• Aucun résultat trouvé

On the Complexity of Linear and Stratified : Context Matching Problems

N/A
N/A
Protected

Academic year: 2021

Partager "On the Complexity of Linear and Stratified : Context Matching Problems"

Copied!
32
0
0

Texte intégral

(1)On the Complexity of Linear and Stratified : Context Matching Problems Manfred Schmidt-Schauss, Jürgen Stuber. To cite this version: Manfred Schmidt-Schauss, Jürgen Stuber. On the Complexity of Linear and Stratified : Context Matching Problems. [Research Report] RR-4923, INRIA. 2003, pp.28. �inria-00071656�. HAL Id: inria-00071656 https://hal.inria.fr/inria-00071656 Submitted on 23 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. On the Complexity of Linear and Stratified Context Matching Problems Manfred Schmidt-Schauß — Jürgen Stuber. N° 4923 Juillet 2003. N 0249-6399. ISRN INRIA/RR--4923--FR+ENG. THÈME 2. apport de recherche.

(3)

(4) 

(5)    !#"%$&"')(*+$,"%.-/#'

(6) 0213"456!798:$6 %;/< >= ?A@B,CEDGFIH:J+KML6NPOQH,RTSJKMLU@V,W XZY[ DG\]FIB:J^R_V6`ZFaD bdcfeTg*hikjmlonTpfqrh%sutwvIqux qrhTs h yzx {|s}x~s^€‚ƒgk„twsuq} I~h †Z‡ˆtw‰EhyŠ€d†Z‡ˆtwyˆcfhTt ‹<{wŒfŒtw‡ˆy#fh%‡ˆhGxcfh ‡xcfhŽp,a‘Iiw’“j”w~fqususrh y•i|–w–I’4j—i|˜*Œ{wvwhG€ ∗. †. ™›š,œT žMŸf ww¡4¢ h•vIqr£Ihz{|suvwtI‡ˆqryˆcfg¤€¦¥§tw‡srqupfhT{w‡{wp0¥§tI‡¨vIh pfhT‡Š{ws©xtIpayˆhªƒyg0{|yŠxcfqupfv*{|p!«qu€Šx~©€ˆ€¨cftM¬ yŠcfh<Œh ‡ˆ¥§tw‡Šg¤{|px h#qrp¤yŠcfh<vIh pfhT‡Š{wsx {I€‚h<xT{|p¤„hzqug*Œ‡ˆtM£IhTkyˆcf‡Štw~fvIc0yˆcfhz~€‚hzt|¥­qrpf¥§tw‡Šg0{|yˆqutwp«hT‡ˆqu£whG ¥§‡Štwg—{|ŒfŒf‡Št_ª«qrg¤{|yˆqutwp€•yˆc©{Mykx {wp®„©hx twg0Œf~«yŠhTqrp¯Œtwsuƒpftwg0q}{|s6yŠqrg0hw° ¢ hqupƒ£whG€EyŠqrva{Myˆhyˆch›xtIg± Œsrh ªƒqryE¤t|¥,xtwpayŠhªƒyg¤{|yŠxcfqupfv*¬#q²yŠc!‡ŠhT€ˆŒ©hGx.yyˆt*yˆcho€‚yˆ‡{MyŠq²³©xT{MyŠqrtIp›t|¥£_{w‡ˆq}{|„srh•tƒxTx~f‡Š‡Šh px hT€T´a¬#ch ‡Šh tI~f‡*g0{wqrpP‡ˆhG€‚~s²y€{w‡ˆh›yˆc{|y0€‚yˆ‡{MyŠq²³hGµx twpayˆh ªay*g¤{MyŠxcqrpfvq}€¶z†U±·x twg0ŒfsuhyŠhw´Z„~«yyŠc{My¤€‚yˆ‡{Myˆqr³hG €ˆqugk~fsryŠ{wpfh tI~€og*tIp{wfqux0xtIpayˆhªƒy%g¤{Myxcfqrpvq}€%qup¸†6°¹¹«º¸»ºqu€hT a~fqu£_{wsrhTpayoyŠt¼€EyŠ‡Š{|yˆqr³hT€‚qugk~s²± y{|pfhTtw~€o¬tw‡¼g¤{Myxcfqrpv° ¢ h¤{|s}€‚t/€‚ctM¬:yˆc{|yoyŠcfh0srqupfhG{|‡%{|p“yˆcfh¤€ˆc{|‡ŠhT«±½suqrphT{|‡ox {I€‚h0{|‡Šhqup¾† {wp0t|¥­yŠqrg0hoxtwg0Œfsuhª«qryE ) ´ƒ{|p0yŠc{My£M{|‡Šq²yE¤i%xtIpayˆhªƒyg0{|yŠxcfqupfv©´w¬#cfhT‡ˆh•£_{w‡ˆq}{|„srhG€Ut«x x~‡¨{My g0ta€EydyE¬#q}xhw´qu€#¶z†U±·x twg0ŒfO(n suhyŠhw° ¿¼ÀaÁ]ŠÃkÄ žMÅ,œw¡ x twpayˆh ªƒydg¤{|yŠxcfqupfv´¬¨tI‡Š›g0{|yŠxcfqupfv©´f€EyŠ‡Š{|yˆqr³©x {|yˆqutwp^´fx twp€‚yˆ‡{|qupayd€ˆtwsu£ƒqrpfv 3. ï ˂ð}ñIòÑÆ|ó,ÇìÈ·åÉ ô§Ê|é.ËEåŠÌQÚÝËEõÍÎå.ȷɛöŠÚ§ç.ÏÑÐGö.ë.ÒrÓ.åÌQõTÔ<×w NJÆ|ÕQNJÍÎ÷wÖwñƒ×ò}Ø_ó,Ù Ú}ìÛ¾åôÝÙ é.ÚÝÜ,åŠÚÝÓTõËÞå.ÕQöŠÉ_ÚÑËÞç.Ú§ö.ßåGÐGä‚ÍåGà×a˂øfÌÝá½ÚÑÍ Ô<Õ½âŠÇՂÍÎ×­ð}ñ ã«á½Ó.È·áQÉ_ÕÝÇÒ}í_ÇȽá½É“á·ù,ä.ÖTäÍ}Ù ÍÎä‚ÐGå%ÒrÓ.æ.ÌÝÔ<çG×]NJèÕ½ÍÎÖ|Ú§é.Ù í_ê.Ð_ê.ëÍ Ú}ìÒrÌQÇÆMÐ_̽ÇÖ ÐGÒrí_Ö Ì§ÒrՈí_٠̧úGÕˆË ×­Ü,˂ÌÝÔ<ÇÐî Ù ï ˂ð}ñIòÑûfó6ü6æ.ýæô§ÏÑæ.þ ö.æŠÿ©Ú§ë.ÈEöÓ.ðÎäˆËdõ]ú_ä.ËEä.á ×MÆ|NJÍÎ÷wÐ_ñƒËEáUò}ó6ú_æ.Ë æôÝæ.Çö.Ð_æŠÈÞÚ§ë.îö+׫éGäˆõä‚ë êGä.ý ×|í_øËdÔ<úGÇíÍÎð}ñØáQÇÕQÌÝí_ú_Ê|ÍÎР˂̽]ù,ÓðÎÓ.Õ·ÌÝÇÍ Ð_ÇGÍ Ù  ÒuÌ í_Ë.×fÆ«Ú§ëìé.ê. ê ,ÍÎðÎðÎËEÌQáÝÚÑð EáQ Ú ÇÐ_ÈÞî ×wÆMÌQÇÐ_ÈEË.Ù ∗. †. Unité de recherche INRIA Lorraine LORIA, Technopôle de Nancy-Brabois, Campus scientifique,.

(7) (›$&" 5 k / '! $, ;< >#= ' -.+$,"k7 '! 5 0#=2 #"$,#=  =^+$6"4.-#=  œ

(8) ¡ ¶ztw~€#Œ‡ˆnG€‚hTpIyŠtwp€#fhT€z{wsrvItw‡Šq²yŠcfg0hT€dŒtw~f‡zsrh%³©s²yŠ‡Š{wvwh«hx twpayˆh ªayŠhT€#suqupfnT{wqr‡ŠhT€#h yzvwnTpfn± ‡{|~fªoh y,pftI~€,g0twpayˆ‡Štwp€xtIg*g0hTpIy6suhT€Œ©hT‡‚¥§tI‡ˆg¤{|p©xhT€f{|p©€suh¨xT{w€vwnTpfn ‡{|saŒ©hT~f£whTpay yŠ‡ˆhd{|g0nTsrqutw‡Šn hG€ hTp“~«yŠqrsuqu€Š{|payzs  qrp«¥§tI‡ˆg¤{|yˆqutwp“«nT‡ˆqu£wnThk  {|ŒfŒf‡Št_ª«qrg¤{|yˆqutwp€#xT{|s}x~fs}{|„fsuhT€zh p¼yŠh g0Œ€•Œ©tIsrƒpftIg0qu{wsQ°<¶ztw~€ n yˆ~fqrtIp€*su{®xtIg0Œfsrh ª«q²yŠn«~ ³sryˆ‡{|vIh!«h¼x twpayˆh ªayŠhT€*Œ{w‡*‡{|ŒŒ©tI‡‚y ¾s}{®€EyŠ‡Š{|yˆqr³©x {|yˆqutwpµfhT€0t«x x ~f‡‚± ‡Šh p©xhT€o«h*£M{|‡Šqu{w„fsrhG€ ´hy4pftwyˆ‡Šhk‡ŠnT€ˆ~fs²y{My4Œf‡Šqrpx qrŒ©{|s,hT€‚y4 a~fhsrh³sryˆ‡{|vwh*«h0xtwpayŠhªƒyˆhG€•€‚yˆ‡{MyŠq²³nG€zhG€Ey ¶z†U±Þxtwg0ŒfsuhyG°¤†U{|‡xtIpayˆ‡Šh*suh*³sryˆ‡{|vwh¤€ˆqrg~fsryŠ{|pn0fhxtwpayŠhªƒyˆhG€%€EyŠ‡Š{|yˆqr³nT€og0twp{I«q} I~hT€T´+ a~fq¦Œh ~«y {w~€Š€‚q  yˆ‡Šh#£ƒ~0x twg0g0h<suhd³s²yŠ‡Š{wvwh<€ˆqrg~fsryŠ{|pn<«h#g0t|yŠ€¨€EyŠ‡Š{|yˆqr³nT€T´|hG€Ey¨{|p€U†6°a¶<tw~©€Ug0twpayˆ‡Štwp€Z{|~€Š€‚q a~fh4suh%x {w€suqrpnT{|qu‡Šh•h y<srh%x {I€Œ{|‡ˆyŠ{wvwn±·suqrpfnG{|qu‡ˆh•€‚tIpIy#f{wp€d†hy< a~fh4srhT~f‡<€‚tIsr£M{w„fqrsuqryˆnohT€‚y#fnTxq}f{w„fsrh hTp“yŠh g0Œ€ O(n ) ° ¦p«³p+´^srh¤xT{w€4«~“³©s²yŠ‡Š{wvwh0«h*x twpayˆh ªƒyˆhT€4«h*£M{|‡Šq²yŠn0i §q½° hw°­t xc{w a~fh*£M{|‡Šqu{w„fsuh Œh ~fyz{|ŒfŒ{w‡Š{ uyŠ‡ˆh4{|~g¤{Mª«qugk~fg2fh ~«ª!¥§twq}€ hG€Ey#g0twpayˆ‡Šn%¶<†U±ÞxtIg0Œfsrh yT° 

(9) Ä Gœ     œ0¡ ³sryˆ‡{|vwh•«h•x twpayˆh ªayŠhT€T´|³sryˆ‡{|vIhz«h•g*twyŠ€T´a€‚yˆ‡{MyŠq²³x {MyŠqrtIp^´a‡ˆhG€‚tIsr~«yŠqrtIp«h•x twpayˆ‡{|qupayˆhG€ 3.

(10)  

(11)        !"#%$. ’.  +$6 ¤' !5Z  »¨tIpayˆhªƒyUg¤{Myxcfqrpvoh ªƒyˆh p©f€6³‡€Eyˆ±½tI‡Šfh ‡6g¤{MyŠxcqrpfv4„ƒyŠcfh<{_£M{|qusu{w„fqusrqryE%t|¥­xtIpIyŠhªƒy¦£M{|‡Šqu{w„fsuhT€,¬#cfq}xc g¤{_0„h•qup€‚yŠ{|payŠqu{|yˆhT„a¤{*xtIpIyŠhªƒyT´Iyˆc©{Mydqu€d{%yŠh ‡Šg ¬#q²yŠc!{kcftwsuhw°¦¹ay{|pf{w‡Š¤³‡Š€‚y‚±·tw‡«hT‡Zg¤{Myxcfqrpv {wsrsutM¬<€6twpsr ÑyˆhT‡ˆg ¦£_{w‡ˆq}{|„srhG€ ´|£M{w‡ˆq}{|„fsuhT€,yŠc{My¨g0{_„©hzqrp€‚yŠ{wpayˆq}{MyˆhG0„ƒ{o³‡€Eyˆ±½tI‡Šfh ‡6yˆhT‡ˆg/° ¢ cfqusrh yŠcfhT€ˆh¾{w‡ˆh¼‡ŠhT€‚yˆ‡ŠquxyˆhGµyŠt®yˆcfh¸srhG{_£whG€0t|¥{yˆhT‡ˆg>{|pg¤{|yŠxctwpfsu{|vI{wqrp©€EyxtIg0Œfsrh yˆh¾€ˆ~f„«yŠh ‡Šg¤€ ´ x twpayˆh ªƒy4£M{w‡ˆq}{|„fsuhT€%xT{|p®t«x x ~f‡{w€4g0twp©{w«q}x0twŒh ‡{MyŠtw‡€o{wpƒa¬#ch ‡Šh*qup€ˆqufh{›yŠh ‡Šg—{wpŒ©hT‡ˆg0qryyˆcfh g¤{|yŠxcfqupfvyˆt «hG€ˆx h p«hTh Œfsuµqup {¯€‚qupfvIsrh“€‚yˆhTŒ^° »¨twpayŠhªƒyg¤{MyŠxcqrpfvyŠca~©€{|susrtM¬<€0g~xcg0tw‡Šh ¥§‡Šh hG«twg—qrp®yŠcfh€ˆh suhTx.yŠqrtIp®t|¥<€‚~„«yˆhT‡ˆg¤€T´+¬#cfq}xc¯g¤{_¾„h¤t|¥#~€ˆh0¥§tw‡h ª«{wg0Œfsrh0¥§tI‡k a~fh ‡Šƒqrpv/{MyŠ{ yŠc{My%q}€{_£M{|qusu{w„fsuhqup¾yŠcfh0¥§tw‡Šg tw¥{su{w‡ˆvIhkyŠh ‡Šg/´+su)q (I+h *o-º , «t«x~g*hTpayŠ€T/° .tw‡%h ª«{wg0ŒfsrhI´^¬h*g¤{_ ¬#q}€ˆc¤yˆt*€‚hTsrhGx.yyˆcfhzyˆqryˆsuhT€t|¥+{wsrs]€‚~„€‚hGx.yŠqrtIp€Zqup!{xhT‡‚y{|qup€‚hGx.yˆqutwp›t|¥{w0p *•-º ,¸«t«x~fg0hTpIyG° ¢ hox {wp h ª«Œf‡ˆhG€ˆ€¨yŠcfqu€<„ayˆcfh%suqrphT{|‡<x twpayˆh ªƒydg¤{|yŠxcfqupfv0Œf‡Štw„fsuh g &. '. X(section( 13254

(12) 68789;:=<%>@?=AB;AC1 , Y (subsection(y, z)))) = s. #¬ ch ‡Šh X {|p Y {w‡ˆhx twpayˆh ªƒy<£_{w‡ˆq}{|„srhG€<{|p y {|p z {|‡Šh4³‡Š€‚y‚±·tw‡«hT‡#£_{w‡ˆq}{|„srhG€ °ED<hT‡ˆhhG{wxc¼€ˆ~f„«± €ˆhTxyˆqutwp0t|¥]yŠcfhz€ˆhTx.yŠqrtIp0¬#q²yŠc¤yˆqryˆsuh ¬#qrsus‡ŠhT€ˆ~fsry¦qrp¤tIpfh<€‚tIsr~fyˆqutwp¤t|¥yˆchzg¤{Myxcfqrpv Œ‡ˆtI„fsrhTg ¬#qryˆc y „tw~fp©/yˆtqryŠ€<yˆqryˆ13suh*24 {w68p78 9;:8z<yŠ>@t?=q²yA€zB=xAtw1 payˆhTpIy€ °<º“tw‡ŠhvwhTpfh ‡{|s+ a~fhT‡ˆquhT€#yˆt›f{|yŠ{w„{w€ˆhT€ g¤{_„©h*hª«Œf‡ŠhT€Š€ˆhT/{w€•pftwpsrqupfhT{w‡z„f~fyo€‚yˆ‡{Myˆqr³hG“xtIpIyŠhªƒy•g¤{|yŠxcfqupfvŒf‡Štw„srhTg0€T°F.tw‡•hªf{|g0Œfsuhw´¬¨h g0quvwcay#c{_£wh%{0f{|yŠ{|„©{w€ˆh db qup/{0g*tI‡ˆFh Gh ªƒqu„fsuhH*•º-,^±½suqI(who¥§tw‡Šg¤{My#srqI(wh .(book(.(author(a1 ), .(title(t1 ), nil))), .(book(.(author(a1 ), .(title(t2 ), nil))), .(book(.(author(a2 ), .(title(t3 ), nil))), nil))),. ¬#ch ‡ŠKh J qu€<{*„fqup{w‡ˆsuq}€Ey•x twp€‚yˆ‡Š~xyˆtw‡yŠt¤h px tƒfh%£_{w‡ˆq}{|„srh%{|‡ŠqryEw° ¢ hkx {wp!Œfq}x(›tI~«y#yˆch%yˆqryˆsuhT€#tw¥ yŠcfh%„tat.(«L €dt|¥,{w~«yˆctw‡ a ¬#q²yŠc¼{* a~fhT‡ˆ 1. „ƒ¼sutƒt5(ƒqrpv!{Myoyˆch*€ˆ~f„€‚yˆqryˆ~«yŠqrtIp¾¥§tI‡ °kbdcfq}€4 I~h ‡Š¼qu€4€‚yˆ‡{Myˆqr³hG­´]„©hGx {|~©€‚hyˆcfhyE¬t!t«x x ~f‡Š‡ˆhTpxhG€ tw¥ X c{_£whoyŠcfh€ˆ{wg0hoŒ‡ˆh ³fª›t|¥6xtIpIyŠhªƒxy#£M{|‡Šqu{w„fsrhG€#{|„tM£wh•yˆcfhTg/´f¬#cfq}xc!q}€#h g0Œ«yE›cfh ‡Šhw° bdcfhG€‚h/yE¬t¯hªf{wg*ŒsrhG€¤€‚cftM¬2yˆc{|y!xtIpayˆhªƒy¤g¤{Myxcfqrpv x {|p„h¼~€ˆhT€‚qug0qrs}{|‡Šsu yˆt@*•†U{MyˆcNM 

(13) O g¤{|yŠxcfqupfv4¬#cfq}xcq}€6~€ˆhT*qrpyˆchK*o¹;,«bµyˆ‡{|p€‚¥§tw‡Šg¤{MyŠqrtIpsu{wpfvw~©{|vwhPM ’ O«¥§tw‡*oº-,¼«t«x~g*hTpayŠ€T´|¬#cfq}xc ¬d{w€›tw~f‡!qrpq²yŠqu{ws•g0t|yŠqr£M{|yˆqutwp yŠtP€‚yŠ{|‡ˆy!€‚yˆ~faqupfv xtwpayŠhªƒy!g¤{MyxcfqupfvR° QÞp yˆcfhxtIpIyŠhªƒy!twS¥ *•-º , Œ‡ˆt«xhG€ˆ€ˆqupfv“yŠcfh ‡Šh¼{|‡Šh!twyˆcfhT‡¤Œf‡ˆtIŒ©ta€‚hG¯¥§tI‡ˆg¤{|suq}€‚g¤€0€‚~©xc {I€‡Šh vI~fs}{|‡0hª«Œf‡ŠhT€Š€‚qutwpµg0{|yŠxcfqupfTv MIUWVWO yŠc{My*«qr‡ŠhTxyˆsu“y

(14) { (wh¤qupayˆt“{Ix xtI~fpay%yˆcfh¤£M{w‡ˆq}{|„fsuh{|‡ŠqryE“t|K¥ *•º , „ƒ¸{|susutM¬#qrpfv/‡Šh vI~fsu{w‡%hª«Œf‡ŠhT€Š€‚qutwp©€ tM£Ih ‡Z{w‡ˆvI~fg0h payŠ€TX° QÞptw~f‡dxtIpayˆhªƒy¦yŠcfq}€x tw~fs}¤„ho€ˆqugk~fs}{MyŠhT0„ƒ0~€‚qupfv*{|‡Švw~fg0h payZsuq}€Ey€ZŒfsu~€‡Šh vw~su{w‡ ‡ŠhT€‚yˆ‡Šq}x.yˆqutwp©€tIpkyŠcfh<xtIpayˆhªƒy€,yˆc{|yZx {|p*„h#qrp€‚yŠ{wpayˆq}{MyˆhG¥§tI‡¦{4xtwpayŠhªƒyU£_{w‡ˆq}{|„srhI°,bdcfq}€6¬tw~fs}{wsrsutM¬ ~©€zyŠt/„©twyˆc¸€ˆh Œ©{|‡{Myˆhkyˆcfh0suqu€‚y%~€ˆhT¼¥§tI‡4h gk~su{|yˆqupfv!£M{w‡ˆq}{|„fsuh{w‡ˆqryE/¥§‡Štwg t|yŠcfh ‡o¥§~fp©x.yˆqutwp®€ˆag„©tIsu€ {wp/yŠt!hTp«¥§tw‡xhkyˆcfh‡ˆhTvw~fs}{|‡•hª«Œf‡ŠhT€Š€‚qutwp/yEƒŒhT€T°4bhTxcpfquxT{|susr¼€ˆ~xc“‡Šh vI~fsu{w‡z‡ŠhT€‚yˆ‡Šquxyˆqutwp€•xtI~fsu¾„©h h ª«Œf‡ˆhG€ˆ€ˆhT„ƒ0»¨tIg*tIp  €6g*hTgk„h ‡€‚cqrŒ¤xtIp€‚yˆ‡{|qupIyE€ M V«5´ Y O·° ¢ h#„h suqrhT£whdyŠc{MyUyŠcfhzxtIg0Œfsrh ª«q²yE‡ˆhG€‚~fsryŠ€ tw¥Uyˆcfq}€•Œ{|Œh ‡o‡ˆhTg¤{|qup¼£_{wsrq}“~p«h ‡•yˆch{w«q²yŠqrtIp“t|¥Z€ˆ~xc¾{›‡ˆhG€EyŠ‡ˆq}x.yŠqrtIp^´ctM¬¨hT£wh ‡z¬¨h*xcftƒtI€ˆhpft|y yŠt¤«qu€Šx~©€ˆ€dqry<qrp¼«h yŠ{wqrs­yŠ/t (wh hTŒ›yŠcfh%Œf‡ŠhT€ˆh payŠ{|yˆqutwp€‚qug0ŒfsrhI° X(book(Y (author(a1 ))))) = db ∧ X(book(Z(title(x))))) = db. ýý Ð Zfìå.ç.æ.

(15) .  " . 

(16)  "8   

(17)  . pft|yŠcfh ‡{|ŒfŒfsuq}x {MyŠqrtIp {|‡ŠhT{¸¥§tw‡g¤{|yŠxcfqupfv®yˆhGxcfpfq} a~fhT€›qu€yˆh ‡Šg ‡Šh ¬#‡Šqryˆqupfv M)U O½° QÞp €‚yŠ{|p©f{|‡ yŠh ‡Šg‡Šh ¬#‡Šq²yŠqrpfvyˆcho‡Š~fsuhT€#{w‡ˆhoqrg0Œfsuq}xqryˆsu›hªƒyŠh p«hG›„ƒ›{wsrsutM¬#qupfv{wp{w‡ˆ„fqryˆ‡{|‡Š¤xtIpIyŠhªƒy<{|„tM£wh•yˆcfh g¤{|yŠxcfqupfvŒtI€ˆq²yŠqrtIp^´ƒ{|p0Œf‡ŠhT€ˆh ‡Š£ƒqrpv•yŠcfq}€¨x twpayˆh ªay¨tM£wh ‡¨{%‡ˆhT¬#‡ˆqryˆh<€‚yˆhTŒ^° QÞpg¤{|pƒ0€‚qryˆ~{|yˆqutwp€Zg0tw‡Šh x twpayˆ‡Štws6q}€%pfhThT«hG¸tM£Ih ‡oyˆch¤Œ©ta€‚qryˆqutwp€4¬#ch ‡Šh*‡Š~fsuhT€%{w‡ˆh¤{|ŒŒfsrquhT^´+¬#cfq}xc®g*twyˆqu£M{MyˆhG€o¥§tw‡%h ª«{wg0Œfsrh €‚yˆ‡{MyŠh vIqrhGE€ M Wi O·° ¢ q²yŠcxtIpIyŠhªƒy¦g¤{Myxcfqrpv%¬¨h<xT{|p¤{wxcfquh £Ihdqrg0Œf‡ŠtM£whGx twpayˆ‡Štws«qup¤{4g*tI‡ˆh<fhTxs}{|‡{MyŠqr£Ih ¬d{_„ƒ›g¤5{ (aqupfv0yŠcfhkxtIpayˆhªƒy<h ªƒŒsrq}xqry<qrp/yŠcfh‡Š~fsuhT€T° €‚yŠ{wpf{|‡!‡ˆhT¬#‡ˆqryˆh%‡Š~fsuh l ⇒ r ¬¨tI~fsu!yŠcfh p „hTx twg0h/{¾yŠ‡Š{wp€ˆq²yŠqrtIp ‡ˆ~srh X(l) ⇒ X(r) yˆc©{My¤qu€0{wŒfŒfsuquxT{|„fsuh/twpfsu {My*yˆcfh/‡Štƒt|yT´{|p ¥§tw‡*³pfhT‡ x twpayˆ‡Štws­{If«qryˆqutwp{ws‡ŠhT€‚yˆ‡Šq}x.yˆqutwp©€xT{|p!„©h%qug0Œ©ta€‚hG›tIp X ´f€ˆ~xc{w€#{*€‚tI‡‚y<«q}€ˆx qrŒsrqupf/h M V3O+tw‡d¬hog¤{_ x twp€ˆq}«h ‡oxtwp©«q²yŠqrtIp{|s,‡Š~fsrhG€z¬#ctI€ˆhxtIp«qryˆqutwp€•‡Šh¥§h ‡•yˆt °%¹ƒqupxh0€EyŠ‡Š{|yˆqr³hT¾xtwpayŠhªƒy•~fpq²³©xT{MyŠqrtIp q}€«hTx quf{w„fsuh MÎ;i U|´fiw3– O½´ 4pƒ~«yŠc«± hTp«qrªa±·su)q (Ih•xtIg0Œfsrh yˆqutwptIXp›‡Š~fsuhT€¨¬#q²yŠc!€‚yˆ‡{Myˆqr³hGxtIpIyŠhªƒyŠ€¨g¤{_¤„©h ¥§hG{w€ˆqr„srhI´©Œf‡ŠtM£ƒqufhT/‡Š~fsrhG€•xT{|p“„hk‡ŠhT€‚yˆ‡Šq}x.yˆhG¼qup¾€‚~©xc¾{¬d{_›yŠc{My4€EyŠ‡Š{|yˆqr³©x {|yˆqutwp“q}€•Œf‡ˆhG€‚hT‡ˆ£IhT/{|p© €ˆ~fqryŠ{w„fsrhyˆh ‡Šg0qrp©{Myˆqutwp¼tI‡Šfh ‡Šqrpfva€#x {wp¼„©hk¥§tw~fp^° ,^twvIquxT{|s+xT{|s}x~fsuq+¬#qryˆc¸xtwpayŠhªƒy<£M{|‡Šqu{w„fsrhG€dyˆ‡ŠhT{|yˆhG €ˆqug*qus}{|‡dyˆt¤{*„f~fqusry‚±·qrpyˆch tw‡Š- MÎ5i Vƒ´

(18) i Y3O+¬tw~su{|s}€‚t0„h{|pqrpayŠh ‡ŠhT€‚yˆqupfv¤{|ŒfŒfsuq}x {MyŠqrtIp^°Ub+tIvwh yˆcfhT‡¬#qryˆc yŠcfh‡ˆhTvw~fs}{|‡‡ˆhG€EyŠ‡ˆq}x.yŠqrtIp€^g0h payŠqrtIpfhT{|„tM£whUyŠcfqu€6x tw~fs}%„h¨~€ˆhT¥§tw‡,‡ˆhTsu{|yˆqutwp€+yˆc©{MyT´M~pfsrIq (whhT a~{wsrqryEw´ {w‡ˆh€ˆh p©€‚qryˆqu£wh0yŠt¾xtIpIyŠhªƒyŠ€T´¥§tw‡h ª«{wg0Œfsrh¤tI‡Šfh ‡‡Šh s}{MyŠqrtIp€4¥§tw‡k¬#cfquxc x h ‡ˆyŠ{wqrp®g0twpftwyˆtIpfqux q²yE¸su{_¬<€ ctws}­° QÞp›yˆcfq}€ZŒ©{|Œh ‡¬¨hoxtwp©€‚q}«h ‡xtIpIyŠhªƒy¨g¤{|yŠxcfqupfvk„t|yŠc¥§‡Štwg {%yŠcfh tI‡ˆh yˆq}x {ws©{|p©0¥§‡ˆtIg {Œf‡{wxyˆq}x {|s Œtwqupaytw¥f£aquh ¬%° •p%yˆchZyŠcfh tI‡ˆh yˆq}x {|sa€‚q}«h¨¬¨hZyˆ‡Š•yŠtzhG€Ey{|„fsuqu€ˆc{z€ˆc{w‡ˆŒ%„tw~fp©f{|‡Š4„©h yE¬¨hTh pŒf‡Štw„srhTg0€ qup/† {|p¶<†U±ÞxtIg0Œfsrh yˆh%Œf‡Štw„srhTg0€T°Ub+t*yŠcfqu€<h p¬h4x twp€ˆq}«h ‡dyŠcfho¥§twsusrtM¬#qupfv0Œf‡Štw„fsuh g¤€ ^ žMŸ« À Å   Ä  À 

(19) Ÿ«G   ¡ .ftw‡khT{wxc®£M{|‡Šq}{|„fsuh*yˆcfhŒ©{Myˆc©€4¥§‡ˆtIg yŠcfh‡Štatwy%yˆt¼qryŠ€ t«x x~‡ˆ‡Šh px hT€c{_£Ih•yŠcfh€Š{|g0h%€‚hG I~h px hotw¥,x twpayˆh ªay#£M{|‡Šq}{|„fsuhT€ §qryŠ€ 3

(20)   )     °

(21) §TŸ ÀƒÄ œœ Tž_Ÿf À Å

(22) Ä ŸfÅ Ý !  Ä  À 

(23) Ÿ«G    ¡ €EyŠ‡Š{|yˆqr³hT4x twpM‰E~fp©x.± yˆqutwp“tw¥UhT a~{MyŠqrtIp€#yŠc{My4xtIpIy{|qup€<tIpfsu!g0twp©{w«q}x4¥§~fpxyˆqutwp¾€ˆƒgk„tws}€ °<bdcqu€zqu€•hT a~fqu£M{|suh pay<yˆt €EyŠ‡Š{|yˆqr³hT!¬tw‡›g¤{Myxcfqupfv Q¹ ¢ º ° ,À Ÿ«ž›  Ä  À 

(24) ŸfT   ¡ {|‡Šq}{|„fsuhT€g¤{_t«x x ~f‡#twpfsutIpxhI° ,Ÿ«ž À Å Â  ,À Ÿ«ž  Ä  À 

(25) Ÿ«G   ¡ .tw‡hT{wxc¯x twpayˆh ªay£_{w‡ˆq}{|„srh{wsrsUyŠh ‡Šg¤€t«x x ~f‡‚± ‡ˆqupfv®qug*g0hG«qu{|yˆhTsrP„©hTsrtM¬2yˆc{|y›xtwpayŠhªƒy¤£_{w‡ˆq}{|„srh/{|‡Šh/qu«hTpayˆq}x {|s½° bdcfq}€¤qrg0ŒfsuquhT€0yŠc{Myqup { €‚c©{|‡ŠhT!‡ˆhTŒf‡ˆhG€‚hTpayŠ{MyŠqrtIp›£M{|‡Šq}{|„fsuhT€d{|‡ŠhosrqupfhT{w‡T° Ÿ«ž ݝ Á   Ä  À 

(26) Ÿ«G   ¡ {w‡ˆq}{|„srhG€¨g¤{_t«xTx~f‡<{|ydg0ta€Ey#yE¬#q}xhI° ¢ h•€ˆcftM¬ yˆc©{MKy ,,»º¯´«;¹ ,,»º {|p›¹¹«º¸»º {w‡ˆhzqrp†6´ƒ¬#cfqusrh4¹»º {wp iI»º {w‡ˆhz¶z†U±Þxtwg0ŒfsuhyŠhw° Q·y•qu€zhT{w€ˆqusr›€ˆh hTp/yˆc{|y•xtIpayˆhªƒy<g¤{Myxcfqupfv¤qu€zqrp“¶z†6´©cfhTpxh%qryŠ€z‡ˆhG€EyŠ‡ˆq}x.yŠqrtIp€z¹»º {wp ia»º {|‡Šh qup¼¶<†6´«yŠtat©´f{|p¬h4pfh hG!tIpfsuŒf‡ŠtM£wh4¶<†U±·c{|‡«pfhG€ˆ€T° •p!yˆcfh%Œ‡Š{Ix.yˆq}x {ws^€‚q}«h4¬hovIqr£Iho{wp¼{|suvwtw‡Šqryˆcfg ¥§tI‡<€‚tIsr£ƒqupfv*x twpayˆh ªƒydg¤{|yŠxcfqupfv0Œf‡Štw„fsuh g¤€~€ˆqrpfv yŠ‡Š{wp€‚¥§tw‡Šg0{|yˆqutwp/‡Š~fsrhG€ ° ¢ h*{wsu€ˆt›«q}€ˆx ~€Š€zcftM¬:yŠt!‡ŠhTf~xhkyˆcfh*€‚hG{|‡xc“€‚Œ{Ixht|¥Uyˆcqu€4{|suvwtI‡ˆqryˆcg „ƒ ~©€‚qupfv/€‚~ x qrhTpIyx ‡ˆqryˆhT‡ˆq}{¥§tI‡o³p«qupfv   =

(27)  #$ 8    w° ¢ h¤vwqu£whkyE¬¨t¼x ‡ˆqryˆhT‡ˆq}{f´]twphyŠc{My {wŒfŒf‡Št_ª«qrg¤{MyŠhT€6yŠcfhzŒ‡ˆtI„fsrhTg „a*suqrpfhG{|‡Šq Tqrpv%yˆcfho£M{|‡Šqu{w„fsuhT€T´I{|p©{|pftwyˆcfhT‡¦yŠc{Myd«h ‡Šqr£IhT€¨{€‚«€‚yˆhTg tw¥ suqupfhT{w‡#hT a~{MyŠqrtIp€¨¥§‡ˆtIg yˆch%pa~gk„h ‡<tw¥t«x x ~f‡ˆ‡Šh p©xhT€tw¥¥§~fp©x.yˆqutwp¼€ˆƒgk„tws}€ ° lohTpfh ‡{|sx twpayˆh ªƒyZg¤{MyŠxcqrpfv%¬d{w€¦Œf‡ˆhT£ƒqrtI~€‚su  (ƒpftM¬#p*yŠt„©h•¶<†U±ÞxtIg*Œsrh yˆSh MÎiwWi O·° xtIpayˆhªƒyZg¤{_ „h/£ƒqrhT¬¨hGµ{w€0{suqrpfhG{|‡¤€ˆhTxtIpƒ±·tw‡«h ‡k¥§~fpxyˆqutwp¬#q²yŠcPtIpfh/{|‡Švw~fg0h payG´¦¬#cfh ‡Šhyˆcfh/„fqup«hT‡¤qu€*suh¥Ñy. . . . . . . .    !#"  $. . &%. ('. ..  . 1. . .. 5. . . /0 0!#"21. .  . . 76. . . . . . . $. . . /0 0!#"  . $. ) +* -,. &%. &% 43. /0 0!#"  1. /0 0!#"8596 $. $. &%. &% :3. 3. 3. . ;. < ,. =, /<.

(28) <. ?>. Ï  ý ÏÑþ.

(29)  

(30)        !"#%$. V. qug0Œfsuqux q²y#{|pyˆcfhocftIsrh•qu€¨yˆcho€ˆqrpvwsuhzt«x x ~f‡ˆ‡Šh p©xhztw¥­yˆcfh4„tw~fp©£M{|‡Šqu{w„fsuhw°6bdca~©€¨x twpayˆh ªaydg¤{Myxcfqrpv q}€Z{k‡ˆhG€EyŠ‡ˆq}x.yŠhT¥§tw‡Šg t|¥­suqrpfhG{|‡¨cfqrvIcfh ‡ˆ±·tw‡«h ‡Ug¤{Myxcfqupfv´a¬#cfq}xc¤¬{I€Z€ˆcftM¬#p0yˆt„h•¶z†U±Þxtwg0ŒfsuhyŠhz„ƒ fh¨lo‡ˆtƒtwyˆKh M 3‘ O½X° D<hT‡ˆhUsuqrphT{|‡+g*hG{|p€^yˆc{|y+twpsro€‚tIsr~«yŠqrtIp€­¬#cfhT‡ˆh¦{wsrs|¥§~fpx.yŠqrtIp€+{w‡ˆhUsuqupfhT{w‡T´GqQ° hw°GxtIpIy{|qup hG{wxc“tw¥UyˆcfhTqr‡4„tw~fp©“£M{|‡Šqu{w„fsuhT€<h ªf{wx.yŠsr/tIpxhI´]{w‡ˆhxtwp©€‚q}«h ‡ŠhT^°obdcfq}€•c{w€•„©hTh p¸hªƒyˆhTp«hT“yˆt!yˆcfh xT{w€ˆh•¬#ch ‡Šh4{0„tw~p›£M{w‡ˆq}{|„fsuh4g¤{_t«x x~‡<{My#g0tI€‚y yŠqrg0hT€<„a ztI~fvwcfhT‡‚yE{wp ¢ qrhT‡ T„fqux (ƒq MIUT – O½´ ¬#ch ‡Šh<¶<†U±ÞxtIg*Œsrh yˆh phT€Š€¦cftIsuf€U¥§tw‡ k = 1 {|p0«hGxq}fk{|„fqusuq²yE¥§tw‡ k ≥ 2 ° p{|suvwtI‡ˆqryˆcfg

(31) ¥§tw‡¦vIh pfhT‡Š{ws €ˆhTx twp«±½tI‡Š«hT‡4g0{|yŠxcfqupfv¼q}€%vwqu£whTp®„a D<~hy{wp ,+{|p@v M)UWY3O½°“»¨~f‡ŠqrhTp^´ •qu{wp®{wp¯¹ƒcfFq M

(32) ˜ O¨vwqu£wh¤{wp {wsrvItw‡Šq²yŠcfgŽ¥§tI‡Z€‚hGxtIpƒ±·tw‡«h ‡,g¤{MyŠxcqrpfv4yŠc{My¨qrg0Œf‡ŠtM£whG€h xquh px ¥§tw‡¦yˆcfhzxT{w€ˆhdt|¥]‡ˆquvwcay‚±·c{wp€ˆq}«hT€ ¬#qryˆc¼g¤{wpa„tw~fp“£_{w‡ˆq}{|„srhG€<{|p¥§hT¬Žxtwp©€Ey{|payŠ€T°<¹ƒhTx twpƒ±·tw‡«hT‡<{|pyŠcfqr‡/tw‡«hT‡<g¤{MyŠxcqrpfv!{|‡Šh ¶z†U±Þxtwg0ŒfsuhyŠh MWO·´]¬#cfqrsuh¥§tI~f‡ˆyˆc«±·tw‡«h ‡•g¤{MyŠxcqrpfv›qu€4«hGxq}f{|„fsuh„f~fy4¶ *z†ZEb QEº U±½c©{|‡ MÎi  O·° .ftw‡ tI‡Šfh ‡€#{|„tM£who¥§tw~f‡zq²yoqu€<€‚yˆqusus+twŒh p¼¬#chyˆch ‡<cfquvwch ‡ˆ±½tI‡Š«hT‡#g¤{MyŠxcqrpfv¤q}€<«hGxq}f{|„sr0h MIU5U O½°d‹#hTx h payˆsu ,+tI{I«h ‡4c{I€%€‚cftM¬#p¸yˆc©{MycfquvwcfhT‡‚±·tw‡«hT‡o„hy{M±·g¤{MyŠxcqrpfv/q}€4~fp«hGxq}f{|„srhI´+„f~«ykyˆcfq}€«tƒhT€ˆp  yqrg0Œfsu {wpƒIyŠcfqupfv¤{|„tw~«y<«hGxq}f{|„fqusuq²yEtw¥yŠcfh%„hyŠ{|±½h yŠ{0x {I€‚/h MIUT3˜ O·° Dzqr‡{My{f´ Z{|g¤{wf{¼{wp@  Dz{w‡Š{wt M)UT  O¨c{_£Ih€EyŠ~«quhTyŠcfh›xtIg0Œfsrh ª«q²yEsu{wpf€Šx {wŒ©h¤tw¥yŠcfh›€ˆhTx twpƒ± tI‡Šfh ‡kg¤{|yŠxcfqupfv¾Œ‡ˆtI„fsrhTg ¬#q²yŠcµ‡ŠhT€ˆŒ©hGx.y*yˆt¸€ˆh £Ih ‡{|s¨‡ˆhG€EyŠ‡ˆq}x.yŠqrtIp€ ´6q½° hI°®pa~gk„h ‡0t|¥z€ˆhTx twpƒ±·tw‡«hT‡ £M{w‡ˆq}{|„fsuhT€T´ƒpƒ~fgk„h ‡#tw¥,t«x x ~f‡Š‡ˆhTpxhG€¨tw¥£M{|‡Šq}{|„fsuhT€T´«vw‡Štw~fp©­´a¥§~fpx.yŠqrtIp«±½¥§‡ˆhThw´f„f~fy<pft|y<€‚yˆ‡{Myˆqr³©xT{Myˆqutwp+° •~f‡zqrpayˆhT‡ˆhG€Ey#¥§tI‡#yˆch€EyŠ‡Š{|yˆqr³hT!¥§‡{|vwg0hTpIy<c©{w€#„h hTpg0twyˆqu£_{|yˆhG/„a›yˆcfhk‡ˆhG€‚~fsryŠ€dtIpyˆcfhkfhTxq}ƒ± {w„fqusrqryE®t|¥z€‚yˆ‡{Myˆqr³hGµxtIpayˆhªƒy*~fpfqr³©x {|yˆqutwp MÎiwiƒ´¦iw–«´6=i U O·° zyŠcfh ‡¥§‡{|vwg0hTpIy€k¬#ch ‡Šh›~fpfqr³©xT{Myˆqutwpµqu€ fhTxq}f{w„fsrh%{w‡ˆh•yˆcfh4£M{|‡ŠqryE›i¥§‡{|vIg0h paPy MIU WO o{wpyŠcfhoyE¬¨tw±·x twpayˆh ªƒy‚±·£_{w‡ˆq}{|„srh#¥§‡{|vIg0h paPy MÎi| ’ O½´f¬#ctI€ˆh x tw‡Š‡ˆhG€‚Œtwp©«qrpvkg¤{Myxcfqrpv*Œ‡ˆtI„fsrhTg¤€d¬¨h%{|s}€ˆt0x twp€ˆq}«h ‡G°

(33) 8:$,#  >"%$, #= ¢ h¤{w€Š€‚~g*h*{³ªƒhG¾qup«³pq²yŠh0€ˆhy X t|¥ Ýqrp©«qr£ƒq}«~{ws •£M{|‡Šqu{w„fsuhT€T´]{›³fª«hT¾qrpf³pfqryˆh¤€‚h y C tw¥¨xtIpayˆhªƒy £M{w‡ˆq}{|„fsuhT€T´_{|p%{d³ªƒhG%€‚h y Σ t|¥«¥§~px.yŠqrtIpk€‚ƒg„©tIsu€­tw¥«³fª«hT%{w‡ˆqryEw° ¢ hZ¬#qususI~€ˆh x, y, z ¥§tI‡+qup«qu£ƒqu«~©{|s £M{w‡ˆq}{|„fsuhT€T´ X, Y, Z ¥§tI‡ox twpayˆh ªƒy•£M{|‡Šqu{w„fsuhT€T´ a, b, c, d ¥§tI‡ox twp€‚yŠ{wpayŠ€z{wp f, g, h ¥§tw‡ot|yŠcfh ‡z¥§~fpx.yŠqrtIp €ˆƒgk„tws}€ °  E Ýtw‡Z‰E~€E+y  #{|‡Šhkx twp€‚yˆ‡Š~x.yŠhT!¥§‡Štwg&yˆcfhk£_{w‡ˆq}{|„srhG€<{|p¼¥§~fpx.yŠqrtIp¾€ˆag„©tIsu€ qup yˆcfh/~€ˆ~{wsd³‡Š€‚y‚±·tw‡«hT‡*¬d{_w´¨¬#cfh ‡Šh¼xtIpIyŠhªƒy¤£M{|‡Šqu{w„fsrhG€0{|‡Šhx twp€ˆqufh ‡ŠhT {w€0g0twp{I«q}x¥§~fp©x.yˆqutwp €ˆƒgk„tws}€ ° 8   

(34) !qup¤{oyˆhT‡ˆg qu€¦{4€ˆhT a~fhTpxh#tw¥ŒtI€ˆq²yŠqr£Ih#qrpayŠh vwhT‡Š€,yŠc{My¦qup«q}x {|yˆhG€6yˆcfh<{w‡ˆvI~fg0h payŠ€ ¬#ch ‡Šh•tIpfhofhT€Šxh p©f€qrp{yŠh ‡Šg yˆt*‡ˆhG{wxc¤yŠcfh4Œ©ta€‚qryˆqutwp+° .tw‡dhªf{wg*ŒsrhI´IyŠcfh a qu€#{|yŒtI€ˆq²yŠqrtIp 2.1 qrp {|p qu€#{|y<Œ©ta€‚qryˆqutwp  ´ƒyˆcfh%‡Štƒt|y#Œ©ta€‚qryˆqutwp+° f (b, g(a))  quf€¤{¾yˆhT‡ˆg ¬#qryˆc{ €‚qupfvwsuhtƒxTx~f‡Š‡Šh px h›t|¥zyˆcfh¼€ˆŒ©hGxq}{|sdtwŒh ‡{MyŠtw‡ ´¦yŠcfh "8 )I°b+t hTg0Œfc{w€ˆq h4yˆc©{My•{*yŠh ‡Šg C q}€z{¤xtIpayˆhªƒy<¬h%¬#‡ˆqryˆh C[ ] tw‡U‰E~©€Ey C[] ° QÞp¼Œ©{|‡ˆyˆq}x~fs}{|‡#¬h%¬#qrsus+g0ta€Ey tw¥^yˆchzyŠqrg0h4¬#‡ˆqryˆh ¥§tI‡ X( ) ° x twpayˆh ªay C[] g¤{_0„ho{wŒfŒfsuqrhG¤yˆt0{kyˆh ‡Šg t ´ƒ¬#‡ˆqry‚yŠh p C[t] ´f{|p yŠcfhk‡ŠhT€ˆ~fsryoq}€zyˆcfhkyˆX[] h ‡Šg xtIp€ˆqu€‚yˆqupfvtw¥ ¬#q²yŠc ‡Šh Œsu{IxhT/„ƒ ° ¢ h*€‚ŒhTx q²¥§/yŠcfh*Œ©ta€‚qryˆqutwp t|¥Z{ €ˆ~f„«yŠh ‡Šg t qrp€ˆq}«h%{¤xtwpayŠhªƒy#„a C[t/p]C°  8!5Zt|¥U{kyŠh ‡Štg t qu€<{wpƒxtwpayŠhªƒy C[] €ˆ~xcp yˆc©{My ¥§tw‡¨€ˆtwg0hzx twpayˆh ªƒy D[] {|p©*yˆh ‡Šg t ° ¢ h<¬#qrsus~©€‚h s, t, l, r ¥§tI‡¦yˆhT‡ˆg¤€Ztw‡Zx twpayˆh ªay€ ´a{|p t = D[C[t ]] § ¥ w t < ‡  x I t a p yˆhªƒy€ ° C, D. Õ½ËEÌÝÔ#+ÍÎÐMÓNJսսË<ÍÎÓ.Õ½ÐÉ_NJ_ÕdÌÝÓTÕ½ÓÉGÒË ÉM_ÇÌÝáÓTÇÓÒ6ÓÇÒ,a×|ú_ÇËEá+ÈEÍÎúMÇÈ·ÇÖ Ê_Ð_ÍÎðÎÓÍ ÕÑî0ðÎËEÓú Ò,.ËEáÝú%Õ½ÌQNJÊÕ½î<Í _ս˂É_ú›ËZÈEÇÓ.íGÐ ÕQÕQÉ_ËÞÓ.÷TÌEÕ<Ù íGÐ_Í MȂNJսÍÎÓ.ÐÍÎÐ*ÕQÉ_ÍÎá _Ç wËEÌdÍÎá |Ç ­ËEúa×á½ÍÎÐ_ÈEË<Õ½ÉGË >. +;. . . . <. . <. , /<. *. 2. >. 2. 2. 0. ýý Ð Zfìå.ç.æ. < 

(35) . 2 0.

(36) Y.  ". 

(37)  "8   

(38)  . ¢ h¨{wsu€ˆtzxtIp€ˆqu«hT‡  

(39) 8! w´ ¬#cquxc{w‡ˆhUyŠh ‡Šg¤€+¬#qryˆck{wp{|‡Š„fqryˆ‡{|‡Šzpƒ~fgk„h ‡t|¥ft«x x ~f‡Š‡ˆhTpxhG€ tw¥ƒyˆcfhcftwsuhw° C  8   

(40) 8!]qu€,{#g~fs²yŠq²±ÞxtIpayˆhªƒy+¬#qryˆc*{My+suhT{I€EyyE¬¨tzcftwsuhT€T° ¢ hZ¬#‡Šq²yŠhZgk~s²yŠq²± x twpayˆh ªƒyŠ€¦{I€ C[ , . . . , ] °U¹«~xc›{%g~fs²yŠq²±ÞxtIpayˆhªƒy¦g¤{_*„©h•£aquh ¬hT¤{I€¦{€ˆhTx twp0tI‡Š«hT‡¦s}{|gk„]f{4yŠh ‡Šg ¬#cfhT‡ˆh4yŠcfh%„©tI~fp£M{|‡Šqu{w„fsuhT€ t«x x~‡#hT{wxchªf{Ix.yˆsutIpxh%{|p© λx . . . λx C[x , . . . , x ] qup¯suh¥Ñy‚±½yˆtw±½‡Šquvwcay%tw‡«h ‡G°!¹ƒt f [ , ] xtI‡ˆ‡ŠhT€ˆŒtwpf€oyŠt λxλyx f, .(x,. . ,y)x „f~«ypft|y%yŠt λxλy f (y, x) ° ¢ h g¤{_/‡Šh Œfs}{wx hk{›€ˆ~f„€ˆhyot|¥ZcftIsrhG€z„ƒyˆhT‡ˆg¤€•„ƒ¬#‡Šqryˆqupfv¥§tI‡•qup€‚yŠ{|p©xh . . , s , . . . , s , . . . ] ¬#ch ‡Šh yŠcfhk«twyŠ€<€‚yŠ{wp!¥§tw‡<ctwsuhT€T° ¢ cfhT‡ˆh¬h%pfhThTyˆt¤„hg0tw‡Šh%Œf‡ŠhTx qu€ˆh4¬¨h%C[. ¬#‡Šq²yŠh ¥§tI‡ cftwsuhT€<{wp ¥§tI‡%yˆch i±QyŠc¯cftwsuhw°/¶<twyˆh0yˆc©{Myk¬h›«t¼pftwy{|susutM¬

(41) £M{|‡Šqu{w„fsuhT€4yŠc{My€‚yŠ{wp¸¥§tw‡g~fsryˆqrk±·x twpayˆh ªay€ ´6{|p© yŠc{My#yŠcfh ‡Šh%{|‡Šh4pft0cftwsuhT€dqup C[ , . . . , ] „©hG€‚q}«hT€#yˆcfh%tIpfhT€dqup€ˆqu«hoyŠcfh€ˆ a~{w‡ˆh4„f‡{wx (Ihy€ °  ;  *q}€,{•g¤{|ŒfŒqrpfvz¥§‡ˆtIgŽqrp©«qr£ƒq}«~{wsa£M{w‡ˆq}{|„fsuhT€+yˆt•yˆhT‡ˆg¤€,{|p¥§‡ˆtIg xtIpIyŠhªƒy£M{w‡ˆq}{|„fsuhT€ yŠtxtIpIyŠhªƒyŠ€T´©€ˆ~xcyˆc©{My•{wsrs^„~«y<³pfqryˆhTsrg¤{|pƒ›qup«qu£ƒquf~{|s£_{w‡ˆq}{|„srhG€#{|‡Šh%g0{wŒfŒhTyˆtyˆcfhTg0€ˆh su£whG€ ´ {wp¾{wsrsU„~«y4³pfqryˆh su“g¤{|pƒ“x twpayˆh ªay4£M{|‡Šqu{w„fsuhT€o{|‡Šhg¤{|ŒŒ©hG“yŠt›yŠcfh g¤€ˆh su£whT€4{wŒfŒfsuqrhG“yŠt›yŠcfh0cftwsuhw° ¹«~f„€‚yˆqryˆ~«yŠqrtIp€<{|‡ŠhohªƒyˆhTp«hT!yŠt0yˆh ‡Šg¤€#{w€¥§tIsrsutM¬<€ *. . ,. ,. 2. n. 1. . *. . <. . 2. n. 1. n. 1. 2 2. 1 k 2. < 

(42) <. 2. . 2. 2i. 2. +. f (t1 , . . . , tn )σ = f (t1 σ, . . . , tn σ) xσ = σ(x). z¶ t|yŠh•yŠc{Myz€ˆ~f„€‚yˆqryˆ~fyˆqutwp€<xT{|pfpt|y#qrpayŠ‡ˆt««~x h4tw‡#‡Šh g0tM£whocftwsuhT€T° !  8    q}€0{|p hT a~{|yˆqutwpµ„hyE¬h hTp x twpayˆh ªƒyyŠh ‡Šg0€T´¨{wp {    8

(43)   

(44)  qu€0{wp hG a~{MyŠqrtIp¤„©h yE¬¨hTh pxtIpayˆhªƒy€ ° p  8    s ≈ t qu€¨{|phG a~{MyŠqrtIp¤„©h yE¬¨hTh p¤gk~s²yŠq²±ÞxtIpIyŠhªƒyŠ€T´a¬#cfquxc vIh pfhT‡Š{wsrq hG€yˆhT‡ˆg {|p©¼xtwpayŠhªƒyzhT a~{|yˆqutwp^° €‚~f„©€EyŠq²yŠ~«yˆqutwp σ q}€o{  ;  t|¥¦{|p¼hG a~{MyŠqrtIp s ≈ t qr¥ ° 

(45) "##$  8

(46)   

(47)  qu€0{wpµhT a~{|yˆqutwp ¬#cfhT‡ˆh «tƒhG€‚p  y¤xtwpay{|qupP{|pƒ¥§‡Šh h £M{w‡ˆsσq}{|„f=suhT€Ttσ°Ubdcƒ~€ σ qu€<{¤€ˆtwsu~«yŠqrtIp!tw¥6{*g¤{Myxcfqrpv¤hT a~{MyŠsqrtI≈p st≈ t q²¥ sσt = t °  !"#%$ C  )  

(48) q}€z{¤x twpM‰E~px.yŠqrtIp¼t|¥Ug¤{MyŠxcqrpfv›hT a~{MyŠqrtIp€T´{|pyŠcfh  Wt|¥¦{|p/qup€Ey{|px hq}€#yˆchpƒ~fgk„h ‡ tw¥6¥§~fpx.yŠqrtIp“{|p/£M{w‡ˆq}{|„fsuh€ˆag„©tIsu€<q²y•x twpayŠ{wqrp©€ °db+¬t¤qup€Ey{|px hT€<{w‡ˆh  ; 3 ) 8#qr¥UyˆcfhT!c{_£Ih4yˆcfh €Š{|g0hz€ˆhyt|¥+€ˆtwsu~«yˆqutwp©€ °  !";%$ C  ) q}€Z{k€ˆhyt|¥^qup€‚yŠ{|p©xhT€T´I{wp0yŠcfh• a~fhG€EyŠqrtIp¤¥§tw‡{vwqu£whTp qup€‚yŠ{wpxh¤q}€¬#cfh yˆcfhT‡qrykqu€€‚tIsr£M{w„fsrhI° ¢ h¬#qusrs{|s}€‚t“xT{|susUyˆcfh›srh ¥Ñy‚±·c{|p¯€ˆq}«hT€%tw¥<{|p®qrp©€Ey{|px h¤yˆcfh 8 4{wp%yŠcfhd‡ˆquvwcayˆ±½c{wp€ˆqufhT€yˆcfS h  !f°Ubdcfh 8 S ) ݇ˆhG€‚Œ+°TyŠcfSh 5

(49)   )5 ,tw¥ {g0{|yŠxcfqupfvŒf‡ˆtI„fsuh g tw‡¨{wp{|suvwtI‡ˆqryˆcfg ¥§tw‡¨q²ydq}€Uyˆchox twg0Œfsuhª«q²yE*¬#cfhT‡ˆh<tIpfsuyŠcfh• a~fhT‡ˆ §‡ŠhT€ˆŒ^°Iyˆcfh {MyŠ{ ¨£_{w‡ˆquhT€#{wp›yˆcfhf{|yŠ{ §‡ŠhT€ˆŒ^°ƒyŠcfh a~fh ‡Š Zq}€d³fª«hG­° ž Ä ZÄ œ ݝ Ä  8  "8 +5  H

(50)  I E

(51)      ≥ 2 "8  (X(t))σ = σ(X)[tσ].. . +. . +. >. < * . . .

(52) <. <. +. . ) +*. +.

(53) . .  .   . .  . ,), /<. < <. '. *. . . (< . <. +hy h „h{¥§~fpx.yŠqrtIp¼€‚ƒgk„tws­tw¥6{w‡ˆqryE k ≥ 2 ° ftI‡<{*x twpM‰E~px.yŠqrtIp s ≈ t ∧ . . . ∧ s ≈ t yŠ{5(wh 1. n. 1. ½i  .ftI‡{“vIqr£Ih p®yŠh ‡Šg hT a~{MyŠqrtIp hG a~{MyŠqrtIp^°. ) +*. , *. . . *. . ,*. *. . . . . 

(54)     ;   

(55)      +8   

(56) <P "= + <  < 

(57)  ; ' *) 8 ! . 

(58)  !   8

(59)   

(60)  "=    <  <S  +; ' *) 8K 8!5E8

(61)   

(62) . E   , U .. (,. . . +. . :,. . . yŠ{

(63) (Ih. . 8

(64)   

(65)  C. . n. {I€yŠcfh!x twpayˆh ªƒy. h(s1 , . . . , sk−1 , h(sk , . . . , h(. . . , sn ) . . . )) ≈ h(t1 , . . . , tk−1 , h(tk , . . . , h(. . . , tn ) . . . )). s ≈ t. h(2, s, . . . , s) ≈ h(2, t, . . . , t). 2. Ï  ý ÏÑþ.

(66) .  

(67)        !"#%$. ž Ä ZÄ œ ݝ Ä  8  "8 + E  ;8! 0W      !   "8   !";%$ 8

(68)   

(69)    S  8 ! 

(70)   ;  ) 8E!  8

(71)   

(72)  E   k‹<h Œfs}{wx hyŠcfhcftIsrh0tIp„t|yŠc¯€‚q}«hT€t|¥yˆcfh¤hG I~©{Myˆqutwp„ƒ¸{¼x twp€‚yŠ{wpIy%pftwyt«x x~‡ˆ‡Šqrpv!qup®yˆcfh Œ‡ˆtI„fsrhTg/° 2 Q·¥6¬¨h%c©{_£wh4{|phT a~{MyŠqrtIp!„hyE¬h hTp/gk~fsryˆqr±·x twpayˆh ªƒyŠ€T´ahI° v©°.

(73) .   #6. 

(74)   . . ,), /<. <. . . . . ) +*.

(75)  . . . . ' *. < .

(76) <. . . * <. . . . . C[f (C1 [2], C2 [2])] ≈ D[g(D1 [2], D2 [2])],. yŠcfh p¼hTq²yŠcfh ‡ f 6= g {|pyŠcfh ‡Šh%q}€<pft›€ˆtwsu~«yŠqrtIp^´ftw‡z¬¨hkxT{|p¼€ˆŒfsrqryzyŠcfq}€<hT a~{|yˆqutwp/qupIyŠt¤yˆchhT a~{|yˆqutwp€ ´ {wp ´M‡ŠhTf~xqupfv#yŠcfh¨g~fsryˆqr±·x twpayˆh ªay,hT a~{|yˆqutwp4yˆto{|phG a~fqr£M{wsrhTpIy C[] x twpM‰E≈~pD[]x.yŠqrtIpCtw¥[] x ≈twpaDyˆh ªa[]yhG a~C{MyŠqrtI[]p≈€ °/DQÞp[]yˆcqu€%¬d{_“¬h¤x {|ph suqug*qup{|yˆh{|sus¦Œf‡ŠtwŒh ‡%g~fsryˆqr±·x twpayˆh ªay€ ´ €ˆh h4†¦‡ŠtwŒtI€ˆqryˆqutwp UT‘k¥§tw‡<{*¥§tw‡Šg¤{|syˆ‡ŠhT{|yˆg0h payG° x twpayˆh ªay¦g¤{|yŠxcfqupfv4Œf‡Štw„fsuh g qup€‚yŠ{wpxhdq}€¦x {wsrsuhT 

(77) •qr¥hG{wxc*£M{|‡Šqu{w„fsrhdt«x x ~f‡€,{|y¦g0tI€‚y6tIpxh {wp 

(78) 5

(79)  %qr¥6{wsrs]¥§~px.yŠqrtIp/€ˆƒgk„tws}€dt«x x~‡ˆ‡Šqrpvqup/q²y<c{_£Iho{wp¼{|‡Šq²yE¤tw¥6{|ydg0ta€Ey<tIpfhw° bdcfh 3

(80)   ) C  Xtw¥^{|p¤t«x x ~f‡ˆ‡Šh p©xhdqrp!{oyˆh ‡Šg qu€¦yˆcfho€‚hG I~h px h#t|¥^xtIpIyŠhªƒyZ£M{|‡Šq}{|„fsuhT€UtIp0yˆcfh Œ©{Myˆc¾¥§‡ˆtIg&yˆcfh0‡Štatwyo«tM¬#p“yˆt/{|p¾qrpx sr~©«qrpv›yŠc{My4t«x x~‡ˆ‡Šh px hw°  xtIpayˆhªƒyog0{|yŠxcfqupfvŒf‡Štw„fsuh g qup€‚yŠ{wpxhq}€zxT{|susrhG  

(81)     qr¥U¥§tw‡zhT{wxc¼qup«qu£ƒquf~{|stw‡zx twpayˆh ªay•£_{w‡ˆq}{|„srh{wsrstƒxTx~f‡Š‡Šh px hT€#tw¥,yŠc{My £M{w‡ˆq}{|„fsuhoqrpyˆch%Œf‡ˆtI„fsuh gc{_£IhzyŠcfh€Š{|g0h4£_{w‡ˆq}{|„srh4Œf‡Šh³fª­°  Ÿ

(82)  À  "=   ) 1. 1. 2. 2. *. . '. ) +*. ,. <. :. ,. . ) +*. . X(f (Y (g(a, x)), Y (g(x, Z(z))))) ≈ f (g(a, b), b).  < <      "= '  #$  "=,  X 

(83)   "= , X  . . X Y.  "=,   . . XY.  "=,   . x. "8 C,  X. . XY x Z. XY Z. XY Zz . z.  Ÿ

(84)  À :.  <HC  <       < . X(Y (2)) ≈ f (g(2)) ∧ Z(X(2)) ≈ h(f (2)).  +; < " "= '   ) +*)-,C  X#. X. <. X.  C. ZX . ž Ä ZÄ œ ݝ Ä

(85) 

(86) 8! 

(87) "##$ C  ) "8 

(88)   E =

(89)  8  

(90)   ;   E   ¹«~fŒfŒtI€ˆh q}€›{wpqrp€‚yŠ{wpxh¾t|¥xtIpIyŠhªƒy›g¤{Myxcfqupfv° QÞp { €ˆtwsu~«yˆqutwp hG{wxct|¥4yˆch¾{My g0ta€Ey |l| xtIpayˆhªƒy4l£M{|≈‡Šqu{wr„fsrhG€oqrp l c{w€•yŠt„h¤qup€Ey{|payˆq}{MyŠhT¸„ƒ¾{/€‚~f„]xtIpayˆhªƒy%qup r ´tw¥¨¬#cfq}xc¸yˆcfhT‡ˆh {w‡ˆh ° •pxhx twpayˆh ªay£M{w‡ˆq}{|„fsuhT€%{w‡ˆh¤qup€‚yŠ{wpIyŠqu{|yˆhG¾yŠcfh ‡Šhq}€{Myg*ta€EytIpfh€ˆtwsu~«yˆqutwp¥§tw‡kyˆcfh qup«qu£ƒO(|r| quf~{|s­)£M{|‡Šq}{|„fsuhT€T´f€‚t*yŠcfh ‡Šh%{|‡Šh4{|y#g*ta€Ey O(|r| ) €‚tIsr~«yŠqrtIp€T° 2  Ÿ

(91)  À "# # I "= "8 K "=   / 8 C    

(92)   =

(93)  )      S  

(94) "##$   I      "=       "8  P 8 5 +  ÓÕQË]Õ½É_NJÕÕQÉ_Ë­áÝÕ·ÇÐ_ú_ÇÌQú¨ú_Ë MÐ_Í ÕQÍÎÓ.ÐËÞ÷GÈEðÎí_úG˂áfà.ÇÌÝÍ ÇÊ_ðÎËEá©ÇŠÕ«Õ½É_Ë­Ó ÈEÈEí_ÌQÌÝËEÐ_ÈEËÍ ÕQá½ËEð ÒÝÙ ï É_ÍÎá«ú_Ë MÐGÍ Õ½ÍÎÓ.ШÍÎá«Ë  í_Í àÇðÎ˂ÐÕ ÒuÓ.Ì­ÕQÉ_ËUú_Ë MÐ_Í ÕQÍÎÓ.Ð4ÓÒfáQÕQÌQÇŠÕ½Í MȂNJÕQÍÎÓ.ÐÇÐ_úoáQÍÎÔ _ðÎÍ MËEá]ÕQÉ_Ë6Õ½ÌÝ˂NJսÔ#ËEÐÕ,ÓÒ   Ê|˂ðÎÓ¦Ù.

(95) . .   . ,. . ) +*. /<. . . /<. ,. * *. . . =< * .

(96) <. . . 2. . 2|l|. :.

(97) <. . ýý Ð Zfìå.ç.æ. . <. . . ,*. <. <. :,. *.   '. . . 4*. ,. . * *. .  <. . . <. ,. ) +*. +* . <. * . * *.

(98) ˜.  " . 

(99)  "8   

(100)  . C ) +*)  <S  ! 0  "# < ,8 ,8 #,C 

(101)  S "=    '   ) +*)   $   8  <      55 << C+* *  ,8  ! <     C5  k  "8  *   

(102) 8!+8     ,. ,*.  . . .  !". . . X1 Y1 hX2 Y2 h . . . hXn Yn (a) ≈ ghgh . . . hg(a)..  "=  0 <+ "= <   0  

(103)      <

(104)    " <  5< "8   '   ) +*)<   

(105) 

(106) *   "= << 0 "8 + S  4  ,8/< <  *I(<  *h;  

(107)  <  . "=,=

(108)      '    *)<  g. X i , Yi. Xi.  "8 <  * ;    ,=

(109)  8 *. 

(110)   / <. . 2. Yi g(2). g(2). 2. C C 58,=   *  E   "= 

(111)  .   <  * ;  

(112) <S <. 2n. K   " .  <. . ®!#"$

(113) 0 13"4,5,79= 8  

(114) ,^qupfhG{|‡z»¨twpayˆh ªƒyzº“{Myxcfqrpv  ,,»º    

(115) suqrpfhG{|‡#xtIpayˆhªƒy<g¤{Myxcfqupfv0hT a~{MyŠqrtIp s ≈ t °  

(116) QE€ s ≈ t €ˆtwsu£M{|„fsu!h ,+qrphT{|‡oxtIpIyŠhªƒyzg¤{Myxcfqupfv›q}€•{wp¼qrpayŠh ‡ŠhT€‚yˆqupfv›€ˆŒ©hGxq}{|s6x {w€ˆhtw¥ZxtwpayŠhªƒy•g¤{Myxcfqupfv¬#cfhT‡ˆh£M{w‡ˆq}{|„fsuhT€ xT{|p„hd‡ˆhTvI{w‡Š«hG%{w€¬#qrs}fxT{|‡f€^¥§tI‡,x twpayˆh ªƒyŠ€T° ¢ hdxT{|pk€ˆtwsu£wh¨srqupfhG{|‡6xtwpayŠhªƒy,g¤{|yŠxcfqupfvzŒ‡ˆtI„fsrhTg¤€+„ƒ fap©{|g0quxŒf‡ŠtwvI‡Š{wg0g*qupfv©° ¢ h#„~fqrs}¤{•yŠ{w„fsrhd¬#cfq}xc*¥§tw‡UhT£wh ‡ŠŒ{wqr‡Utw¥{%€ˆ~f„«yŠh ‡Šg tw¥©yŠcfh#srh ¥Ñy‚±·c{|p© €ˆq}«h•{wp{k€ˆ~f„«yŠh ‡Šg t t|¥­yˆch•‡ŠqrvIcayZc{|p©€‚q}«h•t|¥­yˆch•Œf‡Štw„srhTg ‡ŠhTx tw‡f€¦¬#cfh yˆcfhT‡ ss g¤{MyxcfhT€ t ° ¢ h {I€ˆ€ˆ~fg0h%yŠc{My•¥§tw‡zhT£whT‡ˆ€‚~f„fyˆh ‡Šg ¬¨ h (aptM¬ ¬#chyˆch ‡<yŠcfh ‡Šhq}€•{cftwsuhkqup¼q²!y "]yˆcfq}€<qup«¥§tI‡ˆg¤{MyŠqrtIp“x {wp „hxtIg0Œf~«yˆhG›qup/srqupfhG{|‡dyˆqug0hw°¦bdcfh4y{|„fsuh%q}€d„f~fqus²y<‡ŠhTx ~f‡Š€ˆqu£wh su0¥§‡Štwg yŠcfh%„©twy‚yŠtwg2~Œ # Q·¥ s qu€#{wp›qup«qu£aq}«~{ws^£M{|‡Šqu{w„fsuh<yˆch pyˆcfh%{wp€‚¬h ‡dq}€dwhG€¨qr¥U{|p›twpfsuqr¥+yˆch ‡Šhoq}€dpft0cftIsrh4qup t ° # Q·¥ s = f (s , . . . , s ) {wp t = g(t , . . . , t ) yŠcfh p“yˆcfh*{|p€ˆ¬¨hT‡zq}€<IhT€<qr¥Z{|p©¼twpfsuq²¥ f = g ´ {|p s g¤{MyxcfhT€ t ¥§tI‡ 1 ≤ i ≤ m ° m=n # Q·¥ s = yˆch pyˆcfh{wp€ˆ¬¨hT‡q}€#IhT€dqr¥6{wp›tIpfsuq²¥ t = ° # Q·¥ s = X(s ) yŠcfh pyŠcfh{|p€ˆ¬h ‡dqu€dIhT€dqr¥6{wp!twpfsu›qr¥ s g¤{|yŠxcfhG€#€‚tIg*h4€ˆ~f„«yˆhT‡ˆg t|¥ t ° ,+hy „h/yˆcfh¼€ˆq Th!tw¥zyŠcfh/Œf‡ˆtI„fsuh g/° ¢ h/c{_£wh yŠ{|„srh/h payŠ‡ˆquhT€*t|¥4xtIp€Ey{|pay¤€‚q hI´Z{|pµyˆt x twg0Œfn~«yŠh•hG{wxc!h payˆ‡Š¤¬¨hopfhThT{Mydg*ta€Ey O(n) €‚yˆhTŒO(n €T° Dz)h px hoyˆcfh%{|suvwtI‡ˆqryˆcg ~©€‚hG€ O(n ) yŠqrg0h%{|p© €ˆŒ{wx hw´«{|p©suqrpfhG{|‡#xtIpayˆhªƒydg¤{MyŠxcqrpfv*q}€dqrp!†,°©¶<t|yŠhzyŠc{MydyŠcfqu€d¬tw~su›pft0srtIpfvwhT‡¨cftIsu›q²¥,¬¨h O(n ¬h ‡Šh•)yˆt{|susutM¬ £M{|‡Šqu{w„fsrhG€¨¥§tw‡<g~fs²yŠq²±ÞxtIpayˆhªƒy€ ° . . m. 1. i. 1. n. i. 2. 2. 0. ?>. 0. >. 2. 3. 2. Ï  ý ÏÑþ.

(117) ‘.  

(118)        !"#%$. $6"=+M %$U >"4   7 $,, M %$

(119) 0213"456!7  

(120) »¨twpayŠhªƒy<º“{Myxcfqrpv·»º    

(121) xtIpayˆhªƒy#g¤{Myxcfqrpv*Œ‡ˆtI„fsrhTgqup€Ey{|px h P °  

(122) QE€ P €‚tIsr£M{|„srh Z£wh pkyˆcftI~fvwc*xtIpIyŠhªƒy6g0{|yŠxcfqupfvoqu€6¶z†U±½c©{|‡qupkvwhTpfh ‡{|s½´_q²yUq}€,pfh £Ih ‡ˆyˆcfhTsrhG€ˆ€qrpayŠh ‡ŠhT€‚yˆqupfvzyŠtofh £whTsrtIŒ Œ‡Š{Ix.yˆq}x {ws¦{|suvwtI‡ˆqryˆcfg¤€o¥§tI‡q²yG´,{I€4¬¨h¤ctwŒh¤yˆc{|yg¤{|pƒ¾Œf‡{wxyˆq}x {wsrsu“qupIyŠh ‡ŠhT€‚yˆqupfv/qrp©€Ey{|px hT€%¬#qusrs¨„©h €ˆtwsu£M{|„fsuh#hT{I€‚qusukh ptw~fvIcyŠt„h<~€ˆh¥§~fs½° ¢ h<¬#qusus³‡€‚y¦vwqu£wh<{%vIh pfhT‡Š{wsf{|suvwtw‡Šqryˆcfg

(123) ¥§tw‡Zx twpayˆh ªay¨g0{|yŠxc«± qupfvoqrp*yŠcfqu€U€ˆhTxyˆqutwp^´I{|pyˆcfhTp*qupyˆcfh¥§twsusutM¬#qrpfv4€ˆhTx.yŠqrtIp€,g0tƒfq²¥§*{|phªƒyˆhTpq²y6yˆt4g0tw‡Šhh xquh payˆsu €ˆtwsu£wh4€ˆtwg0h4hT{w€ˆ›xT{w€ˆhT€T´ƒ{wp/«q}€ˆx ~€ˆ€yŠcfhxtIg0Œfsrh ª«q²yEtw¥,€ˆŒ©hGxq}{|s^xT{w€ˆhT€dt|¥6xtIpIyŠhªƒy#g¤{MyŠxcqrpfv©° ¢ h!vIqr£Ih›‡Š~fsuhT€k¥§tw‡x twpayˆh ªƒyg¤{Myxcfqrpv¾Œf‡Štw„fsuh g¤€*xtIp€‚q}€‚yˆqupfv“t|¥o{¾xtIpM‰E~fpxyˆqutwp tw¥zhT a~{|yˆqutwp€ „hyE¬h hTp gk~s²yŠq²±ÞxtIpIyŠhªƒyyŠh ‡Šg0€¬#cfta€‚h!‡ˆquvwcay‚±·c{wp®€‚q}«h›q}€vw‡Štw~fp^°¸‹#~fsuhT€*{|‡Šh›{wŒfŒfsuqrhG¯g0tƒf~fsrt {I€ˆ€ˆt«xq}{MyŠqr£ƒqryE{wp¾x twg0gk~«y{MyŠqr£ƒqryE  » <tw¥ ´­qQ° hw°u´­qrvIpftw‡Šqupfv¤yˆchtI‡Š«hT‡ztw¥ZhT a~{|yˆqutwp€•qrp{!x twp«± ‰E~px.yŠqrtIp^° ¢ cfh p {®‡Š~fsuh!¥Ý{wqrs}€0qry‡ˆhT¬#‡ˆqryˆhG€0q²y∧€¤srh ¥Ñy‚±·c{|p© €ˆq}«hyˆt ⊥ ° ¢ h/³‡€‚yvwqu£wh/«twp  y‚±Þx {w‡ˆh ptwp«h yˆhT‡ˆg0qupfqu€‚yˆq}xo‡ˆ~srhG€yˆc{|y<g0{_›„©h{wŒfŒfsuqrhG›hG{|vwhT‡ˆsu À   Ä

(124) ZÄ œ À q²¥ t = g(t , . . . , t ) ´ f =f (sg {w,p. . .m, s=)n≈"t|tyˆ→ch ‡Šs¬#qu≈€ˆhzt¥Ý{wqr∧s½° . . . ∧ s ≈ t ¼Ä   À À   Ä

(125) ZÄ œ À q²¥ C[] = "ft|yŠcfh ‡Š¬#qu€ˆh•¥Ý{|qusQ° ≈ C[] → >  ݝ Â Ä  À  ݟfœ C[ ] ≈ D[ ] → ⊥ q²¥ m 6= n °  À ž

(126)  À ž ©À q²¥ s = t "ft|yŠcfh ‡Š¬#q}€‚h•¥Ý{|qusQ° x ≈ s ∧ x ≈ t → x ≈ s Ä  À   À ž ©À q²¥ C[] = D[] "«t|yŠcfh ‡Š¬#qu€ˆhoX[] ¥Ý{|qusQ° ≈ C[] ∧ X[] ≈ D[] → X[] ≈ C[] Ä  À   

(127) Ÿf À q²¥ s 6= {|p t = C[t ] "ftwX[]yˆcfhT≈‡ˆ¬#C[] q}€ˆhz¥Ý∧{wqrs½X(s) ° ≈ t → X[] ≈ C[] ∧ s ≈ t ¶zt|yŠhyˆc©{My qu€*{|pµhT a~{MyŠqrtIp¯„©h yE¬¨hTh p g~fsryˆqr±·x twpayˆh ªay€ ´U{wpyˆc{|y t x {wp¯„©h/xtIg0Œf~«yˆhG¯qup suqupfhT{w‡dyˆqug*hIs° ≈ t .,qup{|susr¼¬h*pfh hG¾{›ftwp  y‚± (ƒpftM¬Žpftwp©«hyŠh ‡Šg*qupfq}€EyŠqux‡Š~fsrhkyˆc{|yo‡ŠhT a~fqu‡ŠhT€•„{wx (ayˆ‡{wx (ƒqupfv¤tM£whT‡•{wsrs {wŒfŒfsuquxT{MyŠqrtIp€ Ÿ«ž QŸ« š  À  § q²¥ s 6= {|p t = C[t ] ° X(s) ≈ t → X[] ≈ C[] ∧ s ≈ t  . ;. . 1. m. 1. m. 1. m. n. 1. 2. 2. . $. . $. . . 2. m. 2. n. !. $. $. . . . . !. .  . 0. 0. 2. 0. 0. 5. +. . . . 2. ýý Ð Zfìå.ç.æ. 0. 0.

(128) G– U.  " . 

(129)  "8   

(130)  . xtIpayˆhªƒy*g0{|yŠxcfqupfvŒf‡Štw„fsuh g q}€qup   

(131) qr¥•{|susdq²y€*hT a~{MyŠqrtIp€*c{_£whyˆcfh¥§tw‡Šg tt ‡ X[] ≈ C[] {wphT{Ixc£_{w‡ˆq}{|„srh¼t«x x ~f‡€{Myg0tI€‚y›tIpxhI° bdcfhT‡ˆh¼q}€›{wptw„ƒ£ƒqrtI~€¤twph±½yˆt|±·xtwp≈h I x tw‡Š‡ˆhG€‚Œtwp©«h px hz„hyE¬h hTp/€ˆtwsu£whG¤¥§tI‡ˆg¤€#{|p©€ˆ~f„€‚yˆqryˆ~fyˆqutwp€T°  Ÿ

(132)   À "# # I   !    # ;   8     

(133)  "=  

(134)      . <. :.  * %$   ". /. "= <. . . <. . .  . .   

(135) 8!. . ,*. * * <.  !";%$.  ,. *. .    *IS),*     ,8/<       ,8*IS/ < ) , *     8!5  *   

(136)     ,8/ <     *) +  ,= <  . *. . <. <. . . . X[] ≈ 2 ∧ Y (a) ≈ ga ∧ Y (g 2) ≈ f (a, g 2) X[] ≈ 2 ∧ Y [] ≈ g 2 ∧ a ≈ a ∧ Y (g 2) ≈ f (a, g 2) X[] ≈ 2 ∧ Y [] ≈ g 2 ∧ Y (g 2) ≈ f (a, g 2).   *. . X[] ≈ f (ga, 2) ∧ f (Y (a), Y (g 2)) ≈ f (a, g 2)  X[] ≈ f (ga, 2) ∧ Y (a) ≈ a ∧ Y (g 2) ≈ g 2 X[] ≈ f (ga, 2) ∧ Y [] ≈ 2 ∧ a ≈ a ∧ Y (g 2) ≈ g 2 X[] ≈ f (ga, 2) ∧ Y [] ≈ 2 ∧ Y (g 2) ≈ g 2 . X[] ≈ f (ga, 2) ∧ Y [] ≈ 2 ∧ g 2 ≈ g 2 X[] ≈ f (ga, 2) ∧ Y [] ≈ 2 ∧. ¢ %h pftM¬AŒf‡ˆtM£IhzyŠcfh%xtI‡ˆ‡ŠhTxyˆpfhG€ˆ€t|¥,yˆch{|suvwtw‡Šqryˆcfg/° ¨À

(137)

(138) Ÿ "=/ 5

(139)      

(140)   ! 8  S I E   qup€ˆŒ©hGx.yŠqrtIp^° ¨À

(141)

(142) Ÿ   P S0  

(143) "##$   ). 2. ≈2. X[] ≈ f (ga, 2) ∧ Y [] ≈ 2. . . . X[] ≈ 2 ∧ f (Y (a), Y (g 2)) ≈ f (ga, f (a, g 2)). . 1. , /< <. ) 

(144)  <  5 S "=++8   . , *. . 4,8/< <   *  <   

(145)  %+;  

(146) .    *IS),*     ,8/<       ,8*IS/ < ) , *     8!5  *   

(147) . . S#. 4<. . X(f (Y (a), Y (g 2))) ≈ f (ga, f (a, g 2))..  . . <. . *'. <. . *. <.   <  3'  "8 <  E4< * ;  

(148) < ,. .  . 2. 1. 4, ) +*   C =*)    "=S

(149) 8!   !";%$  C ) +*)  <E) 

(150)     F * *,=< <  +*)  ,),*  

(151)   

(152)  <K   P 1  , . *).. ,)P,n*  !P   !"#%$H+8     "8   < 

(153) <   ;  0 <P(P< * ;      F

(154)  /  * S    <F (< * ;     <     . ,. . P. 1 ≤ i ≤ n. Pi. kbdchx twpayˆh ªay0£M{|‡Šqu{w„fsuh!{My*yˆch‡Štƒt|y0gk~€‚y0„©h¼€ˆ~f„€‚yˆqryˆ~«yŠhTP„a €ˆtwg0hxtwpayŠhªƒyT° .tw‡0hT{Ixc ŒtI€Š€ˆqr„fsuh%xcftwq}xh4tw¥,{0xtIpIyŠhªƒydyˆcfhT‡ˆh%q}€#{0xtI‡ˆ‡ŠhT€ˆŒ©tIp«qupfv0{|ŒfŒfsuq}x {MyŠqrtIp!tw¥ {w‡ˆq}{|„fsuh¹ƒŒfsuq²yG° 2 ¨À

(155)

(156) Ÿ

(157)      !";%$ C  )  0

(158) P  3   "=     "= ) 0 E   . 1. 3. . ,), *.  ) +*). . . ,. ) +*. . <. < * '. . . . * <. . Ï  ý ÏÑþ. <.

(159)  

(160)        !"#%$. UU. E   SQ·¥+yˆcfhT‡ˆh•qu€d{|p›hT a~{MyŠqrtIp¬#qryˆc!{«q hT‡ˆhTpIydpƒ~fgk„h ‡t|¥cftwsuhT€¨twp¤yŠcfhosrh ¥Ñy‚±¦{|p›twp¤yŠcfho‡ˆquvwcay‚± c©{|p®€ˆqu«h0yŠcfh p®¬h{|ŒfŒsr¾º“~fs²yŠq²±‚»¨twpayŠhªƒy*»¨su{I€‚c+° ¥ÑyŠh ‡h ªƒc©{|~€‚yˆqu£wh¤{|ŒŒfsrq}x {|yˆqutwp®{|sus¦hT a~{|yˆqutwp€ c©{_£wh•yˆcfh€Š{|g0h4pƒ~fgk„h ‡#tw¥,cftIsrhG€dtwp„©twyˆc¼€ˆqu«hG€ ° Q·¥6yˆch ‡Šhqu€•{|p/hT a~{|yˆqutwp/¬#qryˆc“{0¥§~fp©x.yˆqutwp“€ˆƒgk„tws+{|y<yˆch‡ˆtƒtwy<t|¥,yˆcfhsrh ¥Ñy‚±·c{|p/€ˆqufh%yˆcfhTp¼¬¨h xT{|p¯{|ŒŒfsr zhGxtIg*ŒtI€ˆhw´,tw‡%qr¥dyˆcfh›srh ¥Ñy‚±·c{|p¯€ˆq}«h¤qu€{/cftwsuh¤¬h{|ŒfŒfsu Dztwsuh zhGxtIg*ŒtI€ˆhw° ¥ÑyŠh ‡ h ª«c{|~€‚yˆqu£whd{|ŒŒfsrq}x {|yˆqutwpt|¥{wsrsayŠcfhd‡ˆ~fsuhT€U{w„©tM£Ih¨{wsrs«hG I~©{Myˆqutwp©€qupyˆcfhdŒf‡Štw„fsuh gŽc©{_£wh¨yˆcfh¥§tw‡Šg x ≈ t tI‡ X(s) ≈ t ° bt›{|p¼hG a~{MyŠqrtIp ≈ t {|‡Šqu{w„fsrhk¹«ŒfsrqryoxT{|p/„h{|ŒŒfsrquhT^° ¥Ñyˆh ‡ohª«c{w~€‚yˆqu£wh{|ŒŒfsrq}x {|yˆqutwp/t|¥ {wsrs]yŠcfh%‡Š~fsrhG€#{|„tM£wh4{|X(s) sus­hT a~{|yˆqutwp€dqupyˆcfh%Œf‡Štw„srhTgc{_£wh•yˆch4¥§tw‡Šg x ≈ t tw‡ X[] ≈ t ° Q·¥d{!£M{w‡ˆq}{|„fsuh tI‡ t«x x ~f‡Š€og~fs²yŠqrŒsrh*yˆqug0hT€oyŠcfh p®b+hT‡ˆg—º¼h ‡Švwhtw‡k»¨twpayˆh ªƒy4º¼hT‡ˆvIh*xT{|p„©h {wŒfŒfsuqrhG­´«‡ŠhT€ˆŒ©hGx.yˆqu£wxhTsrI° X ¢ h¤xtwp©xsu~«hyŠc{My%qr¥ZpftIpfhtw¥¦yˆch*‡Š~fsuhT€•qu€4{wŒfŒfsuquxT{|„fsuhkyŠcfh p¾yˆcfh0Œf‡Štw„srhTg&q}€oqrp€‚tIsr£IhT/¥§tI‡ˆg/° 2 ¶zt|yŠh<yˆc©{Mydgk~fsryˆqr±·x twpayˆh ªƒyŠ€Z{w‡ˆhoxtIpa£Ih ‡ˆyˆhGqupayˆtyˆhT‡ˆg¤€{|px twpayˆh ªƒyŠ€¦„ƒ*yˆchox twgk„qrp{|yˆqutwptw¥ {|‡Šq²± {w„fsuh¤¹«Œfsrqry{|p •hTxtIg0Œ©ta€‚hI´^¬#cfq}xc¸hT£wh payŠ~{|susr¸€‚hTŒ{|‡{MyŠhT€zyˆcfh¤cftIsrhG€otƒxTx~f‡Š‡Šqrpfvqup¸Œ{w‡Š{wsrsuh sU€ˆ~f„«± yŠh ‡Šg¤€ ° •~fh<yŠtkyŠcfh•«tIp  y‚± (aptM¬ pftwpfhyˆhT‡ˆg0qupfq}€‚g t|¥ {w‡ˆq}{|„srh4¹ƒŒfsuq²yyˆcfq}€¨qu€‡{Myˆch ‡Zqupfh ¤x qrhTpay "ƒ¬¨h ¬#qusus+«q}€ˆx ~€ˆ€#{*„hyˆyˆh ‡zg*h yˆcft«qup¼¹«~f„€ˆhTx.yŠqrtIp Vf° ° ¨À

(161)

(162) Ÿ "8+       H I   ! S      O(n)  E   kbdcqu€6¥§tIsrsutM¬<€,¥§‡Štwg †¦‡ŠtwŒtI€ˆqryˆqutw p U 4qupyŠcfh<pfh ªƒyZ€‚hGx.yˆqutwp0¬#cfhT‡ˆhd¬h<€‚ctM¬ yˆhT‡ˆg0qup{MyŠqrtIp¬#qryˆc ‡ŠhT€ˆŒhTx.ydyŠt{|phªƒyˆhTp«hT/€ˆhy#t|¥6‡Š~fsrhG€ ° 2 "=P $%  " "8      "=F 5

(163)    K C 5  8   ) K  3P $%  ÀƒÄ ž À

(164)  . . . 3. 3. 3. . 1. . . . ,), *. *. <. . +;. . <. . /<. <. 8, <. . . 6. .

(165)    

(166)  5/<   3'  ,C ) +*)  . *. . . ,), *. <.    *IK),* #C /< <  * '    . . . <. . . <. * <.  * *

(167) < * ;  

Références

Documents relatifs

[r]

Certes, une partie de la frontière Est avec l’Iran est globalement l’héritage d’une longue histoire marquant la séparation entre le monde ottoman et le monde iranien,

Dans House of Leaves, chaque voix ou presque a son caractère propre et l’hétérogénéité typographique qui en résulte donne à voir un théâtre de voix : Times pour Zampano,

On y présente d’abord une introduction générale à la radiothérapie, puis on cible plus particulièrement la SBRT et le suivi de marqueurs en temps réel pour en venir finalement

Selon les régions, les divers types sont plus ou moins bien représentés. Sont négligées de la même manière les zones montagneuses de l'Est, les Alpes et le Jura,

Ten microalgal strains indigenous to Quebec were examined for biomass and lipid productivity under different growth modes: photoautotrophic, mixotrophic (light), and

Dans le cas où entre les objets, les types d’énonciation, les concepts, les choix thématiques, on pourrait définir une régularité (un ordre, des corrélations,

Les vaccins anticancéreux ont donné des succès cliniques limités dans le cancer de la prostate. Le vaccin de cellules tumorales GVAX en est un exemple. L'immunosuppression