Squelettes euclidiens d'objets discrets n-dimensionnels
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Squelettes Euclidiens d’Objets Discrets n-Dimensionnels Sara Ferna´ndez-Vidal et Gre´goire Malandain. N˚ 2771 Janvier 1996. PROGRAMME 4. ISSN 0249-6399. apport de recherche.
(3)
(4)
(5) "!# $&%'
(6) )(* $ "+,%' - . /0 13254628739:4 ;=<5;?>#9:@BADCFEG>$25H6IJ9BKL4 M:NPO,EQ4 9SRT25HU25;?>$25EQ;VII W XZY\[\X^]6_0_0`aVb cYedfY6gZhjiBkl`6mnho_p]q[e``gsrBhjtZhjYeu W3XZY6vZ`gxw3y:hjz{]qklXZ` c ]6y|y}Y\X~gxzl`XZ`l`XZl`u Bensb e]qu\rBho`X\eb \y{]6[\`t B #x `0t^iBkl`o`gZg^``g]g^X^]qultZY\XZ_0 `p`¡u]¢|`p_0 z:h]6u£t^Yeu\gzl`tYek:gZh¤jtul tz|kSdf`¡tDY6hjuzl` zl X~hoXZ`"zl`¥_]qu:hj¦XZ`§Ye_0y{]qg^`pj`¡t0ylXZY\ylX~hj g^ ¡t0[qoY\d{]o`tz,¨©kluYed:vZ`g¡m3`uy{]qX~gZhok:¤ho`Xj`¡k|XY\XZ_0`\ª Y\XZtzlk ]jk:*zlkSt^iBkl`j`gZg^`\m.h¤)`tZgul `t^t]hoXZ`0zl`pY\ult^`X~re`X«g^XZY6hjtylXZY\ylX~hj g^ ¡t¬=®D¯ °n±6²0±e³Q±´fµ¶·m,¸] ¹ ±qº{ºf¶§®»± ¼½\®¾µ¿·½\³µ±qº§zlkt^iBkl`j`gZg^`\m
(7) `g¸]ÀZ¶¼±6º5¿·³¸ÀÁl¼ ³µ±qº§zl`ÂG¨©Yed:vZ`gVÃy5]6X~gZhjXzlkt^iBkl`j`gZg^`\ª3Ä Y\klt ]r\YeultÅ]hÆgklul`§ g^klz|`§zl`t0]6yly|XZY:l`t`¢nhjtZg]6u\g^`t.¬ ]6t^tDklXZ`XtZhj_k:¤g]6u| ¡_0`u\gp¡`tg^XZY6hjtylXZYey|X~ho g^ t t^`_dno` g^XZ¦tsz:h¤ÇphÆj`6ª{È`y:jklt*j`ylXZY\d:o¦_0`ylX~hjulhoy5]zl` g^Y\k:g^`t*o`t)_0 g^lY:zl`t)`¢nhjtZg]6u\g^`t)`tZg)j`klX [\ ¡u| ¡X^]¤hot]gZhjYeuz:hÆÇph¤o` ]6k ]6t
(8) É}ÊGz:hj_Â`ultUhoY\ulul`Ū\È]6ult
(9) `·g*]qX~gZhoj`\mqu|Yeklt3ylXZY\y}Y\t^Y\ult#k|u]j[eY\X~hÆg^|_Â` yfYeklX«o`p ]ok:*zl`ÂG¨Ë]¢|`_0 z:h]6u£z,¨©Yed:vZ`g^tÉfÊGz:ho_0`ultZhjY\ulul`otª#Ä Y\kltk:gZh¤¤hot^Y\ulty}Y\klX`]§]" ]6X~g^` zl`z:hjtZg]qul``¡k|·¤hjz:ho`ulu|`\m`iBk:hulY\klt§]qt^t^klXZ`"ŨÌhju\r6]6X~h]qul`y{]qXpX^]6ylyfY\X~g]6kB¢g^X^]6ultUYeXZ_p]gZhoY\ult hjt^Ye_0 g^X~hjink|`¡tª `ty}Yqhjueg^tzlkÍt^iBkl`o`gZg^`t^Yeu\gz,¨Ë]6dfYeXZz ]qX^]6g^ X~hjt^ tsjY: ]j`_Â`u\gÃ0Ũ¾]hoz|`Vzl`zl`kn¢ y{]qX^]6_0¦g^XZ`tÎ`gÏ.m
(10) z|Yeu\gj`¡t«r6]j`klXZtY\XZXZ`¡tDy}Y\ulzl`u\gV]qku:h¤re` ]6k£zl`0zl g]h¤*zlkStDink|`·j`gZg^`6mÐ`giBk:h hjueg^XZY:z|k:hotD`¡u\gkluÍ`¡tDy{]6`zl`Vy5]6X^]q_0¦·g^XZ`tu{]g^klXZ`?y}Y\klX o`t^iBkl`j`·gZg^`6ª.w3ult^k:h¤g^`6m`uÑ|¢5]quegk|ut^`k:hÆ yfYeklXkluzl`txz|`¡kB¢"y{]qX^]6_0¦g^XZ`t¡m5Yeu"Y\d:gZho`u\g o`unhÆr\`]qk"zl`zl g]hÆÑ5u{]Ðz|kt^iBkl`j`gZg^`\ª}Òhju{]j`_0`¡u\g¡m Å¨Ó g]qy}`)]qylyf`·j `Ô·XZ`Yeu|tZg^XZklgZhoY\ug^Y\y}YqjYe[qhoiBkl`BÔ
(11) ulYek|t#]6tDt^klXZ`?iBkl`*j`*t^iBkl`o`gZg^`)]=¸] _0Õ_Â`?g^Y\yfY6jYe[qhj` iBkl`ŨÓY\d:vZ`g)hju:hÆgZh]Gª ÖØ×|ÙÚ^Û\ÜÝßÞ ink|`·j`gZg^`6m|YeulgZhjYeu"zl`z:hjtZg]qul`6mlXZ`ylXZ t^`u\g]gZhoY\u`ghou\g^`XZylXZ g]gZhjY\uFz|`¡tYed:vZ`g^t¡ª àoá#âGãZä»åQæ·çUäÆè\é\äÆêGë ìÐíî¸ïð¾ñòóõô
(12) îÅö÷ø ð¾ò ù ð¾úû¸ð¾òù ü¤û ì·ìíýûÅþZýô
(13) îÅö÷ø ð¾ò ù ð¾úûð¾ò ù üÆûÿ fûÅö
(14) ¸þf÷ ð¾ñòûQþÿ Ðö þñþZî ~ð¾öó¾þZî!" $#%0ÿ&'#(*)¡ö·÷ø¡ð¾ò #úQð¾÷eöóÓð¾,î +PþZñ.þ -/10ûQò·2ú Zþ. Unite´ de recherche INRIA Sophia-Antipolis.
(15) % Â s p /0 ?+,%
(16) ·Ù
(17) |Û6Ùe ug^:hjt0y{]6yf`X·m*]qu8]j[eY\X~h¤g^l_ g^YY\ultZg^XZklgg^|`]qylylXZY¡¢nhj_]g^`§_0`z:h] ]¢nhjtVYq]É Ú Ð×
(18) lÜ Y\d:vZ`ghotylXZY\y}Y\t^`z, ª sl`¥]j[eY\X~h¤g^l_ hotd{]6tD`¡z£Yeu£`klÆhjzl` ]6u£z:hjtZg]6u|¡`0_p]qyly:hjul[5m nho [\k{]6X^]qu\g^``¡tÂg^l`hou\r6]qX~h¸]qul`klulz|`¡XÂhot^Y\_0`g^X~hog^X^]qultZY\XZ_p]gZhjYeuY6g^l`XZ`t^knÆg^t¡ª Þ `o`g^Y\u yfY6hju\g^t]qXZ`Ñ5XZtZg0oY: ]Æ {]6X^]qg^`X~"h !`z,m :hj ``ylt]XZ` ]qt^Y\u{]6dno`Y\_0ylk:g]gZhoY\u{])¡Y\tZg0Y6 g^l` _0`g^lY:z,ª0Ò|YeX g^{]gylklXZyfYetD`\m `0zl`Ñ{ul`g Y"y{]qX^]6_0`g^`XZt¡m.Ï ]qulzSÎlm lY\t^`r6]jkl`0¡Y\XZXZ`t^yfYeulzg^Y g^l`zl`g]hÆfo`r\`·PYq,g^|`t `j`·g^Y\u,m|]6u|z0hou\g^XZY:zlkl`]«u{]g^k|X^]Pt^ ]j`Ê t^y5]6`*Y\X?g^l`t `j`g^Yeu,ª Þ `¡Y\ulz,m ]¥g^lXZ`t^lYqoz£hjt|Yet^`uÍYeXY\ul`pYq)g^l`t^`py{]qX^]q_Â`g^`XZt¡m :ho [qh¤re`tg^l`ÂÑ{u{]=z|`·g]h¤*o`re`)Yq)g^l` t `·j`g^YeuPª"Òhju{]¤ Bm3]"[qoY\d{]$tUg^`¡yÍre`X~h¤# g^{]gg^l`0g^Y\y}YqoY\$[ ÍYq*g^l`t `o`g^Y\uSY\XZXZ`¡tDy}Y\ulzg^Y"g^l` Y\ul`Y6.g^l`hju:hÆgZh]ÐYed:vZ`g¡ª %&'P)Ú (* ×
(19) \ +Þ `·j`g^Yeun"h ! ]gZhoY\u,m|z:hjtZg]6u|¡`g^X^]6ultUYeXZ_§mng^YeyfYqoY\[6hj ]PXZ`YeultUg^XZklgZhoY\u.
(20) . Ál¶ ®»¶ ³Å³Q¶¿=Ál¼ ®¾µqµ¶º{¿Ð¯ ± ¹ ¶ ³¸¿ qµ¿·¼ÀZ¶ ³¸¿º
(21) qµ²0¶º{¿µ±qº{ºf¶ ®¾¿ . :)(?. *` t^iBkl`o`gZg^`)`gÐŨË]¢|`)_0 z:h]6ut^Yeu\g#z|`¡t3Y\k:gZhÆjt#u| ¡t
(22) zlkd}`t^Yqhou«zl`)zl X~hoXZ`$o`t#y|XZYeylX~hj g^ t [qoY\d{]o`t z,¨©klu"Yed:vZ`g¡m|`uy{]qX~gZhj¡knÆhj`X)j`¡k|X)Y\XZ_Â`6ª `t$y|XZ`¡_hj`XZt*` PY\X~g^t Å]h¤g^t$yfY\klX3g^XZYek:r\`X*klul` zl Ñ{u:h¤gZhoY\upzlkpt^iBkl`j`·gZg^` t^Y\u\g$z |t)à ª ?jkl _ Ë Gª Ðt^`t^`X~gszlk"¡Y\ul`y:g)zl``kz|`ylX^]hoX~hj`6ml6¨©`tZgZÊUÃÊ z:hjXZ`z,¨©klu`k§y|XZY re`u{]qu\gxzl`tsyfYqhou\g^tsz|k§Yeu\g^Y\klX `ginknh$t^`ylXZY\y{]q[e`ÃprBhÆg^`t^tD`VY\ultZg]queg^`z{]qultŨÓY\d:vZ`g¡ª `t^iBkl`o`gZg^`0`tZgYeXZ_0 y{]6X j`ty}Yqhou\g^tY j`¡tXZYeu\g^tzl`0`t`kn¢Ít¡¨Ìhju\g^`XZt^`·g^`u\g¡ª *`tyfY6hju\g^tt^Yeu\g]qklt^tZh?]6y|y}`j ¡tyfYqhou\g^tz,¨©`¢ngZhoulgZhjYeuPª ul` ]qk:g^XZ`xz| ·Ñ5u:hÆgZhjY\u,m\]6XZ[\`_0`¡u\g?k:gZh¤Æhjt^ `6mB`tZg*]6kltDtZhlhjueg^XZY:z|k:hÆg^` y{]q!X "ª ?ok|_"$ª #upYeu|tZhoz|¦¡XZ`=¸]t^klX~Å]q¡` Y\d:g^`unk|`)Ãxy5]6X~gZhjX#zl`?]Yeu|·gZhjY\uzl`*z:hjtZg]qul`*z,¨Ók|uVY\d:vZ`g¡m]6iBkl`¤o`*u|Yeklt
(23) zlY\ulul`6my}Y\klXÐ{]6iBkl`*yfYqhou\g zl`G¨©Y\d:vZ`·g¡m{¸]Âz:hotUg]6ul`0]6kyfYqhou\gzl`¡Y\u\g^Yek|Xxj`y:ok|tylXZY:l`6ª `VtDink|`·j`gZg^`V`tZgzl Ñ{unh Ye_0_0`o` ¤ho`k"zl`tsz:hjt^Yeu\gZhjuBk:hÆg^ t zl`]zl X~hÆr\ ¡`«zl``gZg^`t^klX~Å]q`\ª #Y\kvZYek|XZtz{]6u|to`?dlkng#zl`?Y\XZ_]¤hot^`XP]su|Y6gZhjYeu«zl`*t^iBkl`o`gZg^`6m % ª )]¸]qd:&h Æ nmna|ml' |Y\ultZhjzl¦XZ`3o` ylXZY\d:j¦¡_0`z,¨©kluyfY6hju\g)zl` r:kl`g^YeyfYqoY\[6hjiBkl`s`g) g^klz:hj`j`¡t*y|XZYeylX~hj g^ t)zlk§tDink|`·j`gZg^`zl`t)Yed:vZ`g^t?iBk,¨ hÆ Yeu|tZhoz|¦¡XZ`«¡Y\_0_0` g]6u\gzl`tx`ult^`_d:o`t `XZ_0 ¡t z{]qulto`yn¸]qu`¡k|·¤hjz:ho`u,ª #z|Yeulu|`klul`zl Ñ{u:h¤gZhoY\u zlkt^iBkl`j`gZg^`ÂiBk:h3`tZgd{]6tD ¡`t^klX j`VY\ul`¡yngzl`dfYek:j`t_p]¢nhj_]j`¡tª 3zl _0Yeu\g^XZ`0iBkl`j`tulYqgZhoY\ult zl`y}Yqhou\gz,¨©`¢ngZhjulgZhoY\u`gzl``¡u\g^XZ`zl`dfYekno`_] ¢nho_p]o`«t^Yeu\g inknhÆr6]o`u\g^`t¡ª ( hjultZhÅm5Yeuyf`k:gxr\Y6hjX j`ÂtDink|`·j`gZg^`pYe_0_0`G¨©`ult^`_d:j`pzl`t`u\g^XZ`¡t«zl`td}Y\k:j`t_p]¢nhj_]j`¡tz|`0G¨©Yed:vZ`g¡ª.È]6u|t¸]¥_0Õ¡_0` ¤ho[\ul`6m|Yeu¥g^XZYeknre`j`t)g^X^]r6]qkn¢z|*` )
(24) ª +]g^|`¡XZY\u§`g|ª Þ `XZX^,] Ó" -Bmfe. Gª `)t^iBkl`j`·gZg^``tZg$z|Yeul=klu0t^Yek|tZÊ `ult^`_d:o`=zl`*ŨÓY\d:vZ`g¡mqg^XZ¦t Ñ5,u /QY\k_Vhjul1` 0
(25) `·g?y:]6 s]qk"Ô·`u\g^XZ`nÔ zl`G¨©Y\d:vZ`·g¡ª `t^iBkl`j`gZg^`Vz,¨©kluY\d:vZ`gxd:hjz:hj_Â`ultUhoY\ul`$]qklX^]0Ũ¾]qyly{]qXZ`ul`z,¨©klu[\X^]6y|l`Y\_ÂyfY\t^ zl` ¤ho[\ul`t?¡Y\klXZdf`t¡ª ]tZg^XZk|·g^k|XZ`z|`s`x[\X^]qyll`su|Yeklt?zlY\ulul`=G¨ hju:YeXZ_p]gZhoY\u0t^klX3]YeXZ_0`zl`sŨ©Yed:vZ`g¡ª Þ h ŨÓY\u]gZg]6l`Ã5]6iBkl`yfY6hju\gxzl`«¡`[\X^]qyll`]r6]j`¡k|Xszl`]z:hjtZg]6u|¡`]qk"y}Yqhou\g)j`y:jkltylXZY:l`«zlk Yeu\g^Y\kl2X /¸o`0X^] \Yeuz|`]dfYekno`_p]¢nhj_]j`V`u\g^XZ ¡`0`u`VyfYqhou\g 0 ulY\kltYedng^`¡u|Yeult`iBk:hGm,z{]qult ¸] ¤hÆgZg^ X^]g^klXZ`6m5`¡tUgsulY\_Â_0 p4½ 3\¶6² 57qµ½qº5&ª )9X 8q¡`Ã`ok:h¤Ê hÅm|ulYek|tx]qklXZYeu|ts]6k|t^tZhÐ]6¦tsëG¨ hounYeXZ_p]gZhoY\u Yeu|¡`XZu{]qu\gsj`Yeu\g^Y\kl X /¸XZY\u\gZho¦XZ1` 0*zl`G¨©Yed:vZ`g¡ª ¨¾]qyly:¤hj]gZhjYeu8zl``tzl Ñ{unhÆgZhjYeu|t§z{]qultpj`]qtz:hjt^XZ`g§yfYet^`df` ]6klY\klyßzl`ylXZY\d:j¦_Â`t¡ªÈ`t :` ,Y\X~g^tsY\u\gx [B]j`_Â`u\gx g^ Å]h¤g^tsyfYeklXzl Ñ{u:hjXsz:hjXZ`g^`¡_0`u\gxj`t^iBkl`j`gZg^`zl`tsY\d:vZ`g^tsz:hj[qhÆg]qkn; ¢ Ó" <.Gm _p]hjt3ulYek|t$y|XZ · XZY\ult3¡Y\ultZhjzl XZ`X#j`t?Yed:vZ`g^t3¡Y\_0_0`) g]6u\g*zl`t$]qylylXZY¢:hj_p]gZhjY\ult?z,¨ÓY\d:vZ`g^t Y\u\gZhouBklt¡ª W knhot^iBkl`j`ÂtDink|`·j`gZg^`0`¡tUg«z|`¡tUgZhoul 0ÃXZ`ylXZ t^`u\g^`XŨÓY\d:vZ`g¡m5¸]Âg^X^]6u|tZYeXZ_0 ``¡u£]¢|`_ z:h]quYek,m y:jklt [e ul X^]o`_0`ueg¡mnj`ylXZY:`t^t^klt=zl`t^iBkl`j`·gZgZhjt]gZhoY\u§z|Y6h¤gxt]gZhjtZÅ]hjXZ` o`t YeulznhÆgZhjYeu|tst^k:h¤r6]queg^`t¬ =?> Ù ,@Ð×f ×|Ù B× A C /DE-Gm|ylXZ`_ho`X){]qy:hÆg^XZ1` 0^ª $`·]tZho[\u:h¤Ñ{`iBk,¨Ìh¤Å]qk:g)iBkl`]g^Y\y}YqjYe[qho` zl` G¨©Yed:vZ`g*t^YqhÆg*ylXZ t^`X~r\ ¡`6ª5W#]qX*`¢|`¡_0y:j`6m:tUh,kluYed:vZ`g)`tZg*Yeulu|`¢|`6mehÆfÅ]6kng)ink|`tDYeutDink|`·j`gZg^` o` t^Y6h¤gx]qklt^tZhŪ B#Ü \ÙÙ ]Ñ{uz,¨©Y\d:g^`u:hoX·m`u\g^XZ`s]qk:g^XZ`t¡mG¨ hjuer6]qX~h]6ul` =
(26) l + #Ü
(27) ?× Ü×PÛ
(28) l#Ü
(29) :Ù × F C zlkVtDink|`·j`gZg^`)y{]qX#X^]qylyfYeX~g ]qkn¢g^X^]qultZY\XZ_p]gZhjY\ultÐhjt^Y\_ g^X~hjiBkl`t¡ª lÅ]qk:g#z|Yeul=ink|`*¸] _0 g^lY:zl` t¡¨¾]vZkltZg^`]qkn¢¥zl Ñ{u:h¤gZhoY\ult zlY\ulul `tsy{]qGX ?jkl_ `g )]¸]qd:hŪ =?> Ù & I H*+ #
(30) #Ü ª ¨ÓY\d:vZ`gszlYqhÆgy}Y\k:reYqhjXsÕg^XZ`XZ`YeultUg^XZk:hÆgÃy{]6X~gZhjXsz|`t^Y\u] ¢l`_0 z:h]6uPª . ,&úKJ L:L4M.
(31) a. ½qÀZ½¶Àºqº \ ¶F µ\½e®¶ ³ =À 5 \±qµÀZ¶
(32) ͽe®»½6º&e½qµº. xÄ Y\kltyfYek:r\Yeu|t·]qt^t^`X g^Yek:g^`tj`t_0 ·g^|Y:zl`tylXZYeyfY\t^ `¡tz{]qult]p¤h¤gZg^ ¡X^]g^klXZ`p`uiBk{]g^XZ`0]g^ Ê [\YeX~hj`t.¬ = ]j[eY\X~h¤g^l_0`¡t=z,¨¾]q_hou|·hjt^t^`_0`u\g¡m = ]j[eY\X~h¤g^l_0`¡t=inknhÐ]j¡kno`u\gsj`t^iBkl`j`·gZg^`«z,¨Ók|uY\d:vZ`gxÃy{]6X~gZhjXsz|`t] ]6X~g^`zl`«z:hotUg]6ul`6m = ]j[eY\X~h¤g^l_0`¡t=d{]6tD ¡tt^klX*]0tZhj_k:]gZhoY\u§zl`¸]ylXZY\y{]q[n]gZhoY\uzl``¡k"zl`ylX^]hjX~ho`6m ` *YeXZY\ulY #zl`ŨÓY\d:vZ`g¡ml` = ]j[eY\X~h¤g^l_0`¡t=inknhÐ]j¡kno`u\g)j`t^iBkl`o`gZg^`Ãy{]qX~gZhoXzlk§znh¸]q[eX^]q_0_0`zl g :yf`zl`_0 g^lY:zl``tZg]6kltDtZh,Y\uluBkl`y{]qX*j`g^`XZ_0`zl`_0 g^lY:zl`Y\uegZhjuBkl`6ª ÄxY\klt0zlY\ululY\ult0z,¨Ë]6dfYeXZz8iBkl`jiBkl`tpXZ`¡_p]qXZiBkl`tp[e ul X^]o`t0Yeul`XZu{]qu\gÂg^Y\k:g^`tp`tÂ_0 g^lY:zl`t¡ª $Å]qk:gXZ`_p]6XZiBkl`XiBkl`]§ynokly5]6X~gzP¨Ó`u\g^XZ`p`Æj`tul`re X~h¤Ñ{`uegy{]6to`tg^XZYqhot«ylXZYey|X~ho g^ tiBkl`pulY\klt re`ulY\ult3zl`sh¤g^`X·ªBw3uVY\k:g^XZ`)j`)ylX~hjulhjy{]5ylXZYedno¦_0`)zl`=g^Yek:g^`t3`¡t3_0 g^lY:zl`t `tZg
(33) o`klX3[\ ¡u| ¡X^]¤hot]gZhjYeu z:h¤Çp·h¤j`)]6k]qtÐÉfÊ znho_0`ultZhjYeu|ul`Gª Þ hj[eu{]jYeult.`¡unÑ{uŨÓk|uVzl`tÐy|X~houlhjy{]qkn¢t^Y\klhot.t^Yekno`re tÐy5]6Xg^Y\kltj`t ]qk:g^`klXZt.¬n]t^`ultUhod:h¤¤hÆg^ zlk"t^iBkl`j`·gZg^`]qk§_0Yqhou|zlXZ`{]qul[\`_Â`u\gsz{]qult=¸]«XZYeu\gZhj¦XZ`zl`ŨÓY\d:vZ`g¡ª ul` yf`·gZh¤g^`t]hƤÆhj` YekpdlXZknhÆgsz|kYeu\g^Y\klX*]vZY\k:g^`xk|ul`xu|Yek:r\`Æj`dlX^]6u|l2` /QY\kpd{]6XZd|k:o` Óe. 0?]qkt^iBkl`j`gZg^`\ª ]y:jkly{]qX~gzl`t"]j[eY\X~h¤g^l_0`¡t¥zl`t^iBkl`j`gZgZhot]gZhjYeuYeu\gk|t]6[\`zl`g^`|u:hoiBkl`t"zl`tZhj_0y:Æh¤Ñ{ ]gZhoY\u /Æ´}ÀÁ:º{µº ³Å¶¼·°Bº5µ Ál¶¿ ËBF 0)]Ñ{u¥z,¨Ó ¤ho_hjul`Xx`g :y}`z|`dlX^]qull`t¡ª . ! "$#&%('*),+.-0/1%(!2&34!))5'*%6'*21". * `)g :y}`z,¨Ë]6yly|XZY:l`l`XZ|`Ã]q_hou|·hjX
(34) G¨©Yed:vZ`g3g^Yekng$`up[B]6XZz{]qu\g t]xg^YeyfY6jY\[6hj`?hounhÆgZh]j` ©a5qmB<nm \4ŪB$`t^Yeu\g)zl`ts]j[eY\X~hÆg^|_Â`t?h¤g^ X^]gZh¤t /Qy{]qX*d{]¸] n]q[e` t^kl`t^tZh¤.z|`¡t$ho_p]q[e`t*Y\ky{]qX*g^`lu:hjiBkl`zl` t^k:h¤rBh#zl`Y\u\g^YeklXZt:^0 ª jty{]6X~g^`u\gzlkY\u\g^YeklX=hounhÆgZh]
(35) zl`ŨÓY\d:vZ`g¡m5 ·g^k|z:ho`u\g ¸]0Y\ulul`¢nhÆg^ zl`5]6iBkl` yfY6hju\gVzlkYeu\g^Y\klXz5]6ultt^Y\ur\Y6hjtZhju{]6[\`p`gÂ`u:j¦re`u\gÂ`kn¢z|Yeu\g¸]t^k|ylylXZ`t^tZhjYeu£u,¨Ë]1P `·g^`y{]6t«¸] g^Y\y}YqoY\[qho`zl`«G¨©Y\d:vZ`·g¡ªBx( hjultZhÅm|Ũ¾]q_houlhjt^t^`_0`uegzl`«G¨©Yed:vZ`g ¡Y\ultZhjtZg^`ÃÂ`¡uno`re`X t^kl`t^tZh¤re`_0`¡u\gzl`t Yek|l`tsY\kSÔyf`·jklXZ`tÔª ]V]qklt^tZhÅm\z{]qult*j` ]6zlXZ` zl` ]_0Y\XZyllYqoY\[6hj`s_p]g^l _p]gZhjiBkl`6mlz|`¡t)]j[eY\X~hÆg^|_Â`t*z,¨Ë]q_Vhjulhjt^t^`Ê _0`ueg d{]qt^ tst^klX=G¨© XZYetUhoY\ut^kl`t^tZh¤re`zlk"Yeu\g^Y\klXsz|`G¨©Yed:vZ`g¡ª w up[\ ul X^]ÅmB`t?g |yf`t)z,¨Ë]j[\YeX~h¤g^l_0`t*t^Yeu\g*ulY\uphjuer6]qX~h]6u\g^t)y{]qX?XZY6g]gZhjYeu,ª 7k{]qu\g)Ã]jY:]¤hot]Ê gZhjYeu"Yedng^`¡uBkl`6m5`¤o`uP¨Ó`tZg y{]6tYeXZXZ`g^`ylk:hjt^iBkl``t _ g^lY:z|`¡tul`t^knhÆr\`¡u\g]6k|¡k|ul`zl`txz| ·Ñ5u:hÆgZhjY\ult zlY\ulul `tsyfYek|X*o`t y}Yqhjueg^tzlk"t^iBkl`o`gZg^`6ª 98. :<;>='?'?""'A@CB&/D"! E+'F/G34/D"'F+'F+!H)5"/2&34'. ¨ÓkngZhƤhot]gZhjYeuzl`*] ]6X~g^`zl`)z:hjtZg]qul`)yfYeklX
(36) j`) ]jk:{zlkt^iBkl`o`gZg^``¡tUg$klu|`)hjzl `*g^XZ¦t$XZ y{]qulzlk|`\ª È ]qult?¸]Ñ{[\klXZ` ulY\klt)]reY\ult*XZ`ylXZ t^`u\g^ ¸]« ]6X~g^` zl`z:hjtZg]6u|¡` z,¨©kluY\d:vZ`g=dnhoz:hj_0`ultZhjYeul`ÅmBY\_Â_0` klul`t^k|X~Å]6` z,¨Ó j r6]gZhjYeuPm:Y0¸]{]qk:g^`klX*yfYeklX?{]6iBkl`yfY6hju\g)zl` G¨©Y\d:vZ`·g*`tZg* [n]j`ø]z:hjtZg]6u|¡` zl` `y}Yqhjueg]6k"Yeu\g^Y\klX)zl`G¨©Yed:vZ`g¡ª. .
(37) . Ál¶ ®»¶ ³Å³Q¶¿=Ál¼ ®¾µqµ¶º{¿Ð¯ ± ¹ ¶ ³¸¿ qµ¿·¼ÀZ¶ ³¸¿º
(38) qµ²0¶º{¿µ±qº{ºf¶ ®¾¿.
(39) = qÀZ±6µ³Q¶Á:º± ¹ . ¶ ³?¶ ³?¿·±qº¿ Ál¶ ®»¶ ³Å³Å¶ \½6Ál¼·°n¶®õ½¼½6À³Å¶ e¶ 6µ¿³Å½qº}¼¶2\¶V®Z¯ ± ¹ ¶ ³
(40) hjt^kl`¤o`_0`u\g¡mP]"XZ`·]gZhoY\u`u\g^XZ`p¡`gZg^`pt^k|X~Å]6`0`go`0t^iBkl`j`gZg^`pzl`0G¨©Y\d:vZ`·g`tZgg^XZ¦t·]hoXZ` ¬}¸] ylXZYqvZ`¡gZhjYeu8z|`¡t]qXZÕg^`tpzl`¡`gZg^`t^klX~Å]q`z5]6ult0j`y:]6u8zlY\ulul`klu|`FtUg^XZklg^klXZ`"g^XZ¦¡ttZho_h¤¸]hjXZ`F]qk t^iBkl`j`·gZg^`zl`«G¨©Yed:vZ`g¡ª$`]qklY\klyzP¨Ó:` PYeX~g^tY\ueg g^ Å]h¤gyfYek|Xxzl`g^`g^`X`t]6XZÕg^`tz{]qult o`t ]qX~g^`t zl`pz:hjtZg]qul`pz:hjt^XZ¦·g^`t¡ª ]" ]qX~g^`pzl`z:hjtZg]qul`0¸]¥y:jkltVkngZhƤhotD ¡`p`tZg¡`¤o`zl`È]6unho`jt^Yeu Æ 4 Åm.inknhGm ]q·g^k|`·¤j`¡_0`u\g¡m`tZg]ynoklt«ylXZY:l`zl`]pY\ulgZhoY\uzl`0z:hjtZg]6u|¡``klÆhjz:hj`ulul`6ªÐȨË]qk:g^XZ`t_ g^X~hjiBkl`t Y\ueg g^ k:gZh¤Æhjt^ `t¡m5_p]hjt)j`klXsk:gZh¤¤hot]gZhjYeu"ylXZY:zlk:h¤gxz|`¡t t^iBkl`j`·gZg^`tg^XZ¦txt^`ultUhod:j`txÃ]XZY6g]gZhoY\u,m5y{]qt g^XZ¦txy|XZ ¡hj t /Qz{]qulto`tD`¡u|ts`klÆhjz:hj`u 0)`gx]·re`ulY\_dlXZ`kltD`¡td{]qXZdlk:j`¡t Ónm.F Ū ÄxY\klty}Y\k:reY\ult YeultUhozl XZ`X)hjhÐklu"g :yf`z,¨Ë]qylylXZY:|`iBk:h# ]jk:j`o`t^iBkl`o`gZg^``uzl`kn¢ ·g]qyf`¡tm zlY\u\g]y|XZ`¡_hj¦XZ`YeultUhotZg^`pÃ¥g^XZY\k:re`Xk|u t^Y\kltZÊG`ult^`_d:j`hounhÆgZh])z|kSt^iBkl`j`·gZg^`6m
(41) y{]qX`¢|`_0y:o`0j`t _p]¢nhj_p]oY: ]qkn¢0z|`)] ]6X~g^` zl`sznhotZg]qul`6ª *`t^Y\kltZÊ `ultD`¡_d:j`)`tZg*ulYeu0Y\ulul`¢|`\ªeÈ]6ult3]zl`kn¢nhj¦¡_0` g]6yf`Y\u `t^t]hj`zl`pjk:hsXZ`ulz|XZ`Y\ulul`¢|`\m
(42) Y\ul`XZ|`zl`tYeu:Ñ5[eklX^]gZhjYeultzl`r\Y6hjtZhju{]q[e`pz{]qult¸] ]6X~g^`pz|`pz:hotUg]6ul`p]Ñ{uSzl`pXZ`g^XZY\k:re`Xzl`tÆhj[\ul`tzl`0XZÕg^`Yek£]6XZÕg^`tzl`p`gZg^`pt^klX~Å]q`6miBk:h?reY\u\g Yeu|ul`·g^`X=G¨©`ult^`_d:j`zl`t _] ¢nho_p]jY:]qkn¢Pª ) hod|d}Y\ult¡mz5]6ult Óq1a Åm zl Ñ{unhÆgÐ`X~g]hjul`tYeunÑ{[ek|X^]gZhjYeu|t,z|` r\Y6hjtZhju{]q[e`6m\ÔBkl_0yÐ Ô /QdfYetDt^`t 0^mÔr6]Æj` |tÔ /¸r6]Æj `¡:t 0^m?Ôt]6z|z:o`y}Yqhjueg^tÔqm3ÔÆhj_dnhoul[ul`ho[\Bd}Y\klX ÔÂm}inknh yf`¡XZ_0`gZg^`u\gzl`Vy5]6XZY\klX~hoX j`tx¤hj[eul`tzl` XZÕg^`zl`ylk:hjtxk|u§_p]¢nhj_kl_ oY: ],Y\k"zl`ylk:hjtskluÔ·t]6zlzno`yfY6hju\gÔqª `t]6k:g^`klXZt«zl,` Ë -4?ylXZ t^`u\g^`¡u\gk|ul`0_ g^lY:z|`]qylyf`o `"Ô·_p] ¢:hj_p]
(43) g^X^]6 houl[fÔinknh$Y\ultZhjtZg^`Âà g^XZY\k:re`Xz{]qultsŨ©`¡u|t^`_d:j`zl`t _p]¢nhj_]VoY: ]qkn¢"zl`kn¢§g :yf`¡tzl`y}Yqhjueg^tm|o`t0Ô·d5]6t^`yfYqhou\g^t*Ô /QyfY6hju\g^t zl`Y\u\g^YeklX«zlYeu\g¸]"Yek|XZdlklXZ``tZg`¢ng^XZ _p]j1` 0`gj`t§Ô]6yf`¢£y}Yqhjueg^t,Ô /Q_p] ¢nho_p]"jY:]qkn¢£z{]qultklu reYqhjtZhou5]6[\`0zl`pg]hƤo` I0^ª
(44) w3u y{]qX~g]quegzl`p`tyfY6hju\gYeu£y{]qXZ¡Y\klX~go`tV]qXZÕg^`t /Ô·X~hjzl[\`tÔqm,¤ho[\ul`t zl`XZÕ·g^1` 0zl`«¸]]qX~g^`z|`Vz:hjtZg]qul`VÃ0ŨË]hjzl`z|`¡tpÔz:hjXZ`·gZhjY\u{]
(45) klyl:h¤Æ3ul`ho[\Bd}Y\klXZtÔª `ty}Yqhjueg^tY `tg^X^]vZ`g^YqhoXZ`tt¡¨Ë]qXZXZÕ·g^`u\gVtDYeu\g_p]qXZink| ¡t`gVXZ`ylX~hjty{]qX]tDk:hÆg^`¡Y\_0_0`ÂyfYqhou\g^tzl`pzl y{]qX~gzl`t g^X^]vZ`g^YqhoXZ`t)g^XZY\k:r\ ¡`tÃG¨Ë]hjzl`zl`tÔ·z:hjXZ`gZhoY\u{].z|Y ulnhƤÐul`ho[\Bd}Y\klXZtÔª È]6ult Ë|qm6a|mB. {YeuylXZY\y}Y\t^`)z|`¡t
(46) g^`lunhoiBkl`t?tZhj_Vh¤]hjXZ`t¡mqiBk:h{z:h ,¦XZ`u\g$z5]6ult
(47) ] Å] Y\uVzl`=]j¡kno`X j`¡t _p]¢nhj_p]jY: ]6kB¢¥zl`]YeulgZhjYeu¥zl`z:hjtZg]qul`6m5z{]6u|t)j`¡tYeu:Ñ5[eklX^]gZhjYeultzl`r\Y6hjtZhju{]6[\`t)k:gZh¤Æhjt^ `t yfYeklX* ]qX^]6g^ X~hjt^`X?o`t?¤ho[\ul`t)zl`XZÕg^`z|`x]«YeulgZhjYeuzl`z:hotUg]6ul` /G]6XZÕg^`t)Y\kÔX~hozl[\`t4Ô 0^m:]houltUh,iBkl` z{]qult)]Å] Y\u§zl`o`tsy5]6XZY\klX~hoX·ª. ,&úKJ L:L4M.
(48) . ½qÀZ½¶Àºqº \ ¶F µ\½e®¶ ³ =À 5 \±qµÀZ¶
(49) ͽe®»½6º&e½qµº. w u[\ ul X^]ÅmPY\uyf`¡kngz:hoXZ`0iBkl`_0Õ¡_0`0tZh3¡`t_0 g^lY:zl`tzlY\ulul`u\gzl`tXZ t^k:¤g]g^ty:jklty|XZY:l`t zlk ]qtY\u\gZhouBk,m,`Æj`ttDYeu\gz:h¤Çh¤o`_0`u\g[e ul X^]Æhjt]qd:o`t]6k ]qt g^X~hoz:hj_0`ultZhjYeulu|`·ÅmP ]qX o`ulY\_dlXZ` zl`Y\u:Ñ{[\klX^]gZhoY\ult)yfYetDtZhodno`t)yfYek|Xs ]6X^]qg^ X~hot^`X*j`t^iBkl`j`gZg^`zl`rBho`u\gsg^XZ¦t [eX^]qulz,ª #uyf`¡kng [n]o`_0`u\g·h¤g^`Xj`¡tg^X^]r6]6kB¢zl` *Bk{]qul["`gV]Ū Æ 4Ū jtylXZ t^`u\g^`u\gklul`p_0 g^lY:zl` ]qu{] BgZhoiBkl`"yfYeklXg^XZY\k:re`X0j` + ( Jz|`¡t0XZ [qhoY\ultpyfY6 :[eY\u{]o`t¡ª (k¤ho`k8zl`" ]jk:o`X] ]6X~g^`"zl` z:hjtZg]qul`z{]qultsg^Y\k:g^`]0XZ [6hjY\u,m|hÆjtzl Ñ{u:hjt^t^`u\gxklu{]6_0y"zl`yfYqg^`¡u\gZhj`#iBk:h#yf`¡kngxÕg^XZ` ]ok:j zl` Å] ¡Y\uhjt^Yqo `0y}Y\klX{]qink|`y}Yqhjueg`·ginknh)zl y}`ulz£zl`p]§z:hjtZg]qul`pzlkSyfYqhou\gÂÃg^Y\kltj`tyfY6hju\g^tzl` Yeu\g^Y\klX·ª *`p{]q_Âyzl`yfYqg^`¡u\gZhj`)`¡tUg ]jk:o pz|`pÅ] Y\uS]qu{] BgZhoiBkl`¥Ã§Å¨Ë]hjzl`zl`t ¡iBk{]gZhjYeultzl`t t^`[\_Â`u\g^tz|k Y\ueg^Y\klX·ª `tr6]¤o `tzl`p`{]q_Ây£t^Y\uegklul`§]qylylXZY¡¢nhj_p]gZhjYeu£zlk + ( ª y5]6X~gZhjX z,¨©kluy}Yqhou\gink|`·jYeu|ink|`pzl`pŨÓY\d:vZ`g¡mÐY\uSz|`¡tD¡`ulz£z{]qult]"z:hoXZ`gZhjYeuzl`0]"YeXZ`6m.Yeu]gZg^`hjuegklul` r6]Æj `\m{`·g zl`Ã0Yeu"yf`¡kng«]gZg^`houlz|XZ`j`¡t]qk:g^XZ`tsr6]Æj `tx`gxY\u"`¢ng^X^]hÆg]houltUho`t dlX^]6u|l`t `·g re`X~g^`¢ zlk"t^iBkl`o`gZg^`6ª *`gZg^`_0 g^lY:zl`«`¡tUgsz:h¤Çh¤o`_0`u\g[\ ul X^]¤hot]6d:j``uF\Ȫ . . : !%6=/ "! 2 +' / B& B&/D/D"! 2 +'' = +'FB& /D! !'. xu«g^XZY6hjtZhj¦_Â`$g :yf`)z,¨Ë]6yly|XZY:l`*`tZg
(50) ¸] tZhj_k:]gZhoY\uVz|`*¸] ylXZY\y{]q[n]gZhjYeuz|`*`kzl`)y|X^]hjX~ho`Ãxy5]6X~gZhjX zl`t)Y\ueg^Y\klXZt*r\`XZt)ŨÌhju\g^ ¡X~hj`klXsz|`G¨©Yed:vZ`g¡ª
(51) # uzl g^`g^`o`t=hou\g^`XZt^`gZhoY\ult Q/ yfY6hju\g^tsz,¨©`¢ngZhoulgZhjYeu&?0 zl`t XZY\ueg^t.zl` `t`kn¢]qkklX`g#Ã)_0`t^klXZ`?iBk,¨Ìh¤jtÐt^`3ylXZYey5]6[\`uegKQ/ z5]6ultPj`?zlY\_]hjul` znhot^XZ`g!¤ qm¡anBm aBnm¡a <.G m Y\k]qu{] BgZhoiBkl` Ë \4^0 ª G¨Ë]hozl`=z,¨Ók|ul`)g^`|u:hoiBkl` zl`)tDk:hÆrBh{z|`sYeu\g^Y\klX·mh¸] Ì aB4{ zl g^`XZ_hou|`)j`sulY\k:re` ]qkXZY\u\g¡ª* 5]6iBkl` y:hõ¢|`·zlk¥Yeu\g^Y\klX)Yek|X^]6u\gs`tZg)Y\ultZhjzl XZ ¡_0`gZg^`klX)z,¨©klul`Y\ulzl`tD`¡Y\ulz{]hoXZ`2Q/ klu¥z:hjt^iBkl`6mlY\kdfYekno` z:hj[6h¤g]o`6m\aqÊ z:hjt^iBkl`1^0 m\j`su|Yek:r\` ]6k0XZY\u\g=`tZg3ŨÓ`u\re`jYeylyf` zl`sg^Y\k:g^`t*`t$Y\ulzl`t¡ªeWÐY\klX?{]qiBkl`xynh¤¢|`Gm6hÆ. p_ ]6XZiBkl`=o`t?y:hõ¢|`·jt3reYqhotUhoult3iBk:h{Y\u\g$y5]6X~gZhj`szl`=G¨©Y\ulzl`)zlY\u\g h¤{`tZg? _Â`gZg^`klX·ª `t y:hõ¢|`ot?zlk0ulY\k:re` ]qk XZY\ueg)iBk:hY\u\g) ·g^ _p]qXZink| ¡t=y:ok|t)z,¨©klul`Yqhot*t^Y\u\g)zl`t*y}Yqhjueg^t=z,¨Ó`¢ngZhjulgZhoY\u,ª5È]6u|t*¡`gZg^`tZhj_k:]gZhoY\u h¤ yf`¡kng ]reYqhjX`X~g]houl`t]qulYe_p]Æhj`t¡ªfW#]qX`¢l`_0y:j`6mfj`¡t XZY\u\g^ty}`k:r\`¡u\gt¡¨ hou\g^`XZt^`g^`X«]qkn¢Fy:hõ¢l`jt iBk:h#ul`«t^Yeu\g y{]6t yfY6hju\g^txz,¨©`¢ngZhoulgZhjYeu /Ô]6X~gZh¤Ñ{h]Phjueg^`XZt^`gZhjYeultÔ 0^ª ¨Ë]qk:g^`klXx`tZg YednÆhj[e z|`g^X^]h¤g^`X `tx]qulYe_p]Æhj`ts]r\`¡«¡`X~g]hou|t)g |yf`txz|`_p]6t^iBkl`t¡ª xu|`F g^klz|`r|X^]hj_Â`u\gg^XZ¦thju\g^ XZ`¡tDt]6u\g^`6m$inknh«yfY\X~g^`t^klX0Ũ¾]qyly:¤ho ]gZhoY\ußzl`ŨË]6u{]jYe[qho`"zl`"`k zl`y|X^]hjX~ho`¥]6k£]j¡kn=z|k t^iBkl`j`gZg^`\m
(52) `tZgÅ]h¤gy{]q*X +` \`¡X«z{]6u|t Óe Gª st¡¨ hou\g^ XZ`t^t^`§Ã¥]¥rnh¤g^`t^t^` zl`pylXZY\y{]q[n]gZhjYeuzlkÍ`kj`VjY\ul[z|kSt^iBkl`j`·gZg^`6ª
(53) w3uSk:gZh¤¤hot]qu\gV`0Yeul`y:g¡m,h¤$zlY\ulul`pk|ul`pulY\k:re`¤o` zl Ñ{u:h¤gZhjYeußz|k8t^iBkl`o`gZg^``gÂhju\g^XZY:zlk:h¤g§]6k|t^tZh)] $ ¹ µ¿¿·¶¼ ³¸Àµ¼¶¼±6&º 6µ³¸µ±6º5º}¶ ®®õ¶·m
(54) k|u8t^Yek|tZÊ `ult^`_d:o` zlktDink|`·j`gZg^`p"Y j``kt^`0ylXZY\y{]6[\`0Ãklul`0rBh¤g^`t^t^`t^klyf ¡X~hj`klXZ`à ª Þ k:hÆg^`Ã`¡t«zl Ñ{u:h¤gZhoY\ult¡m}hÆ ylXZY\y}Y\t^`zl`t_0 g^lY:zl`tsh¤g^ X^]gZh¤re`t¡m{k:gZhƤhjt]6u\g zl`tY\k:gZh¤ot zl`_0Y\XZyllYqoY\[qho`_p]g^l _p]gZhjiBkl`6mfy}Y\klX=o` ]jk:zl`]d:hotDt^`·g^X~hj`Yeu|z:hÆgZhjY\ulul`Æj``gxzlk"t^iBkl`j`·gZg^`6ª ¨¾]j[eY\X~hÆg^|_Â` ylXZY\y}Y\t^ y{]6DX hjul`ue g ©aB4 P`tZg)klu_0 ¸]qul[\`xz|`¡t]6yly|XZY:l`t*y{]qX)]6_hjulhotDt^`_Â`u\g^t t^kl`t^tZh¤t#`g*zl`t$]qylylXZY:l`t?k:gZhƤhjt]6u\g3¸]]qX~g^`sz|`sz:hjtZg]qul`\ª }`tZg?k:gZh¤Æhjt^ y}Y\klX
(55) g^XZYek:r\`X j`t?¡`u\g^XZ`t zl`d}Y\k:j`¡t _p]¢nhj_p]j`t¡m5iBk,¨Ìh¤ ]qylyf`·¤j`yfY6hju\g^txz,¨Ë]qulX^]6[\`6ªfw u|t^k:h¤g^`\mlhÆÐÅ]h¤gzl`t]6_hjulhotDt^`_Â`u\gt^klÊ `t^tZh¤ty{]qXt^k:h¤rBh=z|`Yeu\g^Y\klXÃ¥G¨Ë]hozl`pz|`0Ñlo`tz,¨¾]gZg^`u\g^`\ª Þ `·jY\u]§g^X^]q_0`pk:gZh¤Æhjt^ ` /Ql`¢5]6[\Yeu5]j`6m ]6XZXZ `6m?`g^1 0^m hÆXZ ¡`zl`t0g]qd:j`]qkn¢]re`"g^Y\k:g^`t0o`tY\u:Ñ{[\klX^]gZhjY\ult0zl`§r\Y6hjtZhju{]q[e`"y}Y\t^tZhjd:j`t¡m3`u z:h , XZ`ulh]6u\g0¡`¤o`tiBk:hxt^Y\u\gVlY\_0Y6g^Y\y:hjiBkl`tVzl`¥`·¤j`¡tiBk:hxu|`po`¥t^Y\ueg0y{]qt¡ª #Y\klt«o`t0y:hõ¢l`jt0zlk Yeu\g^Y\klX*t^Y\u\g)_Vhjt*z{]qult*]Ñlj`z,¨Ë]gZg^`u\g^`6mlt]6k:`kn¢iBk:ht^Yeu\g*zl`t)yfY6hju\g^t)z,¨Ë]6u|¡X^]q[\`\ªnWÐY\klX*5]6iBkl` y:hõ¢|`·z{]qult*]«Ñlo`z,¨Ë]gZg^`¡u\g^`Y\u`¢5]6_hjul`t^Y\u0reYqhotZhju{]q[e`6mn`g)Yeu§]vZYekng^`xz{]qult*]«Ñlo`zP¨¾]gZg^`ueg^``kn¢ .
(56) . .
(57) Ál¶ ®»¶ ³Å³Q¶¿=Ál¼ ®¾µqµ¶º{¿Ð¯ ± ¹ ¶ ³¸¿ qµ¿·¼ÀZ¶ ³¸¿º
(58) qµ²0¶º{¿µ±qº{ºf¶ ®¾¿. . . iBk:h}tDYeu\g)ÃŨÌhju\g^ X~ho`klX*zlkpY\u\g^YeklX?Y\klX^]6u\g¡ªnw u|t^k:h¤g^`\mnY\uÂXZ`[B]6XZz|`xtZh5¸]¡Y\u:Ñ{[\klX^]gZhoY\u0zl`reYqhotZhju{]q[e` `tZg?lYe_0Yqg^YeynhoiBkl`6ª Þ hf`Æj`sul`ŨÓ`tZg?y{]qt¡mqj`sy:hõ¢|`·ful` y}`k:g?y{]qt$Õg^XZ` `u:o`r\ xzl`=G¨©Y\d:vZ`·g /GÃ`g hjultZg]qu\g 0 `gY\uj`ÂXZ`_0`gVt^k|X¸]Ñlj`pz,¨Ë]gZg^`u\g^`6ª *t^`0yf`¡kngiBkl`y{]qX¸]"t^knhÆg^`0]§Y\u:Ñ{[\klX^]gZhoY\uzl`p`py:hõ¢|`· 5]6ul[\`6m|`·g zl`rBho`ulul`«lYe_0Yqg^YeynhoiBkl`6ª xu|`r6]6X~h]gZhoY\u z|``·gZg^`£zl`XZu:hj¦¡XZ`£_0 ·g^|Y:zl``tZgy|XZYeyfYetD ¡`y5]6& X ]odfYqg ©Ia <4ÅmY j`tyfY6hju\g^t z,¨Ë]6u|¡X^]q[\` /Q`u\g^XZ`tzl`dfY\k:o`t_p] ¢nho_p]o`t 00tDYeu\g§ ]ok:j tz,¨©klul`Å] Yeußynoklt¥ylXZ hot^`6m=ulY\u y{]qt rBh¸]Íj`¡tp_p] ¢nho_p]jY: ]6kB¢8zl`"] ]qX~g^`zl`z:hjtZg]qul`6m?_p]hjtp`u8Å]hot]qu\gpklt]q[e`¥zl`"¸]Ízl Ñ{u:h¤gZhoY\ußzl` ÊGd:hjt^t^`g^X~ho`Yeu|z:hÆgZhjY\ulul`Æj`6m5`·¤j`·ÊGh. g]qu\gx ]jk:j ¡`ÃŨ¾]hjzl`zl`]]qX~g^`zl`znhotZg]qul`6ª . . . :<;>='?'?""'A@CB&/D"! E+&= +!/D /% % ' +'. . 2. . `?y}Yqhou\gÐzl`*z| ¡y5]6X~gÐzl`*`gZg^`)]qylylXZY:|`$`tZgÐz|Yeulu| $y5]6X xhoX y{]g^X~ho z{]qul!t Óe. GmYhÆ:yfYetUg^k:o`?iBkl` j`tDink|`·j`gZg^`z,¨Ók|ul` YeXZ_0` y}Yq :[\Yeu5]j`s`tZg)klut^Yek|tZÊ `ult^`_d:o`zlkz:h]q[eX^]q_0_Â` zl` *YeXZY\ulYÐzl`¡`gZg^` Y\XZ_Â` /Qz:h¸]q[\X^]6_0_0`§zl` *YeXZY\ulY xz,¨©klu`ult^`_d:j`§z|`§t^`[\_Â`u\g^t¡m
(59) y{]qtz,¨Ók|uÝ`ultD`¡_d:j`§zl`¥y}Yqhou\g^t0^ª *`gZg^`hjzl `V`tZg_hotD`V`uY:`k:r:XZ`Vy5]6X `` Ë 4Ū $ ]ok:j`z,¨¾]qdfYeXZzj`Vznh¸]q[eX^]q_0_0`zl`.*YeXZY\ulY*zlk yfY6 :[eY\ul`0`g`ult^k:h¤g^`hÆ*t^kly|ylX~ho_0`0j`tV]qXZÕ·g^`ty5]6X~g]qu\gzl`tt^Y\_0_Â`g^tzl`ty{]qX~gZho`tY\ul ]re`tzl`p` yfY6 :[eY\ul`6ª +]hjtŨÓkngZhƤhot]gZhjYeuzl`¥`·gZg^`hoz| ¡`¥y}Y\klXg^XZYeknre`Xo`tt^iBkl`o`gZg^`t0zl`tÂY\d:vZ`g^tÂ] n]queg0klul`YeXZ_0` ]qXZd:hÆg^X^]hjXZ`V`tZgY\X~gz:hÆÇph¤o`6ªÈ¨©klul`y{]qX~g¡mPŨË]6yly|XZY¡¢nho_p]gZhoY\uy}Yq |[\Y\u{]j`z,¨©klul`Y\XZ_0`ViBkl`j¡Y\uliBkl` `tZgÐkluy|XZYed:j¦_0`=]qt^t^` !
(60) z:hÆÇph¤o`6m`gÐz,¨¾]qk:g^XZ`?y{]qX~go`? ]ok:\zlkz:h]6[\X^]q_Â_0`?zl` *YeXZY\ulY :`¡tUgСY\_0y:j`¢|` /Qt^klX~g^Y\k:g¥oY\XZt^iBk,¨ hÆ ]£zl`tg^XZY\klt§z{]qultpŨ©Yed:vZ`g 0^m$oY\ul[lm*`g"ylXZY:zlk:h¤g§klug^XZ¦¡t¥[eX^]qulz ulYe_dlXZ`zl` d{]qXZdlk:j`t¡ª cs `_Â_0`u\g)t^Y\ueg ]6yly5]6XZkl`t*zl`t ]6yly|XZY:l`t Ó Bm nm5. .iBk:h ]ok:j`ueg*j`t^iBkl`j`·gZg^`Ãy{]qX~gZhoX=zlk z:h]6[\X^]q_Â_0`)z|>` *Y\XZYeulY /GÈ 20.z,¨Ók|uÂ`ultD`¡_d:j`xzl`y}Yqhjueg^tm\`·g?`ult^`_dno` ·g]qu\g*klu0 ¡{]quegZh¤¤oY\ulu{]q[e` z:hjt^XZ`g=z|kp¡Y\u\g^Yek|X /QY\u\gZhouBk 03zl`ŨÓY\d:vZ`g¡ª `t?z:h]6[\X^]6_0_0`t?zl>` *Y\XZYeu|Y Dm6`·g?j`t*t^iBkl`o`gZg^`t?g^XZYeknre t rBh¸]0`tx]qylylXZY:l`tsY\uer\`XZ[e`u\gxr\`XZtsj` ]6t=hoz| ]Ð]6k¥klX`·gÃ0_0`¡tDklXZ`iBk,¨©Yeu]6k|[e_0`u\g^`¸]0zl`ultUhÆg^ zl`Ũ© ¡{]quegZh¤¤oY\ulu{]q[e`6ªÈY\ul6mz{]6u|t§`tF]qylylXZY:l`t¡m$o`y|XZYed:j¦_0`ylX~hjulhoy{]`tZg"zl`g^XZY\k:re`X"klu {]qu\gZhƤjYeulu5]6[\`Vznhot^XZ`giBk:h)]qylylXZY¡¢nhj_Â`p]qk_ho`kn¢Í]YeXZ_0`0zl`0ŨÓY\d:vZ`g¡m]Ñ{uzl`piBkl`0`gZg^`0hozl ` ylk:hjt^t^`Õg^XZ`Â_hjt^``¡uylX^]gZhjink|`\ª *`t_0 g^lY:zl`tt^Y\ueg]qklt^tZh
(61) zl tZho[\ul `txtDYeklt j`g^`XZ_0`0zl`¥² 5 ³°:4± \¶¿ ¼±qº}³¸µº{Ál¶¿]qX§`¤o`t"k:gZh¤Æhjt^`u\gFzl`t¥g^`lu:hjiBkl`tylXZYey|XZ`¡tã¸][\ Ye_0 g^X~hj`S]j[\YeX~h¤g^l_hoiBkl`6m`SiBk:h yf`¡XZ_0`gxz|`t¡¨Ë]6dltUg^X^]hjXZ`zl`][eX~h¤Æj`z:hjt^XZ¦g^`\ª È]6ult ¤. G$m *X^]qulz:g*ylXZY\y}Y\t^` klul` _0 ·g^|Y:zl`y}Y\klX3g^XZYeknre`X*kludfYeup {]6u\gZh¤ÆjY\ulu{]q[e`zlkYeu\g^Y\klX /¸h¤$¤hj_Vh¤g^`§]qklt^tZh3ŨÓ`ult^`_d:o`pz|`¡tYeXZ_0`tVÃg^X^]h¤g^`X·mÔ·XZ`[\k:]6Xt^`g^t4Ô 0^ª ) ]ok:j`o`1 È Jzl`p`·g`¡unÊ t^`_dno`6mP`gYeu|·jk:giBkl`j`t^iBkl`o`gZg^`zl`Ũ©Yed:vZ`g`¡tUg]py{]qX~gZhj`Vzlk1È iBk:h3`tZgg^Y6g]o`_0`u\gÃVG¨ hounÊ g^ X~ho`klX zl`Ũ©Yed:vZ`g¡ª Þ klXj`t^iBkl`o`gZg^`]hjultZhg^XZY\k:re 6m5h¤ÐylXZY\y}Y\t^`klu|`g^`lunhoiBkl`zl`ÔylXZklu:hjul[fÔy}Y\klX t^kly|ylX~ho_0`Xzl`ulYe_dlXZ`klt^`tdlX^]qull`tÑ{gZh¤re`t¡ª,È]6ult ¤e' Gm{hÆ3zlY\ulul`z|`¡tylXZ`k:r\`tzl`Y\u\re`XZ[e`ul` `gxzl`«¡Y\u\gZhouBk:h¤g^ zl`«t^Yeu"]6y|ylXZY:l`6ª #[eunho` hj !`g]Ū Ó .x]6[qhjt^t^`u\gÂzl`¸]F_ÂÕ_0`¥Å] Y\u,ª jt]qyly}`¤o`u\g *YeXZY\ulY +`z:h] ( ¢nhjto` t^iBkl`j`·gZg^` ]ok:j Ãy{]qX~gZhoX*z|k§È Vª jt)tZhj_0y:Æh¤Ñ{`u\g)j`tDink|`·j`gZg^`Yed:g^`uBk§ÃG¨Ë]hjzl` zl`X~hÆg^¦XZ`t) ]6X^]qÊ g^ X~hot]6u\gs]XZYed|kltZg^`t^t^`zl`tdlX^]6u|l`t zlktDink|`·j`gZg^`z{]qult)Ũ©Yed:vZ`g¡ª . ,&úKJ L:L4M.
(62) ½qÀZ½¶Àºqº \ ¶F µ\½e®¶ ³ =À 5 \±qµÀZ¶
(63) ͽe®»½6º&e½qµº -. ]p]6k|t^tZhÐzl`t g^X^]r6]qkn¢yfY\klXs ]ok:j`Xsj`t^iBkl`j`gZg^`\mlrnh] *Y\XZYeulYDm5zl`t Yed:vZ`g^tg^X~hoznho_0`ultZhjYeunÊ ul`jt ÓeBm54<nm .GªI+]hjtÐ]t^klyly|XZ`¡tDtZhoY\uz|`¡t?dlX^]qull`t zlk.ÈßiBk:h5u,¨¾]qyly{]qX~gZhj`¡u|ul`ueg?y{]qt$]qk0t^iBkl`o`gZg^` zl`rBho`u\g`¡u|¡Y\XZ`y:jkltsznhÆÇphÆj`6ª . ÄxY\klt]ÆjYeu|tFy|XZ ¡tD`¡u\g^`Xklul`ulY\k:re`¤o`_0 g^lY:zl`inknhV ]jk:j`Sj`tt^iBkl`o`gZg^`tzl`tYed:vZ`g^tÉfÊ z:hj_0`¡u|tZhoY\ulul`jt¡ª|ÄxYqg^XZ`]qylylXZY:|`kngZhƤhotD`x] ]6X~g^`zl`z:hjtZg]qul``¡k|·¤hjz:ho`ulu|`\ª5W.YeklX={]qiBkl`y:hõ¢l`zl` ŨÓY\d:vZ`gsYeu¥t^klylyfY\t^`inkP¨ÓY\uY\ulu{]jg)k|u§r\`¡g^`klXinknhÐy}Yqhou\g^`r\`XZtsklu"zl`tsyfY6hju\g^tszl`«¡Y\u\g^Yek|X)y{]qXZ_Vh t^`t#ynoklt
(64) ylXZY:|`¡tª"#xuVyf`k:gÐg^XZY\k:re`X3zl`t ]o[\YeX~h¤g^l_0`tÐg^XZ¦t#`Çp ]6`t#iBk:h:Y\u\g#`t# ]jk:jt ¤. Gmq`g iBk:h t^Y\u\g#Å]q·h¤j`¡_0`u\g ]qz{]6yng]6d:j`t à u,¨ ho_0yfYeX~g^`iBkl`Æj`)z:hj_0`¡u|tZhoY\u,ªqÄ Yek|t#ylXZY\y}Y\t^Y\ultÐklu|`) ]6X^]qg^ ¡X~hjt]gZhoY\u jY:]j`pzl`tyfY6hju\g^tVzlkt^iBkl`j`·gZg^`6m
(65) d{]qt^ `pt^klX«G¨Ë]qu{] :t^`pzl``tr\`·g^`klXZtm3t]qultV]qklklul`p :y}Yqg^l¦t^` t^klX=¸]z:hj_0`ultZhjYeu¥zl`ŨÓY\d:vZ`g¡ª{W.Yek|X)Å]hoXZ``]|m|ulY\kltx]·reY\ultszl Ñ{unhÐzl`kn¢"y{]qX^]6_0¦g^XZ`t¡m5Ï`gxÎlmf]re` j`¡tDink|`·jtsu|Yeklty}Y\k:r\YeultXZ [6j`X)j`u:h¤re` ]6k"zl`zl g]hÆÐz|kt^iBkl`j`gZg^`\ª *`"{]qy:h¤g^XZ`Ft¨¾]qX~gZhok:j`"t^`oY\uo`"t^l _]Ít^k:h¤r6]6u\g.¬$z{]qult0j`Fy5]6X^]q[eX^]qyll`"|ªÆY\u8zl Ñ{u:hjX^]j`t Y\k:gZhÆjtz|`Âz| ¡y5]6X~gyfY\klXulYqg^XZ`p_0 ·g^|Y:zl ` Ðz5]6ulto`ty5]6X^]q[eX^]qyll`t:ª¾¥`gV:ª¾¥ulY\klt]ÆjYeu|tzl g]h¤¤o`X zl`tylXZYedno¦_0`tÂiBk:ht^`yfYet^`u\gÂ]qk_ÂY\_0`ueg0z,¨Ë]6y|y:ÆhjiBkl`Xj`t0zl Ñ{u:h¤gZhoY\ultzl` =]]6dnh)`·6g ?jkl_ ]qk ]6t0z:hjt^XZ` g 3z{]qulto`"y{]qX^]6[\X^]qyll`§:ªÓaFG¨Ë]6y|ylXZY:l`¥iBkl`u|Yeklt0ylXZY\yfYet^Y\ultt^`X^]`¢lyfY\t^ `\ª Ȩ¾]qd}Y\XZz ulY\kltzl Ñ{u:hjXZYeu|to`ty{]qX^]6_0¦g^XZ`tiBk:h3reY\u\gulYek|ttD`¡X~rBhjXà ]6X^]qg^ X~hot^`XoY: ]o`_0`u\gzl`tyfY6hju\g^tzlk t^iBkl`j`·gZg^`6m=`g§Y\u z:hjt^k:g^`XZYeu|tpo`t"]r6]6u\g]q[e`t`ghjulY\uer\ u:ho`u\g^t§z|`G¨©k:gZh¤Æhjt]gZhoY\u zl`{]q¡k|ußzl`t y{]qX^]6_0¦g^XZ`t¡ª?È]qulto`¥_ÂÕ_0`§y5]6X^]q[eX^]qyll`6m
(66) Y\u `¢5]q_Vhjul`X^]j`tÂy|XZYeylX~hj g^ tÂiBkl`o`¥t^iBkl`o`gZg^`"z,¨©klu Y\d:vZ`·gzlY6h¤gxt]gZhjtZÅ]hoXZ`6ª|W#]qXZ_VhÐ`¤o`t¡m|]Yeulu|`¢nh¤g^ ylXZ`ulzlX^]0k|ul`y:]6`]qt^t^` ! ho_0yfYeX~g]qu\g^`6ª . 8 . / (*/Ý/p .
(67) ,/D. "'F+'F+!)5"/2&34'*). Þ Y6h¤g G¨©Yed:vZ`gPzlY\uegÐu|YekltPr\YeknoY\ult`¢ng^X^]hjXZ`3o`3t^iBkl`o`gZg^`6ªÈ]6ultk|u`¡tDy{]6`3z:hjt^XZ`·gÉfÊ znho_0`ultZhjYeu|ul`Gm `tZgÐzl Ñ{u:h:Y\_Â_0`*klut^Y\kltZÊ `ultD`¡_d:j`#Ñ{unh|z|`|ª `?Y\_Âyno _0`ueg]hjXZ`*zl` /¸o`3Y\ulzz|` Ũ ho_p]q[e`10 `tZgxu|Y6g^ ª ] ]qX~g^`zl`znhotZg]qul`zl` m {m5`tZgszl Ñ{u:hj`y{]qX . !. #"$&%' Î "$)( *%',+.-0/ 5Î "$6(879% 132 4. /D10. YÎp`tZgsk|ul`Y\ulgZhoY\u§zl`«z:hotUg]6ul`iBkl`j¡Y\uliBkl`6m5¸]qt^tZhjiBkl`_0`¡u\g¸]z:hjtZg]qul``¡k|·¤hjz:ho`ulu|`\ª ]´fÀZ± ¶¼ ³µ±qºÂz|kyfY6hju\g `u `tZg)j`t^Y\kltZÊG`¡u|t^`_d:j`zl` zl Ñ{unhÐy{]6X ! : "$&%;'=<>7@? BA5Î "$6(879%'CD"$&%FE /GI0 G g]qu\g*zlYeu|ul sklupyfYqhou\H g zl`)ŨÓY\d:vZ`g¡mBulY\klt?yfYek:r\Yeu|t g^XZY\k:r\`¡X?klupz|`¡t*yfYqhou\g^t?zl` t]ylXZYqvZ`¡gZhjYeuPm 7VmnÃŨ¾]hoz|`szl`G¨Ë]o[\YeX~h¤g^l_0` zl`È]qu:hj`ot^tDYeu Æ 4 Åm\j`iBkl`,ulY\klt?zlY\ulul`6mByfY\klX3o` y}YqhjueH g Tm6o`re`g^`klX =7 IJ Vª .
(68) . Ál¶ ®»¶ ³Å³Q¶¿=Ál¼ ®¾µqµ¶º{¿Ð¯ ± ¹ ¶ ³¸¿ qµ¿·¼ÀZ¶ ³¸¿º
(69) qµ²0¶º{¿µ±qº{ºf¶ ®¾¿ . " '*) +'*) = ' ) % /<!H%C/ '*). 8 98.
(70) ,'*2. 8 . 9 / !% /A <34/=% +' /634/D "' +' +!)5"/2&34'. ] ylXZ`_Vhj¦XZ`x ]qX^]6g^ X~hjt]gZhjY\uzlk0t^iBkl`j`·gZg^` zl` t^`sd5]6t^`=t^klX
(71) o`)Y\ul`y:g$z|`sdfYek:j`t _p] ¢nho_p]o`t zl` |m j`t^iBkl`o`gZg^`6m " %^mf g]6u\gsŨ©`¡u|t^`_d:j`zl`j`klXZtx`u\g^XZ`t¡ª xu|`sdfYek:j` >"$&%
(72) `tZg*zl Ñ{u:hj` y{]6X?t^Y\u0X^]eY\u
(73) ? `g*t^Y\uÂ`u\g^XZ`Tª$#upz:h¤g*inkP¨Óklu|`xdfYekno` >"$&%*z|` '`tZgx_p] ¢:hj_p]j`tZhÐ`gst^`k:j`_0`¡u\g tZhe¬ >"$&% `g " ( .% '= " ( &% g^`Ðink|` "$ % '`g >"$&% "$ % )]¸]qd:hylXZY\k:re`ink|`\m{tZ h !#"" : "$&% %%$&|mf]oY\XZt)j`yfYqhou\g `tZgsj``u\g^XZ`Vz,¨©klul`«d}Y\k:j`_p]¢nh¤Ê _p]j`6ª ¨¾]j[eY\X~hÆg^|_Â`pz|`È]qu:ho`jt^t^Y\uulY\kltzlYeu|ul`zl ~v^ÃkluyfY6hju\g 7&zl`p]ylXZY6vZ`gZhjYeuzl` Tª3Ä Y\klt yfYek:r\Yeu|tsXZ`g^XZYeknre`X)j`tsyfY6hju\g^tsiBk:hÐ_p]6u|ink|`¡u\g zl` : "$&%)]Fr\`¡J Ũ©l`kl #X~ho tU gZhoiBkl`tDk:IhÆ r6 ]qu\g^` ¬5ulY\ 5klts l`X~Ê |Yeult=z{]6u|t*o` r\Y6hjtZhju{]6[\` zl` TmBj`t)yfY6hju\g^t g^`ot=ink|(` ' = ) 7 ''*' =7(' m|"Y 7 `tZg j`XZ t^k:¤g]gsz|`G¨Ë]o[\YeX~h¤g^l_0`zl`È]qu:hj`ot^tDYeuyfY\klX*j`y}Yqhjueg ª WÐY\klX)g^Y\k:g ? IJ : "$&% 'B<>7 Eem =7 Yek|XZu:hÐy{]qX)Ũ¾]o[\Y\X~hÆg^l_0`zl`È]6u:hj`otDt^Yeu W.YeklX=g^Yekng F#J z|k§r\ #Y6hj tZ hju{]6[\,` + zl9` IJ (' Þ h-' = ) 7./' ' D"$&% ' ' =7 : "$&% ' : "$&%10 <>7 E Ñ{u Ñ{u 2 ú ïöð¾î¸ð¾úò·ýþ 3546ù 0 (' m6]jYeXZ1t 7#"" : "$&% %8$&`g `tZgj`?¡`u\g^XZ` 7 g^`·:iBkl6` ' =7 Þ ¨Ìh¤ ]skluy}Yqhjueg 7 '6 ./' '*' =7 z,¨©klul`pdfYekno`0_p]¢nhj_p]j`0zl` ª $`·gZg^`0_0 g^lY:zl`p`tZg]qt^t^` !`·Çp ]q¡`yfYeklXg^XZYek:r\`Xo`t`u\g^XZ`tzl`t dfYek:j`ts_p] ¢:hj_p]j`tszl` m5_p]hotul`zlY\ulul`y{]qtsz|`d}Y\ultsXZ t^knÆg]g^ t /¸r\Y6hjXsÑ5[eklXZ`I 0^ª5Ä Yeklt=g^XZYeknreY\ult zl`tt^iBkl`j`gZg^`¡t«ulYeuY\ulul`¢|`t¡m ]qXYeuu|`Âyf`k:gy{]qtzl g^`g^`¡Xj`t`ueg^XZ`tz|`¡t«d}Y\k:j`¡t_p] ¢nho_p]o`t iBk:hÐul`tDYeu\gsy{]qtsyn¸]q ¡t ]6k¥_hƤho`k"z,¨©kluynh¤¢|` /QY\kreY¢l` 0^ª `thjulYeu\r\ ¡unho`u\g^tpzl`¥¸]z|`¡XZunho¦XZ`"_ g^lY:z|`\m#z ltpÃ]z:hjt^XZ ·gZhjt]gZhoY\uzl`Ũ©`¡tDy{]6`6m3yf`k:re`u\g Õg^XZ`xy5]6X~gZhj`Æj`_Â`u\g) rBhÆg^ t)]r\`¡klul`]6kng^XZ`xzl Ñ{unhÆgZhjYeupz|kpt^iBkl`o`gZg^`6m:`¤o`Ê h{ g]qu\g]qklt^tUhlo`=Æhj`kpzl`t z:hjt^Yeu\gZhjuBk:hÆg^ t zl`]zl X~hÆr\ ¡`«zl`]V ]qX~g^`zl`z:hjtZg]qul` {ª *`tz:hjt^Yeu\gZhjuBk:hÆg^ tt^Yeu\gj`t_p] ¢:hj_p]¥oY: ]qkn¢Ízl`0¸]" ]qX~g^`pzl`pz:hjtZg]6u|¡`pz5]6ult¸]"z:hjXZ`·gZhjY\uSzl` =@=@?B?BA<A<CC m5jY\XZt^iBklF` : #"$&% 'H IG ª t^Y\u[eX^]qz:hj`¡u\g¡,m : {ª Þ Y6h¤6g ;klure`g^`klXklu:h¤g]hjXZ`zl Ñ{u:h y5]6<X ; ' D :> E : D `yfY6hju\g `tZg)klu¥_] ¢nho_kl_JjY: ]fzl` 0tZh`·gt^`k:o`_0`u\gstZhPklul`zl`tsz|`¡kB¢¥¡Y\ulz:h¤gZhjYeult=t^k:h¤r6]6u\g^`t t^`r\ ¡X~h¤Ñ{` ¬ = D"$&%KJ #"$ ) ; %?`g #"$&%$ #"$ ; % ,&úKJ L:L4M.
(74) 4<. ½qÀZ½¶Àºqº \ ¶F µ\½e®¶ ³ =À 5 \±qµÀZ¶
(75) ͽe®»½6º&e½qµº. $. = D"$&%. #"$. ) ; ?% `g. D"$&%. J. #"$. . Þ hYeu¥Å]h¤g)j`zl re`jYey|y}`_0`ueg zl` 3 ]BoY\X)zl` D"$. . ;. % . D"$&% . ; :. ; %. #"$. ; %)]qk§ylXZ`_ho`X YeXZz|XZ` ¬. #"$&%'CD"$&% . ':. #"$&%. '. Y\uy}`k:g«reYqhoXiBkl`0]¥zl`kn¢nho¦_0`py{]qX~gZho`pzl`tz|`¡kB¢£¡Y\ulz:h¤gZhjYeult«ylXZ ¡ zl`u\g^`tt^`r\ ¡X~h¤Ñ{`pg^Y\kvZY\klXZt`g iBkl`Ñ{u5]j`_Â`u\gxiBkl` t^YqhÆgklu_p] ¢nho_kl_JjY:]XZ`rnhj`u\gÃ0z:hjXZ`iBkl` ¬ #"$&%$ D"$ ) ;% /GI 0 WÐY\klX?¸]«_hot^``uY:`k:r:XZ`6m:u|Yeklt=tZho_0y:¤h¤Ñ{Yeu|t*¡`gZg^``¢|ylXZ`t^tZhjYeu§]·re` o`t*Y\dlt^`X~r6]gZhjY\ult)t^k:h¤r6]queg^`t¡¬ I A ' =7 (' %^m =7 8 g]quegj`XZ ¡tDk:Æg]gzl` X ;8y5]6X " =7 = ÄxY\kltyfYek:r\Yeu|t]6yly|XZY¡¢nho_0`Xo`re`g^`kl I F'0`·giBkl`pj`pre`g^`klX =7 `tZg G¨Ë]j[\YeX~h¤g^l_0`pzl`È]qu:ho`jt^t^Y\u,ª #u t]h¤giBkl` 8 # "$&%9' ' =7 G¨Ë]6y| yl XZ Y¡¢nho_p]gZhoY\upI ]6 k0ylXZ`_hj`¡X3Y\XZzlXZ`xz|` :' =7F' /¸Ã"Y #"$&%
(76) `tZg$znh P XZ`¡u\gZh]6dno1` 0^ª:W3k:hjt^iBkl` : ' =7 (' ' ' =7(' : #"$&%^m?ulY\kltpyfYek:r\Yeu|t]qylylXZY¢:hj_0`XV]znhoXZ`gZhoY\u8zl` : D"$&%y{]qX =7ª X #"$ ) ;%y5]6Xhjueg^`XZyfY6]gZhoY\u,m3ulY\kltŨ¾]qylylXZY¡¢nhj_0Yeult0y{]qX #"$ %^m = (k¤ho`kzl`" ]jk:o` ·g]qu\gsj`y}Yqhjuego`«y:ok|tsylXZY:l`à ) ;Sz5]6ult=¸]g^X^]q_0`z:hjt^XZ¦·g^`«k:gZhƤhjt^ `\ª *`gZg^`]qX^]q·g^ X~hjt]gZhoY\uzlkßt^iBkl`j`·gZg^``tZgt^knÇt]6u\g^`"y}Y\klXpzl`tpY\d:vZ`·g^tptUho_0y:j`t¡m?_p]hotp`¤o`ul` zlY\ulul`)y5]6t3zl`)dfYeu|t XZ t^k:¤g]g^t¡mq`uV`)iBk:h{Y\ul`XZul`*]¡Y\ulul`¢nh¤g^ \mqyfY\klX z|`¡t3Y\d:vZ`·g^t
(77) y:jklt Y\_0y:ÆhjiBkl t /¸reYqhjX)Ñ{[\klXZ`t«B
(78) m - 0^ª cs`_p]6XZiBklY\ultiBkl`p`gZg^` ]qX^]6g^ X~hot]gZhjYeu£]§kluX^]qyly}Y\X~gz:hjXZ`gV]re`p`Æj`tzlY\ulul `ty{]q2X +]Ê g^l`XZY\u Ó" -..Y\k +` e`X Ó\4 Ŭ:h¤jt)hjueg^XZY:z|k:hotD`¡u\g)j`tsulYqgZhjYeult=zl`0Á ´}¿³ÀZ¶½q² `·g e± º5¿·³¸ÀD¶½6² z,¨©klu§yfYqhou\g zl`Ũ©Yed:vZ`g¡m|iBk:h#YeXZXZ`t^yfY\ulzl`u\gsXZ`t^y}`gZh¤re`_0`¡u\g]6kB¢"z:hjXZ`¡gZhjYeu|t : p`g : {ª ] ]6X^]qg^ ¡X~hjt]gZhoY\u Ñ{u{]j`Âz|`¡tyfYqhou\g^tzlkÍt^iBkl`o`gZg^`6m.zlYeu|ul `Vy{]qX +` e`Xz{]qult Óe. Gm,`tZgylX^]gZhoiBkl`_0`u\g¸]¥_0Õ_Â`0iBkl` `Æj`zl`Å¨Ó iBk{]gZhoY\u /G 0^m5`gsylXZY:z|k:hÆgo`t _0Õ¡_0`tsXZ t^knÆg]g^tx`¢|yf ¡X~hj_0`ueg]qkn¢Pª 8 . . . )5B&/134'F+'AB&/ /% ?"'*) B = /6); ='?'?""!)5/D"! 2. xÄ Y\klts]¤oY\ultsy|XZYeyfYetD`¡X=z{]6u|tx`gZg^`t^`gZhoY\u§k|ul`ulY\k:re`¤o`«]qX^]q·g^ X~hjt]gZhoY\u§zl`t_] ¢nho_p]jY: ]6kn¢ zl`¥¸]Í ]6X~g^`"zl`z:hjtZg]6u|¡`6m36¨©`tZgZÊUÃÊ z:hjXZ`"klul`"_Â`h¤Æj`klXZ` ]6X^]qg^ ¡X~hjt]gZhoY\uzl`tpz:hjt^Yeu\gZhjunknhÆg^ tpzl`¥¸] zl X~h¤re `zl`] ]6X~g^`z|`z:hjtZg]6u|¡`6ª *Y\_Â_0`ulY\klt*Ũ¾]·reY\ult)r:k]qkly{]qX^]r6]qu\g¡mlu|Yeklt=y}Y\k:reY\ults]qylylXZY¢:hj_0`X)j`[\X^]qz:ho`u\gszl`]]qX~g^`zl` 8 m =7 IJ ·g]qu\gj`XZ t^k:¤g]gzl`0Ũ¾]o[\Y\X~hÆg^l_0` z:hjtZg]qul`]6k£y}Yqhou\g TmK: #"$&%y5]6X«o`0r\`¡g^`klX =7 zl`§È]qu:hj`ot^tDYeuyfY\klXj`yfY6hju\g Tª ul`znhot^Y\u\gZhouBk:h¤g^ zl` : S]qkSyfYqhou\g ]qyly{]qX^>] ÆgjYeXZt^iBkl`Âo` yfY6hju\g ]«klupr\Y6hjtZhju zlYeu\g*]ylXZYqvZ`·gZhjY\u 7 /QiBkl`ulYek|t*y}Y\k:reY\ult*Y\d:g^`u:hjX?rnh]È]qu:hj`ot^tDYeu 0.`tZg g^XZ¦t q µ 5ÀD¶ºf³Å¶?zl`]ylXZYqvZ`·gZhjY\u 7Vmnzl` TªB$`·gZg^` q µ 5ÀZ¶º}¼¶$yf`k:g)Õg^XZ`_0`¡tDklXZ `y5]6X*klu¥zl`t)zl`kn¢ 'ª y{]qX^]6_0¦g^XZ`tst^knhÆr6]qu\g^t /¸r\Y6hjXsÑ5[eklXZ`I 0{¬fÏ ' "
(79) ( %ml`gÎ '*' .
(80) . Ál¶ ®»¶ ³Å³Q¶¿=Ál¼ ®¾µqµ¶º{¿Ð¯ ± ¹ ¶ ³¸¿ qµ¿·¼ÀZ¶ ³¸¿º
(81) qµ²0¶º{¿µ±qº{ºf¶ ®¾¿. \. P. φ d. M M’. P’. l´ ½qÀZ½6² ³ÀZ¶¿sÏ8¶ ³ÐÎ5"$7H(87 % ]¥Ñ{[ek|XZ`_0Y\ueg^XZ`¥iBkl`ŨÓkngZhƤhot]gZhjYeuzl`¥`¡tzl`kn¢ y{]6X^]q_0¦g^XZ`¡t0yfYek|X ]6X^]qg^ X~hot^`Xo`zl`[eXZ z,¨Ë]6y|y{]6X~g^`u{]qul`z,¨©kluyfYqhou\gs]qk§t^iBkl`j`·gZg^`6m|`tZgsklu|`hozl `g^XZ¦t)hju\g^k:h¤gZhÆr\`\ªfW.Yek|X*G¨©Y\d:vZ`·g Ã[B]6k|l`zl` `gZg^`)Ñ{[\klXZ`6m\ulY\klt?]reY\ult?XZ`ylXZ t^`ueg^ `u x¸]r6]j`¡k|X zl` Î /Qt^k|X~Å]6`xÃ[B]qkll`=zl`)]_0Õ_Â`=Ñ{[\klXZ1` 0Ð`g zl`*Ï /Qt^klX~Å]q`=ÃzlXZYqhÆg^`10PXZ`t^yf`gZhÆr\`¡_0`u\g¡ª *`tÐy{]qX^]6_0¦g^XZ`thjueg^XZY:z|k:hotD`¡u\g3klul`?t^Y\X~g^`$zP¨Ó`t^y{]q`Ê l`¤o` u{]g^klXZ`Ðy}Y\klX*j`t^iBkl`j`gZg^`\ª , =. } = Ï. ¶ \½6Ál¼·°n¶ q ÀZ±6µ³Q¶Ð®D¯ ± ¹ ¶ ³
(82) µº{µ³µ½\®
(83) ®Z¯ ¶¿Å´l½\¼¶\¶)´l½qÀZ½6² ³ÀZ¶sÎF¶ ³$®Z¯ ¶¿Å´l½\¼¶\¶)´l½qÀZ½6² ³ÀZ¶. Þ hulY\klt§zlY\ululY\ult¥klu tD`¡knhÆyfYek|Xklu zl``t§zl`kn¢ y{]6X^]q_0¦g^XZ`¡tmulYek|t§yfYek:r\Yeu|tg^XZY\k:re`X¥o` t^iBkl`j`·gZg^`z,¨©klußY\d:vZ`g0Å]6h¤o`_0`ueg /¸r\Y6hjX0Ñ{[\klXZ`t§`g4< 0^ª ( re`klußyf`·gZh¤gt^`k:h¤u|YekltpY\d:g^`ulY\ult klu t^iBkl`o`gZg^`"g^XZ¦t§zl g]hƤo 6m g^XZ¦tzl y}`ulz5]6u\g§zlkdlXZk:h¤g§zlk Y\u\g^YeklX·m$_p]hjt§]B]6u\g§`uß[\ ul`X^]¸] _0Õ_Â`0g^Y\yfY6jYe[qhj`ÂiBkl`p`¤o`pzl`0Ũ©Yed:vZ`ghju:h¤gZh¸]Gª
(84) È]qult]"y{]6X~gZhj`p{]qk:g^`pzl`pŨ©`¡tDy{]6`0zl`py{]qX^]q_¦g^XZ` Y\uFY\d:gZhj`uegzl`tt^iBkl`o`gZg^`tulY\ut^`ultUhod:j`t]6kÔ·d|XZk:hÆgÔ«zl`Y\ueg^Y\klX·mfz|`y:jklt`uFynokltY\_Ây5]6g^t¡m5`g _p]jl`klXZ`klt^`_0`u\gs] n]qu\g=tDYek:r\`ueg)k|ul` g^YeyfY6jY\[6hj`)z:h , XZ`u\g^`zl`¡`¤o` zl`G¨©Y\d:vZ`·g?hju:h¤gZh¸]Gª|WÐY\klX3Å]hoXZ` j`t^`k:h¤Æ]6[\`Yeu"]6[qh¤gszl`]Å] Y\u§t^k:h¤r6]queg^` ¬ = WÐY\klX{]qiBkl`Vynh¤¢|` Tm,]6y|y{]6X~g^`u{]qu\gÃpŨÓY\d:vZ`gxhju:h¤gZh¸]Gm,Y\uFl`XZl`0z{]qultt^Y\u"reYqhotUhou{]q[\`\mlo` y:h¤¢|` iBk:hÐXZ`ulz"_p]¢nhj_p]P]r6]j`klXszlk"y{]qX^]6_0¦g^XZ`lY6hjtZhŪ ,&úKJ L:L4M.
(85) . ½qÀZ½¶Àºqº \ ¶F µ\½e®¶ ³ =À 5 \±qµÀZ¶
(86) ͽe®»½6º&e½qµº. Þ h¡`gZg^`r6]j`¡k|Xx`tZgsynoklt [\X^]6ulz|`ink|`o`tD`¡knhÆŬ ` = ? A C "$ %`tZghjulok|t^`z{]qult]"d}Y\k:j` =@?BA<C "$&%«Y\uSul`[B]qXZzl`piBkl` = Þ h*]"d}Y\k:j( z{]qult=G¨©`ult^`_d:j`Ñ{u{]Ū ` =@?BA<C "$&%`tZghjulokltD`pz{]6u|t¸]¥dfYek:j
(87) ` = ? A C "$ %YeuÍul`p[n]qXZzl`0iBkl` = Þ h3]dfY\k:o
(88) z{]qult=G¨©`ult^`_d:j`Ñ{u{]Ū `g9 z{]qult = Þ h?]6k|¡k|ul`0zl`tzl`kn¢Í¡Y\ulz:h¤gZhjYeulty|XZ ¡ zl`u\g^`tul`0t^`re X~hÆÑ5`pYeu[B]6XZz|` ŨÓ`ultD`¡_d:j`Ñ{u{]Gª *`¥g :yf`zl`]qX^]q·g^ X~hjt]gZhoY\uu,¨Ó`tZgy5]6tpulY\k:r\`]qk,ª #uß]Íg^XZYek:r\ zl`kn¢ ]6X^]qg^ ¡X~hjt]gZhoY\ultg^XZ¦t ylXZY:l`tpzl`"¸]£u qg^XZ`\ª #Y\k:g^`t0j`¡tpz|`¡kB¢ k:gZhƤhjt^`uegpj`Yeul`y:gzl`"`k8zl`ylX^]hoX~hj`6ª)W
(89) ]6X`¢|`_0y:j`\m +` e`X?z{]qult Ë\4 fzl Ñ{u:h¤g*¸]xrnh¤g^`t^t^` zl` ylXZYey5]6[B]gZhjY\uÂzP¨Óklu0XZY\u\g)zl``¡kpY\_0_Â` /¸r\Y6hjX?Ñ{[\klXZ`xa 0 `gxh¤#]6t^tUhÆÑ{`j`ty}Yqhou\g^t zl`Ũ©Yed:vZ`gxtD`·jY\u`gZg^`rBh¤g^`¡tDt^` ¬P]qkn¢yfY6hju\g^txzP¨Ó`¢ngZhou|·gZhjY\ u /Qt^iBkl`o`gZg^1` 0*j`t XZY\ueg^t?zl`t
(90) `kn¢ptD`)ylXZY\y{]6[\`u\g=Ãklu|`)rBhÆg^`t^tD`st^klyf X~ho`klXZ` à \ª (kB¢0yfY6hju\g^t$iBk:h5u,¨¾]qyly{]qX~gZhj`¡u|ul`ueg*y{]qt ]qkt^iBkl`o`gZg^` ]rBh¤g^`¡tDt^`xz|`y|XZYey{]q[B]gZhjYeup`tZg) [B]j`Ãp6ªlÒ,hou{]j`¡_0`u\g*hÆt¡¨ hjueg^ XZ`t^t^`á`X~g]hou|t*t^Yek|tZÊ `ult^`_dno`t zlkt^iBkl`o`gZg^`6ª ]qyly}`j` ÊGd:hjt^t^`g^X~ho`Y\ulz:h¤gZhoY\ulul`¤o`]6k"t^Y\kltZÊ `ultD`¡_d:j`zlkt^iBkl`o`gZg^` Y 0¸]«rBhÆg^`t^t^`zl` ylXZY\y{]q[n]gZhoY\up`tZg)t^klyf X~ho`klXZ`Y\kp [n]o`à ª|w uXZ`¡[B]qXZz{]6u\g*j`t?Ñ{[ek|XZ`¡t`g)aY\u XZ ]¤hjt^`Å]6h¤o`_0`u\g¡m5ink|`o`t ]6ul[qj`¡tÏ`g 0t^Yeu\gÆhj tsy{]qX)Å¨Ó iB k{]gZhoY\u /Qa 0 '& ) Ï ]prBh¤g^`¡tDt^`pzl`pylXZY\y{]q[n]gZhoY\u g]6u\g [B]*à m,j`¡t«y}Yqhou\g^tz|kSt^iBkl`j`·gZg^`Âre X~hÆÑ5`¡u\g ª *` iBk:h)`tZg iBk:h¤r6]j`ueg¡m#y}Y\klXu|Y6g^XZ`p ]qt¡m
Documents relatifs
Chez l’Homme, les segments de gène V H ont été classés en sept familles (la famille 7 n’est pas représentée ici car aucun segment fonctionnel n’y a été décrit) qui ont
Le Négus consacra une énergie considérable en vue de gagner cet appui international, mais, malgré la force de son discours prononcé en juin 1936 devant ses pairs à la tribune de la
In this paper, we propose a novel approach based on the barycentric coordinates of automatically tracked 2D facial landmarks from videos to objectively evaluate the facial
Dirk Obbink (dir.), Doctrine and Doxography. Studies on Heraclitus and Pythagoras, Berlin / Boston, De Gruyter, 2013, p.. et le logos auquel les hommes devraient accorder
Les exorcismes ne sont pas publics, les sœurs noires elles-mêmes sont tenues le plus possible à l’écart, et c’est chaque fois Jeanne qui force les choses pour que, finalement,
Toute- fois, d’autres marqueurs des cellules POMC tels que NeuroD1 n’ont pas été induits dans cette expérience, ce qui indique que Tpit suffit in vivo pour provoquer la
Mais elle y occupait une place modeste : il faudra la liberté et le goût de la transgression du roman en langue vulgaire pour que la situation soit renversée :
Les thèmes majeurs (tab.5.4) abordés par les îliens interrogés sont, pour la grande majorité, les mêmes sur toutes les îles : ils concernent les usages anciens