The Shortest path synthesis for non-holonomic robots moving forwards

Texte intégral

(1)The Shortest path synthesis for non-holonomic robots moving forwards Xuân-Nam Bui, Philippe Souères, Jean-Daniel Boissonnat, Jean-Paul Laumond. To cite this version: Xuân-Nam Bui, Philippe Souères, Jean-Daniel Boissonnat, Jean-Paul Laumond. The Shortest path synthesis for non-holonomic robots moving forwards. [Research Report] RR-2153, INRIA. 1994. �inria00074519�. HAL Id: inria-00074519 https://hal.inria.fr/inria-00074519 Submitted on 24 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. The Shortest Path Synthesis for Non-holonomic Robots Moving Forwards

(3) !. "$# &%'% )*!( +* " -, .) . N˚ 2153 Dećembre 1993. PROGRAMME 4. Robotique, image et vision. ISSN 0249-6399. apport de recherche. 1993.

(4)

(5)

(6) "!# $%&&' )( *+-,. / 102)3 4- 657 98: !

(7) ' !. <;. "$# &%'% *( +* " ), .- . ;. = >@?BAC>EDF&F&GIHJ K9?BLM?BN@OQPSRTGVUTOWFD)ACGXGYN[Z\O^]_OW?B` = >@?Ca_GYNb= >cO^]dFeG KfD)gTgh?C>@NjikGl>@G)monTGY>EmpnTGb`q\r\sYtBuvJ w"Gyx mzGYF-LT>@G1sY{B{Cu|J uBu|ghD)ACG)] &} ~))T C :G-mYDQmzRT^D)N@GNcnTG gD>@NcOWNcOW?C`:?N@nTGemz?B`khACR>oDNcOW?B`.]dghDBmzGe l? DmYD)>@WOG >c?CLh?CN%U6?C`TF&?)Z\OW`TA&?C>c[D)>oiT]U[ON@n.>@G)]_ghG)mzNN@?NcnTGN_kghG&?)XNcnTGWGY`TABN@n ?CgTNcOWFD)MgDN@n]z

(8) 6nTO^]6\OW`hi-?<>@?BLh?CNbO^]6]_RTLTa_G)mzN

(9) N@?\OW`TG%FDNcO^m6m?C`h]_N@>oD)OW`\No]6?BÒNo]ghDNcn mz¥ RT>@ZBD)N@RT>cG:D`hi ¥©¨fONoª

(10) ] « ?B>@OWG%`kNEDN@O?C`¡£¢NoD)>@NcOW`TA>c?CF N@nTG">@G)]_RTWNE]|?B`¤]_nT?C>cN@G)]_N&ghDNcnh] L\ wfRTLtS¦)§ID`hi {Cr§¬U66G"ACOZG`GY?CgN@OWF DWON_mz?B`hikON@OW?B`h] ?B` N@nG)]dG"ghDNcnh]zUbDì mz?CF&gRTN@GXNcnTGlghD>cN@ON@OW?B`&?C>ID`\&nT?C>cOWY?B`kNED¡gTQD`TGl?)N@nTG1mz?B`khABRT>oD)N@OW?B`]_ghDCmzGV ®¯°¡±@²1³h´<C&µbgTN@OFD\m?C`\N@>@?B¶Uk¢Vk`\N@nTGy]dO^]<gT>@?BLTWGYFU)·f?C`TnT?BW?C`?CF&OQm>@?BLh?CNYU ¨ ?BRT`hik G)i&>oDCi\OWRh][?¸mzRT>cZCD)N@RT>cGUhwfRTLOW`h]b]dnT?B>@NcG)]dNbghDNcnh]. Ê[ß×)Ë@ÒÌzÆcÎ)ÇSÍ_ÎYÍfÈ<Ï)àhÈ ÍáâÉ ÐYÚzÏlÚ

(11) Ñ#ãÒÛÓÔÒÚÎÚ6Í_Ó\ãÚÕ¡ä%Ò)ÊÖØ×)ÙbÍåBÙ9ËEÚæ1ÛcÜzàhÊá ÊÚÝÚ[Òzã)Ï)Û ÓÔÒÚÏ)Ú[ÞØÍ ãpäçzç èéQêXÝ¡ËoëÔ×ÓëõàTÞ¡ÞØö#ÒÒÏ)ìØÍd÷[ìÍ_ëÔÞ@Þ¡íEïBîðï)ËoÓòìØñ<øÓÔÓòùbËzËoÞØÏ)Þcóï)ôì ïCÒìøØÍcÐXúYùbèTÞØï)ìëÔøâßìÒcî¶Í@Ö¶øâßhÕ¡û üXÒzøëÔÒÎXãçpä%ã. Unite´ de recherche INRIA Sophia-Antipolis. ¹»ºv½¶¼ ¾_¿YÀ ½6¼ Á<ÂW¾_ÃÄpÅ.

(12) â 8 v$ (9 6 ' : : *+-, - & !#&$Y& ' â $%

(13) (b / 9([ 0 ¯k ¯ ·f?CR]mYD)^mzRT?C`h]&QD ]_k`\N@n G) ]dGgh?CR>WGgT>c?CLTGY F&Gi ?CgN@OWFeO^]@D)N@O?C` ikG ^D?C`TABRTGYRT>"ikG)]-N@>oD)a_G)mzN@?BOW>cG)] D mz?BRT>@LRT>@GF&O`T?C>GYx GUi ©RTª ` >@?BLh?CN`?C`TnT?C?C`T?BF&G:ikG Nd\ghGZ?CON@RT>cGU`G:]dG:i

(14) GYx g^D m% D`\N&PR G%` FD>EmpnTG"DYZBD`\NY G%N@N@G:]_k`\N@n G) ]dGmz?C`h]_O^]_N@GGY` ^D&ghD>cN@ON@OW?Bì\G G)]_ghDCmzG-i\G)]lmz?C`kACRT>EDN@O?C`h] ikR >@?CLh?BNYU¡GY`?C`hmzNcOW?BìkGy!] Nd\ghG)]XikGvmpnGYF&OW`]6?CgTNcOWFD)#R "#h·b?CRh]fgD>@Nc?C`h]Xgh?CR>mGY^D\UhikG)]f>G)x ]dRTNoD)No]XD)`kNGYx >@OGYRT>o]bikG ¥ wfRTLtS¦)§hGYN ¥©¨fª

(15) « {CrC§¶UBgM?BRT>[i\?C`T`TG%>6i\G[`T?CRTZG%WWGy] mz?CìkOWNcOW?C`]¸`G)x mzG)]c]@DO>@G)]âi ?BgTN@OFDOWNG x GYNbmYDQmzRT?C`h]6QDghD>cN@OWNcOW?Bì\GlmpnDCPRTGlgT^D)`n?C>@OY?C`\NoD)<ikGl$ ©G)]dghDBmzGIikG)]bmz?C`kACRT>EDN@O?C`h] DC]@]_OWF&O%%G x D ' &) ( ³T)±o* )+¯ ª ?C`\N@-> ?C, WG1?CgTNcOWFD)¶U#¢\`\N@n G) ]_GUhK[?CLh?CNX`?C`TnT?C?C`T?BF&GU ª ?CRT>cLTRT>cGFDa_?C >TGYx GU= WRh]bmz?CR>@No][monTGYFeOW`h]ikG1wfRTLOW`h].

(16) s.

(17)

(18)

(19)

(20) ! #"$ %& '( )*+-,. /0

(21) 1#23 456879 :; <=. CBAØ³ @ > ?@ y³¡´ < ¯\ )»y D E )¯ FGAØ³ < C. H Q. r\Ws K[GY^D)N@G)i-6?C>c IJIKILIJIKILIKIJIMIJIMIJIMIJIJIMIJIKILIKIJIMIJIMIJIJIMIJI r\Ôr wfRLTOW`h][]_nT?C>cN@G)]_NfgDN@n] ILIKIJIMIJIMIJIMIJIJIMIJIKILIKIJIMIJIMIJIJIMIJI N ° @ PO¯\5A u\Ws ¢\F&F&GN@>cgT>c?CghGY>cN@OWGy]RIKILIKIJIMIJIMIJIMIJIJIMIJIKILIKIJIMIJIMIJIJIMIJI u\Ôr SXiikOWNcOW?C`D#?BgTN@OFDOWN_-mz?B`hikOWNcOW?B`h]IMIJIMIJIJIMIJIKILIKIJIMIJIMIJIJIMIJI u\Ôu wf?BFDO`h]?)G)DBmpnN_kghGX?)ghD)N@n IJIMIJIMIJIJIMIJIKILIKIJIMIJIMIJIJIMIJI u\Ôuks TVU;T ik?CF DOWW` IJIKILIKIJIMIJIMIJIMIJIJIMIJIKILIKIJIMIJIMIJIJIMIJI u\Ôukõr L Uâik?BFDO` IKILIKIJIMIJIMIJIMIJIJIMIJIKILIKIJIMIJIMIJIJIMIJI u\Ôukõu L UXT D`hWi TVUâik?BFDO`h] IMIJIMIJIJIMIJIKILIKIJIMIJIMIJIJIMIJI u\Ôuk©H T T ik?CF DOW` IKILIKIJIMIJIMIJIMIJIJIMIJIKILIKIJIMIJIMIJIJIMIJI u\Ôukõt Tik?BFDO` IKILIKIJIMIJIMIJIMIJIJIMIJIKILIKIJIMIJIMIJIJIMIJI u\ H = D)>@NcOWN@O?C`?[ ZG\.IJIKILIJIKILIKIJIMIJIMIJIMIJIJIMIJIKILIKIJIMIJIMIJIJIMIJI u\ HTs ^¶`kNcGY>o]_G)mzN@O?CèL Uâ` _1L UXTaIMIJIMIJIJIMIJIKILIKIJIMIJIMIJIJIMIJI u\ HTõr ^¶`kNcGY>o]_G)mzN@O?CèL UXTb_*TVUâ IMIJIMIJIJIMIJIKILIKIJIMIJIMIJIJIMIJI u\ HTõu ^¶`kNcGY>o]_G)mzN@O?CèL Uâ` _1 Ta IMIJIMIJIJIMIJIKILIKIJIMIJIMIJIJIMIJI u\ HT©H ^¶`kNcGY>o]_G)mzN@O?Cè T` _*T TcIMIJIMIJIJIMIJIKILIKIJIMIJIMIJIJIMIJI u\ HTõt ^¶`kNcGY>o]_G)mzN@O?Cè T` _J U;TcIMIJIMIJIJIMIJIKILIKIJIMIJIMIJIJIMIJI e¯k )^) e1³ @ * ) <5 A³ @. C H. H Q. H {. sYr sYu szH sYt s¦. 5s Y r] rks rks rCu rCu rCt D d D f.

(22) r. L%&"

(23) %. 0

(24)

(25) %&G )* <.

(26)

(27)

(28)

(29)

(30) ! #"$ %& '( )*+-,. /0

(31) 1#23 456879 :; <=. u.

(32) 8 :(b % . G6?\mzR]¸nGY>@G

(33) ?Cèmz?CF&gWGYNcOW`TA[NcnTG[]_N@Rhik?B`-]dnT?B>@NcG)]dNghD)N@nh] ?B>

(34) mYD>cØOWG>@?BLM?BNo][nTO^mon mYD`&?B`TWFe?ZG6?B>@D>oi]OWèDg^D`Gf>@GYG[?)<?CLh]_NoDBmzWG)]T6nTGy]dGb>@?CLh?BNo][D>cGlmz?B`h]dNc>oDO`TG)i N@??CW?) Nc>oDa_G)mN@?C>cOWG)]-[OWN@n Lh?BRT`hikG)i mzRT>@ZBD)N@RT>cG N@nG>oDCi\OWRh]&?emRT>@ZBDNcRT>@GF-Rh]_N LMGeAC>@GyDN@G%>NcnhD` D"mz?C`h]_NoD)`kNvikGY`T?BN@G)i ID`hiNcnTGYO>?B>@OGY`kNEDNcOW?C ` OQ]XWOW`G)iN@?"N@nTG ikGY>@OZBDN@OZG?hNcnTG6gh?]_OWNcOW?C`1? Db>@GzGY>cGY`hmzGâgM?BOW`\ N

(35) h?B`N@nTG

(36) >@?CLh?BNYU)Lk1DbikO GY>cGY`kNcO^D) G)PSRDN@O?C`[nTOQmpnO^]6`?CNIikOW>cG)mzN@OW`\N@GYAB>oD)LTWG N@nTGl>@?BLh?CNbO^]6`T?B`TØn?CW?B`T?CFeO^m " ]dO` m?] ] &" %" '. ( * $". ! "# ). +OWABRT>@Gs,.-0/2143652387/2589 523652:<;>=@?A52BC5ED. ¢VnT?C>cN@G)]_N6ghD)N@nh]?C>

(37) ]_Rhmpn->@?BLh?CNo]nhDYZG6h>o]_NLMG%GY`&]_N@Rhi\OWG)iLk « G F9\wfRLTOW`h] O`sY{Ct¦ ¥ wfRTLtS¦)§¶U¡[nT?g>@?)ZG)iNcnhDNvD]dnT?B>@N@Gy]dNghD)N@nOQ]N@?LhG ?BRT`hi.DFe?C`TADh`TOWNcG&]_GYN? ghDNcnh]zUh]_O "N@?LhGXg>@G)mzOQ]dG SX]@]_RTF&OWÀNcnhDN[NcnTGY>cGfOQ]`T?v]dWOgTgTO`TA?)<N@nTGX[nGYGY^]D)`hi&N@nTG >@?CLh?BNl]dghGYG)i&OQ][mz?C`h]_NoD)`kNbG)PRhD¡Nc?sCUTOWNE]6kO`TGYFD)N@OQm9F&?\i\GY#OQ]6N@nTGY`NcnTGX?CW?)[OW`TAH IJ L6M IJ mz?V] L6M cRs K N K ]_P4OWO` Q N [nTGY>@OG 6 ST D>cGNcnTG[m??C>oi\OW`hD)N@G)]¡? Db>@GzGY>cGY`hmzGâgM?BOW`\N?B`NcnTG>@?CLh?BNY<U [N@nTG?B>@OWG%`kNEDN@O?C` ?lNcnTG&>@?BLh?CND)`hi P O^]NcnTG?C`T.mz?B`kNc>@?C[gD>oD)F&GYNcGY>YU¡ZGY>cO \OW`TVA U P UXW sBX +T>@?CF N@nTG DRTNc?CFD)N@O^m%]#gM?BOW`\N?)hZ\OWGYlUN@nTG)]_G>@?CLh?BNo] D)>@G

(38) mz?CFegTWGYNcGYWbm?C`\N@>@?B^D)LTWGU%]d?XNcnhDN¡ONF DG)] ]dGY`h]_GlN@?e]dN@Rik&N@nG]_k`\N@nG)]dOQ]6gT>@?BLTWGYF 6n\Rh]Uf?CR>D)OWF OQ] Nc? ]_nT?) N@nhD)NOWNOQ] gh?V]@]dOLTWG:N@? mz?CFegTRTN@GNcnTG ]d\`kNcnTG)]dOYOWÀ RT`hmzNcOW?C`:?N@nTOQ]f?CgN@OWF DWON_&gT>@?BLTWG%FUM[nO^mon:mz?C`h]_O^]_No]XOW` DC]c]d?\mzOQDN@O`TANc?G)DCmongh?COW`\N.

(39) H. L%&"

(40) %. 0

(41)

(42) %&G )* <. 6 ST4T

(43) OW`NcnTGmz?B`khABRT>oD)N@OW?B`]_ghDCmG D-RT`TO^PRTG1Nd\ghG?]dn?C>@NcG)]dNIghDNcn ]dNoD)>@NcOW`TA-D)N[N@nTGl?C>cOWABOW` ] 0 ]G0 ] D`hi&GYìkOW`TAvDN[NcnTO^]

(44) mz?C`kACRT>EDN@O?C`¡h:GXN@nTG%`&?CLTNEDO`D ghD>cN@OWNcOW?B`?) [ON@n>@G)]_ghG)mzN[N@?NcnTG1]dO " ikO GY>cGY`\N6N_kghG)]6?)

(45) ]dn?C>@NcG)]dNbghD)N@n¡ 6nO^]6ghD)gMG%>fOQ][D>@NcO^mzR^DNcG)i&DB]?BWW?)b]+ O>o]dN

(46) 6Gl[OW#gT>cG)]dG%`kN]d?CFeGX>@G)mGY`kN

(47) >@GYQDNcG)i. 6?C>cT]UhD`hi>@G)m%DW N@nTGI>@G)]_RTWNE]6?¸wfRTLTO`h]9?B`"]dnT?B>@N@Gy]dNbghDNcnh]zh6nTG%`

(48) Gl[OWW Rh]dGlNc??C^] >@?CF ?BgTN@OFD¸mz?C`\N@>c?CN@nTG%?C>@:D)`hiABGY?CF&G%N@>@VU#N@?gT>c?ZGe]d?BF&G-]d\F&F&G%N@>@egT>@?BgMG%>@N@OG)] OW`-N@nTGI]d\`kNcnTG)]_OWYO`TAfRT`hmN@OW?B`-D`hi-`TGY ?BgTN@OFDOWN_1mz?CìkOWNcOW?C`]¸?B` NcnTGI]dnT?B>@N@Gy]dN6gDN@n]z +OW`hD)W6G-[OWW

(49) mz?BF&gTRTNcG NcnTGe]d\`kNcnTG)]dOQ]zU¡[OWNcn>@Gy]dghG)mzNlN@?NcnTG-?C>@OGY`\NoDNcOW?B` ?)bN@nTG h`hD mz?B`khABRT¨ >oD)N@OW?B`¡ bGY`hmzG

(50) 6Gb[OWW?CLTNEDOWèDXghD>cN@ON@OW?B` ?)<N@nTG[gD>oD)F&GYNc>@O^mgT^D)`T#G Z \

(51) l RTN1]dOW`mzHG m%D`ZBD>c2>cGYGYOW`: U

(52) G&D)^]_?nhDYZG NcnTG&ghD)>@N@ON@O?C`?)bN@nTG [nT?CGm?C`khABRT>oD)N@O?C`:]dgDCmzG . 6l02%

(53) v :$% .

(54). . (. )+*-,/.1032425-62789532. d] OWFeOW^D)>#

(55) ?C>@1nhDC]<LMG%GY`-ik?C`GbDW>cG)DCi\?C>âN@nTGK9GYGyiT]D)`hi&¢nTGYgTgFe?CLTOWG >c?CLh?CN%k6nO^] >@?CLh?BN nhDC]¡N@nG6]cDF&G¸mpnhD)>oDBmzN@GY>cO^]_N@O^m%]MLTRTN<F&?B>@GY?)ZGY>%UpON¡O^]¡D)WW?)

(56) G)ifN@?bFD)G FD`!RZk>cG)]z K9GYGy¥ iT][D`hi¢VnTGYgTg"DggT>@?VDCmonTG)i >o]dNbN@nGgT>c?CLTGYF?]dnT?B>@N@Gy]dNbghDNcnh]?B>X]_Rhmon>c?CLh?CNE] OW` Kj¢\{ ]§¬ SI]OW` wfRTLOW`h] Ô]m%DC]dGVUN@nGY?CRTì D&h`TON@Ge]dR " mzOWG%`kNX¬DFeOWW"?bN_\gMGy]? ghDNcnh]zUhmz?B`h]dOQ]dNcOW`TA?)D)N[F&?]_N¸ZGXghD>cNo]UTGYOWNcnTGY>

(57) D>EmY]6?¸mzOW>EmzWG[?) >EDCikORh

(58) ] ?C>b]dNc>oD)OWACn\N WOW`G&]_GYACF&G%`kNE]zU D`hiD)NF&?V]dNl¥ N_6?FD)` lRTZk>cG)]z¨ 6nTO^]l>@G)]_RTWNlª nhDB]LhGYGY`:gT>@« ?)ZG)i:DAVDO` Lk¥ ¨f¤ª

(59) ¢« R]@]dF D` Dì¤D)`TA O` ¢\[{ks§¶U[D)`hi L\ ?BO^]@]_?C`T`DNYU ¥ ¨&GYx % >G%x Y?.Dì GYLT?C`hi OW` {CrC§¬UMR]dOWÀNcnT$G #D "\OWF-RTF = >@OW`mzOWgTG?)[=<?C`\N@>@\D)« ACO` = #Cr§¬U#D&

(60) GYWØ\`T?)[` N@??COW`?BgTN@OFD\m?C`\N@>@?BN@nTG%?C>@V. +O`hDWU)¢?CR GY >@G)]âD`hi DRTF&?B`hi>@Gh`TG)iXN@nG[]d'R "mzOGY`\N ¬DF&¥ OW« ?)<ghDNcnh]zUD`hieDCmonTOWGYZGyiN@nTGI]dNcRhik-?<N@nGX]_k`\N@nTGy]dO^] gT>c?CLTGYF ?C>N@nT?V]dGX>c?CLh?CNE] OW` ¢ {CuC§¶UBGYF&gTnhDB]dOYOW`TAbN@nG[gT>@?BgMG%>@N@OG)] ? N@nGXDB]@]d?\mO^DNcG)iF&GYN@>cO^mCY:G[[OWT]_GYG[N@nDNOW` ?CRT>bmYDB]dGU]d?BF&GfgD>@NE]6?<NcnTGX6?B>@ UTikGy]dgTON@Gb?âN@nTGXAB>@G)D)N[]_OWF&O^D>cOWN_U)nhDYZGfLhGYG%` ?CRTì N@?-LMGlF&?B>@Glm?CF&gTG " USLhG)m%DRh]_G?)N@nGD)Lh]dG%`hmzGl?¸D|FeGYN@>cO^mC S. G>@GymYD6N@nDN-D +0 ;:G6

(61) O^]N@nGNc>@OgTWGYN8< 6 ST4T jikGzh`TO`TAN@nGgh?V]dOWNcOW?B` D`hi¤N@nG?C>cOWGY`\NoD)N@OW?B`¤?-NcnTG>c?CLh?CNO`¤N@nTG gT^D)`TG.Dì N@nTG +0 ;:G6

(62) b>= + eO^] 7 +T?C>-]dRmpn.>@?BLh?CNo]U OWNnhDB]LhGYGY`.gT>@?)ZG)i U >o]dNO` ¥ wfRTLtS¦)§[D)`hiF&?C>cG >@G)mzG%`kNcWO` ¥ ¨fª

(63) « {BrC§¶UN@nDN6?C>

(64) ACOZGY`&OWÒWN@OQDhD)`hi h`hD)<mz?C`kACRT>EDN@O?C`h]6O`D`?BLh]dNEDCmzGY >@GYG[GY`\Z\OW>@?B`TF&GY`\NYUN@nTG]dnT?B>@NcG)]dNghD)N@n-G "kOQ]dNE]D)`hi|OQ] DFe?C`TAl]_O "1Nd\ghG)]?)#gDN@n]zUmz?B`h]dOQ]d N@OWÀ&?DNbF&?V]dNbN@nT>cGYGghD)>@NE]f[nTO^monD)>@G1GYOWNcnTGY>ID>om%]f?

(65) mOW>omWG)]6?)6>EDCikORh] ikGY`T?BN@G)i.

(66)

(67)

(68)

(69)

(70) ! #"$ %& '( )*+-,. /0

(71) 1#23 456879 :; <=. t. EU#?C>l]_N@>EDOWABnkNIWOW`G]_GYACFeGY`kNE]

(72) ikGY`?CN@Gyi U ESf`D>Em?mzOW>EmzWG mYD`LhG?BWW?)

(73) G)i OW`N_

(74) ? ?BgTgTgh?]_OWN@GvikOW>cG)mzNcOW?C`]zUTGYON@nTGY>bmW?\mok[OQ]dGN@nTG%`N@nGD)>om [OW#LhGvikGY`T?BN@G)i" ?C>@>@OACn\N@¬D>Em

(75) ?C>Imz?CRT`\N@G%>omz?\mp\[O^]_G NcnTGD)>omX[OW¡LhGikGY`?CN@Gyi T ?C>@GzN@¬D>Em o 6nkRh][6GjmYD`mz^DB]@]dOò NcnTG1]dO &" N_kghG)]6?)]_nT?C>cN@G)]_NfghD)N@nh][OW`\N@?N_

(76) ?¬DF&OWOWGy]zUCOWWR]dN@>EDNcG)i OW` + OWABRT>@G1rH . . Ë ø^ùYïCÍ . ú. ø^ùYïBÍ

(77) . Ö. ø^ùYïBÍ

(78) . +OWABRT>@G1r 2: 9 15 "!$#CB ; 3%E/25 ?>D 1 D&'8D /( +hDF&OW *+ O`hmzWRikG)]6rN_kghG)]. ). ). dN \ghGKT-,5T D`hiNd\ghG1T,Y [nTGY>cG*.-O^]6N@nGD)`TACGl?NcnTGlOW`\N@GY>cF&G)ikOQDN@GbD)>omCUTZG%>@O \OWÀ*./10 +hDF&OW U OW`hmzRhikG)]H N_\ghG)] Nd\ghKG T UXT D`hiNd\ghG1L Uâ Nd\ghKG T Uâ D`hiNd\ghGlL UXT.

(79) L%&"

(80) %. 0

(81)

(82) %&G )* <. 2 ) 6nTGmz>cOWN@G%>@OW?B`Nc?LhG?CgTNcOWF&OYG)iO^]NcnTG&GY`TACNcn?bNcnTG&ghD)N@nh]U?B>N@nG&N@OF&G-]dO`hmzG-N@nTG ]dghGYG)i ?)<N@nTGI>@?CLh?BN[O^]mz?C`]dNoD)`kN%T6nTGj]d\`kNcnTG)]dOQ] ?<?CR>6?CgN@OWFeOW)D)N@OW?B`gT>@?BLTWG%F O^]NcnTGY` N@? ikGYNcGY>@F&O`TG ?B>&G)DCmon m?C`khABRT>oD)N@O?C` <?) NcnTG:]dnT?B>@NcG)]dN&gDN@n >c?CF N@nTG?B>@OWABOW` < ] 0]G0]

(83) N@/? <IT:GXF R]dN6`?CN@OQmzGlN@nhD)N[OW`?CR>fghD)>@NcO^mzRTQD>mYDC]_GUhDC][N@nTGl>c?CLh?CNb?C`T F&?)ZG)]M?C>c[D>Ei#UCNcnTG[gT>@?BLTWG%FO^]¡`T?BN6]_kFeF&GYN@>cOm Oò Nd

(84) ?lmz?B`khACR>oDNcOW?B`h] < D)`h/i < D)>@G ACOWZG%`¡UCN@nGl]dnT?B>@NcG)]dN

(85) ghDNcn >@?BF < N@? < O^] OWèF&?]_NmYDC]_G)]6i\O GY>@G%`kN >@?BF N@nTGI]dn?C>@NcG)]dN ?C`TGX>@?BF < N@? < T6nhD)NfOQ]6[nk-N@nTGlGY`TACNcn?âN@nTG1]dn?C>@NcG)]dN[gDN@nik?G)]6`T?BNXi\Gzh`TGlD F&GYN@>cO^m[?C` ¡?-]d?BWZGbN@nTGI]d\`\N@nTG)]_O^] gT>c?CLTGYFUC

(86) Gf[OWTh>o]_N[]_nT?) N@nTGbG "\O^]dNcGY`hmzGb?â]_kFeF&GzNc>@OG)] OW`-N@nTGbmz?B`khABRT>oD)N@OW?B`]dgDCmzGID`higT>c?ZGb]_?CF&G[`GY `TGymzG)]@]cD>cmz?B`hikOWNcOW?B`h] ?¡?BgTN@OFDOWN_ ?C>N@nTG"N_kghG)] ?)ghD)N@nh] X]_OW`TANcnTG)]_G>@G)]_RTWNE]zU6G[OWfLhG:D)LTWGNc?6?B>@ OW` l ¥ ] 0#§6OW`]dN@GyDCi?j l|: 6nTGY` U N@?:]dOF&gTO NcnTG"D`hD)W]dOQ]zU 6G[OW[m?CF&gTRN@G-N@nTG ik?CFD)OW`h]6?)gh?CNcGY`kNcO^D)¡?CgTNcOWFD)WOWN_?B>XwfRLTOW`h][ghD)N@nh][OW`"DghD>EDF&GYNc>@OQmfgT^D)`TKG Z \YUTNcnhDN O^]9?B>j`hDm?C`khABRT>oD)N@O?C`h]l[OWN@nNcnTG-]@D)F&G?B>@OGY`kNEDNcOW?C`] k¡6nGghD>cN@OWNcOW?B`? ZG\X[OW N@nTGY`"LhG?CLNoDO`TG)i"DyN@G%>bikO^]cmzRh]@]_OW`TA-N@nG>@GyD¡?CgN@OWF DWON_?NcnTGlghDNcnh]fOW`NcnTGik?BFDO` OW`\N@GY>E]dG)mzNcOW?B`h]z6nGfghD)>@NcOWN@O?C¥ `&?) ¥ [OWhLhGX]_OWF&gTlN@nTGl]_RTghGY>@gh?V]dOWNcOW?B`&?âD)WhghD>cN@ON@OW?B`h] ?NcnTGlgT^D)`TG)] ZG\YUk?C> ]Gor 0

(87).

(88) 78 67 9.2. ð` ¥ ¢ « {BuC§¶UkON6OQ]6]dn?[`NcnhDN[G)DBmpnegT^D)`TGJZG\6nhDC][N_6?D"kGy]?¸]d\F&F&G%N@>@VUNcnhDN

(89) >@G)ikRmzG)] N@nTGv]dN@RikNc?D&PRhD>cN@GY>b?

(90) N@nGgTQD`TGU DìD^]_?&N@nG`\RTF LhGY>

(91) ?]dn?C>@NcG)]dNIghDNcnNd\ghG)] N@?1mz?C`]dOî\GY>Y bGY>@G[

(92) Gf[OW]dGYGbN@nhD)NN@nTGY>cG[G "\O^]dNE]?C`W?C`GXD"kOQ]¸?)<]_kF&FeGYN@>cXD)`hi|NcnhDN N@nTGl`\RTF LhGY>

(93) ?âN_kghG)]6Nc?&]_N@Rhike[OWW ?C`T&LhGikGymz>@G)DB]dG)i&L\ ?B`TG 6¯ . C&> L

(94) 6=

(95) ' \ !- &

(96)

(97) \ ==06

(98) B6=

(99) 1- 6 ^. ! )*)80

(100) !

(101) /=

(102)

(103) !-Z \ ! =

(104) K3Z \ < 0

(105)

(106) =

(107) 1 ' < 63

(108)

(109) W+0 1:G6

(110) K !# W

(111) 8)*)80

(112) +W ! :;

(113) 1 0> = +

(114)

(115) \

(116) 13

(117) 1 0

(118) =

(119) )*'=

(120) 1! # )80

(121) +8

(122) " ' < 6

(123)

(124) K+0 ; :G6

(125) . T . T . « G%NR] mz?C`]dOî\GY>X+OACRT>cGbuk=?BOW`\N$OQ]?CLTNEDO`TG)i-DyN@G%> N@nT>cGYG6>cOWABOî N@>ED`h]¶?C>@F DN@O?C`h] ) 6nTGb]d\F&F&GN@>c&%('*)? ZGY>cN@O^m%DD "\O^],+OF Dgh]¡N@>cO^DÀCWG&+- Z ?C`\N@? N@>@OQD`TABW.G +- Z ` / 3521 4 ' ?

(126) ZG)mzNc?C> 4 1 + FD)gh]9Nc>@OQD`TABWG +Z ?C`\N@? ) 6nTGNc>oD`]d^D)N@O?C0 N@>@OQD`TABW.G +- Z B !#.

(127)

(128)

(129)

(130)

(131) ! #"$ %& '( )*+-,. /0

(132) 1#23 456879 :; <=. 4 4.

(133). \. . \. . .

(134) . . . . +OACRT>cG1u : :1 D8? ? D 8\ FD)gh]XN@>@OQD`TABWG! +#Z & ) 6nTG >c?CNEDN@O?C` ?ImzGY`\N@>cG+7D)`hiDÀCWG ?C`\N@?N@>cO^D)`TACG. +Z 6nkR] TOQ] N@nTGXOFDABG[?$+ L\ NcnTGfOQ]d?BF&GYN@>cO^mN@>oD)`h]ð?B>@FD)N@O?C` / 3 1 4 ' %('*))UhD`hi"]d?-O^]6ghD)N@n MOQ]d?BF&GYN@>cO^m[N@?-ghDNcn <UhDC]6OWRh]dNc>oDNcG)i&OW` + OACRT>cGXHT . +. \. . +OWABRT>@GlH 8D /; 5 D61TVUâ 23 '8D / ; 5 D61¡JU;T. ¦.

(135) L%&"

(136) %. 0

(137)

(138) %&G )* < Y. WGYN<Rh]g>@?)ZGN@nhD)N$\mYD)`-D^]_?XLhG6?BLTNoD)OW`TG)iDB]N@nG[]d\F&F&G%N@>@OQm ?) gM?BOW`\N$ LkeN@nTG1]d\F&F&G%N@>@1?¸D "\O^#] 8\ ^¶`hikGYG)i Uk6GInhDYZGNcnTGX?CW?)[OW`TA>cGY^D)N@O?C` +- . ¢?-N@nTGlLTOQ]dG)mzNc?C>bD"kOQ]6?¸D`TABWG Z.+&. . Z+- . Z.+- . . Z.+-. O^]6GyPSRhD)¡N@? . +& . Q r Z.+-. Z.+&. . . Z.+-. ?C>cGY?)ZGY>YU\N@nTG1DÀCWGy]6OW`hmzOQikGY`\N[D)N& ]@D)N@OQ]ðN@nTGlG)PRhD)N@OW?B` #. . Z+- . . Z.+-. . Qr. . D`hinTGY`hmG Z.+& Z.+- ¢?.6G:mz?B`hmzRhikGNcnhDNeO 1N@nTG%>@GG "\O^]_No]-D` ?CgTNcOWFD)[ghDNcn >@?BF < Nc? < T<oUhN@nTG%`N@nGO^]_?CF&G%N@>@OQmfN@>ED`h]¶?C>cFDNcOW?CìkGzh`G)iDLh?)ZGFD)gh] ?C`\N@?D`T?BN@nTGY>?BgTN@OFDâghDNcn >c?CF < N@? < T EU¡[nTGY>@G! OQ] N@nTGgh?BOW`\Nl]d\F&F&GYNc>@OmfNc?&gh?COW`\N [ON@n>@Gy]dghG)mzNbN@?D "kOQ&] \ SX][6G-m%D` `T?CNcO^mzG[NcnhDNâN@nTG[?B>@OWG%`kNEDN@O?C`h]<? N@nTG[OFDABG)]¡?9 < D)`hi <L\lN@nTG[OQ]d?BF&GYN@>cO^m N@>ED`h]¶?C>@F DN@O?C`-D)>@G6?BgTgh?]_OWN@G[Nc?XN@nG6?C>cOWGY`\NoD)N@O?C`h]¡? <D)`hi < mz?CFeghD>cG +OWABRT>@Gy]6uDì H oU\O ¡

(139) Glmz?B`h]dOQikGY>6NcnTGXghD)N@n DC]

(140) D6?C>Ei FDBikGf?) GYN@NcGY>o] GU T¤Dì U

(141) U#N@nTG-6?B>oi? <O^]X?BLTNoD)OW`TG)iL\>@GyDCikO`TAN@nTG-6?B>oi? OW` >@GYZG%>o]dGI?C>oi\GY>Y 6nO^][>@G)]_RTWNbD)WW?)b][Rh][N@?->@G)]_N@>@OQmzN6?BRT>I]dN@RikN@?eD|nhD) gT^D)`TGi\Gzh`TG)i&L\ \ UhDì N@nTG&N_\ghG)]?)bghDNcnh]mz?)ZGY>@O`TAOWN%U NcnhDNOQ]N_\gMGyM] T T

(142) o T 0TVUXT

(143) oL UâU

(144) D`hiGYON@nTG%> LUXT ?C#> T Uâ 6¯ . C1D )*)80

(145) 3:

(146) # +O + 6 b =

(147) )*'=

(148) 1 ' < 6 . . ST 6 S O O .

(149)

(150) 3+0 ;:G6

(151) +0 ;:G6

(152) .

(153) )80

(154) + =

(155) )*' =

(156) ' < 6

(157)

(158) . 6nTOQ]gT>c??âO^]

(159) ikOW>cG)mzN@1ikG)ikRhmG)i|>@?BF N@nTGIgT>@?BgMG%>@N@OG)]?)<N@nTGI]d\F& F&GYNc>@ %(' V fGY>cGN@nG6?C>Ei ?) OQ] ?CLNoDO`TG)i >c?CF NcnTG?C`G?). L\ mpnD`TABOW`TA-N@nTGKT.OW`\N@?-D)`hiZ\O^mGXZGY>o]cDk ON@n&NcnTO^]]_G)mz?Cì|gT>c?CghGY>cNdVUS

(160) GXm%D`&>cG)]dNc>@O^mN N@nTGb>oD)`TACGI? XN@?1N@nTGbOW`\N@GY>cZBD ¥ ]G 0#§¶U O â O^][DC]c]dRTFeG)i&N@?LhGNcnTGlOW`\N@GY>cZCD)#§ 0#§¬ B !. . . .

(161)

(162)

(163)

(164)

(165) ! #"$ %& '( )*+-,. /0

(166) 1#23 456879 :; <=. {. 03/.>9. 032 GvmYD`"ghD>EDF&GYNc>@OYGlwfRTLOW`h]fgDN@n]fLkeN@nT>cGYGZBD>cO^D)LTWG)][>@G%gT>@G)]_GY`\N@OWÀN@nTGlWG%`TACNcnh]f? N@nTGYO>D>EmY] D)`hi ]_GYACFeGY`kN%BSf`RTgTghGY>Lh?CR`hi|?B` NcnTG[WG%`TACNcn?¡NcnTGbD>EmY] O^]?BLkZ\OW?BRh]d1r 0 ^ð` ¥ ¨fª

(167) « {Br§<?C`T&N@nTGvmz?CìkOWNcOW?C` . / 0

(168) ?C`"N@nTG1OW`\N@GY>cF&G)ikOQDN@GID>EmXWGY`TABN@n"?ghD)N@nh] ** O^]ABOWZGY`¡¡:G"mYD`.OWFegT>@?)ZGN@nGLh?BRT`hiT] ?B`.N@nTGghD)>oDFeGYN@GY>E]DB]v?BWW?)b]U ]dNcOW Rh]dO`TA NcnTG #D "\OWF-RTF = >@O`hmzOWgWGb?

(169) =?B`kNc>@\D)ACRTO`LRTNbDQ]d?-ACGY?BF&GYN@>cO^mYD) D>@ABRTF&GY`\No] E )³³h5A»PAØ³ @ C > =

(170) )*'=

(171) 1 $

(172) 1 ' 6/ + ) !

(173) + 6' = / '

(174) -45' M' 0K

(175) 1 &r 0

(176) * =

(177) )*'=

(178) +0 / $+0 < <*=L8+0

(179) X! +

(180) L! ) ¥ ] %sz§

(181) ¥ Xr 0 or 0#§ ,)*

(182) "G-m%D``T?BN@O^mGN@nhD)NXN@nTOQ]fgT>c?CghGY>@N_]dGYNE]XD`:OWF&gh?B>@NoD)`kNIikOò GY>@G%`hmzG[ON@n NcnTG:mYDC]_G?vK[GYG)iT]&D)`hi¤¢nTGYgTg >c?CLh?CN% ^ð` ?BRT>mYDB]dGUD`\ mz?C`\hACRT>EDNcOW?C` T<oU#[ON@n ¥ ]Gor 0 ¥ UTF Rh]_N[LhGmz?B`h]dOQikGY>@Gyi O`N_6?eikOò GY>@G%`kNXDYT] #GYOWNcnTGY>lDB] T<X?C>vDC] r 0 b[nTOQmpn D>cG NcnTGe]@DFeG mz?C`\hACRT>EDNcOW?C`]OW`1N@nTGgTn\T]_O^mY¥ D)\]dghDBmzGU)LTRTN<`T?CN<OW`lNcnTG[mz?B`khABRT>oD)N@OW?B`-]dghDBmzG 6G1mz?B`h]dOQikGY>YUTNcnhDN[OQ][ Ir 0 or 0#§¶ 6nTG)]_GNd

(183) ?&gh?]c]dOWLOWWON@OG)]9nDyZGNc?&LhG-mz?C`]dOî\GY>@G)i?B`TW"OW`"N@nTG-mYDB]dG[nTG%>@G D>EmY]6D)>@Gb`T?CNDWh?)<N@nTGI]@D)F&Gf?B>@OGY`kNEDNcOW?C`]z ^¶`hikGYG)iOò¡NcnTGY-D>cGU\D`hi-O ¡NcnTG ghDNcn&>@?CF <bN@H? T âO^]6O` ¥ Xr 0 or 0#§¬UCN@nGY`&N@nGgDN@neWG)DBikOW`TANc? T &r 0 ¡[OWk`T?BNLMGb?CgN@OWF DLhG)mYD)Rh]dGbOWN [OW\OW`hmWRhikGDèD>Em6?¡GY`TABN@n ]dNc>@O^mN@W-AC>cG)DNcGY>[N@nD`"r 0 ]_OW`hmzGI6G1mYD`NcRT>@ÒWè?C`T&?C`TGl?B>@OWG%`kNEDN@O?C` E ¡?XgT>c?)ZG6= >c?Cgh?]_OWN@O?C`vukWsBU

(184) G[OWW\]_RhmYmzGy]@]dOZGYWb]_N@Rhi\GyDCmonN_\ghG?) wfRTLOW`h]gDN@n]z 6¯ . C C ;0

(185) $+0 <

(186) 1 =

(187) 1 $ , [: = )8

(188) . <

(189) 1K 6' !- + +M !L+5 + ' =

(190) 1 +0 / K =

(191) )*' ! 0]W1 H . W .cr 0 < ]W W1. ]W1 . 0 ]W . 0 B !.6nTGXh>E]dNImz?C`hi\OWN@O?C`?C` .|nDC][LMG%GY`D)W>@GyDCik&ABOWZGYèOW` ¥ ¨fª

(192) « {Br§¶ ^¶` NcnTO^]gDghGY>YU\D1mpnhD)>oDBmzN@GY>cO^]_N@O^m

(193) ]dNc>oDOACn\NWOW`G. 6O^]ikGh`TG)i?B>GyDCmon ?BgTN@O FD¡gDN@n U#[nTO^mon]_RTgTgh?C>cNo]X]_N@>EDOWABnkNIWOW`G]dG%ACF&GY`\No][D)`hi[nTGY>cGO`hG "\OW?B` gh?COW`\No]l?\mYmzRT>% µf`:?C`G&]_OîkG-?N@nTOQ]WO`TGN@nG ghD)N@n:N@RT>c`h]mW?\mok[OQ]dGU D`hi ?C`:N@nTG1?CNcnTGY>l]_OîkGU mz?BRT`kNcGY>omW?\mok[OQ]dGh6n\Rh]fOò / .hUMNcnTGD)>om?)6GY`TABN@n mz>c?]c]dG)][N@nTGlOW`TG! UT[nO^monOQ]6`T?CN[gh?V]@]dOLTWGV (. 8/.>9. 03 67-9.. 1.> .

(194) s5]. L%&"

(195) %. 0

(196)

(197) %&G )* <. ,. . , . . +OACRT>cGlt 52345 D ; :89 *+ '8D /(. +T?C>XNcnTGQDC]dNImz?B`hikOWNcOW?B`¡U#]_RTgTgh?]_G NcnhDNbN@nGmz?B`kNc>oD>cOQ]9Nc>@RTG . 0 D`hi . 0 ¡6n\Rh]lN@nTGY>cGG \" O^]dNE]XD`?CN@nGY>mzO>omzGNED`TABGY`kNlNc?NcnTG-Nd

(198) ? G \" N@>@G%FDâD>EmY]zU<]d\F&F&G%N@>@OQmXl >Y©NY#NcnTGe]dGYABF&GY`\Na_?BOW`TO`TANcnTGYOW>jmzGY`\N@>@Gy]jNc? N@nTG mzO>omzG]dRgTgh?C>@NcOW`TA N@nTG:OW`\N@G%>@F&G)i\O^DNcG"D>omB[6nTGY` ?C`¤NcnTO^]emzOW>EmzWG"6G mz?C`]dOî\GY>NcnTG&D)>om .?)bWGY`TABN@n r 01 . .OW`:?C>oi\GY>Nc?LTRTOî:D]dnT?B>@NcGY> ghDNcn l ]dGYGH<+ OWACR>@Gt N@nTG >o]dN-D)>om&]_nT?C>cN@GY`G)iN@?WG%`TACNcn . 0 U mz?C`mYDNcGY`hDNcG)iNc?&D)>omUT[nO^monO^]?BW?

(199) G)i&LkeN@nTG1^DC]_NXD)>om1]dnT?B>@N@G%`TG)iNc? WGYÀCN@n . 0 ¨ RTNXOWNbO^]b`T?CNX?BgTN@OFD¡LhG)m%DRh]_GOWNbLMG%W?CÀ]XN@? ¬D)F&OW. [ OWNcn"DÒ`kNcGY>@FeG)ikO^D)N@GbD)>omXWGYÀCN@nG)]@]6NcnhD` 0 +T?B>ghD)N@nh]¡LhGYW?B`TACO`TAbN@?[¬DF&OW U UN@nTG

(200) mYDB]dG?hN_\ghG)]¡LUXTD`hi*TVUâ OQ]¡]dOF&gTWG ]dOW`mzGG)DCmon:D>Em|nDC]XWGYÀCN@nG)]@]XNcnhD` r 0 U#NcnTGYO>lDACGYLT>EDOQm]dRTF OQ]XDQ]d?WG)]c]fN@nD` r 0 +?B>fN_\ghG)][L UâD)`hi TVUXT

(201) G`GYG)i h>o]_N[N@nTGX?BWW?)[O`TAWGYFeFDk 6¯ . C H

(202) IL Uâ : K

(203) 1J ) !K

(204) * +M' 6

(205) 1

(206) '

(207) r 0 +0 / *+. =' + < /5 )8

(208) +&=

(209) 1 TVUXT

(210) <45+ K4= . . . « GYNeRh]&mz?B`h]dOQikGY>-Nd

(211) ?.mz?B`khACR>oDNcOW?B`h] < 2T vDì < <T<6[ON@n UhDC]fO` +OACRT>cG \^¶`"LM?BN@n:mYDB]dG)]UMNcnTG]_RTF7?NcnTG D>EmWG%`TACNcnh] D)>@G"G)PSRD[N@? r 0 #?B>@GY?)ZGY>%UNcnTGOW`TG]_GYACFeGY`kNE]D>cGGyPSRhD) LhG)mYDR]dG =ZBZ<O^][DghD)>oDWGY?CAB>oDFM¢?-Lh?CN@ngDN@n] D`hi nhDYZG ]@D)F&GXWG%`TACNcnh]z bGY`hmzG6GmYD` ]dNEDN@G"N@nTG?CW?)[OW`TA:WG%F&F&D\U¡[nTO^mon gT>c?)ZG)]= >@?Cgh?V]dOWNcOW?B` ukWs?C> ghDNcnh]9?)N_kghG)][J U D`hi TVU;T[ 6¯ . C Q =

(212) - Uâ , T U;T, +0

(213) / K =

(214) )*'9 ! ./ r 0

(215) B !0 . . .

(216) sCs.

(217)

(218)

(219)

(220) ! #"$ %& '( )*+-,. /0

(221) 1#23 456879 :; <=. . . . . . . . . . +OACRT>cG G ED /( LUâ 23XTVUXT 9 ;A3 ; 3 0D<5 = 523

(222) # ? 8D ;>523% 5 2:1<5 ? ;>183 D 8D ;>523% B !# ^Ø . / r0 UC6GmYD`h`hi?C`NcnTG6h>o]_N0 >=C?C>â^DC]_N â D>Em[DXgM?BOW`\N [OWNcn NcnTG9`hD@0 0>=?C>O`TOWNcO^D8¡ ?C>cOWGY`\NoD)N@O?C`¡ I]dOWÀNcnTGbgT>@GYZ\OW?BRh]GYF&FD\U. N@nTG]dRTLghDNcn LhGYN_6G%GY`.N@nTG)]_GN_6? mz?B`khACR>oDNcOW?B`h]&?v]@D)F&G?C>@OGY`\NoDNcOW?B`h] mYD`-LhGX>@G%gT^DBmzG)iL\DèO^]d?BF&GYNc>@O^m]_RTLTghD)N@nLUâ Oò¡ON [DB]VTVUXT9U\D)`hi|Z\O^mG ZGY>o]cDkU#Nc??BLTNoD)OW` DÒQ]d?CFeGYN@>cO^ml]d?BWRTNcOW?C` ^¶NlO^]X`T?BN1DwbRTLTOW`]ghD)N@nVf]_GYG +OWABRT>@G¦ oU\nTGY`hmzGlON[O^]6`T?BN[?CgTNcOWFD)¶ . . . . '. ' . +<OWACR>@G¦<h Uâ , '8D /,; D / . / r0. :Gm?C`hmzRhikGXNcnTO^][]_G)mzNcOW?C`L\&N@nGj?BW?[O`TANoD)LTWGl[nTOQmpn"]_RTF]6RTgN@nG`G)mzG)]c]@D>c ?CgTNcOWFD)WOWN_-mz?B`hikON@OW?B`h]?C>IwfRTLOW`h]6ghD)N@nh] Nd\ghG , . § 0 or 0 ¥ D`hi S ¥ ] .§ D`hi ]W 1 . 0?C#> ] W 1 . 0 Nd\ghG1 ,5U @ ?C> T,BU T S . ¥ ] or 0 ¥ D)`hi . W r 0 Nd\ghG1 ,5U T ?B> T,=U _ S . ¥ ] Er 0 ¥ . . .

(223) sYr. L%&"

(224) %. 0

(225)

(226) %&G )* <. 5 -7 7895 OWN@n"N@nTG1gT>@G%ZkO?CRh][]_kF&FeGYN@>cgT>@?BgMG%>@N@OG)]zUh6G1mYD)`>cG)]dNc>@O^mN[?CRT>l]_N@Rhi\Nc?&D)WâwfRTLTO`h] ghDNcnh]G "mzGYgNJTVU 1U O`NcnTG-OW`kGY>cOW?B>XnhDòØg^D`G ?)#Z \1ikGzh`TGyiLk \lD`hi[ON@n 0 ¥ ] 0#§¶ ¨ RTN[N@nGfhACR>@G)]6[OW¡]_nT?) >cG)]dRWNo]?B>[N@nTGI[nT?CGg^D`JG Z \YUhD)`hiD#N@nGgDN@n]z FDBmpn.i\?CFD)OW`:O^]lmz?CFegTRTN@GyiOW`NcnTG&]cDF&GDY<6nTGmz?B`kNc>@?CghD)>oD)F&GYN@G%> OW`\N@>@?B ikRhmzG)i:OW`.]_T]_N@GYF cRs lO^]lk`?[` ?C`.G)DCmon:ghD>cN?IDwfRTLOW`h]lghDNcn <OWNlO^]lG)PRhP D

(227) N@?s DW?B`TAD)`D)>o*m T[XU s-D?C`TA"D)`D)>om-U<D`h3i ]DW?B`TA"D]dN@>EDOACn\NOW`TG-]_GYACFeGY`kN%#¢?6G mYD`.m?CF&gTRN@G-N@nTG&gD>oD)F&GYNc>@O^mGyPSRhD)N@O?C`h]l?bN@nG&gh?COW`\No]l>@G)DBmpnG)i>c?CF < [OWNcn.D`\ Nd\ghG?)lghDNcn¡ULkO`kNcGYAC>EDNcOW`TA:N@nTGikO GY>cGY`\N@O^D)[]_T]_N@GYF @s ?B` G)DCmon.ghD>cN [ON@n N@nTG DgTgT>c?CgT>cO^D)N@G&ZBDRTG-? ¢O`hmzG6Gemz?BF&gTRTNcGN@nG >cG)]dNc>@O^mN@OW?B`?N@nTGeik?CF DOW`]jNc?N@nTG gT^D)`TWG Z \ U GyDCmonghD)N@nOQP ]X`T?) ghD>EDF&GYNc>@OYG)iL\?C`TNd

(228) ?O`hikGYghGY`hiD`\NgD>oD)F&GYNcGY>o]U D`hi `?F&?B>@G[N@n>@GYGbLhG)mYDR]dGXNcnT?]_GXN@nT>cGYGID>@GbWO`TG)iNc? XLk-DlWO`TG)D>G)PRhD)N@OW?B`¡G +OW>E]dN%U 6Gl`TGYG)i]_?CF&Gli\Gzh`TON@OW?B`h] ]dG%G +<OWACR>@KG Y E . ) . .10-2 .

(229) . . .

(230) 4 . .

(231) . . . .

(232) . +<OWACR>@GKY ?>D ; =%#89 ?65 ; 3 D 9 ; 3 1&23S= ; ?A= 9 1. O^][N@nTGlgh?CO`kN ]dOW`GT m?]0<o O^]6NcnTGlgM?BOW`\N 6]dO`G mz?]4<o 0 0>=

(233) O^]6NcnTGlgM?BOW`\Nb]d\F&F&GYNc>@OQm6N@? 0 0>=

(234) l >% N%kN@nG?B>@OACOW`0+1 ? 0 0>= 6l ©>Y©NYkgh?BOW`\N 0 >=!OQ]6N@nTGlgh?CO`kNb]_kF&FeGYN@>cO^m6N@" .0 0>= O^]6NcnTGl>oDY >c?CF N@?)[D)>oiT]6gh?V]dOWNcOWZG "\¶zm ??B>oikO`hDNcG)]zUT?)?C>cOWGY`\NoD) N@O?C` ] >= E ).

(235)

(236)

(237)

(238)

(239) ! #"$ %& '( )*+-,. /0

(240) 1#23 456879 :; <=. . sYu. 0 0>= &

(241) O^]6N@nG>EDY >@?BF ghD)>oD)WWG%¡N@? . >= o 6Gi\GY`T?CNcGN@nTG mzOW>EmzWGHb?C>NcnTGikOQ]@m X?)ImzGY`\N@>@G-N@nG ABGY`TGY>cO^mgM?BOW`\N*Z7Dì >oDBikOWRh]br.T. ¤´<³.A @ G

(242) ikGY`?CN@G T,BU T D6ACGY`TG%>@O^m<ghDNcn?N_kghG TVUXT9%6nTGghD>EDF&G%N@GY>E]#]@D)N@OQ]ðlN@nTGâ>@GYQDN@O?C` . k ^Ø¡6GIGYGYgH .4 %.DB]O`hikGYghGY`hiD`\N6ghD)>oDFeGYN@GY>E]zUN@nGf?BgTN@OFDOWN_mz?B`hikON@OW?B`h] N@nTGY`"mz?B`h]dOQ]dNbOW` S . ] D)`hi . W r 0 +T?BWW?)[O`TAlN@nTG6h>E]dN

(243) D>EmCUCNcnTGf>cGzGY>cGY`hmzG

(244) gM?BOW`\N >@G)DBmpnG)]N@nG[gM?BOW`\N?<m??C>oi\OW`hD)N@G)

(245) ] ]_OW` . mz?V&] . 6nTGY`?BW?b]6OW`TGj]dGYABF&GY`\.N U UhD`hiN@nTGlgh?CO`kN[>cG)DCmonTG)i-O^] ]_OW` . -%mz?V&] . mz?V&] . -%]_OW-` . +OW`hD)WUTDYN@GY>[QDC]dNbD)>oKm T \ $,4U .O^]6?C`"N@nTGlgh?CO`kNbi\Gzh`TG)i&L\ ]dO` . &%<mz?V ] . O]dOWO` ]dO` . mz?V ] . &%<]dO-` . Omz?&] . mz?V] 6nTG)]dGemz??B>oikO`hDNcG)]mYD)`LhGe]dOF&gTWOòhG)i#Uh]_?N@nhD)N

(246) G ?BLTNoD)OW`:N@nTG TVUXT¤ik?CF DOW`:DB]XN@nTG ]dGYN[?)gh?COW`\No#] |?)

(247) mz??B>oikO`hDNcG)] ]dO` -%<mz?&] . [OWN@n . ¥ ] T)§

(248) mz?]4 -%<]dOW` . ¬r %. 6nO^]ik?BFDOÒQ]]dn?[`.?B` +<OWACR>@G{\; SX]lOW` ¥ ¢ « {CrC§¬U ONOQ]]dNc>oD)N@O G)iLkNcnTG&O^]_?C ghD>EDF&GYNc>@OQm[mzRT>@ZGy] DC] ?CW?)b]z nTGY` .lO^] "\G)i#U %XmYD)ìkG)]cmz>@OLhGX D)`hi gh?CO`kN ?CW?)b]6N@nTGlnhD) WOW`Gf[ON@n?C>cOWGY`\NoD)N@OW?B`NoD-` .eD`hi]dNED>cN@OWÀ-DNbgM?BOW`\N hK9G)mOWgT>c?\mYDWU [nTGY` % O^]f "\G)i:D`hi .ZBD>cOWG)]X[ON@nTO`>ED`TABG ¥ ] T)§¶U#gh?CO`kN ikG)]cmz>@OLhG)]XD` D>om? mzOW>EmzWGX?)mGY`kNc>@G D)`hi>EDCikORh#] %S6nTG)]_GmzRT>cZG)]6D)>@G1DQ]d?-O^]_?C¬ikO^]_NoD`mzG1mzRT>@ZGy]?C>[N@nO^] Nd\ghG?9wfRTLTO`h]XghDNcn #?B`]_Rhmon:DmOW>omWG&U ."D`hi %&D>cG "\G)i#U¡]_?D)>@G .Dì N@nTGlghD)N@nGY`TABN@n[nTO^monO^]6G)PRhD)#N@? $. % ¡ C C&>. TVUXT. . . . . . . . . . . . .

(249) szH. L%&"

(250) %. 0

(251)

(252) %&G )* <. \. . . < . . +OACRT>cG{GTVU;T 2 52: ; 3. Uâ´<³ .A @ L 6nTGmYD)^mzRTQDNcOW?C`]D>cG]dOF&OWQD>XNc?N@nTG-gT>cGYZkO?CRh]1mYDC]_G:GikG%`T?CNcG ,5U @ N@nTGeghDNcn ?1N_kghGJ U 1UNcnTGghD)>oD)F&GYN@G%>o]-]@DNcO^]¶kO`TANcnTG>cGY^D)N@O?C` . r 0 :Dì N@nTG mz?C`hi\OWN@O?C`h] . ¥ ]Gor 0 H§ Dì % \6nTGY` UCN@nTGIL Uâ¤ik?BFDOÒ^] N@nGb]dGYN?<gh?BOW`\No] ?

(253) mz??B>oikO`hDNcG)] ` &%<mz?V ] . [OWNcn . ¥ ]Gor 0 )§

(254) O mz]_?OW ¬u 4] &%<]dOW-` . %. C C1D. . . . . . . &. 8\. . < . +OWABRT>@G-s] LUâ 2 52: ; 3. .

(255)

(256)

(257)

(258)

(259) ! #"$ %& '( )*+-,. /0

(260) 1#23 456879 :; <=. sYt. 6 nO^]Xik?BFDOÒQ]fD)^]d? ]dN@>EDNcO hG)iLkNcnTGOQ]d?CghD)>oDFeGYN@>cO^mlmzRT>cZG)]

(261) ]dG%G+OACRT>cG&s5]Ho 6nTGYD)>@G[nhD) WO`TG)]¡? ?C>cOWGY`\NoD)N@OW?B`HNoD)`-.D)`hi]dNED>@NcOW`TAjDNgh?COW`\N UY[nTGY`.OQ] ABOWZGY` ¨ RTNl[nTGY` % O^]9 "kG)i U NcnTGYD>@GeD>EmY]X?9mzOW>EmzWG1?ImzGY`\N@>cG Dì2>EDCikORh]%SGSX]XO`N@nTG gT>@GYZ\OW?BRh]mYDC]_GUN@nTGy]¸QDC]_N6mRT>@ZG)]âD>@GIDQ]d?lO^]_?C¬ikO^]_NoD)`hmzGImzRT>@ZGy]â?B>ghDNcnh]?)¡N_kghGbL Uâ UXT£ @ ´ TVU ´<³ . A @ C C C L 6nTG)]dG

(262) N_6?lik?BFDO`h]¡D>cGb]d\F&F&GN@>cO^m¡[OWN@n1>@G)]_ghG)mzN<N@?ID "\O^] \z¢?b6G6[OW\mz?BF&gTRTNcGN@nTG G)PSRDN@O?C`h]b?[NcnTG-L UXT ik?CFD)OW`¡U Dì2NcnTG?BN@nTGY>1mYD)`LhG-ikG)ikRhmG)iL\]_kF&FeGYN@>cG ikGY`T?BN@GlN@nTGIghDNcn- ,=U T Uk[nTGY>cGXN@nGXghD>EDF&G%N@GY>E] a_Rh]_N6nhDYZGXNc?-]@DNcO^]¶ S . ¥ ]Gor 0 ¥ 6nTGY`¡UN@nTG]dGYN-?1gh?CO`kNE]|>cG)DCmonTG)i.LkV ikGy]@mz>cOWLTO`TADghD)N@n ?1N_\gMG"L UXT nhDC]-N@nTG ?CW?)[OW`TAghD)>oD)F&GYN@>cO^mfGyPSRhD)N@O?C`h] ]_OWO` -%<mz?] . .,r ]_OW` . DYZG)m . ¥ ] or 0 ¥ H

(263) m?4] -%]_OW` . .,r m?] . %. . . . . . . . . . +OACRT>cG sBs. LUXT 2 52: ; 3. ^¶N

(264) O^]NcnTGXgTQD`TG$Z \[F&OW`\Rh]NcnTGXO`kNcGY>@O?C>?¸mzOW>EmzWG ^¶`&NcnTO^]

(265) mYDC]_GUk[nGY` .O^]¸ "kG)i U gM?BOW`\N# i\G)]d>cOWLhG)]6DnD WO`TGXNED`TABGY`kN

(266) N@?-mzO>omzG UT]_NoD)>@N@O`TA>@?BF NcnTO^][mOW>omWGbDì ?¥ b?C>cOWGY¥ `\NoD)N@O?C`VNoD)` .h¡K[G)mzOWg>@?\mYD)WW"[nTGY` %&O^]f "\G)iD)`hi .ZBD>cOWG)]XO`NcnTG O`kNcGY>@ZBD) ] Er 0 U\gh?COW`\N- &ikG)]cmz>@OLMGy]N@nGmOW>omWGX?)mzG%`kNc>@G D)`hi>EDCikORh] % H< ,)*

(267) .¢\F&F&GYNc>@OmYDòUMNcnTW G TVUâ7ik?CFD)OWÒQ]NcnTG&gTQD`TGWZG\F&OW`\Rh] N@nTGlO`kNcGY>@O?C>6?)

(268) mzO>omzG . . .

(269) s. L%&"

(270) %. 0

(271)

(272) %&G )* <. _]_?C¬ikO^]_NoD`mzG1mzRT>@ZGy]¸?C>bghD)N@nh][?âN_kghG1LUXT :G[OW[gT>c?)ZGNcnhDN-N@nG)]dGmzRT>@ZGy]D>@G"OW`\Z?CRTN@G)]l?1mOW>omWG « G%N Rh]-mz?B`h]dOQikGY> Nd

(273) ?&gh?CO`kNE] D)`hi0 ?C`:N@nG-]@DFeGO^]_?CghD>EDF&G%N@>@OQmmzR>@ZG[O N@n % "\G)i#UhN@nhD)NOQ]fD mzOW>EmzWG[?)mzG%`kNc>@G D)`hi >EDCikORh] % H k6n\Rh]6NcnTGXJ U;T.ghDNcnh] , 4 U T 4 Dì , U T >c?CF < G)DCikO`TA>cG)]dghG)mN@OWZG%WNc ? Dì UknhDYZGXNcnTGl]@D)F&GbWGY`TABN@n ?OW`TGl]_GYACFeGY`kN% SX][]dnT?)[`"?C` +<OWACR>@Gs%rkUhN@nTG1ikO #G% >@GY`hmGXLhGY N_6GYGYèN@nTGlN@?BNoD)GY`TACNcnh] mz?CF&Gy]â>c?CF« NcnTGlD)>omY]UTDì O`&N@nO^]6m%DC]dGlNcnTGl]dRF ?) NcnTGlD>EmY]?) O^]W?B`TACGY>

(274) N@nhD)`N@nTG ?C`TG1? GYN[Rh][ikGY`?CN@G 1. . N@nTG1D)`TACGOÀC>oDY&?B`mzO>omzG UT[nO^mon&O^][D)^]d? G)PSRDhN@?lN@nGbikO GY>cGY`hmzG k¢?1N@nTGbikO GY`hmzG[?)¡WG%`TACNcn LhGYN_6G%GY` D)`h"i O^] ,r O^]XD)^]d?NcnTG&D)`TACGOWÀB>oDY?C` mzOW>EmzWG #NcnTG-]dG%ACF&GY`\Nb?[gDN@n O^]XghD)>oDWGYâDì G)PSRD<N@?e]dGYABF&GY`\N 6nTO^]bDQ]d?-nT?CQ iT ]?B>XN@nG]_GYACFeGY`kN

(275) ?

(276) ghD)N@n D`hi]_GYACF&G%`kN ¢V?N@nGXD)`TACGXLhGYN_6GYGY`-]_GYACFeGY`kNE] D)`h i OQ] \6nTGY`¡Ugh?CO`kN & LRTOWN DC]6N@nGXgh?COW`\N[i\O^]dNED`\N>c?CF Lk-,r Dì kO`TAl?C`N@nGX]cDF&GbWO`TGfNED`TABGY`\N[N@? DC] UO^]6]_Rhmon NcnhDN[NcnTGfgDN@! n & ?<N_kghGIL UXT nhDB]NcnTGl]@D)F&G[WG%`TACNcnDC]ghDNcn ^¶`hikG%G)i N@nTG1D>EmY][? & D`hi D)>@GlG)PRhD¬UTD)`hiNcnTG1]dGYABF&GY`\N6? & OQ]6G)PSRD#Nc? % .,r ^. . . . . . . ! . 40. 20. . . . . -40. . . . . -20. 0. 0. 20. 40. 60. -20.

(277). -40. -60. +OWABRT>@G-s%r 587 8; D 236= 1 =%# ? 21 5 ? D61 LUXTR5234D /21 ? ; /ED 5 ?. 0 Q u ¨ "ikGh`TOWNcOW?B`?D)ÒW`\Z?CRTN@GyzU & O^][?C`NcnTG]cDF&GlO`kZ?BWRTNcG?)

(278) mzO>omzG DB]& 6nkRh]UNcnTG&O^]_?C¬ikO^]_NoD)`hmzGmzR>@ZG)]f?C>1ghDNcnh]?)XN_\ghG&LUXT D>@G-OW`\Z?CRTN@Gy]j?)ImzOW>EmzWG 6nTGfFeOW`TOFRTF¤WG%`TACNcn?<]_RhmonghDNcnh]OQ] k U\mz?B>@>@Gy]dgh?C`hi\OW`TAlN@?lghD)>oD)F&GYN@G%>o] ] 0 ]GT â Dì. N@?]_OW`TABWG-gh?COW`\N ¡GemYD` `T?CNcO^mzG-N@nTG%`¡U¡N@nhD)N?C` nhDòØOW`TG NcnTG GY`TABN@n:?ILUXT úYùfø×)È Í ï)Í_ì¶ÎBËÐyÖ¶ïBøØë ÒzÖdëõËoÎYÓ\ø¡Ö¶ÒpÒzôMÎ)ËÞøØìÞÏBøØìÖ¶ëÔøØÎëÔ[ÒÎbøØ×BÒpËoôø¡ËpÒzÎ[Î)ëõÍ ÎYÌzö ÒÒzÓÔÏ)Ï)øÓòÐ[Í¡Òpö¡ôì¬Ë

(279) ËpïXÖðëõÒì¶Ö¶ì¡ÓÔÍ<Ï)ÎYëÔÞ#ö¡øì¬×)ËpÍ ïlôËoÒìÓÔÓÔÒzÒoÏ)ö¡ÎBëÔÐfÎ

(280) ø×àYÍ¸ëÔøhÖðëÔëõÞ#ì¶Ö¶øÓÔ×)ÍÍ ó Ö¶Ï)ìÌzÍÐYÍ_Þ¬ÖðìëÔúBÍ@Ð .

(281)

(282)

(283)

(284)

(285) ! #"$ %& '( )*+-,. /0

(286) 1#23 456879 :; <=. s¦. ghDNcnh]OQ] ikO^]cmz?C`\N@O`kRG ?CW?)[OW`TAjD`&O`kZ?BWRTNcGUYN@nTGbghD)N@n-WGY`TABN@n-FDGy]D6a_RTF&g1? r 0STU ]dOW`mzGlghD>EDF&GYNcGY> .G)PRhDQ]]|?B`D)`hiLhGY? .)UhDìN@G%`hiT]6N@?er 0:DLh?)ZGlOWN% T£´<³ . A @ C C H T 6nTGghD)N@n"O^][ikGY`?CN@Gyi T ,T SI]6`T?CNcO^mzG)i&O` ª ?BF&F&GY`\N

(287) uksCUT6GlnhDYZGXN_

(288) ? gh?]c]dOLTWG GYRhP\DN@O?C`h] OW`T\OW`TAbN@nG)]dGbN@nT>cGYG6gD>oD)F&GYNcGY>o]Nc? CGYON@nTGY> . X?B> .X

(289) r 0 k; SI]@]d?\mO^DNcG)iNc?N@nG&?CgTNcOWFD)WONd"mz?B`hikON@OW?B`h]zU<6G-ACGYN1N@nTG-?CW?)[OW`TA"ZCD)>@OQDN@O?C` OW`\N@GY>cZCD)^]?B>[N@nTGlOWìkGYghGY`hikG%`kN[ghD)>oD)F&GYN@G%>o] "D`hi .|NcnhDNb6GlGYG%g . D)`hi ¡§ 0 or 0 ¥ D)`hi . ¥ S or 0 ¥ ) ?B> ¡§ 0 ¥ D)`hi . ¥ 0 or 0 ¥ ) . r 0H kU ¥ ] T ¥ D`hi . ¥ r 0 or 0 ¥ 6nTGghD)>oD)F&GYN@>cO^m[G)PRhDNcOW?C`]9?) gh?CO`kNE]9O`N@nTKG T T ik?BFDO`D>cGNcnTGY`"N@nTGX?CW?)[OWÀ ` I.r ]dOS` . 0 ..r ]_OW`

(290) mz]_?OW 4] I.r mz?] (. 0 @.,r m?] [ON@n . ¥¥ r] 0 T ¥ Gor 0 ¥ ?B> . ¥¥ 0 0 ¥ Sor 0 ¥ ?B> . ¥¥ S or0 0 ¥ or 0 ¥ ¬t . . . . . . . . . . . . . . . . . . . . .

(291). . +OACRT>cG s%u TT 2 52: ; 3. :G?BLT« NoD)OW`"N@nT>cGYG1]dRTL ik?BFDO`h][mz¨ ?C>c>@G)]_gh?C`hikO`TA&Nc? NcnT?]_GN@n>@GYGlZBD>cO^DNcOW?BÒW`\N@G%>@ZBDQ] ? S .o GYNRh] FD)G[N@nTGYF mzWGyD>Y RTNh>E]dN6

(292) GbmYD`-`T?BN@O^mGfNcnhDNgh?CO`kN O^]mz?BF&F&?C`.

(293) s5Y. L%&"

(294) %. 0

(295)

(296) %&G )* <. N@?lD)WT?)#NcnTGYFU)]_OW`hmG6OWNâmz?B>@>@Gy]dgh?C`hi]¸Nc?lN@nTG

(297) WOWFeOWN . r 0 UVD`hiNcnhDN Oò .jOQ] "\G)i#U)gh?COW`\N ikGy]@mz>cOWLhG)]6D)`D>Emf?âmOW>omWG6?)âmzGY`\N@>cG Dì >EDCikORh]6r, r.r mz?V]&.M\6nTG)]_GlD>EmY] D>@G1D)^]d?OQ]d?B¶ikOQ]dNED`hmzGjmzRT>@ZGy]zU\]dO`hmzGX[nTG%` . O^] "\G)i#UT]_?O^]N@nTGl]_RTF U\nTGY`hmzGIN@nTG ghDNcn GY`TABN@n

(298) . XOQ]mz?B`h]dNED`\NY :G&F-Rh]dNl`T?BN@O^mG NcnhDNNcnTG&ghD)N@n.WGYÀCN@n O^] OW`\ZGY>o]_GYWgT>c?Cgh?C>cN@O?C`hD) N@?NcnTGl>oDCi\OWRh][?âN@?V]dGmOW>omWG)] sC ¥ ] T ¥ D`hi . ¥ r 0 or 0 ¥ 6nTGmz?B>@>cG)]dgh?CìkOW`TA]dRTL ik?BFDOÒ^]XNcnTG >cGYACO?C`LhGYN_

(299) GYGY`N_6?D>om%]j?)ImzOW>EmzWG 5 D`hi ?>EDCikORh]f,r TU#D)`hi>@Gy]dghG)mzNcOWZGY ?)

(300) mzGY`\N@>cG D)`hi 6]_GYG +OWABRT>@GeszHH o nTGY` O^]9 "kG)i UMNcnTGO^]_?CghD>EDF&GYNc>@OQmmzRT>cZG)]bD>@Ge D>EmY]f?)bmzO>omzG)]6?mzGY`\N@>cG D`hi:>oDCi\OWRh]1.r TU ]_NoD)>@N@O`TAD)Ngh?CO`kN <=?BOW`\N O^]l?C`.D"mzOW>EmzWG-i\GY`T?CNcG)i ? >oDBikOWRh]br.eD`hi&OWNE][mz??C>EikOW`DN@Gy]fD)>@G

(301) mz]d?O`] .r .r mz]d?VO` ] . . . . . . . . . +OWABRT>@G-szH #2B 252: ; 30= 5 ? ?A1 5 3 8; 3 0D 5 ¥ ] T ¥ 23

(302) . ¥ r 0 Er 0 ¥ rk ¥ 0 ¥ D`hi . ¥ 0 So r 0 ¥ 6nTO^]I]dRTL ik?BFDOÒ^]bN@nTG1>@GYABOW?C`:i\GYWOF&OWNcGYi L\N@nTGvD>EmY]f?mzO>omzG D`hi & ? >oDBikOWRh]br.T U Dì>@Gy]dghG)mzNcOWZGY?

(303) mzG%`kNc>@G D`hi ]dGYG +OWABRT>@G-sYu oT nGYÒ^]. CA OZGY`¡Ukgh?BOW`\N# &i\G)]@mz>cOWLhG)][D)`D>EmX?

(304) mzO>omzGf?)

(305) mzGY`\N@>cG uk ¥ 0 or0 ¥ GYN . ¥ Sor0 ¥ G1ACGYNIN@nTGv]d\F&F&GN@>@OQmf]_RTL ik?CF DOW`"?

(306) N@nGgT>cGYZkO?CRh][?C`G[OWNcn>cG)]dghG)mzNbN@? D "\O^] \ ^¶NO^] NcnTG>@GYABOW?B` LhGYN_6G%GY` D)>omY]&?|mzOW>EmzWGD`hi ?)>oDBikOWR]r,TU[Dì >@G)]_ghG)mzN@OZGYW?)

(307) mzGY`\N@>cG Dì ! ]dGYG +OACRT>cG s%u E . . T´<³ .A @ GbikG%`T?CNcGfNcnTG[ghDNcn& T,Y UD)`hi-DC] OW`NcnTG[gT>@G%ZkO?CRh] m%DC]dGVUCN_6?Xgh?]c]dOLTOWOWN@OG)]?\mYm¨ RT>

(308) N@nTG[ghD)>oD)F&GYN@G%>o]<]@DNcO^]¶GYON@nTGY><N@nG6G)PRhDNcOW?B` H . r0 f?B>. k RTN C C Q. .

(309) sY{.

(310)

(311)

(312)

(313) ! #"$ %& '( )*+-,. /0

(314) 1#23 456879 :; <=. OW`¬DCmzN%USNcnTG[h>o]_N6m%DC]dGIACOWZGy]`T?]_?CRTN@O?Cèmz?CF&gDN@OLTWG

(315) [OWNcn&N@nTGb?CgN@OWF DWON_lmz?CìkOWNcOW?C`]z CRh]dNl>@G%FDO`h]9NcnTG-mYDB]dG-[nTGY>@G . kU GYOWNcnTGY>b[OWN@n ¡§ 0 V Er 0 ¥ Dì . ¥ Gor 0 ¥ Uk?B> ¡§ ] 0 ¥ Dì . ¥ 0 or 0 ¥ 6nG Ti\?CFD)OWÒ^]6NcnTGY`N@nTG1]_GYN[?âgh?COW`\No][?¸ghD>EDF&GYNc>@OQm9G)PRhD)N@OW?B`h] O]_OW` I.r ]dO` I.r ]_OWS` (. 0

(316) mz?4] I.r mz?] I.r mz?] (. 0 ¡§ 0H Er 0H ¥ ¡§ ] 0 ¥ [OWN@n ?B> . ¥ 0 Er 0 ¥ . ¥ Gor 0 ¥ . . . . . . . . . . . . . . . . . . . +OWABRT>@G-s%t T 2 52: ; 3. nGYÒ^]6ACOZGY`"D`hi .|ZBD)>@OWGy]zUTgh?CO`kN- ikGy]@mz>cOWLhG)][D`D>Em?¸mzO>omzGX?>EDCikORh] r.D)`hi-mzGY`\N@>@G V6nTO^]gh?BOW`\N ? mz??C>EikOW`hD)N@G)]

(317) Omz]_?VOW`]0 r.r.mz]d?O` ] OQ] DQ]d?X?B` DmzO>omzG ?<>EDCikORh]r.Dì&mzGY`\N@>cG <]dGYGO+OWABRT>@G1sYto Sb`hi|[nGY` .OQ] "kGyi#U ikG)]@m>@OWLhG)]-D` D>Em?mzOW>EmzWG&?)1mzGY`\N@>cG D`hi.>oDCi\OWRh]-r. r .r mz?V]&.T66nTGy]dGmOW>omWG)] D>@G D^]_?OQ]d?C¬ikOQ]dNoD)`hmzGemzRT>cZG)]zU¡D)`hiNcnTG gDN@n WGY`TABN@n¡U<DB]j?C>lN_\gMG T T[UOQ]jO`kZG%>o]dG%W gT>@?BgM?B>@NcOW?C`D Nc?N@nTGl>oDBikOWR]9?) NcnTG1mzOW>EmzWG sC ¥ 0 or 0 ¥ Dì . ¥ or 0 ¥ 6nTG1]dRTL ik?BFDOÒQ]6N@nTG1ikOQ]@mX?¸mzGY`\N@>cG D`hi>oDBikOWRh][,r T rk ¥ ] 0 ¥ D`hi . ¥ 0 or 0 ¥ 6nTO^]b]dRL#i\?CFD)OWÒQ]f]_kFeF&GYN@>_OQm9Nc? NcnTGlgT>@GYZ\OW?BRh][?C`TG1[OWN@n">@G)]_ghG)mzN[N@?eD "\O^#] \zU ]d?-OWN[OQ]6N@nTG1ikOQ]@mX?¸mzGY`\N@>cG D)`hi>EDCikORh][.r T . . . . . . . . .

(318) r]. L%&"

(319) %. 0

(320)

(321) %&G )* <. b· ?CN@OQmzGlN@nhD)NXN@nG)]dGvik?CFD)OW`h]6O`kNcGY>o]_G)mzN[G)DBmpn"?CNcnTGY>ID`hiik?-`T?BNXghD>cN@ON@OW?B` ZG\

(322) ]dGYG +OWABRT>@G"s o ¨ RTNlN@nTG%:]dnhD)>@G-N@nTGe]@D)F&G g>@?CghGY>cN_ NcnTGYD>@G ikGzh`TGyi2L\N_6?ghD>ED F&GYN@G%>o]zUVD`hi&N@nGXO^]_?CghD>EDF&GYNc>@OQmfmzR>@ZG)]

(323) mz>@G)D)N@GbN_6?]_G)mYD)`kN?CWOQDNcOW?C`]6?<N@nGlik?CF DOW` U gT>@?)Z\OW`TANcnhDN6?B>[D`\&gh?CO`kN

(324) OW`&NcnTGlOW`\N@GY>cOW?B>?)DN_\ghGlik?CF DOW` USNcnTGY>cGXG "\O^]dNE]6DRTÒ^PRTG ]dnT?B>@N@Gy]dNbghDNcn?âN@nDNbNd\ghG ÛcÚ ç. ÛÛ . Ú Û. cÛ ÊÜ ã . Û . ä. +OACRT>cGs G !.5 : ;A3; 3 D 1? E1 = D ;>523%5C?< 0 Q H. s LUâf¬LUXT¸ TVUâ sBs r L Uâf¬ Tf TVUâ u H L Uâf T Uâf¬ TX TJT t Tf T Uâ ¦ Y Tf T# T¸ TVUâ { s5] Tf T# T %s rcsYu . . .>9. 0. . '. ¬LUXT TVUâ âf¬Tf¶JU;T âf¬LUXT¸¬Tf T6T f¬L UXT f T# T¸¬L UXT TVUâ. . . . . . TVU;T LU LU T T LUXT. G1]dNcOW#nhDYZGXNc?-ikG)mzOQikGX[nhD)NfOQ]6N@nTGlN_kghGX?) NcnTGl?CgTNcOWFD)#ghD)N@nOW`G)DBmpn>cGYACO?C`?[Z \ mz?)ZGY>@G)i-Lk&Fe?C>@GIN@nhD)`?C`Gi\?CFD)OW`¡.

(325)

(326)

(327)

(328)

(329) ! #"$ %& '( )*+-,. /0

(330) 1#23 456879 :; <=. rks. : GD)>@G]_RT>@G-?bNcnTG&?CgN@OWF DWON_?)bN@nTG-[nT?BWGWTVUXT£ik?CFD)OW`?C>lN@nGWTVU;T¤N_\gMGVU GYZGYÒ ?CNcnTGY>1ik?CF DOW`]D)>@G-OW`\N@GY>E]dG)mN@OWÀ&OWN% ^¶`hikGYG)i U#N@nTOQ]lik?CFD)OWÒQ]j?BgTN@OFDâOW`:N@nTG K9GYGyiT]6D)`hi¢nTG%gTgmYDB]dG SX]NcnTGXwbRTLTOW`][]dR" mzOWG%`kN¬D)F&OW?)<Nd\ghG)]OQ]O`hmzWRikG)iOW`-N@nTG K9GYGyiT]lD`hi ¢nTG%gTg?B`TG bG "TmGYgTNXNcnTG +* gDN@n]zU[nO^monD)>@G]_nT?C>cN@GY`TGyiN@? U U ghDNcnh]zUh[nTGY>cGNcnTG1]d\F Lh?B

(331) UF&G)D`]6DFD` lRTZ\>@G oUhD-mz?C>c>@G)]_gM?B`hikO`TA&?CgN@OWF D#>cGYACO?C` ?C>6NcnTGlK[GYG)iT]D)`hi¢nTG%gTgmYDB]dGbO^]6DX?C>cN@OW?B>@Oh?CgN@OWF DTO`&N@nTGIwfRTLOW`h]

(332) mYDC]_GT¢?