• Aucun résultat trouvé

On Improving the Convergence of Radau IIA Methods Applied to Index 2 DAEs

N/A
N/A
Protected

Academic year: 2021

Partager "On Improving the Convergence of Radau IIA Methods Applied to Index 2 DAEs"

Copied!
28
0
0

Texte intégral

(1)

HAL Id: inria-00073949

https://hal.inria.fr/inria-00073949

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.

On Improving the Convergence of Radau IIA Methods Applied to Index 2 DAEs

Anne Aubry, Philippe Chartier

To cite this version:

Anne Aubry, Philippe Chartier. On Improving the Convergence of Radau IIA Methods Applied to Index 2 DAEs. [Research Report] RR-2744, INRIA. 1995. �inria-00073949�

(2)

ISSN 0249-6399

a p p o r t

d e r e c h e r c h e

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

On improving the convergence of Radau IIA methods applied to index 2 DAEs

A. Aubry , P. Chartier

N˚ 2744

De´cembre 1995

PROGRAMME 6

(3)
(4)

$6798:+<;=/

>@?A>CBADFEHGJI*K?L%M*NOE3PHQSRTEVU

WYX[Z]\OX3^`__abc d^TegfHhieYj[flkmanpoqksrFtOhua]vA_ZuwxaHeskyj[^`oqkmZ]nzao4emZ]\`kyflkmaHe{nihu_JxaX|kgtOhua

W}X[Z]~qao4%ey^]wOkmn

€%^`u,Z]X[owiaCX[a‚flƒuaX3f[ƒuan.„p…‡†‚ˆ]ˆCcЉzxa‚fHa_‹uXlaŒ‚O]ŽcŠ…`ˆV^`\]a‚j

’‘“”‚•—–V˜`”]™š4ƒikyjV^›VaXuX[a‚jqanio3j^znuaœjžkm_iemazo[a‚f[ƒunikytOhua’o[Zzkm_uX[Z`Ÿ]a’o[ƒua2Z]X3wiaX‹VaƒV^—ŸOkmZ]huXZ` ¡€¢hunu\]a£

¤'huolo3^_ao[ƒuZuwuj4œ%ƒuan¥^`uieskma‚w¦olZkmnVwiaH§¨…‰%©j«ª­¬žo%kyjo[ƒuan¦jqƒuZ`œ%n’ƒuZ`œ0o[ƒikyj'f^`n’‹VakmnVfHZ]X[VZOX3^`o[a‚w®k¯nio[Z@^

_Z]X[a'aH°®flkmanpo'Ÿ]aX3jžkmZ]nzZ` Yo[ƒua.fHZ‡wia€4‰%±'ŽwiaŸ]aHemZ]Va‚wz‹i²®©ªV³'^—kmX[aX¡^›nVwz´ªiµ=^`nunuaX‚ª

¶¸·p¹º¼»½A•T¾“]™0wOks¿*aX[anioqky^—em£À^—em\]a‹uX3^—kyf2jq²ujqo[a_@j'Z` kmnVwiaH§Á…Âv*€4hunu\]a£À¤'huo[o3^¸_ao[ƒuZuwujv­€^]wu^`h¥¬q¬ÀÃ_aolƒuZ‡wujv

XlZpZ]ola‚wo[Xlaa‚jvVjžkm_iesks Ä²Okmnu\¨^]jljqhu_uoqkmZ]nVjv,fHZ]_VZijžkmoqkmZ]n*ª

ÅSƏÇ

È|ɼʂË

Ç

ÈÌÍsɼÎÄςÐ

ÑÀÒÔÓ­ÕAÒSÖ×ÄÕAØqقٗؼÚqÛ]Ü*ÝlÞ4߂à‚Úá‚Øâ,Ø[Ýlàãå俨qà]Ûuç3èHé[êë4ÕAØqقٗؼÚYÜAØqá‚Øqì`Û]íuÕAÖYÓ­Ü*î

Unite´ de recherche INRIA Rennes

IRISA, Campus universitaire de Beaulieu, 35042 RENNES Cedex (France) Te´le´phone : (33) 99 84 71 00 – Te´le´copie : (33) 99 84 71 71

(5)

’& $4/ ­.$4/ $ #"%$"'&)(*(,+ "%21 &44/ " $4/;J8 + $ 43

$&.6

·u“·@™Cdao4^`X[oqkyflemauXuxa‚jqanpolahunuanuZOhuŸ]aHese¯aola‚f[ƒunikytOhua¡jžkm_iema,Z]huX%^`_JxaHeskmZ]X[aX}ey^fHZOnpŸ]aXl\]anVfHa¡wia‚j4fHZ]_£

,Zpj[^`nio[a‚j^—em\]a‹uXqkyt]hua‚j}emZ]X3jlt]håhunua'_Jxao[ƒuZ‡wia'wia€%^]wu^`h’wia%oq²iVa'¬¼¬ž0a‚jqo4^`uieskgtOh4xaa^hun’jq²ujqoa_a%wOk¿xaX[anpo|k¯aHe

^Te¯\Yxa‹uXqkytOhua®wkmnVwOkyfHa¨wiahi§*ªYWZ]huXCey^¦_Jxao[ƒuZuwia@wia¦€%^]wu^›h=¬q¬ÀwåZ]XHwiX[a®ŽÂv­j[^z_kyjqa2anhuŸpXla@X[a‚ftOhikmaX[o@wia

j¼k¯_ie¯a‚j_ZuwOksrFf^`oqkmZ]nVj'wih¨fHZuwia.€%^]wu^`hVŽ2wxaŸ]aHemZ]u4xaV^›X©%ªu³'^—kmX[aXao´ªiµ=^`nunuaX‚ª%Z]hVje¯a‚jaH§uiekyflkmo[Z]nVj'ao

uXuxa‚jqanio[Z]nVj}ema‚j^›_ aHeskmZ]X3^`o|k¯ZOnVjZO‹uo[anphua‚j'jqhuXwOks¿xx aXlanpo3juX[ZO‹iea_a‚jª

½,”‚“º[˜·=™ jq²‡j|oa_a‚j^—em\Yxa‹uXlZ]£ÀwOks¿¡xaX[anioqkmaHegj4wkmnVwOkyfHa…Âvp_Jxao[ƒuZuwia‚j4wia.€4hunu\]a£À¤'huo[o3^Âvp_Jxao[ƒuZuwia‚j4wia.€%^]wu^`h

¬q¬žvA^`X[‹uX[a‚j«v‡fHZOnVwOk¯o|k¯ZOnVjjžkm_ieskrFf^›o[XqkyfHa‚jv*fHZ]_,ZpjžkmoqkmZ]n*ª

(6)

<

(A* *C$2&}­3

¬žn X[a‚fHanio²]a‚^›X3jvYwOks¿ aXlanpoqky^—e.^—em\]a‹uX3^Tkgf¸a‚t]hV^›oqkmZ]nVj=¼‰¡©j>ƒV^—Ÿ]a’‹Vaan0jqo[hVwOkma‚w!‹p² ŸT^`X|k¯ZOhVj@^`huolƒuZ]X3j=¼j|aa

?

³%µ0uŒ@Àv

?

³BA*€C]D@Àv

?FE

d4WuŒ5@G>3v‚^`nVwo[ƒuaHkmXk¯_VZ]X[oH^`nVfHa%^]f'HinuZ`œ4ema‚wi\]a‚w‹i²o[ƒua%wiaŸ]aHemZ]u_anioYZ` VjqVa‚flksrFf'jqZ`emŸ]aX3j

j|hVf[ƒ@^OjY‰%JIKIA2 ÔX[Z]_

?

WaoC]b@uZ]X€4‰%±'Ž' ÔX[Z]_

?

³%µ0uŒ@Àª`'na‚jq,a‚flkg^Teem²km_VZ]Xlo3^`niofleg^Oj[jYZ` ­‰¡©jY^`Xqkyjžkmnu\

kmnzuX3^]fHoqkyfHa^›X[a¡j|a_km£ÔaH§‡ieskyflkyoj|²‡jqola_@jZ` {olƒua' ÄZ]Xl_

='LM>ONQP$R

=TS'>VU WX=

P

=TSY>1Z1[\=TS'>'>Z

] U ^=

P

=TSY>'>1Z

S`_

?

Sa1ZYS)b@cZ

œƒuaX[aJ^-dWeCkyj^]j[jqhu_a‚w¦olZ@‹,aZ› ‹VZOhunVwia‚wzkmnpŸ]aXHjqaCk¯n ^nuaHkm\]ƒi‹VZ]huXlƒuZpZuw¥Z` 4o[ƒuajqZ›e¯huo|k¯ZOn Z` ='IK>3ªA³aX[a]vAœ4a

^›X[a4kmnpolaX[a‚jqo[a‚wCkmn’Z]‹uoH^—kmnik¯nu\^nphu_aX|kgf^Te ^`uuX[Z—§ikm_@^`oqkmZ]nolZ='IK>Y^]ffHhuX3^`o[a¢ ÄZ]X‹VZ]olƒo[ƒuawOks¿*aX[anioqky^—e­^`nVwo[ƒua

^Te¯\Oa‹uX3^—kyffHZ]_,Z]nuanpoHjªue¯olƒuZ]hu\]ƒ¦jqZ]_aZ` ­o[ƒua'kywia‚^]juX[a‚jqanio[a‚wkmn’o[ƒikyj%V^›VaX^—eyjqZ2^`uiem²@o[Z_Z]X[a'\]anuaX3^—e

€¢hunu\]a£À¤'huo[o3^2_aolƒuZ‡wujv,œ4a.œ4ksese ÄZufHhVj'Z]n¨€^]wu^`h¥¬q¬À#_ao[ƒuZ‡wuj«vV\`kmŸ]an¥o[ƒV^›o%o[ƒua²¦œ4aX[aChVjqa‚wzo[Z‹uhikseyw¥o[ƒua

fHZuwia%€4‰%±'Žuª`š4ƒuaHkmXfHZ]nVjqo[XlhVfHoqkmZ]n^]j*œ4aHeseF^]jjqZ]_aZ` Vo[ƒuaHkmXYuX[Z],aX[oqkma‚j^›X[a‹uXqkmafV²X[a‚f^—esema‚wCkmnI]a‚fHoqkmZ]n¦Œ]ªgŒ]ª

µ ƒuan¦^`uiem²Okmnu\®^j|£Àjqo3^`\]a€%^]wu^›h¦¬q¬À _aolƒuZ‡w2o[Z='LM>3vio[ƒuaZ]X3wiaXHjZ› }fHZ]niŸ]aX[\OanVfHa.^`X[aX[a‚jq,a‚fHoqkmŸ]aHem²¦…ghJŒ

 ÔZ]X%olƒua

P

£ÀfHZ]_,Z]nuanio¡^`nVwigC ÔZ]X%olƒuaj[›£ÀfHZ]_VZOnuanpok=¼j|aa

?

³lA*€C]-@>3ªu¬žn j|Z]_aj¼k¯olhV^`oqkmZ]nVjvAœ%ƒuaXla.\]ao[o|k¯nu\¦^›n

^OffHhuX3^`o[aŸT^—emhua%Z` [_@^—²‹Vakm_,Z]X[o3^`nioM=Ôkmn_a‚f[ƒV^`nikyfj ÔZ]Xk¯nVj|o3^`nVfHaD>3v`Z]nua}kyje¯a‚w o[ZhVj|a^wOks¿*aX[anpoY^`uuX[Zi^]f[ƒ*ª

´'anuaX3^—esem²¦jqVa‚^-H]kmnu\Vv,o[ƒuaZ]X3wiaXX[a‚wihVfHoqkmZ]n¦uƒuanuZO_anuZ]n¦_2^‚²2‹VaCZ`Ÿ]aX3fHZ]_a'‹i²@o[ƒua' ÔZ`esemZ`œ4kmnu\@o[a‚flƒunikyt]hua‚jnm

o1pGq

^CrVX3jqo4VZij[jžkm‹iksekmoq² fHZ]nVjžkyjqo3j¢kmn¨^`uiem²Okmnu\@o[ƒua€%^]wu^`hz¬q¬À _ao[ƒuZuw’olZolƒuakmnVwiaH§¦Z]nua ÔZ]X[_hiey^`oqkmZ]ni= Lr>Z` 

='L:>3v

= L:>ON

P R U WX=

P

Z[>1Z

] U ^-dD=

P

>)Ws=

P

Z1[\>1t

I`k¯nVfHa.€^]wu^`h’¬q¬À0_ao[ƒuZ‡wuj4^`uieskma‚w’olZkmnVwiaH§®ZOnua¡‰¡©jYaH§uƒikm‹ik¯o¢ Ähiese*Z]X3wiaX4Z` ­fHZ]niŸ]aX[\]anVfHa ÔZ]X

P

^`nVw

[=qjqaaš4ƒuaZ]Xla_u;`£[Œ

?

³BA€C]D@>Hv`o[ƒua%Z]X3wiaXZ` ­fHZ]niŸ]aX[\]anVfHakyjYnuZ`œ …gvhzŒ¡^Tegj|Z ÔZ]X"[uªi³%Z`œ4aŸ]aX‚v]j|Z`emŸ]kmnu\

= Lr>¢f^›n’‹VafHZ]nVjžkywiaX3^`‹iem²z_Z]X[a.fHZpj|oqem²mV^Oj^_2^`o[o[aX4Z` Y À^]fHo‚vio[ƒikyjX[a‚t]hikmX[a‚j'olZaŸT^—emhV^`ola.o[ƒuakw]^]fHZ]‹iky^`n

Z` Fo[ƒua¢ ÄhunVfHoqkmZ]n xJ=

P

Z1[>vUy=)Ws=

P

Z1[\>1Z^d5=

P

>)Ws=

P

Z1[>Y> ^`oYa‚^Of[ƒjqo[az=ÀZ]XYœ%ƒuanuaŸ]aXo[ƒua%fHZ]niŸ]aX[\]anVfHa%XH^`o[a4Z` 

o[ƒua aœ%o[Z]n2kmo[aXH^`oqkmZ]n¦\Oao3j4o[ZiZjq_@^—ese>3vÂk¯nVj|o[a‚^]w’Z› {o[ƒua' ÔhunVfHoqkmZ]n{xJ=

P

Z1[>rU|=)Ws=

P

Z[>1Z}^=

P

>>ªu'nuZ]o[ƒuaX

wiX3^—œ%‹V^]fYHkyjYo[ƒV^›oYo[ƒua%nihu_aXqkyf^—e j|Z`emhuoqkmZ]nkyjnuZ]o ÄZOX3fHa‚w^`ni²emZ]nu\]aXo[Z'eskmaZ]no[ƒua%fHZ]nVjqo[X3^Tk¯nio_2^`niks ÄZ`eyw

^=

P

>rU

] ª

o1ppGq

^%j|a‚fHZ]nVw'kywia‚^%fHZ]nVj¼kgj|o3jAkmnfHZ]_uhuoqkmnu\'o[ƒua:[`£ÀfHZ]_,Z]nuanio*‹p²jqZ`emŸOkmnu\o[ƒua4^]wuwOkmoqkmZ]nV^—epa‚tOhV^`oqkmZ]n9^dD=

P

>WX=

P

Z[>3v

k ªa]ª]kmn2uX[Z]~qa‚fHoqkmnu\.olƒua%nphu_aXqkyf^—e jqZ›e¯huo|k¯ZOn@Z]no[ƒua¡j|Z]£Àf^—esema‚w~Hƒikywuwian¦fHZ]nVj|o[X3^—kmnio1€uª]š4ƒuafHZ]X[X[a‚j|VZ]nVwOkmnu\

nphu_aX|kgf^Te}j[flƒua_anuZ`œ0X[a‚^Owuj

='L‚>„ƒ…

……

†………‡ ] U ^ˆ=

P

‰ŠG>1Z

P

‰Š‹U

P

JŒŽK`Ž

‘'’“s”

Š‘ WX=

P

$‰

‘

Z1[n‰

‘

>Z • U ŒZ–––ZgZ

P

˜—

“ U P

JŒ™‚"



Š

’“ˆš

ŠWs=

P

‰ŠZ1[5$‰ŠT>Z

] U ^-d$=

P

˜—

“

>)Ws=

P

˜—

“

Z[5˜—

“

>1t

š4ƒuaZ]X3wiaX4Z` {fHZOnpŸ]aXl\]anVfHa' ÄZOXolƒua

P

£ÀfHZ]_,Z]nuanpo¢kgjjqoqksese{…g`h Œ¡^›nVw@f^`n’‹,a.jqƒuZ`œ%n2o[Z‹VanuZ`œ0…g`h=Œ

^—eyjqZz ÄZ]XolƒuaO[`£ÀfHZ]_,Z]nuanio‹i²¥hVjžkmnu\¥o[ƒua@¬ž_ieskyflk¯o›uhunVfHoqkmZ]nJš4ƒuaZ]X[a_zª­³ZTœ4aŸ]aX—vAo[ƒikyjo[a‚flƒunikyt]hua2kyj

Z]nVfHa¨^`\i^—kmn fHZ]_uhuoH^`oqkmZ]nV^—esem² _ZOX[a¦wia_@^`nVwOkmnu\Jo[ƒV^`nJolƒua¦Z]Xqkm\`kmnV^—eZ]nuamj|Z`emŸ]kmnu\ o[ƒua¦nuaœ<km_ieskgflkmo

V^`X[oZ` l='L  >%X[a‚tOhikmX[a‚j^`n ^]ffHhuX3^`olaaŸ`^—emhV^`oqkmZ]n Z` :^ d = P

>^`oa‚^]flƒ jqo[a*v*^`nVw nuZ]oZ]niem²]v­^]j'uXlaŸ]kmZ]hVjžem²

_anpo|k¯ZOnua‚wAvuœ%ƒuanuaŸ]aX4o[ƒuafHZ]niŸ]aX[\]anVfHaX3^›o[a%Z` ­olƒua aœ%o[Z]nkmo[aX3^`o|k¯ZOn@‹,a‚fHZ]_a‚j4o[ZiZj|_@^—eseÀªu¬Ào%f^`n2‹Va

nuaŸ]aX[o[ƒuaHema‚j[jnuZ]o[a‚w o[ƒV^`okmn®^'V^›X3^—esemaHe aniŸOk¯XlZ]nu_anio‚v]o[ƒikyj^]wuwOkmoqkmZ]nV^—e fHZijqoYœ4Z]hieyw‹,ajqƒV^]wiZ`œ4a‚w‹i².o[ƒua

hVjqa.Z` ^jqa‚fHZ]nVw¸uX[Z‡fHa‚jljqZ]X‚ª

¬žn’o[ƒikyj4V^`,aX‚viœauXla‚jqanpo%^Co[ƒikmX3w’^`uuXlZp^]flƒ@œ%ƒikyflƒ¨wiZia‚j4nuZ]o4X[a‚tOhikmX[a.^`n¦^`nV^—em²ioqkyf^—eA ÄZOX[_ Z` X^d.^`nVw2œ%ƒuZpj|a

fHZO_uhuo3^`oqkmZ]nV^Te¢fHZpjqokyj.‹V^Ojžkyf^—ese¯² a‚tOhV^—e%o[Z¦œ%ƒV^›okmoCkgj ÔZ]X.olƒua®jqoH^`nVwu^`X3wz ÔZ]X[_hiey^`oqkmZ]n*ª¬ÀoCkyjC‹V^]jqa‚wÁZ]n o[ƒua

(7)

ZO‹VjqaX[ŸT^›oqkmZ]n=olƒV^`o.o[ƒua2aX[X[ZOX3jk¯n o[ƒua [`£ÀfHZO_VZ]nuanio^`X[a2a‚j[jqanioqky^—esem²=Z` ^2emZ‡f^TenV^`o[huX[a]v^`oema‚^]j|ohu=olZ¦o[ƒua

ZOX3wiaXZ` ¢fHZOnpŸ]aXl\]anVfHaZ` o[ƒua

P

£ÀfHZ]_,Z]nuanpo—ª*j^’fHZ]nVjqa‚tOhuanVfHa]v*_@^DHOkmnu\[2_ZOX[a^]ffHhuX3^`o[aCkyj.^2_2^`o[o[aX'Z` 

Xla‚fHZTŸOaXqkmnu\ o[ƒua¨j¼k¯\OnikrFf^›npo’o[aXl_@jo[ƒV^`o2^`uVa‚^`X k¯n o[ƒua¥jqZ]£Àf^—esema‚w ~ E

£ÀjqaXqkma‚jZ` ¡olƒua¦aX[X[ZOX1€uªYš4ƒikyjkyj_@^]wia

,Zpj[jžkm‹iema‹i²¨fHZ]nVj¼kgwiaX|k¯nu\¥o[ƒuafHZ]_VZpjžkmoqkmZ]nÁZ` o[ƒua‹V^]jžkyf_aolƒuZ‡wzœ4kmo[ƒzkmo3jqaHes %Z`Ÿ]aX¡j|aŸ]aX3^—ejqo[aVjªA¬žo.f^`n¥‹Va

nuZOo[a‚wo[ƒV^`o4jžkm_ksey^`Xkgwia‚^Ojœ4aX[ahVjqa‚w‹i²@€ªW­ª¤ªudƒV^`no[Zwia‚^—eAœ4kmo[ƒ2o[ƒua%Z]X3wiaXX[a‚wihVfHoqkmZ]n’Z` Y´^`hVj[j_ao[ƒuZuwuj

œƒuan¦^`uiesk¯a‚wzo[Z2fHaX[o3^—kmn¨j|oqks¿ uXlZ]‹iema_@jl=¼jqaa

?E

d;@>3ª

š¢ƒuanuaœ0ZOX3wiaX%fHZ]nVwOkmoqkmZ]nVj4œ4ksese­‹Va.wiaolaX[_kmnua‚wkmn{I]a‚fHoqkmZ]n¦…uªOµ ƒikemaCo[ƒua²@f^`n’‹,a.wiaXqkmŸ]a‚wkmn¦^j|o[X3^—km\]ƒioq ÔZ]X[£

œ%^`XHw_@^`nunuaX4 ÔX[Z]_o[ƒuaœ4Z]X'HZ` {©ªu³^—kmX[aX—vVd'ªAAhu‹ikyflƒ¨^`nVw ªp€¢Z‡flƒuak=

?

³lA*€C]-@>3v]olƒua²®^`Xla¡jqo|kese*X[aHey^`oqkmŸ]aHem²

hunKHinuZ`œ%n j¼k¯nVfHaÁo[ƒua² ^`X[aznuZ]o®jl^`oqkyjžrVa‚w ‹p²J_Zpjqo’fleg^Oj[jžkyf^—e€4hunu\]a£À¤'huolo3^ _ao[ƒuZuwuj2=qjqaa ^—eyjqZ

?FE

d4;@Z]X

?

d%d]Žn@>3ªY¬žoœ4ksese.o[ƒuan ‹,a¨jqƒuZ`œ%nJo[ƒV^›o@jqZ]_a’Z› ¡o[ƒuZijqa¨fHZ]nVwOkmoqkmZ]nVj’^›X[a¦^]fHo[hV^—esem²JX[a‚wihunVwu^`nio’^`nVwJ_@^—² ‹Va

ZO_kmo[o[a‚wAª*š4ƒikyjkyj^zfHX[hVflky^—e¢^OjqVa‚fHoCZ` %o[ƒua_ao[ƒuZuwAv­j¼k¯nVfHa2kmo^—ese¯Z`œjo[ƒua’fHZ]nVjqo[X[hVfHo|k¯ZOn Z` 4 ÄZOX[_hieg^Oj'œ4kmo[ƒ ^

_2^`nV^`\]a‚^`‹iema'emaŸ]aHeYZ` {fHZ]_ie¯aH§ikmoq²]ª

¬žniI]a‚fHoqkmZ]n ;uvio[ƒua'km_ieskma‚wz_Z‡wOksrFf^`o|k¯ZOnVj%o[ZCo[ƒua.fHZuwia.€4¡‰±'Ž^`X[a'eskyjqo[a‚wAª›kmnV^—esem²]vVnihu_aXqkyf^—eX[a‚jqhiemo3j%^`Xla

uXla‚jqanpola‚w2o[ƒV^`o4ksesemhVjqo[X3^`ola.o[ƒua.^]wiŸ`^`nio3^`\]a‚j4Z› {o[ƒikyj4nuaœ o[a‚flƒunikyt]hua]ª

!"#!$%'&(*)+-,,.0/1"2)

€^]wu^`h’¬q¬À_ao[ƒuZuwuj%f^`n’‹VawiaHrVnua‚wz‹p²2o[ƒua.g`Œ Œ.tOhV^]wiX3^`o[huXla' ÄZ]Xl_hiey^]j

3465

798

=TS'>;:$S0<  

‘'’“ ” Š‘ 8

=>= Š>1Z

• U ŒZ–––YZ1gZ

3 “

7 8

=TSY>;:$S <  Š

’ˆ“ š Š 8

=>= Š>1t

 V^`X[oqkyfHhiey^`X4_ao[ƒuZuw?œ4kseeA‹VaflƒV^`X3^OfHo[aXqkA@a‚w‹i².olƒua%o[Xqkmiema.=>B.Z

š

ZC=>uœ%ƒuaX[a=

” Š‘

>TЉ

‘'’“

‰EDEDED‰

kgj^.gGF.g%_@^›o[Xqks§ v

š U = š “ Z–––'Z

š 

>H ^2g«£ÀwOk¯_anVjžkmZ]nV^—e%Ÿ]a‚fHo[Z]X.^›nVwI=kU =>=

“

Z–––Z=



>H ^2g£ÀwOkm_anVj¼k¯ZOnV^—e%Ÿ]a‚fHo[Z]X‚ªA¬žn o[ƒua@j|a‚t]huaHeÀv

œ4aœ4ksese* ÔhuX[o[ƒuaX[_Z]X[ahVjqaCo[ƒuanuZ]o3^`o|k¯ZOnVj JlUy=3Œ$Z–––'Z‚Œ->H _KL  ^`nVwM=ONlUy=;=ON

“

Z–––'ZC=ON

 >H  ÔZ]X^Teek¯nio[a\]aXHj PAª

QSR6Q!R6Q T

½U “«”‚•*˜`”

p

½VU ½SW –V¾*–YXZX =·i”[F½*¾“

š¢ƒuaHk¯XfHZiaH°®flkmanpo3j'^`X[a'hunikyt]huaHem² wiao[aX[_ k¯nua‚w¸‹p²2o[ƒua ÄZ`esemZ`œ4kmnu\®fHZOnVwOk¯o|k¯ZOnVj5m

ŒOª =

“

Z–––'ZC=



^`Xlao[ƒuaZ]X3wiaX[a‚w$@aXlZpj4Z` Yo[ƒua€^]wu^`h’Xqkm\]ƒio%VZ›e¯²inuZ]_ky^—e

\ =>]ˆ>rU

:

>^

“

:_]

`^

“ba ] >^

“

=;] hJŒD> >c t

…ª

š “ Z–––Z

š 

j[^›oqkyjž Ä²dk=gD>1m e

P2_(f

]

Z–––Z1ghJŒgZ

š H = N U Œ

=>PJŒ ŒD>

t

;ª%š4ƒuafHZiaH°®flkmanpoHj

” Š‘

Z` Yo[ƒua_@^`o[X|k§hB j[^`oqkyjž Ô²bij=)gD>m

e

P2_(f

]

Z–––Z1ghJŒgZBj=

N U Œ

=;PJŒ Œ->

= N — “ t

¡j4olƒuak=ŠY^`X[a.^—ese{wOkyjqoqkmnVfHo‚vB kgjnuZ]nu£Àjžkmnu\]hiey^`X—ª

QSR6Q!Rml n

½=· *“·_W o•—½*o·u•—”

p

·u“

µÁaœ4ksese¢XlaH ÄaXCƒuaX[a@olZ¦o[ƒua@^OwuwOk¯o|k¯ZOnV^—ejžkm_iesk Ô²Ok¯nu\J^]j[j|hu_uoqkmZ]nVjp2=#q>4kmnio[X[ZuwihVfHa‚wAvY^]j'dj=srˆ>.^`nVwIij=;t3>%Z` 

uXlaŸ]kmZ]hVj'jqhu‹Vjqa‚fHoqkmZ]n*v‹p² wuª¯dª

E

huoHf[ƒuaXJ=¼jqaa

?

³µ0uŒ@AV^`\]a†`Ž>3ª

(8)

ŒOª%‰'hua¨olZ=o[ƒua fHZ]nVwOkmoqkmZ]nVjMik=)g->3vdj=)gD>@^`nVw9=

 U Œ]v4€%^]wu^›h ¬q¬ž _ao[ƒuZ‡wuj2^`X[a jqo|k2² ^]ffHhuX3^`o[a =ÔkÀªåa]ª

š

Š2U

” 

Š)Z

•

U)ŒZ–––Z1g->3ª=qš4ƒua¥Ÿ]a‚fHo[Z]X3j

š

^`nVw = ”  “ Z–––'Z

”

c

>H ^`Xla¨jqZ`emhuoqkmZ]n Z` o[ƒua j[^›_a dX3^`_aX

jq²‡j|o[a_2>3ª

…ª%š4ƒua²¦^`X[a.fHZ`esemZuf^`oqkmZ]n¦_ao[ƒuZ‡wuj =¼š4ƒuaZ]X[a_ †‚£TC

?³ %µ0uŒ@ÀviV^`\Oa.…uŒ‚…>3ª

;ª dk=¼…glhJŒD>}kgj'j[^`o|kgj¼rVa‚w=)AAa__@^Ž`£[Œ‚Ž

?

³µ0uŒ@ÀviV^`\]a.;\>3ª

ˆ,ª p2=)gh ŒD>kyj'j[^`oqkyjžrVa‚w =)AAa__@^Ž`£Ôˆ

?

³%µ0uŒ@ÀvV^`\]a†˜C>Hª

%uo|k¯_2^—e{fHZ]niŸ]aX[\]anVfHaCX[a‚jqhiemo3jƒV^—Ÿ]a‹Vaan¥Z]‹uo3^Tk¯nua‚w® ÄZOX%o[ƒuZpjqaC_ao[ƒuZuwuj%‹i²2wuªsdª

E

huo3flƒuaX'Z]n¦o[ƒuaZOnua.ƒV^`nVw

=qš4ƒuaZ]X[a_Ž›£T;Z` 

?

³%µ0uŒ@>^`nVwz©%ªV³'^—kmX[aX‚v dªAAhu‹ikyflƒ=^`nVw ªV€4Zuf[ƒuaCZ]n¦olƒuaZ]o[ƒuaX%ƒV^`nVw =¼š4ƒuaZ]Xla_@j;`£[Œ]v

ˆO£Ôˆ ^›nVw’ˆ]£ÀbZ› 

?

³lA*€C]D@G>3ªuš4ƒua²¦^`X[a.fHZ`esema‚fHo[a‚w¸kmn¨š^`‹iema@Œ]ª

kmnVwiaH§

]

=‰© > kmnVwiaH§=Œ kmnVwiaH§¨…

P



>^

“



`^

“



`^

“

[ £ 

`^

“  

š­^›‹ie¯a2Œm%uoqkm_@^—eY\`emZ]‹V^—e*aX[X[ZOX%a‚jqoqkm_@^`ola‚j ÄZOXolƒuajq£ÀjqoH^`\]a'_ao[ƒuZuw¦€%^]wu^›h’¬¼¬ž

, S* "2 V)Sh% ! %'"2OV/1 "

µ ƒuan¦^`uiem²Okmnu\¦^jq£Àjqo3^›\]a¡€^]wu^`h¦¬q¬ž _ao[ƒuZuw? U|=;B.Z

š

ZC=>*o[Zo[ƒuajq²ujqo[a_ ='L:>Hvpœ4aZ]‹uoH^—kmn

ƒ………

†………‡ ] U ^ˆ=

P

‰Šc>1Z =3ŒD>

P

$‰Š U P  ŒŽ   

‘}’ˆ“

” Š‘ Ws=

P

‰

‘

Z1[ $‰

‘

>1Z

• U ŒZ–––'Z1g$Z =¼…>

P

D—

“ U P

.ŒŽ‚ Š

’“

š Š Ws=

P

‰ŠZ1[n‰Šc>1Z =);>

[n˜—

“ U  

Љ

‘'’ˆ“Xš

Š Š‘ [5‰

‘ Z =ÀˆK>

œƒuaX[a Š‘

^`X[a¥o[ƒua fHZpaH°’flk¯anio3j¸Z` .o[ƒua _@^›o[Xqks§YB ^ “

ª4¬žn =ÀˆK>3vM[  Ÿ`^`nikyjqƒua‚j’‹,a‚f^`hVjqa LJ= >U ] ª`AAao’hVj

nuZ`œÃXlaieg^OfHa¦o[ƒuazŸ]a‚fHo[Z]X2=

š

H*B

^ “

>H ‹p² ^›n ^]w—~¼hVj|o3^`‹iema¦Ÿ]a‚fHolZ]X U =

“

Z–––'Z



>H kmny=Àˆ‚>3ª

E ² wiZ›k¯nu\JjqZVv

œ4a¥wiaHrVnua=^ nuaœ_ao[ƒuZuw ?ª4¬žokyj¸a‚^]jžksem² j|aan olƒV^`o’o[ƒua¥Z]X3wiaX2Z`  fHZOnpŸ]aXl\]anVfHa¥Z` .o[ƒua

P

£ÀfHZO_VZ]nuanio

Xla_@^—kmnVj%hunVflƒV^`nu\]a‚wAª,j4 ÔZ]X%o[ƒuak[`£ÀfHZ]_,Z]nuanio‚vVolƒuaey^]fYH’Z` ^]ffHhu_hiey^`oqkmZ]n¦_2^DH]a‚jo[ƒua.aX[XlZ]X3j4uhuX[aHem²¸e¯Zuf^—eÀª

š¢ƒua¦fHZ]npŸOaX[\]anVfHa¦‹,aƒV^—Ÿ]kmZ]huX2Z` o[ƒua [`£ÀfHZ]_,Z]nuaniokyjo[ƒphVj anpoqkmX[aHem² wiao[aXl_kmnua‚w ‹i² o[ƒua’ ÔZ`esemZTœ¢k¯nu\ Z]X3wiaX

fHZOnVwOk¯o|k¯ZOnVj4 ÔX[Z]_š¢ƒuaZ]X[a_ C`£Àb^`nVwC`£TCCZ` 

?

³%µ0uŒ@Àª

C•—½*o½F“

p” p

½VU

Q"!

#d2!#$#e'J/0!/ˆ Y,. )n,TK1/r5

P

!#k[ \$3, }.! %$&%

'.%!2k# )(X+*r.!

# P

U-,k=)/.

— “ > 0 e

S"_Mp B)1…DdZ2=TSY>43 rXZ5v=TSY>

š

H76=TSY>rU ŒZ

#D[JU-,j=)8

— “ > 0 e 9

_Mp B)1…DeDZ23=

9

>:3<;Z5v=

9

> H 6=

9

>vU ŒZ

*v p B)1…Dd p B)1…De !$ ) ,5,O 5,=6 !i$ 1!/5%3Ž!$#>5rZ2{,5!/0! kn,j!-,1,5!#?*r

+ 5,

“

aŸ]aX[olƒuaHe¯a‚jljv@ƒV^]j¸nuZ]o2anuZ]hu\]ƒ fHZ]_VZ]nuanio3j2o[Z ^—esemZ`œ ÔZ]X’^`n Z]X3wiaX’Z` fHZ]npŸOaX[\]anVfHa \]Xla‚^`o[aX2o[ƒV^`nyg

=A U = š H B ^ “ >H kyj2o[ƒuazZ]uoqkm_@^—eŸ]a‚fHo[ZOX5>3ª³anVfHa]v4o[Z \]ao®j|hi°®flkmanpo2 ÔX[aa‚wiZ]_¦vœ4a¦nuaa‚w o[ZJfHZ]nVjžkywiaX’o[ƒua

fHZO_VZpj¼k¯o|k¯ZOn ?>B’Z` ?Z`Ÿ]aXDC jqo[aVj«ªA¡jŸT^`X|kg^›‹ie¯a2jqo[aVjlKŠ[v

• U ŒZ–––ZC ^`X[afHZ]nVjžkywiaX[a‚wAvAœ4a^—eyjqZ’ƒV^—Ÿ]a.o[Z

kmnio[X[ZuwihVfHa.o[ƒuaXH^`oqkmZpj@EnŠXU ‚ŠGFr

BŠ

’“

KŠqv

• U ŒZ–––'ZHCYª_?>Bkyj%flƒV^`X3^]fHo[aX|k@a‚w¸‹p²2o[ƒuaCo[Xqkmiema=GIZHJZLKr>­œ%ƒuaX[a

M

I#kyj4olƒua.‹iemZ‡fYHi_@^`o[Xqks§i=;BŠ

‘

>TЉ

‘}’ˆ“

‰EDEDED‰B@œ4kmo[ƒ g F gC‹iemZ‡fYHuj%Z` o[ƒua ÔZ]X[_

NO

ØqØQPSRTVU&WXY[Z\­Ýá‚Ø]`Ùä_^Sä_ZHÙ`ZY^a‚ØqÚÔØYÙbZ^Sä_Z3ٗÚAc

(9)

BŠ0Š U EnŠ BJZ

‘ U E ‘ J š H Z ks 

•

Z

‘ U ] Z ks 

„•

t

M

JJkyj4olƒua.‹iemZ‡fYHiŸ]a‚fHo[Z]X=>dŠc>TŠ

’ˆ“

‰EDEDED‰B2œ4kmo[ƒ’‹iemZuf'Huj%Z› {o[ƒua' ÔZ]X[_ dŠrU-EnŠ

š ª

M

K¨kyjo[ƒua‹iemZ‡fYHiŸ]a‚fHo[Z]X=>i`ŠT>cŠ

’ˆ“

‰EDEDED‰Bœ4kmo[ƒ’‹iemZuf'HujZ` {olƒua' ÄZ]Xl_ i`ŠXU E5Š6=rŒ

a  Š^ “

N

’ˆ“

E N c JOª

€¢aieg^Oflk¯nu\

a J H I ^ “ c H

‹i²®^`n¦^Ow—~¼hVjqoH^`‹iemaŸ]a‚fHo[Z]X@ Z`¿*aX3jQChF gwia\]Xlaa‚j4Z` * ÔX[aa‚wiZ]_¦v‡k ªaƒuZ]VaH Ôhiese¯²zanuZ]hu\]ƒ

 ÔZ]XDC Œo[Z k¯nVfHXla‚^]jqao[ƒuaZ]X3wiaX'Z` fHZ]niŸ]aX[\]anVfHaCZ` {olƒua+[`£ÀfHZ]_VZ]nuanio‚ªu¬žo%kyjZ]huX^—km_nuZTœ o[Z@jqƒuZ`œ0ƒuZ`œ0o[Z

fHZOnVjqo[X[hVfHoD ^`nVw’ƒuZ`œ0o[ZCkm_iema_anioo[ƒuanuaœ0_aolƒuZ‡w ?B‰ª

7 0/,* &}3-' 4Y*'

¬žn.o[ƒikyjjqa‚fHoqkmZ]n*v—o[ƒuaaH¿*a‚fHoqkmŸ]a4fHZ]nVjqo[XlhVfHoqkmZ]n.Z` Ákyj­wia‚jlfHXqkm‹Va‚wAª`¬ÀoYjqƒuZ]hieywC‹Vaa_uƒV^]jžkA@a‚wCo[ƒV^`okmo3j*fHZ]_VZ]nuanio3j

wia,anVw Z]n E “ Z–––'ZHE



v*o[ƒihVj ÄZ]XHflk¯nu\¥Z]nua2aŸT^Te¯hV^›oqkmZ]nJVaXjqo[a*ªY³Z`œaŸOaX‚vAo[ƒua‚jqa’^]wuwOkmoqkmZ]nV^—e¡fHZO_uhuo3^`oqkmZ]nVj

‹,a‚fHZ]_aCnua\`esk¯\›k¯‹iema@^Ojj|ZpZ]n¦^Oj4o[ƒuawOkm_anVj¼k¯ZOn¦Z` Yo[ƒua.jq²ujqo[a_ =YIK>Ykyj4ey^`X[\OaanuZ]hu\]ƒ*ª

h)!( )6"

š¢ƒua.fHZ]nVwOkmoqkmZ]nVj ÄZOXZOX3wiaXjP’^`X[aanihu_aX3^›o[a‚w’‹,aHe¯Z`œ0olZ]\]ao[ƒuaX%œ¢k¯olƒ’o[ƒua^]jljqZ‡flky^`ola‚w2o[X[aa‚jª

M

PU g]v3g 0Œ$mˆ=;i



>YkyjX[a‚t]hikmX[a‚w¸œ4kmo[ƒ

=>i

 > ƒ

†‡ H U ŒZ = ] >

e

P2_(fiŒZ–––Z1ghJŒg HK N U ŒZ

?? N

Z––5–Z

@d@eDt =>P3>

M

PU g`Œ Œ]vKg …Kmˆ=;i



>^›nVwi=;i

 — “

>^›X[aX[a‚tOhik¯Xla‚w’œ4kmo[ƒ

=;i

 — “ > ƒ……

†……‡ H K  U ŒZ

?? 

Z––5–'Z

@d @e Z =)gD>

H I ^ “ K  — “ U ŒZ

?  — “

Z–––Z

@et =)g`Œ ŒD>

AAao



‹Va I K  h “

 — “ K  — “

ªu¬ =)gD>kyjjl^`oqkyjžrVa‚wAv,o[ƒuani=;i

 — “

>}kgj¢a‚t]hikmŸT^Te¯anioo[Z

H I ^ “  U ] t

M

PU g`ŒJ…uvKg ;Kmˆ=;i



>3v =;i

 — “

>^`nVw =;i

 —

>^`X[aXla‚t]hikmX[a‚w¸œ4kmo[ƒ

=>i

 — > ƒ……………………………………

†……………………………………‡ H7K

— “ U ŒZ

?? — “

Z––5–)Z

@d5@eZ =g`Œ …\>

H I ^ “ K  — U gŒ=…‚Z

?  —

Z–––Z

@e Z =g`Ϊ;\>

H I K  U “

 — “ Z ??? 

Z––5–Z

@d@d5@eZ =g`Œ=ˆ‚>

H

K:tSI ^ “ K  — “ U Œ$Z

?? Z ?  — “

Z5–5––Z

@e5@d5@eDZ =g`Œ Ž\>

H I ^ “

=K:tSI K  >VU  —

 — “ Z ? Z ? 

Z–5–5–Z

@d@eDt =g`Œ b\>

AAao

— “

‹Va I K — “ h “

 — K  —

`ªi¬ =)g`Œ=…>}kgj'j[^`o|kgj¼rVa‚wAvuo[ƒuan{=>i

—

>Ykyj%a‚tOhikmŸT^—emanioo[Z

a—ØYábZ^*Ú^ÀÝ[ٗá‚ÚYZH\^a—ØAZ3Þ4ßZ3ٗØqÙ&^AäæÚÔØ4ß \Zá‚àA^Ac

(10)

H7I

^ “  — “ U ]

=)g ŒŽ;>1Z H

 U ]

=)g Œ ˆK>1Z

H K:tSI

^ “  U ]

=)g Œ=Ž>1Z H I ^ “

=K:t  > U ]

=)g Œ=b>1t

M

PU g`Œ ;uvKg !ˆmˆ=;i



>3v =;i

 — “

>3vˆ=;i

 —

>^`nVwi=;i

—

>4^`X[aX[a‚tOhikmX[a‚w’œ4kmo[ƒ

=;i

 — > ƒ…………………………………………………………………………………………………………………………

†…………………………………………………………………………………………………………………………‡ H K — U Œ$Z

??  —

Z––5–)Z

@d5@eDZ =)g ŒJ†>

H7I

^ “ K  — U g Œ™;KZ

?  —

Z–––Z

@e˜Z =)g ŒŽC>

H I K  — “ U “

 — Z ???  — “

Z––5–Z

@d @d @e Z =)g Œ=>

H K:tSI

^ “ K  — U g Œ …KZ

?? Z ? —

Z5–5–5–'Z

@e@d@eDZ =)g Œ Œ ] >

H7I

^ “

=K:tSI K  — “ > U  —

 — Z ? Z ?  — “

Z5––5–Z

@d@eDZ =)g Œ Œ]ŒD>

H I ^ “

=K:tSI K  > U —

 —

 — “ Z ? Z ?? 

Z5–5–5–'Z

@d @d @e Z =)g Œ Œ‚…>

H I ^ “

=K:tSI=K:tSI

^ “ K  — “

>'>VU

 —  — “

— Z ? Z ? Z ?  — “

Z5–5–5–Z

@e@d5@eZ =)g Œ Œ;>

H7I

^ “

=K tSI K  > U  —

 — “ Z ? Z Z ? 

Z5–5––Z

@d5@eZ =)g Œ ŒˆK>

H I K  U “

 —

 — “ Z ???? 

Z–5–5–'Z

@d @d @d @e Z =)g Œ Œ‚Ž>

H I=K tI ^ “ K — “ > U  — “

 — Z ??? Z ?  — “

Z5–5–5–Z

@e@d5@d@e˜Z =)g Œ Œ‚b>

H

K:tSI K  U “

 — “ Z ?? Z ? 

Z5–5–5–'Z

@d @d @e Z =)g Œ Œ`†>

H K:tSI

^ “

=K:tSI K  > U  —

 — “ Z ?? Z ? Z ? 

Z5––5–Z

@d@e1@d5@eZ =)g Œ ŒC>

H K tSI

^ “ K  — “ U g Œ ŒZ

?? Z Z ?  — “

Z5–5–5–Z

@e@d5@et =)g Œ Œ‚>

AAao

—

‹Va I K — h “

 — K  —

ªi¬  =)g`ŒJ†>}kgj'j[^`o|kgj¼rVa‚wAvuo[ƒuan{=>i

—

>Ykyj%a‚tOhikmŸT^—emanioo[Z

H I ^ “  — U ]

=)g`Œ C>1Z H  — “ U ]

=g`Œ \>1Z

H

K:tSI ^ “  — “ U ] =)g`Œ Œ ] >1Z H I ^ “

=K:t  — “ > U ] =g`Œ ŒOŒD>1Z

H I ^ “ =K tI

 > U ]

=)g`Œ Œ‚…>1Z H I ^ “

=K:tSI =K:tSI

^ “ 

>'>VU

]

=g`Œ Œ;>1Z

H7I

^ “ =Kt  > U ]

=)g`Œ ŒˆK>1Z HI

 U ]

=g`Œ Œ—Ž>1Z

H I =K:tSI ^ “  > U ] =)g`Œ Œ‚b>1Z H

K:t  U ] =g`Œ Œ›†>1Z

HK:tSI

^ “

=K:t  > U ] =)g`Œ ŒC>1Z H7K tSI

^ “  U ] =g`Œ Œ—>1t

š¢ƒua‚jqa¡fHZOnVwOk¯o|k¯ZOnVj%^`X[a%ZO‹uo3^—kmnua‚w2‹p²2WYX[Z],ZpjžkmoqkmZ]n¥Œ^`nVw‹i²hVjžkmnu\@jžkm_iesks Ä²Okmnu\®^Oj[jqhu_uoqkmZ]nVj=Ôkmokyj}k¯_VZ]X[oH^`npo

olZnuZOo[ao[ƒV^`o%olƒua.fHZ]_VZijžkmo[a._aolƒuZ‡w$?>B@j[^`o|kgj¼rVa‚jjdj=¼…gh ŒD>3vik=gD>^`nVwhpz=)ghJŒD>'>3ª

#/1G Y++

¬žn’Z]X3wiaX%olZey^`o[aXjžkm_iesks Ô²¦o[ƒuaa‚tOhV^`oqkmZ]nVj¢ ÄZOXD.viœ4anuZ`œ jqo3^›o[a¡j|Z]_a‹V^]jžkyfX[a‚jqhiemo3jª

¨– Q"! Xx Y B ^

“

B ^ “

*r

UYJ

š H

: xJ=#K+h

B ^ “

>rU ]

C•—½F½SW3™

E ² wiaHrVnikmoqkmZ]n*vœ4a¦ƒV^—Ÿ]ax U B ^ “ J š H B ^ “

ª¡jo[ƒua¥_ao[ƒuZuw ? U =>B.Z

š

ZC=>%kyj’jqo|k2² ^]ffHhuX3^`o[a]v

x U_J H

œ%ƒuaX[a U B ^ “

JÁ^`nVw9J



UV=

]

Z–––Z

]

Z‚ŒD> H ª%³%anVfHa]vlxJ=K h B ^ “

>U J H

=#K h1J

š H B ^ “

>iU

_J H h J H

JZJ H U_J H

h J H U ] ª

¨–

l !

v= Љ

‘

>TЉ

‘}’ˆ“

‰EDEDED‰B Yk.g Fig5/0,+kk! 4 I ^ “

:

(11)

iЉРU “5 B ^ “ Z

ЉŠ^ “ U h “5 x`Z

Љ

‘ U ] Z

U

•

!#

U

•

hJŒt

C•—½F½SW3™

E

²¦wiaHrVnik¯o|k¯ZOn*vI I ^ “

U%vikÀªåa]ª

e • Z _ fpŒZ–––ZHC gZ E5ŠsB iЉ

‘ Œ Š^ “

N

’ˆ“

E N N ‰‘ U-#Š

‘

Kt

A a__@^…Ckyjo[ƒuan’a‚^]jžksem²’uX[Z`Ÿ]a‚w2‹i²kmnVwihVfHoqkmZ]n¥Z]n

•

ª

¨– ! XU

a

H

“ ‰

Z–––'Z HB‰

 c H

'JDC FOg#+K,5$!/3 I K  h “

˜—

“ K

˜—

“

!#

9

('J

g#k‚, !$/1 jB =  h “

D—

“ =

˜—

“

*ri_K )(s 5 .!$//X ?3 …glh …_ X{,B O

e •

_(fiŒZ–––ZHC gZ XЉ U 

N ’  P

E N — “

Š g  ^ N

Š 9 N t

C•—½F½SW3™ˆAAao¦‹,aema‚j[jo[ƒV^`n’Z]Xa‚t]hV^—eo[Z…gh …uªK›uZ]X^Tee •

_(fpŒZ–––)ZC gpviœ4aƒV^—Ÿ]asЉU<1ˆŠ‰Œ„L3Љ,vuœ%ƒuaX[a

1ˆŠ‰ U  Š^ “

N

’ˆ“

E N

=E

N = Ϊg

N

JD>

 Z

LЉ U E5ŠmB{=AE5Šs=MŒŽgnŠJD>

 h “

˜—

“

=GEnŠ=MŒŽgnŠJD>

˜—

“ t

L3Љ2f^`n’‹VaCaH§‡V^`nVwia‚wz^]j ÔZ`esemZTœ'j

L3Љ U  N ’ 7

P E N — “

Š g  ^ N

Š

Bj=ONlh

“

D—

“ 

D—

“

N ’ 7 Œ Œ

P

ENŠ g

D—

“ ^ N

Š

=ON

U  N ’ 7

P E N — “

Š g  ^ N

Š 9 N h “

˜—

“ g

D—

“

Š

Jt

%œ¢k¯nu\2o[Z ik=gD>3viœ4aƒV^—Ÿ]a

9 N U ]

 ÔZ]X%^—ese­kmnio[a\]aXjP„g]vuƒuanVfHa

L Љ U 

N ’  P

E N — “

Š g  ^ N

Š 9 N h Œ

Œ Œ g

D—

“

Š

Jt

I`km_ksey^`Xqem²]v71ˆŠ‰@f^`n’‹,a.aH§uV^`nVwia‚w¦^]j

1ˆŠ‰kU

Š^ “

N

’“

E N 

’ 7 E N g  ^

N = t

Z`œ.vdk=¼…$gh Œ->­km_ieskma‚jolƒV^`o

e _ f ]

Z–––Z3…$g`h=…_gZ =

UYJ

š H = U Œ Œ Œ

JZ

^›nVw’^]j+3 …gh …uvuœ4aZ]‹uo3^Tk¯n

1ˆŠ‰ U “

˜—

“  Š^ “

N

’ˆ“

 ’ 7 Œ Œ Œ Œ E — “

N g  ^

N J

U “

˜—

“ a  Š^ “

N

’ˆ“

=GE

N Œ g N >

˜—

“

h{g

˜—

“

N c J

U “

˜—

“ a  Š^ “

N

’ˆ“

g

D—

“

N — “ h{g

D—

“

N c J

U “

˜—

“ g

D—

“

Š

J$t

Références

Documents relatifs

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

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

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

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

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

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

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

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