Checking the Convexity of Polytopes and the Planarity of Subdivisions
26
0
0
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Checking the Convexity of Polytopes and the Planarity of Subdivisions Olivier Devillers — Giuseppe Liotta — Franco P. Preparata — Roberto Tamassia. N° 3527 Octobre 1998 THÈME 2. ISSN 0249-6399. apport de recherche.
(3)
(4)
(5) !"#$%&'(*) + ,- ."/) )0, #1 !24356+7 #4 8(, 8 ( 97:<;>=?;<@BACD@B=?;E:<:E@FA
(6) GIHKJL;<M,GN@FO,OP@'Q;<R S
(7) SUTVHXWXAYT1Z[FR]\_^K\`A
(8) @FOXT ANT1SUTaHXb4Rdce@FA
(9) SNRgfhT i]T G
(10) GN;<T jlknmYoqprsut vYwyx>p{z>|~}x>Yx>pYz pYFz>Yyze # o|~zx>np 8|F#pY#x> #oqp Fy|~#yp{8pU8knpY8/knpw%rsu$Y8|~y8pqDsd ?F}pU ' U¡¢B£y¤¡¥ jlkyx> ¦?F,pYU|~wn #x>ypY8 #knphy8|~yz>pYo|F§,¨pY#x©§ª xwy} #knp`U|~#8pUY#wnpU 8 ¦|F§,}pU|~oqpY« #x>$ ###nY#y8pU ¬®w6?F##x>YyzEF¯d°hp ypU #x}wI 8xoLyz>p|~y#xo6FzX8knpU/±pY8 l§²|~_U|~w¨pN³I,|~z 8|~pU xw´°_|µFwn.kyx}knpYIdxoqpYwn #x>|~wn ¯`Fwn¶§²|~q¨F#x>|~n 6®1pU 6|F§ yzEFw?F· #y,dx¨ x> #x>|~wn ¯h #n/k ~ ##xEFwy}yzEF#x>|~wn ¯¸ pYzEFyw?UV##xEFwy}yzEF#x>|~wn ¯¦FwnaU|~w1¨pN³! #ydx¨1x> #x>|~wn ¹¬'jlknpYx,pY§²|~« o6FwnUpqx> Fw?Fz1ºpU»Fz> 8|·xwa8pY#oq 4|F§l#knp6Fz}|~#x#kyoLx>6ypY}8pUp¯e°`kyx>8k¼8k?F/~Y8pY#xºpU #knp F#x#kyoqpY#x>y8pUYx> #x>|~wg8pU1yx8pUX¬ ½g¾¿À8Á ¢Bà ¥ Ä |~oLyy/F#x>|~w?Fz%}pU|~oqpY##¯¸ pYzEFyw?UD##xEFwy}yzEF#x>|~wK¯1U|~w1¨pN³Dk1yzzůpN³n~Y F#x#kyoqpY#x>¬ Ú Í8Û1Ô~ÐÒ×eKÆ
(11) Ü Ý²NÜǹݴáÈÅÞÉÔNÞ_ʲÎʲñNÉÐàÊñßFË%Þ/ȲÌ_ÝÅÐÒÍBÔá`ÎÕ<Ý´ÉÉÞ/âUÏÑÒÝÅôUÐÒÜKÑÒÍ ÑÒÉÓÇBÈÅÐNÊÕªÔ~âBÕ<ãäÖÜ
(12) ÈÅ×eáÕØÞ8ÆÙÝÅÍÐæåÓÞKÉ,ç¹ÐÒÊØÝÅÉá`ÐÒÊØÝÅÐàåÞÔNèPâFÐÒÏYÉÓÈÅʲÐéÝ´êXÇBÐN×PÜ
(13) áÞëªÛ1ÞKçBÞ
(14) ßBÐÒÉâFì#Þ8íÅÔ
(15) îPÐàÞPç¹Þ
(16) ÑàÞ/ÈÅÐàÞ õûïNï#ÈÅÍNð Ü#öyüKÈÅÉâ ßFè/Þ È´Bâ Þ/ÐàÝ´ÏNÞÉÓÈÅÞ/ïʲâ~ÐéòNݪǦó ôUÔ×ÙïNÍ
(17) ï#÷dýÙÞ/þ áÞ
(18) Þ8ʲÝÅʲÉÓÐàÈÅÞ¹áÔÞ
(19) ø,â ÉâUçÝÅݲÉÓÈÅÈyÉÉÓã©Ü/Ý#È ÔFöyÚ ÈÅÉÓÜ/ÜNÏá`ÐàÇBÉÓÉÓݲâ~ÈÅÐàåÓåKÉNø,ÔB×eÜNá`Õ,ñNßBÿ ùBò¹ÝÅïÐÒâFÿú¹Í ÔNÎÉß~Þ8ȲÝÅá`ÉâUÝdÜ
(20) ãø,ÜNá`ßFù¹ÝÅÉÓÈ?ç¹åÓÐÒÉâ~åÓÉ
(21) Ô
(22) ! "$#%&' (&)+*, (
(23) %-. /, ' 0/,%1 2 (%343.6587/9 : ;8:&;<9=4 >! " ?A@B*,@.C
(24) DEF G 2
(25) IHKJL
(26) M/,%1 2 (ON CPCQ$RS"5878T 5/U 5/RR&U :&= ! "$VW3LVO*XY Z&[0\. /1][,
(27) D^ _ G 2
(28) >XOa`b GcC\434Hed _Z&[f/,E " Gg;/R ;SS<=g h! "i3.#jXOa`b G kl DF'm3Y D6"<'GnGo ,&)B /
(29) 'p qCO,) ' bn' "4 ))rqlg22sO mp&)O3.CN%=2tW ,> u34leC \v/,F (2 G ;U&7w/9 @]xM y> ! "%sY
(30) z ! < {<| DFuu $}A 8o)BF ">}e i~bo/1u! <03e"$|G l DF' 03Y DP(/1]& }c?<~ o@0xE y> ! "E (p ! < P<|G DF> 4}+ /o)B% "M}e $}co! ! <3e"4|G l Dh
(31) ' 3Y DP(/1i&c4 }cv?<~
(32)
(33) 8@. Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles, B.P. 93, 06902 Sophia Antipolis Cedex (France) Téléphone : 04 92 38 77 77 - International : +33 4 92 38 77 77 — Fax : 04 92 38 77 65 - International : +33 4 92 38 77 65.
(34) 0 7P)`, 8 + "8) +D-&'"#$%&6( + "/) &7"8) )0 -+D-(,3 +7 #4 8(, 8 ( ¥ ¸{Fwn 6UpYIF##x>Yz>p¯`|~w xw8vY8pU / 8p]F.y8|~yz>mYoqp ypzE ¨vY#x ?F#x>|~w ypzE ¨Fzx>dx8v yp UpY#/FxwnpU 8##nY#y8pU ·}vU|~oqvY##x>npU ¬ w?F##x>Yyzx>pY¯$wn|~n Iy8|~| 8|~wn Iyw ¨vY#x ?F8pYy¯ #xoLyz>p6pY|~y#xo6Fzůe|~y4z>pU ,|~z 8|~,pU U|~w¨pN³ypU pYw!dxoqpYwn #x>|~wn DypYd³apY 8y,vY#x>pYy8pU ¯?pY|~ydx¨pY8 ®1pU yp4 8y,dx¨ x> #x>|~wn yzEFw?Fx8pU 8pYzz>pU 1np{##xEFwy}yzEF#x>|~wn ¯ ##xEFwy}yzEF#x>|~wn yp¸ pYzEFyw?U |~V #y,dx¨ x> #x>|~wn $U|~w¨pN³ypU ¬ KpU $pY§Ø|~#o6FwnUpU { 8|~w1{vY}Fz>pN« oqpYw1Fw?Fz /vUpU hpYw·8pY#oqpU `yp ypY}8v4Fz}|~#x#kyoLx>1np{yxF/~Y8vY#x> 8p zEy8vUYx> #x>|~w8pU1yx> 8p |~y`z ÒF#x#kyoqvY#x>1np4y#xzx> 8vUp¬  ¡ À ¤ ¥ t vU|~oqvY##x>p»Fz}|~#x#kyoLx>np¯$##xEFwy}yzEF#x>|~w ypV¸ pYzEFyw?¯$pYw1¨pYz>|~y,p U|~w1¨pN³dp¯%F#x#kyoqvY#x>nppN³y~Y8p¬ . . . . .
(35). . . . . .
(36). .
(37) .
(38) "!"#%$ '&()$ '$*,+'-.& /0 /#" 1 #. %0,{+73e, 8 jlknp{ypY¨pYz>|~yoqpYw1|F§8knpU/±pY8 §²|~l}pU|~oqpY##x> ###nY#y8pU `x> n ##x ?pU1'#knp{pN³dpUY/F#x>|~w #k?FLxLx> Lp~ 8x>pYL8|VpY¨~Fz?F8p#knp1?Fzx´µ|F§#knp|~y#yy6#k?Fw¶#knpU|~#8pUY#wnpU 8 6|F§$#knp Fz}|~#x#kyo y8|1dnYxwy}¼x¯`Fwn¶x> L§Øy##knpY6oq|~#x¨F8pU.1µ#knpgxwnY8p~ #xwy}µU¨FxzEFyxzx´|F§ }pU|~oqpY##x> 8|F§Ø´°hF8pD|~wg#knp´w18pY#wnpY% 4Ø 8pUp¯%p¬ }n¬6¯ 5 7
(39) 8N¯%Fwng#knp4pYoqpY#}xwy}·Yzx>pYw«´ 8pY#¨pY dx> 8##xyy8pUqoq| ypYz> ¦|F§X}pU|~oqpY##x>U|~oLyy#xwy}|¹¨pYÙ#kn:p 9apY; 4Ø 8pUp¯p¬ }n¬'¯ 5Òr 7
(40) 8N=¬ < pYkyzkn|~#w > $ )? 5Òrd 7?x>ypYw#x©§Ø7#ky8pUpl§ØywnnFoqpYw/Fzn§²pF#y8pU Ù|F§K$}| |1L/knpU8±pY0 @ *"*> A B#C# ¯ # /DE!'F A>
(41) A ¯ Fwn
(42) GHI 'I ¬ ´w7#kyx> ?FpY¯°_p`U|~wn #x>ypY¦/knpU8±pY8 ¦§Ø|~ #ydx¨1x> 8x>|~wn PxwL®°_|4Fwn7kyx}knpY¦dxoqpYwn #x>|~wn ¹¬ ®wL?F##x>YyzEF¯1°_pU|~wn #x>ypYÙ´°_|F«´dxoqpYwn 8x>|~w?Fz,yzEFw?F_ #y,dx¨ x> #x>|~wn ÙFwn6U|~w¨pN³L,|~z 8|~pU xw y³dpU.dxoqpYwn 8x>|~K w Jn¬jlknpg #ydx¨1x> 8x>|~w.8|Vp8knpU8±pU Fw.pgpYx#knpY' y#xoLx#x¨p 8##nY#y8p¯e|~·ypY#x¨pUa ###nY#y8p6U|~oLyy8pUV§Ø8|~o Iy#xoLx#x¨p6|~wnLp 4Øp¬ }n¬¯K#knNp M¦|~8|~wn|~x dxEF}/Fo |F§{ 8pYL|F§$ #x8pU 7xwµ#knp·yzEFwn p 8N¬!jlkyx> q?F,pYLU|~wn #x>ypY8 q/knpU8±pY8 q§Ø|~7¨F#x>|~n ®1pU h|F§eyzEFw?Fh 8y,dx¨ x> #x>|~wn lFwn6§²|~_U|~w1¨pN³'|~z18|~pU _xw'®°_|LFwn6kyx}knpY`dxoqpYwn #x>|~wn ¹¬ 9apn #?Fzz ~ 8 8yoqp4#k?F$#knppYopUydxwyO } 4ØYx8YyzEF{|~8ypY#xwy}I|F§¦#knpDpUd}pU $F8|~ywn p~/k ¨pY#8pNP³ 8|F§#knpIxwyyyq #ydx¨1x> 8x>|~wµ|~7|~z18|~pIx> D}x¨pYw~ 7?F#7|F§$#knpIxwyyyO¬ 9 knpYw #kyx> x> $wn|~#knpD~ 8p¯,xŬép¬¯%wn|'pYo,pUydxwy}xwd§²|~#o6F#x>|~w x> y8|¹¨1x>ypUX¯°hpFzz#knp78knpU8±pY #I A*Q RS * ¬ 9ap ~d¨| F8pVawnpY° 8pU1yx8pYoqpYw#k?F·}| |1}pU|~oqpY##x>V8knpU/±pY8 g #kn|~yz> /F#x> §Ø¯ Fwn'y8pU 8pYw1 #xoLyz>p$Fwn·p T6Yx>pYw1 ##8|~wy}D/knpU8±pY8 l§²|~l 8pY¨pY/FzX ###nY#y8pU _§Ø|~h°`kyx>8kg|~wyz /knpU8±pY8 k?¨pÙpUpYwD /|`§ÅFPypU #x}wnpUXV¬ U1pUYx ?Fzz¯|~yU|~w1##xyy#x>|~wn FwpÙ #yoLo6F#xºpU ~ `§Ø|~zz>|¹° ¬ X¬ W DFw¼~ydx#x>|~w?Fzhoqp~ #y8p6|F§p YXpUY#x¨pYwnpU 8 §Ø|~]8knpU/±pY¯°_pI~y|~y#knp6wn|~#x>|~w |F§ &Z1 * 5y¯y¯,[ 7´¯°`kyx>/kV/F±pU xw8|g~UU|~yw1{#knpw1yopY|F§Ùyx8 8pU1yx8pU #knp48knpU/±pY$8|6F##·|~y$pY#8|~«²§ª8pUpU|~oLyy/F#x>|~wn :¬ W }|1| g/knpU8±pY #kn|~yz>gk?¨p ypY}8pUpwn|Ikyx}knpY{#k?FwV#knpDy8|~yz>pYo F k?FwnVFzz>|° \¬ 9ap}x¨pDz>|¹°_pY4|~ywny |~w #knp{ypY}8pUp|F§8knpU8±pY8 §²|~`yzEFw?F #ydx¨1x> #x>|~wn FwngU|~w¨pN³|~z18|~pU ¬ rd¬ 9ap_y8pU /pYwÙ$8knpU/±pY§Ø|~U|~w1¨pN³D|~z18|~pU #k?Fxw¨|~z¨pU wn|¹¨pYzyx>yp~ ¦FwnDk?~ #knp ,|~8pYw1#xEFze8|qz>p~]8|6L #xoLyz>pYxoLyz>pYoqpYw/F#x>|~wV#k?Fw #knp4|~wnp4}x¨pYw x]w 5ÒrdI 7´¬`y 8knpU8±pYL°h|~#± Dxw.Fw»dxoqpYwn #x>|~w.Fwn»8pUYy8 8x¨pYz!8pUdnUpU D#knpI¨pY#x ?F#x>|~w.|F§$ J~«´dxoqpYwn #x>|~w?Fz|~z18|~p8|#knp¨pY#x ?F#x>|~wg|F§PFw~ 8 8| YxEF8pU; ^ J_a`b²«´dxoqpYwn #x>|~w?Fz ,|~z 8|~,p¬»jlknp8knpU/±pYqx> L|~y#xo6Fz°`x#k¶8pU #pUY78| |~#k¶#knp·#xoqp·U|~oLyz>pN³ x® Fwna#knpIypY}8pUp¬gjlknp'ypU 8x}w»|F§|~y/knpU8±pYD§²|~U|~w¨pN³»,|~z 8|~,pU 8pY¨pFz> wnpY° U|~oyxw?F8|~#xEFzFwn}pU|~oqpY##x>{y8|~pY##x>pU #k?Fo6Ip{|F§xwnypY,pYwnypYw1xw8pY8pU 8¬ 2. 3. . . . . . ×P× â c ðYý ÿd.
(43) ?%0
(44) / *"#X? A 1 $ (? * !$*Q$ $
(45) ?'$DN$#C# A$. d¬9apy8pU /pYwlzxwnpF«Å#xoqp{|~y#xo6Fz©«´ypY}8pUp48knpU/±pY8 l§²|~_##xEFwy}yzEF#x>|~wn ¯?U|~w¨pN³ #yd« dx¨1x> #x>|~wn ¹¯Fwn»}pYwnpY/FzlyzEFw?FL #y,dx¨ x> #x>|~wn ¬ U1n8k¶8knpU/±pY8 7n 8p·~ #yy8|~y#xwnpU pYz>pYoqpYw/F#!}/Fyk.Fz}|~#x#kyoq qFwnµy| wn|~8pU1yx8pI8|]8pU #D#knp'yzEFw?F#x´µ|F§#knp ywnypY#z1xwy}qxwyyy}/FykK¬ n¬ ³ 8pYwndxwy}#knpF,|¹¨p`8pU #yz8 _|~wq8knpU8±pY8 ¹¯1°hp`y8pU 8pYw1¦zxwnpF«Å#xoqp|~y#xo6Fz©«´ypY}8pUp ##8|~wy}'/knpU8±pY8 $§²|~##xEFwy}yzEF#x>|~wn 4Fwn]U|~w1¨pN³ #ydx¨1x> #x>|~wn ¹¬`jlkyx> 8|~z¨pU $ #x}wyx©§ª« x>Fw 8,pUYxEFzÙ~ /pU 4|F§Fw!|~,pYw!y8|~yz>pYo oqpYw#x>|~wnpU» x#± ?F##x>8± 5[ 7_|~w!#knp pN³ x> #8pYwnUp`|F§XFw ^ bPFz}|~#x#kyo 8| ¨pY#x©§ØD#knplyzEFw?F#x´L|F§X$}pU|~oqpY##x>}/Fyk °`x# k ¨pY##x>UpU ¬ dX¬ W ¦$§Øy##knpYÙFyyzx>F#x>|~wK¯ °_p`}x¨plzxwnpF«Å#xoqp|~y#xo6Fz©«´ypY}8pUp 8#8|~wy}8knpU/±pY8 ¦§²|~ ¸$pYzEFyw?7##xEFwy}yzEF#x>|~wn ¯ z>|1Fzz1«ÅoLxwyxoyo7«Å°hpYx}kl##xEFwy}yzEF#x>|~wn `Fwnq¸ pYzEFyw?U dxEF}/Foq ¬ pFg#knp»U|~oLyz>pY#x>|~w |F§L|~y xw¨pU ##x}F#x>|~wn ¹¯4°_p!,pUFoqp¼U°lF8p»|F§q®°_| |~wy}|~xwy} y8|F#pUY8 |~w!#knpqypU #x}w!|F§8knpU/±pY8 4§²|~4yzEFw?FD #y,dx¨ x> #x>|~wn ¯exwnYzndxwy}]##xEFwy}yzEF#x>|~wn FwnVU|~w1¨pN³ 8y,dx¨ x> #x>|~wn ¬ W o6Fw?FEz 5Ò r !7¦ypU 8Y#xyxwy}g#knp§ªywnY#x>|~w?Fzx®V|F§ #Ä "" §ØywnN« #x>|~wn 7#k?FLxoLyz>pYoqpYw168knpU/±pY8 L§²|~L¸$pYzEFyw?µ##xEFwy}yzEF#x>|~wn ¯ M¦|~8|~wn|~xdxEF}/Foq 'Fwn U|~w1¨pN³'yzEFw?F` #ydx¨1x> 8x>|~wn _x> `¨~FxzEFyz>p$§Ø8|~o < pYkyzkn|~#w é 9apY·?F}pV¬ W o6Fwn /Y#xyxw y8|~}8pU / 5Òrr 7U|~w1/Fxwn 8k?F/~Y8pY#xº¹F#x>|~wn |F§e##xEFwy}yzEF#x>|~wn FwnIU|~w¨pN³·yzEFw?Fl 8y,dx¨ x©« 8x>|~wn #xoLxzEF8|7#kn| 8p|F§#knp y8pU 8pYw1?FpY¬ U1xwnUp#knpU /p®°_|·U|~wnU|~oLx/FwFwn xwnypYpYwnypYw{8pU 8pF8/k p YX|~#8 {~yd8pU 8 $#knp7 /Foqp YzE~ / K|F§ y8|~yz>pYoq ¹¯¹oLxwn|~e|¹¨pY#zEFn F8pyw?¨|~x>nFyz>p%¬ $|¹°_pY¨pY¯~|~yPFyy8|~/kx> Xo6F#±pUdz dx YXpY8pYw 4²Fz#kn|~y}kpUyx¨Fz>pYw" 88| #k?FL|F%§ 5Òrrn¯ r ![7´¬»´w.~ydx#x>|~wK¯_°_p #kn|¹° #k?FL|~y /knpU8±pY8 Fw4po6~ypÙ 8#8|~wy}°`kyxz>p¦o6Fxw1/Fxwyxwy} #knp¦ /FoqpÙp T6Yx>pYwnY~ e#knXp 4ªwn|~w 8#8|~wy} 8 /knpU8±pY8 $|F§ 5Òrrd¯% r ![7´¬ jlknp8pU 8 |F§_#kyx> ?F,pY x> |~#}FwyxºpUa~ $§Ø|~zz>|¹° ¬48pYzxoLxw?F#x>pU Fwn yp nwyx#x>|~wn F8p }x¨pYw]x;w U pUY#x>|~w rd¬_y/knpU8±pY§Ø|~U|~w1¨pN³g,|~z 8|~pU `x> `y8pU 8pYw18pUgxw U pUY#x>|~w d(¬ U pUN« #x>|~& w ax> 6ypY¨|~8pU8|a/knpU8±pY8 '§Ø|~'##xEFwy}yzEF#x>|~wn ¯U|~w1¨pN³ #y,dx¨ x> #x>|~wn ¯`Fwn}pYwnpY/Fz yzEFw?F #ydx¨1x> 8x>|~wn ¬ U1#8|~wy}I/knpU8±pY8 4F8p 8#ndx>pUgxw U pUY#x>|~wVd¬jlknpypY}8pUp|F§¦8knpU/±« pY8 4x> {pN³ yz>|~8pUVxw U pUY#x>|~(w 'd*¬ )Pxw?Fzz pN³d8pYwn #x>|~w»FwnV|~pYwVy8|~yz>pYoq F8pqdx> 8Yn / 8pU xw U pUY#x>|~w ¬ .
(46). . ÕªÖ×eÕØÆ.
(47) .
(48) "!"#%$ '&()$ '$*,+'-.& /0 /#" 1 #. . L #, 8 ( . .
(49) "!# $%&&$' "!# ( $) * (+ ,.W J«´dxoqpYwn #x>|~w?Fz Z DN> A*" 1 *$"!P x> ·!}/Fyk d/°`w °`x#k ##/Fx}k1«ÅzxwnpVpUd}pU Ixw J« dxoqpYwn 8x>|~w?Fz_ #?~Up¯exŬép¬¯P·}/Fyka°`kn| /pL¨pY##x>UpU 4k?¨p ~J «´dxoqpYwn 8x>|~w?Fz_U| |~8dxw?F8pU ¬6®w #knpg§Ø|~zz>|¹°`xwy}n¯`°_p |F§ª8pYw ypYwn|~8p]°`x#k/ }pU|~oqpY##x>]}/FykK¯Fwn.°`x#k10 x8 'ywnypY«. z xwy}aU|~oyxw?F8|~#xEFz$ ###nY#y8p¬µje|a 8xoLyzx©§ª»#knp·wn|~/F#x>|~wK¯lFwnµ°`knpYw¶#knpU|~w18pN³ 6x> yw?Foyx}n|~n ¯K°hp7o6U ypYwn|~8p7°`x#2k 0 ,|~#k #knp7}pU|~oqpY##x>7}/Fyk!Fwn x8 ywnypY#z xwy} U|~oyxw?F8|~#xEFz 8##nY#y8p¬ W®°_|F«´dxoqpYwn #x>|~w?Fzh}pU|~oqpY##x>L}/Fy3 k /x> !')$ '$* x©§hx{k?~ 4wn|Y8| 8 #xwy}gpUd}pU ¯exŬép¬¯ Fw1 ®°_| pUd}pU 4|F4§ /.xw8pY8 8pUYD|~wyz F·U|~oLoq|~wa¨pY#8pN³X*¬ )n|~pY¨pY# yzEFw?F4}/Fy5k 0q¯ #knpY8ppN³ x> 88 7yzEFw?F$}pU|~oqpY##x>}/Fy6k /!°`x#k ywnypY#z1xwy}I}/Fyk 0q¯nxŬép¬¯%pY¨pY#yzEFw?F }/Fyk¼~doLx8 IyzEFw?F ##/Fx}k1«Åzxwnp6d/U°`xwy} 4Ø 8pUp¯ep¬ }n¬V¯ 5> 7
(50) 8N¬ $$|°hpY¨pY¯I}pU|~oqpY##x> }/Fyk]°`x#k FwywnypY#z1xwy}'yzEFw?F}/Fykgx> `wn|~wnpUUpU 8 /F#xzIyzEFw?F¬ WyzEFw?F_}pU|~oqpY##x>7 / }/Fyk'ypY8pY#oLxwnpU ` !')$ '$ *:#"-.&
(51) 0 /#" 1 98 ¯xŬép¬¯1{?F##x#x>|~wI|F§ #knp4yzEFwnp4xw8|68pY}x>|~wn Fzz>pU§²~UpU ¬hzEFw?F$ #y,dx¨ x> #x>|~w 8 x> /Fx>8|q,p
(52) '&-C& 1: /_¬ W yzEFw?F #ydx¨1x> 8x>|~w]x> x©§¦#knp|~ywnnF#g|F§Ùp~8k §Å~Up4x> qU|~w¨pN³ ,|~z }|~wK ¬W yzEFw?F4 8y,dx¨ x> #x>|~w 8 xwndnUpUV }pU|~oqpY##x>L}/Fy;k /¶x> DN$0
(53) DN$ x©§h#knpY8p7x> $wn||~#knpY yzEFw?FL}pU|~oqpY##x>·}/Fy<k / =Ù #n/k¶#k?F> / x> 7 #yy}/Fyk.|F?§ /=جa®wµ o6B³dxo6Fz`yzEFw?F 8y,dx¨ x> #x>|~wK¯P#knpq|~ywnnF#!|F§p~8k¼xw8pY#w?Fzh§²~Up6x> g##xEFwy}z>p¯¦Fwna#knp',|~ywnnF#a|F§ #knp pN³d8pY#w?Fz§²~Up$x> DU|~w¨pN³|~z1}|~wK¬ W o6B³ xo6FzXyzEFw?F 8y,dx¨ x> #x>|~w·x> `Fz> 8|LFzz>pUg A* 1$ - $ A A ¬ W }/Fy6 k 0 x> *&Z*& 4Ø|~@ 0 k?~ $Fw *&Z* / 8lx©§§Ø|~p~/k]¨pY#8pNB³ A'|F+§ 0L¯nqYx8YyzEF |~8ypY#xwy}µ|F§{#knp]pUd}pU 'xwnYx>ypYw|~Cw A¼x> 6}x¨pYwK¬*jlknp |~8ypY#xwy}µ|F§V}/Fykx> 'n #?Fzz ypYwn|~8pU¼°`x#Ek D7¬ jlknp '$ A- *Q$ *&Z*
(54) |F§$]´°_|F«´dxoqpYwn 8x>|~w?Fz}pU|~oqpY##x>·}/FyFk / x> }x¨pYwV1]#knp7Yz>| 8± °`x> 8pLYx8YyzEF4 8pU1npYwnUpD|F§h#knpLpUd}pU xwnYx>ypYw|~wVp~/kV¨pY#8pN³¬jlknp B$ A-*$ *Q&ZI*"
(55) |F§¦D#ky8pUpN«´dxoqpYwn #x>|~w?FzU|~w¨pN³|~z18|~p x> #xoLxzEF#zyp nwnpUX¬ Ww6|~8ypY#xwyG } D |F§K4}/Fyk6xwndnUpU `4 /pYÙ|F§Kdx8pUY8pU I
(56) *I- A
(57) # ¯ °`knpY8p#knppUd}p ^,A HJI b §²|~zz>|°`xwy} ^,KHJAb$xw!·Yx8Yyx4x> {#knpL #nUUpU / 8|~4|F,§ ^,K HJAbxw!#knpLYx8YyzEF|~8ypY#xwy} |F§h#knp pUd}pU xwnYx>ypYw7|~2w A%¬ ¨pY#apUd}pI|F§l#knp6}/Fyk»x> #/U¨pY8 8pU»apN³n~Y#zV´°h| Yx8Yyx8 ¹¯ |~wnUp4xwgp~8k dx8pUY#x>|~wK¬ KpYL /»,pL}pU|~oqpY##x>}/FykK¯?z>pYM D p{x8 w?F#y/Fz|~8ypY#xwy}n¯,Fwn]z>pYL A',pD7¨pY#8pN³ |FN§ /¶°`x#kVzEF#}pU #M O«´U| |~8dxw?F8p¬ KpY ^,KHJAb Fwn ^,A&HJI bpD´°h|pUd}pU {|FN§ /¶xwnYx>ypYw14|~w A6 #n8k#k?F`#knp °hpUd}p4yp nwnpU'´°h|L/Ud pYo6Fw?F#xwy}L§Ø8|~P o A'Fwn·?~ 8 #xwy}7#ky8|~y}Qk K Fwn I U|~w1/Fxwn Fzz|~#knpY{pUd}pU xwnYx>ypYw4|~ w A?,¬ 9ap7Fzz -S * I
(58) *QI- A |FN§ /¶#knp7Yx8Yyx xwndnUpU]R D #k?FU|~w/Fxwn pUd}pU\ ^,K HJAbFwn] ^,A&HJI b/¬`jlknp48pYo6Fxwyxwy}·Yx8Yyx8 xwndnUpU 15 DF8p' /Fx>!8|]p / P I*" '$ I
(59) *QI- A
(60) # ¬ ÅS§ / x> DyzEFw?F¯#knpYw»#knpIYx8Yyx8 7xwndnUpU» . . . . . ×P× â c ðYý ÿd.
(61) '. ?%0
(62) / *"#X? A 1 $ (? * !$*Q$ $
(63) ?'$DN$#C# A$. DF8p#knp,|~ywnnF#x>pU |F§¦#knp4§²~UpU $|F§¦#knp #ydx¨ x> #x>|~w 8 xwndnUpU]1Q /Ù¬`®w]?F##x>YyzEF¯ #knp6|~y8pYYx8YyxDx> {#knpq|~ywnnF#a|F§`#knpqpN³ 8pY#w?FzÙ§²~Up6#/U¨pY8 8pU»Yz>|1/±1°`x> /p¯Fwna#knp xw18pY#w?FzPYx8Yyx8 $F8p #knp{,|~ywnnF#x>pU |F§#knp4xw8pY#w?FzK§Å~UpU `#/¨pY8 8pU]U|~yw18pY8Yz>|1/±1°`x> 8p¬ jlknp|~8ypY#xwy>} D |F§XFwI|~8ypY8pUq}/Fyk 0 x> !B $ B$* x©§#knpY8ppN³ x> 88 Ù yzEFw?FÙ}pU|~oqpY##x> }/Fyk /°`kn| 8p6ywnypY#z xwy} }/Fyk»x>> 0Fwn!°`kn| 8p'w?F#y/Fzh|~8ypY#xwy} x>> DL¬ W yzEFw?F |~8ypY#xwy}V|F@§ 0 x> L~ 8 8| YxEF8pUa°`x#k.]yzEFw?FR 4ª8|~|~z>|~}x>F/z 8DpYopUydxwy}V|F@§ 0L;¬ W }/Fyk 0 ~doLx8 7yzEFw?F$|~8ypY#xwy}·|~wyz·x©§xx> yzEFw?FX ¬ Wz> 8|y¯n#knp4wyo,pY |F§Ùdx> ##xwnYyzEFw?F |~8ypY#xwy}% 4ª8|~,|~z>|~}x>FzpYopUydxwy}" 8`|F§¦DyzEFw?F}/Fyk]Fw],p{ #ypY«´pN³d,|~wnpYw1#xEFzŬ * - #& W & /D #" 1 '$ !SF ! x> ¦#knp 4ØU|~w1¨pN³ 8B«´dxoqpYwn #x>|~w?Fzxw8pY8 /pUY#x>|~wI|F§B«´dxoqpYwn #x>|~w?Fz k?Fz©§ª«´ #?~UpU ¬ W #"
(64) DX!B 1I 1$ & /D # A '$Z!SF [&* / x> lB«´dxoqpYwn 8x>|~w?Fz,}pU|~oqpY##x>}/FykI°`x#k w?F#y/FzKyzEFw?F|~8ypY#xwy}L#k?F`xwndnUpU `§²~UpU l#k?FF8p B«´YdYz>pU ¬jlknp$§Å~UpU lxwndnUpU· #knpyzEFw?F{|~8ypY#xwy}U|~#8pU #,|~wn 8|'#knp§Å~UpY8 $|F § /ÙL¬ /µx> x©§_xx> #knp|~ywnnF# |F§l'U|~w1¨pN³ |~z 8|~,p¬4®$x> 0C$/F P x©§Ù§Ø|~{p~8kapUd}Rp ^ .
(65) H 0 b ^ ^ HJO H bb/¯ °`x#k·xwnYx>ypYw1l§²~UpY8
(66) Fwn
(67) ¯1#knp$ #xoLyz>pN³ ^
(68) H H H bzx>pU hxw'#knp$xw8pY#x>|~ k?Fz©§ª«´ #?~Up |F§p~/kg|F§P#knp ®°_|7yzEFwnpU #yy|~##xwy}7#knp$§²~UpY8 ¹=¬ 9ap ~ / #yoqp$#k?Fl§²~UpY8 `|F§ B«´dxoqpYwn 8x>|~w?Fze|~z1knpUd/qFwn]pUd}pU |F§ ¹«´dxoqpYwn 8x>|~w?FzP|~z1}|~wn F8p{|~,pYw] /pY8 ¬ W #"
(69) DE!'F AI 1$ J &
(70) DNI #" 1 '$!S S& *Q x> D #xoLyzx>YxEFz ^ J _ `b²«´dxoqpYwn 8x>|~w?FzP #y§Å~Up °`x#kn|~y,|~ywnnF#V¬ W J & /D #" 1 '$ !S "! x> l#knNp 4ØU|~w¨pNP³ 8:J~«´dxoqpYwn 8x>|~w?FzKxw8pY8 8pUN« #x>|~w |F§ J«´dxoqpYwn #x>|~w?Fzek?Fz©§ª«´ #?~UpU ¬ "! ; # 5 %G$
(71) C ' & * ,
(72) (+$ %N( * &
(73) 1 jlknpgwyoqpY#x>Fz U|~oLyy/F#x>|~wn '|F§4 }pU|~oqpY##x> Fz}|~#x#kyo F8p?~ #x>Fzz¶|F§{´°h|a´ pU 0@ 8pU 88N 4ªy8pUdx>F8pU" 8{Fwn U|~wn ###nY#x>|~wn ¬7jepU 88 F8pL~ 8 8| YxEF8pU °`x#kVy/Fwn8kyxwy}]ypUYx> #x>|~wn xw7#knp`Fz}|~#x#kyo #k?F¦ypY8pY#oLxwnpl#knp)?|°.|F§%U|~w1#8|~zů°`knpY8p~ ¦U|~wn 8##nY#x>|~wn ÙF8phwnpUpUypU 8|7y8| dnUp{#knp4|~y#yynF/L|F§#knpFz}|~#x#kyog¬ Wyy8|³ xo6F#x>|~wn xw #knppN³ypUYy#x>|~w |F§ÙU|~wn 8##nY#x>|~wn o6Ugp~UUpYy/Fyz>p7ypYpYwndxwy} |~w'#knp8pU /|~zy#x>|~w'8pU1yx8pUq1q#knpFyyzx>F#x>|~wK¬_wI#knp|~#knpYhk?FwnX¯dFyy8|U³dxo6F#x>|~wn `xw #knp$pN³ypUYy#x>|~w·|F§P8pU #8 Ùo66y8| dnUp$FwIxwnU|~#8pUY`y/Fwn8kyxwy}q|F§K#knp Fz}|~#x#kyo Fwn'}x¨p #x> /p`8| ###nY#y/FzzLxwnU|~#8pUYh8pU #yz8 ¬jlknppN³y~Y«´U|~oLyy/F#x>|~w·?F/~dx}o 5Ò r 7%#knpY8pN§²|~8p 8pU1yx8pU `#k?F8pU 88 `,p{pN³ypUYy8pU°`x#kg8|~/Fz~UYy/~Y¬ t pU|~oqpY##x>Fz}|~#x#kyoq Fwp ##ndx>pU|~w#knp ?~ #x> `|F§P#knp{U|~oLyz>pN³dx´·|F§#knpYx`8pU # U|~oLyy/F#x>|~wn ¹¬ Ww' 8n8kgU|~oLyy/F#x>|~w U|~wn 8x> #8 `|F§pY¨Fz?F#xwy}q#knp{ #x}w|F§¦FwFz}pYy/Fx> pN³dy8pU 8 #x>|~w |¨pY#knpxwyyy¨F#xEFyz>pU ¯nU|~wn ###nY8pU n #xwy}'Fw ~ypU?F8p 8pY|F§¦|~,pY/F8|~8 ¹¯. ÕªÖ×eÕØÆ.
(74) .
(75) "!"#%$ '&()$ '$*,+'-.& /0 /#" 1 #. 8 n8kk?~ H0_MH#H>H ¬ jlkyx> 'Fwp8pUdnUpU8|V#knp]pY¨Fz?F#x>|~w |F§{#knp #x}wn 6|F§ oyz#x¨~F#xEF8p,|~z wn|~oLxEFz> ypY#x¨pU§ª8|~o #knp{pN³dy8pU 8 #x>|~wK¬ 9ap{o6F±p{knpY8p #knp{8p~ 8|~w?Fyz>pD~ 8 #yoLy#x>|~wg#k?FxwyyynF/7p{dxoqpYwn #x>|~w?FzzU|~wd« 8x> #8pYw¯yxŬép¬¯?#k?F¯yx©§ÙFw]pYw#x®°`x#kg#knp{yk1 #x>FzdxoqpYwn #x>|~w |F§¦7z>pYwy}#kgx> 8pYy8pU 8pYw8pU °`x#k
(76) yx8 ¯ #knpYw|~wnp°`x#k·#knp{dxoqpYwn #x>|~w|F§FwF8pp8pYy8pU /pYw8pU°`x#k
(77) yx8 ¯yFwn /||~wK¬ wnypY4#knpLk11|~#knpU #x> |F§`dxoqpYwn #x>|~w?FzlU|~wn #x> #8pYwnY 4l°`knpY8pL|~xwDU|1|~8dxw?F8pU F8p
(78) 8«ÅyxpYw1##x>pU" 8N¯I,|~z wn|~oLxEFzÙpN³dy8pU 8 #xwy}]I8pU #4x> kn|~oq|~}pYwnpU|~n pUFn 8p6Fzz¦|F§lx8 oq|~wn|~oLxEFz> on #k?U¨p4#knp{
(79) Foqp{ykd #x>FzedxoqpYwn #x>|~wK¬ W y#xoLx#x¨p7¨F#xEFyz>p7x> 4Fw xwyyy{¨F#xEFyz>pL|F§_#knpLFz}|~#x#kyo Fwn k?~ {U|~w1¨pYw#x>|~w?Fz F#x#kyoqpY#x> ypY}8pUp `¬ jlknp F#x#kyoqpY#x>VypY}8pUp |F§D!,|~z wn|~oLxEFz$pN³dy8pU 8 #x>|~ w x> '#knp U|~oLoq|~w!F#x#kyoqpY#x>LypY}8pUp7|F§Ùx8 oq|~wn|~oLxEFz> ¹¬4jlknpLF#x#kyoqpY#x>LypY}8pUpD|F§`qoq|~wn|~oLxEFz x> h#knp #yo |F§e#knp{F#x#kyoqpY#x>{ypY}8pUpU `|F§Px8 h¨F#xEFyz>pU ¬ WwFz}|~#x#kyo k?~ &Z *C J7x©§Px8 8pU 8U|~oLyy/F#x>|~wn xw1¨|~z¨p6#knp6pY¨~Fz?F#x>|~w¼|F§loyz#x¨~F#xEF8p'|~z1wn|~oLxEFz> |F§F#x#kyoqpY#x> ypY}8pUpFoq| 8 JN5d¯y[ 74²$8pYzEF8pUqU|~wnUpYyx> ¦yp nwnpU7xLw 5Ò 7
(80) 8N¬ Wy8|~yz>pY o k?~ &Z1 * Jqx©§Fw1gFz}|~#x#kyo #k?F 8|~z¨pU k?~ ypY}8pUpDF`z>p~ #X Jn¬ `0,( U0 a"#$%&6( ®w #kyx> 4 8pUY#x>|~wK¯X°hpqypU 8Y#xp7#knpLypU #x}wa|F§'/knpU8±pY§Ø|~4U|~w1¨pN³ |~z 8|~,pU xw! y³ypU dxoqpYwn 8x>|~w Jn¬ hpUFn /p|F§Xx8 _FypFzn8|4xw1#yx#x>|~wK¯ °_pU|~wn 8x>ypYÙ#knp1npU ##x>|~wL§²|~ J N 4Ø #pUYx ?Fzz §²|~ J Fwn J 8Fwnxwndx>F8p_zEF8pYkn|¹°¼8|$pN³d8pYwn#knph8pU #yz8|kyx}knpYdxoqpYwn #x>|~wn ¹¬ ®w U1yn 8pUY#x>|~wn 7d¬Òr]Fwn!d¬Òd¯P°_p' #xoLyzx©§Ø #knpqwn|~/F#x>|~w¼Fwnan /pL#knpL8pY#o |~z knpUd8|~w 8|]ypYwn|~8p' #xoLyzx>YxEFz B«´dxoqpYwn #x>|~w?Fz ! S&*Q Fwn!#knpL8pY#o !S "! 8|]ypYwn|~8pI B«´dxoqpYwn 8x>|~w?Fze|~z18|~p¬ jlknp{xwyyy8|7#knp4/knpU8±pYx> @ B«´dxoqpYwn #x>|~w?Fze}pU|~oqpY##x>}/FykQ/ Fwg|~8ypY#xwy:} D |F§ /! #n/kg#k?FpY¨pY#Yx8YyxxwndnUpUg1 D k?~ `#ky8pUp4pUd}pU ¬ jlknp/~ #±L|F§K#knp/knpU8±pYlx> ¦8|¨pY#x©§ª7#k?F4 /]x> Ù#knp|~ywnnF#6|F§e4U|~w¨pN³',|~z 8|~,p°`x#k w?F#y/FzP|~8ypY#xwy:} D7¬ ! % !+#"&$+* epY /',pÙz>|1Fzz{U|~w1¨pN³,|~z }|~wK¬t$x¨pYwDFwpUd}&p %Ù|F§ /_¯¹#knpÙzxwnp¦#ky8|~y}'k %_dx¨1x>ypU e#knp yzEFwnpxw8|I®°_|'k?Fz©§<«ÅyzEFwnpU ¬$jlknpDYz>| 8pU]k?Fz©§ª«ÅyzEFwnp7U|~w/Fxwyxwy}·#knp´°_|·pUd}pU $xwnYx>ypYw ( ÆPâUôßÜ
(81) ÑÒôÝÅÜ
(82) ßɦåÞ
(83) *â )ÉϹÐÒÉÓü,É#Ç Þ/ÊeʲÐÒá`ßBÑàÐàåÓÐàÞ/+Ñ )UôݲÈÅÐàÏÐàÞ
(84) ÑãÞ
(85) åÓÉݲÈÅÐàÞ
(86) âFú
(87) ùFÑàÞ/ÝÅÐÒÜ
(88) â . . . . ×P× â c ðYý ÿd.
(89) . ?%0
(90) / *"#X? A 1 $ (? * !$*Q$ $
(91) ?'$DN$#C# A$. |~w %'x> D /Fx>!8| pq#knp B1 $ A / k?Fz©§<«ÅyzEFwnp·|F§*%¬ jlknpI|~#knpY7k?Fz©§<«´ #?~Up'x> 7 /Fx>»8|]p ¬ jlknp * |F§ /_¯ypYwn|~8pU 1 ^,/Vb/¯x> ·#knp xw8pY#x>|~g|F§D#knp U|~w¨pN³ ,|~z }|~w ~| y/FxwnpU~ L#knp·xw8pY8 8pUY#x>|~w |F§ Fzz`wnpY} F#x¨pk?Fz©§ª«ÅyzEFwnpU 6yp nwnpU.¼#knppUd}pU q|F§?/_¬ $|~8p$#k?Fl#knp F|¨p yp nwyx#x>|~wg|F§U|~8px> ldx YXpY8pYwl§Ø8|~o #k?Fl|F§#knp$±pY#wnpYz|F§ 8xoLyz>p 4ªxŬép¬¯nwn|~`xw8pY8 8pUY#xwy} 8,|~z }|~wK¬ t$x¨pYwg{§Å~UpY ]|F§z>|1FzzIU|~w¨pN³'|~z knpUd8|~:w /_¯#knp$yzEFwnp$ #yy|~##xwy} dx¨ x>ypU #knp] #?~Upxw8|!´°h|ak?Fz©§ª«´ #?~UpU ¬ 9ap]Fzz B1 $ A / #knpk?Fz©§ª«´ #?~Up#k?F'U|~w/Fxwn '#knp §Å~UpY8 4~F8~UpYw48| ¬jlknp C* |FN§ /_¯XypYwn|~8pUV ^,/b/¯Kx> #knp7xw8pY#x>|~|F§h#knpLU|~w¨pN³ |~z 8|~,p ^,/VbÙ|~y/FxwnpU]~ l#knp xw8pY8 /pUY#x>|~w |F§FzzXwnpY}F#x¨p4k?Fz©§<«´ #?~UpU yp nwnpU·I#knp §Å~UpY8 |F§ /Ù ¬ < pYkyzkn|~#w7pYFzŬ 5Òrd 7dk?U¨phy8|¨pUD8pU #yz8 pUyx¨Fz>pYw8|#kn| 8p_ 8/F8pUxwD#knpÙ#knpU|~8pYoq Fwngz>pYoLo6~ `#k?F`§²|~zz>|°4¬ £ 5ÒrdI 7 6I / .C $; $
(92) O P !SF > Z H$ '&; I .CL$ N!S
(93) P
(94) ^,/b ? Ù¾ a. !#" A A /. . . . * *$ LDN$ '$ A
(95) "*D
(96) P *"#>>
(97) #%
(98) S\#I$D - D .*
(99) %&0 "#$ B& * *I A AC#
(100) . / ?. ¾1Â ¢ ¾. Òrd. 5 7 0C$/F P%! 0 / /# )Z.$
(101) F C %$ '& %$R*$ ID $ '$ A
(102) *D $ !S
(103) P ^, $ #"
(104) I* ? / b
(105) P *"#>>
(106) # / $ ($ "#
(107) & Z * $ (. . Ù¾. a£ 5ÒrdI7 6I / .%$ $
(108) C \! S&*Q a$ '& I L.C $ !S
(109) P ^,/b ? * a*Q$ ID $ '$ A
(110) *Q D $ '&
(111) P *"#>> A
(112) / P ]$ >$ C>
(113) #R
(114) P *"#>>
(115) #R
(116) R#>$D P-D .*%
(117) I$ZCI
(118) #%
(119) / ? $ E!SF "! ¾1Â ¢ ¾ ! 5Òrd7" 0C$/F N E!SF S&* / /#X
(120) S,.- '& $*
(121) E $ B&L F %$ P *$ LDN$ '$ A
(122) # *Q D $\!S / P :
(123) ^,/Vb $ '&
(124) P *"#>> A
(125) L$$ I$ "I
(126) / &Z "# ' V $$
(127) S*\ / P I*C#0> A 1 &%
(128)
(129) / ?. l~ /pUq|~w6jlknpU|~8pYo n¯< pYkyzkn|~#wIpY_FzŬ 5Òrd 7%/knpU8±L°`knpY#knpYl z>|1FzzLU|~w1¨pN³q,|~z knpN« d8|~wx> l#knp |~ywnnF#·|F§DU|~w¨pN³|~z18|~p$ n8 #`U|~oLyy#xwy}I,|~xw1 |F§ ^,/VbÙFwn /U 'pYo6Fw?F#xwy} §ª8|~o §ª8|~o Fwna?~ 8 #xwy} #ky8|~y}k!#knp'UpYw#8|~x>µ|F§Fw¼F#yx#/F#xz /kn| 8pYw§Å~UpY¯nFwn·#knpYw]8knpU/±1xwy}6#k?Fwn|L|~#knpY`§Å~UpY`x> lxw8pY8 8pUY8pU](' ¬ Ä z>pF#z¯n#kyx> /knpU8±pY#ywn xw#xoqp{zxwnpFxw]#knp wyopY|F§¨pY##x>UpU ¯?Fwngx> `#knpY8pN§Ø|~8p|~y#xo6FzŬ ! * & )3,+- ( /.%,.-0- , ( 9ap7 #/F#$ 8k?F/~Y8pY#xºUxwy} #knp}z>|~?FzU|~w1¨pN³ x® |F§h'z>| Fzz U|~w1¨pN³ |~z1}|~wK¬ epY? / p7qz>| Fzz]U|~w¨pN³ ,|~z }|~wK¯,}x¨pYwa~ 'Yx8YyzEF{ 8pU1npYwnUpD|F§_¨pY##x>UpU ,¬ W ¨pY#8pN6³ A|F§ /!x> /Fx>·8|7p2 1 #>$D *I |F§ /!x©Q§ @ . . ÕªÖ×eÕØÆ.
(130) .
(131) "!"#%$ '&()$ '$*,+'-.& /0 /#" 1 #. #knp{xw8pY8 8pUY#x>|~w |F§#knp4wnpY}F#x¨p{k?Fz©§<«ÅyzEFwnpU yp nwnpUg1'#knp{®°_|'pUd}pU #k?F#xwy}. A. x> U|~w1/FxwnpULxwL|~wnp`|F§?#knplYz>| 8pU7k?Fz©§ª«ÅyzEFwnpU yp nwnpU7#knpl¨pY##x>Fz64ªxŬép¬¯?F/Fzz>pYz 8|7#knp O«®B³dx>" 8_zxwnp #ky8|~y}Qk A%¯?Fwn #knpÙyypY 4²~UU|~8dxwy}{8|#knp_,| #x#x¨Np O«´dx8pUY#x>|~'w 8pUd}pÙxwnYx>ypYw1¦|~w A x> U|~w/FxwnpU xwg|~wnp4|F§#knp|~,pYwk?Fz©§ª«ÅyzEFwnpU yp nwnpU] ~¬ jlknp #>$D |F§ /ax> `#knp4 /pY|F§x8 ¹«´ 8pFo ¨pY##x>UpU ¬_jlknp §Ø|~zz>|¹°`xwy}6#knpU|~8pYox> ##/Fx}k« §²|~#°hF8X¬ ¾1 ¢ ¾ $
(132) ;!S 0 /# )Z.$
(133) P $ '& F ] A
(134) # #>$D . . C #" /#
(135) #\
(136) % *I A 1C"#>?. 9ap wn|¹° dx> 8Yn 8 I#knp oq|~8pVU|~oLyzx>F8pa~ /p |F§78knpU/±1xwy}.#knp U|~w1¨pN³ x® |F§L 4B« dxoqpYwn 8x>|~w?Fz/8l|~z1knpUd8|~wK¬ epY7/ap4Dz>|1Fzz·U|~w¨pN³g|~z knpUd8|~wK¬ WwgpUd}p %4|F§ /!x> /Fx>8|7p4 #>$D & Z |F§/ax©§@ % x> `wn|~¨pY##x>Fzů #knp xw8pY8 8pUY#x>|~w]|F§#knp wnpY}F#x¨p{k?Fz©§ª«´ #?~UpU yp nwnpU16#knp{®°_|7§Å~UpY8 ` #k?F#xwy} % x> U|~w1/FxwnpULxwL|~wnpl|F§%#knplYz>| 8pUDk?Fz©§<«´ 8?~UpU yp nwnpU7#knpl¨pY##x>F6z 4ªxŬép¬¯?F/Fzz>pYz 8|7#knpF«®B³dx>" 8_yzEFwnp #ky8|~y}k %¯%Fwn #knpÙyypY( 4²~UU|~8dxwy} 8|#knpÙ| #x#x¨p~«´dx8pUY#x>|~'w 8e§²~UpYPxwnYx>ypYw|~w %_x> U|~w/FxwnpU xwg|~wnp4|F§#knp|~,pYwk?Fz©§ª«´ #?~UpU yp nwnpUg# ¬ jlknp #0$D |F § /_¯1ypYwn|~8pUI1 =^,/b/¯ x> Ù#knp$ #yy}/Fyk|F § / xwndnUpUILx8 l 8pFo pUd}pU ¹¬ £ 6* $ZN*I A
(137) =^,/Vb
(138) * $* $ $# % \#>$ D &0 "#E
(139) 'I 1&Z P A ? Ù¾ a ¢ ÂX Â 9ap4 #k?FzzKU|~wn ###nY#x¨pYz #kn|¹° #k?F¯y}x¨pYw 7 /pFo pUd}N p ^,KHJAb/¯n°_pFw nwn Fwn|~#knpYh 8pFopUd}p ^,A HJK = b/¬ Ä |~wn #x>ypYl{ #yknpY8p 8 °`kn| 8pUpYw18pYÙx> ADFwn6°`kn| 8p/~dxn Ùx> 8o6Fzz%pYwn|~y}k 8|{#k?F`Fw6|~#knpYh¨pY#8pN³'|F § / Fwn'pUd}p$|F § / wn|~ÙxwnYx>ypYw1h8| ADx> _|~y8 8x>yp 8 ¬jlknp{xw8pY8 8pUY#x>|~w ,pY®°_pUpYw 8 FwnB /!yp nwnpU $7 #yknpY#x>FzK|~z1}|~ w
(140) |~w 8 ¬ jlknp6z>| Fz_U|~w1¨pN³ x®»|F7§ / xwndnUpU Dz>|1FzlU|~w¨pN³dx´¼|~w
(141) q¬ 9ap'|~n 8pY#¨p'#k?F7 8pFo pUd}pU l|F § / xwnYx>ypYw`8| ALU|~#8pU #|~wn68|¨pY##x>UpU l|F§
(142) #k?F_k?¨p #yy|~##xwy}oqpY#x>dxEFw 4ªxŬép¬¯$»}8pF·Yx8Yz>p xw »¨pY##x>Fz yzEFwn p 8N¬ $pYwnUp¯ypYwn|~#xwy}¶ I ,p #knp ¨pY#8pN³ |F§
(143) yp nwnpU ~ 6#knp xw8pY8 8pUY#x>|~w |~xwI,pY®°_pUpYw ^,KHJAb6Fwn 8 ¯l°hp]k?¨p #k?F Ik?~ 8yy,|~##xwy}IoqpY#x>dxEFwK¬jlk1n ¯% 8/F##xwy}·F@ I x #S T6UpU 8|L§²|~zz>|° #knp 8pU1npYwnUpD|F§pUd}pU . . . . . . . ×P× â c ðYý ÿd.
(144) !. ?%0
(145) / *"#X? A 1 $ (? * !$*Q$ $
(146) ?'$DN$#C# A$. x}y8pD @W z>|1Fzz'U|~w¨pN³'|~z }|~w'#k?Flk?~ lypY}pYwnpY/F8p{ 8pFog¬jlknp$ 8pFo pUd}pU `F8p d/°`wg°`x#kg#kyx>/±IzxwnpU ¹¬ |~w
(147) 8| nwn·Fwn|~#knpY_¨pY#8pN³ I = |F§
(148) °`x#k· #yy,|~##xwy}DoqpY#x>dxEFwK¯d°`kyx>8kU|~#8pU #|~wny h8| DwnpY° 8pFo pUd}Np ^,A HJK&=Ab/¬ 9apL /U #k?F{#knpL 8pFo =^,/bx> &Z1 B*$ x©§_x k?~ '¨pY#8pN³ °`x#kVoq|~8p7#k?FwV´°_| /pFo pUd}pU xwnYx>ypYw$|~wx¬ )x}y8pq{ #kn|¹° 7ypY}pYwnpY/F8p /pFog¬ Ù¾ a£ =^,/Vb /# &Z1 Z *Q$
(149) S / /# ' .$
(150) Z? ¢ ÂX Â epY %
(151) H% ¯nFwn % $,p$#ky8pUp{ 8pFo pUd}pU `xwnYx>ypYw1|~w#knp{ /Foqp ¨pY#8pN³ A?¬ ¦d}pU %
(152) H% ¯ Fwn % `k?¨p#ky8pUp¨pY##x>Fz% #yy|~##xwy}yzEFwnpU
(153) ¯ ¯1Fwn ~¯8pU #,pUY#x¨pYz¬ epY p7#knp6U|~oLoq|~w»xw8pY8 8pUY#x>|~w¼|F§l#knpqwnpY}F#x¨pqk?Fz©§ª«´ #?~UpU yp nwnpU!
(154) ¯ ¯Fwn ~¬ 9 x#kn|~yz>| / |F§}pYwnpY/Fzx´¯%z>pY
(155) Fwn ,p{#knp4yzEFwnpU ypYzxoLx#xwy}¬_´w |~8ypY 8|q,p{}z>|~?FzzgU|~w1¨pN³¯ /»on #,p{xwn 8x>yp ¬ $$|°hpY¨pY¯ x> wn|~xw8pY#w?Fz8| ¬_´§x x> lpN³d8pY#w?FzX8|¯ 8|Dx> % x©§ex`U|~xwnYx>ypU `°`x#kK¯y /¯
(156) ¹¯ #knpYw % x> l ##xzzXpN³ 8pY#w?Fz8| ¯ |~#knpY#°`x> /pxh°_|~yz>·¨ x>|~zEF8p$#knp 8pFo-pUd}p yp nwyx#x>|~wK¬¦®w·pYx#knpY~ 8p¯°hp U|~wnYznyp #k?F /!x> `wn|~`}z>|~?FzzU|~w¨pN³X¬ jlknpL§²|~zz>|°`xwy} z>pYoLo68pY¨pFz> D#knp6U|~oyxw?F8|~#xEFzl 8##nY#y8p6|F§#knpq 8pFo =^,/b/¬®w #knp z>pYoLo6d¯?#knp{8pY#o dx> Ø#|~xwYdYz>pU k?~ 8|7,p xw18pYwnypU]xw#knp{}/Fyk 8pYwn 8p¬ Ù¾ a£ =^,/Vb /#, ' '&Z Z B*$ :
(157) S A V /# $R / > A 1 ]
(158) \& /#
(159) >
(160) P I I "#0? ). . . . . . . ÕªÖ×eÕØÆ.
(161)
(162) "!"#%$ '&()$ '$*,+'-.& /0 /#" 1 #. . ¢ ÂX U1xwnUp =^,/blx> wn|~wnypY}pYwnpY/F8p¯XpY¨pY#¨pY#8pN³]|F§ =^,/Vb_k?~ Foq| #´°_|'xwnYx>ypYw /pFo pUd}pU ¦yp nwyx#x>|~wK¬ h KpYoLo6 'd¯pY¨pY#¨pY#8pN³7|F§ =^,/bKk?~ ¦Fz>p~ #´°h|{xwnYx>ypYw /pFo pUd}pU ¬ _ !'*Q >0 A A |F§e }pU|~oqpY##x>|~dpUY 4ª,|~xw1¯pUd}p¯§²~Up 8°hpoqpFw'x8 ¦y8|F#pUY#x>|~w ?F/Fzz>pYze8|L#knp F«®B³dx> Fwn·°_pypYwn|~8p{x~ =²¬ Ù¾ a£ I =^,/Vb .\ ' '&Z1 ZI B*$ I L.C $ !S
(163) P ^,/b V I ' .%$ P ' I* A 1$6*Q$ LDN$ '$ A / *Q D $ '& I ' = .C
(164) S !B*Q 0 > A 1 ' ?
(165) S
(166) P *"#>> A 1 O
(167) ' % A
(168) / /#,$ I$ "I
(169) #V
(170) S
(171) S,
(172) P *"#>0 A A
(173) ' = % A
(174)
(175) S !'* > > A A = ^,/b =^,/Vb. . . /#\$ &0 Z#$ '& * *I A 1C"#>?. ¢ ÂX W$ 8 #yoqp#k?Fl#knpxw8pY8 8pUY#x>|~wg|F§P/U '{°`x#k / x> lF_#knp §²~UpY8
(176) H.H 1¯ ¬ Ä |~wn #x>ypY#knp4¨pY##x>FzeyzEFwnp
(177) µU|~w/Fxwyxwy}('d¯?Fwngz>pY ¼,p4#knp4k?Fz©§ª«ÅyzEFwnp U|~w1/Fxwyxwy} 'LFwnzxoLx8pU1·#knp ¨pY##x>Fzezxwnp #ky8|~y}k ¬ KpY p#knp$xw8pY8 /pUY#x>|~wg|F § '4°`x#k ¬|~xw8 4 `H H 8Ù,pYz>|~wy}D8|LYz>| /pU Yy#¨p x w 4Ø #xwnUQp / x> ·a #y§Å~Upg°`x#kn|~y·|~ywnnF# 8N¬ U1xwnURp / x> Iaz>|1FzzU|~w¨pN³ |~z knpUd8|~wK¯e #n/k!Yz>| 8pUVYy#¨pLxw x> Iz>| Fzz U|~w1¨pN³V,|~z }|~w»Fwn 7#/U¨pY8 8pU #knp U|~8p`|F§ #n8k6,|~z }|~wK¬ W$ ¦ U|~wn 8pU1npYwnUp¯p~/kq,|~xw1 pYz>|~wy} 8|4 dx> ##xwnY|~z }|~w?Fz /k?Fxwgxw 4Ø 8pUp )x}y8prD§²|~`#knp{~ 8p 8N¬ U1/F##xwy} §ª8|~o FwnDy8| UpUpUdxwy}4|~w7#knphU|~#8pU 8,|~wndxwy}{|~z1}|~w?Fzy/k?FxwLxwnY8p~ #« xwy} °_p$8p~8k4|~xwl|F§Ko6B³dxoyo xw ¯1ypYwn|~8pU 4ØpYx#knpY x> l4z>| Fz?o6B³dxoyo x w _¯y|~ x> l|~w 08N¬ Ww?Fz>|~}|~n #z¯dx©§P°hp y8|1UpUpUI§Ø8|~o 'ypUY8p~ 8xwy} 7°_p °`xzz8p~8k ]|~xwq|F§oLxwyxoyo x w ¯¦ypYwn|~8pU
(178) ¬ ´ § x> Dwn|~L |~xwL|F§ ¯#knpYwµx7~doLx8 ]kn|~#xº|~w/Fz` #yy|~##xwy} zxwnp6x w Ù|~#knpY#°`x> 8p¯#knp·Fwy}z>p I§Ø|~#oqpU¼1a#knpI~ /UpYwndxwy} |~z }|~w?FzXzxwnpF! °`x#k#knp{¨pY##x>Fze x>
(179) "$#% 4Ø 8pUp )x}y8pr 8N¬ Ww?Fz>|~}|~n #z¯
(180) pYx#knpY~doLx8 Dkn|~#xº|~w/Fze #yy|~##xwy}qzxwnp{|~`#knp{Fwy}z>p4|F§#knp{U|~#8pU #,|~wndxwy}IFwy}z>p x> ='& #% E ¬ 9apDU|~wnYznyp7#k?F$#/U¨pY8 #xwy}y|°`w1°hF8y #knp #y8k?Fx)w ( §ª8|~* o 8|
(181) °hp 8p~/k!I,|~xw1, + °`kyx>8kVx> #knp n8 # 8|g~doLx'¨pY##x>FzÙ #yy|~##xwy}zxwnp7x-w ¯xŬép¬¯ + pYz>|~wy} $8|6#knpD 8pFog¬4n 8pY#¨p#k?F¯,pUFn /p|F§¦#knpDz>| FzU|~w1¨pN³ x® |F § /_¯?#knpY8pDx> wn| |~#knpY,|~xw1|~w ( k?U¨ xwy}'7 #yy|~##xwy}q¨pY##x>FzPzxwnp¬ jlkn ¯§²|~ p~8.k ( _x-w xw8pY8 /pUY8pUV 'q#knpY8p7x> {'ywyx>np7|~xw, +¦#k?F{pYz>|~wy} 8|#knp 8pFog%¬ $$pYwnUp¯ 8xwnUpxw18pY8 8pUY#x>|~wx> hy8pU 8pY#¨pUI'y8|FpUY#x>|~wK¯yp~/ k + y8|F#pUY8 l8| 6|~xw4|~w #knp ~«Åy8|FpUY#x>|~w ' =P|F§ ' ,¬ Wz> 8|y¯,,pUFn /p =^,/Vb`x> wn|~wnypY}pYwnpY/F8p¯ex{Fwywn|~ k?FypYwI#k?F_®°_|Ldx> ##xwnY! + Fwn +0/y8|F#pUYl8|#knp$ /Foqp,|~xw1h|~(w ' = ¯ °`kyx>/kIy8|¹¨pU h#knp z>pYoLo6d¬ jlknpF|¨p{8pU #yz8 Fzz>|° n 8|qypY#x¨pD7wnpY° /k?F/~Y8pY#xº¹F#x>|~wV|F§U|~w1¨pN³g,|~z 8|~pU Fwng8pUdnUp{·|~wnp{#knp4dxoqpYwn #x>|~w?Fzx®g|F§#knpY#x8pY#x>|~wg}x¨pYwgjlknpU|~8pYo n¬. . . ×P× â c ðYý ÿd.
(182) r. ?%0
(183) / *"#X? A 1 $ (? * !$*Q$ $
(184) ?'$DN$#C# A$. . . . . . . .
(185) .
(186) . . x}y8prS@ ³yFoLyz>p4|F§Y8| 8 /pUY#x>|~wgxwyzEFwnp, §Ø|~`#knp y8| |F§|F§ KpYoLo6'd¬ ). . . . ¾1 ¢ ¾. & /D #" 1 '$ # /DE!'F A> A$ ! S&*Q / /#L
(187) S #"- * >$ C
(188) $ ! "! $ '& F N
(189) S I /) %
(190) N % R B&
(191) A 1 #, & ? / /# $
(192) R . 1 ? =
(193) ^,/Vb /#\$ )Z.$ /F RC \! 0 B?. ¢ ÂX 9ap n8 8' #kn|¹° #k?FIx©§M/ x> 6}z>|~?FzzU|~w¨pN³X¯`#knpYw Ä |~wndx#x>|~wn ¯Fwn r F8p
(194) F#x> ?pUX¬ Ä z>pF#z¯hx©§?/ x> L}z>|~?Fzz¶U|~w¨pN³X¯_xLx> 'Fz> 8| z>|1Fzz¶U|~w1¨pN³¬ Wz> 8|y¯Ù#knp ~«Åy8|FpUY#x>|~w¼|F§`I}z>|~?FzzVU|~w¨pN³V|~z1knpUd8|~w»x> {}z>|~?FzzVU|~w¨pN³!FwnaU|~xwnYx>ypU °`x#k #knp ~«Åy8|FpUY#x>|~w |F§x8 /pFog¬ 9apwn|° y8|¨p$#k?F_x©§ Ä |~wndx#x>|~wn $¯dFwn·rF8p
(195) F#x> ?pUX¯ #knpYw / x> Ù}z>|~?Fzz'U|~w¨pN³X¬ h Ä |~wndx#x>|~w'rd¯1Fwn7pUFn 8p|F§ KpYoLo6d¯°_p`k?¨p#k?F =^,/bPx> wn|~wnypY}pYwnpY/F8pV¬ Wz> 8|y¯. . . . . ÕªÖ×eÕØÆ.
(196) .
(197) "!"#%$ '&()$ '$*,+'-.& /0 /#" 1 #. 8xwnUp =A^,/Vbx> I}z>|~?FzzVU|~w¨pN³V|~z1}|~wK¯ex8 4U|~8pqU|~xwnYx>ypU 4°`x#k!#knp7,|~z }|~wax8 8pYz©§#¯ xŬép¬ ^ = ^,/bb = ^,/Vb/¬ 9appY}xw'16 #kn|¹°`xwy}D#k?Fl#knp$U|~8p |F§ /Ù¯ ^,/b/¯ x> hwn|~wnpYoLy´¬ÙjPF±p{Fw',|~xw1 =?|F§ ^ = ^,/bbFwnqU|~wn 8x>ypY_ ¨pY##x>FznyzEFwnp #ky8|~y}k = ¬jlknp`xw8pY8 /pUY#x>|~w6pY´°_pUpYw Fwn /.x> ·Yz>| 8pUVYy#¨p¯e 8xwnU9 p /.x> 4· #y§Å~Up7°`x#kn|~y4|~ywnnF#¬ KpY (!p7 #n8k¼·Yy#¨p¬ n /pY#¨p#k?F (Ix> _{z>|1FzzLU|~w¨pN³',|~z }|~w6 #xwnUp¯1 Ä |~wndx#x>|~w ¯ / x> ¦z>| FzzqU|~w¨pN³X¬ Wz> 8|y¯hp~8k ¹«´ 8pFo ¨pY#8pN³.|F§ (U|~#8pU #|~wny q8|!a 8pFo pUd}pg|F§ / #k?F6x> q¨pY##x>Fzz y8|F#pUY8pU 8| =1^,/b/N¬ U1xwnUp xw8pY8 8pUY8 =
(198) ^,/Vb$F{´°h|gpUd}pU Fwn F|~{¨pY##x>UpU ¯e°_pLk?¨p #k?F' (6FwLk?¨p`|~wyz®°_| ¹«´ 8pFo ¨pY##x>UpU ¬jlk1n ¯7jlknpU|~8pYod¯ (qx> ¦}z>|~?Fzz7U|~w¨pN³ |~z }|~wK¬ $pYwnUp¯¨pY##x>Fzhzxwnp 7#ky8|~y}k =xw8pY8 8pUY8
Documents relatifs
We extend to infinite dimensional separable Hilbert spaces the Schur convexity property of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case
Khorram, Convexity of chance constrained programming problems with respect to a new generalized concavity notion, Annals of Operations Research, 196
For the present study, the mycobacteria (M. tuberculosis) used was a clinical isolated strain resistant to Isoniazid codifies as AC 45 (this strain was obtained
To assess whether modulation of Sirt1 activity alters MAP kinase acti- vation, HAECs were examined at different time points after TNF-a stimulation. The MAP kinases p38, ERK, and
In this paper, we have used the power-ratio method (PRM) to quantify the 24 µm IR morphologies of young SNRs. We have demonstrated that Type Ia SNRs have statistically more circular
pylori ACE detection was evaluated on 127 gastric biopsies in comparison to conventional bacterial culture followed by the determination of susceptibility to clarithromycin by
To get a really well defined Riemannian manifold we would need to specify more closely a set of convex functions with prescribed behaviour at infinity,and then define the tangent
Let X be the normed vector space of all real null sequences with metric d induced by the usual
