A geometric optics method for high frequency electromagnetic fields computations near fold caustics - Part II - The energy
63
0
0
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. A geometric optics method for high frequency electromagnetic fields computations near fold caustics - Part II - The energy J.-D. Benamou, O. Lafitte, R. Sentis and I. Solliec. N° 4627 novembre 2002. ISSN 0249-6399. ISRN INRIA/RR--4627--FR+ENG. THÈME 4. apport de recherche.
(3)
(4)
(5) ! " # $&%!'( )* +' -,.) !/01!% +2 3'4'+ 5 ) "+%!6 87 9 + /:
(6) :;7;<;='!> ( ?@BACD@*E0FHGJILKNMPO>QJRS@TUIWVXYXYFLQ*Z[@*\FHG6XY]_^ILG`ba @c\MPded_]_Fgf h>ikj3l&m2nporqtsulvkwyx z{s}|g~.mz|z{s}l&syxzsu|~ mtzjl&m|gl&kw}m3m c|mzhhU UxkL|z m2mYikm3ikm;~LnHgHo~W| m3l0k{mggorgWxm. 3¡ ¢k£ ¤ h>iksyWx¥msyx[m¦Hvkmw*|§¨ © ª x~ k{mm3~Hz{2z{ikm3|l&kvzx zsu|~S|§>zikmxl&kw}s}zv m W~ m3m m z|m3 xwuvWx z{m2zikmm3~kmg m¥|Hs}zm HziWmwuxgm¬«>x#m2s}~[xkwuxgl x&«ikm~[xp§®|w 3xvWz{su §®|gl ¯ °²±H³P´{µ¶ ¡ ·¤ ¸ xlpsuw}z|~k¹»ºHx3|ks_¼ ¸ xlpsuw}z|~Wsux~½qtzm3l.¼¬x#¾h
(7) x3s}~k¥¼¿Usy3|gsÀzÁqt|gw}vkzsu|~¼ ÃUt«s}~ qikmlpmg¼Äm3|glpm3z{su>zsy3¼ Åcx#gmcÅc¦HvWxzsu|~¼Æxm3Y¼*wyxl xk¼ Å*wumz{|l xg~kmz{sul.¼ Æ
(8) xm3 Ç[È3gx¹»ºg|vWw}m. Unité de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay Cedex (France) Téléphone : +33 1 39 63 55 11 — Télécopie : +33 1 39 63 53 30.
(9) . . ' = ! ! +) %!) =!+1!4)* +' $&% !+% 8 # $p%!'!8+%
(10) 3''!+= ! +%!6 $&%!/ !- L(pD !) + % 5) $&%!
(11) $&%! 7 -% ¬ .+ 7 '!> 3. . . . .
(12) . ¤ m²Wxksum3Y¼ wux vksÀz{m mS¨ ©#ª»¼ WÈYm~gz{m.w}m[xwyvkw mxlpWw}s}zv m ~kÈYmY{xsum!L|vk È xwuvkm3 w È3~Wm3{sum È¥|HÈmUWxvk~Wm|g~ mwuxgm x~Wvk~kwyxl xm~k{Èm3~W3m vk~kmxvWzsy¦Hvkm m ztLmkwuse¯ ¶ Y ´ £ ¤"¸ xl&s}w}z|g~¹»ºHx3|ks_¼6qtz{j3l&m ¸ xl&suwÀz{|~ksum3~¼Æ
(13) x~¥m3 mp{x#g|~W¼6qt|wuvzsu|~ mp¿Usy¹ 3|gzÈg¼¥qikÈl&x UÈYm3~Hz{ÈY3¼Lkzsy¦gvWm0ÄÈ3|glpÈ3z{su¦Hvkmg¼kÅc¦HvWxzsu|~ mY~ mY3¼¥Æ
(14) xm3Y¼k*wyxl xk¼¥Å*w}mY ¹ z{|gl x~WÈzsylpmg¼Æ
(15) xm3DzÈgx¹»ºg|vkwum. .
(16)
(17)
(18)
(19) !" $#&%' )(*( +. ©. :L'0
(20) !%c '. h>iWsu Wx¥m syzikm2m|g~ x~ wyxz>Wxz-,®zikm.Wz Wxz su2¨ ©#ª0/kmYm~Hzsu~k0x0Å*vkwum3{sux~~tvkl&m3{sy3xw l&m3zik| §®|>z{ikmsulvWwuxzsu|~!|§
(21) z{ikmk{|Wxgxzsu|~|§xpwyxm3«>x#ms}~.x&l x zmsyxwPl&m s}vkl.¯ ¨ 5#ª0/. h>ikmm3wumz{|l xg~kmz{su1.Wmw 32 sy*z{ikm|wuvzsu|~ |§PzikmU§®|wuw}| «su~k§®{m¦Hvkm~Wp« x#gmm¦HvWxzsu|~4, m3m. 687:9;6 2< =?>A @ B @
(22) 2?=DCFEG> A 2IHKJ!L ,FMN/ h>iWm¥xm xsyxkwumPO=¥mw}|g~kg¬z|RQRSTVUW,X HZY su~.ziWm0m¦Hvkm3w / ¼[6/syz{ikmg{x sum3~Hz|Lm3x z|g¬su~ QRSTVUY¼ > A sy zikm«>x#m2~tvkl0¥m|§zikmwyxm3«>x#ms}~!z{ikm xvWvkl.¼ H 9&O < su¬xpgs}gm3~.l&|t|z{i L|gs}zsum§®vk~Wzsu|~²«iksyi²|{{m¥|g~ z|&z{ikmm3§®{xg z{s}gmsu~ m3|§z{ikB ml&B m suvkl5x~ \E xp¥|Hs}zsum ¥xxl&mz{m3i¥xx z{m3{s^] s}~W2zikm2xW|{z{s}|g~|tm` _ sum3~Hz |§Âz{ikmwyxm3m3~kmg0t&z{ikml xzm3{syxw_¯h>ikm z{m3l/sy¬vkmY z>z|x~su~Ws m~gz¬Wwux~km2« x#gm 2ba^cedfHg2 Aih
(23) jk 9 CF> A O L 9&l`monGprqsnstvu'p <*< e, e/ «iWm3{mbD p sucziWmx~kwum¬|§s}~W3s m3~W3mx~ ziWm{3xzzmm W. m3w 32wFdyxz{HK2}|~2ba^ced xzsyFW. mY*x syx z{s}|g~ L|vW~ x{3|~ s}zsu|~¥x zs}~GW. ~ks}z¯ su~;¨ ©#ª_¼xP zmiW~ksu¦Hvkm suvWm , m3m §®|mkxl&kwum ¨ Yª0/ ¯ ~Ás}z{!s}l&kwumz§®|{l1zikm |H3s}wuwyx z|g&vk~!H ~W| «~ 2 sy¬xWk|#sul x zm t 2IK av L , ©:/ ~Áxtlpkz|z{su[mWx~¥su|~ |§mY¦gv¥x zsu|~,*MN / ik| «¬&z{iWx zzikm kiWxm sy|wuHsu~k z{ikm[m3sv |g~Wxw mY¦HvWx z{s}|g~ 6W @ H B @ ®, no/ x~ zikmxlpWw}s}zv m syxp|wuvz{s}|g~z{| E-=} 6 6 =D 6 L 96 <rHKJ!L ,&e/ h>iWmWiHsuxw¦HvWx~gz{sÀzR H @ «iksyi{m3WmYm~gzzikmwyxm3m~km3{{x z{su*W. m E = 6 L 9;6W <{HgJ , :/. |ziNgm3|glpm3z{suxw |z{supvk~Gt ~k| «~W¾ x~ } iWx#gm!w}| «8 xsyx z{s}|g~W03|l&Wxm z| 2 x~ x{m iWmxLm3Uz|.xkW|#sul&xzmx~ 3|l&kvz{msu~[zml |§c3|l&kvzx z{s}|g~Wxw|HzY¯h>ikmWP xkW|#s}¹ l xzsu|~[sy|§ zm~[z{ikm0|g~kwu.x$L |g xkwum«>x#z{|!sulvkwyx z{miksui²§®{m¦Hvkm~W²«>x#mk|gWxHx z{s}|g~!Wikm¹ ~W|l&m3~WxW¯. »z>su ik| « m3gm3«mw}w t~k| «~ zi¥x z>zikm2s}~kgw}mkiWxgmx~W{x z], ©o/*sy ~k|z|g{mzcsu~ziWmtsysu~ksÀz |§ xvWzsy3§®|gz« |pmwuxzm mYx|~W".W{z¼Hz{ikm{x#«iksyix{mzikm2su~gz{m3g{xwP3vk{m|§zikm2g{x s}m~Hz G *¡N¢.
(24) #. n. .
(25) $$
(26) { ;
(27) ! ; P$ ( . |§Wz{ikmkiWxgm 6x~ xwu|~k«iksyisu m`.W~km {|g{x~ & m`.¥~km¬xlvkw}zs}¹_ xw}vkm WiWxm §®vk~W z{s}|g~¯ qm|g~ z{ikmp{xl&m0{x#Uxmzikm&iWx{xg zmsyzsy3|§*zikm&|g~Wm3{#xzsu|~²wyx#« , o/ ¯¬mYxzikm&3xvWz{su ~Wm3suit¥|gsu~k {x#&{|g{&x~ zikm.wyxkwyx3sux~N|§UziWm²kiWx\ m 6 L 9;6 < sy su~kgvkwux x z&zikm²xvWzsy¯ Åcm3~Hz{vWxwuw}g¼Hzikm2m3~Wm3{ 3|l&kvz{m H l&mYx~W |§zik-m P¾xkk{|#tsul x z{s}|g~ ¥mY|l&mYsu~ .W~WsÀz{m¯. h>ikm¬xkk{|k{syx zm m~km3xwusv]x z{s}|g~|§ ,e©:/suJzikm¬Ç[xgwu| z{ikm3|g|§¥gw}|gWxw|H3s}wuwuxz|g2§®vk~¥ zsu|~¥3¼ «iWsui x~[LmWmYm~gz{m xw}|g~k z{ikm0wusu~km|§Jz{ikmz{ikm3|g!|§W|vk{sum3 ~gz{m3g{xw¥m{xz|g{U|§ ¸ ¹ l x~ m3P,¨ #ª0/ ¯ x~s}~Hz{| vWzsu|~¼t« mz{mYx zxl&|Hzsul&kwumm3xl&kw}m, xw}{mx vWm s}~D¨ © ª / x~ ik| « ik| « zikm|gw}vz{s}|g~ |{§ ,FM /sy*wus}~Ggm z{|zikmU~k|z{s}|g~ |§6lvkw}zs}¹»#xw}vWm |wuvzsu|~ |§), n¹Fe/fÆÂm3zcvW 3|~Ws m3x ¹ iWxwÀ§PWxgmk|gkwum3 l "O H 9 Vq < "! #%$ @ "& J' «iksui0«s}wuwsul&kwusÀ§®su~Hz|2x M3¹ W|gkw}mlxg«m0x{vkl&m2z{ikml&m suvkl5z| Lm0i¥xx z{m3{^s ]m H.x s}l&kwumsu~ m B @ 9( Gq) <1HZY'|
(28) ¯ h>iWmsu~W|gl&s}~k&«>x#m mz{m3{lpsu~kmYcz{ikm2¥|gvk~ x3|~ sÀz{s}|g~ xz{xpx *z HJ ¼x~ su~W3m B |tm ~k|z m3Lm3~ |+ ~ « m03x~ m3
(29) m ²x!|gw}vkzsu|~[|§Jzikm0§®|{l 2 9( Gq) <'H-, 9 < h
(30) jk 9 C )nstvu'p < ¯Åc¦HvWxzsu|~ ,FMN/ z{ikm3~²s}l&kwu^s .Wm z{|. . . 9 < =?> A@ 9 d | <(, 9 <V=DCF> A E,~HgJ «iWm3{m/ d H l`mon @ p¯ h>ikm|g~kwu10WiHsuxw32|wuvzsu|~ , 3|l&Wx z{s}Ww}m2«s}zi.ziWmx suxzsu|~!¥|gvk~ x3|~ sÀz{s}|g~/suP , 9 <)5 H 4P> A7U 6)8 s%9 | > A@ 6): 9* 9 d | < =DCyE!<> A ; U >< = z{ikm|tm
(31) _ 3s}m~Hz > A U)6)8 z{x~ su~k ikm3{m§®|~k|gl xw}sv] xzsu|~!kvk{¥|HmY3¯?W|*"@A d ¼Wxg > CA B = D ¼«m ik| «¼tvWs}~W&zikm3wuxgsuxw6xtl&z|zsym3Wx~Wsu|~|§z{ikm su{ §®vk~Wzsu|~, m3mx~k~km²t¯vMN/ ¼tz{iWx z 4 ; Ja I 6
(32) K h`jGk 9 CF> NA M < = T Oa I 6
(33) K h
(34) jk 9 |'CF> NA M L< P}R= Q 9 > A ; U < , 9 <) FE G-H 9 d | < U76LK 9 d | < U76
(35) K «iWm3{m M H S 9 d | =CFEG> A ; U < : 6 @ ,%. . . z{iWx z¬sy z|{x#. 9<. , . . T ; aOI 6
(36) K h`jGk 9 Cy> A T < = ; T aOI 6
(37) K h`jGk 9 |'Cy> A T < =. Q. 9 >%A ; U < ,_$/. H @: 9 d | <>:U6 @ x~ ; H VE4 G 9 d | Y < U76LK XWZY []\ ; [ q T H VE4 G 9 d | Y < U76
(38) K ; WNY [N\ ; [ ,5:/ Dmcx~mxgsuwuUs m3~Hzs}§®_, e/6xÂzikm vkl½|§tz« |' ¯ &¯ x~W{x z]§®|{l&m tUz{ik m_^Nkx~WiWm¯ ~ mm ¼ xgÂsu~¨ ©#ª_¼ « mcx~m3m*z{iWx zzikm{x#6|§km|l&mz{sy3xw|z{su6§®|gÂziWsusul&kwus .Wm z| k{|kwum3l½k{| vWm x§®|w zxsuiHz xvWzsyU3vk{m` H d , m3mbW. vk{m M / ¯ÅcxgiL|su~gz>|~zikm2suw}wuvkl&s}~¥x zm s m|§Âzikm xvWzsysy*{mxgikm tz« |x#t*«iksuixmwyxLm3wum | x~ 3= ¯Jh>ikm | Wxzc|§Lz{ikm¬x#Jk{|Wxgx z{m «iWm3{m. T. . acb aed.
(39)
(40)
(41)
(42) !" $#&%' )(*( . vW~gz{|pzikm3xvWzsyx~ suxwuw}m su{m z«iksuwumz{ikm = ¥xz sy zikm{mz{vk{~L|zsu|~!|§
(43) z{ikmx#t x § z{m3 ¥x{su~k0zikmxvWzsy¯*h>ikmYmz« |p§ xl&s}wusum m
(44) .W~km2z« |pWiWxm. H ) nst u'p ^ S 9 d | < : 6 @ =. 4. ,:/. «iWsui xmp|gw}vkzsu|~[|§b,®n/¬«s}ziDx ¹»ik|su~ks}zsyxwJx~ ¥|gvk~ x²3|~ s}zsu|~¥,®zikm&|g~Wzx~Hz 4/ m¹ Lm3~ Â|g~z{ikmcL|vW~ x{U3|~ s}zsu|~/ ¯h>iWm3~« m*m3z6zikmJ§®|gw}wu| «su~k¬xkW|#sul&xzsu|~§®|6z{ikm*L|z{m3~Hzsyxw. 2gH ,
(45) h jGk 9 C )nstvu'p < 2g ; ; aJI 6
(46) K h
(47) jGk 9 CF> A ; < =} T aJI 6
(48) K h
(49) jGk 9 CF> A T < = Q 9 > A; U <L ,*M:/ W|{lvkwyx ,*M o / l&mx~Wzi¥x zJx zJiksui§®{m¦Hvkm~Wg¼ 2 suz{ikmvkI l |§kz« |b ¯ &¯ Sx~W{x z]c§®|gl&m t zikm ^;kx~WiWm¯*h>ikm Oa I 6
(50) K2zml {m3k{mm3~Hz>ziWm t~k| «~ ki¥xmiks}§ zxg{|g{ xvWzsy3Ux33| su~k z{| Ç[xw}| &z{ikm3|gg¯c~3W. gvk{mk¼«m2iWx#gm2kw}|zz{m s}~ziWm@ 3xm EHJ L|zi!z{ikmmkxz¬|gw}vz{s}|g~ 2 , kwyxsu~pwusu~kmNJ/ x~ sÀz{ ¯ & ¯ ¯xkk{|#s}l x z{s}|g~~e, zx/1, |~kwu0su~pzikmUwuxgz*«>x#mw}m~kz{i0sy*x s^Lmm~Wm z{|Lmpm3m~¼Lzikm&xWk|#sul x zsu|~.kwu| «¬x zUz{ikm&3xv¥z{suN/ ¯ xwus xkW|#sul&xzsu|~²|§ 2 ~kmYxzikm xvWzsys}~!z{ikmWs}{sÀz|§ ¨vMeM ªÂsyk{|L|gm s}~ ¨ ª0/ ¯ W|gl z{ikmxkkwusux zsu|~&L|su~Hz|§6tsum3« zikms}l&L|z{x~gzkittsy3xw¥¦gv¥x~Hzs}z0syJz{ikmxW|{¥m wyxm3 m~km3{ E 2 @ X:O=|~.x.km . |l xs}~ ²¯~km3x~{mx suw}iWm&§®{|l ,»$/ 2 @ 9 T' @ = ; @ <V=K| e T ; C B 9 :> NA M < = Q 9 <> A; U < ¬m3xw}w¥zi¥x z ziksy>xkk{|#s}l xzsu|~ ik|gw >xgtl&z|zsy3xw}wu0su~ > A x~ zikmm3§®|{mU|~Ww}pziWm2z{xzsu|~Wx L|su~Hz{|§ M «s}wuw|~Hz{sukvz{mz|zikmpsu~gz{m3g{xw
(51) |§Jz{ikmpwuxgzzm3{l.¼6x z{vWxwuwu|g~kw}!z{ikmpxvWzsyL|su~Hz¯ iWm3~ ziWm |l xs}~
(52) su0x²z{su U )q @ «iksyi |tm~k|z0|g~Hz{xsu~DzikmxvWzsy¼« m mzt zikm ¾ z{xzsu|~Wx WiWxm§®|{lvkwyx 2 @ FX H 9 T' @ = ; @ < FX = Q 9 > A; < ,*MeMN/ [ [ [ [ s}§ ~² xksy¥¬mx~ z> s}z iWm 3¼kx«v¥mz{xgsu zLv¥|xsuwu~gw}zWd| ¯ gmsu~!zikmx$ _ ~km2s}~ m|§{m§®xzsu|~.3xgmziWxz,FM:MN/ ik|gw >mm~ @ h>ikm~tvkl&m3{suxwkl&mz{ik| k{mm3~Hzm s}~ ¨ ©#ª6x~ s}~ z{iksy*Wx¥mcsy mYsu~km z|0«|gs §®|csu~ m3p|§ {m§®xzsu|~ B 9 !
(53) q < k{| vW3s}~kx&§®|w 3xvWzsy2ziWxzx~²LmWx{xlpm3zmsv3] m t" W¼Ws_¯ mg¯zikmp3xvWz{su sy¬{m3WmYm~gz{m tz{ikm3vkgm H d 9 < ¯U~km03x~[iWm,emm¨ ª
(54) §®|gx mz{xs}wum ² m3l&|~Wzx z{s}|g~ |§
(55) z{iksu¬mYvkw}z/ z{iWx zY¼k«ikm~ E HJ ¼§®|gl0vkwux~,FYM : / zsuw}wÂiW|w x#« x#&§®{|l/zikmxvWzsy¯ ~Dm~km3xw3xgmY3¼LziWmpWiWxmP x~ z{ikm xl&kwusÀz{v mY 3x~ |~Ww}²Lm |l&kvkzm ~tvkl&m3{sÀ¹ xwuw}g¼6ziWmwyx{sy3xwl&m3zik| ¥ms}~W²{x#.z{{xgsu~kW¯ ~ ¨ © ª_¼«m&k{|L|gm x~DÅ*vkwum3{sux~ l&m3zik| §®| z{ikm²|glpWvz{xzsu|~N|§- ¯ ~Nz{iksy&WxLm3Y¼c« m§®|3vW&|~Nzikm²¥mYs^¥. s _ 3vkwÀz{s}mY&w}su~Gg m z|Dzikm 3|l&kvzx z{s}|g~!|§z{ikmxlpWw}s}zv mUx~ s}~²¥xzsyvkwyx>z{ikm{¦gv¥x{m|§z{ikmxlpWw}s}zv m H @ ¯. mY3xv¥m2|§ziWmsu~kvWwuxs}z|§ziWmkiWxm|tm` _ 3s}m~gz¬x zz{ikm3xvWzsy2~km3s}zikm ,&:/ §®| ~k|g , :/ G *¡N¢.
(56) #. . .
(57) $$
(58) { ;
(59) ! ; P$ ( . §®|g x{mv¥m su~ kxzsym¯- ~WzmYx «mpvWmziWm&3|~Wm3{ x z{s}gmk{|Lm3zsum|§cmY¦gv¥x zsu|~?, :/¬z| mYzxkwusyizikm2§®|gw}wu| «su~k0{m3WmYm~gzx z{s}|g~§®|>z{ikmm3~Wm3{sum. H ,*MYe/ «iWm3{m syz{ikm|{sum3~Hzm g|wuvkl&m|§*x~.su~W. ~ks}zmYsul xw
(60) zvkLm|§x#P, |l&mz{s}l&m3xw}wum 0m3|gl&mz¹ {sy3xwk{mx su~kX2*/«iksui² x~ksuikmY¬x z¬z{ikm0xvWzsyx~ ½sux&§®vk~Wzsu|~ mY3x#tsu~kxwu|~kpz{ikmx# xz x{xzmUg| m~km H E ¯h>iWmmU~km«Ávk~Gt ~k| «~Wx{m|wuvzsu|~¥c|§ÂÅ*vkwum3{sux~ zx~WL|zm¦HvWxzsu|~W x~ k| ts mxp|gkvWz>m xwuvWx z{s}|g~|§Jx3|H>xvWzsy3¯. h>ikmWxLm3suc|{gx~ks^]m x*§®|wuw}| «¬¯ m'.¥{z vkl&l x{s^]mWxsu§ x zx~ {mvkwÀzJ§®{|l5¨ ©ª¥|g~ z{ikm>ks}¹_ xwuvkm kiWxgm' ¯ m ziWm3~ m3{s}gmcsu~pmzsu|~p©¬z{ikm>m¦HvWx z{s}|g~W«m «suw}wtvWm z|2|l&kvkzm zikm xl&kw}s}zv mx~ ~tvkl&m3{sy3xwuwum3 xw}vWxzm§®|gl0vkwyx\,FMeM / ¯UqtmY z{s}|g~²n mzxsuwuUlp|gmzmiW~ksuxwmYvkw}z{ |g~z{ikm>lp| ^s .¥x zsu|~p|§¥zikm3|l&kvzx zsu|~¥xw |l xs}~px~ ¥|gvk~ x s}~ks}zsyxwt|g~ s}zsu|~W¯Jqtmzsu|~W m3kwuxs}~¥zikm s _3vkwÀzpwus}G~ gm z{|zikm .W~ks}zm ^s Pm3{m3~W3mUxkW|#sul&xzsu|~p|§PziWmzx~WL|z*m¦HvWx z{s}|g~ ~Wmx&z{ikm[3xvWzsyg ¯ Dm²k{|L|gm²x .W{z | m3{ikmlpm[x~ iW| «4~tvkl&m3{suxw{mvkw}z{5 ¯ s}~Wxw}wu mzsu|~Dik| «¬~HvWlpmsy3xwmYvkw}z{2x~ k{mm3~Hzx~tvkl&m3{suxw xwus x zsu|~ |§*§®|gl0vkwy x ,*M: /x~ ,*MeM /csu~!zikm M3¹ xm¯. . . . ! + +'! +' b%)> +' !)
(61) +2 3' ! ) +%!6 . Dm2sums}~zikmz« |§®|gw}wu| «s}~W0vkWm z{s}|g~¼x~WmmY {x{&| mtsum3« |§zikmkiWxgml&| m3w6k{mm3~Hzm su~ ¨ © ª_¯*h>iksyk{mm3~Hzx zsu|~suUwus}giHzwu s^L mm~gz¬x~ ik|Lm§®vkwuwuwumxm ziWx~z{ikm|~kmz{iWx zUx~.¥m §®|gvk~ su~ ¨ © ª»¯. ~ ziksy2mY zsu|~ x~ zik{|vkgik|vkz¬zikmpWx¥m« mv¥mWX H Y zi¥x zsyO H 9 !q
(62) < sys}~ $ x~ 6 H 9 q [ < ¯ D m¥mw}sum3gm>ziWxz*Hgzik m¬3| ~Hz m~Hz*|§Lziksy* Wx¥m*3x~pLm¬m3Hz{m3~ m z|2z{mYx zJ§®|w 3x@ vWz{su xm su~z{ik{m3m sulpm~Ws}|g~W ,X x~ [ syx0g{x sum3~Hz/ ¯ . "! #$!&%(')+*,' -/. 0 12' %(3. #546'17. #5438. Dxm~.iWz{xx~z wu«msÀ¯z{ih>ikxm~ susu~~ .Wm3~k s}zm 9( Gm3q)t sy< m¬syULm3|x~WvWz{xmU~gs}zzcsy, cHZsu~Y />mYsu~.m3~WziW3mm«iWxiWw}x §Jz k|wyxvk~km k{ |L@ |gJ m « ikÅ*mvkwum2m3{z{suikxm~ sul&~Wms z iWm| ~g z Wwux~km2« x#gmW_, e/ k{|Wxgx z{B mc§®mm3wu¯*h>ikm2sul&¥|gzx~Hz¬x{vkl&z{s}|g~|g~z{ikmkitsy3 |§z{ikmk{|kwum3l su~b¨ ©#ª>¹z{s}wuw> xwus s}~NziksypWxLm30¹« xgx~ x[k{su|{sitt¥|zikmYsy0|~NxD¦HvWxwusÀzx z{s}gmLm3iWx#tsu||§ z{ikm&{x#¯P ~ |gvk9 V q < mzzsu~k e, mmWW. vk{mn/ ¼Â« mpvWm0ziWm !xtsy2xxWsuts}wum3gm s}{mzsu|~ |§ W|gWxHx zsu|~
(63) ¯h>ikm {x#z{xzxz{{xs}gigzwus}~Wml xeH su~k²x~Sx~kwum Á p «s}ziDziWmmz{suxw*x sysu~ z{ikm R@ J iWxw}§Wwux~km~e, |g~Wzx~Hzs}~ m[|§{m§®x z{s}|g~/ ¼Pz{ikm3~ ziWm3[m~gz{m3ziWm & J xmYx«iWm3{m z{ikms}~ m iWx>l&|H|zi xsyx z{s}|g~WcvWi z{iWx z>{x#0 §®|gw L2x~ zikmwu|t3vW |§6z{ikmU§®|gw su 3xw}wum zikm J |gl&xs}~ x~ xvWzsy¯ § z{m3z{vk{~ks}~W!¥x xzz{ikm3xvWzsyz{ikm {x#m3gm3~Hzv¥xwuw}²m3ts}zziWm A& . . acb aed.
(64)
(65)
(66)
(67) !" $#&%' )(*( . {m3gm3zz{| x z{{xs}gigz>wus}~kmsu~!zikm3|~Wz{x~Hz su~ m3Wxz|§ziWml&m s}vWl!¯ h>ikm 0 §®|gw xvWzsy 2Uxgvkl&zsu|~x~ LmUl x z{ikm3l xzsy3xwuwu0m3tWmYm tz« |3|~ s}zsu|~¥3¯ s}z z{ikm {x#vWgm
(68) x~0¥m Wxxl&m3zm3{sv]3m t x~ |suz{ikm xvWzsy m3~k|zm t H d 9 < ¯qm|g~ ¼ mmp¥|gs}~Hz 9Vq < |~ z{ikmUsuwuw}vkl&su~Wx z{m s mU|§6zikm3xvWz{suUsuWxgm tpz«|{x#¼ziWm|zikms m ,®zikm i¥x | « ]3|g~kNm /Psy~k|z
(69) {mxgikm ¯
(70) h>ikm323x~¥m wyx{^s .Wm s}~Hz|¬z«| 0kx~WiWmL21 $ s ` {x#Pz{iWx z {mxgiziWm¥|gs}~HzJ¥m3§®|{m¥x{su~kzik{|vkgiz{ikm¬3xvWz{su x~ s
(71) ; x#Âz{iWx zJ{mxizikm>L|su~HzJx§ zm¯. Dm
(72) m .W~km&ziWm § xl&suw} |§{x#[3vk{m [9 !q7 A < q A Q\q su~ sy3xzmYz{ikmR.W{z {|g{su~k[L|gsÀz{s}|g~N|§¬zikm.x# «sÀz{i ziWm |wuvz{s}|g~W3¼ A x~ 1&A A |§ziWmM¹ ¸ xl&suwÀz{|~ksyx~.tzml. . . ' H J xA tsy e, m, ma^ce.Wd /vW¯Nm&h>noik/m!«{iWx#m3{pm x {Am. &. . 9 Gq <)H 9 !q [q < 9 Gq AA <)<{H8H | [ 9( Gq q < <| ,*M©:/ 9 !q A 7 9( Gq [q 9( Gq q < «iWm3{m 9 !q
(73) Vq <)H8| B @ | @ ¯h>iWm |zcz{x~ §®| msu x z{s}|g~0«s}zi&{m¥mY zJz| W¼x~ [ x~ m~k|z{mz{ikm m3{s} xzsum|§ «s}ziDmYLmzz{| Sx~
(74) ¯ m ¥mYs}§®.zikm&su~ks}zsyxw*|g~ s}zsu|~W |g~z{ikmx sy HJ [9( 7q <{HJ V9 9( AA q q7 AA <{<)H H nsnst tvu'u'p p ,*3M no/ A A A h>iWmpsu~ks}zsyxwc3|~ sÀz{s}|g~Wx{m m3{s}gm §®|gl zikm su~W3s m~Hz2Wwux~km « x#gm03|~ s}zsu|~K_, e/ x~ xwuw*x# x~SLmm3Hz{m3~ m Wxgt« x 2t z{{xs}giHzw}su~km~, z{ikm3S|wum&z{ikm{xl&mmY¦gv¥x zsu|~Ssu~Sz{ikm @ J ]|~km / ¯ ( ( . 7 . . . . .
(75) . . . . . . . . . . 0. ! 4 . ). . $! ). . . ! ) ). . $ 1 $! # "!&%(') *. ± ¡ !£¢ ± ·#"c¢%$¥¡ ¢%&$('e¢% ¶ · ± ~²W{xg zsym|vk m3tsymsy .¥~ksÀz{m0x~ zikm0s}~ m B m`.¥~km su~ x L|vW~ m s}~Hzm xwe¯'Dm0x~[zsuw}w xgvkl&mzikm |l xsu~!z| Lms}~G.W~ks}zmsu~.zikm "@ J iWxw}§Wwux~kmx>z{ikmk{|Wxgxzsu|~syz{sutsuxwPzikmm Wvz« m~kmm xwu| z{|¥|gvk~ zikm |l xsu~²su~[ziWm s}{mzsu|~¯ÆÂmzvWm3z J q Wxgz{ikmx~kgmsu~ 0«ikmmz{ikm2s}~ msy `m .¥~km ¯*h>iWm3{msy>~k| ^s _ 3vkw}zsum z| z|gz{ikm2{x#3|l&kvzx zsu|~¥ xz` H x~ z{vk~Wx zmpz{ikm |gl&xs}~ ziWm3{m¯hvW~W3xzsu~k²x 1 z H J sy2l&|{m k|gkwum3l x z{su¯ ¬|z{su3m s}~ m3m z{iWx z0su«m vWm z{ikm{xl&m su~ksÀz{suxw}vs ]xzsu| ~ ,*M3on /Wvz0|g~kw} §®|0¥|Hs}zsum A ¯ »zpm3~Wm3x zmY ^s Lmm~gz ]]||~k~kmYm wyx«Likm3mwum m2 z{,*ikMNm/§®||g~ w .WgxvkvW{3m zsyitLtm3wu¥| |« zikzmYikmsy¬.¥x{L|z{m x# |HmYik|~kz|§®zU|g~kl-m3mz{ik{m x|su{wus}gs}x~ Wk9 J w}suqmJ<¯>¼h>mikkm3{mYmsymU~HzWx m .Wsu~ z z{iksy wus}~Wm¼«iksuiSsy~W|z| gm3{m tDx~H {x#¯ m3|~ ]|~kmwyxLm3wum ,_e / mw}sul&sÀz{m t zikm s}{mz>¥xzUx~ {mzvW~!Wxz|§ziWxzUxl&-m .W{z{x#su>|g~kw}mYxikm t s}{mz¬{x#¯ D-m .W~Wxw}wu |g~ ziWm{m3l xsu~ksu~kWxz |§6z{ikmsuwuw}vkl&su~Wx z{m |l xsu~¼Hwux¥mw}m ,e:© /J|g~ ziWm .Wgvk{mU«ikmm¬« mUgmz zikm v¥vWxw 0 §®|gw 3xvWzsy 2{m3gs}l&m2«ikmm2m3gm3{ ¥|gs}~Hz¬sy>mYxikm tx su{m z¬x~ x0{mz{vk{~x#¯ . G *¡N¢.
(76) #. 5. . .
(77) $$
(78) { ;
(79) ! ; P$ ( . . ± ± ± · ± · "%¢ $W¡ %¢ &$ ' %¢ [ ¶·± >xwumYx piksu~gz{m ¼kx~ m3tzm3~¥sumw}&mkwyxsu~km s}~D¨ ©#ª_¼tz{ikmz{vk~W3xzsu|~|§ÂziWm2Æxg{x~ksyx~&l&| m3w syxp|gvk{3m|§ s^_vkw}zsum>«iWm3{ms}z{>Å*vWw}msyx~z{mxzl&m3~Hzsu3|~W3m3{~km ¯ ~ m3m ¼k¥|zizikm su{m z x~ m3zvk{~&Wxz*|§Pz{ikmU|wuvzsu|~ x{m¬|vkgigz§®|gcx*3|vkWw}m Å*vkwum3{sux~&|wuvz{s}|g~WJ|§Pm3g|wuvzsu|~&Wx¹ z{suxw ^s Pm3{m3~Hzsyxwm¦HvWxzsu|~Wsu+ ~ x~ z{ikm03|vkWw}su~kx~k~k|zULm0x#|gs m z|!|l&kvkzmz{ikm0xvWzsy¯ ~WsÀz{suxwÂ|~ sÀz{s}|g~Wx{mzikmm3§®|{m2~km3m m §®|L|z{i!W{x~Wikmx`z HJ ¯ . ~ ¨ ©ªP« mUW|g¥|Hm s}~WsÀz{suxwP3|~ sÀz{s}|g~W m3{s}gm §®{|l8xp|l&Wxzsukwumz{x z{s}|g~Wx{pk|gkwum3l zikm su~ m3su.Wzm3Hz{m3~ m su~0zikm* @ J tm3zz{s}~k B 9 !q
(80) <)H B 9 J q) < q& 1@ J ¯ z{ikm* m3Lm3~ m~Wm ys UvkkWmYm ¼Lxwuwx#syvkm §®{|l5~kmgx z{s}gm1 A iWx#gm2zikmpxlpm¥miWx#ts}|gUx~ zikmp3xv¥z{susyUx zxsuiHzcwusu~kCm d 9 <)H54 A ¯) »z>3x~Lmik| «~²¨vM#ªPzi¥x z ziksy>zx zsu|~¥x{p|wuvzsu|~x~ |gvk kittsy3xw |wuvz{s}|g~ 3|~k~Wm zl&|t|ziWw}[«s}ziW|vzsu~Hzm§®mm~Wm4,emm.Wvk{m :/¯h>iksym3Hz{m3~Wsu|~Dk|3m{iWx z« |x #x~Hz{xgm¯ su{z*«mU~k| « i¥x#m>z« |k{x~WikmYm3mt«ikmm>su~&zikmUkittsy3xw |l xsu~¼tmY|g~ z{ikmz{x z{s}|g~Wx{|wuvzsu|~W>xCz HJ x{m2mxg&z{||l&kvkzmx~ x~!¥mvWm x>su~ks}zsyxw x z{xW¯ Dm3x~!zikmm3§®|{m2z{vk~W3xzmx~km3« ziksym3Hz{m3~ m l&| m3w
(81) xz/ HIJ x~ m3zzikmsu~ks}zsyxw|~ sÀ¹ z{s}|g~W§®|gUz{ikmx#z{m3l |~.z{ikm x sy ,0.Wvk{mpe/ ¯`U|zmziWxzxg3|g s}~k&z{|z{ikm/0§®|w 3xvWzsy 2 ittL|ziWmsu>mYxi!¥|gs}~Hz 9( HJ q
(82) A < §®|g* A | D q 4 A tsymYxikm tz« |&{x# |§ziWmmtzm~ m l&| mweD ¯ Dm!~k| «/iWx#gmz« | § xlpsuwus}mY0|§Ux#tpvWgm a 9 !q
(83) < q |5D q 4 q & J' §®| C H Y q «ikmm U 9( Gq) A < ¼Â{m¥mY z{s}gm3wu @ 9 !q
(84) A < ¼
(85) x{mz{ikm&{x#A su{vWAm §® {|l z{ikm A sumY z¼6{mLm ¹ z{s}gm3wu²m3zvk{~¼6x#3|Hs}~W HZJ x z A ¯0h>ikm&x#tU|§ mxi[§ xl&s}wu {x z{su§®.§®| & J |§zikm {xl&mzm3l ,*M:© /cx~ zikms}~WsÀz{suxwP3|~ sÀz{s}|g~Wc~W| « m3{s}gm§®{|l z{vk~Wx zsu~kzikmmtzm~ m l&| m3w . aa 9 J q
(86) A <)H aA ,*MNe/ a 9 9 J J )q
(87) q A A <)<{H H a A A 99 A A < < J U x A ~ x m a 9 xL q
(88) z xA |< §6xz{~ ik mka9|gL k
(89) q wum3A l.< ¼ xm@ AziWxm~ |{{@ m A¥x|g{~ mU tsu~kH¹_pW|| wuvvWz{s}|gz{~Wc |§Â|§'z{ik,FmM©o/ z{¯ xzsu|~Wx . . . . «iWm3{m U A x~ W|gkw}ml/su~ @ . . "! #$!. ' %. . . . . . . .' * # "!. h>iWm{x#|§PziWm @ § xl&suw}0«s}wuw¥xw}«>x#Lm¬{mz{vk~px#t¼ z{ikm30Wx{m z{ikmUxvWzsy>s}~pz{ikmmtzm~Ws}|g~ J |§ÂziWm |gl xsu~«m«s}wuw m3~W|zmziWmmx# T ¯*h>iksusy~W|z zikm23xgmU§®|zikm § xl&s}wu su~ «iWsuizikm2x#t z{xzx sumY z{x#¼g¥x{cz{ikm3xvWz{@ sux~ Lm3|l&m{mz{vk{~x#t, .¥vkU {m©o/ ¯*h>ikm s}{mzWxz2|§>x x#U«suwuwLm m3~W|zm U ; x~ zikm&{mz{vk~ Wxz UT ¯pÇ[x z{ikm3l xzsy3xwuwu¼ < A ¼ z{ikm3{m2suUx m3z{i Ud 9 A < vWi!ziWxz @. x~ zikm~. U 9( d 9 A < q
(90) A <)H d 9( d 9 A <*< UT; 9(9 G !)qq
(91) AA <)<)HH UU 99 ! !
(92) qq
(93) AA << qq # #
(94)
(95) dd 99 AA << L U. . acb aed.
(96)
(97)
(98)
(99) !" $#&%' )(*( . mx~~W| « xgm3z*z{iWx z>m3gm3{0L|su~Hzb9 !q
(100) <_ J q J q
(101) d 9 < gsycWxgm D M /PT Ux sumY z{x#!«iksyi syU~kmYmY{x{s}wu.x U; x#U x~ x {mz{vk{~[{x#!«iksyi @ {x#g¯h>itvW¼t§®|¬xw}w A ziWm2§®|{lvkwyxm ; 9 !q <;U (9 G)q A <*<)H U 9 !q
(102) A <L . . . §®|g>zikm s}{mz>W{x~Wi!x~ . tpz« |x#t , .Wgvkm syUmsÀz{ikm3x UT | x. ,*M:/. T 9( Gq UT 9( Gq) A <s<{H U 9 !q
(103) A < q T 9 !q @T 9 !q
(104) A <*<{H @ 9( Gq) A < ,*M#$/ §®|g6ziWmJm3zvk{~2k{x~Wi¼ m`.W~WmJz«|¬su~kwum#xw}vWm Å*vkwum3{syx~2kiWxgm§®vk~¥ zsu|~¥V[Tf9 !q
(105) < x~ ; 9( Gq) < ¯ Dm2mY3xwuwLzikm§®vkwuwÂÅ*vWw}msyx~lp| mwP§®| x~ x{|syx z{m su~ks}zsyxwÂx~ L|vW~ x{|g~ s}zsu|~W m3{s}gm s}~D¨ ©ª f9( G)q <i= 9 !
(106) q q6 [ < HKJ §®|P(9 G)q _< $ T
(107) J
(108) q d (9 < ,*M"5:/ DmvWmx~!s}~W3|l&su~k&¥|gvk~ x3|~ sÀz{s}|g~W>|~4 ; ; (9 Gq Jo< H avced 9 < §®|` JGL ,*M :/ ~WmsÀz{zsusux|wL~!3nW|~¯vMN / s}¯ zsu|~¥xm m3{s}gm §®{|l8x3|l&Wxzsukw}m2z{x z{s}|g~Wx{W|gkw}ml ¨ ©ª , «mm3zvk{~ z{|ziWsu su~ h>ikm sumY z0x~ m3zvk{~SkiWxgmY , x~ ¼*xg2zikmSxzsy§® zikmxlpmm¦HvWx z{s}|g~¼zikms}0x sum3~Hz/ l xz{i.x zziWm2xvWzsy T (9 G)q d 9 <*<)H ; 9 !
(109) q d (9 <s< §®|` JGL _, :/ x~ |~km3x~²ikm& z{iWx z d 9 <)H 9 !
(110) q d (9 < q d 9 <*< q d 9 <)H [ (9 G)q d 9 <*< _, MN/. |z{ie, M. / x~ ,FMN5:>/ x{m2|~¥mY¦gvWm3~W3m |§zikms m~gz{s L. 3x z{s}|g~§®|gl0vkwyx (9 G)q A < H [ 9 !q [9( G)q A <s< _, e/ «iWsui0ik|w
(111) §®|¥|zi0§ xl&suw}sum|§¥{x#Â|gW{x~Wikm¯VD m vWmziWsuk{|Lm3zz| m`W. ~Wmz{ikm Å*vkwum3{sux~ | «¬b f9 !
(112) q <)H (9 G)q Vq [ '9 !
(113) q <*<{H8| 9 !
(114) q [ q (9 G)q (9 G< )q <*< H| [ 9(9 ! G
(115) q)q << [ 3|{mYL|~ s}~Wz|&z{ikmÆ
(116) xx~kgsux~ | «¬¼tse¯ m¯z{ikm-W. zwus}~km|§f,*M ©o/ ¯ . . . . . . # . . . . . . . # . . G *¡N¢.
(117) #. MY.
(118) $$
(119) { ;
(120) ! ; P$ ( . . ± ¡. . ¢ ´ "¢%$W¡ ¢%&$ ' ¢% &£ ' ¶ £ ¶ ¡#¡ ± ¶ · ± £ ± cxw}{mx |g~km§®|gJzikmks}¹_ xwuvkm kiWxm ,*M ¹M#e/ ¼« mUz{m3l x z{suxwuw} m`.W~Wm¬ks}¹_ xwuvkm Å*vkwum3{sux~ §®vW~W z{s}|g~§®{|l ziWm3su>Æxg{x~ksyx~ |gvk~HzmWxz3¯ Dm3|~Ws m3>x03|vkkwumU|§Æ
(121) xx~kgsux~&§®vk~Wzsu|~W 9( Gq) A < x~ 9 !q
(122) A < «iksuixm¬zx~W¥|gz{m xw}|g~k2zikm U @ {x#*xg33| s}~W2z|z{ikmU|g s}~Wx s PU m3{m3~Hzsyxw6mY¦HvWx z{@ s}|g~ '%. . H # 9 a < q a5. >s}~,*M ¹M#e/¬¼W«mxHxsu~ m
(123) .W~km2z« |&Å*vkwum3{sux~§®vk~¥ zsu|~¥ 9( Gq) < t ; (9 Gq U; 9 !
(124) q A <*<)H U 9 !q
(125) A < q T 9 !q aT 9 !q
(126) A <*< H a 9( Gq) A <C H Y q q % A L ,_©:/ ± N¢¡ 8¤ 0x# T x~ T ~Wm3mp3|H«m«s}wuwsu~ z{ikmm¦HvkmwvW~Wxl0ks}gvk|v¥wu ~W|zm sulpWw} GT §®|>z{ikmm3zvk{~!{U x#>x~ @ ; §®|>ziWm s}{mz{x#-,®su~Wzmx |§ <;U /¯ h>ikmÅ*vkwum3{sux~ §®vk~Wzsu|~W {x zsy§®0z{ikmU¥xzsyxw s P m3{m3~HzsyxwLm¦HvWxzsu|~Wc|zxsu~km H msuts}~kzikm x¥| gm{m3wyx z{s}|g~W = 19( G)q < 7 [ H #
(127) 9 19 !
(128) q <*< . . . !. . z{iWx z¬sy z|{x#. . = [ 7 [ H #
(129) 9 9( Gq) <*<. ,_ no/. T 9 !q
(130) d 9 <*< H ; 9( Gq) d 9 <*<. ,_ee/. ¬m3l xxwy|pz{iWx z¬kx~¥ikm ~kmYm{{x{s}wu l x z{i.x zz{ikm3xvWzsy. mSxwumYx vWm z{iksy.mk{m{su|~ §®|gz{ikm kiWxm e, :/x~ «s}wuw2vWm s}z.xgxs}~¾z{| m3{s}gm D L|vW~ x{3|~ }s zsu|~¥3¯ < ! '!> (+1.) %! !). >h iWmxsul|§z{iksyvkWmzsu|~.suUmkwyxsu~²ik| « zikmm~km3{sum H @ vWm s}~.z{ikm3|~ mY zvWm §®|gl0vkwyx\,FMeM />x{mm3 xwuvWxzm ¯ h>ikm3wuxgsy3xw
(131) lpm3zik| §®|gzikm0|l&kvkz{x z{s}|g~²|§zikmm3~kmgvWm¬x Æxg{x~ksyx~ §®|gl0vkwyx0|gz{xs}~Wm §®|gl8ziWms}~Hz{m3x z{s}|g~|§f,e:/ |~²xpx# zvkLm¯r m-.¥{z mzxsuw6ziWsu m3{s} x z{s}|g~wumx s}~WUz{|§®|gl0vkwy x ,*MYe /x~ su~Hz{| vWm m|l&mz{sy3xwHk{mx s}~k x~ zikmxvktsuwusux xsyxkwum b¯ Dmz{ikm3~ sumzikmpÅ*vkwum3{sux~[m¦HvWxzsu|~WvWm z{|!3|l&kvz{mz{ikmm0~Wm3«;¦HvWx~Hz{sÀz{s}mY3¯ su~Wxwuwu«m2gs}gm2x~mY¦Hvks} xw}m~gz§®vWw}wuÅ*vWw}msyx~ m3{su#xzsu|~!|§zikm{xl&m2m¦HvWxzsu|~W¯ . "! #$!. . $7 7 '1"4 &- '1 . Dmz{xzt 3|~Ws m3{s}~k² x!z{vk¥mx{|vk~ L x.{m§®m3{m3~¥m x# ; 9 !q A < su~ z ikm su{m z0Wxz |§>zik m Æxg{x~ksyx~ |wuvz{s}|g~Dx~ «s}wuw*|l&s}zzikm ; ~k|zx z{s}|g~ §®|g|g~Hgm3~ksum3~¥m¯ x#.zvW¥msy m
(132) .W~km xg H o9 !q [9 !q
(133) A <*< q A q7 U q A 9 A q <7' «ikmm 9 A q < sy2zikm ¥xwuw*|§>{x suvW x~ . . acb aed.
(134)
(135)
(136)
(137) !" $#&%' )(*( 3m3~Hzm A ¼kx~ A Ä{m3m~ §®|{lvkwyx:/ . . 2 . M:M. q7 U x{mb.km , m3m.WvWm-5:/¯h>iWmsu~Hzmx zsu|~|§m¦HvWx z{s}|g~,e:/|~ ¾gs}gm-,®t. 9( U q
(138) < 69 U q
(139) < 7 B X H
(140). 9( A q
(141) < 69 A q
(142) < 7 B X = E 9 !q
(143) < XFX ¯{ »zUsy¬s}l&kwuikmm>9 ^ Y q Jo< s}~.z{ikm2z« |&zm3{l xL| mx~ . . 2. .
(144). . « iWm3{m
(145) syziWmmtzmsu|~k|gl xwPz| z{ikm3~\6B 7 B
(146) H ^ ¯ch>ikm2ml xsu~ks}~W0Wxz |§ bx{mx#cL|zsu|~Wx~ zikms}¬3|~Hz{s}Wvzsu|~su ]m3{|pxg 6²sy>z{x~km~gz>z{|0z{ikmx#t t3|~Wz{vWzsu|~¯. Dm~k| « i¥x~kgmz{ikm2s}~Hz{m3x z{s}|g~ xsyxkwum/ B A H ; U9 !q
(147) < , se¯ m¯ H [9 !q
(148) A < / 9 U q [9 U q
(149) A <s< 9 U q 9( U q
(150) A <s< [ 9( U q
(151) A < X A [ H (9 A q [9 A
(152) q A <*< 9 A q
(153) A < XF A [ = E 9( Gq [9 !q
(154) A <*< [ [9 !q
(155) A < XF A X [ x~ |zxsu~ x§®|{lvkwyx§®|Jz{ikm¬m3~Wm3{¹xw}|g~k2m3gm3{{x#R, < A J/ x~ §®|cxw}w< A q U #¹H0w}m3zz{s}~k ¬|pz| J (9 Gq 9( G)q A <s< 9 !q [9 !
(156) q A <*< [ [9 !
(157) q A < H 9 A )q A < (9 A
(158) q A < [ [9 A )q A < = E 9 !q [9( G)q A <s< [ 9( A
(159) q A < X L _, :/ Æ
(160) mzv¥0xgvkl&m §®|px²«iksuw}mziWxz E}HJ ¯[h>ikm3~ mY¦HvWx z{s}|g~e, o/ s}l&kwuDz{xzmYziWm« m3wuwÀ¹t ~k| «~ 3|~Wm3{ x z{s}|g~!W|g¥mz!x33| su~kpz|«iWsui4 9 R7 < su|~¥zx~Hzxwu|~W {x#¯1 ~ m3m z{ikm!|{s}m~gz{m g|wuvkl&m|§x~ s}~¥. ~ksÀz{ms}l xwz{vkLm!|§Ux#tm [ vW3mz| [ s}~Nzikm.Wx{xsuxw . . . . . . . . . . . . . . l&| mwe¯. U§2|vW{m¼§®|gl0vkwux?,e:/su&l&mx~ksu~k§®vkwxg0wu|~W x0z{ikm.{x#DzvW¥m |tmp~k|z&3|wuwuxWm >«m {mxwuwziWxz«mxm&su~ zikm s}{mzWxz|§ zikm{x#2x~ [ ; 9 !q
(161) A <H J ¯ zxvWzsy&¥|gs}~Hz3¼ ; 9 !q
(162) A < x~ksuikmYÂx~ ,_o/Lkm sy z{x~ su~.W~ks}zmm3~kmg¯Âh|¬| m{3|l&mzikmcxvWzsy s^_vkw}z « [ m `m .¥~kmxp~km3« §®vk~Wzsu|~ ; 9( Gq) < ; 9( Gq ; 9 !q
(163) A <*<{H 9 !q ; 9( Gq) A <*< ; 9 !q ; 9( Gq) A <s< ; 9 !q
(164) A < L ,_g$ / [ D-m .W~ §®{|l ,_o /*z{iWx z ; 9( Gq ; 9( Gq) A <*< {x zsy* .Wm z{ikm0 UÅ. . {9 !q {9 !q A <s<7'H8| E ; ; 9( G9( Gq q ; ; 9 !9 !q
(165) q
(166) A A<*<<*< ; 9 J
(167) q A <)H 9 J q
(168) A < ; 9 J q
(169) A <. ; <;
(170) . G *¡N¢. . . ,_$5:/.
(171) #. M#. .
(172) $$
(173) { ;
(174) ! ; P$ ( . , mY3xw}wtz{iWx z [9 J q
(175) A <)H A /¯Jh>iHv¥3¼xgJ« m>xgvkl&m & J ,emY z{s}|g~&k¯^M / ¼ ; ml&xs}~¥¥|gvk~ m mm~!xz z{ikm3xvWzsy¯ Dm¬x~k| b« T²3§®xvk~p~¥{ m3zLsu|m~ xzxzik~&mU¥xm ¥ | m`g.Wm~Wm | l&zkiWvkxz{zcx z{xs}|gzsy~WF.¥Jmsu~pzziWikmm¬{mUz{vkÅK{~p,_$¥5:x/xz*§ |z§LmJzikzmUikm¬|wuxvvWz{s}|gzsy~p¯ x~ {s}vk~ l&Ws}x~k ¹ z{su3vkwyx* z{iWx zz{ikm2§®|wuwu| «s}~k&|g~Hzsu~HvWsÀz3|~ sÀz{s}|g~|g~ , k{| m s}~ v¨ M#0ª / ik|gw - T 9( Gq T 9( Gq) d 9 <*<s<{H ; 9 !q ; 9( Gq) d 9 <*<s< q ,_ :/ « m2|zxsu~!xpvk~WsÀ§®|gl&wu xwus §®|{lvWwux ,®m3km3kzUx z¬3xvWz{suL|su~Hz{ /§®|>ziWmm3~kmgxwu|~k xp{x#\ . . 9 !q /^9 !q
(176) A <s<)H ^ 9 !q ^ K9((9 G Gq)q A ^<s< 9 !q
(177) 9 A !<*q < (9 Gq) A <s< x{mzikmvWvWxw s}{mz m3zvk{~Å*vWw}msyx~!§®vk~Wzsu|~W , m3me, ©:/*/ x~ 9 !q (9 G)q A <s<{H [ 9 !
(178) q A <L . . «iWm3{m-. x~ . . . ,e©:/. . ~.Å*vkwum3{syx~.|t| su~Wx z{m>« mi¥x#mzikm2§®|gl0vkwuxm H L ,e©GMN/ «iWsui!vWm s}~,*MeMN/ mm3~Hz{vWxwuw} gs}gm §®|g¬x~tvk¹ |l xsu~5|§ o9Vq < ¯ zY¯ & J q7 & J' 2 @ XeO 9 ; ; ; = T b T T < XeO ,e©ge/ «ikm3{m H o9 V q < ¯ z¯ d 9 7< ' * 2 #"! +. #' ! 8 - ' "! ). h>iWm&Æxg{x~ksyx~ Åb§®|gP(9 Gq 9( G)q A <s< e, $5o/ |~¥s m3{m xx§®vk~W z{s}|g~ |§b9( Gq) A < sy2sum~ su~ z{ikmk{m3tsu|vW>m z{s}|g~¯*h>ikm|wuvzsu|~!suzikmm3§®|{mgs}gm3~!H E 9 !q [9 !
(179) q A <*<)H P9 J )q A < h`jGk 9 | VX < V ( 9 G q [9 !q
(180) A <*< A x~ s}wuw}v¥z{{xzm>ziWm¬xW|{zsu|~0m`P mz*|§Lzikm E zml s}~\e, :/ ¯ r6 T H 6 ; xzzikm¬xvWzsy¼ z{iksy*§®|gl0vkwuxsu |g{mzcm3gm3~xg{|g{zikm23xvWzsy , z{iWx~G cz|~e, o/*/ ¯[ ~WxzsyvW[ wuxc«ikm~ EHJ ¼ . . . . . . syJx2|g~Wzx~HzJx~ ziksyJ|g~Wz{x~HzJsykmYmgm L|z{i xwu|~kzikm su{m z*x~ {mz{vk{~0WxzJ|§WziWm{x#¯. Dm|§J|gvkmxWkw}zikm0Æ
(181) xg{x~ksyx~z| Å*vkwum3{syx~.zx~¥§®|gl x z{s}|g~|§mzsu|~[¯ © x~ W. ~ x mz|§z« |&m¦HvWx z{s}|g~W§®| . = 47 [ H 9 !q
(182) E q < [ . ,e©©:/ . acb aed.
(183)
(184)
(185)
(186) !" $#&%' )(*(. MY©. 9 Gq d 9 <*<)H 1T 9( Gq) d 9 <*< |g~z{ikm3xvWzsyW, vWm ,ee:/*/¯. x~ . ; ( ). Äm|l&mz{sy3xwk{mx s}~k m3Lm3~ !|~Áz{ikm m3 xwuvWxzsu|~Á|§ [9( Gq) A < ¯ ~Áz{ikmD{x# zx3s}~W l m3zik| ¼z{iksy>su |g~kmzik{|vWizikm2wus}~kmYx{s^]Yx z{s}|g~|§zikm ¸ xl&suwÀz{[ |~ksyx~.zml ,FMY©:/«sÀz{i{mLm z & z{| A ,®§®|L|zi su{m z¬x~ m3zvk{~!3|l&L|~km~gz/. [9 !q V9 !q. .
(187) [
(188) H [. . x~ s}~ks}zsyxw|~ sÀz{s}|g~W. . >§®| . AA << P H H | [ 9 !(9 Gq [qq [q < < | (9 G(9 Gq [qq q < < [Z[ [. «m m
(189) .W~km. . . [9 J q
(190) A < P H V9 J
(191) q A <. [ H [ . . . Y @ A. H [. P. . [9 !q 9 Gq.
(192) [ ( ) H [. AA <<. P. ,e©no/. P. 9 !q
(193) < vWs}~kpz{ikmÆ
(194) xx~kgsux~|t| su~Wx z{m (9 Gq 9( G)q A <s<{H (9 G)q A < [ . . Dm.W~ , xHxsu~bm z{s}|g~ ¯ ©:/ ziWxz.zikmÁxzsy§® ziWmDÅcvkw}msyx~½zml1|§Wxz{suxw s^Pm3{m3~Hzsyxw mY¦HvWx z{s}|g~ msum §®{|l , ©n/ ¨ Yª»¼ (9 G)q Vq6 < 7 [ P = P H H H H | [ [N[ (9 G(9 Gq)Vq)Vq6Wq6 < < | [ 9( G9 !q)Vq
(195) q6q6 < < P H P ,e©:e/ «s}zi ; 9 !
(196) q d 9 <*<-H fT19 !
(197) q d (9 <s< x~ ~kmYmY{x{s}wu ; (9 G)q d 9 <*<-H T1(9 G)q d 9 <*<-H J |~Dzikm . . . xvWzsy¯. 6! "* . #4 "* $7 7 '1"4&. ' . 4 ' ! 4 .% Dmp~k| « m`.¥~km s}{mzwu t H ¯Dm&xwy|!m3z H gmz " ± ¢
(198) G
(199) 4[ '`v
(200) y - G. 6 L 6 H 6 7$9;6 < ¡ ¶Â¶ |g su~k0z|pziWm `m .W~WsÀz{s}|g~!|§ ¼k « mi¥x#mzikm3wuxgsuxwP{mvkwÀz . . q¥z{ikm3~. ~.|gvk3xm,X H. H [ Y /¼ks}z¬sux&s}l&kwum|g~WmY¦Hvkm3~W3m2|§
(201) z{ikm{m3wyx zsu|~ . 9 [ 9 19 !q
(202) A <*<s<{H [ 9 19 19 !q
(203) A <*<s<{H [ 9 f9 !q
(204) A <*< . . G *¡N¢. . . . . . «m.
(205) #. Mn. .
(206) $$
(207) { ;
(208) ! ; P$ ( . h>ikm~¼Wxg3|g s}~k0z|&{m3wyx z{s}|g~ _, no/¼tzikmÅcvkw}msyx~.¦HvWx~Hz{sÀz. . {x z{su*.Wm. 6 L 6 H [ 9 [ < [ h>itvWtl0vkw}zsukw}tsu~k t ¼«mgmz 6 L 6 H 67e9;6 <| [ L [ qs}~W3m H = ' x~ H , «m&xwu« x#iWx#m x~ T [ J /« mgmzz{ikm [ ms}{m {mvk[ wÀzY ¯ ¡ ¶ ¶ ® ¶ ! ` P f`v
(209) - G. E = 6 /6 HJ h>iksymY¦gv¥x zsu|~!sy>mkxzwu zikm{xl&mxPe, ©©o/ ¯ ¡ ¶Â¶ Ç[vkwÀz{s}Ww}tsu~k&mwuxzsu|~ , : / t tsum3w E = 6 L 6 HJ h>itvW>« m2m3z E = 6 7e96 <i= 6 L 6W HJGL. ,e©:/ J. ; . ' '. x~ vWsu~kpziWmkmts}|gvW w}mlpl x&« m2mz>z{ikmmYvWwÀzY¯ 1.% + '!+) + ' '!. . . . %'! + (. +' . '! 3+)='! ! {7. ~Wm m!sy{vkm|§JziWmk{|kwum3l syz{ikm mzml&su~Wx z{s}|g~²|§Jz{ikm03|l&kvzx zsu|~¥xw |l xsu~ xU«mw}wx Åcvkw}msyx~!su~ksÀz{suxwÂx~ L|vk~ x{|~ sÀz{s}|g~W¯h>iWm |l xsu~syx&z{su!¥|gvk~ m |g~z{ikm "& J s m ,eiW|vkw ziWmwyxm3&|glpm§®|gl zikm @ J s mN/HDz{ikm!xvWzsy!vk{m H d 9 < x~ |~Nzikm |zikms mH ziWm H J x sy , m3mx~t .¥vk{mN/¯!h>ikmkitsy3sysu~ mm z{sutsuxwcsu~ zikm @ J i¥xw}§Âkwux~km¬«ikmm¬zikms}~ m su x{vkl&m z|0¥m|g~Wzx~Hz¯ Dm t~k| « ziWxzcz{ikm su{m z-, | /c|gw}vz{s}|g~ su~ziksyf ]3|g~km2suxg|syx zm z{|z{ikms}~¥s m3~Hzkwyx~km2«>x#m 2 A h
(210) jk 9 CF> A 9 )nst u'p = l
(211) m:nGp <*< «iWs}wum2zikm {mz{vk{D ~ , = /|gw}vz{s}|g~²sumLmzm z|W|gWxHx zm2§®{m3mw}²x#«>x#su~²ziW1 m @ J sumY zsu|~²LmxvWm|§ z{ikmUx suxzsu|~&¥|gvk~ xp|g~ s}zsu|~ sulpL|gm |~&ziWm{3x zzmm .¥m3w ¯Jh>iksusyJziW_m 0kittsy3x3w 2 x z{x « m2lvWz¬kvksuw |g~z{| mz{m3{lpsu~km|gvk¥|gvk~ xx~ s}~WsÀz{suxw
(212) |g~ s}zsu|~W¯. . . ' ! ) $ . . 4 ' ! ) # .#' ! 8. 0xw}{mx & l m~gz{s}|g~km ,emY z{s}|g~W0©W¯ k¼J©k¯ ©:/ ¼z{ikmL|vk~ x{D3|~ Às z{s}|g~W|g~ zikm!3xv¥z{sus mxw}w m3{s}gm§®{|l ®§ |{lvWwux ,e:e/ ¯ wuw*¦gv¥x~Hzs}zsumzi¥x zx{mz{{x~WL|zm t .ziWmpx# | «;l0vWz2l x zi. . acb aed.
(213)
(214)
(215)
(216) !" $#&%' )(*(. M . xz>zikmxvWzsy¼kx~ s}~²x W sÀz{s}|g~gm3|glpm3z{suxw6kmYx su~kpsu H ~W| «~z| x~ksuizikmmg¯. *su~²¨ ©ªLxwuw s}{mz , | /*¦HvWx~Hzs}zsum*xmwus}~!m z{|2zikms}~¥s m3~Hzckwyx~Wm¬« x#gmP,ee/ gs}z{cm3|gl&mz{sy su~Hzmk{mzx z{s}|g~[§®|{l xvW~ksÀ§®|gl m3z|§x#2x zx~ x~kgw}mp¾«s}ziDziWmpL|vW~ x{" H J , .Wgvkm o / ¯ »z2W| ts mU¹>zikH m&su~ m |§c{m§®xzsu|~ sy2|g~WH zx~Havcez2dm¦HH vWxwz{||g~km&|~[ z{ikm&¥|gvk~ x.¹msÀz{ikm3 x ¬m3vWl&x~k~ [ ; l`monGpb|gx s}{syikw}m3zW ; )nstvu'p ¥|gvk~ xD|g~ s}zsu|~ §®|zikm s}{mzkiWx4 m , m3m²¨ ©#ª§®|l&|{m mzxsuwu / R ¯ mmY3xwuwzi¥x z ; 9 !q[9 !q
(217) A <*< q ; 9 !q[9 !q
(218) A <s<7'RH [9( Gq) A < q 9( Gq) A < ' «ikmm A syUz{ikmps}~ks}zsyxwL|gsÀz{s}|g~ |§Jzikm0zx gm x# [9( Gq) A < |~ zikm [ [ x su¯h>iWmmY|gw}vkzsu|~.|' § , ©on />sy¬zxsuiHz§®|g«>x su~.zikm @ J «ikmm2z{ikmsu~ m.|§{m§®x z{s}|g~ sy|g~Wz{x~HzY¯h>iWm|gw}vz{s}|g~sy|g~Wz{x~Hz¬x~ s}z{ z{{xgm2|~ HJ sumz{ikm¥|gvk~ x|~ sÀz{s}|g~W. . {9 !q Jo<)H8Y q ;{9( Gq Jo<)HJGL h>iWm2¦HvWx~Hzs}z ; sy>w}su~Ggm z|pziWms}~W3|l&su~k xl&kwusÀz{v m 2 A z{ik{|vkgi§®|gl0vkwux ,e©GMN/b ; H ; ; ; H 2 A @ ; ; ,e©H$/ h>iWmsu~Ws m~gz«>x#m*l&| m3wyx¬wyxm3¥mYxl |§¥xUgs}gm3~z{iksyH ~Wm{Âz{iWx z W. zk{|Wxgx z{m6vW~ syz{vkLm su~¾z{ikm @ J ]|~kmg¼U| «suw}w¥m 3] m|Smmt«ikmm²|g~ H J mkmz|g~Áx gs}gm3~ «s}~ | « A q U H«ikm3{ms}zsul&kw}su |~Wm¯ ~W{xg zsym«mvWmxplp|t|zikm , m3Lm3~ su~k&|~!x¥xxl&mz{m3 / i¥xx z{m3{suzsy§®vW~W z{s}|g~ ; 9 !q J<)H @ n*t ufp L Æ
(219) s^gm§®|gpWiWxm§®vW~W z{s}|g~W3¼ ~k|D¥|gvk~ x 3|~ sÀz{s}|g~Wp|~R H J x{m~kmm m §®|g xwuw {mz{vk{~ ¦HvWx~Hzs}zsum T ¼ 1TSx~ S T xgc« m2x{ vkl&m, x§®mxzvk{m|§ÂziWm§®|gw 3xvWzsyU3xgm J/ z{iWx z>z{ikm{mz{vk{~ ; . . . . | «b|tmY|gvz¬|§|vk¬3|l&kvzx z{s}|g~Wxw |gl xsu~¯. . . . . ! # .#"*4 ' ! ) # . #' ! 8 .. «mxw}{mx mY3xw}wum , m z{s}|g~&k¯ :/ ¼ z{ikmwu|txwus^]Yx z{s}|g~|§¥zikm¬xvWzsy>vk{m m¥m~ J|g~pxl&| m3w 3 |vkWw}su~k.¥|ziDziWm s}{mzx~ {mzvW~DkiWxgmY2«sÀz{i z{ikm3xvWzsy0mY¦HvWx z{s}|g~ s}z{m3w}§¯ Dm&zikmm3§®|{m ~Wm3m z| W| ts msu~ks}zsyxw xvWit x zxp§®|¬xw}wP¹ su{m z , | / x~ {mzvW~ , = /¹c¦HvWx~gz{sÀz{s}mY3¯. . Dm¬mkwyxsu~km su~.¨ ©ªWik| « z|m3Hz{m3~ z{ikmU|wuvzsu|~pz|x2¥mv |¹ z{x z{s}|g~Wx{2ks}¹_ xwuvkm l&| mwWsu~ z{ikmC @ J ]3|g~km , z{ikm¬su~ mpsuc|~kwu0x2Wsu|{ssum~ J /ziWxzcm vW3mz{|x~ mxgsuwu|glpWvz{xkw}m M3¹ W|gkw}ml.¯Dmpzikm~ ik| « m ziWxz2s}zk{| ts mY2x~k|g~ su~Hzm§®msu~k xvWit xz{x§®|2z{ikm&zikm z{m3l ,FMN5:/¹ ~k|g~[su~gz{m3§®m3{s}~Wikmml&mYx~ksu~kz{iWx zziWmpz{xzsu|~Wx!|gw}vz{s}|g~ x~ zikm&xzvWxw|¹ wuvz{s}|g~!xg|syx zm z|&su~Ws m~gzkwyx~Wm«>x#m |p~k|z| mwyxx~ l&|t|z{ikw}3|~k~Wm zY¯) »z m`.W~Wm>su~ ¥xzsyvkwyxx~!su~ksÀz{suxw
(220) 3xvWzsyL|su~Hz d 9 J<)H54 A ¼kmm .Wvk{m&x~ ¨ ©#ªÂ§®| mz{xs}wy¯. . G *¡N¢. .
(221) #. MY. .
(222) $$
(223) { ;
(224) ! ; P$ ( . . h>ikmxlpmz{{xzm3g xkkwus}mY2z|²z{ikmz{{x~W¥|gz{m ¦HvWx~Hzs}zsum0xL| m x~ zikms}~ks}zsyxw xvWit x z{xpx{m2sum~t ziWm2|wuvz{s}|g~W9 A q A < |§z{ikmzx zsu|~¥x{ m¦HvWx z{s}|g~W-,®L|z{i§®|g`^ kx~WiWm/. A P H A 9 J q
(225) q6 9 J q
(226) <*< |H [ [N[ 9 J q
(227) Vq6 9 J q
(228) <s< | [ 9 J 9 J q
(229) q
Documents relatifs
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des
[…] Chez nous, le parterre […] est composé communément des citoyens les moins riches, les moins maniérés, les moins raffinés dans leurs mœurs ; de ceux
But on another hand, increasing q at constant operative pressure results in decreasing the equilibrium pressure, by decreasing the operative temperature (Figure 9), and finally, it
R´ esum´ e : On pr´esente des r´esultats autour du probl`eme suivant: pour un point mat´eriel dont l’acc´el´eration est born´ee par une constante donn´ee, et pour un
Ensuite, pour déterminer lesquelles des voix créées pouvaient être qualifiées d’« androgynes », nous avons fait un test de perception dans lequel nous avons demandé
Toutefois, des améliorations sont à prévoir car bien que la protection induite par ces glycoconjugués soit significative, elle n’est cependant pas optimale pour mettre
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des
Venant compléter les nombreux guides spécialisés qui informent le touriste gay sur les différents lieux et structures qu’il pourra fréquenter s’il recherche son
