A Stochastic Particle Method with Random Weights for the Computation of Statistical Solutions of McKean-Vlasov Equations. Part I: Foundation of the Method and Empirical Evidence
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. A stochastic particle method with random weights for the computation of statistical solutions of McKean-Vlasov equations. Part I: Foundation of the method and empirical evidence. Denis Talay — Olivier Vaillant. N° 4326 Novembre 2001. ISSN 0249-6399. ISRN INRIA/RR--4326--FR+ENG. THÈME 4. apport de recherche.
(3)
(4)
(5)
(6) !" $#%& '( )$
(7) *+
(8) ,%-.$/0 1 
(9) *34 1 5 5. &6&5/0 5&#%
(10) *879:;< &#=?>@
(11) (AB<C/ 1 5&#%D E
(12) 4GFH%I%&/# 1 &#J
(13) *6 @ K &# 2( 5 5. $LA 5 (#
(14) D MNPOQSR TVUXWYU[Z]\_^LWYQa`QYNPb%c&UXQSWSWdUXOe fg?h5ikj1lnmoqpri&s?tvu+wxpzyP{Ljw<y}|[wxpzikpv~uwpry}{ j
(15) ~q~whikj~< yPik|?tzj5[j~ xyj5wVikjPu (u||yPw j1xj !g?jx !g?j{XlPmB(y+Pj5i$?jP?m2$|u}}j~. ¡¢5£+¤?¥}¢}¦ ¡¢5£+¤?¥}¢§¨ j0uxjkpz{wjj©~wxj pr{6~wxuwpv~wxpr utª~y}trs[wxpzyP{~k« }¬.y}®<¯° 5±1ju}{ §³² tvu}~y+ j©´su+wxpzyP{~5µ¶({ j?uik|?trjy}®4ikywpr+u+wxpzyP{0pr~ªwgj·Vuprj5 § owyP¸}j~_j´su+wxpzyP{k®ay}.wg?j·}yPwxpr 5p¹wny®unº pr{ 5y}ik|?xj~x~pr?trj_»s?p »y+¼µ ¨ j|?yP|y~ju{$y}xpzPpz{utqu{ j½0 prj5{w {qs?ikj5xpr utinj5wg?y wy yPik|?s[wj ikyPinj{wx~(y}®_~s !g°~y}trs[wxpzyP{~5µ<¾³wVpr~·u0~wy[ !gu}~wpv 1|u}wxpr 5tzj
(16) ikj5wg?y ¼<pzwg°!u{ y}i ¼.jpzPgPw!~5µ<fg?j©~j ¼j5pr}gw!~(uxj j¿{?j wxg?yPs?}gL{?yP{?|u}xu}inj5wxpr ·j©~wxpziu+wxy}!~<y®_ukxj5Pj©~~pzyP{%®as{ ÀwxpzyP{4ÁXu}{ yP{Pj5 wxg?js?{ 5j5wxu}pz{wy}{wxg?jpz{p¹wxpru}t4 y}{ p¹wxpzyP{Ly®wxg?j
(17) yP{~p jj j©´su+wxpzyP{4µ ¾Â{Lwxg?pr~(¿!~w(|u}w(y}®yPs?<¼y}x¸XÁ¼.j|?xy+}j1u{Lj5qpv~wj5{ j
(18) u{ s?{?pv´Psj5{?j©~~<xj~s?tzw<®ay}u 5truP~~y}® {y}{?trpz{ju·~wxy[ !gu}~wpv pzÃXjj{wpvutj©´su+wxpzyP{~&Ädo[ºVÅ.ÆÀÁ4u{ ¼.jn~wxs wg?j$jtruwpry}{ÇXjw¼j5j{Çwg?j©~j {y}{?trpz{ju0o[º·Å_~ u{ ~w!u+wxpr~wpv 5u}t~yPtzs?wpry}{~ny®·wgj° y}xxj~|yP{ pr{?6¯° 5±1ju}{ §³² tvu}~y+Èj©´su+wxpzyP{~5µ fgpr~1xj~s?tzw·®ayPs?{ ~1yPs?~wxy[ !gu}~wpv &|uwpv trjnikj5wg?y Á®ay}1¼<g?pv !g¼j~g?y+¼j©~s?tzwx~1y}®.{qs?ikj5xpv 5ut j5[|jprikj5{wx~yP[wxu}pz{?j ®ayPwg?j
(19) És?x}jx~u}{ wxg?j&ºuqpzj § owxy}¸}j©~ªj©´su+wxpzyP{4µ ÊÇËÌÎÍxÏ&Ð £+Ñ¡}¦. ~wy[ !guP~wxpr ·|u}wxpr 5tzj~[~wxj5iLÁ¯Ç 5±1j©u{qÒ ² tvu}~y+kj´su+wxpzyP{~Á?~w!u+wpv~wpv 5ut4~y}trs[wxpzyP{~. Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex (France) Téléphone : +33 4 92 38 77 77 — Télécopie : +33 4 92 38 77 65.
(20) ;
(21) 5/ & 5-
(22) 4 C/ & , &< & < $/% 5. &5/6-&5/0 5&#% 4 1 5 5Ck/ < < C/ 1 $#%,79.:-< &# n >@
(23) (A°D %@ AV $5 1 5&# E
(24) -F HÇI%&# 1 $#2 . # . (K 5 5Ck/
(25) D.
(26)
(27). . . . . ¡ ¦ y}s~V{?yPs~pr{w j©~~y}{~us[°~y}trs[wpry}{~V~w!u+wxpr~wpv´s?j~&« }¬ ©´su+wxpzyP{~ jk¯Ç 5±1j©u{ § ² rt uP~y+ § yP¸¸Pj5 § _tru}{ !¸Îµ ({j[j5ik|?trj j$ikywxpz+uwpry}{°j©~w1t ´suwpry}{ j$tvu0Py}wpv pzw s{ »sp j pr{ 5y}ik|?xj~x~pr?trj u{~ªs?{ yPs?trj5ikj5{w.|tru}{4µ (y}s~ª|?xy}|XyP~y}{~_s?{?jVi wgy jV{qs?i 5xpv´Psjy}xpr}pr{utrj j5w&j½0 u} j|Xy}s$u||?y[ !g?jtzj©~iky}ikj5{w!~ jwxj5trtzj©~
(28) ~y}trs[wpry}{~µ¾Ât.~ u}}pzw s{?j%i wxg?y j0|u}wxp § 5s?tvuprj~wxyq !gu}~wpv´Psj |yPp ~nu}t ©u+wxy}prj©~5µ .j©~$|Xy}p ~k~y}{w ¿{?pv~ t up j j©~wxpziuwj5sx~n{?yP{ |u!ui wxpv´s?j~ s?{j%®ayP{ ÀwxpzyP{ j }xj~x~pry}{6jwnw!u s?pr~j5{wns?{?j%pr{ 5j5wpzws jL~s?$tvu 5y}{ p¹wxpzyP{ pr{?pzwpvutrj jt Å_º·µ º·u{~ j5wwxj|?xj5ikprh5xj(|uwprj jV{?ywxj(w!uu}pzt{?y}s~_|?xy}s?Py}{~_s?{0 ~s?t¹w!u+w j5qpv~wj5{ jj5w.s?{p § 5p¹w _|Xy}s?s?{?jª 5truP~~j ´suwpry}{~ pzà j{Pwxpzjtztrj~~wxy[ !gu}~wpv´s?j~{y}{trpz{ ©uprj©~u}s
(29) ~j{~ j¯Ç 5±1j©u{4Á j5w{?yPs~ 5ws pry}{~(trj~(xj5tvu+wxpzyP{~<j{Pwxj$ j~ ´suwpry}{~<j5wVtrj~V~yPtzs[wxpzyP{~(~wxuwpv~wxpr´s?j©~ j©~ ´suwpry}{~ j&¯Ç 5±1j©u{ §³² tvu}~y+0 yPxj~|yP{ u}{Pwxj~µ .j
(30) ~s?t¹w!u+w<®ayP{ j
(31) {?y}wxj1i 5wg?y j&|uwpv s?tvuprxj1~wy[ !guP~ § wxpr´s?jPÁª|Xy}s?ntvu}´s?j5trtrj {?yPs~niky}{wxy}{~ j©~$ ~s?tzwxuwx~ j[| prikj5{wxuwpry}{~${qs?i 5xpr´s?j©~n ©utrpr~ 5j©~ |Xy}s<t ´suwpry}{ j
(32) És?Pj5!~ªj5w(t ´suwpry}{ j
(33) uqprj5 § oqwy}¸Pj~.j5{ prikj5{~pzyP{L?µ. ! " % . )~wxuÐ w¢©pv~¡ wxÍ pr¥+´*s?
(34) j©¡ ~ ¦. . # & "" . $". !. % ' (. i 5wg?y j0|uwpv s?tvuprj~wy[ !guP~wxpr´s?jPÁ, ´suwpry}{~ j%¯Ç 5±1j©u{ §³² tvu}~y+ÎÁ~y}trs[wpry}{~.
(35)
(36)
(37) "!#$ %& '()*!+-, . /. . FÎ#&L/%ª $#. u}wxpru}t p¹ÃÎj5xj5{wpvut j©´su+wxpzyP{~kÄS_º·ÅªÆ1¼<pzwgÈxu}{ yPi pz{?pzwpvut_ 5y}{ p¹wxpzyP{Èu}jn|y~~pr?tzjkiky j5tv~V®ay} ~y}ikj yPik|?tzj5 |?gq[~pr ut4|?gj5{?yPinj{uk~s !gLuP~ws?stzj{ j0ÄY~jj}ÁjPµ µzÁX¯Ly}{?pr{ ªu}}try}i;« }¬u{ ² pr~g?pr¸ § s?x~pr¸}y+ « +¬ Ƶ1fgj5°utv~y% 5u}{°j[|?xj~x~u%truP !¸y}®_pz{?®ay}xikuwpry}{°yP{Çwgj$pr{?pzwpvut ~w!u+wxj&y®ªu ~[~wxj5iLÁu}~pr{$¼juwg?j®ayPj© 5uP~wxpz{?nÄS~j5j .g?yPpr{ « ¬ Ƽ<g?jj uwxu·uxj 5y}trtzj© Àwj ®axy}i u¿{?pzwj u}{ xj5tvu+wxpzPj5trn~iutrt{qs?i$j.y}®ikjwjy}xy}try}Ppr ut~wxuwpry}{~µ ® y}sx~j}Á}wg?jj·uxjiu{qn®as?{ wpry}{~ ¿wwpr{?0~s !gLu&¿{?p¹wxj
(38) ~j5w(y®u}tzsj~wxg?j5xj®ayPj1~|u!~j u+w!uny® wj{Ltzj©u wy0~wxu+wxpr~wpv 5u}tiky j5tv~5µ ¾Â{ Xywxg 5uP~j©~5ÁyP{?j% 5u}{ y}{?tr6~pri&s?tvu+wxj0ikju}{ ´Psu{wpzwprj~$y+}j1wg?j~j5w$y®<pr{?pzwpvut y}{ p¹wxpzyP{~
(39) y}® wxg?jiky j5tdµ (y+¼j5Pj5©Áp¹w
(40) pv~1y® wxj5{ pz½ 5s?tzwwyÇj~wpriu+wxj$wxg?j0u} s?!u} 5Çy®s~sut xj5tvu+wxj {sinj § pv 5u}t<ikjwgy ~~s !g3u}~ 5tzy~sjiky j5tv~ÇÄS~j5j}Áj}µ µrÁ¯Çy}gu}iniu p prxy}{?{?j©us « P©¬³Á ² pr~g?pr¸ s?!~pr¸}y+È« }¬³Á y «r5l+¬aÆÀµ y}trtry+¼<pz{?u ´s?pzwj pzÃXjj{wu}|?|?xyPuP !g4Á¼jng?j5xj$|yP|y~jnu{ yPpr}pr{u}t ~wy[ !guP~wxpr V|u}wxpr 5tzj1ikjwxg?y ¼<pzwgL!u{ y}i ¼j5pr}gwx~wxy y}ik|?s?wj. . . "8. . . 1032. 4 576. 90. . :0. ;<:=>?A@9BCED&F
(41) G&H7I JLKNMPORQ SUT I J9V >?BXWYBXZ[@\C4>WE@]^WYB Ä©Æ ¼<gj5xj C pv~ukPpzPj5{wj©~w(®as{ ÀwxpzyP{°u{ V >?BXW_B`Z[@ pv~wxg?j&~y}trs[wpry}{Çy}®u%¯° 5±1ju}{ §³² tvu}~y+j´su+wxpzyP{ ¼<pzwg!u{ y}i'pz{?pzwpvutX yP{ pzwpry}{4µ_Vs?_ikywxpz+uwpry}{0 yPikj~®axy}iwg?j<®SuP Àw_wxgu+wªwg?j(qpv~ 5y}s~ªÉ.sPj5!~. j©´su+wxpzyP{°u{ wxg?jn}ºpr{ 5y}ik|?xj~x~pr?trj&uqprj5 § owxy}¸Pj~<j©´Psu+wpry}{L®ayPwxg?j&Py}wpv pzw Xj5try}{0wy%wg?j 5truP~~y}®ª¯Ç 5±1j©u{ §³² tvu}~y+j´suwpry}{~Á?u{ wxgqs~<guPj
(42) uk|?yPupztrpr~wpv ·pz{wxj5x|?j5wxuwpry}{Lq%ikju}{y}® ~wy[ !guP~wxpr V|u}wxpr 5tzj~q~wji~ÄS~j5j}Áj}µ µrÁo 5{?pzwiu}{È« ¬ Ƶ ¨ j{?y+¼ ¿~y}ikj1{?yw!u+wpry}{Á?u{ yP{~p jwg?j&¯Ç ±1ju}{ §d² truP~y+kj©´Psu+wpry}{. ba. )c. dee h V >?BXW_B`Z[@iOkj h >lLm>?BXWYBXZ[@ V >?BXW_B`Z[@&@(npo hsr >l(vw>?B&WYBXZ[@X@ r V >?BXWYBXZ[@xyB q h W rut f e V h >? z{BXWYBXZ[@ O V{| h >WYW BXZ[@&B ÄY}Æ eg lLm>?BXW_B`Z[@ MPO~} I J >WYB&w@ V >?BX(B`Z[@\])(B lLvw>?B&WYB`Z[@ MPO } I J >WYBXs@ V >?B&(B`Z[@]^(B ¼<gj5xj1u{ uxj
(43) ~inyqy}wgÇu{ Xy}s{ j ®as{ ÀwxpzyP{~<®axy}i r wy &µ y}<wxj !g?{pr ut4xjuP~yP{~¼.j wxg?j5xju® wj_~s?||y~jwxgu+w wxg?j(|XyP~x~pr?trjpr{?pzwpvutX y}{ p¹wxpzyP{~y® ÄYPÆuxj|u!uikjwxpa5j q$j©utrp7a©u+wpry}{~ >Z[@ y}® u0j©ut4+utrs?j xu}{ y}i +uxpru}?tzj ¼<pzwg tru¼kL yP{ j{Pwxxuwj yP{°u0 tryP~j pr{wj5x+ut4y}®#
(44) Á ~xu j B µ o o fg?j|u|Xj5<pv~y}xPu{p7a j uP~®ay}trtzy+¼(~ j ~pz|!~j©w© Á.pvu¼trtzjk?wxg?prj·j»{? ywxpzy}yPs[{%wxtzypr{?®jinwyPgikjLj5w{g?wxj~y}yx® u$y~® wxu wpv ~wxpr utÎ ~yPtzs[5wxPpz
(45) yP{45Á['u { y}®·¼.u}j·{ |?jx}j~y}j5trs[{wwxpzyP~y}{ ik|?j·xy}¸q?{?try+j5¼<iL{ Á j©~st¹w!~
(46) y}{6wxg?j}º pr{ 5y}ik|?xj~x~pr?trj0uqpzj § owxy}¸}j©~1j´suwpry}{4µ ¨ j0wxg?j5{ ~ws È~wxuwpv~wxpr ut ~yPtzs?wpry}{~1y}®.wxg?jiky j5t |?xy}?trj5i ÄY}Æ1u}{ wg?jpz
(47) ikyPinj{wx~µ¾Â{|u}wxpr 5s?tvu©Á4¼.j~g?y+¼ wxgu+w ¾ j5{wxp¹wÈÄ©Æ j¿{?j©~wg?j1¿x~w<inyPikj5{w(y®wg?j
(48) ~wxuwpv~wxpr ut4~y}trs[wpry}{y®<ÄYPÆÀµ. _ .
(49) 7 s $$7 5'{ l. . . oqj 5y}{ Á¼j(|?xy+}j(u}{0y}xpr}pr{ut?|yPu?prtrpr~wpv <pr{Pwxj5x|?xjwxuwpry}{y}®wg?jVinyPikj5{wx~µ fywxg?pv~.j{ Á ¼.jÇ|y+Pj%wxg?jL®ay}trtzy+¼<pr{?6xj~s?t¹w¼<g?pv !g3pr~kpr{wjj©~wxpz{?6pr{3p¹w!~jt¹®µ .yP{~p jkwg?jÇ{y}{?trpz{ju ~wxy[ !gu}~wpv p¹ÃÎj5xj5{wxpru}tj´su+wxpzyP{. de f eg ]> B @ O Q S ¼<p¹ wx g>WYtvuB ¼ @
(50) > w @
(51) >WY@]^#W ]^?L n >] wQ S @&B >W_B @
(52)
(53) #] B{? B | xu}{ y}i,+u}pvu?tr j1pz{ j5|Xj5{ j5{w(y® "! ({ j5(u||?yP|?xpruwjgqq|Xywgj~j~y}{%wg?j1¸}j{j5tv~ V u{ u Á?¼j·~g?y+¼ wxgu+wwgpr~j©´Psu+wpry}{ gu}~. . u s{?pr´s?jL¼ju}¸6~y}trs[wxpzyP{ u{ ¼j j©~ 5prXj%wxg?jLjtruwpry}{ Xjw¼j5j{ wgpr~~y}trs[wpry}{ u{ wg?j iky}ikj5{w j5¿{?j pr{ ĩƵ fg?pr Á¼.j j}j5try}| wgj1®ay}trtzy+¼<pr{?k~wxyq !gu}~wpv V|uwpv trj·ikj5wg?y . . de #%(H $'*& ) K(+ O #%'*$ + & n , & > #0'1$ + & B -'1$ + & @32 ?En , & > 5#%'*$ + & B -'1$ + & @ H('*) K(+ j6. # = fe = - - t - / - =4. # = . # g #%$ & O |# B | ¼<g?j5xj$wg?j ! # B 879;: u}j$pz{ j5|Xj5{ j5{wj©ut Éy+¼<{?pvu{Çiky}wpry}{~µ
(54) fg?jn¼.jpzPgPw!~ uxj j¿{j ®ayPi o {?yP{?|u!uikj5wxpr Vj~wpriu+wyPx~y}®wxg?j1®as?{ wpry}{~ l m u{ l v µ ¨ j~g?y+¼ wxg. u+# w ;< = >?A@9BCED`F G HI J(=K < : o , & = C t #%$ & ?x >. ~w!pzu+{wxu}pr~tztrw}pv 5ÁVu}¼.tj~y}wtrs[j©~wwpry}{wg~jy®{qws?gikj$j5Éxpvs? 5ux}tVj5|!~(ju}®ayP{ iwu}g?{jn j©~%uqy}pr®j5 w§ g?ojÈwxy}|¸Puj~wpvj ´trjÈsuinwpry}j5w{g?~y µ( ¶ ik pz 5wy}wj ik |?tr}s[ÁXwxwpz{?g?j #. ikjwgy pr~{?yw·pr}yPyPs~tr1s~wpz¿j pz{Çwxg?j~j& u}~j~Áu}~y}s?(wj !g{?pr utu}~x~s?ik|[wxpzyP{~(yP{Lwg?j ®as?{ wpry}{~ .u{ j5? trs j.wg?j(~pz{}s?tvupz{wxj5!u} ÀwxpzyP{&¸Pj5x{?j5tv~ 5y}xj©~|Xy}{ pz{(wy·wxg?j<É.sPj5!~ u{ wxg?j
(55) uqprj5 § owxy}¸Pj~.j´su+wxpzyP{~µfgpr~|Xy}pr{w(¼<pztrt4g?yP|j5®as?tztr%Xj1wxjuwj pr{wg?j1®as[wxs?xj}µ. . N. ¾Â{ wg?j6~j yP{ |uwy}®
(56) wg?pv~¼.yP¸]« ¬
(57) ¼jÈ|?y+Pj°j~wpriu+wxj~y}{ w g?j yP{q}j5x}j{ jÇ!u+wxjy}® wxg?jÇuXy+}jLu|?|y[prikuwpry}{ pr{8wji~ky®Vwg?jL{qs?i$j : y}®1~pzi$s?tvu+wj | uwpv trj~ku{ wgj wxpzikj pr~x xjwxp ©u+wpry}{~wxj5| 2 µ. 7a. y?. @BADCFECHGIAKJML. w yyPOyPNQ P%jV R&N%ÁTu}S jm ' > yP V{U wpr@ {prs~.y}wsg~<j·u}~{ jwys®4{?®ap¹s®ayP{ ÀikwxpztryP0{X~.y}®as?yP{ ip j WUky+}wxjy U ¼<Á g?y~j·|uwpvut jpr+u+wpr}j©~ªs| QuS { pv~ ÁÎw®agy}jju[{q|XÇj|? wxxu+y}wxpzu}yP?{kprtzy}pzw|XLj5!inu+wj©yPu}_~s?s?x{ jy j5 y}wx{Ug?j j tvu¼ B Q XKÁ Y Q SMy}[ ®u1pr~Vxwjgu}jnt+j5u[tr|s?j©j À wxuÉwxpry}y+{¼<{?y}pv|Xuj5{k!u+ikwyPywpry}s?{ { Zj5 ! o o wg?j|y s w(ikju}~s?xj Q XKY]\ Î Á S B S %> @ u}j~wxpr wtr0|XyP~p¹wxpzPj·xju}t4 yP{~w!u{wx~¼<g?pv !gÇ 5u}{ !gu}{?}jV®axy}i trpz{j1wytrpz{?jPµ 4. ^0_ ^(`. '1# + . xB.
(58)
(59)
(60) "!#$ %& '()*!+-, .. &/ D. 1 4 &. . &/ &#
(61) *. -K (È<C/% &#. c. . L(. D. L5 5. &#. ¾Â{nwxg?pr~ ~j wpry}{4ÁP¼.j j5¿{?jwxg?j<{?ywxpzyP{$y}®X~wxuwpv~wxpr ut?~y}trs[wpry}{ku{ y}®iky}ikj5{w!~ y®Î~s !gku1~yPtzs?wpry}{4µ ¨ jPpzPj(u}~x~sin|?wpry}{~ªs?{ jª¼<g?pv !g%u
(62) ~wxuwpv~wxpr ut~y}trs[wxpzyP{0u{ ikyPinj{wx~_j5[pr~w_®ay}Å_´su+wxpzyP{ ÄYPÆÀµ fg?j {?ywxpzyP{ y®~wxuwpv~wxpr ut.~y}trs[wxpzyP{ ¼uP~1¿!~wn|?yP|y~j (yP|[®
(63) «r¬pz{ y} j5wxy j©~ 5prj wxs?x?s?trj5{ 5j}µfg?pr~ u}|?|?xyPuP !g
(64) gu}~wxg?j5{kXj5j{k~ws pzj q&~j5Pj5!ut[us?wg?yPx~Á+pz{n|u}wxpr 5s?tru} y}pvu}~«r}¬dÁ y}pvu}~ § fj5iu}i «r©©¬³Á«r¬³Á[u{ %² pv~g?pr¸ § s?!~pr¸}y+« }¬³µ_¶ ~y}ikj5¼<gu+w p¹ÃÎj5xj5{w{?ywxpzyP{%y®~wxuwpv~wxpr ut ~y}trs[wxpzyP{Ègu}~1Xj5j5{ ~ws pzj q ux!uxy u{ ºVs !g?yP{ « +¬·ÄS~j5j0u}tr~ywg?j%j5®aj5xj5{ 5j~·wgj5xj5pr{ÆV®ay} wxg?jpr{qpv~ 5p És?x}j5!~j´suwpry}{4µ .yP{~p j<u{Lj5Py}trs[wpry}{ j´su+wxpzyP{ yP{u~wxpr| WU. . . . . zB ]^l n9l O ].? l
(65) % O |. 8. .
(66) B zB l | P r > VU @sB. ÄSPÆ. l | pr~u$!u{ y}i,+uxpvu?trj1¼<p¹wxgtvu¼ µ F *Ë'(7¢a Ð'w!
(67) #"G%$&@A"(;H' 7IY@* ^ 5*),'s+% 5-E7
(68) &, *)5!#/$.1 032-N4658-
(69) 7s9K4;J :=< b b 5'{?>Ny { L87M L5w & )@ 7 $'w'B$A < 5+[A5 5's5y$\5' b Cl . $ E' D 75 b! | ^
(70) 5 = L 7ONQP{ 55' 'BA <y
(71)
(72) 'wR P{ P
(73) ' S l | P SUTA zB B r > VU @BV 6 W5'1' .A X 7N b 5LP
(74) ' = L 'BA < !#$ %$'{$ _'($' b[w&@& @ $-$"
(75) & r T z{B Y r > V U @ V ^R Z+'s[ @* \ MPO [] S_^ = > 032Ë4C76by¤[% £,ZN` '{
(76) "$*
(77) "?d' c) be6 c,7Y's(5e6 c/2f526' 53<)a 6 L W 's\ 5) , 7N b.[ >NP
(78) { '" s &f @@A79 ^R Z+'BA 's< $ 'u
(79) / . & ,^ \'s 5& 5bA 5L$'bP,
(80) ' ' g .' L $^ 's bC . "7! F * '(7 'w
(81) G @Ah 7i@
(82) \ !+ ^'([A5' ) ^ ${ 55'1 b&6 oqs|?|y~jn{?y+¼]wxgu+wÄSÆ(guP~Vu ~w!u+wxpr~wpv 5u}t~y}trs[wxpzyP{ ¼<g?yP~j&iux}pr{u}tYÁXy} \
(83) 5 5_ 5P
(84) 5' Áuwwprinj ? ~xu+wpv~¿j~ \ ' @ n pn o > ®ayP(~yPikj·pr{wj}j5VNKj B T F G HI J k)#K l l l F
(85) GAH7I mJ k5K >])l_ ÄalÆ o ¾Â{Ç|uwpv s?tvu©Ápz® N O Á¼j&uP~~s?ikjwgu+w(wxg?j&ikju}{°j5{j5x} uw(wprikj ? pv~<¿{p¹wxj}µ y}Vu}{q V NÎÁ o 5y}{~p j5wgjtzpr{?ju}®ay}xi y}{q r > V @+M O9\ r r > VU @ j¿{?j q \ s r fM t Pq r > V v@ uw T F G HI J k)mK x \Rr l48B ty FG&H K >])l_ @ > ¼<gj5xj. r. _ .
(86) 7 s $$7 5'{ . . s r < > ?A@ r > @ V \ r. &a. Éwgj u}s !gq § o[ !gq¼uw pr{?j´su}tzpzwÇu{ ¶V~~s?ik|[wxpzyP{ ÄalqÆÀÁÎwxg?jnu}|?|?trpr u+wxpzyP{ pv~1 y}{wxpz{qs?yPs~5µ j5{ 5j}Á4qÇwxg?j0<prj~ kj|?j©~j{wxu+wxpzyP{°wxg?j5yPjiÁ4wg?jjkj[pv~w!~1u s{?pr´s?jjtzjikj5{w P ~s !g wguw. 8. &a. t q r > V @AB ; < r >?A@AB8tLD F G H r K O T F G HI Jk)\ K x r l 1B ty
(87) F GAH K > ]^l_@ Ä c}Æ r É j¿{?pzwpry}{Á < >?A@ pv~wg?j V § wxg '{ y®wgjinj©u}~s?xj µ ¨ j{?y+¼ pztrtzs~wxxuwrj·wg?j©~j1{?y}wpry}{~pr{wg?j|uwpv s?tvu< 5uP~j1y}®wxg?juqpzj § owxy}¸}j©~j´su+wxpzyP{E . V. . N. B. . \. P. >. dee h 9Z >?BXW_B`Z @iO j Q> >+>?BXW_B`Z @Z9>?BXW_B`Z @X@Ln r 2Z9>?BXW_B`Z @&B | | | q | fe ÄSPÆ O +Z9B ¼<g?jj > N@ O o X > [ j X B . . = A @ B r eg
(88)
(89)
(90)
(91) r q Z9>zBXW_B`Z | @iO Z | >WE @ > ¾³®ªwg?jktvu¼ y®_wxg?jnpz{?pzwpvut_ 5y}{ p¹wxpzyP{°y®VÄYPÆpr~1 5y}{ 5j5{w!u+wxj yP{E = T r V T r V Äapdµ jPµwg?j ~s?~|uP jy®I = T r V T r V y}®®as?{ ÀwxpzyP{~
(92) ¼<pzwg y}ik|uP Àw$~s?|?|Xy}w!ÆÁ .y}{~wxu}{Pwxpz{ u}{ 6¨ s «r+¬4gu}j·~g?y+¼<{%wguw(Å_´su+wxpzyP{ÈÄYPÆ.gu}~uns?{?pv´s?j~w!u+wxpr~wpv 5u}tÎ~y}trs[wxpzyP{%¼<pzwgpz{?pzwpvut4 5y}{ p¹wxpzyP{K µ ¯Çy}xj5y+}jÁ©pz® pr~ 5y}{ 5j5{w!u+wxj yP{nu1 5tzy~j u}tzt[y}® = T r V T r V Áwg?j(~|u+wxpru}t[ y}xxj5tvu+wpry}{~ y}®wxg?j}jtzy[ pzw u}j·xj5tvu+wj wxyiky}ikj5{wx~ÄY~jj ² uprtztvu{w« ©¬aÆ T # >?BXWYBXZ | @ >])Z | @ O ;E< = >?A@&B # >W j >7@4D&F G HI J G KwB 7#O o B q ÄSinj©u{}jtzy[ pzw?Æ B T r >?BXWYBXZ | @ >])Z | @ O r= ;E< r >?A@&B >W"j >7 @ > >W j >7@4DXF
(93) GAHI J G K YFG&H7I J G K ÄSinj©u{¸qpz{?j5wpv 1j5{?jP?Æ > qo . fgpr~xj5|?xj~j5{w!u+wpry}{ iupr{?tz%j[|?tvupr{~y}s?<pr{wjj©~w<pr{L~pri&s?tvu+wxpz{?kiky}ikj{Pw!~5µ ¨ j°{?y+¼ ws?x{3wy6wxg?j ~wxu+wxpr~wpv 5u}t(~wxs 8y®·wg?jÇiky jtj´suwpry}{]ÄYPÆÀµ ¨ j°xj utrtwguw0wg?j s{ jw!upr{Pw6yP{ pr{?p¹wxpru}t( yP{ pzwpry}{~$y®kÄY}Æ&pv~n~s?|?|XyP~j wy6 yPikj%®axy}i u xu}{ y}i |u!uikjwxj5 ¼<pzwg tru¼ ε1¶ ikpzwwj tr}ÁXwg?pv~1u}~x~sin|?wpry}{Çpv~V´s?pzwj$j©~wxpv ÀwxpzPj®ayPi u0|?gq[~pv 5u}t|Xy}pr{wVy®_qprj5¼µ j5Pj5wg?jtzj©~~Á}pzwpv~}jns~j®as?t®ay}{qs?ikj5xpr utXj©u}~y}{~ Pj5{?jxu}tztr}Á}wg?j·tru¼3y}®4wg?jVxu}{ yPiGpr{?pzwpvut 5y}{ p¹wxpzyP{
(94) y®Äd}Æpr~uVikju}~s?xj_y}{nu{
(95) pr{[¿{p¹wxj pzikj5{~pry}{u}t}®as{ ÀwxpzyP{ut[~|u} 5j +wxg?j.|u!uikjwxp uwpry}{ u}tztry+¼(~s~wyxj s j1pzw<wynwg?jtvu¼ y}®u$¿{p¹wxj pzikj{~pry}{ut!u{ yPi +uxpru}?trj}µ yPi {?y+¼ yP{4Á4¼j j{?ywxj$q ]wg?jkyP{?j&wxyLy}{?jku|?|tzpv 5uwpry}{uP~~pr}{?pr{?0wxyÇu{qÇ|u!uikj5wj5 P > µ u{pr{?p¹wxpru}t yP{ pzwpry} { ¨ j {y+¼ |y+PjLwguw%wgj iky j5tV|?yP?trj5i"ÄYPÆkgu}~ u try+¼ <j5q{?yPt ~%{qs?i&Xj5 pz{ wxg?j~j5{~j°y}® ºVj¿{?p¹wxpzyP{°[µr}µ fg?pv~pr~(uk~w!upr}gw®ayP¼u 5y}{~j´s?j{ j·y®wg?j1®ayPtztry+¼<pr{?$|yP|y~pzwpry}{. . j B o o . . > w@+MPO V | > 7B {@. m #"!
(96) "#" )
(97) . £ Ð_Ð ¡ ¢ aÐ. $. z{B o ). - { b 5 WP S mr T r VNB . . $&% ('*),+MP. P S. a. E. mr ).- T r V '(,7&L5 ' >W_BXs@ P r B >W_BXs@ j /10 zB. ÄÆ. 4. ^0_ ^(`.
(98)
(99)
(100) "!#$ %& '()*!+-, . . !
(101) AX7&L5 NQPu R 7 S m '*).- > WU @ ^'( 7^ \ )=L L
(102) 's' ' A 7 6 ,^6 7 032653<56 W '
(103) 7 5 b& ^ $e. ' 'w { u b %7 >W_BX(B{BXl_@ P B
(104) >WYB&w@_j > B&lY@1
(105) n
(106) >W_BXs@_j >
(107) {BXl_@
(108) F >
(109) W"j /
(110) n
(111) j lD
(112) @T> ÄSPÆ " ) y
(113) + b_ L
(114) 's' Z $&% ' > j o B o @ S mr ).- > @ r $ = > @ '( > j o B o @ u aL w&@& @ $-$ )' $ L
(115) 's5'h7 $&% ' w ^$ 'w$'w{b L b's $' = > @ 6 $&% ' { b 5 > > B w@ Y "G ! # HI J(K n p no > l ^ = $ = lV{|
(116) ' 7&L 5T' P j o B o 7N byh P{ 55' dee $ r H $ $ $ K Okj $ $ >lLm >?BXWYB w@ V >?BXW_ B w@X@Enpo $ $ G G >lLvs>?B&WYB {@&@ r V >?B&WYB {@\xyB q t f e V >zBXW_B w@ O V{| >WYB {@AB Ä&%PÆ eg l(m>?B&WYB {@ MPO~} I J >WYB&w@ V >?BX( B w@]^(B l(vw>?BXWYB w@ MPO } I J >WYBXs@ V >?B&(B w@]^(B
(117)
(118) 'wR P{P
(119) ' $' b[a L wAf @Af @$P$ %)' $ h 7 5's" . 5P
(120) 5' Z = ) - > zB @ S T zB B r > @ V B > >7B >7B {@#O M
(121) > S ]O @{> {@ PS m $ r V
(122) !
(123) A S ).m =- $ r ) - > zB
(124) @
(125) a L1L
(126) 's5'Q L& z{B \ a L"7 A S = $':$ 5's S m r $'1\
(127) ^A6. & =L µ ¶~®as?{ wpry}{~Nªu{ y u}j)(4pr|~x !g?pzw&a y}{wxpz{qs?yPs~u{ yPs?{ j Á+wxg?j5xjpr~u·s?{?pv´s?j<~yPtzs[wxpzyP{ wxy1wg?j({y}{?trpz{juªiku}wxpz{Putrj|?xy}?trj5i'¼<p¹wxg0 yqj½0 prj5{w!~ } >W_BXs@Q X >]^s@ u{ } >WYBXs@Q X >])s@ u}{ pr{?p¹wxpru}t y}{ p¹wxpzyP{ V{| >WYB w@]^W ÄY~jjVoba{?p¹wxiu{ « )c¬ Ƶ ¯Çy}xj5y+}jÁPu{q j5{~p¹w V >?B >B w@ ~yPtzs[wxpzyP{ wxynÄ*%PÆpr~wxg?j j5{~p¹wy}®,+ >w@ Á+¼<g?jj.wgj.|?xy[ j©~~ > + >w@X@ | $ - ~uwpv~¿j©~wg?j.®ay}trtzy+¼<pr{?·~wxyq !gu}~wpv p¹ÃÎj5xj5{wpvutj©´su+wxpzyP{ n .(T I J >WYB&s@ V >?BX( B w@]^0 /
(128) 21 H K ] B f dg ] + > w@iO .(T I J >WYB&s@ V >?BX( B w@\])0 /
(129) 21 H K ].?L3 + | > w@ ¼<p¹wxgLtru¼ > w@ >WY@]^W > fgqs~ V >?B > B w@ pv~ u}tr~y6wg?j j5{~pzw y}® > {@ Á(¼<g?jjÇwxg?j |y[ j©~~ %> > w@X@ | $ - ~xu+wxpr~¿j~0wg?j ®ayPtztry+¼<pr{?${y}{?trpz{juo?ºVÅ[ 4 ] > w@iO Q S > >WY B > w@X@
(130) H K ].?Ln Q SR> >WY B > w@X @
(131) H K ] B ÄPÆ > w@ ¼<pzwgLtvu¼ > w@ >WE@\])W > | '. QX. _ .
(132) 7 s $$7 5'{ . Q. fgj5{Lwgj&s?{?pv´s?j5{j~x~(y® X prik|?trpzj©~<wgj&s?{?pv´s?j5{j~x~(y® wxg?j j5{~p¹wL~y}trs[wpry}{Çy}®<Ä*%PƵV¯Ly}xj5y+Pj5©Á ®axy}i Å_´su+wxpzyP{6ÄÆÀÁqwgj1®as?{ ÀwxpzyP{~ u{ ~xu+wpv~®a. l m l v s l(m>?B&WYB w@ ~O Q S >WYB. > {@&@{B Ll vw>?BXW_B w@ O~Q S >W_B >w@X@/> Ä}©Æ Vu}~jpr{?y}°®Å_ 5tr´uPs~~?u}tzSpzwprmr j~ pr{ ÄPW ©µÇÆ1fu{ g? j56(8 uqx|j0y}wug?tv~j©y ~pv~08 }tÄ ÆÀjÁ&y}{ yPj0{PjwxuPpz{q~prs?tzyPs !~g?y}j !®¸[yP~1 wxgj5u+w
(133) }wxg?jpz{ ®as??{µL Àw¾Âpr{y}{ j5~ j lL m Á®auyP{ $ ulL{qv >^B&?BXW_B w@ P z{B r j o B o Á. Q S
(134) > w@Yj > w@
(135) r q Q S 4 T Q S >W_B
(136) > w@&@. ]
(137) r. 4 n q Q S T Q S >WY B > w@&@^] r B q l l rF [HI J G K
(138) ?4j
(139) r n q l l rF [HI J G K
(140) ?Yj
(141) 1> 8j5{ 5j}ÁuP~[V u}{ % u}j (4pr|~x !g?pzw&·a ®as?{ wpry}{~Á
(142) lLmL>?B&WYB {@_j lLm(> )B&WYB {1@
(143) B n
(144) lLv>?BXW_ B w@Yj l(v> ^B&WY B w*@
(145) O
(146) Q S >WY B > {@&@Yj Q S >W_B > {@&@
(147) n
(148) Q S >W_B > w@X@4j Q S >WY B > w@X1@
(149) B Q S
(150) > w@Yj > w1@
(151) q l l rF [HI J G KLn q l l rF [HI J G K
(152) ?_j
(153) > ) fgj5{4Áu}~? > {@ P S m r ).> - @ Áfgj5y}xj5i [c µr}µ % pr{ (4s?{u p(« ¬.~g?y+¼(~·wxgu+w&Å_´suwpry}{ Ä&%Æ·gu}~u = s{?pr´s?j
(154) ~y}trs[wxpzyP{ pr{ S m $ r > zB
(155) @ µ ¨ j
(156) 5u}{%wxg?= j5{ ).- j5¿{?j1wxg?jy}|Xj5!u+wxy} S M > O j o B > ow @v@ wwu SS m $ r MPO > z{>B >B >B
(157) w @T> @ Ä©}Æ V| V| =V ¯Çy}xj5y+}jÁy}~jPjÇwguw > j B @ P S m > @ Z r $ > @ = > @ > @ r > @ µ fgj5{4Áy+¼<pz{Lwy°¶~x~s?ik|[wpry}{ Ä o ÆÀÁo wgj yP¸¸Pj5 § _tru}{ !¸°j´suwpry}{ Ä&%Æ·gu}~$uLs?{?pv´s?j%~y}trs[wpry}{6pr{ SUT z{B Y r > @ V ÄY~jj·jPµ µ&.j~x~j{u+w<j5w<u}t_« ¬dÁ|4µ %PÆÁ?u{ S ]O > j o B o @ S m= $ r ).- > z{B
(158) @ S T z{B Y r > @ V > Éj5®ay}xj<ws?x{?pr{?ny}s?u+wwj5{wxpzyP{wy$wg?j1´s?j~wpry}{%y®4iky}ikj5{w!~.y}®wg?j1~wxu+wxpr~wpv 5u}tX~y}trs[wxpzyP{4Áq¼.j·~w!u+wj u}{ |?y+Pj·u$wxj !g?{?pv 5u}tj}s?tvuxpzwj©~s?tzw<¼<g?pv !g¼<prtrtj{?jj j pz{wgj|?yqy}®y® (4jiniu ?µzPµ. m #" " 's^ b b y=L ' &
(159) $'d2.6 A 7 b )s$'., j o B o uw >
(160) S @w> w@ q T zB Y = > @ V. £ Ð_Ð ¡ ¢ aÐ. "c. . P. # { .$ 5'{$'{{b6. . . P. . 4. ^0_ ^(`.
(161)
(162)
(163) "!#$ %& '()*!+-, . %. & =L µ ¨ j
(164) ~¸Pjwx !g wgj|?yqy}®pz{ ² u}pztrtru}{w
(165) « ¬dµ_fu¸Pj = VB r P j o B o u{ Á[®ay} 74O o y}?Á?~j5w dee V # O V T Rj ?B >B # V B ee l >?A@ O } I J > >7B&s@ >w@\])(B v >?A@ O = T } I J >W_BXs@ >s@]^;V r B ee #m # # V# e # O v# >?A@ h(r n V T q h v# >?A@Yj l #m >?A@ V r h B fe ÄPÆ ee N # O h l #m >?A@Yj hsr v# >?A@&B ee s O T v= >?A@Yj vr >?A@ V h r = n T l rm >?A@_j l m= >?A@ V n q Th v= >?A@Yj h vr >?A@ V h = V V eg n h 5l rm j h 5l m= n hsr v= >?A@Yj hsr vr >?A@ V = > ¶|?|?tr0wxg?j j{iku}{ § ±u} ®ay}xi&s?tvu
(166) wxy0Å_´su+wxpzyP{ÈÄ*%PÆ ®ay}(u{q >?BXWY@ P z{B
(167) Á # #%$ $ x
(168) j T - N # #%$ $ x ] B Q S Ä5lÆ # >WE@iO t V V| t >WE@ MPO V r >WE@Yj V = >WE@ O Q S t V r| t - r $ $ xuj V |= t - r $ $ xLx
(169) j T - N r t r $ $ x ] Äc}Æ '. j[Q S T -. s T r V . j T r t r x ] / ] B ¼<gj5xj pv~wg?j(¯Çu}¸Py+V|y[ j©~~¼<g?y~jpz{?¿{?pzwj~priku}t[}j{?j5!u+wxy}pv~ u}{ ~s !g
(170) wxgu+w W ¯Ly}xj5y+Pj5©ÁuP~9 mr T r V Áq®ay} z{B o B q u{ 4O o y} q Á l l m >?A@ l F HI JsK O l h T I J F > HI J BXsG K @ V >s@]^ l F HI J(K B l h l o[pzikprtru}tr}Á dee l h l F HI J(K Rn np~o B l h l l F HI J(K ~n npo B f e h | - v= >?A@Yj h .rv >?A@ F HI J(K n h | - l m= >?A@Yj h lsrm >?A@ F HI J(K F # HI J(K B l l l l l eg l >s WY@ l l F # HI J(K T V = >WY@ n h V = >WE@ n h r V = >WY@ V /> >. ! #%$ $. $ $. . WP S. >. . #. . . #. .
(171) . _ . .
(172) F. S. . #. $. . . . O. >. . #%$ $. #. . $. #. 7. P. .. $ $. . N. . >. S. ÄPÆ.
(173) 7 s $$7 5'{. ©. c T I J
(174) >WE@
(175) ]^W S > @bT I J Q S V r| t - r $ $ x j V |= t - r $ $ x n T - Q S s T r $ $ V ] ]^W_B O M S > @{>3>?A@Ln >?A@X/@ > Ä Æ ¯Çy}xj5y+}jÁy+¼<pr{?nwy"( 8 q|Xywxg?j~pr~Ä ÆÁ¼j·gu}jutrj©u yP~j5x}j wguw(wgj1®as?{ ÀwxpzyP{~ lLm u{ lLv u}j1y}® 5truP~~VS m r pz{ W u}{ 8 Pt j yP{wpr{sy}s~y}®yP j5 q pz{ ? µ (8 j5{ jwxg?j j5{~pzw >^BX(BA?BXWE@ y}®wxg?jtru¼ y® $ pr~<j5[|yP{?j5{wpvutrtr0yPs?{ j ÄY~jj xpzj o iu{È«z ©c ¬|4µ<© % § c PÆ 0 l l F [HI J G KwB )FS | 0 zB > ^BX(BA?BXWE @ 9S j| ? . j q > W">j [j s@ ?Ar @ / > ÄPÆ ¾Â{%prj5¼ y}®¾Â{?j©´Psutrp¹wxpzj©~VÄPÆÁ}wxg?j1 y}{~w!u{w S | 5u{%j· !g?yP~j5{0s{?p¹®ayPi pr{ P j B µ fgqs~.¼.j o o gu}j T I J Q S V r| t - r $ $ x j V |= t - r $ $ x ])W O T I J T I J
(176) - >s@
(177) >9BX(B&?B&WE@\])
(178) ]^WYB T I J 4
(179) - >s1@
(180) &T I J RS | j ? W V . j q > W">Uj sj @ r?A@ / ]^W ])(B S T I J
(181) - >s@
(182) `]^(B ®axy}i ¼<g?pr !g >?A@ S l`V r| j V |= l F # H7I JLK > Ä %PÆ Éj5®ay}xjj~wprikuwpr{? >?A@ Á ¼.j0yP~j5x}jkwgu+w
(183) wxg?j%gqq|y}wg?j©~j©~ $&% $('ku}{ $&% 'nj{~s?j0wguwÁ®ay} u}{q P j B Áwg?j~yPtzs?wpry}{ V > >7B >7B w@ wyÅ_´su+wxpzyP{ Ä&%Æ1jtzyP{?P~
(184) wy6S T zB B r $ = > @ V ÄS~j5j u}{?{u}x~xu §³² oj~|?oxp_« +c ¬ Ƶ$¯LyPjy+}j5©Á?®axy}i wxg?j j5q{?iu}{ § ±uP ®ayPi$s?truÄlÆVu{ ¾Â{?j´su}tzpzw ÄÆÀÁ ¾Â{Lqprj5¼ y}®wxg?j~jyPs?{ ~u{ y® Å_´sutrpzw Ä }ÆÀÁ[¼j j s j. yP{?j1juP~prtz ~g?y+¼(~.wxgu+w. = $ =. ^.
(185). h V > ?B 7B {@. | $ -. l`V >?B B w@ l F # HI J(K n~npo > . >. h(r V > ?B B w@ 8. > u}{ > ~uwpv~®a0_º·Å_~(~prinprtvuwyLÄ&%Æ.~y$wguwÁ[xj5|Xju+wxpz{ fgj5{%yP~j5x}j(wxgu+w wxg?j
(186) ~xuikj1¸pr{ y® ux}s?ikj{Pw!~u{ s~pz{ q|y}wg?j©~pv~ $ % 'Á?yP{?j 5u}{~g?y+¼ wxgu+w. = $ =. ^.
(187). | $ -. l\V >?B B w@ l G"! # HI J(K n npo > . Y. >. ÄdPÆ. 4. ^0_ ^(`.
(188)
(189)
(190) "!#$ %& '()*!+-, . ¨ 1 j 5u{{y+¼ j~wprikuwj y}®ÄPÆ. T I J
(191) T - Q S s . P. ">?A@ pr{wgj·~xuikj¼u$wgu}{ >?A@ µ ¾Â{ jj Áqs~pr{? ÄPƪu{ . wg?jVwg?pr trpz{?j. T V ] ]^W G T I J T - l l F # HI J(K T I J r h V = >s@ [o j ? ^
(192) ]^Ww]^ | r O T - l l F#XHI J(K T I J h V = >s@ 4 T I J [o j ? ^
(193) G ]^W ])
(194) ] | r T - l l F # HI J(K T I J h V = >s@ ]^
(195) ] | = l V l G ! #AH7I JLK T l l F #`HI J(K ] )B | = =
(196) l V >?B 7B {@ l G"! # HI J(K T l l F # HI J(K ] ^ | $. . . S. #. ,. S. . S S. #. $. S. $. . # . . Y. . . ,. . # . # . #. . ,. > . Y. >. $. ? P z{B Á. >?B >B = @Yj >?B >7B r @ F # HI J(K S . r j = F # HI J(K nUT >^B >B = @Ej >^B >B r @ F # HI JsK ] /"> V V lV | V | l V | V pr{utrtr}Á[¼j j s j·®ayPi,wgj|?jqpzyPs~pz{j´sutrpzwwguw S ]O > = @Yj S ]O > r @ F[H V >?B >B = @Yj V >?B >7B r @ F # H7I JLK O F H I s J K K # . | $- $ | $ S > r @Yj > @ F # HI J(K l - = =l n S T S ]O > @Yj S ]O > r @ F H | $ $ F #`HI JsKK ].? > | S fgj(4pr|~x !g?p¹wAa
(197) yP{Pwxpz{qs?pzwy® ]O wg?j{Ç®ay}trtzy+¼(~®axy}i wgj·yP{q¼u}tzttrj5ikiu0u{ wg?j(pz|~ !g?pzw&a. ¨ j{?y+¼ s~j xy}|Xj5w ÄdPÆu}{ Pjw<wxgu+w©Á[®ay}(u}{. 5y}{wpr{qs?pzw0y®wg?j1®as?{ Àwpry}{5Vµ. iË L65y¤[£, b`
(198) "[
(199)
(200) " ,^ b %5Ay b G. 5e. $A
(201) h Pw{ ''{'26 h<W 's) 5' ,79@Au$' &7 b b 5 L 79
(202) !+[ ) 's' !# $ u' 5<%' $\' 5'{ %' 7 $'w\\,)& fL . . V >?BXW_B w@ O {V | >W_B w@_j T |. _ . . ^ h >l m >^BXW_B w@ V >^BXW_B w@X@b] ^B . . .
(203) 7 s $$7 5'{. . !
(204) A >WE@#Ok> q r ?A@ ^ = . j q W r r ? /
(205) b )5 '(6 V 7 A bs& =L 5's W 'sh P{ P$ ' c <,7+$= b' 1"")5{A b = >?B >7B @Ej >?B >7B r @ F # HI J G K S > @ > >7B @Yj > >7B r @ F # HI J G K > V V Vw| V{| ¾Â{Çqprj5¼ y®_ºj5¿{?pzwpry}{ ?µzu{ yP|y~pzwpry}{Ç[µ ?Á?wg?j
(206) s{?pr´s?j$~w!u+wpv~wpv 5ut~yPtzs[wxpzyP{ y}®(ÄY}Ƽ<pzwg pr{?pzwpvut 5y}{ p¹wxpzyP{K O ^ = pv~ \ M O [] S ^ = O p ] > S ]O @ ^ = > Äd[©Æ \ . fgj
(207) ®ay}trtry+¼<pz{?%|?yP|y~pzwpry}{ÇPpzPj~V y}{ p¹wxpzyP{~Vs?{ jV¼<g?pv !gÇwxg?j&wxpzikjniux}pr{utv~<y® wxg?jninj©u}~s?xj gu}~iky}ikj5{w!~<s?| wyy} jO Nµ £ Ð _Ð ¡ ¢ aÐ '. m #"
(208) "
(209) b 5 b buaL & $' 2.6 A b57)61
(210) "
(211) bA
(212) & 5's"
(213) L
(214) '(' 5 L )HN P% R B Äd}}Æ \T ^ = = l >w@ l 'F G HI JsK >]w@n npo >
(215) ' 7&L 5T' ? P z B 74 b
(216) A +MPO \ ] S b 5 '{ \u&^ N 6 ' & = L6 ¨ j{?j5j wxyk|?y+Pjwxgu+w<wxg?jikjuP~s?xj \ ~uwpv~¿j©~.y}{ p¹wxpzyP{ÈÄSlÆÀÁ?wguw(pr~Á T F G HI J(K l\OV l 'F
(217) G&H7I JLK >] V @ nRpn o > \. É j¿{?pzwpry}{Ly}®. y}{j·gu}~. \. T F G H7I JLKl`VOl F G HI J(K s>] V @iO T F G HI J(K#lVl 'F G HI J(K t p] > S ]O @ ^ = xy>] V @{B = O T = l > S ]O @{> {@ l 'F G HI JsK >]w@ > ^ ¶V~ªpr{wxg?jV|yqy®y}® (4j5ikiu$?µ lÁ}wxg?jV~y}trs[wxpzyP{ > S ]O @{> {@ wynÅ_´su+wxpzyP{ Ä&%Æ_~xu+wpv~¿j~u jq{?iu{ § ±uP (®ayPi$s?tvu?Áq®axy}i ¼<g?pv !gL¾Â{?j´su}tzpzwprj~ÄÆ.u}{ ÄÆjuP~prtztrju wy > S ]O @{> {@ l F G HI JsKK S \ l > w@ l F G HI J(K > l fgj·xj~s?tzw<®ay}trtzy+¼(~.®axy}i uP~~s?ik|[wxpzyP{ÈÄd}}Ƶ ¾Â{Lqprj5¼ y}®Ä}c ÆÀÁ?wg?j1¿!~wikyPinj{w(y®wxg?jikjuP~s?xj pr~wxg?j5{ j5¿{?j q C Pq r > @wBU;<:= >?A@&BACED&F
(218) G&HI J(KiO T I J ; S V{| BACEDXFG&HI J(K >] Vw| @wB = ÄdPÆ O T = ; S ]O > {@ABACED&F G HI J(K >] w @ > ^ '. ¾Â{%y} j5ªwy j}jtzyP|%u{0u}|?|?xyqpriu+wxpzyP{nikj5wg?y y}®wg?jViky}ikj5{wx~Á¼.jV{?y+¼3|?y+Pj(u
(219) |?xy}u?prtzpv~wpv xj5|j©~j{Pw!u+wxpzyP{%y®wg?j©~jikyPinj{wx~µ. 4. ^0_ ^(`.
(220)
(221)
(222) "!#$ %& '()*!+-, .. . 5 4 <<(#
(223) 1 $#. ©
(224) * -K&(#&.D. VsyP[j wpr}j·pr~{?y+¼ wyk}pr}j1u&|yPu?prtrpr~wpv xj5|j©~j{Pw!u+wxpzyP{0y®4wxg?j1iky}ikj5{wx~y}®4wgj1~wxuwpv~wxpr ut ~ y}trs[wxpzyP{°y®VÄd}ÆÁpz{y} j5Vwy jutzj&wyLu|?|?xy[pziuwjwxg?j~j$ikyPinj{wx~·qLu~wy[ !gu}~wpv
(225) |uwpv trj ikj5wg?y µ y}wg?j
(226) ~xu¸PjVy}®~pzik|?trpv pzw}Á[¼j·trprinpzw<y}s?!~j5tr}j~ªwy 5y}{~p j5xpz{?$wgj1¿x~winyPikj5{wµ_fg?j j5qwj5{~pry}{ wykiky}ikj5{w!~y®g?pzPg?j5<yP j5pr~~wxxu}pzPgPw®ay}x¼u} ÄY~jj .y}xy}trtru}0µ lqÆÀµ O y®.Å_´suwpry}{3&Ä %Æ(pv~Vwg?j j{~pzw ¨ jnj© 5utrtwguwÁήayP1u}{q P Áwxg?j~yPtzs?wpry}{ y}®wg?j·!u{ yPi u}pvutzj Á¼<gj5xj ! pv~ªwg?j·¼.j©u¸~y}trs[wpry}{y}®4wg?j1~wy[ !gu}~wpv pzÃÎj5xj5{wpvut j©´su+wxpzyP{ÈÄPƵ (j5{ j}Á?®ay}(u{q0Xy}s{ j u}{ ikj©u}~s?xu}?trj®as?{ Àwpry}{ Á. . . #8. u}{ ¼.j1guPj. > S ] @w> w@ j B > w@ o o $> w@ C ;`> S ]O @{> w@9B9CEDXF
(227) GAHI JsKiO Q SC >% >w@X@sB. = ;\<:=>?A@&BCEDXF G HI JsKiO T = ;X> S ]O @{> {@9BCEDXF G HI J(K >] w@&B ^= O T = Q S C> A> w@X@ >] {@ > ^ fgpr~xj5|?xj~j5{w!u+wpry}{~s}}j©~w!~.wg?j1®ayPtztry+¼<pz{n{ud}j·inj5wg?y y® ~pzi$s?truwpry}{E }µ.y}{~p j5 : = xju}tzpa uwpry}{~ B :y=B y® unxu}{ y}i,+u}pvu?trj ¼<p¹wxgtvu¼ µ o [µ yPjuP !g1pz{?pzwpvutP|u!uikj5wj5 Á+ 5y}{~p j5 : r pYµ pdµ µ!u{ yPi +uxpvu?trj~ # > @ Á¼<p¹wxg& yPikinyP{ | tru¼ > @ >WE@\])W Áu{ j¿{?j·wxg?j|uwpv trj~[~wji% dee ] #0$ & G > \@ O o -& G = #%$ & G > \@{B - $ & G > \@ x ]^? : t r G 7 : B f n o t #%$ & G > @{B - $ & G > @x ] # B Äd+lÆ r eg o -& = : r @> #%$ & G > @ O # > T | | fg?j5{Á G Q S C> > @X=@ < : o , & = C t #%$ & G > @ x > Äd)}c Æ r# fg?pv~&tvu+wwj5nu|?|y[prikuwpry}{6pv~
(228) s?{ j5!~wxyy pr{6wgj%®ayPtztry+¼<pz{°~j{~j^& wxg?jinj©u}~s?xj § u}tzsj |?xyq 5j~x~ = G & G =
(229) ! G yP{q}j5x}j©~
(230) pr{3tru¼Áu}~ : r wj{ ~kwxy6pz{[¿{?p¹wPÁªwxy µ3fgpr~ wq|jy}® 5& y}{q}j# Pj5{ 5j pv~wg?j
(231) ~y 5u}tztrj w&
(232) ,^ 55' aL b ^ µ ¨ j
(233) j5®aj5wy%¯ 5t u « ?À¬y} ob5a {p¹wxiku}{6« ^©c ¬4®ay}®aswxg?j5 j5wxu}pztv~5µ ¨ j1¿{u}tztr0Pjw # G ;<:=>?A@ABACEDXF G HI J(K < : o = , & = : o , & = C t #%$ & G > @ x > ÄdPÆ r# _ .
(234) 7 s $$7 5'{. l. y=. r. : fgpr~u}|?|?xyqpriu+wxpzyP{ pr~k{qs?ikj5xpv 5utrtr }j5x6j[|Xj5{~pzPj}Áu}~np¹wxj´s?prj©~ : ~pzi$s?tvu+wpry}{~$y}® |u+wg~y®(~wy[ !gu}~wpv n|?xyq 5j~x~j©~5µfg?jikjwxg?y ¼<p¹wxg uLi&s !g try+¼.j
(235) y~w
(236) ¼<g?pv !g6pr~ j5Pj5try}|Xj pr{ o[j ÀwxpzyP{0l
(237) xj5trpzj©~_yP{wg?j· yP{~wxs Àwpry}{y}®u
(238) ~wy[ !gu}~wpv <|?xy[ j©~~ª¼<g?yP~j(iux}pr{uttru¼(~.uxj(j´su}t?wy O \ µ¾Â{&prj5¼ y}®Å_´su+wxpzyP{%Ä©PÆu{ Ū´Psu+wpry}{~.Ä}©ÆÁ+u({uws?!ut 5u{ p u+wj pv~wgj¼.j©u¸%~y}trs[wpry}{6Äapz®p¹w(j5qpv~wx~!Æy®wxg?j1®ay}trtry+¼<pz{?k~wy[ !gu}~wpv pzÃXjj{Pwxpru}tj´suwpry}{. > S. ] {@ > w@ >WE@\])W >] w@ E f dg ] O > l( mE> ?B j o B B o@^ @].?LB n Q UlL>Xv9> >?|B B @ B @^] @4O B } > {@ >WE@]^W >] {@AB !u{ y}i,+uxpru}?trj·pr{ j|j{ j{Pw(y}® $B . . P. lm. X. lv. . . P. 5. Z!. . . Äd Æ. . 8. ¼<gj5xj0wgj%®as?{ Àwpry}{~ u{ u}j%wg?jL yqj½0 5pzj{Pw!~&y}®VÅ_´suwpry}{ Ä*%PÆÀµ y+¼.j}j5©Á¼.j 5u}{?{?yw j s 5ju{qs?ikj5xpv 5utinj5wg?y ®axy}i ÄYÆÀµ¾Â{ j5j ÁP¼j 5u}{?{?y}wª~pri&s?tvu+wxj<wgjV~y}trs[wpry}{ky®_Äd Æ_~pr{ j u}{ ¼<pzwg?yPs[w·~y}trqpz{0Å_´su+wxpzyP{ Ä&%PƵ(fy ¼j y%{?yw¸q{?y+¼ wgj$ yqj5½ 5pzj{wx~ y+Pj5! yPinjwg?pv~<|?xy}tzjiÁ[¼j1¼<pztrt4yP~jPjwxgu+w©Á[®ay}(u}{qk®as?{ ÀwxpzyP{ PS S Á. > w@. l m >?BXW_B w@. l v >?BXW_B w@. = Q S [ > !@4O T = Q S > !> w@X@ >] {@AB ^. ¼<gj5xj ! pv~1wgj0~yPtzs[wxpzyP{y}®1ÄÆkÄS~j5jfg?j5yPji?µrkjtzy+¼Æµ |y+Pjwxgu+w ! pv~wg?js{?pr´s?j
(239) ~y}trs[wxpzyP{ y}®wxg?j1{?y}{?trpr{?ju}o[ºVÅ. mE> > z{B B @wB @. ÄdPÆ. xy}i@wg?pv~|?xy}|Xj5w}Á4¼j¼<prtzt. de f eg ]> B @ O Q S ¼<pz w gL>WYtvuB ¼ @
(240) > w @
(241) > WY @]^#W ].?E n >] wQ S @&B >W_B @
(242)
(243) #] {B ? | !u{ y}i +u}pvu?tr j·pz{ j5|Xj5{ j{wy® "!B. Äd P% Æ. ÄY~jjfg?j5yPji ?µ $jtzy+¼Æµ ¨ j{?y+¼ |?y+PjVyPs?( yP{+j ws?xj~µ. . . ËqÐ £ Ë. M"R$" " )
(244)
(245)
(246) 5
(247) aL ' A $5'E2b6 A
(248) 7^6 b'. hP. . $ '; b \
(249) 5 A'w 54 { 55' $ ' _ '
(250) 's' P S m > S > zB B . -. 1L. ' 2 :=< b "
(251) '{RP{ !+ ,) -
(252) 5's6 @{B @ 7. = Q S [ > Q!@4O T = Q S >Q!$> {@&@ >]w@AB ÄY}PÆ ^ !
(253) A !> {@ y
(254) P
(255) ' aL ' c X<% '(,7[ L Q X Y \ 5's_Ly
(256) 7 5! =L b 9&!#'w ' ' Z! 7 Q S [ by ' & 5\5
(257) 's^ b9w&{
(258) & Q X Y]\ 6 ' & =L6 ¨ j°¿x~w{?j5j wy !g?j© !¸ wgu+wwgj°iu|?|?pr{? P j B uw Q S >%!$>w@&@ pr~ (4j5Xj~}sj ikj©u}~s?xu}?trj}µ¾³wpv~<u} wsu}tztr% 5y}{wpr{qs?y}s~Á[u}~|?xy+}j{%pr{ (j5ikiu o c?µzo· ¼<g?y~j1|?xyqy®pv~|y~wx|yP{?j wy. wxg?j
(259) ¶(||j{ pzε. 4. ^0_ ^(`.
(260)
(261)
(262) "!#$ %& '()*!+-, . '. & =LaL. c . . $ 'µV~jPjwxgu+wŪ´Psu+wpry}{6ÄYÆ 5u}{ Xjxj5¼<xp¹wwj5{ÇuP~. f dg ]] OiO z{lLB mL>?B AB &@.]^?En l(v>?B &B A@b] 5 B ÄY?©Æ P > j o B o @B Q XU>&> | B | @ P @ O } > w@ >WE@\])W >] w@ > ¾Â{
(263) wg?j|?xyy}®?y® xy}|XyP~pzwpry}{$?µ Á©¼jªgu}jª~g?y+¼<{wxgu+w#8(q|Xywgj~pr~Ä}Æ4j{~sj©~wgu+wwg?j.®as?{ wpry}{~ l m u}{ l v uxj98}t j_ y}{wxpz{qs?yPs~pz{ ? µ oqprikpztvuxtzPÁ}yP{?jju}~prtzn !g?j !¸wxgu+w+8q|y}wg?j©~pv~(ÄSÆprin|tzprj~ Xy}s{ j {?j~x~<u{ (pz|~x !g?pzw&
(264) a 5y}{wpr{qs?p¹w%pz{ W y® l m >?BXWYB w@ u{ l v >?BXW_ B w@ µ pr{utrtr}Á(j5ikiu0[µ l j{~s?j©~wguw l m u}{ l v u}tr~y1uxj (pz|~x !g?pzw&( a 5y}{wpr{qs?y}s~pr{ µfgqs~ Å_´su+wxpzyP{ÇÄS?ÆÀÁ}u}{ y®X 5y}s?!~j Ū´Psu+wpry}{6ÄYÆÁ?gu}~<uns?{pr´s?j
(265) ~y}trs[wpry}{pr{ tvu¼µ ' & = La L $ '+µ ¨ j1¿x~w<¿? ~y}ikj1{?yw!u+wxpzyP{4µ S3O S > z B B j o B o @ u{ > @ pv~wxg?j
(266) 5u}{?y}{?pv 5u}tÎ|?y[ 5j~x~.yP{ S µ yP<ju} !g P j o B o Á !> w@ j5{?y}wj©~wg?j
(267) 5y}{~wxu}{Pw(u}|?|?trpr u+wpry}{ ? P z B uw µ yP<ju} !g P j o B o u{ u{q®as{ ÀwxpzyP{ t PS r > @ Á?¼j~j5w t_>WY@ O l m >?BXW_ B w@ t>WE@En qo l rv >?B&WYB {@ t >WY@&B ÄYP}Æ u{ Á[®ay}<j©u} !g ®as?{ ÀwxpzyP{ P S r > j o B o @ Á V >W_ B w@iO > > > B w@X@s>WE@ > ÄY}PÆ V~jPj_wgu+w V pr~wxg?j<pz{?¿{?pzwj~priku}t[}j{?j5!u+wxy}y®wxg?j(¯Çux¸}y+1|?xy[ j©~~ %> ! B ! @ Á}s?{?pv´Psj(~yPtzs[wxpzyP{ pr{ tvu¼Gy}®(Å_´su+wxpzyP{ ÄS?ÆÀµL¾Â{ ywxg?j5$¼.yP ~5Áwg?j tru¼Gy® %> ! B ! @ pv~wxg?j%s?{pr´s?j%~y}trs[wxpzyP{ y®wg?j iu}wxpz{?utrj&|?xy}tzjiu}~x~y[ 5pruwj ¼<p¹wxgyP|jxuwyP W Áwguwpr~·wxg?jy}{?trÇ|?xy}u}?prtzpzwÇikju}~s?xj Q X [ yP{ S ~xu+wxpr~®aqpz{?nwxg?j1®ay}trtzy+¼<pr{?n|?xy}|Xj5wprj~ $ ¤ ' Q X [ (>z@ ^ = O >w@ >WY@]^W \ >] w@ Á $ '°®ayP(u{qk®as?{ wpry}{ P S m r > j o B o @ Áqwg?j|y[ j©~~ < ! > 6B @ Á j5¿{?j q. < s> 8B @iO >s>?A@X@Yj >s>z
(268) @&@Ej T >s> )@X@.] 6 ÄYlÆ | pr~u Q X [ § iu}wxpz{?utrj}µ ÉÇs?{pr´s?j{?j~x~5Á4Ū´Psutrp¹w ÄY}PÆV¼<prtztwxgs~1jk|?xy+}j p¹®¼.j~g?y+¼]wguw1wg?jk|?xy}u}?prtzpzwLinj©u}~s?xj Á j5¿{?j q. . . _ . P S. = m > S > zB B j o B o @B @wBU; B D MPO T = Q S %> !$>w@&B $! >w@X@ >] w@&B ^. ^c. ÄY }Æ.
(269) 7 s $$7 5'{. ©. u}tr~yk~uwpv~¿j©~< xy}|Xj5wprj~ $ ¤ '·u{ $ 'µ É j5¿{?pzwpry}{%y}®wg?j·|?xy[ j~x~ ! qÁ ~y}trs[wxpzyP{0y®Åª´Psu+wpry}{ÄÆÀÁ y}qqpzyPs~trk~uwpv~¿j©~._yP|jw $ ¤ 'µÇy+¼'trjw P R&Á P S > > > P Á P S u{ Á?~s !gwguw. V R. zB r. $> w@ m >A> j o B o @ r @ z R?X=9B> > > B ? r. ¾Â{LyP jwy~gy+¼ wgu+w ~xu+wpv~¿j~< xy}|Xj5w. Q S >(>?X=@&B > > >B&(>? r @X@{>\<. ?. . r > j o B o @ U? >. >?X= B B&? r B ^BA?A@. $ '+Á?p¹w(pv~<~s[½0 prj5{w<wy !g?j© !¸wguw > B @Yj < > B @&@ O~zT> . 8. 6. . $> w@. V~jPj$wxgu+w ! pr~
(270) wg?j%pz{[¿{?p¹wxj~pziu}tª}j{?j5!u+wxy}y}®wxg?j%|y[ j©~~ ! µ°fgs~5Áu|?|tzqpr{?Ǿ³w ~ ®ayPi$s?tvu
(271) wxykwg?j1®as?{ Àwpry}{ u}{ s~pr{? j¿{?p¹wxpzyP{~
Documents relatifs
« On ne fait pas que des psychothérapies en clinique/…/On en parlait encore ce matin : est-ce qu’on a le temps de faire des psychothérapies, parce qu’on voit les gens
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des
« La prophétie, ou interprétation et conférence des Écritures se fera par les ministres du Colloque, en l’assemblée où chacun dira la tête découverte ce que Dieu lui
Pendant six ans, jusqu’au premier janvier 1568, le clergé de France doit fournir chaque année au roi l’équivalent de quatre décimes, un million six cent mille livres tournois,
AMC PAPI : Spécificités du contexte torrentiel – Rapport de Phase 1 Page 18 sur 46 Dans le cas des laves torrentielles, on peut résumer les conditions nécessaires au
Gillard, “Combinaison de la DG-FDTD avec un mod` ele de substitution pour un calcul de dosim´ etrie locale dans un probl` eme variable et fortement multi-´ echelle”, dans 18`
Le jugement porté par les femmes lettrées sur leurs soigneurs doit donc être nuancé en fonction de la personnalité de chacune, de la gravité de la maladie,
3.3 Processus d’alimentation d'entrepôt de données : Nous devons extraire, transformer et charger les données à partir des sources précédemment citées, dans l'entrepôt de