Exact and efficient computations on circles in CGAL and applications to VLSI design
18
0
0
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Exact and efficient computations on circles in CGAL and applications to VLSI design Pedro M. M. de Castro — Sylvain Pion — Monique Teillaud. N° 6091 Janvier 2007. ISSN 0249-6399. apport de recherche. ISRN INRIA/RR--6091--FR+ENG. Thème SYM.
(3)
(4)
(5)
(6) "!#$ %'&() !* ,+#-/.10
(7) 2
(8)
(9) ) (
(10) !3 4/065879
(11) !:;. <>=@?BADCEGFEGFH?B=JILKNM OPAQC RHS:T:UWV KNXZY[<2XZCNY R E[C\YBXZ]_^B=a`b=cX UZU Kd^B? efhgQiLj$kclnmpoqksrutwvxg iLjDtytwrsizd{@|~}chjQt {j v tynjQ{iLjv x} yhN{xvhj2xjDfhj fhjN(@
(12) o@cs}j y@c o 8¡@jQt ∗. †. ‡. ¢ £(¤Q¥ ¦¨§h©¥ª$«\¬_:®a¯°H±²y³\´uµ·¶µW¸¹±ºN¶»H¼½±²L½ µW¾'¿2À>» Ác±¨¾'¸ÂµÄÃs²ÅÆB¸¹Ç ¾x¶¾'¿È }t$|x¡@jy{||jQ'v }~{@É{ÊË¡jQ{iLjv x}{@zujQv tQÌchv twvx 'v h jQt86|¡{ }~vxfhiÉtQÍ «\¬::® h j cvx|rÎ{Ï\j t$iL{@twvx|rÐÊÄhvx}{|~}~vx}jQt8ÊÄ{@|}~jQ8{zhjQ'vtÒÑÄN{}@vt ÌtwjQ¡iLj cv tQÌ |}~jQtQÌuvx }h¡|jQtQÍÍ~ÍÔÓ'Í efhjÕ twvyjQ tx}{
(13) {ÊLÖjQxhjQ|ËÊÄ{>} |~jDtyÒ }~h|> t}×ØÙtyxjDj cv |~r"xjQ|~jDtxjQ"}~ «\¬::®Ú Í hÍÛÐj$twf{¨Ù }av fh}t>djQn Px}jvr
(14) {ÊHv jQfh}chjDtyv f¨vnÙj$vxjQtwvxjDÜv { }i8x{¨@j2vxfhjjÝ}j drÒ{ÊHv fhjLØG }~|bÖjQxj |ZÍ>efhjDtwj }iLhx{¨@j iLj cvty j i8{vx}¨¨vxjDÒzsr
(15) hh|}Q¨vx}{dtvx{Þ ®cßQà hjQtx}~¡@_ÌdÒxjD|ËÞ ®sßQà }udtv x}|(h¨vÉ j2twjD
(16) vx{ÉiLjQ@twxj v fhj2}~iL@'vy{Ê:vxfj vxjQfh}chjDttxjQ vx{ÉjQhfdjnvxfh}tÖ@j hj |ZÍHefhj }~iLh {¨jQi8jQcv tÙ}~||_zNj2}~cv j ¡¨v jQ }~ «\¬_ ®ÉÚ Í Ú Í áÜâcã\äxåæ ¦¨ç(¤ª }iLh|j iLj cv vx}{_ÌjÏ\jQ'v }~@j ¡j {@iLjvx rÌu|~¡@j zh}bshizdjQ tQÌhx@jQt. û021·éP13
(17) ÷þè_4!5÷éP5BêÔ68ë7üdìË9;î¹í'í:<7îW¹ï÷9;:>êÔòB=ëN?2öð¨@APñ:CøPîÄBòZ÷Dêóîñ5 ôÔ\ô õíëZöPòWîWðDñðí'ò îÄòW :÷wí>øbú¹ùûQõè òW !éP÷ "ú¹ûè
(18) #$%ü 'îWí'&(ý':îWñû)þ þ&(ôÔ÷ ý'íí'ÿî¹ê òWòZéPéD÷ þ òë(Wéÿí'¨î*îZËñþí'þ÷ ìËðDôÔí'÷î¹+2ïûQüé¨îWñí'ðý'îW÷ñëBþì:þê òZ÷_é,íÿ@÷òWî¹éPòWê ÷ -¨÷ø
(19) òWñí'ëËðí'ñôÔí'ûQýè õ$ñNP ü ø, Q
(20) öPdþè ÷î¹ (ê.ðë/÷ è:éDêÔëì\í'îWïì_ñëøPí P÷ì:éPêÔôÔ÷üu÷øPî¹,í E)FGE)F@øPH÷ ËñëWòWîWí ì_ñëìËí'î¹ïQ.ê Dýñ ò!ú (:Iú &FA\öPî¹îW÷ òñøPøDîW÷ëZë J\÷ òZ÷îí(ÿ \í'þðPöQòZ÷îû êÔ÷ ÷wë K (Pê L÷î¹ëZêÔø¨ñøD÷¨÷øP÷îWñôuøP÷üu÷îM¨ñþùPöíKON\îWñPêÔô>F 3QQO7SR878T/B
(21) :C?2U38VG:CW2= ∗. † ‡. XY DSZ26[T/B
(22) :>\T]B8R89]30^T6G:_T/B2=T6
(23) :>U= 02113
(24) 4!55```^aS9]3
(25) :_T/B2=T6G:>U=85@2V2]QV1=OTS7S62512V6Q^5 XY DSZ26T/B
(26) :>\OT]B b ] B^Tc?8VG:>d2V[TDD6S?2e2R89]30^T6G:_TB2=T6G:>U= 02113
(27) 4!55```^aS9]3
(28) :_T/B2=T6G:>U=5S@2V2]QV1=^TS7S685S12V6Q^5 b ]B^Tc2?8VG:>d8V[TD2D6S?2e. Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex (France) Téléphone : +33 4 92 38 77 77 — Télécopie : +33 4 92 38 77 65.
(29) + )
(30) )! !3 !3!: "&
(31) !# &() !
(32)
(33) !1+#-/.*0 2
(34)
(35) ) 2
(36) ! )
(37) %
(38) '&B "(!
(39) &B !
(40) { zh¤ j v tQÌBu ª jt v xdzh'vx}zh|~x}jD{t2v fhugQjchuj {«N ¬: :jDt2®jv$¯ ° ±
(41) ²y|³\¡{@´uxµ·}~¶vxµWf¸¹±i8ºNjD¶¨t »8¡ ¼yQ{½±¨i ²É½v xµZ¾'}c¿ÐhÀ>jQtQ» ÍÁc±¨«\¾'¸Â¬_µÄÃs:²® Å
(42) {ÆBc¸¹v Ç }~¾xjQ¶¨@¾'v$¿È @'{v hÏ\jx|j×|~jQhiLhj jacv|jQ t ¡twjajQc vx{}j||~|jD|~jQ'i8vx}{c v ujDtÊÄ{cv }~{@h|}~v QtN{yujQt{@zujvt|~} Q}~ jQt2ѹd{@}~cvt Ìtxj ¡@iLj cv tQÌuux{@} v jQtQÌsvx }h¡|jQtQÍÍ~ÍÔÓ'Í. ÎhxjQiL}~gQxjÜ@j tw}{
(43) h h{¨rc d{@h |jQt j |jQtÉj v |jQt QtÉuj× j |jQtÉjQ u}~iLjQtw}{[Î v × Dj iLiLj cv }|txj2ht «\¬::®LÚ ÍÔuÍ b{tiL{cvx {dtt jndh}j ujDtvxjQfh}chjDt¨ } QjQt@}_{cv v nv jQtwv jDtd{@hyi Q|~}{ j |
(44) j Ý } v nh"h{¨rc }~|}~ jÍ jQti Q|~}{¨v }~{@ttx{cvi8{vx} QjQtujQthh|}Q¨vx}{d t | { j uv }~{@ uj2} h}~v t }iLhx}i QtQÌdj v>|
(45) }iLv>ujDtvxjDfhh}chjQt>jQtwvbiLjQtxh $tw>ujDtbu{@h jDty}utwvx }j ||~jDty j ||jQtQÍ jQt>i |}~{@ vx}{ttxj {cv }cv ¡@ QjQ t «\¬_ ®LÚ Í Ú Í æ ¥Q¤ ä !© ¤"ª }~iLh|cv¨vx}{:Ìu¡ {@i vx }jnj ÏNjD'v }~@jÌuh{@i$zh jQt|~!¡ zh }chjDt Ìu {h zdjDt.
(46) ¶ µ¶¨º ½ . ¸¹½ºdµ ±²y³\´uµ·¶µW¸¹±ºhÅ$±¨º ¸Â¾
(47) »~½Å¸Âº °¼ÀbÆ. Ú. N7 :&BÉ
(48) " . efhj¡@{@|c{Êdvxfhj «\¬::® djQLks{@hjx{jQv(}t(vx{nh {¨c}ujjQ@twr2QjDtxt vx{njÝ }~jQ@v j |}zh|j¡@j {iLj vx }|¡{@x}~vxfhiÉt v {>txj t }~}~htv xr2QujQiL}Í efh}t:}tBfh}j @jQ }v fhjÊÄ{@xi {Êhvxfhj °±¨²b³N´uµ ¶¨µZ¸¹±¨º\¶¨»_¼y½±¨²É½µZ¾'¿yÀ>» Á@±¾'¸ÂµÂÃu²$Å ÆH¸¹Ç¾x¶¾' ¿ ·Íbefhj «\¬_:® Ö¨¡jQtbu{@uvyvxfj$¡jQhj }2h {¡iLiL}h¡Lu}¡i D ·ÌdiÉÖs}h¡j cv j tx}jtxj{ Ê |@txtv j iLh|¨vxjDtyd ÊÄ'v }~{@"v j iLh|¨v jQtQÌ"v fhj }bujDtw}¡
(49) }tyfhjQPs}|~r}txh}xjDÊÄ {i vxfhj kcv h
(50) e:jQi8|vxj. }~zh{ r }~d t·vÍ jÌs|~j vt{dtw}uj vxfj Qtxjb{Ê ¡jQ{iLjv x}bx¡j iLjQ@vt ( ¶¨¾'¾x¶ºcÁc½²É½ºdµ {Ê Õdh} v j2twj v{Ê(x@jQt}~ v fhj2h|hj }tv fhj2wv } v }~{@ {Ê vxfhj2|hj>}cvx{8ʹ jQtQÌujQu¡@jQtd @j xvx}jQtQÌcvxfv}t}u jQ
(51) zsrLvxfhjDtwj2 hx@jQt sÌhÌË ·Í ¡@j hjQx}}iLh|j iLj cv vx}{L{Ê\ h¨vntwvx vxh jv f¨vfdu|jQtHx¡j iLjQ@vt:}tHf}~jQjQ$zsr2vxfh j "!! ##%$'&)(%*,+-*'&).)/0 |@tx1t .%*,+)243$.%* 31$)6687#$)9.46 3$)668 ##%$&)(*,+-*&).%/0 efh}tH|t t <i$5 twvHzdj}~dtvc>vx}¨5 v jQÙ}~vxfLn|t t ̨ jÊÄjQx jQ v {n@tB µZ¾x¶¨¸ÂµWÅ |@txt ·ÌPvxfd¨vHi$twvujÕdhjbvrsdj j h jQtxj cv }~h¡ É j xv }ʹiL}~|r {ÊB hx@jQtQÌu
(52) tw{@iLj>ÊÄ'v }~{@t{Nj ¨v }~¡8{@
(53) h jQt{Ê v fh}tʹiL}~|rÍ efhj «\¬_:;® :@½¾'º\½»ÔÅ hx{¨s}uj2v fhjdtwjQ tbÙ} v faztx}¡jQ{iLjv x}2{@zujQv tbÜz@tw} ÊÄhd'vx}{d|} v }~jDt>{@ÒvxfhjQiÒÍ «\¬::® hx j cv |~rÉ{ÏNjQ tÖjQxj |tÊÄ{@|}hjQ{@zujQv t ÑÄN{}cv tQÌhtwjQ¡iLj cvt Ìs|}~hjDt Ìsv x}¡|jQtQÍ Í ÍÓ'ÌudÉvxfj>Õd twv@j tw}{ {Ê(ÖjQxj | ÊÄ{@$} |~jDt2Ð}h| Qt>} ØÌ: |~|jQ <= ¸Â
(54) ¾ ´u»¶¨>¾ :@½¾'º\½» }Jv fhjtxjQchj |ZÌ:Ùt jQ j cvx|ra j |jQ@twjDa} «\¬::®ÜÚ Í ·Í Öj hjQ|:
(55) zNj2ÙhNjQ
(56) }@v {8vx}~v ty |@txt{ÏNjQx}h¡Lv fhj2}~cv j xʹj ÊÄ{@btx{iLj ¡j {@iLjvx }n|~¡@{ } v fhiÉt ?hvxfh}tÙt u{@hjÊÄ{@vxfj «\¬_:® } h|Ö@j hj |@ 1"!! ##%$&)(%*A+-*&).)/0@ Í By{¨Ùj @j DÌ2ÖjQxj |h}tiLjQcvvx{{ÏNjQ¡jQhj |hh d{ctwj ÊÄhd'vx}{d|} v }~jDt ÌhÙf}~|jvx}~v t|t t{Ï\j tvxfhj2iL}h}i$hi*twj vy{Ê(ÊÄh'v }~{@|}~vx}jQt jQch}xjD zsr LtxdjD}~Õd2|t t Í {@zhtwvxhjDtxtQÌsfh}j @jQvxfh {¡fLvxfjb'j h@'v¡@j {iLj vx }y {iLhuv¨v }~{@Éu}¡i Ú@Ú ·Ìc}thx{@zz|~r$vxfhjbÕ twvtwvx j ¡vxf {Ê «\¬::® Í6efhj «\¬_ ® h¡jQi8jQcv@ÖP¡j@Ì{@i8|~j vxj |r jQujDtw}¡hjD ÊÄ{@ «\¬::®ÎÚ ÍÔ Ú sÌ Ú , >{Ï\j t8J {zhtwvÉ j ÝÉ }~jQcv}iLh|j iLj cv vx}{_Í xh¡@j iLj cvtxjntxjQ @tÊÄhhi8jQcv |Ëtwvx 'v h jQtÊÄ{iÉsrh|~} vx}{tQÌcÊÄ{'j hi8|~j zN{s{|jQJ{Nj ¨v }~{@ty} «d" CDs«d" E aÞ ®cßQà ujDtw}¡ % ZGÍ F ß H ®@Ià CJ K·Ì\vxfh{@h¡fJztxjQÜ{@×j u@'v {iLhhv ¨v }~{@_ÌËiÉPr @twf{ ujQ¡jQhj ¨v jÜ}~huv"hv - L¨Í ma{@twv}~htv x}|ntw{ÊÂvÙxjÜ {iLhuv jÒvxfhjDtwja{@djQ vx}{tÉhh { u}~iɨv j |rÌfhj dj xjÉh{v$ {zhtw1v ?Bv {Ü{h$Öc{¨Ù|~jDu¡j@Ì:v fhj{|~rÐ{iLiLj }|tw{ÊÂvÙxjLÙfh}f h {¨c}ujDt 'j hv$zd{s{@|~jDÎ{Nj ¨v }~{@t { N{|rs¡{dtBÙ} v f} h| tB}t ® F C\8 K·ÍHjQ|uÞ ®sß à h¨v2twj v t {tx}tv{ÊN|}~jytwjQ¡iLj cv tL}h|H tQÌ {cv }~h}h¡ iÉsr8uj ¡@j hjQ vxjÌ{ |~{ctwjv {uj ¡@j hjQ vxjÌ@ txjQtbÑÔhvx}{tQÌc}ujQcvx} |}~cvxjQ txjQvx}{LN{}@vt Ìv h¡jQ}jQtQÍ ÍQÍ Ó2 jQch} }~h¡ fh}¡f|~r"x{@zhtwv {uujÍ MHÝ }~jQra}t |tw{
(57) " xd}|B@d|} vrÒÊÄ{@>v fhj8twj8{Ê «\¬_ ® {@× jQ| }utwvx }|Hh¨vhÍÞ ®cßQà }hhuvtn {tx}tv {Ê@j r | ¡jhv Étxjvt ÌNÙfh}fÜ|~jDhtv {Évxfjhj jDÒÊÄ{b}~iLh {¨jQi8jQcv t}Òvxfhj$jÝ}j r"{ÊBvxfhjLØ }~|Öj hjQ|WÍÛÐj$twf{¨Ù }v fh}tdjQ¨x}jvr8{ÊËv jQfhh}chjQtÊÄx{@i#u} Ï\j j cv¨v hxjyvxfvÙjvxjDtv jQvx{}iLhx{¨@jvxfjnØ }h|Öj hjQ|WÌc j sNj }i8jQcv |\jQc}ujQjn{Ê vxfhjQ}~}i8d'v}ttv u}jQzsrÉzNj fiLxÖs}h¡8{ jQ|dÞ ®cßQà }utwvx }|Ëh¨vhÍHefhjnvxjDfhh}@jQt jQtxh|~vx}h¡L}~ÒiLjQ@twhz|~jn}~iLh {¨jQiLj cv tÙ}|~|_zNj2}@v j ¡@ vxjQ }~ «\¬::®ÉÚ Í Ú Í ksjD'v }~{@Ð
(58) ch}Ös|rÜh jQtxj cv tbvxfhjØ#} h|>Ö@j hj |HujDtw}¡:Ì_ÐksjQvx}{ uÍÔÉÊÄ{udtwjDt>{@av fhjLztx}Qtn{×shizdjQ vrsNjQtQÍ efhjj udjQx}iLj cv |ÊÄiLj Ù{ Öy}t:txjvwv |~jD2}$ksjQvx}{ Ú OÍ N $ksjQvx}{2 dÌPÕd twv txjv:{Êcv jQfh}chjDtËÊÄ{ }~iLh {¨jQiLj cv t }ttv u}jQP Bzh}~Rv QZÕj |htQÌsci$zNj vrcNjQt{hvx}i8T} SQvx}{tQÌs f}~h¡8xj ÊÄj j jb{@hcvx}h¡ÍksjD'vx}{U KuÍb}tujQ{vxjQÉvx{v fhj j h jQtxj cv¨vx}{"{ÊH|¡jQzh }bshi$zNj t ÌhÜksjQvx}{V KuÍÔ$vx{L¡jQ{iLjv x}>Õ| v j }~¡Í & ] &B " ) W XZY W\[ + &( ") 2^ e {8txÙjQv fhj hj jDÊÄ{@ {ztv hjQt t{ iÉh}~h|vx}{t{Ê(}h|{zujD'vt Ìu$Õ twvj tx}~{@{Ê vxfhjØ }~h|ÖjQxj | ÙtÉ j |jQ@twjD }~ «\¬::® Ú Í hÍ ÛÐjJujDtx x}zNjÜ}~ v fh}t txjQ'v }~{@} vt iL{ jÜ j |j ¨cv f @'vxjQx}twvx} tQÍ[ÛÐj×|tw{ txfh{¨Ù*} vt ÙjQÖcjQt twjDtntxhhN{xvxjD×zsraj udjQx}iLj cv |Hj s}hj j@Í N ujQjQËÌ:ÊÄ{ v fhjLÕtv2 j |jQtxj8{Êv fhj}h| ÖjQxj |ZÌËvxfhjLÊÄ{u t Ùthhvy{"vxfhjujDtw}¡Òd v fhj2 {zhtwvxjQt t{Ê v fhj2@ÖP¡j@Í. _ `
(59) a. bdc"egfihkj. efhjLujDtw}¡a{ÊHvxfhjÉØ9 }~h|>ÖjQxhjQ| K(txjQtbvxfjj cv j tx}zh}~|}~vraa@hhv z}~|} vrÒh {Nj xvx}jQtb{Êv fhj «N¬::® |~}hjD @Ö j hj | Ú ·Í(efj }~h|(ÖjQxj |c}t( i8j vxjQx}TS jD2zsrÌ}hfhjQx}~v t ÊÄ {iÒÌ 9,&4*$1#l)*#1&)*%3biLj vxj DÌDÊÄ{B{zhjQ'vt(|~}Öj N{}cv tQÌ_} |~jDtbdashi$zNj >vrsdjDt Í\N·v ftn txjQ {aiLjv j DÌm )31(%*n%#%$)9 5 l%*#1&4*%3Ì(h {¨s}u}h¡ |~¡@j zh}2{@djQ vx}{t v f¨vbxj hjDjQt t rÊÄ{@b{@iLhuv vx}{t{@Ò }~|jQtQÍ .%*,+)243$.%*po 3$)6689A&4*$#l%*#1&4*%3mq 3$)668 %31(%*n)#$)9 l)*1#1&4*%3r 3$%66 5 5 )9# 3$#)/,t4*5 #1&4*3/0u!v2 n39 9,&)*5 $#l)*1#1&4*%3 5As s 5 w ëW÷÷ 02113
(60) 4!55S=2V89SV6=70
(61) :<79;:>126Q? :IVe?5
(62) x8V Y 9SV=5S@2V8]/Q^5V[9]D[Te85 ( )y
(63) ,z[#.
(64) @½°¶PÅ'µZ¾x±
(65) ½µ¶¨». . N "vxfh}tÙPrÌcvxfj} h|Öj hjQ|N}t|}~iL}~vxjD"j }~vxfhjQvx{Ésrwv } h||~}hjDÖjQxhjQ|Ë}~iLh|j iLjQ@v¨v }~{@_Ìuh{v {Ésr wv } h|}i8|~jQi8jQcv ¨v }~{@"{ÊB|~¡@j zh}y{@djQ vx}{tQÍ efhj ¡@j {iLj vx }n|j jQ|Ë}~cv j xʹj h {¨s}hjQtvrsdjDt|xjDuruj ÕhjD"zsr vxfhj |}~hjDÖ@j hj |ZÌuh|tvxfxjQjnj Ù vrcNjQt1 )9# 3$#)/1$# /'2 9,&).)/0bÊÄ{@(N{}cv t {8} |~jDt ̨dv )9'# 3$1#)/$# /0>v9A&4*%/$# /0 jQtxNjQ'v }~@j |r> j xjDtwjQ@v }~¡>}h| Qty5As Ò|}hj$5 txj ¡iLjQ@vtyujQ|~}iL} v jQÒzsr
(66) txfÜN{}cv tQÍ N·5,v s |tw{Lh 5 {¨s}ujDtytxj jQ |Ëh5 jQu} vxjQtbÜ {twvx 'v }~{@tQÌujÕdhjQ {@"{@zujQv t{Ê(vxf{@txjbvrsNjQtQÌtÊÄhd'vx{@ t _{@¡|{z|dÊÄ'v }~{@t Í ³\¾xA½ ¨¸ ¶¨µ ½ }tvxjDtvÊÄhd'vx}{Ò jv hx}~h¡ÉLu}tx xj vxj txjv{Ê_¨|hjDt>ÑÄÊÄ{}~twv j xu{$vxfhjbvÙ{8h jDt c c }~cv j twjD'v wÓ'Í ±ºhÅ'µZ¾'´ µZ¸¹±¨º }t2ÊÄ'v }~{@vxfd¨v {twvx v t hjQÙ {@zujQv t2ÑÄÊÄ{}tv 4j x{@i8uvxjnvxfj2}~cvxjQ txjQvx}{
(67) zdj vÙjQj c c ÓÍ N vxfh}tÕd twv j |jQ@twj@Ìh jQh}Q¨vxjDt {twvx 'v }~{@tÙjQxjy}iLh|j iLj cvxjD} {@ ujQv {$iLj j vv|jQ@tv||dv fhjnxjD@}~ 'j Q iLj cvt{Ê vxfhjxh¡@j iLj cvÖ¨¡jÍHksjQj ) ËÊÄ{iL{ j2ujv}|tQÍ . . . 0. . _ ` _. 0. cc.
(68) . kcv {@i8uv vx}{t{ |}hjQ¡@j {iLj vx }É{@zujQv t8 zdj"djQwÊÄ{@xiLjD tx}~h¡J{h|r {@i8d }tx{t${ÊyN{|rsh{iL}| jsxjDtxtx}~{@t }Îvxfhjzdtx}LshizdjQ2vrsdjdtwjDÐÊÄ{2v fhj j h jQtxj cv vx}{Ð{Ê{zujD'vt ÍÒefh}t$ ÎzdjNj xÊÄ{ iLjQÎt$tw{s{ @t2vxfjshi$zNj 2vrsNj ×}t$ ¾'¸ÂºsÁaµZ¿ ³½ ÌBiLjQh}~¡Òvxfv$} v8{Ï\j t vxfjÉÊÄ{||~{¨Ù}h¡Ü{@djQ vx}{1t $u} v }~{@_ÌBtwhzhvx'v }~{@_Ì ih| v }~|~} vx}{_Í }~|j}~ «\¬::® }tHÖsh{¨Ù8zcr$vxfhj>{s{u}¨v jQt({Ê\} vt j cvxjQ8}~v tt c jQu}tQÌtwhd{ctwjDvx{2zNjxjQhxjDtwjQcvxjQ zsrÉtw{@iLjyx}h¡2shizdjQvrsNjÍ |}~jy}tÖsh{¨ÙÉzsr}~v tjQcvx}{_Ìctwhd{ctwjDLvx{$fPjy {cj Ý}j cv t}~Év fhj>t iLjy }h¡2vrsdj@Í N cvxjQ txjQvx}{t}c@{|s}~h¡} |~jDt|jQ@Év {iÉ}~h|vx}h¡|~¡@j zh}yshizdjQ t{ÊBuj ¡@xjQjyvÙ{${ vxfh}tx}h¡dÍBma{ j {¨jQQÌ iL{@twv¡@j {@i8j vx }hxjDu} ¨v jQt${ }~h|8 t j'j uh jQt twjD t{iLx}tx{t2}s{@|~s}h¡×txf {c{v tQÍ×Ø>jQ|}h¡×Ù}~vxf {s{v t({ÊNN{|rsh{iL}|t(Q8zdju{@hj}~Étxj @j |cÙPrut vxfvH¡j j }{uujtxfh{h|8twhd{@wv hx{ u}iɨvxjfdu|~}h¡ÉÑÄdtw}h¡ j@Í ¡dÍ s n3*P'Ó ? hh { s}iɨv jzhuvjQwv } ÕdjQÜfu|}~¡"tx}h¡ }cvxj ¨|H }~vxfhiLjv } D bÑÄj@Í ¡dÍ "!! ,&).%*# %$%3/'&%. {@> n 6. !! 9,&).%*1# %$%3 @, Ä,Ó ?yj u@'vÉfu|}~h¡Îtx}h¡ twjQ¨v }~{@ zN{htLvx{ }iLh|~jQiLj cv ½ ¶ µ ±²y³¶¨¾'¸Å ±ºhÅ zdj vÙjQj shizdjQ t ѹ@t} « H F Ú Ë{ ® F C\ K·ÌcdtwjD}vxf\j F Ë« :ß h {v {vrsNjb|}~zh r ) ÂÓÌhtwjQj @1 \ÊÄ{8twh jQr ?cj u@'v fu|}~¡tx}~h¡"d{@|~rsh{@iL}|_xjQh jQtxj cv vx}{Ò{ÊBvxfjQtxj$ {c{v tya|~¡@j zh}ni8j vxfh{uht8ÑÄ|}Öj jQtxh|~v cvtbdÜØbjDtxQxvxj
(69) t h|j2{Ê(tx}¡dÓÙfh}fÒxjDujnv fhj{@i8uv vx}{tv {L {iLx}tw{@t{Ê(d{@|~rsh{@i8}|Ëj uhxjDtxtx}{t Ú Ìd hÌË ) ZÍ N·vÙtHtxfh{¨Ù8vxfd¨vv fhjy|¨vwv j f{}jÌÊÄ{Hv fh}ttxdjD}~ÕdtwiÉ|~|hj ¡ j jvÙ{Ì@Ù@tBiL{ jjÝ}j cvv fLtx}~¡2¡jQhj | |}~z xrÎ|}~Ö@j « H F { ® F C\ Ú Ì¨1 ZÌtw{Jvxfh}tLfh{}j"Ù@t$iÉ@uj"}6vxfhj
(70) }~iLh|j iLjQ@v¨v }~{@ {Êbvxfh;j )31(*n)#%$)9 5 /'t4*#&4*%3 j |jQ@twjD} «\¬::®Ú Í @t2iL{uuj |ÊÄ{vxfhj %31(%*n)#$)9 l)*1#1&4*%3 i8j vxjQQÍ vxjQiLh|vxjn|t t .)/ /0o %7%r2}thx{¨s}ujQ ÊÄ{@y|¡j z }>shi$zNj t{ÊHuj ¡@xjQj hÌutx}~h¡8v fhj ÊÄ{||~{¨5 Ù}h¡L}@v j |Ë j xjDtwjQ@v¨v }~{@ vxfxjQj {sjÝ}j cv t{Ê vrsNj twNjQ } ÊÄrs}h¡8vxfhj2N{|rsh{iL}|Ë{Ê(ujQ¡ j juÌ • {jnzN{s{|jQ"¨|hjtxdjD}~ÊÄrs}~h¡LÙfhj vxfhjQvxfhjtxiÉ||~jQ{Ê(vxfhj {s{v t}t{@tx}ujQxjDËÌu{v fhj2{v fhj {s{vDÍ •jQtx}ujQtQÌQÙfj vxfj}hhuv:}t_¡@}~@j 2zsr>y vx}{|¨vrsdj@ÌPtxf2t srbih|~vx} QZh jQ }tx}{ vx}{|ÑÄj@Í ¡dÍ O ¬ E ¨v }~{@|t 4 {@ "!! s .49*&).)o "!! 4/ )3 $. 4rPÓ'ÌhÙj {dtw}uj v fhj d{@|~rsh{@iL}|tÙ}~vxfÒ{sjÝ }~jQ@vt{¨jQv fhj x}h¡8vrsdj2uj Õh}h¡ v fhj ci8jQ vx{@d ujQh{iL}¨v {{Ê_v fhj>¨v }~{@|tQÌ@}twvxjQ@{Ê_vxfhjn¨vx}{d|tHvxfj iÉtwjQ|~@jQtQÌszcrtx}i8|~rÉih| v }~|~rs}h¡$v fhj N{|rsh{iL}|ËjQcvx}{
(71) zsr uj {iL}~d¨vx{@ tQÍ . . . . "!. $#. %!. %. '&. )(. +*. ,. '&. .-. ". 0/. 1-. 2 . 4. 3. 65. _ `6<. =. 87%9 0:. . . $;. c j c >@? jBADC)E?fFC eHGI>J?ege. e fhj «\¬_ ® x¡j iLjQ@vdÖ¨¡@j {@i8jDt$Ù}~vxf ×uj ʹh|~v8vx}~v t8|t tÊÄ{@|}~j
(72) txj ¡@i8jQcv t$ }~| tQÌ |~|jQ * $ 31.)/1.#%$)9.46}"vxfhj2txjQchj |ZÍBÛJj ÙhNjQvxfhj2 }~h|ÖjQxj |N}~cvx{Lvx}~v t|t t{Ï\j }~h¡vxfjnt iLjn}~cvxjQwʹ@j@Í t iLj cv s }~{@hjQ"}~ vxfhj }cvx {sh'v }~{@_ÌsÖj hjQ|NÉv } vt |@txtxjQtfP@jb}i8N{xv cvu}~Ï\j j jQtQÍ(ÛÐj iLj cvx}{"fhj jbvÙ{$iÉ}~ u}twvx}'v }~{@t v } vt |@txt}tvxhhjDÊÄ{@8txdjD}~Õdntwj@Íks}~dj>vxfhj2 h¡@j iLj cv@Ö¨¡jbxjD@}~ jQtvxfhjnv } vtv {8x{¨s}uj> h}chj • vrsNvj s # %*%/0@Ìvxfhjuj ʹh|~vvx}~v t |@txth{cjDth{v{ÏNjQytwjQ¨v jbvrsNjQtÊÄ{@|~}hjtxj ¡iLjQ@vtÒ}h| tQÍ efhjn} h|Ö@j hj |ZÌiLjDcvv {$zNjb¡jQhj |dhh d{ctwj@Ì@{ÏNjQ tvÙ{u} Ï\j j cvvrcNjQtQÌ )9'# 3$1#)/$# /0$ 9,&4*%/1$# /0Í efhjDtwju}twvx}h¡h}txfhjQ$vrsdjDt(xjP¨}|zh|ju}xjD'v |~r2ÊÄ{@(vxfhjtxj DÍ mÜ{@xjQ{¨jQ_vxf}tHfh{@} jÙ5,}|s |h||~{¨Ù >5 ¡jQhj |T} SQ¨v }~{@25vx{2 Ö@j hj |@ÊÄ{(iL{ j{@iLh|~j h jDt:}v fhjÊÄhvxh jÍBefhjvx}~v t(|t t:zh}~|~v({@2vxfj }~|:ÖjQxj |ctwjDt_v fhkj n 6. !! %$#49$&). |@txt ' ·Ì\vxfvn|~|{¨Ùytyv { ÙÜv fhjvÙ{
(73) {iLh|'j ÒvrsNjQtn}~J{hjhh}chj$vrsN>j s # %*/0@Ì_}J"tw}iL}~|nÙPrÜ@t> &-9 & h{cjDtÊÄ{zdtx}>vrsdjDt Í s .ê òW÷w!î L'ñGô öPþù÷îËòÂõQð÷Hÿ~îWí'þ è_÷/+DéPñ÷ ò*E öPbô òWêcôÔêÔùPüîZîWñ÷îÄõbêÔëZêÔþí ê +D÷ëËôÔí.ê bñ ò_ÿÿ~ñ îW í'ò:þ ëZ/÷ L÷îZñôuíÿuòWéP÷ëZ÷ñðPðDîWíñ ·éD÷wë IF 02113
(74) 4!55```
(75) :CW]]291A:!]S=@85DTW[95SZ86=T6SB2185[T/B2eV A:C081Q^D û ÷w÷ 02113
(76) 4!553?WDT/W
(77) :CW]?DSe2ÿVí'=Aî:: ñT/WøPQ ÷ë_:M7îW]/êÔQ^ðQ5òZêÔT/íB22U]2í7Sÿ VSB8&12V9 =852& DF B 3[7]/Q35SZ Z 5T/B8e2V
(78) : 893 ÿ~í'î(Hñ Ðôóñ Pý'ö¨ñý'÷î¹÷ÿ~÷îW÷ ÷ Kuñ Dø2ëZ÷wñMî Zéÿ~í'î K. /. %!. %. NM. . L!. %!. PO. Q. SR$TVUVW. X. ZY+UV["R. ;. Z\ ] N^. SR$TVUVW. _. `. a. jkikmlPnpoFq%renpq"otsvuxwzy|{}q"y$~zy$u. s. `. 1b %ced%c. `. gf. hih. . ú! (:úI&.
(79) ¶ µ¶¨º ½ . ¸¹½ºdµ ±²y³\´uµ·¶µW¸¹±ºhÅ$±¨º ¸Â¾
(80) »~½Å¸Âº °¼ÀbÆ K.
(81)
(82) %$
(83) ('
(84) ,+
(85) .
(86) /
(87) 10
(88) (2
(89) .5. " "#) ) "& " & # ! ! " 3 &# " !. 6 739;:=<73>@? :7AB@9 8 CD <=EGF D B@9 DHJIK 9=L I <9 DMH > K. ! ## &# ! ! " # & # # "& " "" !. . ! " " " * * " && #! * !& ! & ### 4 #". * !!. " !!. "!# !!& !!& ! " # )& ! "!" !&) " #& ! . # ). (}¡h j4 ajhiLh|j{ÊyÞ ®sßQà ¨v ×ÑN »ÔÅ'¸ OQP Ó'ÌË {iLd{ctwjD
(90) {ÊhÌ c8d{@|~rs¡@{tya } |~jDt ÌhÊÄ{>Évx{v|_shizdjQ {Ê hÌ h tQÍHefhjS {s{@iLtbtwfh{¨Ù[vxfhj {iLh|j'u}~vr{Ê(vxfhj¨v Íefhj2zN{vxvx{i h}'vxxjtxfh{¨ÙytvxfhjvÙ{Étxrccv fhjv }2hv txjvt Í efjLv z|~jDt ¡}j8vxfhj"fvxj }tv }Qtb{Êv fhjh¨vÜtwj v t1 }t v fhjÉshi$zNj ${Ê QtÉÑÄ|}~j twjQ¡iLj cvt {}h| Qt ÓÌ V }tv fhj2shi$zNj {Ê(@j xvx}jQt{Ê v fhj h¡jQiLj cvQÌ E }tNv fhj2shi$zNj {Ê(jDu¡jDt F v fhj2shi$zNj {Ê:ʹ jQtQÍ |tx{ÌyvxfhjÎtwj v"{Ê2ÊÄh'v }~{@|}~vx}jQt"}~[vxfhj×vx}~v t"}t"iL}~h}iÉ|ZÍ x¡j iLjQ@vt|¡{@x}~vxfiLt }~iLh|j iLj cv jQ } v fh}t"•@ÖP¡jatwv wvzsruvxvx}h¡6|~|nh jDtÉ}~cv { xQ·iL{h{vx{ja tQÍ R ks{Ì}ʹv ÊÄhd'vx}{d|} v }~jDt|}~Ö@ja}~cv j twjD'vx}{ {iLhuv¨vx}{dtxj"hx{¨s}ujQÎ{@h|rJÊÄ{@ QZiL{@h{v {hj
(91) t}6avx}~v t8|t tÊÄ{@8x¡j iLjQ@vt ÍJefhj
(92) }~|$ÖjQxj | }iLh|~jQiLj cv tv fhjQtxj ÊÄhvx}{|~}~vx}jQtÊÄ{@¡xjQhj |_ Qt Í 4/0 5L7 [ 5L (!3
(93) ,+
(94) "'
(95) !3M TÉJ &B ! S ÛÐj {ud'vxjDÜ'j uNj }~iLjQ@vtv { j ¨|~vxj2v fhj$ @'vx} |:}V UhjQj{Êtxj jQ |_}i8x{¨@j iLj cvvxjDfhh}chjQt>{Òv fhj «\¬::® Ø }h|Ö@j hj |ZÍ y'j uNj }~iLj cvty{@tw}twvy}~a {iLhuv }~h¡" h¡jQi8jQcv t{ÊBxjD|_}udtv x}|(h¨vL{ÊyÞ ®sß à iL{uuj |t j h jQtxj cv }~h¡8j |jQvx {h} } h}~v tQÌuÙ} v f"v fhj jÝ}j cvbtxÙjQj Q·|}~hj |¡{@x}~vxfi#hx{¨s}ujQ"zsrÉvxfj2hj Ù «\¬_:® x¡j iLjQ@v @Ö¨¡j Ú ·Í efhjbÞ ®cßQà h¨v fPjiÉsr8 txjQt{Êshvx}{tQÌchj ¡jQhj }~jDtB8vh¡@j }~jDt Ìc dtw}h¡hx{ u}iɨvxj {iLhuv¨vx}{ v { ʹ}~|uj$v {" {hdu}~¡"jQx {t Ì\daÙfh}f×iÉÖ@jv fhj iphh {h }¨vxjÊÄ{ 'j hv {iLhuv¨v }~{@_Í$ksj j (}~¡@h j"ÊÄ{ }|~|twvx¨v }~{@_ÍHefhjyvzh|j>¡@}~@jQtvxfhj twT} S jDt{ÊËvxfhjn}hhuvÕ|jQtÙjn jytx}~¡ÊÄ{vxfj>j sNj }i8jQcv tQÌv {¡j vxfhjQÙ}~vxf vxfhj tx} SQjQt {Ê v fhj{@x jQtxd{@u}h¡x¡j iLjQ@vt Í ÛÐjÜ{iLh|jv jÒ{hL'j uNj }~iLjQ@vt8Ù} v ftxrscvxfhj vx} }hhuv×ÑWtwjQjÜ|tw { (}~¡@hxjÐQ'Ó ÒÐ@j rÎhj txjÜu}twvx }zhuvx}{ ÙfhjQxj }~|jQt j> j cvxjQxjDÉ{ $¡ } "||d}~t{Ê:}|jQt}~cvxjQ txjQvnÑW@Ó'Ìu tw txjbu}twvx }~zhhvx}{ Ù}~vxf{uv}~cv j twjD'vx}{ ѹzdÓ'Í efhj f hÙxj>{Ê {@h'j uNj }~iLj cvtÙ@tBj cvx}hi 8vyhÍ K8\ B S2Ù}~vxfÐD {Ê iLjQi8{@xr@Ìsxhh}~¡ }~s ÐÑWuÍ ÍÔ W jQxhjQ|ÓÍefhj2{@i8}~|j Ùt¡ > Í hÍÔ ?s||_{hÕ¡h¨v }~{@tÙjQxj2{@iLh}~|jQ"Ù}~vxfÒvxfj Q Ø bØ M 8X> Q 1 Ud¡@tQÍ N JvxfhjLtxjQchj |ZÌËv fhj8hjʹ| v vx}~v t |@txt * $ 31.)/.#%$)9.)6 Ù}|~|BzNjLtwjDJ@t jÊÄjQxjQj$ÊÄ{ iLjQtxh }~¡vxfj8Nj xÊÄ{
(96) Q iÉdjQt_{Êcvxfhj }~|ËÖj hjQ|WÍ {vxf {ÊcvxfhjQi xjHs dtwjD>Ù}~vxf v fhjt iLjHztx}B'j hv_x}h¡shi$zNj ËvrsN4j " "!! 4/ %3 $.sÍ Y îW÷ëWöPôòWòZéPë êÔëd.ê b÷ +QòÂðPì\ôóí ñ.ê LP÷ëdî¹òZòWéP.ê ÷ ÷wë( öPñ þPønù÷òÂîdìËííÿ ÷wLøD÷ý'î¹÷wòW.êë:÷.ê >ë KòWZéPZ ÷[ñKQî¹.ê îZñ òZDéPý'÷:÷wþëZðP÷ ñîWò ëW÷ øPêÔë¹òZî¹êÔùPöDòWêÔí ~Où íÿ hêÔý'öPîW÷ #Jh÷wñ ·é êÔMî ôÔ÷:êÔë öDòN.ê òWíHòÂìËíé¨ñô ÿ IêÔMî ôÔ÷ë K'ì:éP.ê ·é 3. 3. K. 3. t7%9 0:. z]. ( )y
(97) ,z[#. /. .
(98) @½°¶PÅ'µZ¾x±
(99) ½µ¶¨». . K. B@L@? :
(100) .
(101) $
(102) %'
(103) +
(104) (
(105) ./
(106) 0
(107) %2
(108) (5 D <=E F D B49 D L I <9 D. "
(109) 4
(110)
(111) 28.0 48.0 135 569 125 611 690 3, 650 2, 320 335 0.91. K. * / $ 13 .%/1.#%$)9'.46 s 8.55 2.59 26.7 26.9 14.3 137 192 220 581 77.9 0.51. e(zh|j e}i8j@Ì } txjQ{@htQÌ txdjQ@v vx{ {iLhuv j vxfhj h¡jQi8jQcvÎÙ}~vxf9v fhj «\¬::®Ú Í }~h| Ö@j hj |" * $ 31.)/1.#%$)9.46Í s /. b{vxj$fh{¨ÙjQjQv f¨vv fhj$uj ʹh|~vyv } vt|t t}tb|xjDurÉ{@uvx}iL} SQjQÜd"dtwjDty } v fhiLjv }nÕ|~vxjQx}h¡aÑWtwjQj$ksjQvx}{Ò Í Ú ÍÔÓ Ùfh}fÎiÉÖjDtn} v$ch}~vxjÉj ÝÉ }~jQcvQÍefhj «\¬_ ®ÜÚ ÍÔ }~|2Öj hjQ|(}t2h{v2rjv Õ|~vxjQxjDΨv||WÍ b{v jL|tx{
(112) vxfv vxfhjÉtxj {Ê n 6. !! %$#491$'&).Ðѹtxj jksjD'v }~{@×uÍ Ú Ó}cvx {shjDtbtx|~}¡fcvb{¨@j fhjQ@ }Òvxfj$ hhh}h¡Év }~iLjQt>{zhv }hjDÒzcr"vxfj}h| Ö@j hj |ZÍ efhjDtwjbj |j iLj cv txvx|r$j uh|}~Lv fhjyN{s{Nj xÊÄ{ iÉ j{Ê\vxf}tÖj hjQ|twf{¨ÙÉ}~e(zh|j@Í(efhjbxjDtv{Ê\vxfh}tÙ{ Ö}t ujQ{vxjQÉvx{Ltwfh{¨Ùfh{¨Ù txj @j |vxjQfh}chjDtQzNj {izh}hjQLv {$h {uu j>"}~iLN{xv @v}~iLh {¨jQiLj cv}vxfj> hhh}h¡ v }~iLjQtQÍ & ] &B " ) X "
(113)
(114) ; Y W\[ + &( ") 2^ N Lv fh}ttwjD'vx}{:ÌÙj}~iLh {¨jvxfjb} h|HÖjQxj |u}ÉPx}{dtHu}~ jQvx}{1t _zh}~Rv QZÕjQ|ËÌc{hvx}i8T} SQvx}{L{ÊË|¡jQzh}shizdjQ tQÌ Qfh}h¡Ìh"xj ÊÄj j j {hcv }~h¡dÍ t!. ". `
(115) a. . . ?.G. f
(116) j h degfRj h fFC"!$#@fic >vA. njQ{iLjv x}$|~¡@{ } v fhiÉttx||~rÒujQiLÜ{@djQ vx}{t}s{@|~s}h¡ ½ ¶ µ ±¨²b³N´uµ ¶¨µZ¸¹±¨º ѹh{v>vx{zNj$iL}tvÖjQÜÙ} v f×j u@'v x}~vxfhiLj vx} tQÌstxj j>ÊÄ{}twv dj2ksjQvx}{ dÍ Ú Í ¨ÓÍyjQj xvxfj |jQt t Ìcvxfj> jQtxh|~v t{Ê tx{iLjn{@twvx|rÉ{Nj ¨v }~{@t zdj2twvx{ jQÉvx{ P@{}$ jQ {iLhuv }~h¡ v fhj i9txj jQ |svx}iLjQtQÍ(Û fj Lvxf{@txj{Nj ¨vx}{dtBxj vxh twrsizd{@|~}¨|hjQtQÌ|}~Ö@j DZQ±»~½¶¨º Ì@vxfjyiLj iL{ r tx jytxjQQÉzNjb@j r$|{¨Ù :v fhjb jQtxh|~v tQÉzNjbj ÝÉ }~jQcvx|rLtwvx{@xjDL}~ ǸÂ&µ %'½ » Ùfh}f {tx}twv t}~vxfhj>iLh}hh|¨vx}{ {Ê(}u}s}ud|_zh}~v t{ÊB"jQcvx}xj zh|{uÖ{ÊHh¨v 1 ·Í )9# 3$#)/1$# /0$}t¡@}~@j
(117) zcr } vtytwhd{@wv }~¡L }~|j2"}~v tjQuN{}@vt2ÑÄ¡@}~@j
(118) }~Ü{@hcvxjQ |~{uÖsÙ}txjb{@ hj 'Ó'Ìsvxfd¨v QafP@j5As |¡jQzh }25 {s{u}~d¨vxjDt Íefhjzh}~Rv QZÕj |ÜÙj}~cv x{uu j$t>a@hu}~vx}{| hv ÉiLj izdjQbf@tnÉzcrcv jQt$ѹ}~aʹ'vDÌ {@h|~r×D$ÊÄx{@i#vxfj vx{v|D$z} vty j twjDÓ'Ìd"}thjQ| jQ"}"v fhj ÊÄ{||{¨Ù}~h¡8ÙPr .(124*0 %* / 6.# &-69(1&4*" s-6,+ 5 s &-69(1&4*" 6,+ s &-69(1&4"* 6,+ s &-69(1&4"* 6,+ s &-69(1&4*" 6,+ s &-69(1&4*" 6,+ s &-69(1&4"* 6,+ 4 sn-9.%/ 91*%31 </. . -n 9.%/ / 91*%31 *) #. 9A&). 96/ / 33! 0.// 96 .0+)* $# $ / 33 9# 3*1 5 q&($4;+s & . 5 &4*5 $# 1 # . 9A&). 96/2)s /A+ & . &4*! 0.// 96 9. $3)02P 5 #. 9A&). 96/()/A+ & . &4*! 0. #. 9A&). 96/ +)231*,+-*&).%/02)/A+ & . &)*P!5// 96 9. .0+4* +)23*,+*&). 0/ $6)02Pq&($4V+ & . 4& * $ # 1 5 5 #. 9A&). 96/ 5 +)231*,+-*&).%/0()/A+ & . &)*P!5 5 #. 9A&). .87 /*&| )/,2 9,&).)6/ &/ 224*#%/'24$#.P! 0.-9// $#%* .0+)* .87 *&| 12 9,&).46 & .0+4*3) 224*#Pq 3* / :. 4 s #. 9A&). 8. 7 /*&| )/,2 9,&).)6/ &/s 3* / .)/,24$#. ! 0.- //V24$#. 1/ .0+4* 9# 31*;1 5 5. M@f×{@hj$zh}~v2j cvx r ÑÄj@Í ¡dÍ 96/ +%23*,+-*'&).)/02)/ + & . &4*¨Ófdt>vÙ{
(119) u}~ÏNjQxjQ@v2twv ¨v jQt1 µZ¾'´½ >= ¶»ÔÅ ½ Í8efhjvÙ{"zh} vt jQ@v x}jQt>ÑÄj@Í ¡dÍ 96/ s 33@Ìm96/2)/A+ & . 5 &4*PÓfdPjbhu}~vx}{d|dtwv vxj @±¨ºdµ O:ºN±$? ÌciLjQh}~¡vxfd¨vv fhjb{@djQ vx}{LÙt{v r@jvb{@iLhuvxjDËÍefh}tvxfh}
(120) twv vxj }ttxjÊÄh|Ëv {LiLÖjnvxfj{iLhhv ¨v }~{@"{@h|rÙfhj ÒhjDjDtxt rÍ ÛÐjÐ|~ jQ@ur@}Ös|r iLjQ@v }~{@hjQ vxfv"v fhjÎ h¡jQi8jQcv"|¡{@x}~vxfhiÉt"tvxv"zsr uvxvx}h¡||>}hhuva Qt}@v { Q iL{{vx{@hj t ÑZksjQvx}{ Ú ÓÍe {Lvxfh}ty}iÒÌdÊÄhvx{@ +-$'t4*%/02)/ + & . &4*ÉitvyzNj2h {¨s}ujD zsr vxfhj2v } vt|t t{v fhxj Ö@j hj |ZÍ srzh}~Rv QZÕj |L{ jQtxd{@ht:vx{2 twj v{ÊdN{@t tx}~zh|jtwd¨vx}|h {uÕd¡h¨v }~{@t:{Êv fhjy} h|HÍ W h{¨Ù}~¡nvBÙf}f N{}cvbL¡}j Òn}tbuv>|~|{¨Ùytvx{ujDu j vxfhjtxjvy{Ê(N{@t tw}zh|jtwd¨vx}|_ {uÕd¡h¨v }~{@t{Ê(vxfhj$txiÉ||~jQy t{zhv }hjDËÍ efhjQ_Ì:Ùfj Ðvxfh}ttxjv2{Ê{@uÕ¡@h vx}{t>|jQtnvx{Ü
(121) hh}@jÉzh}
(122) v QWÕdj |Ð {uÕd¡h¨v }~{@_ÌËÙjÉQ"tv¡@jv2}~v}~ {@twv cv . /. . . . . . . . . . ú! (:úI&.
(123) ¶ µ¶¨º ½ . ¸¹½ºdµ ±²y³\´uµ·¶µW¸¹±ºhÅ$±¨º ¸Â¾
(124) »~½Å¸Âº °¼ÀbÆ . v }~iLjÍ N Òʹvb}~vy}tbjQtxrÉv { fhjQÖvxfv>uvxvx}h¡ Ò n}cvx{ xQZiL{{vx{@hj2 tʹ|~|ty}cvx{Lvxf}t> ¨v j ¡@{ rÉ{ÊuvDÍefstQÌ v fh j +$t4*%/02%/A+ & . &4*8ÊÄhvx{QÒtwj v|~|\v fhj2{dtv xvxjD tzh}~vRQZÕjQ|htÙ}~vxf
(125) h{8hj jDÊÄ{@srÉj'hvy{iLhhv ¨v }~{@_Í . `. _. . . ?.G. . . . . f
(126) j h jZC c e-c G+C f kj e. }. )C. fRj h fe GI>icOe. e {{@i8uvxjv fhjy}cvxj txjQ'v }~{@{Ê\vÙ{2}h| Qt ÌÙjÕtv{iLhhvxjvxfjy}~cv j twjD'vx}{8{Ê\v fhj } jQtxdjD'vx}jytxhhN{xvx}h¡ }~|jQtQÍON 8ʹ@'vQÌ@}~Lv fhjÞ ®sß à }hhuv¨v Ì@txj @j |u} h| tHxj{ÊÂvxj txhhN{xvxjD8zcrvxfhjbt iLjy }~|jÍBks{Ì@} vtx{ht }cvxj jQtwvx}h¡Lv {Évx rv { ¶ ý vxfhj}cvxjQ txjQvx}{t{ÊB }~|jQtQÌuv { P{@} vx{É jQ {iLhuv j vxfhjQi jDf
(127) vx}iLj$ t {cv }~hjD
(128) }~ v fhj i xj$ {tx}uj jQËÍÛÐjv x}jQÜvx{ dtwj8 6. !! +-$'2
(129) Ùfh}fÒvÖ@jQtb }b{Ê} |~jDtbÒxj vxh tyvxfhjQ}~Lѹv>iL{@twvbvÙ{cÓ }cvxj txjQ'v }~{@"N{}cv tQÍ Bb{¨ÙjQj D̨jQ@f8chjQxrÊÄ{n}~{Ê\txhhN{xvx}h¡2}|jQtB}LvxfhjiÉ8vÖjDtH2twiÉ|~|hi8{@hcv{ÊNvx}iLjvx{2zNjbtxÙj jQËÌ ÐÙfhj Ðvxf}ttxÙjQ2}t jQi8hvr6ÑÄzNjQQtxjLvxfjÉ}~cvxjQ txjQvx}{Ðfth{vzNj jQÎ {iLhuv jQÐrj vÓÌ_vxf}tchjQxrJ}~dujDt2 {¨@j fhjQ@ËÍmatQÌ|}~Ö@j 6'. !! +$2hÌ\fPj O(log(n)) chj rv }~iLj$ {iLh|'j u} vrÒd O(n) tx j{iLh|'j u}~vrÌdÙfhj j n }tyv fhj$shizdjQb{Ê} ty{ÊtxhhN{xvx}h¡ }|jQtQÍ MudjQx}iLj cv t>{ÜÞ ®sßQà Õ|~jDtbtxfh{¨ÙjQ
(130) vxfd¨vyv fh{@txj$iÉdty}hnzh}¡¡@j ¨ }¨vx}{"{"vxfhj hhh}h¡8vx}iLjQtQÌhzhuvÖ@j j "vxfjniLjD
(131) hfh¡jD{¨jQ||NÞ ®cßQà txjvt ÍHmÜ{@xjQ{¨j DÌsiLjQi8{@xrÉ{¨@j U{¨Ù {u ht{
(132) vxfhj2z}~¡@¡jQtwvÕ|j N »óŸ O Ñ (}~¡@h j8PÓ'Íku}~ j vxfhj2}udtv x}|:hh|}Qzh}|} vr{Ê({@hÙ{ Ö}tb }|ZÌuÙjh{8{v {tx}hj vxf{@txj>iÉdtt
(133) }@v j jQtwvx}h¡É{@@v x}zhuv }~{@v {v fhj2j f j iLj cv{Ê vxfhj }~|Ö@j hj |Ë"hx{@ v fhj i }~ v fhj2xjDtv{Ê v fh}tyÙ{@xÖ\Í " . % .
(134) Vj. `6<. efhj. . }?jGPf
(135) j h C . Rh cBE?feG >. c Sc.
(136) . . vrsdj2Ùt}iLhx{¨@jQ zcr ÊÄ{||~{¨Ù}h¡vÙ{Éu} jQ'v }~{@th jQtxj cvxjD }"vxfh}tytxjQ'v }~{@_Í ¥ !#"b§u¦P¥$¹© ¹§h¦%§h¤ â ¤ N atx{iLj2 @twjDt Ìuv fhjvx|:ujQ¡ j j {Ê(vxfhj|¡j z }>shi$zNj ty{@iLhuvxjD
(137) }t{@h|r {jÌh}ZÍ j@Ív fhjQtxj2shi$zNj t j2}~
(138) ʹ@'v ¨v }~{@|shizdjQ t ÑÄjÍ ¡Í
(139) ÊÄ{@vxfj}~cv j twjD'vx}{ÎN{}cv${ÊvÙ{Òv ¡j cv }~|jQtÓ';Í By{¨Ùj @j 2} «\¬_ ®ÜÚ ÍÔuÌ .)/ /0
(140) }t h{v${hvx}i8}TS jDÐÊÄ{2v fh}t$txdjD}|QtxjÌ(tw{dÌ(|~|{@djQ vx}{t {@ÎvxfhjDtwj ci$zNj t2fPj8v fhj t iLj{@i8|~j s}~vrÌ(ÙfhjQhj @j .%/ /0$}tL¨vx}{d|\shi$zNj {@h{vDÍ ÛÐjbujQÉ. Ud¡Ì 96/1#%$.)9 &4$%3Ìsv {2vxfj .)/ /0nshizdjQHvrsdjyÙf}fÉ}u} vxjQtÙfhjv fhj } v}t ¨v }~{@|ushizdjQ {@bh{vQÍefh}t Ud¡ twf{h|Òzdjtwj vyvx{ µZ¾'´½ Ùfhj hjQjQvxfhjshi$zNj >}tb}ujQcvx}~ÕjQÜ@ty¨vx}{d|ZÍ |~|({Nj ¨v }~{@t}c@{|s}~h¡ .%/ /0LfPjtxNjQ}| txjQty{uv }~iLT} S jQ× {u}h¡8vx{Év fhj$¨|hj{Ê 961/1#%$.49 &4$%3@Íne Ù{ {twvx vx{tÊÄ{ .)/ /0 xjP¨}|zh|jÌu}Ü{uj v { P{@} vxfjtxj v {twj \v 961/1#%$.49 &4$%3Lu}xjD'vx|rÍefhj2Õtwvb{dtv xvx{@v Ö@jQty '½T» shizdjQ vrsNjujQh{v jQa@'t & )(×twj v t 96/1#%$1.49 &4$3uv {iɨv }Q||~r"vx{ µZ¾'´½ ÍbefhjtxjQ {
(141) vÖ@jQtv fhjv fh j j$ {cj Ý}j cv t
(142) {Ê v fhjyN{|rc{iL}|_ÑÄh|tH{@hjyu} v }~{@|uzN{s{|jQ_ÌtxdjD}~ÊÄrc}h¡2Ùfhj vxfhjQHvxfjy|¡j z }shi$zNj }tBv fhjytwiÉ|~|jQtwvx{s{vB{Êdv fhj N{|rsh{iL}|h{@h{v'Ó'Í N·v}thLv {2vxfjytxj Hv {}hj cvx}~ÊÄrL{8vxfhjQ}~h|~} vx}{8vxfh{ctwjyQtxjQtLtxjvxfhj>x}¡fcv {twvx 'v { }Ò{uj vx{É{@uvx}iL} SQjnvxfhjQ}~y{¨ÙÒ{uuj@Í )31(%*'n)#%$)9 /'t4*#1&)*%36}t v fhjÎiÉ} v x¡@jvÒ{Êv fh}tÒ{uv }~iLT} SQ¨v }~{@_Ì>tx}jÐ} vÜ}t
(143) xjDtwN{tx}zh|~jJÊÄ{Ü xjD¨vx}h¡ .)/ /0 shizdjQ t8ѹtxj 5jLksjQvx}{ÐÓ'\Í MjQxr"vx}iLjÙfj av fhj$¨v }~{@|}~vr"{Ê .)/ /0É}tnujv jQv z|~j8}~J{dtvcvbv }~iLjÌ\Ùj$txj v fhj Õtvb {twvx 'v {DÍ(ef{@txj QtxjQtdjD Q}
(144) vxfhj2}cvxj txjQ'v }~{@"{Ê:vÙ{8v ¡j cvy}|jQ1t ? Q}
(145) vxfhj2}cvxj txjQ'v }~{@"{Ê(8|}~hj
(146) É} |~jnvxfd¨vy jnv ¡j cv ? Q}
(147) vxfhj2}cvxj txjQ'v }~{@"{Ê(8jQwv }Q+| *Pfh{@xT} S {@cv |d|~}hj2Ù}~vxfÜL} |~j@Í -, ¢.¦ Ä$¥ / â $¥ ¹1© 02 Ä¥ â .¦ ! efhj¡jQhj |_}ujD{Ê '»óµ ½¾'¸ÂºsÁ {iLx}tx{t {tx}twv tb}~J{iLhhvx}h¡"×hx{ u}iLvxj2 jQtxh|~vQÌdvx{¡@jv fhj yÙ}~vxfÐÜjQx { zN{hdËÍ N·ÊNv fhjbjQx {BzN{hdÉ}ttwiÉ||jQh{¡f_Ìc{iLx}h¡nvxfjbhx{ u}iLvxj¨|hjQt}tj h{@h¡f8vx{$¡}jvxfhj>xjDtw| v{ÊNv fhj {iL }tw{@{Êhv fhj'j hv ¨|hjDt ̨Ùfh}f|~|{¨Ùyt:vx{ {d|ujj r2ch}Ös|rÍ vxfhjQxÙ}twj@̨Ùjt Pr>v f¨v(vxfjÕd| v j < = ¶¨¸Â»ÔÅ Ìc v fhj> {iLhuv¨vx}{L}tu{@hjytx}h¡2'j hv }~vxfhiLjv }Í |jQx|rÌvxfhjbj x{@ tBhjQjQ8v {zdjbÖj hvttxiÉ||d@tHd{ctxtx}zh|~jyvx{$P@{} v {c{ÒiÉsrÜÕd| v j ʹ}|hxjDt Ì tw}jLj sNj dtw}j8'j hv{iLhhv ¨v }~{@Jitwv zNjÉtxjQJ}~Jvxfd¨v$ @twj@Ì_×vxfj{iLhhv ¨v }~{@t {Êj {nzd{@hJ{h|ra}u jLJ{¨@j fhjQ@ D ·ÍLefj8 {i$z}~vx}{J{Êj h'v {iLhuv¨vx}{Ð×Õ|~vxjQx}h¡
(148) vxjDfhh}@jQt |~|{¨Ùytvx{É¡j vzd{vxf
(149) ʹtwvb"'j h@'vxjDtw| vt Í ÛÐj"@hujQ twf ÜÕ| v j }~¡×h {ujQt t v {avxfj .)/ /0Üci$zNj vrcNj"@t2ÊÄ{@|~|{¨Ùyt Íaefj . /9,&).%*# %$%34365 ÊÄhvx}{ vÖjDtH8'j hv .)/ /0>shi$zNj xj vxh tH8}@v j ¨-| 7{cv}h}~¡>}~vQÍ N·ÊNvxfhj}cvxj ¨|tH{@@v}h}h¡bvÙ{2|¡jQzh } 8= .êñ b-¨òZ÷éDôÔø>÷BÿòÂí'õQî¹ðþ :÷ 9íÿd ñ <í ; ÷ î¹ ë:"!òWéP!÷H,òZ&)éD.%îW*÷÷# %ù¨$%ñ3ëZ.ê/'H&%í'. ð ÷îWöPñ þòZêÔùí ÷PîËë òÂíõQÿdðñ÷ îW.ê Dý KPðPôÔöPë_òWéP÷Bÿí'öDî¹òWé ù¨ñëW.ê Hí'ð÷îWñ òZêÔí níÿ ñ -¨÷ôÔ;ø JdøPê LDêÔëWêÔí -. %. .)/. 0/. /0ci$zNj. c. -. '-. %. %. 0/. 0/. -. . -. ". ". 0/. 0/. -. . ". 0/. . . . . -. -. -. .-. %. 1/. . ( )y
(150) ,z[#. "!. %. 0/. %. 0/. . "!. ". 0/.
(151) @½°¶PÅ'µZ¾x±
(152) ½µ¶¨» . shizdjQ tnu{
(153) h{vn{¨j |_ÌNÙj8 Étwv {iL j2v fhj } 'j svx j iL}~vx}jQtbvx{
Documents relatifs
cosinus (en bleu à gauche) et d’une droite (en noir à droite) sur les données simulées pour 4 années à une température de 45°C, avec un bruit de fond interne réduit de 100,
Florence CARRÉ ~ Réoccupations funéraires de sépultures collectives néolithiques dans la boucle du
2 Vue plus en détails dans le chapitre 1... 2 phénomène d’agrégation des protéines amyloïdes en fibres et d’autres facteurs impor- tants doivent être pris en compte comme
In this chapter, we prove an a posteriori error estimates for the generalized overlapping domain decomposition method with Dirichlet boundary conditions on the boundaries for
Revue française d’héraldique et de sigillographie – Études en ligne – 2020-10 © Société française d’héraldique et de sigillographie, Paris,
Dans ce cas, comme les coulées du Bras de Sainte-Suzanne appartiennent au massif de La Montagne daté à plus de 2 Ma (McDougall, 1971), l’ensemble des coulées pahoehoe
In infantile Pompe disease patients, the glycogen storage diffusely affects brainstem motor and sensory neurons, and the whole spinal cord sensory neurons, interneurons, and
De ce point de vue, il est possible d’affirmer que la mission est accomplie : les projets de renouvellement urbain (GPV et ORU) élaborés depuis 1998 dans une centaine de villes
