Discrete Version of the She Asymptotics: Multigroup ... - HAL-Inria

1 downloads 0 Views 828KB Size Report
May 23, 2006 - Thierry Goudon, Antoine Mellet. Discrete Version of the She Asymptotics: Multigroup Neutron. Transport Equations. RR-4302, INRIA. 2001.
Discrete Version of the She Asymptotics: Multigroup Neutron Transport Equations Thierry Goudon, Antoine Mellet

To cite this version: Thierry Goudon, Antoine Mellet. Discrete Version of the She Asymptotics: Multigroup Neutron Transport Equations. RR-4302, INRIA. 2001.

HAL Id: inria-00072285 https://hal.inria.fr/inria-00072285 Submitted on 23 May 2006

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published 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 destin´ee au d´epˆot et `a la diffusion de documents scientifiques de niveau recherche, publi´es ou non, ´emanant des ´etablissements d’enseignement et de recherche fran¸cais ou ´etrangers, des laboratoires publics ou priv´es.

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Discrete version of the She asymtpotics: multigroup neutron transport equations Thierry Goudon — Antoine Mellet

N° 4302 novembre 2001

ISSN 0249-6399

ISRN INRIA/RR--4301--FR

THÈME 4

apport de recherche

         !" #$% '&(*),+- /. )#  0)  1  2#34 5 6!)27 / 8!9 :=?=A@CBEDGFH DGIKJELKM,IONPDQ:SNPU VXWZY/[]\7^`w _b \tu|Kxdadty}lceju[mvYA~[]fZ\/gij\Ahktjl€cnzm>hvm>opce[][]\hrqZjo gnmr\/{sqs\Ajlcnt []cituhvjucemro ‚ƒhvqZqQmr}uj w \7}u\?z-WZ\/}-z-WZ\„oQ… ^‡†rˆ‡‰$_ŠoZmk‹r\A[ŒZ}l\‰rˆrˆŽ0_b†d%q‘hv’r\?t ljjl“2WZ\/}l” \[5•A£–/m>hv—k˜Zogžjl™rw,¤/–r[!w š hvcžŸGVXoZfoWZtucicn\At0m>¡‡o,q‘fhvhkz/qQjlfZcn\/}um>}ƒ}lo4\/ci¥o‡t j-VXwt/WZ¥\/‹>\ƒmvgejucn[]\ w cnjXjum!tuxsjltWZjl\/\ [¦w \/z}lm>cnfZ‹khkqZjlge\Acnm>tœoEjuWZmv\›œ\/[oZfZ\Agž}ujl’>cn’>x}ugem>\/fZ‹>q \/gitKw cn›¢ŸQ}lmrf‘[§tycemrŒQo mvju\?W¡‡f¤/hk\/jl}lcnmvm>jloW!tXmr›¢}}lwmr\/[ } ¨E²hv©‡}lªG[]«l¬mroZ­ ci—kz/® tX•r³š {sq£hromrtygnjucemr¤A[!o¯ZhvVoZ}-o,hvo\A¡‡tuqQfmrhv}ujujycemr´ wo4cž¯sŸG°ftucžŸGcnm>fotucn\?m>¡>o,f‘hrhkqZjuceqZmr}lo mP{dce[!hkjlcnm>o4¯‡±ƒ\/fsjl}um>ojl}lhrotuq‘m>}yj?¯sasqZWZ\/}lciz/hvg

ƒµ ¶3·,·s¸d¹‡º»A¼-½0¼/¾ž¿vÀyÀlÁϼĿP½ÄÁÆÅ‡Ç‘ÈÊÉÄËÌÍÄÎ?ÏvÐÄÍ-ÑKÒ-Î?ÏvÒ-ÓÄÔQÎÄË?ÏrÒ-Ð-Ñ ÉÄË?ÏkÕPÖÑÓÄÎ ÎÄÍ?Ïl×Ù÷kêqz/oq‘mrt m>fZw }y}-j0\hvo‡\?£j-ttj7mrgnw zju\mr¤A[!o‘w tuhvcžh>ŸGoZzfo4} tu¥ cnm>4o4g\¥  m>tuŒsxsjut\Ajlo>Y/jl[]cnm>\!o gecnw []\Atcnju\A¡‡zfm>hvfZjuqZcemrge\ot ge\Aw t%\ oZw ce‹rcžŸG\?fhvfstucn{ m>o w [AoZfZ\/gn}lju’rce’rce\}lmrwfY?q‘t%\gn\ W‘ hv}l­ [`–?• m>« oZ™ ci ¡> f•p\AtXš tyq³œW ¡‡/f}lcehv¡‡jufZcemr\?o t/¯!w ?\¡‡f£'hkm>jlgžcnjlm>¤/o[!t hvw o\o4z¯‘m>hro‡qZ‹>qZ\A}lzmPju{dcemrce[!os´ hkw jlcnŸQcnm>fotuceqmrhro } w cnŸQftucemro4¯‘ju}-hvotuqQmr}uj w \oZ\/fZju}lmro4¯

       !"#$ &%' (

†

   p)Ù  |œ}uWm \/w o$ftuzfZjuceŒsmr~o\?zÄmrju›4\ wodfjlzm2ge\Azhrm>}Ùgnge\/ciotyce\/mr}lo’rt x`}u\AcžjlgnceW \AtÙoZmr\Ao!fsjujl}lWZmr\ otAw ¥7cituVXcno‡WZju\/\A}l’r\}-›¢hkm>jl}ucn\>m>¯o!}lmv\A›hrzhkjujlm>mr} [!w t,\?+.ty-0ce’r}-oEhvoZ}l\AcefZ¡‡[§fZce}umr\?}Xtƒ|Khrgeo$fsjuhrm>zAoZzcefZfZ}-[0hkjl/Ä\ ¯ 1 wjlWZ\A}ltlmrz}lfZcn’>qsWƒjlcnjlm>WZo\œmr\/›‹>jumrWgefs\ju[`cemrmro7jucemrmr›>o`jlWZmv\ ›‘wjuWZ1\A\otyqQcnjmr3x qZf25ge4(hv6ju7ce89mr7o`:mv;‘›‘mvo›d\/oZfs\Ajlfs}ujum>}lomrt/o¥ t4VXmdzAWZz\fZ[]qdxdmvcejloZcn’m>ohkj4mvjl›GcnoZ[]\A}l=@mro?t jlcitWZ\œw \AqQtlm>ztu}lcžcejlŒ‘cnm>\ ow 8BABCED hvo w WhP‹dcno’‹r\AgnmszcnjF :GACHD¥ I j 1 cngegŒ‘\]zm>o‡‹>\/oZce\/o‡jƒceo 1 W‘hkjƒ›¢m>gngem 1 tƒjum2tu\/\juWZcitgeh>tj ‹RXkhr}uAZcihvY ŒZD\ge\2[^h>] tjuWZ:@\ JLw cn}lK \AzMOjuNcemrPo,QSmv› R0jux¯NB=W? cnjlt`\AoZ\/}l’rx hvo w \ _ce’rW‡j?¥VXW\%fZ'o `doZm 1 a o 2E‹r\A}u&c b\?thjl}lhrotuq‘m>}yjX\A¡‡fhvjucemro ced 2 fg:h!i jk2lJnmo4p29; +qŽ / jlŒdWx,hkjujKW}l\\/gioZhkjl\A\Afst ju}ljumrWo\'t›¢}lhv\/o \w jl}lw hr\AotltyzqQ}lcemrŒ‘}u\rj w +¢geju\WZ›øjÙ}lmrWfhr’ro Wpw jutyWc w \q\ /m>q‘jlm7\A}ljuhvWZju\Xmr3} ‹khvmo}lcn4(m>29f;lt ¥cnVXo‡jlWZ\/\`}-hrgezÄhvjljycnjlm>\/o}qZhr}l}ums\z\A\?tltutytu\A\Ao‡t jufZcihvo gew gnxp\/}lz’rm>mrgnogecž\ ´ jltutuWcefZmrhv[]oo tA\,¥0jujuWZsZW\,fZhvj!}uodjufZWju[WZ\/\E}lŒQ[`\/[]m>}`m‡}umv\>t›ƒj!¯OjuhvqZWju}lm>\!mr[`Œo‡hrcifz2ŒZ[geo‡\2ŒQf‘\/\Az}‹rge\/\/mrc o‡›'j!+uoZtvci\A? tfs]w]juhv}lo mrcito\/th gihrcntyjo x‡juciqzphvceodzAzx hvmrgge‹>ge}lcemrtuhvgecnjufZm>ce[]oem /\r¯tucnm hvjuWjjlWhvjuhkodWj]xE\ cnjlj`tycnfZ[]ci}lt`}l\rmr¯ }ufZ\?}lhro \/tuw[!mrcnooZhvcehr’ oŒZt%[]gn\]tu\ []jlw m cehrfZgnh>[pge\/t}´ ¥ €'m>otu\A¡‡fZ\/o‡jlgnx>¯djuWZ\7}lcn’>W>jWhro w tyc w \7mv›r+Ž!/cetXf‘tyfhrgngex’>cn‹>\/o,Œ‡x21 h`£m>gžjl¤/[!hvoZo,gecnoZ\?hv}m>q‘\A}lhvjumr} )

*

mo4p29;9Jnxzy{48|7w:7w:e}(;>254(67897:}~;kk:}€g‚ƒ4897:;>254.67897:;w„

+’ o0y{4cn8|juW 7w:‹r7w\/: ge} ms;Ez=…cnjxB?7:citÙtufcez-geW`gjuWWhPhv‹rj>\2y{‹r4\/89gems7:†zcn7j: x } ;(cnko :ju}lW\/\,qZ}l‹>\Amrtu\/gefZo‡[]jlt \‡jlWZk\0:qZhv}l}lmrmrŒ‘fhvo ŒZw cegncnj:xhkjl›øWjlhk\/j} jlz/WZmr\Eotuz\/m>}l‹kgngehkcetujlcecnmr‹>o‰\ˆ ctlt`y{ty\?4zÄ8|ju7wce:mro7w¥Œ:;eI O›ƒ: jlWZ¯G\pjuWZmr\AqQo \/}-hrhkŒjltymrm>}`}uqZcet´ jl}lcn\Am>h>o†zđqjlmrbQ}tutucecntm>oz/}ucn\/ju‹rciz/\Ahro‡gOjlt`cno2hvju}lWZ\!cit0oZ\/zA’>hrgntu\?\rzÄ{¥ ju\ I jw 1cemrt }`zmrm>}u[`juW,qQ}u\/\Ao‘[!tuhvhvju } \ `‡w ceoZ1 ’cžjujlWW hvtujAzA¯hktujucno‘ju\/z}l\ceoZju’WZ¥“\7}-’hko}jlcn\m`hvmvgi› tym3ju} WZtu\%hP[!xst7hrjltlWthkmvj`› jujuWZWZ\\ odmr›4fz/juWgn\A\cQoZjum`\AfsjujuWZ}l\mro2[!cehrttltqZ}-mvhr›zjljuWZciz/\hroZgnge\/xfsfjlo}um>z-oWthvoce1tX’r\ ‹>w \/}lˆ>x]jlWZge\hr}u[]’>\rhr¯>cno2juWZ\\AŸGo4\A¯ zw jXfZmr}l› cnotu’`fz-hrW2o2h\Agezh>mrtgejlgececeztucnm>zomrgegecicet'tucnm>m>oZo4ge¯‡x]jujuWZm`\7[`\AoZm \/w }lcn’r›¢xx jlqQWZm>\ tltuw cnŒZce}uge\?\rzįsjuŒcemrfso,j0cžmvjƒ› zAjuhvWZo,3\ mr_oZce’rgexW‡j?ms¥z/±ƒz/fZmv}Xjlce›¢z/mr\7}hrWgetucn’>mWZjugnWx2hv\/j0oZcn\AoZ}u\A’>ge\h>jltcejlzcezoZtl\/z/fZhkjuju}ljumr\Ao}utAceoZ¥ ’¯ 1 cnjuWpgem>tlt'mr› \AoZ\/}l’rx>¯‡}l\/[!hrcnot mvq›Gfstycejl[]hvjuqZcemrgec”obhr\ g‘w z[]m‡tm j?w {¥ \AIñgeo t jljlWWZ\Ahktuj ’\pw ohv\AjutlqZWZzqZ}l\XgececiŒ‘mrz/\ƒjuhkWZjljucn\AWZm>} \oW‘tAqZhv¯œWdo mrxsw oZty¯rci\,z/o‡t'f‘\/o‘zhrgezz/\Amrz/hvfZf}}-o>\AhkjloZju\/\A’r}-gntcex`oZh3\/\/\Ao‹r}lmrt\AfZ}uhr’>x }uW!\gihvŒZ[]}lfs’rmvjX\2juce}u‹k}l\Ahkhr[]jloZ\ hr’rw cn\2o!cnomvmr›ƒ›4juWZ[]\A\oZm \/w w }l\A’r\/}u}-cece\Ahk‹ktAjuhk¯\jl›¢cnzm>}um>m>o[`• [ t!P–k?GN— jum tym>[]\ ˜™Nq:†ˆƒhvo w h“b‘}ltyjtyce[]qZgec”b‘zAhkjlcnm>o hv}lcetu\At`Œdx ŒZ}l\AhO`dcnoZ’ jlWZ\ \/o\/}l’rx}-hvoZ’>\pcno‡jumtu\/‹>\/}-hvg w citT~mrceo>j \A’>oZ}um>\/fZ}l’rqx!ªt ’>©!}ucim>œt fZbqoZvt šœcnju\>› N!>¥ œ’ž&Ÿ^oZ7 \%Nk ¢hrtl¡ tyj!fZ£ []Jn\?t¤$juž¥ W¦ hv] j› N!južWZ7wN!\ž¨§z/}u] m‡›žtuH¥ tIño2ty\?[]zÄjlm‡cnm>tojt mvw› m!juWoZ\7mrtujXcnju‹kfhrhv}ujux!cemrjlomdtAm`¯d[juWZf\7z-W,jlmvmrj-hvo2gOjuodWZfZ\%[\AŒQoZ\/\/}}l’rmrx › ’>z/}u}um‡m>tufZtÙqtyt]\?zÄhvjuo cemrw o‘ot/¥œ\/fs€'jlmr}um>ootu\At!¡‡\/fZ‹>\Amro‡geju‹rgexr\E¯rhrm>zAoZz\0m>ci} tœw gece\oZw ’3jljummtuhP\/[]‹>\/cž}-´ hvw ’rcitu\ z/w }u\/¡‡juf\hv‹>o‡\/jl}-cžtyjlcecnmr\?ot/¯tmrtuf›4z-\AW ¡‡fh>hvtjucehPmr‹rao \A}l+Ž/hr´ñ’rk‰ \,/Ä¥tuzAVXhkWZjyjlcet \/}lcnocegn’ g ŒQ\ w ±ƒ\/\jl{dhvjAcege¯‡\ hw z/cnmro []ad[]\?zÄmrjuoZcemrgex%o f‰tu\ŒQw \/getm jl1 }lhv¥ ju\/’>xzm>otycityjlt cno`oZ\A’rge\AzÄjlcno’ƒjlWZ\hvoZ’>fZgehr} ‹khr}ucihvŒZge\>R hvo w }lcžjl1 cnoZ’ h\AoZw\/}lcnŸQ’rf‘x]ty‹kcemrhvo}lcihv\AŒZ¡‡gef$\ hk+ jlw cnm>cetlo z}l›¢\mrjl}!\h3m>}[!z/mrhro‡z}ljum>ceodtlfZzm>mrqZf‘ci t z!/{¥ \/¬oZ\Az}uju’>fx hrgngew xrce¯dtyjum>}loZceŒZ\ fsw ju\Acemrhvogit'›¢cnfZo2ojuzWZjucicetXmrXo zm>«o>jl4(6\7{d8|j 7 Nk;ucžt \rz/¥5hv’ƒo›Œ‘z/\ mrwfZ\/}-}ltyce\>‹r¯P\ mrwoZw\'cnmr}lŒs\Azj-juhvgecexot ›¢}utum>ce[[`cehƒgihvŒ}hvtygixshvtyo‘juz\/\Ù[!}lt \/gicnhkojljucnm>WZo \ m>VXoW\jlWZw \cžqQŸGmrfqZtucnfZm>gioÊhkjlz/cnm>mdo\mr›Qzceo\/\/o‡fsjljlt]}um>hro}u\t/¯vw juWZfZ}l\,mrfZjlm ’>W\Agehh>tqZjlWZcezp\AoZtlmrz/[]hvjy\AjuoZ\Amr}ucegeoZmr’’>cezAhvWZgs\/hvoÊohroZgnxs\Atufscejut }lmrmr›o‘jut Ww\0m tuzAohkmvjyjlj\/}lgem>cnotu’\2\A\A‹roZ\A\/o>}lj-’rt/x ¥ w+TcWoEgem>qZtl}ltœmdz/mv\A›4tl\At/oZ¥\/Q}l’r\/}l'x mv/ jlm>WEE} mrb‘} tlw ty\/cemr}ojl5¥\/}ls[!fZt}yjlhrWZ}u\/\ }l[]w fZmr}l\1 \rjl¯‡m2tyxshvtyŒ‘ju\/tym>‹[ }uqs+Tjle† cn/œm>o4zAhv¯o!ceoZŒQ\A\ƒgeh>’rtjl\AceoZz\/tu}-zAhvhkgecejy¤/jl\ \/w }lcnŒdox’ qQm>tyjufgehvjuceoZ’`juWhv1 jjuWZ\ w cnŸGftycemropm>q‘\A}lhvjumr}Xzm>fZqZge\AtjlWZ\%\/oZ\A}u’>xge\/‹r\AgetXh>t›¢mrgegnm 1 t w cn‹j x 4897wNe7wN } ;>i j«†4.67897wN } ;keN }  „ Iño w \/\ w ¯s’r}-h w ce\/o‡j-tÙmr›4juWZ\ w \Aotucžj0 m>o,hr²ƒoZm mvjlWZ\A‹r\/}\/}?\A¯oZcn\/j}l’rcitx!hrge\/getu‹>m,\/g‰ju\/N‡[]¥ qsjlcnox ’ «!jumEhvjm>hŒsjl’rhrcecn‹ro\Aotuxs\AtoZjl\/\/}l[!’rŽxt%geN &c } `>G\z/hr+Toe† /WhP›¢}u‹>m>\[ tumrjl[]WZ\0\ \/`dŸQceoZ\?zÄ\jjlcemrz!o2[]jumWw \ \Aw gncecžoZŸG’f¯ tucn\Am>¡Qo ¥ 1 +yŽ´O‰ /¯Qhro w jumc w \Ao‡jucn›¢xpjuWZ\`zmd\ zce\/o‡j-t0jlWZ}um>fZ’rW hro hrtuxd[`qZjumvjlcezhvohrgnxstucetA¥ƒVXWZ\Ao4¯Gtj-hv}ujuceoZ’!›¢}lmr[ jlWZ\zm>o‡juceo‡fcžjx\?¡‡fhkjlcnm>o ced «3f w ce‹ j"!$J x$#&%('*) mo4(29;kOR +¢e^ / tlhkjlcet b\ w Œdx!jlWZ\%[!hrz}lm>tlzm>qZciz w \Aotucžjx 1

+T\/oZ\A}u’>x‡´ / w

«4(67897wNk;5J x # %('*) 254(67897 K MNP!QVRr;kOR\7

hro w juWZ\%[!hrz/}um‡tuz/mrqZcizzfZ}l}u\Ao‡j

!4(678|7 Nk;{J

x # %('*) K MNP!QVR 254.67897 K MNPQ Rr;eR\7

¢›1 m>\}u[5tu\Ahvmv}-›Kz-hW’>›¢m>\/oZ}ƒ\Ah }lhrw gncnceŸQ¤/\ f‘w tyces mropciz` \A¡‡ tXfgihvh ju1 cemropŒdxqQm>tyjufZgihkjlcno’h]}u\Agehvjucemro,Œ‘\/j 1 \A\/oF«hvo w ! juW‘hkjjlhO`r\?tXjuWZ\ !4.67897wNk;5J

€Gx  4897wNe7wN!};>i j «4(67897wN!}~;ekN!}(„

l}[]as\/f\giz-hkw WEjlcn\ fhvw [ oEjum`hvcno‘qZjuzqWZ}l}u\%\AmPhrq{stu}uce\A[]m>tAŒ¥hvhvjuI ŒZcej%mrcegeo,gncž\?jhcex!t0w mrtcno‡› jljuzmp\Am>o gntuwgececioZ\tycew’rmrfZojlgimthv}ŒdhvxqqQqZ\/fZ}ugnox2jufZcžjcn}lo,Œge\/hkjloZWZjl’rcn\m>juo$WEgecn[]hvqZo}lcnjƒmrw2Œmvw gn›K\A\A[]tyz/[!}ut7\?hrhrhrgntug4o \A[]w t \?1jlhvWZWZo,ce\At o›¢}u\Ajlmr\%WZ} \ `Eqhkw cijlt\/Wo‘w tAty\/¯ cnj‹r1 xmrWZjumv\ci› z-w WpjuWZjucem\t tufz-Wp+ h]\¡>}u\/f›¢\A\/ty}ju›¢cemrm>o4} ¥ w \j-hvcegetm>ojlWZ\qZWdxstyciz/t mr›Qodfz/gn\?hv}}u\?hrzjumr}-t jumjuW\0zgihrtltyciz/hrg‡ŒQ1 mdmO`stmv›O£¥v°hP‹dcitym>o , ŽP"-ì¯0³¥+ ce’roZ\A} , ^Ž.- ¯ƒ³¥/+ h>z-Wtyq}u\?tut , ^>ˆ-ì¯10¥'£ftltlhrzÄ´ñ| ¥Ù‚\Aftut , ŽP‰"- ¯10Z¥|Kgihvoz-Whr} w , †‡2- ¯€¥ ú¢î è4úøÑ

       !"#$ &%' ( , wmr€'›0cž\AŸG}lqZfz/Wdtucn’>xscnm>otyo cihvz/otvhrcˆ qZqZŽ }l\"-mP{d¥}u\/ceVX[!›¢\/WZ}`hk\jlhvcnm>[![]o hvmrjuoZciWZt]’$\AŒ‡[]mvx juhvWjuoZ\/cimz/}-1hrt%g juhtym juf z/³wgeh>¥ x2tutumrcehvzA›K}-hvtujugX\/WZos\qZ´ }l0Z‹Pmrhr¥ ŒZoZ7ge\/city\/[ WZgegnce\AoZ1 } ’cnju, []†>W ‰"\?- hrhv¯EqZoE¬qZ›¢ge¥K}lcezA\/£hk\\/juoq‘cemrtuhko‘mrjut]f‘W$tucngntloÊcehv[]os‹kcž´ j7hv0}l¥hvcn´ m>oœfw ¥ t$mrb›Kcnm>\/juog WZw t\t´ ¥°hvfZ|juhv}-hPqx>hr´ oZ0ci¥zÙmr1 ¥gihv4m>cef mro‘, Ž?t ˆ -ì, ޝ'€-쯥s£X¥ hv} Ew m>hvtyge´ñ‹k‚%hv’r¥ cn´ñas°hro>¥ jl4m>\Aty´‹r‚\/}l¥ []admr\A}lo>\jl´ cet ¥', | -Xmrhr[]o w }-hv¯oZ›¢m>ceoZ}’ }l\A, †z/\/"-o‡ì¯jsqZ¥0}lmr| ’>mr}u\?fZtuqtuhr\AftA¯4w jlm3, † ‚%-쯥 s¥ mrgitu\ , ‰ - ¯%€¥£Xhv} w m‡t´ s¥ mrgitu\´ñ£¥| \/}ujuWhr[`\ , -쯀¥£Xhv} w m>ty´ps¥ mrgity\/´ £¥X| \A}yjlWhv[]\/´ ‚%¥ , , , |mr as›Ù\/m>o‡fZjljuWZqci\thvf tywf-ì}u|¯ }l, ‰rsmrˆ fZ¥ - o ¥n¥ew B¥ m>cnoge¬0tu’,\oZ ´ []mrsju\¥QWZw | \Acn} mrff[,w qc ¥0hvf ¬zw fzAgžzj‰>m>x 2} w- ce¯4oceoZ| ’>}l¥ \Agnx>œhr¯Oz¥ juju4m>WZ}ce\mrqZo‘z/Wdt}u´m‡xstutyt7ci¥Oz/tutV\Am‡zcittujuzAcemr}lhv\/ooZgit chkjlw \†v\Aw ^ q‘-œ\Ajl| m o ¥w jl°WZmr\2\/o3’rWm>jucnWo ’>\w W´ñtyV7WZq¥\h>jlz\/\]}lm>mrf‹k’>hvw \/}lm>oZceoshr\A´pŒZcžsjgex \ ¥ jlhrWZo m>\w getum>qZ\ } }lw , \A‰k\Atu^Z}u\/ce¯Oo‡oZ‰j0’‘‹r¯-ì\A¯ jl}uWZœx2\¥Qge°ƒWZhr}um>fZ’>[`[!\7m>h>m>’rttl\A´ zsoZcegncn¥ gi¤?hkhkjljlcnm>cnm>m>geotuo \t/¥Xq, ‰rVX}u‰"msWZ- z¯Qci\ t0| w gefZ¥ \A}lh \w /tXz/}-hvhrju}omw WZ´ Œ‘smr\[]¥ qQmr\/’>mr}u›¢\/gimrtyoZ\ }lce[]¤A, hv‰r\ ju† w ce- mropm>hv}j¡‡w jufZWZce\A}ul\ ty\?juzÄ`dcejlmrcngnoZoxp\/tAmrju¥ciopz!°ƒjl\AgeWZ\/q‘‹r\ \A\Ao w gm>soo ¥ , , `cehro$qZ¥sqZ³€}l¥ mPhr{sq cnwhr[!}l\/tuŒQhk\/jlm>o cntlm>z/o, †r¡ ˆshr, ¯Gt'‰ -ì†Zcn¯ o Ž-ì0Z¯G¥ ¥d³¬0°¥ gemrgehr}lhvcnoZ}l}-cn\tuo ´\/’vsos´ñ´¥ ‚%Ee¥ ¥$hr- + gnwZce’rw ce\ gncegeosci, hv† ´ñ²[!- ¥ ¥t +3Q, †rW\7†hrz/-ìoZhr¯4’ o€hv¥Q‰sgi£X.Ž ty-mhr`} zw mr¥Zm‡[€t´ŒZhrœqceoZ¥Zw \°\/ŒQhrfZgžm>[!jltlmrz/hr’r¡ ty\/´ñju| WZŽA¥ †s\A}K¯GjuŽ//W^ }--ì\Ahv¯ tu} \ƒw ´ \¥ sŸG¬0¥ \AgezgejlhrmrtXcn}lgihrtu\\t´ , "- ¯ ¥ ¬ƒgngihvce}l\´ ¥>£Xhvg , Ž -ì¯ ¥d£Xhvg , ^ -ì¯sV7¥ mrf w m>os ´ s'¥d| mrfZq‘hvf w , ‰ -ì¯sV7¥ mrf w m>os ´ ¬¥ p\/gegn\/j , ‰ -ì¥ ’>scnfZ‹>}u\²ƒjuWZ}lm \Ace1tu}u\[]\A‹rjlmrm\/}l}?\rw¯G¯ cžcžŸGj\/WZci}lt%\A\/o`oh z/ty1\jlhr\Am>}ygnjlo gn(´cn`dojuoZ’ƒWm \›¢1}lmrgeo$cn[[]›Tcnhr[jzfZjzmdgžjljl\Wcn’>hk}ujzm>cefZ\/w qo‡cnŸGj-\?t/\/¡‡¯O}lf\/tuo‡hk\/0j\jlcnm>+ø, †Z›¢omrŽt }l-K[!hrmro hv} w g /, q‘†d[`2\A-ì}y\/¯›¢m>ju, WZ}uŽ[]m- ¯ w ceoZ,t7Ž?’0† mr-jl›WZ›¢hrmr\ qZ}7w qZtycž}lŸGm>mP[]f{dtuce\cn[!m>\/o`hk{sjlhrhrcnm>qZ[]o$qZqZ}lz/gnmP\?hr{dt/o ´ ¥ ce, [!‰"- ¯hkjl, cnŽAm>† o2-pšƒgecnjl[]WZ\]cnjA¯‘gn1 cemr[]oZcž\7jfqtu}ufmshvzge\ gewxfZmr}lŒs\j-›¢hvm>ce}uo’>t0\h]jlttujlcnoZWZ’>\]gn\ [w fZcngnŸGjucef’rty}lcemrmrfZopq \?¡>hrf‘tuq‘hk\?jucezÄmrj?o,¥ceVXo2WZjlciWZt7\cet7tuqŒQhr\Az/zA\hvf‹ktuhr\}ucijlhvWZŒZ\!ge\7tymrxsoZtyjugexr\A[¯Ztu\/ce\t z/tlhvmr[]otu\`c w tu\/zA}lhv\ gew \r¥%jlm]²0}um \Agehv\/{!‹>\/ju}?m ¯‘1 cnjhv} zw mrt'fhrg w oŒ‘\?¡>\`fcncno‡gecnjlŒ\/}u}lce\AfZty[juceoZfZ’o jlw m \/}w \AŒQ}umvcejl‹rW2\\A[]geh>mrt}ljl\cezzm>hv[]o w qZgnce\/oZ{ \/gi[]hrtymjuciw z\/z/git/mr¯ gegncituWZcnm>ciz-oW$tXhk}l\jXj-juhvWZceo \ jl‹kWZhr\}ucemr\/oZf\AtÙ}u\/’>oZx]\A}uh>’>t'xhge1 \/‹k‹>hv\/}lgicet/hr¥ŒZgeVX\ƒWZhvciotw cetÙ1 juWZWZ\\/}l’r\m‡juhvWZg‘\ mv›Ow cnjuŸQWf\tuqZcemr}lo2\Atuh>\/to‡jÙ1 q‘\/hvgegOqQhr\/tÙ}?¥juWZV \7mcejloZW\/hkgihrjtyqZjucifZzƒ}lz/q‘mrm‡getygnci\>tu¯dcnm>mrofZ1 t'}z/hvmrofZhrqgnxsgn\tucejutÙWZce\t cemro›4tumrqZŒsce}uj-\ hvw ceoZŒdceoZx2’}uh\?hrw tu}umrcnoZ›øjyce´oZw ’>cntŸQfw tu\Ace‹rmr\Aognm>\?q‘¡‡\ fw hkjlceopcnm>o4juW¯ \[]\hrm }uw \ƒ\/gegncn\ oZw ’!jumrm`›œhvtyo\A[`ceo‡cijuz\Am>}uo []w \fw zcejuhvm>ju}l\t tuw xs\At‹djlce\/z/[p\At ¯‡Œ‡1 xoWZ\A`>}u\/\>\/¯ZqcecnooZt’jl\AjuhWZw \ \jlAWZoZ\,\/}l}u’r\?xz\/h>o‡tj!h]hv‹kqZhvq}lgncecihrz/ŒZhvgnju\>cemr¯so ty\A\jlm$£'jl\AWZ‡o \p¬ƒqZŒ WZw mrhvogemrgehroWst 1´ | w xd¥o°hv\/[]’>mrciz/o t`w Œd, x - ¯0Z| ¥K¥‘| °¥œ\/£’rmrm>fZo }lw ’>h , Ž w \ ¯4,Ž Žr.Ž -ì- ¥ ¥ + VX\WZhv\?gityty\,m]ty[]mr´ \/zAo‡hvjlgecngnm>\ ow aZ²ƒ³´ []m w \/gitƒWhP‹>\%Œ‘\A\/o$tuWZm 1 opjlmŒ‘\‹r\A}ux,hrz/z/fZ}-hkju\>¯ceo qhr}yjlcez/fZgehr}›¢mr}odfZ[]\/}lcezAhvg tuce[fZgihkjlcnm>ot/¥ I jcet 1 mr}ujuWoZmrjucizceoZ’hvjÙjlWZ\ƒ[]mr[]\Ao>jjuW‘hkjÙjlWZ\\/oZ\A}u’>x`z/mrfZqZgeceoZ’z/hroŒQ\m>ŒsjlhrcnoZ\ w \/cnjuW\/}'juWZ}lmrfZ’>W jljlWZWZ\ƒ\ ¤Aw \/cžŸG}lmvfjltuWcnm>mro} wm>\/q‘}Ù\A}ljuhv\Aju}umr[!} t 1 WZWZ\A\/oo!ceoZjlWZ\/\gihrcntyoZjuci\Azƒgeh>qt}ujlmscezz\?ztum>tugn\Agecet'tucehvmr}lo\0t'jlhv}u}l\?\hkjuju\ }lw \Ahvcejuo2\ w hhr[]tœmrqQ}l\/\ƒ}ucejuo>fjl}u}uŒciz/hvhvjujucemr\ otA¯‡hPx>mr¯d}'h>jutÙWZ}lcnjmrfZW’>hrW t ŒQ\AoZ\/\/\A}lo ’rxw m>gn\AoZ‹r\\AgeŒdtAx ¥ ²ƒ| m ¥°\A\/‹r’r\Am>}A1 o ¯kwjlWZ\, Ž hro- ¯Khvcegeoxstycijut WZ\w \/›¢‹r}l\Ahrgn[]m>q‘\ \1 w mr }cno]`$jlmvWZ›0\ƒtuq\/[]}u\?cityz\Amro>o j'w qfhvzÄqQjlmr\/}?}-¯rt%jljlWZWZmr\/fm>’r}uW!x>¯ gihv›¢m>}l1 ’r}\/z/gexmro‡cejuocetuodqZfZcemr}u\fw t ›¢k/}lÄmr¥[ ±0mr, Žju\- jl¯W}lhk\Ajœ¡‡fZjlWZce}uci\?t 1 t7gnmr\? }tu`t%ce}ltÙ\AtymrjuoZ}lgecixzÄjuz/ce‹rmr\`oz/Wd\/xd}lq‘oZmr\ juw WZ\?tycn\?juW]t0jl+TtuWZ\/\ \!w cecno ŸQf‘qtyhvcemr}ujuocizhrfZqZgihvqZ}}lmPas{d\Ace[!zÄjlcnhkm>jlo cnm>o†EqZhv}lo mrw Œgn|K\A‡[ }lmrˆrqQjum>WZtu\cžjlWZcnm>mvo ´ [jl]WZm>\7’r\/\/‹>omrcn¤?gefshkjujucecemrmro2oqZ¡‡}ufZm>\?ŒZt1jlge\/cnm>[¦o ŒZ1 fscej?gngQ¯ZŒ‘mv\7›zh m>wfZw }l}utu\?\rtu¯dtu\m>wfZ}\A1 gehvtuo\ 1hrgnWxs\/tuce}lt\r¥z/hr±0o2mvjlŒQ\\%hrhvgeqZtum%qZgejuceW‘\ w hkj jum]1 \\/ceW’rhP\Ao‡‹r\ƒ‹khrz-gnWfZm‡\m‡qZty}l\Amro]ŒZjugem\/[!ju}ltX\Ahkhrjt 1 \/gegì¥ w X V Z W  \  q v h Q q / \ 0 } i c 0 t > m u } ‡ ’ v h Z o e c / ¤ \ h>tyqQ\Azj0mropjlWZ\£mrgnju¤A[]hroZoE\A¡‡h>ftXhv›¢jumrcegemrgnmo41 ¥tAadcit o$w ‰s\/¯‹r1mrju\ \ w 1 cejlgnmg tyh \/jƒw cifZtlqEzfqZtlty}lce\Amrz/opcetu\/mrge›KxtujlmrWZ[]\\%[qZf}lgžmrjlqQcn’>\/}u}um>jucefZ\Aq t 





































 



è è ä­ZÕÉÄÎÄÍ









































\k Z &  

mr\Age› h>jltWZjlce\zzqm>hvgnge}ucijAty¯cemrjuo,WhvmrjqQge\/\A}-hPhk‹rjl\?mrtX}?¥5juWIñop\odqfZhr[}yjlceŒQz/\/fZ}gihvmv}?›œ¯ oZ1 \A\fsjuhv}lcemr[5otƒhvjƒcno tyqZhgecn’rjyjuce‹rceoZ\/’]oEjl\AWZoZ\\/}l£’rmrx2gnjugn¤/\A[!‹r\AhrgoZfZopoz-mrW‘qQhv\/oZ}-hk’>ju\ m>w }X¯Qcnhvo‡o juwm!hrhroo ceIñoZo3\Agetyh>m>t[`jlce\zqty\Ahro}ytyj?\>¥¯VXjlWZWZci\`tgezAhvhvjyo7ju\AŒ‘}ƒ\ }lw \mrj-hvoZce\Ùo\/tƒcnjutuWZmr\A[]}4\gnms}lzA\/hvge\/gegn‹kxhrmro>}4joZcnosmr›¢jm>hr}utG[!›Thvhrju}cehrmrtOoEjumrWZo \œ\AjuoZWZ\/\}l’r\/oZx\A‹k}uhv’>}lx2cehr\/ŒZ{sgn\z-W‘cithvoZz/mr’>o\ z/w \/fZ}loZ}lcn\ oZw ’ ¥ jlh>WZtyxd\[]z/mrqsgejlgnmvcitujucncim>zpotgecn[]1 cncnjjuWEjlcnWZjuWÊ\[]juW\ \ w cn}ufZ\?[p¡‡fZ¥\cn}lIñ\/o$[]as\A\Ao>zÄj!jlcnm>jlWo hk^j21 \/gi\%hrty›¢jumrci}lzv[!¯hvmrge}2gnx ¡>wf‘cihrtutuz/cžf´ \/tlgitXhrtyjujuWZci\`zv¯ty[!qZ}lhrmdgnz/g \A[`tlty\?\?hvt oEw ›¢mr}l[]\/\ceoqhkhkjljl\rW ¥ 1 ¬zjufhrgngexr¯dm>fZ}X[`\/juWZm w z/hroŒQ\7‹‡ce\ 1 \ w hrtXhWZ\/fZ}lcitjlcezqZ}lmsz\ w fZ}u\ƒjum w \A}uce‹r\[!hrz}lm>tlzm>qZciz[]m w \/git/¯ 1 Wcez-W hv}l\]cno‡ju\A}u[]\ w cehvju\]ŒQ\j 1 \/\/o h2›¢fZgegE`dcno\juciz w \?tuz/}uceqsjucemro hvo w hptucn[]qZge\ w cnŸQf‘tycemro \A¡‡fhvjucemro4¥ s ceohvgegexr¯ad\?zÄjucemro citzmro‘z\/}loZ\ w 1 cnjuWEh`}uce’rm>}um>ft'qZ}umdmr› mv›Kzm>od‹r\/}l’r\Aoz\>¥   )2+Ä . )2# 6!)27  qQVXmrW}u\jX\/ju‹rm!m>cegno‡fZjuju\/cemr}-o]hrzmvju›Gcemrjuo2W\0qZ}uq‘msm>z/qZ\AfZtltygihk\?jltcnm>h>o`t›¢mrmr›OgegnoZm \/1 fst jl}um>otKcit w \?tuz/}uceŒQ\ w juWZ}lmrf’rW!hvo]\A¡‡fhvjucemro]}l\/gihkjuceoZ’7jl}lhrot´ 4 c d fg:h!i mo4(29;5J  Y ‚ƒ48|7w:;EJ

j p; 2FJ mŽ4(29;w7 t x  % y{4.8|7w:7w:e}(; 254:}~;kk:}'€Œ‚ƒ4897:;p254:;w7  + O/ Dr[‰]   t x  % y{4897: } 7:;kO: } „   Y D\[^]  oVX\/W’r\7ge\AjuzWZjucece}oZw ’]}lcn\/o‡gijlhk\/jl’rcn}-m>hvo2Œ[]cngecž\?jxhvo¡‡tXfZjl\?Wtjlhkcnjƒm>ojuWZt\›¢mrm>}Xq‘jl\AWZ}lhv\7jujum>ce},[]m \%Œ‘cit0\Acnz/omr’o¯ tu1 \/}l\7‹khkWjuhPce‹r‹r\\>¯smr}ƒz/}ucnjuciz/hrghr[]gnce¤Aqhvhvju}lcemr\ wo!juŒdm]x jl WZ#&\%(] '*Iño‡) jl}u›¢mm>w}ÙfqZzfju}ucemr\ƒo4z/¯ mr1od‹r\\AW‘oZhPce\/‹ro\z/\Oz-Wˆrhrcnj oZ1’r\ cngew g‘hrjlWZgnge\m 1 z/}ufm‡tœtutyjl´ m tu\A1 zjumrce} mr` ot1 Œdcnjux,WcnoZo‡m>ju}l}um [!w hrfgnz/ce¤/cnoZ\ w’][`jlWZ\?\hroZtufZm>}l}y\ ´ hro w + 1 \ cngegtu}ucncn[]ju\7qZjlgeWZcž›¢\%x,‹rty\Am>gn[]msz/\cžj›¢x!m>}ymrjl› Wzjlm>WZ[]\%cnqoZhv’!}ujuz/cimrzge[]\AtXqZfsh>tj-hk›¢jumrcegemrgnmo‘t/¥ t 1 1  : J  :  RgJ K MNP!QVR\7  RŒJ :'P  :  J hroZ’rfZgihv}X‹khv}lcihvŒZge\AGY Dr[‰] 7  NJ Q‡: !PMJ \/oZ\A}u’>x!‹Phr}ucihvŒgn\AFC § „ °cn\/juoW mv juceoZJ ’0 Œd: 3x  J RpK juWMO\œNPoZQ mr}l¯k[!hvohvgew cn¤Ajl\ WZw \/}l³K\f›¢m>z/}ugnc\Ew  cihv o%J []\Ah> ty f}u¥(\K+m>$o \ Y w D\\ w [^f] z¯ \œ1 ju\œWZW\KhP›¢‹rm>H\gngem k:oceJoZ’0 Yz-WDrhv[‰o]’r\ D\mv›s[‰‹k] hv }l cehrŒZR0ge\ ¯ 1    ›¢1 m>}u[fZgih eN 1

x %ª4.:;kk:oJ x  Y D\[^]  x # %('*)ª4 K MNPQ Rr;4(MNPQZ; D MON OR 

Wcez-WphvqZqgnce\Atjlmhvodxceo>jl\/’>}lhrŒZgn\›¢fZozjucemro¥

ú¢î è4úøÑ



       !"#$ &%' (

geg‡\}lj\/f[!t hrw cnceotlzb}l{d\\jlcnw ¤A\ÙjlWZjl}uWZm>\fZ\/’roZW\Amr}ufs’>j xjugeWZ\/\‹>\/qgithvqQŒd\/x7}?ce¯vo>hvjlo }umw w f‘cezgncegdoZoZ’ƒmrjlj WZjl\\/o \/woZ\Aju}um’>¤/x7\/ty}ljume\A/q¥(T+ @\ty? \/j+ 1 \\'ž9qQJmrce›o‡j e7vm>4fsj fljltW;hk›j c e 1 hro 1 w juWZ\Ao4¯ \7z/mrotuc w \/} 1

2 ž 4.67897uRr;{J Mt x 254(67897 K MNP!Q‹Rr;4pMNP!Q ; D  kMNN  1 Wcez-W 1 cegng4ŒQ\h]oZ\ 1 fZo‡` om 1 o4¥œ³œ¡‡fhkjlcnm>otX›¢m>}juWZ\2ž t0hv}l\7mrŒsj-hvceoZ\ w ŒdxhP‹r\A}lhr’rceoZ’l+ O/¥EIñopjuWZ\ ge4 \c ›ød jfgWhv:o ž^w hqi tyc j w ;p\r2¯ žy1¥E\Zs mrhv}XqZjlqWZ}u\m‡hrzz-m>W‡gngeci2: tycemrŒdo2x‡ju:\AžH}uJ[p¯sK mroM \ PW‘!hrQ t R hro w juW\ju}-hvo‘tyqQmr}ujju\A}u[ citƒhvqqZ}umP{sce[!hkju\Agnx t eN M x  mŽ4(29;w4(67897  :  Rr;  :  D MON J M t x  x  x # %('*) y{4 K MNP!QVR\7 K MN } P!Q‹Rq‘\A}lhvjum>}œcno‡jlm\/gihrtyjuciz0hvo w w ceodoZfZ\A[geh>Œ‘tjl\Ace}z7mvq› hroZ}y\/j-t/fs¥Xjl}u²0m>o\A}ut\mrhropo h’>ŒQcn\/‹>ge\/m o,15\/4 oZ\/\Agi}uhr’>tyjux]ciz gn4\A‹r[]\/gì\A¥Ehv¬ƒo‘tXtXjuceoWhv, j0Ž ju-ìW¯ \mr\ qQ\/}-cngehkg4jltumr\/}\ge\AjuhPW‹rhv\?jtcžj0ceo‡ci‹ktXhr}u}u\Acignhv\Ao‡‹kjXhvo‡juWZj'\jlm]jumvfj-tyhv\ g hW‘phPz/‹‡mrceodoZ‹r’0\/ce{Eo[]z/mrce[o w ŒZcnjlo‘Whkhkjuj cemrjuo W\'mv\?›'tjujlWZcn[!\?tyhk\!jl\Atut qZwgecžcijutujuz/ceoZf’>tututA\ ¥Žw sZŒ‘mr\A}%gnm z/mrodhr‹r}u\A\ÙoZfZcn\AoZo1 cn›¢zmr\>}l¯1 [ 1 \`cžtwjl`dWcnq3}l\AjutuWZq‘\\?zÄtujqjlh>mƒz8 \ ¥ w £\/qQ\?\/tyco w w \A\/tAo¯ z/\r\ ¯ tuz/Wmrgehrgngncig‘tucnmrm>oZogex!mrqQtj-\/hk}-juhk\ƒjlmrqZ}-}ut'\?juzWcityhv\Aj gnxjucnWgeg4\ŒQh>\%tutuoZfZ\A[]z/\Aqstljutucehrmr}uo‘x]tœgimrhko]ju\Ajl}WZmr\71 ‰o zˆs}lqm>}utlmdt´ñmvty›T\?tzÄjlhrcn}um>\7oqQtH1 m>ytyž juqQhvmro oZw \ w juWZceo‡\juqZm]}lmrjlWZqQ\\/}uhvjuqZce\AqQtœ\/mro ›Ow jucž1 WZ{O\¥ 1 Iño]jlWZcit'tu\Azjucemro4¯ 1



687:9

;=(?,@?BADC:}+ k/Xh>t ݢmrgegnm 1 t 

  mo4p29;(žw4~Rr;5J   x # %('*)8H yž 4R\7uR1 tWZjuWZcegn\\ 1

jlWZ\/o 1 7\ WhP‹r\

\j0ftom 4LU‰tO;

Iño!m>} w



O ž 4~R } 7uRr;5J   y ž 4~R } 7uRr; 7



‚ ž ~4 Rr;5J x$#&%('*) O ž 4R } 7Rr;kOR }

m N M 4p29; ž J x$#&%('*) O ž 4~R } 7uRr;QPp2 ž 4R } ;9€2 ž 4~Rr;NR‰OR } JTSŒ4(29; ž €B‚ ž 2 ž „  1 tj-hkjl\7juWZ\b }-tyjh>tutufZ[]qsjlcnm>otzm>oz\A}uoZceoZ’juWZ\>` \/}loZ\/g‰yž 4~R\7uR } ;wš

s ce}ltyj0tyxd[][]\ju}lxh>tutufZ[]qsjucemro|šE‚ªžw4~Rr;5J x # %('*)(O9žw4~Rtucnjuce‹r\odfZ[ŒQ\/}-tA¯rtuhvjucit›¢xdceoZ’š J4 U; +3\Acn’>W>jƒh>tutufZ[]qsjlcnm>o‰šœ4 ž ; žZY\[ cit0tyf‘z-WjlWhkj  ž X ž Jn˜ ] 7 ž T+ cžj0cit\?hrtux]jumz-WZ\?z]` juWhvjƒtyfz-Wph]ty\?¡‡fZ\/oz/\%hvg 1 hPxst\{scitj-t / ¥œ±0mvjl\juWhvj¢J4 U†MÙ; hvo w L4 U 'œ; x‡ce\/g w



žex # %('*) ‚ ž 4~Rr;eR ] ˜  ˜ ] „

ž

\?¡‡fIhkj,jlcnm>cet o4¯1 1 mr}ucžjljuW,WÊjWx‡hPq‹dcezAceoZhv’gegnx ceo ž[`J ceo Nw  [ jlž WZ¯ \E›¢m>gngem 1 cno ’tyce[]qZgn\$\{Zhv[]qZge\ mv›juW\$citymrju}lmrqZcizp£'m>gžjl¤/[!hvoo

yž 4R\7uR