°Þ;­Ž©CE±:DJSUF¬†Ff¶

(7)

þ A # û A

wU~;|=|lG|}nEˆj‰zJp“‹| D ™

a ¥0¥â0F¬ ?

í

53

³GF+Qt³)C“ÞJH;RvFR?­‘F@“Þ;FH;©FÄTUHGD ­†Þ;©Œª¬†ª)Qd¬

* ? * $ <

! Å

â0F¬"ó

#?

í å

þBA # P ?

! Å

ªJFH#?

í #ù

# 3b#

:

#

Tm­ŽRvF/¬F¨±:TUHJFbR:³°¯¬†ªJFߛC“S´SUCdݎTUHJI+­†¯v­•¬F± ó

õö

÷öø #3 í #ù ûêù

à # í þ # 3

à #

í þ #3 Ã Ã

ݎªJF¨F#

ù

TU­¬ªJF"ÞJHJT@oÞJF"­‘C“SUÞv¬†TUCEHCfß$¬†ªJF"òdQf¨TmQd¬T´C“H;QfS)F6@oÞ;Qf¬†TUCEHró

#ù

þ

#

ù

a þ +-,

% #ù % ' è þ +-,

#ù ' è í

þ 3

a

þ + ,

%=ù % ' è þ + , ù ' è û + ,

' è û + , ' è C

à Á

ߛ¨†C“± ݎªJTm©Œª ÝFIEF¬MFbQ“­‘TUSU¯¬ª;Qd¬

* #ù *

<^@ * ? * $

þ

!

ªJFÄÞ;­‘TUHJI+¬†ªJFĬ†¨ŒQE©FM¬ªJFC“¨†Fb±^­/®oÝF©QEH;H;RD)Co­‘T´¬T´ò“FM©/C“H;­•¬ŒQfHo¬@魑Þ)©Œª:¬†ª;Qf¬ß›CE¨QfSUS

!

ÝFª;Q²ò“Ftó

#3

,

.+ ,1 þ * #3 *

.

+",

1

<^@ * #3 * < @ * #ù * þ * ù *

þ

I°TUH;©/FM¬†ªJFÄTU±=³GFbRJRJT´H;I“­$ߛ¨CE±

P [ è P QEH;R

[ è P TUHo¬†C

] [ è P

Qf¨FO©/C“±:D;QE©/¬®“ÝŽT´¬ªvµ

CEÞv¬SmQE­­&CfßIEFbHJF¨ŒQfSUT´¬•¯f®fÝFO©QEH^QE­­‘Þ;±:F¬†ª;Qf¬

# 3

:

QEH;R#3 ©/CEH°ò“F¨IEFŽ­•¬¨†C“HJIESU¯+TUH

] [ è P

MCdÝ-S´F¬

)ë³GF+QfHCE¨†¬†ªJC“HJCE¨±^QfSG­‘F@oÞJFH;©FT´H

] [ è P

¶<B¯BF­†­†FS <­<TUHJF@“Þ)QfSUT´¬•¯=ÝF

á°HJCdÝ ¬ª;Qd¬

Å

T´H

] [ è P

QfH;RœHJCEH­†ÞJ³;­†F6@oÞJFbH;©/F Cfß

©/CEH°ò“F¨IEFb­"­‘¬†¨CEH;IESU¯rTUH

] [ è P ªJFb¨†FߛCE¨Ff®&HJCEH筑ÞJ³)­‘Fµ

@oÞJFH;©FCfß

# í

Ã

+ þ #3

©/CEH°ò“F¨IEFb­$­‘¬†¨CEHJI“S´¯TUH

] [ è P ªJTm­ D;¨†Cdò“Fb­¬†ª;Qf¬ å þA # P

Tm­HJCEHvµÛ©/C“±:D;QE©/¬TUHGD¢¶

(8)

Ò/Ë U

ÚÛH ¬†ªJTm­Ž­†Fb©(¬TUCEH®vÝF )¨­‘¬ŽFb­‘¬Qf³;S´Tm­†ª:¬†ª;F"D)C“S´¯°HJC“±:TmQfS;FbHJF¨IE¯^RJFb©Q²¯¨Qf¬†FߛCE¨M­†±:CoCE¬†ª

­‘C“SUÞv¬†TUCEH=CfßGF6@oÞ;Qd¬TUCEH à ¶H

¶OFF°¬ŸÝFD;¨†Cdò“F¬ªJFM­‘¬†¨CEHJI­•¬ŒQf³JTUSUT´¬•¯ÄߛCE¨&¬†ª;FŽÝFQfᭆCESUÞv¬T´C“H¶

VêF=QE­­‘ÞJ±:F¬†ª)Qd¬Ž¬†ª;F¨F"FFvTm­•¬ Å QEH;R ë C¢åæ [

­†Þ;©Œª¬†ª;Qf¬®;DJÞJ¬‘¬†TUHJI í û 듮

ÝF"ª)Q²òEF=ó

!

$#

P C¢è

P

QfH;R < Å Cèë

Á

cg |w

P [ #

[

[ C ] [ è P pdlW€

ù

jpfwkUjmŒˆ^wm~J|/dumu´dƒ@kmlonr‹flG€fk›wykyflJj

õööööö

÷öööööø ù C

ý [ ù C ] [ ã

ý=ùþ Mû

P ù í P

dl è P

ý=ù

:

þ Žû [ ù

í [ þ [

b þ # [

dl è P

ù í ù

í Å dl

è ë Á Ã

~J|l–ƒ<|~Jpf²|

û

"!

ý [ ù

%=ù ('

< û Ã "! )

ùK*'

þ @ ë + , 5#

P #[ þ # [ #[

þ/#

[ #[

*'

è û + , # [

%=ù ('

è Á Á

ƒ ~J|}†|

kUjpÄz;²j(k›wkm²|‹Œdl;j(w„pdlGw€“|„z;|/lW€dkml°n¢dl;uxˆdl–wm~J|t€Efqpfkml

㠙

a ¥0¥ g LO­­‘Þ;±:F:¬†ª;Qf¬ P [ C

[ è P QfH;R [

)#

[ C P [ è P ªJFbHÝF^ª)Q²òEF

ù C Y ã ­‘TUHJIĨFFH><­ß›C“¨†±tÞJSmQ à E

ÝF"ª)Q²òEF=ó

! ý [ ù

%=ùK*'

í ! )

ùK*'

þ +

ý=ù

þ Žû [ ù

%=ùK*'

è û +

ýù"þ Mû

P ù

%=ù

' è

þ Ã +

[ ù

[P [ þ [ ù

[[ [ þ Ã [ ù

[P [ ù

[[ þ Ã û

[ ù

P

[ [ 1 Á 2

I°TUH;©/F

ù í ù

í Å CEH¢èëf®JT´¬ß›CESUSUCdÝM­Ÿ¬ª;Qd¬

%=ù

í Å P ù í Å

%=ùK

:

í

†ý=ù

C“H¢è0ë Á Æ

[ ù

[P [ þ [ ù

[

[0

[ þ Ã [ ù

[P [ ù [[ þ Ã

Žû

[ ù

P

[ [ í ý=ùK

[

C“Hè ë Á

NH¬†ªJF"CE¬†ªJFb¨Žª;QfH;R®JÝF"ª;Q²ò“Fó

[ ù

[P [ þ [ ù

[[ [ þ Ã [ ù [P [ ù

[[ þ à Žû

[ ù

P

[ [

(9)

! Žû

[ ù

[

P"

þ [ ù

[

[0

þ Ã [ ù

P

[ 1 Á Ç

ÚÛH;­†F¨†¬†TUHJI Á Æ µ Á Ç

TUHo¬†C Á 2 I“TUòEFb­

! ý [

ù

%=ùK*' !

! )

ùK*'

þ

-+ , [ þ # [

%=ùK*' è û

"+ , P

%=ùK

' è û

-+ , [

%ùK

' è

þ

Žû

Ã= +-, [ ù

[P [ þ [ ù

[[ [ þ Ã [ ù

P

[ [ 1 Á

LéRvTU¨†F©(¬M©/C“±:DJÞv¬ŒQd¬†TUC“H^IETUòEF­

::::

%=ù

:::: < :::: ù

:::: þ æ [ ù

[

P"

[ þ [ ù

[

[0

[ þ Ã [ ù

P

[ [ 1 ,

Á À

::::

%=ùK

:::: < :::: ù

:::: þ æ [ ù

[P [ þ [ ù

[[ [ þ Ã [ ù

P

[ [ 1 , Á Å

ݎªJF¨F"æ

í * *.! 1

Tm­¬†ªJF+RJTUQE±:F/¬F¨Cfß&ã¶ ª;FHߛCE¨MQEHo¯

Å

®JT´¬ß›C“SUS´CdÝM­<¬†ª)Qd¬

+ , P

%=ùK

' è

!-û

ÃJ + , # P #[ ' è û

+ , :::: ù

::::[ ' è

û

æ[

-+ , [ ù

[P [ þ [ ù

[[ [ þ Ã [ ù

P

[ [ 1 ' è Á

jE

+-,

[

%=ùK

' è

!-û

Ã8 +-,

#

[ #[ ' è û

+-, :::: ù

::::[ ' è

û

æ[

-+-, [ ù

[

P

[ þ [ ù

[[ [ þ Ã [ ù

P

[ [ 1 ' è Á Ã

+-, [

%=ù ('

è ! û

ÃJ +-,

# [ #[ ' è û æ [

à +-,

#%=ù #[ ' è Á Á

ÚÛH;­†F¨†¬†TUHJI Á

P µ Á Á

T´Ho¬C Á

j

®)ÝFCE³J¬QfTUH¬†ª;Qf¬

"!

ý [ ù

%ùK('

Á 2

! ! ) ›ù

ùK*'

þ + , # [

%=ù ('

è û Ã + , # P #[ þ # [ #[

þ/#

[ #[ ' è

þ

Žû

Ã:

û Ã æ[

"+ , [ ù

[P [ þ [ ù

[[ [ þ Ã [ ù

P

[ [ 1 ' è û Ã þ æ[

à -+ , #%=ù #[ ' è

Références

Documents relatifs

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

The aim of this study was to assess, in three experimental fields representative of the various topoclimatological zones of Luxembourg, the impact of timing of fungicide

Attention to a relation ontology [...] refocuses security discourses to better reflect and appreciate three forms of interconnection that are not sufficiently attended to