• Aucun résultat trouvé

A Simple Method for Compressible Multiphase Mixtures and Interfaces

N/A
N/A
Protected

Academic year: 2021

Partager "A Simple Method for Compressible Multiphase Mixtures and Interfaces"

Copied!
34
0
0

Texte intégral

(1)

HAL Id: inria-00072340

https://hal.inria.fr/inria-00072340

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-

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non,

A Simple Method for Compressible Multiphase Mixtures and Interfaces

Nikolai Andrianov, Richard Saurel, Gerald Warnecke

To cite this version:

Nikolai Andrianov, Richard Saurel, Gerald Warnecke. A Simple Method for Compressible Multiphase Mixtures and Interfaces. RR-4247, INRIA. 2001. �inria-00072340�

(2)

ISRN INRIA/RR--4247--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

A Simple Method for Compressible Multiphase Mixtures and Interfaces

Nikolai Andrianov — Richard Saurel — Gerald Warnecke

N° 4247

September 2001

(3)
(4)

)/*102/!)3!

4576982:<;95!= >?(@A5<;9>(8CBDFEHG5<IJ(;9@A?LK;9M(@ONP:<QESRTNP@A;9:<?VUW;9@A>NPI69NPX

Y[Z]\^._a`cbedgfh^i]jlkmnfporq$_#m!otsCmnfp^.fluvkwmvfhotq

x _uvyguzmv\O^._Ou!{#or^.s]jp_|C_Ou

}~now€_m‚d]ƒT„‚d]…

†‡kws]s9ot~vm

x

_ˆ~n_O{'Z]_O~n{'Z]_‰q2Š`P‹w`gŒTbdg_OsCmv_O^Ž9_~‚‹tt]‡b‘tcs’kw“r_Ou

”•–O—˜™]št—t›œ _ x _Ožt_jhots$kŸ o x i]q]ožP¡¢mygs£_ˆun{'Z]_^._a¤¥ot~‚k.q]otqC¡¦{#orq’uv_~nž§kwmvfhžt_r¨Pi’q’{#orq x fpmvfhotq’ktj©Zgyr¡

s9_~nŽ9otjhfh{ˆ^ªi]jpmvfhs]Z’ktuv_^.o x _Oj<«‚¬­m‚fhqPžrotjhžt_Au‡k*uv_#m®ot¤Suz_Ožt_OqTs’kw~vmvflkwj x f°¯2_~n_qPmnfhktj_A±ri£kmvfhotq£u®kwq x Z’ktu

mnZ]_‚ktŽ]fhjpfpmymnoªuvotjhžt_!fhqPmv_~v¤7kt{_‡s]~notŽ]jh_^uSŽ£_m²³_O_qs]i]~n_®^kwmv_~nflkwjluHktuS²³_Ojpj9ktuS{ot^.s]~n_OunuzfhŽ]jh_‡^i’j°mnf°¡

s’Z’ktuv_³^.fp|gmvi]~n_Ou²!fpmvZm²o žt_jhoC{#fpmvfh_Oukwq

x

q]orqC¡¢_A±Pi]fpjhfhŽ]~vfhi]^LmvZ’_~n^co

x

ygq’kt^.fh{Ou´¥m²³o s]~n_Ounuzi’~v_Au¨Am²o

mn_^.s9_~'kmvi’~v_Au¨µm²³o x _Oq’uvf°mnfp_Au¨_#m'{w«·¶-«$¬­mnuˆqgi]^._O~vfl{ktjH~v_Auzorjpi]mvfhotq¸s£oPuz_Auuv_žt_O~nktj x f°¹{i]j°mnfp_Au«TY[Z]_

^.o x _Oj’s9orunuz_Auvuv_OuHkjhkt~v“r_!qPi’^Ž9_~Sot¤©kt{#ori’uzmvfl{‡kwq x {otqgžt_A{-mnfpžr_!²k§žr_Ou!´7uv_žr_q²[k§žt_Aun¶(ktq x f°mfhuSq]owm

_Aktuvycmvoi’sP²!fhq x kwjhj£mnZ]_Ouv_®²[k§žt_AuSkr{{#i’~nkwmv_jhy.kwq x uzfh^.s]jpyr«„‡jluzo£¨rmnZ]_auzyCuzmv_^ºflu³q]otqC¡¦{#orq’uv_~nž§kwmvfhžt_r¨

ktq x mvZ]_qPi’^c_O~vfl{ktjµkws’s]~vo§|Cfh^kmvfhotq£u³ot¤mnZ]_{ot~n~v_Auzs9otq x fpq]“ªmv_O~v^u®q]__ x mnoŽ9_s]~nožPfx _ x «H¬¦q$mvZ’fhu

s£kws9_~²_¤¥oC{i’uorq»kT^._#mnZ]o x ¨HŽ’kruz_ x otq»k¼{'Z’kw~'kt{#mv_~nflumnfh{ x _A{#or^cs9oruvfpmvfhotq½²!Z]fl{'Z½uvotjhžt_OumvZ]_Auz_

s’~vorŽ]jp_O^uHfhq*kuvfp^.s]jh_®²[k§y.kwq x ²!fpmvZ*“togo x kt{O{#i]~'kt{yt«Y[Z’_®~notŽ]i’uzmvq’_Ounu¨Pkt{{i]~'kt{#y.kwq x žt_~'unkmvfhjhf°my

ot¤µmnZ]_ˆ^._#mvZ’o x flu‡{#jh_Okt~vjhy x _O^corq’uzmv~'kmv_ x orq uv_žr_~'kwj9mv_Aum‡s’~vorŽ]jp_O^u[²!f°mnZ _|]kt{-m‡uvotjhiCmvfhotq£u«

¾T¿PÀ2ÁnÂÃ

˜Ä–t›

Y²ow¡­s]Z’ktuv_ Å’o²‡uO¨’Zgygs£_O~vŽ9otjhfh{a^.o

x

_OjhuO¨’q]orqC¡¦{#otq£uz_O~vžkmnfpžr_‚_A±Pi’kmnfporq’u¨2Ÿ o

x

i]q]ož

^._mvZ]o

x

uO¨]fhqrmn_~v¤7kt{_‚s]~notŽ’jp_O^.uO«

ƈÇÉÈ(ÊHË£ÌÍ<Í<Î'ÏlÐ#Î-ÑAÏ¥ÒӧԁÕ<Ö·×­Ø-ÔٵѧÖÐ#ԁÕ<Ú<ÖÍ­ÛnÍ!܈Ý'Þ-ߧԁà§Ó§Õ7ާ˵á2âOã¼ä§åzæ-çAËéèÏÉê-ë-çAåzìªÜˆÝ'Þ-ߧԁà§ÓAÕ<ާ˵ÒԁÕ7í‡Ý'Ñî#ïð’í‡Ý'Ö·ñlò

ѧַØ-Î-ñóÝ'ÖlïÝ'ѧߧÕ7ÖóÝ'ѧÎvЧôí‡ÝnÍ<õ§Ôí‡ÝnÍ¢Ö·ØwïӧѧÖÏÉí‡Ý'Þ-ßAÔzàAÓ§Õ<Þ§ïßAÔ

ö

ÇÉÑAÚ<Í<ÖÍ¢ÓAÍ.ÙѧÖÐ#ԁÕ7Ú¢ÖÍ¢Ý'Ö·Õ<Ô*ߧԁÚâ#îAÚ7Í¢÷í!ԁڪø©õ§ÔÕ7í!Ö·ùOÓAÔzÚªÇÉѧߧӧÚ7Í¢Õ7ַԁñ·Úvˇú$Õ7Ó§Ô*ð£ÑAÕ<ַׁÎûãԁÕ<í!ÖlË®åzê'ä#ú-êû܈Ý'Õ<Ú<ÔzÖ·ñ·ñ·Ô

ü ԁߧԦýTåzêAË©ãÕ<Ý'ѧׁÔÝ'ѧß*Ç¥Êþ©ÇÉÈÿá’Õ<Î<Ԧ͂âAÜaÈ(âSË9æ-ç-ç'ä.Õ7Î-ÓA͢ԈßAÔzÚgÓA×zÖ·Î-ñ·ÔÚzË©ç-ì-ë-ç-æâOΧõAÖóݪÈÑ#Í<ÖtÎ-ñ·Ö·Úzï$ð’í‡Ý'Ö·ñlò

Õ<Ö·×­õ§Ý'Õ<ßwôÖ·ÓAÚ<Í<ÖlïӧѧÖÐÏÉí!Õ<Úzï

ÇÉÈ(ÊHË£ÌÍ<Í<Î'ÏlÐ#Î-ÑAÏ¥ÒӧԁÕ<Ö·×­Ø-ÔٵѧÖÐ#ԁÕ<Ú<ÖÍ­ÛnÍ!܈Ý'Þ-ߧԁà§Ó§Õ7ާ˵á2âOã¼ä§åzæ-çAËéèÏÉê-ë-çAåzìªÜˆÝ'Þ-ߧԁà§ÓAÕ<ާ˵ÒԁÕ7í‡Ý'Ñî#ïð’í‡Ý'Ö·ñlò

Þ-ÔzÕ<Ý'ñ·ßPï©Ý'Õ7ѧԁ׭Ø-Ôvôí‡ÝnÍ<õ§Ôí‡ÝnÍ¢Ö·ØwïӧѧÖÏÉí‡Ý'Þ-ßAÔzàAÓ§Õ<Þ§ïßAÔ

(5)

3 ! µ " ! º & ' ) &*! W ! O/!)3³!

– › ori’u x _Ožt_jhots’s£orq’uci]q un{'ZO^.k x _$mygs9_TŸ o x i’q]ož s£ori]~i]q uzyCuzmv\O^c_$Zgygs£_O~vŽ9ow¡

jhfl±ri’_q]otqC¡¦{#orq’uv_~nž§kwmvfp¤³^.o x jhfluvktqrm x _OuA{#ori]jp_O^._qPmnua^ªi]j°mnfps’Z’ktuvfh±Pi]_Au«©_^.o x \Ojp__Aumª{ot^.s9oru

xi]q _Oq’uv_^Ž’jp_ x _uz_OsCmO±Pi’kwmvfhotq’ukwiC| x ~nfpž_Auas’kw~vmvfh_jhjp_Auˆ_#mªfpjk$jhkû{Okws’kr{#fpm x _{Okwjl{#i]jh_~ x _Ou

s’~vorŽ]jp\O^._OufpqPmv_O~z¤7kr{#_Au‡_qPmn~v_ x _Ou‚^.kwmO~vflkwiC|$s]i]~'u®kti’unuzfŽ]fp_OqF±Pi]_ x _Ou‚s]~vorŽ]jh\^._Ou x _^jlkwq’“t_Ou

^ªi]jpmvfhs]Z’ktuvfl±ri’_Ou{#or^.s]~v_AuvuvfhŽ]jp_Au x _iC|žgfpmv_Auvuv_Ou(_mk§žr_O{³i]q]_[mnZ]_~n^.o x yPq£kw^.fh±Pi]_[_Oqªq]orqC¡­_O±Pi]fhjpfhŽ]~n_

´x _i]|.s’~v_Auvuvfporq©¨ x _iC|cmv_O^cs~'kmni]~n_OuO¨ x _OiC|.^.kruvuv_OuSžtorjpi]^.fl±Pi]_OuO¨t_mn{w«h«h«¶#«dCotq*kts]s]~no§|gfh^kmnfporqªqgiC¡

^O~vfl±Pi]_®s9oruv_®s]jhi’uvfp_Oi]~'u x f°¹{#i’j°mOuO«µ_‚^.o x \Ojp_‚s£oPuvuv\ x _ i]q“t~'kwq x q]or^Ž]~n_ xorq x _Oukt{oti’uzmvfl±Pi]_Ou

_m‚{#orqgžt_O{#mvfhžt_Au´7uv_sCm otq x _Ou'¶[_#m fpjq _Aum s’ktu‚kwflu x _ x A{#_qPmn~v_O~‡mvoriCmv_Au®{_Ou‡orq x _Au x i]q]_ª^.ktq]fh\~n_

uvfh^cs’jp_c_#mˆs]~O{fhuv_t«!‚_.s]jhi’u¨µjp_c^.o

x

\jh_c_Aumaq]orqC¡­{otq’uv_~nžkmnf°¤H_mai’q]_kws]s]~no§|Cfp^kwmvfhotqûqgi]^~nfl±ri’_

x

_Oumv_O~v^._Auq]otq]¡­{otq’uv_~nžkmvfp¤7u

x

otfpm#"#mn~v_

x

Ožt_Ojpors]s$O_t«!‚ktq’uH{#_mn~nk§žkwfhj¢¨wq]oti£u(q]oti’u{otq’{_qPmv~notq£uuvi]~

i’q]_®^#mnZ]o

x

_ Ž’ktu_®uvi]~i]q]_

x

O{ot^.s£oPuzfpmvfhotq{kw~'kt{#mO~vflumnfh±Pi]_‡±Pi]f9~OuvotiCm³{_Ou³s]~notŽ]jh\^._Ou

x

_‡¤7k%#orq

uvfh^cs’jp_ _#m!k§žt_A{‡i]q]_ Ž9otq]q]_ s]~O{fhuvfporq©«µkª~vorŽ]i’uzmv_Ounuv_t¨Ps]~A{#fluzfhotq*_#m[“&q'~'kwjhf°m x _ jhkª^#mnZ]o x _‚_Aum

{jhktfp~n_^._Oqrm x O^corqPmv~_ˆuzi’~!s]jpi£uzfh_i]~'u[s]~notŽ]jh\^._Aumv_Ouzm x orqrm!jlk.uzorjpiCmnfporq_|]kt{-m!_Aum®{otq]qgi]_r«

—A– Á š&) –‚›+* {#ori]jh_^._qPmnu x fps’Z’ktuvfh±Pi]_Au¨A^.o x \jh_OuéZgygs9_~nŽ£orjpfl±Pi]_OuO¨A±ri£kmvfhotq£uéq]otq]¡­{otq’uv_~nžkmvfhžt_Au¨

d]{'Z^k

x

_Ÿ o

x

i]q]ož2¨]}~notŽ]jh\^._

x

fhqrmn_~v¤7kt{_

(6)

/

02/$&*3S#ª/

ƒTi]j°mnfps’Z’ktuv_‡Å’o²‡ukw~n_‡fhqgžtotjhžt_ x fpq kZgi]“r_®qgi]^Ž9_~ow¤µ¤¥i]q x kt^c_OqPmnkwj2kwq x fhq x i’uzmv~nfhktj9kts]s]jhfh{Okmnfporq’u«

ƒTi]j°mnfps’Z’ktuv_ˆ^.f°|gmvi’~v_Au[^.k§yZ’k§žt_auv_žt_O~nktjéot~nfp“rfpq£u«10®uvi’ktjpjhymnZ]_y kw~n_a{otq’uv_O±Pi]_Oq’{#_Auow¤k.s]Zgyguvfl{kwj

^.fp|Cfpq]“ˆs’~voC{#_Auvu(ot¤2uv_žr_~'kwjPŒi]fx uor~H^kmn_~nfhktjhuO«32iCmHi]q x _~Suvot^._‡{fp~'{#i]^uzmnktq’{#_Au¨mnZ]_yª^k§y{#or^c_

¤¥~not^ kw~vmvf4£{#flkwj©uv^._Okw~nfhq]“ªot¤({otqPmnkr{-m x fluv{otqPmvfhqgi]fpmvfh_Ou!uv_s’kt~nkwmvfhq]“Å£i]fx u!ow¤ x fp¯9_O~v_Oqrm!s]ZgyCuvfh{Okwj©kwq x

{'Z’_^.fh{Okwjés]~nots9_~vmvfh_OuO«

œ _ {otq’uvfx _~³Z]_~n_‡mnZ]_®qgi]^._~nfl{kwj£~v_Auzorjpi]mvfhotqow¤µkª{#or^cs’~v_AuvuvfpŽ’jp_‡^ªi]jpmvfhs]Z’ktuv_‡Å£o² ^.o x _Oj<¨54’~'um

s’~vors£oPuz_ x Žgy62kt_~(kwq x i]q(7flkmvo98·‹:C¤¥ot~ x _mvorq’kmnfporq²k§žr_Oufpqª“t~'kwqgi]jlkw~_#|Cs]jhoruvfpžr_OuO¨§ktq x ^co x f4’_ x

fhqûdCkwi’~v_Oj2ktq x „‡Ž]“r~nktjpj;8h<:µ¤¥ot~[mvZ’_ˆ~v_AuzorjpiCmnfporqot¤^ªi]j°mnfps’Z’ktuv_a^cfp|gmvi]~n_Ou®kwq x fpqPmn_~v¤7kt{#_as]~notŽ’jp_O^.u

Ž9_#m²__Oqs’i]~v_{ot^.s]~n_OunuzfhŽ]jh_‚^kwmv_~nflkwjlu«

¬¦q¸mnZ]fhujhkrumª~v_¤¥_~n_q’{_.mvZ]_“rorktjH²kru mvoûi£uz_mnZ]_*unkw^._qgi]^._~nfh{OkwjH^._mvZ]o

x

¤¥ot~mvZ]_*s]Zgyguvfl{kwj

s’~vorŽ]jp_O^ufhqgžtotjhžgfpq’“ûm²ow¡­s]Z’ktuv_*^.fp|gmvi]~n_Ouc²!fpmvZ m²³o žt_OjpoC{#fpmvfh_OuO¨Skruª²_jhj!ktucfhqrmn_~v¤7kt{_s]~notŽ’jp_O^.u

²!fpmvZ mnZ]_uzfhq]“rjp_as]~n_Ounuzi’~v_akwq x žt_OjpoC{f°myr«(Y[Z’fhu‡ktfp^ ²kru[~v_Akt{'Z]_ x Žgyi’uvfpq’“(=

>

„‡qTi]q£{#otq x f°mnfporq’kwjµZPygs9_~nŽ£orjpfl{ˆ^.o x _j©¤¥ot~!Œi’fx ^.fp|Pmni]~n_OuO¨’f¢«_r«]mvZ’_uzyCuzmv_O^ ~n_^kwfhq’u!Zgygs£_O~z¡

Ž£orjpfl{ ¤¥ot~‡ktjpj©k x ^.fhunuvfpŽ]jh_ˆum'kmn_OuO¨

>

„‡qTkt{O{#i]~'kmn_a^c_mvZ]o x ¤¥ot~[Å£iC|{#or^.s]iCmnkwmvfhotqTktu²_jhjµktu¤¥or~[mvZ]_ˆq’otqC¡¦{#orq’uz_O~vžkwmvfhžt_‡mn_~n^u¨

>

}~n_Ounuzi]~n_ˆkwq x žt_OjpoC{f°my~n_jlk|]kwmvfhotq*s’~voC{#_ x i]~n_OuO«

Y[Z’fhu^.o x _Oj£kwq x qgi]^._O~vfl{ktj]uzorjpiCmnfporq.s]~voC{_ x i]~n_Ou(Z£k§žt_[Ž£_O_qkts]s]jhfp_ x mnouz_Ožt_O~nktj x f°¹{i]j°m³s]Zgyguvfl{kwj

s’~vorŽ]jp_O^u®jhf?r_ x _#mnotq’kwmvfhotqû²[k§žt_Au®fhqF^ªi]jpmvfhs]Z’ktuv_c^cfp|gmvi]~n_OuO¨é^i’j°mnfx fh^._q’uvfhotq’ktjfpqPmv_O~z¤7kr{#_Au®i]q x _~

uvZ]oC{?fhqrmn_~'kt{#mvfhotq©¨Ci]q x _~n²kwmv_O~_|Cs]jpoPuzfhotq£uS¤¥or~‡_#|]kt^cs’jp_r¨]kwq x {k§žgfpmnkmnfporq*fhq$jpfl±Pi]fx u@8pO`:­«

…®o²³_Ožt_~A¨rmvZ]flu^c_mvZ]o x Z’ktuuvot^._ x ~'k§²!Ž’kr{?guO«Y[Z’_a†‡fp_O^.ktq]quvotjhžt_O~Si’uv_ x fpqA8p*<:µkwq x fpqB8h`:

²[ktuS^i’{'Zmvogo x fluvuvfhs’kmnfpžr_t«¬­mfhqgžtotjhžt_ x otq]jhycm²³o²[k§žt_Aufhq’umn_Ok x ow¤µuv_žr_q©«C³otq’uv_O±Pi]_OqPmvjhyªq]otmktjpj

mnZ]_!²[k§žt_Ou²_~n_³i’sP²!fhq x _ x ¨rktq x mvZ]_!qgi]^._O~vfl{ktj]uzorjpiCmnfporqª²[ktuq]otmSkt{O{#i]~'kmn_³_Oq]oti]“rZ©¨wfhq.s’kw~vmvfl{#i]jlkw~

¤¥or~S{#orqgžt_O{#mvfhžt_²k§žr_OuO«…®_~n_!²³_!s]~nots9oruv_!kˆuzfh^.s]jh_‡²k§ymvokr{{#ori]qPm(¤¥ot~mnZ]_Ouv_‡²[k§žt_Oufhq.mvZ]_‚uzorjpžr_~A«

¬¦qcmvZ’_!jpfpmv_O~nkwmvi]~n_!uz_Ožt_~'kwjP²[k§yguot¤2uvotjhžgfpq]“‚mvZ’_‡uzyCuzmv_^ ¤¥~vor^D8‹:¢¨8p*<:­¨w²!Z]fl{'Zªm'kE?r_fhqPmvoˆkt{O{#ori]qPm

ktjpjµ²k§žr_OuO¨]{kwqTŽ9_ˆ¤¥ori]q

x

«GF‚q]_ˆot¤mnZ]_{ot^.^.otqTkws]s’~voPkt{'Z]_Au[fhu[mnoq]_O“tjh_O{-m!mnZ]_q]orqC¡¦{#otq£uz_O~vžkmnfpžr_

mn_~n^u‚fhqûmnZ]_uzyCuzmv_O^%ow¤S“rožt_~nq]fhq]“_A±ri£kmvfhotq£u«Y[Z’fhu flu

x

otq]_c_t«“’«2fhq¸Ÿ orqrmnZ]fh_~akwq

x

}o²³_O~nu8·Œ*:¢¨

²!Z’_~n_mnZ]_kwiCmnZ]ot~'u®“rfpžr_mnZ]_c¤¥otjhjpo²!fhq]“ ~v_Aktuvotq’u‡mvo

x

o$uzo£«"Hfh~nuzmO¨2mnZ]_yûq’owmv_cmnZ’kma_žr_q ²!f°mnZ]otiCm

mnZ]_q]orqC¡­{otq’uv_~nžkmnfpžr_mv_O~v^u mnZ]_uzyCuzmv_O^ ~v_O^kwfhq’ua{#otq£uzflumn_qPmˆ²!f°mnZ mvZ]_uv_O{otq x jhk§²ow¤mvZ]_O~v^.ow¡

x yPq£kw^.fh{Ou« Y[Z]_qµ¨(¤¥ot~mnZ]_$kws]s]jhfl{kmnfporq’uˆmnZ]_y {otq’uvfx _~A¨ x _#Å£kt“t~'kmvfhotq]¡<mnow¡ x _#mnotq’kwmvfhotqFmv~'kwq’uvf°mnfporq

´! ! Y‡¶-¨gmnZ]_Ouv_‚mv_~n^u x oq]otms]jlk§ykuvfp“rq]f4£{ktqrm~vorjp_‚fpq*mvZ]_ s]~noC{#_OunuO«IHfhq’kwjhjpyr¨PmvZ]_Oy^c_OqPmvfhotqmnZ’km

mnZ]_~n_Ouvi]jpmnu²!fpmvZ’otiCmq’otqC¡¦{#orq’uz_O~vžkwmvfhžt_cmv_O~v^u@4’m²³_OjpjSmvoTmnZ]_*_|Cs£_O~vfh^._qPmnktj x km'k]«TY[Z]_~v_Auzi]jpmz¡

fhq]“*uvyCumn_^%{#ori]jx Ž£_mvZ]_Oq¼_#|Cs]~n_Ounuv_ x fpq x fpžr_~n“t_Oq’{#_a¤¥or~v^%kwq x mvZ]_c†!og_^._#mnZ]o x fhu‚i’uv_ x ¤¥or~®fpmnu

uvotjhiCmnfporq©«

„®q]owmnZ]_~(^._#mnZ]o x ow¤’uvotjhžgfpq’“!mvZ]_[unkw^._Hmygs9_³ot¤]^co x _Ojg²!f°mnZq]_O“tjh_O{-mn_ x q’otqC¡¦{#orq’uz_O~vžkwmvfhžt_(mv_O~v^u

fluˆs]~nots9oruv_ x fhqJH]_ x ?Pfh² _#mA«kwj¢«8`E:­« Y[Z’_k x žr_O{-mnfporq¸_O±Pi’kmnfporq¼¤¥or~ˆmvZ’_žtorjpi]^._.¤¥~'kt{#mvfhotq¸fhu²!~vfpmz¡

mn_q$fhqû{#otq£uz_O~vžkmnfpžr_®¤¥or~v^$¨’ktq x mvZ’_{'Z’kw~'kt{#mv_~nflumnfh{ x _O{ot^.s9oruvf°mnfporq ^._mvZ]o x ²!fpmvZ mvZ]_i]sg²!fpq x fpq]“

x _Oun{#~nfpŽ9_ x kru¤¥orjpjho²‡uªfhuªi’uv_ x mnoFuvotjhžt_*mvZ]_$uzyCuzmv_O^ « kw^._jhyt¨(mnZ]_ uv_žr_q½jh_#¤Ém_Ofp“r_qgžt_A{-mvor~nukw~n_

i£uz_ x mvocs]~now€_O{#m³fhqPmvomnZ]_a{'Z’kw~'kt{#mv_~nflumnfh{K4£_jx ¨g²!Z]fpjh_ otq]jhycmvZ]_4’~'um[uzfp|_qPmv~nfp_AuSot¤©mvZ’_ uv_žr_q~nfp“rZPm

_Ofp“r_qgžt_A{-mnot~'u³kt~v_ i’uv_ x mvo.s]~now€_A{-m!Ž’kt{?*otiCm!ow¤mvZ’_Ouv_L4’_jx uO«

(7)

…®o²³_Ožt_~A¨!ktu*²³_¼uvZ]o² fhqÿdg_O{#mvfhotq ‘’¨‡q]_“rjp_A{-mnfpq]“¸mnZ]_¼q’otqC¡¦{#orq’uz_O~vžkwmvfhžt_$mv_O~v^u{#oti’jx jh_Ok x

mno½i]q]s’ZPyCuvfh{Okwj®uvotjhiCmnfporq’u¨!fhqVs’kt~zmnfh{i]jhkt~²!Z]_Oq {#otq£uzfx _~nfhq]“ fpqPmn_~v¤7kt{#_¼s]~vorŽ]jh_^uŽ9_#m²__qVs’i]~v_

^kwmv_~nflkwjlu«

Y[Z]_[^._#mnZ]o x otjhot“ryˆ²!Z]fl{'Zª²_S¤¥orjpjho²½fhqcmvZ]flu(²³or~?a²[ktufhqrmn~vo x i£{#_ x fhq.dCkti]~n_jCkwq x „‡Ž’“t~'kwjhj 8h<*:¢«

¬¦qc{#orqrmn~nkrumµmvo‚mvZ]_[^._#mnZ]o x u^c_OqPmvfhotq]_ x kwŽ9ožt_r¨O²_ x o‚q’owm(q]_“rjp_A{-mq’otqC¡¦{#orq’uz_O~vžkwmvfhžt_mn_~n^.uO«Y[Z’fhu

ktjpjho²‡uHi£uSmnoªs’~v_Auz_O~vžr_!mvZ]_ˆ{otq x fpmvfhotq£uSot¤µi]q]fp¤¥ot~n^.f°my.¤¥or~s’~v_Auvuvi]~n_®kwq x žt_OjpoC{#fpmy.Žgy{#otq£umn~vi’{#mvfhotq©¨

uv__dg_A{-mnfporq ‘’«

Y[Z]_qgi]^._O~vfl{ktj^._mvZ]o x ²!Z]fh{'Z¸²_ª_O^.s]jpoy¼Z]_~n_c¤¥ot~ mvZ]_i’sP²!fhq x fhq]“$ow¤³mvZ]_{otqgžt_A{-mnfpžr_ªkwq x

kr{#ori’umnfh{®{#otqPmn~vfhŽ]iCmnfporq’uHot¤émvZ]_‚Å’iC|flu x i’_‡mvo.Ÿakwjhjpori]_#m[kwq x ƒTktuv_jhjhk 8<:¢«(¬­m[fhu³Ž’ktuv_ x orqmvZ’_‚jhoC{kwj

~n_OuvotjhiCmnfporqûow¤³mvZ]_.jhfpq]_Akw~nf7O_ x †‡fp_O^.ktq]q s]~vorŽ]jh_^$«Y[Z]_.qgi]^._~nfh{OkwjŒiC|¼flu x _4£q]_ x ¤¥otjhjpo²!fhq]“mvZ]_

Ÿ o x i’q]ož*un{'Z]_^._t¨£ktumvZ’_ˆs]Zgyguvfl{kwj2Å£iC|$kwm[mvZ]_fhqPmv_O~z¤7kr{#_ažkwjhi]_ˆow¤mvZ]_uvotjhiCmnfporq ot¤mnZ]_†!fh_^kwq’q

s’~vorŽ]jp_O^$«Y[Z]_Oq mvZ]_q’otqC¡¦{#orq’uz_O~vžkwmvfhžt_ mv_O~v^u‡kt~v_ x flun{#~n_#mvf7_ x ¤¥otjhjpo²!fhq]“.mvZ’_jpfhq]_Au!ow¤SdCkti]~v_Ojµkwq x

„®Ž]“t~'kwjhj;8p*<*:­«HY[Z]flu!kws]s]~norkr{'Z*^kE?r_Oui’uv_ˆow¤mvZ]_a¤7kr{-m!mvZ£km‡Z]or^cor“t_Oq]_ori’u[um'kmv_Au[fpq$s]~n_Ounuvi]~v_akwq x

žr_jhoC{#fpmyuzZ’oti]j

x

Ž9_‡s]~n_Ouv_~nžt_

x

«µY[Zgi’uO¨w¤¥or~H{#otq£uz_O~vžkmnfpžr_uvyCumn_^uO¨wmvZ’_‡uv{'Z]_O^._fluH{otq’uv_~nžkmvfhžt_[kwq

x

{otq’uvflumn_qPm®²!fpmvZ]oriCm‚¤¥i’j-4’jhjhfpq]“$†!og_

u {#otq

x

f°mnfporqûotqûmvZ]_cjpfhq]_Akw~nf7O_

x

kt{#orŽ]flkwqT^kmn~vfp|é«

œ _ x

oq]owm

q’__

x

mno${ot^.s]iCmn_.mvZ]_†‡oP_^kwmv~nf°|¼fhq¸ot~

x

_~ mnoTZ’k§žt_k${#orq’uz_O~vžkwmvfhžt_c^c_mvZ]o

x

¨²!Z]fl{'Z¸{oti]j

x

Ž£_

±Pi]fpmv_ˆ{oruzmvjhykwq x {#i]^ªŽ£_O~nuvot^._‚¤¥ot~[Ž]fh“cuvyCumn_^uot~[²!Z]_q i’uvfpq’“c{ot^.s]jhfh{Okmv_ x _A±ri£kmvfhotq£u³ot¤uzmnkmn_t«

Y[Z]fluµ¤¥_Okmni]~n_Hfhuµ_Ouvs£_A{#flkwjhjpy i’uv_#¤¥i]jr¤¥ot~µmygs]fh{Okwjrs]~vorŽ]jh_^u¨§kw~nfluzfhq]“!fhq^i]jpmvfhs]Z’kruz_HŒo²¸^co x _Ojpjhfhq]“’¨

²!Z’_~n_®²_®ow¤Émn_qZ’k§žt_!mnoc{ot^.s]jh_#mn_‡mvZ’_ uv_žr_q_A±ri£kmvfhotq*^co x _Oj2ŽPy._|Pmn~nk_O±Pi’kwmvfhotq’uO«Y[Z’_Ouv_‚{#ori]jx

Ž9_mnZ]_.{#otq£uz_O~vžkmnfporq$_O±Pi’kmnfporq$¤¥ot~‚mvZ]_ªqgi]^Ž9_~ ow¤Hs’kt~zmnfh{jp_Au‡s9_~ i]q]fpm žrotjhi]^._t¨9²!Z]fl{'Zûfhu‚q]_O_ x _ x

¤¥or~SmnZ]_a{kwjl{#i’jhkwmvfhotqot¤émvZ]_ s’kw~vmvfl{#jh_ x fhkt^c_mv_O~O¨ x ~'kw“ˆ¤¥or~n{_t¨P_#m'{w« œ _ {Okwq*ktjhuvoª{otq’uvfx _~HmnZ]_ ^cfl{#~now¡

^kr{#~no${oti]s’jpfhq]“T_#¯2_O{#mnuªjpf?t_Ž’i]Ž]Ž]jh_s]i]jlunkmvfhotqµ¨s’kt~zmnfh{jp_~nowm'kmnfporq©¨s9ot~n_{#orjpjlkws£uz_r¨µ_#m'{w«h¨uz_O_$8E:¢¨

8hA‹*:¢«dgi’{'Z.mygs9_‡ow¤éuzyCuzmv_O^fhqPžrotjhžt_Au(^cor~v_!_A±Pi’kmnfporq’u¨tŽ]iCmS~n_^kwfhq’uZgygs9_~nŽ£orjpfl{[kwq x Z’kru(mvZ’_®uvkt^._

uzmv~ni’{#mvi]~n_t«

Y[Z]_s’kts£_O~fluµor~v“Pkwq]f7_ x ktuµ¤¥otjhjpo²‡uO«©¬¦q.dg_O{#mvfhotqc‹‡²³_³Ž]~nfp_Œya~v_OžPfh_²¸mnZ]_^.kwmvZ]_O^kmvfl{ktjr^.o x _Oj<«

dC_O{-mnfporqF‘*fhu x _Ožtowmn_ x mno*mnZ]_ x fhun{#i£uvuvfporqûotq¼mvZ]_cq]_A{#_Ounuvf°my$ow¤{#otq£uzfx _~nfhq]“mvZ’_ªq]orqC¡¦{#otq£uz_O~vžkmnfpžr_

mn_~n^u«Sdg_A{-mnfporq’u!`w¡ x _Oun{#~nfpŽ9_amvZ’_ˆqPi’^c_O~vfl{ktjé^._#mvZ’o x ¨£kwq x dg_A{-mnfporqûŒc{otqPmnktfpq£u!uzor^c_aqgi]^._~nfl{kwj

_|]kw^.s]jh_OuO«

(8)

! ‡/)a/ ‡

µ_#mi’u x _q’owmv_.mnZ]_“Pktuˆkwq x jpfl±Pi]fx s]Z£ktuv_²!f°mnZ¸mvZ]_*uvi]Ž’un{#~nfhsCmnuFkwq x ¨µ~n_Ouvs£_A{-mvfhžt_Ojpyr¨ktq x mvZ]_

fhqPmv_O~z¤7kr{#_Ss£kw~'kw^._#mn_~'ué²!f°mnZmnZ]_[uzi]Ž£uv{~vfhsCmzfhqrm '«©_m[Ž9_SmnZ]_³žrotjhi]^._H¤¥~'kt{#mvfhotq’uO¨!mvZ]_^kmv_O~vflkwj

x _q’uvf°mnfp_Au¨mvZ’_s]~n_Ounuzi]~n_OuO¨Ckwq x

!

mnZ]_uvs£_A{#f4£{ mvotmnkwjµ_q]_O~v“rfp_Au¤¥ot~#"$%& «HY[Z]_

s£kw~'kw^._#mn_~'u(' kwq x*)ûx _#mn_~n^cfhq]_‚mvZ]_ ~n_jlk|]kmnfporq~nkwmv_OuSow¤µžr_jhoC{#fpmvfh_OuSktq x s’~v_Auvuvi]~n_Ouot¤©mvZ]_ s]Z’kruz_Au¨

uv__ 8h<:­«.¬¦q 8p*<:¢¨µmvZ]_c¤¥orjpjho²!fpq’“ x _4’q]fpmvfhotq£uˆkw~n_ªs]~nots9oruv_ x ¤¥ot~amnZ]_.fpqPmn_~v¤7kt{#_.s]~n_Ounuvi]~v_+-,/.10Hkwq x

žr_jhoC{#fpmy*2 ,3.10¨

,3.10 4-4567879&

2:,3.10; <=-4>4?4@6731787=A

<B4C4@67817=AED

´A¶

F®mnZ]_~({'Z]orfh{_Oukw~n_³s9orunuzfhŽ]jh_³kr{{#or~ x fpq]“®mvo‚mvZ]_s]ZgyCuzfl{ktjPuvfpmvi’kwmvfhotqot¤’fhqrmn_~n_OuzmO«(Y[Z]_qmvZ]_“tožr_~nq]fhq]“

_A±Pi’kmnfporq’u³¤¥ot~[mvZ’_ˆotq]_¡x fh^._q’uvfhotq’ktj©{#ot^.s]~n_OunuvfpŽ]jh_‚m²³ot¡¢s]Z£ktuv_®Å’o²Lkw~n_"8h<*:

F 4

FG

62 ,3.H0 F 4

FJI

) <= 4LK 7A

F 4 4

FG

F 4 4 4

FI

M

F 4?14>4

FJG

F 4 4 J

4

4 4

FJI

-,/.10

F -4

FJI

6'N<O 7JK 4 A

F 4?4 4

FJG

F -4?4 <B14 454HA

FJI

-,/.1082:,3.10 F 4

FJI

P'Q<B 7JK 4 AR2S,3.H0

K) ,/.10<B 4TK 7A

F

-737

FJG

F

7317UJ7

FI

M

F 7 7 7

FG

F 7 7

7

6 7 7

FI

K ,/.10

F 4

FJI

K 'N<O 7K 4 A

F 7 78#7

FJG

F 7 7<B 78T7 6 7A

FJI

K ,/.102 ,3.10 F 4

FJI

K 'Q<B 7JK 4 AR2 ,3.H0

)

,/.10

<B 4TK 7AVD

´<‹t¶

Y[Z’_ _A±Pi’kmnfporq’ua´<‹t¶kt~v_a{#jhoruv_

x

Žgy.m²³o._O±Pi’kwmvfhotq’uot¤uzmnkmn_´

*

Fad]¶#¨CZ]_~n_a²³_ai’uv_ mvZ]_

'WG X )

Y[Z ¨]kwq x mvZ’_uvkwmvi]~'kmnfporq {otq’uzmv~'kwfhqPm³¤¥or~[mvZ]_ˆžrotjhi]^._‚¤¥~'kt{#mvfhotq’uO¨

<O\ KP] AB K \ ^J & ´7‘r¶

4 6

7 ] &

(9)

²!Z’_~n_ \ kwq x ^

kw~n_{#orq’uzmnkwqPm'u¨éuvs£_A{#f4£{¤¥or~‚_Akt{'Zûs’Z’ktuv_t«@H]or~a“rktu®²³_ªmnk.?t_ \ 4 ] D ¨ ^ 4 M]¨

¤¥or~!jpfl±Pi]fx \ 7 D ¨ ^ 7 ] M }k’«H„‡qgyotmvZ]_O~‡{#otqgžr_#|_O±Pi’kwmvfhotq ow¤uzmnkwmv_a^k§yŽ9_ˆi’uz_ x ¤¥or~[mvZ]_

mnZ]_~n^.o x ygq’kw^.fl{kwjé{jpoPuzi]~n_aow¤mvZ]_ˆ^.o x _j¢«

¬¦q ot~ x _~³mvo.fhqgžt_Ouzmvfh“rkwmv_®mvZ]_a^kmnZ]_^kmnfh{Okwjéuzmv~ni’{-mni]~v_aot¤³´<‹r¶Sfpm!fhu!{otqgžt_Oq]fh_qPmSmnoc~n_²!~nfpmv_ f°m!fhq

s’~vfh^.f°mnfpžr_ žkt~vflkwŽ]jh_OuO¨

F

FG

F

FI

& ´¥`P¶

²!Z’_~n_

<B4H&V141&VJ4H&V41& 7R& 7R&V7RAV& ´<t¶

mnZ]_ˆžt_A{-mnot~¸{#orqPmnkwfhq’u³mvZ’_ˆq]otqC¡x fp¯9_O~v_OqPmvflkwj©uvoti]~'{#_‚mv_O~v^uO¨]kwq x mvZ’_ˆ^.kwmv~nf°| fhu[“rfpžr_q$ktuO¨

2S,3.H0 M M M M M M

<O 4TK 2 ,/.10A 4 4 M M M M

,3.10

M 4 ] 4 M M M

,/.10

<B 4#K 2S,3.H0BA M 4! 4 4 M M M

K #"

$"

<O7

K 2 ,/.10A M M M 7 17 M

K "

,/.10

$"%&"

M M M M 7 ]

7

K

#"' ,/.10(

"

"

<O 7JK 2 ,3.H0A M M M M 7) 7 7

*+

++++++++++++

, & ´

²!Z’_~n_

.-#/

/ K10!2

/

0 / 333

-#/

0!2

/

0

-#/

333 /

kwq x

,/.104

,3.10

/ K50!2

/

0 / 333

-/

062

/

0

-/

333 /

kt~v_mvZ]_.uvoti]q x uzs9__ x u‚¤¥ot~ mvZ’_ªs]Z£ktuv_+"¼kwq x ¤¥ot~ mvZ]_cs]Z’kruz_ "ûkwm‚mnZ]_.fpqPmn_~v¤7kt{#_r¨2~v_Auzs9_O{#mvfhžt_jhyt«„

uzmv~'kwfh“tZPmv¤¥ot~n²kt~ x {ot^.s]iCm'kmvfhotq “tfhžt_Au[i’umvZ’_a¤¥otjhjpo²!fhq]“._#|Cs]~n_Ounuzfhotq£uH¤¥or~[mvZ]_uv_žr_q _fh“t_qgžkwjhi]_Au

' 72

,3.10

&

' 4 C4 & '98L 4K: 4 & '<;L 4 &

'<=# 7 7 & '9>L 7JK? 7& ' @# 7D

´¢Œw¶

Y[Z’_a{ot~n~v_Auzs9otq x fpq’“ª~nfp“rZPm[_Ofp“r_qgžt_A{-mnot~'u³kt~v_

A 7 BCCCCCCCCCCD 4 7E 7 E KGF17)E

<B 4 <E 7 K:

,3.H044 A 4TK ,3.10AE&

7)E

<B 4#K 2 ,/.10AV<= 4LK ,3.H0 K 4!

,/.104

4 A 4 &

F 7E

<B14

,3.10(4

4

<O4 K 2 ,3.10A K: 4

<B4 K ,3.10AVAV&

KGF146E 7<O 7 <

,/.1047 K:E

A K 7 6 ,3.10A

46E 7 <O 7JK 2 ,/.10AV<K 7 6 ,3.10 7(

,3.10(4

7A 7&

F 4 E 7 < K 7

,3.1047

<BJ7 K 2 ,3.10A 7

<B7 K ,3.H0A A HJI

IIIIIIIII

K & ´Lr¶

(10)

A BCCCCCCCCD M 4

4

46 4

MMM

HJI

IIIIIII

K & A 8 BCCCCCCCCD M 4

KG 4

46 4

MMM

HJI

IIIIIII

K & A ; BCCCCCCCCD M]

MMMMM

HJI

IIIIIII

K & ´r¶

A = BCCCCCCCCD MMMM

7

7

7) 7 HJI

IIIIIII

K & A > BCCCCCCCCD MMMM 17

KG 7

7) 7 HJI

IIIIIII

K &A @ BCCCCCCCCD MMMM]MM HJI

IIIIIII

K & ´zOr¶

²!Z’_~n_

E 7T

4 K <O 4TK 2 ,3.10A & E 7 K <B 7JK 2 ,3.10A D

Y[Z’_~n_#¤¥ot~n_t¨rmvZ’_ uvyCumn_^ ´<‹r¶HfluZgyPs9_~nŽ9otjhfh{t¨P²!Z’_~n_žt_O~HmnZ]_a_fh“t_qgžr_O{-mnot~'uHkw~n_®jhfhq]_Okt~vjhy.fpq x _s9_q x _OqPmO«

owmn_.mvZ’kwmˆmvZ]_*uvyCumn_^ ´<‹t¶ fluˆq]otmumn~vfl{-mnjpyFZgyPs9_~nŽ9otjhfh{t«¬¦q x _O_ x ¨(uzfpmvi£kmvfhotq£uˆkw~n_s£oPuvuvfpŽ’jp_r¨µ²!Z]_Oq

uvot^._ot¤rmnZ]_H_fh“t_Oqgž§ktjpi’_Ou2ow¤PmvZ’_H“rkru2s]Z’ktuv_H{ktqˆ{#otfhq’{fx _²!fpmvZuvot^._ot¤rmnZ]_Hjhfh±Pi]fx s]Z’ktuv_t«(ƒ$ot~n_ožr_~A¨

fpmflua_Oktuvy$mvoTuv__cmvZ£kmˆmvZ’__fh“t_qgžr_O{-mnot~'uª´Lt¶­¡-´Ar¶‚Ž9_O{#or^._jpfhq]_Okt~vjhy x _Os£_Oq x _qPmfhq mvZ]_.s9otfhqrm'uˆfhq

mnZ]_aŒo²ˆ¨C²!Z]_O~v_ˆktqPyorq]_ˆow¤({#orq x fpmvfhotq’u

4 %M:& -7Q M:&

E 7 M:&ÿot~

E

%M

Z’otjx

¬¦q mvZ’fhu[²ot~ ?²³_ x orq m®{#otq£uzfx _~mnZ]_ˆ^ktunuktq x {#orqPžr_O{#mvfhžt_®Z’_Okm[mn~nktq’u¤¥_O~[mv_O~v^uO¨C²!Z]fh{'Z Z’k§žr_

q’ofh^.s£or~zm'kwq’{_ª¤¥or~ mvZ]_ x _Auzfh“tq ow¤³mvZ]_.Zgygs£_O~vŽ9otjhfh{cuvotjhžt_~A«Y[Z]_.~n_Ok x _~aflu‚~n_#¤¥_O~v~n_ x mvo 8h`:¤¥or~ak

x _Oun{#~nfpsCmnfporqot¤uvi’{'Zmv_~n^u«

owmv_*mvZ’kwmmnZ]_*Zgygs£_O~vŽ9otjhfl{#fpmy¼ow¤!mnZ]_*^.o x _Oj³fluorq]jpy¸kû{otq’uv_O±Pi]_Oq’{#_ot¤[mvZ]_ {#ot^.s]~n_OunuvfpŽ]fhjhf°my

ot¤mvZ]_Œi]fx uO«LF‚q]_c{kwqF{#otq£uzfx _~®owmvZ’_~aktunuzi]^.sCmnfporq’u‡orqTmvZ’_fhqrmn_~v¤7kt{_s’kw~'kw^._mv_~'u´zA¶®²!f°mnZ]otiCm

jhoruvfhq]“ªZgygs9_~nŽ£orjpfl{#fpmyt«

(11)

e)+/*/’3³ª/* ! )a+!( Fµ)/

œ _H²!fluzZ mno‡uzZ]o²FmvZ’_Hfp^.s9ot~vmnktq’{#_ot¤rmnZ]_Hq]orqC¡­{otq’uv_~nžkmnfpžr_µmn_~n^.u©ŽPy i’uvfpq’“[mvZ]_¤¥orjpjho²!fhq]“[s]Zgyguvfl{kwj

s’~vfhq’{#fhs]jh_ x i]_amno„‡Ž]“r~nktjpj18h : =SkcŒo²ˆ¨]i]q’f°¤¥or~v^ fpq$žt_OjpoC{f°my*ktq x s]~n_Ounuzi]~n_t¨C^ªi’uzm‡~v_O^.ktfpq i]q]fp¤¥ot~n^

x i]~vfhq]“fpmnu®mv_O^cs9ot~'kwj_žrotjhiCmvfhotq©«¬¦qûotmvZ]_O~‡²³or~x u¨£i]q x _O~‡mvZ’_i]q]fp¤¥ot~n^.f°my${#orq x fpmvfhotq’u®otqTžt_OjpoC{f°my

ktq x s]~v_Auvuvi]~n_t¨Ck{#orqPmnkt{#m x fhun{#orqrmnfpqgi]fpmy^ªi’um‡Ž9_ˆs]~n_Ouv_~nžt_ x «

C³orq’uzfx _O~mvZ]_®^.kruvuSkwq x ^.ot^._Oqrmni]^ {#otq£uz_O~vžkmnfporqª_A±Pi’kmnfporq’u¤¥ot~³otq]_!ot¤9mnZ]_‡s]Z£ktuv_OuO¨t²_!ot^.f°m

mnZ]_uvi]Ž’un{#~nfpsCmor~ ¤¥or~!Ž]~n_žgf°myr¨

F -

FG

F -1

FJI

MS&

F -H

FG

F -H(

FI

? ,/.10

F

FJI

D

´ztA¶

…®_~n_*mnZ]_$s’kw~'kw^._mv_~

]

¤¥ot~.oti]~.^.o

x

_j!ktq

x

M¼¤¥ot~cmnZ]_$^co

x

_Ojhuc²!fpmvZ q]_“rjp_A{-mn_

x

q’otqC¡

{otq’uv_~nžkmnfpžr_³mn_~n^u 8`E:­¨8óŒ :­«µ_#mi’uSuvZ]o² mvZ’kwm³²!fpmvZ.mvZ’_‚uv_O{#orq

x

{'Z]orfh{_!ow¤  mvZ]_‚uzyCuzmv_^

x

og_OuSq]owm

s’~v_Auz_O~vžr_‚{#orqPmnkt{#m x fhun{#orqPmvfhqPi’f°mnfp_Au«

¬¦q x __ x ¨ x fp¯9_O~v_Oqrmnfhkwmvfhq]“T´rA¶³otiCmA¨]²_ Z£k§žt_

F -

FG

F -

FJI 6N

F

FJI

MS&

F -

FG 6N

F

FG

F -

FJI 6N

F J

FJI 6

F

FI 6

F

FJI

?

,/.10 F

FJI

D

0‚uzfhq]“mvZ]_.ktunuvi]^.sCmvfhotqFow¤HmnZ]_ªi’q]f°¤¥or~v^%žr_jhoC{#fpmy$ktq x s’~v_Auvuvi]~n_64’_Ojx kwq x mvZ]_c_Ouzmvfh^kmv_Au.´A¶#¨é²³_

“r_#m

,3.10 %5& 2 ,3.10 &

F -

FG

F -

FJI

MS& ´zA‹t¶

F

FJI

MS& ´zO‘r¶

F

FJI

MSD

Y[Z’fhu[fh^.s]jpfh_Ou!mvZ’kwm

- F

FG 6

F

FJI C

F

FJI

D

¬­m®kts]s9_Okw~'u[{#jh_Okt~vjhy.mvZ’kwm‡fpq$or~ x _O~¤¥ot~[mvZ’_aŒo² mno~v_O^.ktfpq i]q]fp¤¥ot~n^ ²!fpmvZ$~n_Ouvs£_A{-m[mvožr_jhog{f°myr¨Cf<«_t«

F

FG

%M:& ´z`P¶

fpm‡flu[q]_O{_Ounuvkt~vy.mnZ’km

[ ] D

(12)

Y[Z’_akruvuvi]^.sCmnfporq Mcflu!žkwjhfx otq’jpyfhq mvZ]_ˆs£kw~vmvfl{#i]jlkw~!kwq x žr_~ny~v_Aumn~vfl{-mnfpžr_ {Oktuv_aow¤

F

FJI M:D

C³orq’uzfx _O~!q]o² mnZ]_ˆ_q]_O~v“ry_O±Pi’kwmvfhotq©¨gmno{'Z]_O{?.mnZ’km!mnZ]_ˆs]~n_Ounuzi]~n_ _žtorjpi]mvfhotq fhuK7O_~noªmnogo’¨

F -

FG

F -<=N A

FI

> ,3.10 2 ,/.10 F

FJI

D

!‚fp¯9_O~v_Oqrmnfhkwmvfhq]“.otiCm®ktq x i’uzfhq]“cmvZ’_ˆi]q]fp¤¥ot~n^cfpmy*ot¤žr_jhog{f°mykwq x s]~n_Ounuzi]~n_t¨g²_ˆ“t_m

N F

FG 6-H

F

FI 6[

F

FJI

C[

F

FJI

D ´z<t¶

2y¼´z`r¶orq]_aZ’ktu

F

FG

F

FG

&

uvoT´*<w¶Ž£_A{#or^c_Au

N

G 6[

F

FJI

>[

F

FJI

&

²!Z’_~n_ G F

FG F

FJI «dgfpq£{#_ 1<B5& Av¨

G F

F 3333

G F

F 3333 G &

ktq x ŽPyF´O‘P¶-¨

G F

F 3333 F FG

F

F 3333 G D

0‚uzfhq]“cmvZ’_k x žr_O{-mnfporq_A±Pi’kmnfporq¤¥ot~‡mvZ]_ažtorjpi’^c_ ¤¥~'kt{#mvfhotq

F

FG

F

FJI M

ktq x mvZ]_{otqPmvfhqgi]f°my*_O±Pi’kmnfporq ´zA‹w¶²_a“t_m

F

FG

F

FJI MS&

uvocmvZ’kwm

G

%M

Z’otjx «Y[Z]_ˆ_q]_O~v“ry_O±Pi’kwmvfhotq Ž£_A{#ot^._Au

- F

F 3333 F FG

6[

F

FJI

?[

F

FJI

&

(13)

²!Z’fh{'Z$um'kmn_Ou!kw“Pkwfhq*mnZ’km

F

FG M

orq]jhyf°¤

[ ] D

Y[Zgi’ucmnZ]_ Œo² ~n_^ktfpq’uci]q’f°¤¥or~v^ ²!f°mnZ ~n_Ouvs£_A{-m.mvo mnZ]_Tžt_OjpoC{#fpmy½kwq x s]~n_Ounuvi]~v_ otq’jpy½²!Z’_q mvZ]_

q’otqC¡¦{#orq’uz_O~vžkwmvfhžt_‡mn_~n^u!kw~n_a{otq’uvfx _~n_ x «

owmv_mvZ£kmcmvZ]ori]“tZ fpq»mvZ]_T{kruz_ow¤‚k x fluv{otqPmvfhqgi]oti’uŒo² mnZ]_T{#jlktunuzfl{ktj x _O~vfhžkmvfhžt_Aui£uz_ x fhq

mnZ]fluuz_A{-mnfporq¸kt~v_.q]otm x _4£q]_ x ¨²_{kwq “t_mˆmvZ]_*s]~v_A{#_ x fpq’“ ~n_Ouvi]jpmfpq mnZ]_*uv_q’uv_.ow¤ x fhuzmv~nfhŽ]iCmvfhotq£u«

dC__ˆdC{'Zg²kt~zm 78h *:2¤¥ot~mnZ]_a“t_q’_~'kwj]mnZ]_or~vyot¤ x flumn~vfhŽ]iCmnfporq’uO«¬¦q x __ x ¨]ktunuzi’^cfhq]“mvZ]_ažt_OjpoC{f°mykwq x

s’~v_Auvuvi]~n_G4’_Ojx u[mvo.Ž9_ˆi]q]fp¤¥ot~n^ ¨C²_{ktq~n_²!~nfpmv_ mvZ]_uvyCumn_^´ztO¶fhqTkc²³_AkE?*uv_q’uv_t¨

¨-Q ¨NQ

<I &VM:A= <I &VM A=<I &EM A I M ´z

¨NQ

¨NQ

¨ K

¨ Q

<I

&VM:A= <I

&VM A=<

I

&EM A I M:& ´z§Œw¶

²!Z’_~n_

7

<7¬†M:&AHfhu!kªmn_Ouzm!¤¥i]q’{-mnfporqTkwq x

¨ I G D

ƒTi]j°mnfps’jpygfhq]“û´ t¶Žgy$ûkwq x uvi]ŽCmn~nkr{-mvfhq]“cmvZ’_ ~n_Ouvi]jpm!¤¥~vor^´Œ¶-¨’otq]_a“t_mnu

!

¨- ¨ D

0‚uzfhq]“ckw“rktfpq.mnZ]_ i]q]fp¤¥ot~n^cfpmy.ow¤µs’~v_Auvuvi]~n_®kwq x mvZ]_‚¤7kt{#m³mnZ’kmmvZ]_‚_O±Pi’ktjpfpmy.^i’uzmZ’otjx ¤¥ot~_žr_~ny ¨

orq]_aq]_O{_Ounuvkt~vfhjhy“t_#m'umvZ’kwm

[ ] D

(14)

& !(#3)¸

H’otjhjpo²!fhq]“ 8p*<:­¨]²³_ai’uv_amvZ’_dPmv~'kwq]“.uvs]jpfpmzmnfpq’“.mv_O{'Z’q]fh±Pi]_a¤¥or~[mvZ]_ˆqgi]^._O~vfl{ktj2uvotjhiCmnfporqot¤[´¢‹t¶ =

7

&

²!Z’_~n_

fhu[mnZ]_ˆžt_A{-mnot~[ow¤(um'kmv_ˆžkt~vflkwŽ]jh_Ouorq kc^._OuvZT{#_jhj³ktq x mvfh^c_

G

¨’f<«_t«

<= 4 &V 4 4 &V 4 4 4 &E 4 4>#4 &E 7 7&E 7 7 7&V 7 7U#7AV&

fhuˆmvZ]_ors£_O~nkwmvot~aot¤³qgi]^._~nfh{OkwjHuvotjhiCmvfhotq ow¤mvZ’_ZPygs9_~nŽ£orjpfl{cs’kw~vmˆow¤mvZ]_uvyCumn_^ ´¢‹t¶#¨kwq x

flucmvZ’_ ors£_O~nkwmvor~ªot¤‚fhqrmn_“r~nkwmvfhotq»ot¤®mnZ]_Tuzori]~n{_ ktq x ~v_Ojhkw|Ckwmvfhotq mn_~n^u« …‡_O~v_$²_¤¥oC{i’u.otq mvZ]_

Zgygs9_~nŽ£orjpfl{ors£_O~nkwmvor~2mnZ]_ x _#m'kwfhjhu otqF~v_Ojhkw|]kmvfhotq¼s]~voC{_ x i]~n_Ou ^k§y$Ž£_c¤¥ori]q x fpq µktjpjh_^kwq x kwq x

d]kwi]~n_j18*:­«

"!# $&%'(# ")+*,#-

Y[Z’_ Zgygs9_~nŽ£orjpfl{ s’kw~vm!ow¤mvZ]_uvyCumn_^´¢‹t¶[{ktqŽ9_ˆ~n_²!~nf°mvmv_q fhqmnZ]_a¤¥otjhjho²!fpq]“ª¤¥ot~n^$¨

F 4

FG

62 ,3.H0 F 4

FJI

M ´z Lr¶

F.

FG

F0/ <. A

FI 21

F 4

FJI

& ´z

²!Z’_~n_ . fhu[“rfpžr_q ŽPy

. <=-4>4 &E-4>4>J4H&V4C4 41&V7317 &V731787R&V737 7=AVD

H’otjhjpo²!fhq]“*mvZ]_cf

x

_Okow¤G8h<:­¨é²_ª²[kwqPm®mno 4£q x k x

fluv{~v_mvf7Okmnfporqûow¤SmvZ]_.q]orqC¡­{otq’uv_~nžkmnfpžr_ˆs’kw~vm ot¤

´¢‹t¶#¨£f¢«_r«mvZ]_mv~'kwq’uvs£or~zm‡_A±Pi’kmnfporq¤¥or~L

4

´z Lt¶®kwq

x

mnZ]_ˆmn_~n^31 0

0

fhq»´z t¶[fhq¼uvi’{'Zûk.²[k§yt¨]mnZ’km

mnZ]_qgi]^._O~vfl{ktjkws’s]~vo§|Cfh^kmvfhotq$mnomnZ]_ªuvyCumn_^ ²³ori]j

x

s]~n_Ouv_~nžt_k*{otqPmnkr{-m

x

fhun{#orqrmnfpqgi]fpmyt« ©_m‚i’u

²!~nfpmv_ x o²!q mvZ’_ˆ“rktuz¡­~v_Ojhkwmv_ x _O±Pi’kwmvfhotq’u!ot¤[´¢‹t¶#¨’ot^.fpmzmnfpq]“.mnZ]_uvi]Ž’un{#~nfps]mT£¨CmnZ]_jhfh±Pi]fx s’kw~vm®{#ori]jx

Ž9_{#orq’uvfx _O~v_ x ktq’kwjhot“roti’uvjpyr¨

F

FG 62

,3.H0 F

FI

M

F -

FG

F N1

FI

M

F N1

FG

F -1J(6-

FJI

,3.10

F

FJI

F N

FG

F -<O 6 A

FJI

N,3.1032S,/.10 F

FJI

D

´¢‹wr¶

µ_#m‡i’u x _q]otmv_Žgy / fhu!mvZ]_s’ZPyCuvfh{Okwj2Œi]|¤¥i]q£{-mvfhotqTot¤[´¢‹wt¶#¨04 uzor^._ x fhun{#~n_#mn_a¤¥ot~n^ ow¤ 0

0

¨£²!Z]fl{'Z

fluSuzmvfhjhj]mvoˆŽ9_ x _#mv_O~v^.fhq]_ x ¨rkwq x .65

<. 7 & .

7 7

A©mnZ]_®žkwjhi]_!ot¤

.

kwjhotq’“‚mnZ]_‡jhfpq’_

I I 7 7

¤¥ot~SmvZ]_

Références

Documents relatifs

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe -

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe -

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe -

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe -

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe -

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe -

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe -

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe -