• Aucun résultat trouvé

The Non-Smooth Approach applied to simulating Integrated Circuits and Power Electronics Evolution of electronic circuit simulators towards fast-SPICE performance

N/A
N/A
Protected

Academic year: 2021

Partager "The Non-Smooth Approach applied to simulating Integrated Circuits and Power Electronics Evolution of electronic circuit simulators towards fast-SPICE performance"

Copied!
49
0
0

Texte intégral

(1)The Non-Smooth Approach applied to simulating Integrated Circuits and Power Electronics Evolution of electronic circuit simulators towards fast-SPICE performance Pascal Denoyelle, Vincent Acary. To cite this version: Pascal Denoyelle, Vincent Acary. The Non-Smooth Approach applied to simulating Integrated Circuits and Power Electronics Evolution of electronic circuit simulators towards fast-SPICE performance. [Technical Report] RT-0321, INRIA. 2006. �inria-00080839v2�. HAL Id: inria-00080839 https://hal.inria.fr/inria-00080839v2 Submitted on 21 Jun 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 Non-Smooth Approach applied to simulating Integrated Circuits and Power Electronics Evolution of electronic circuit simulators towards fast-SPICE performance Pascal Denoyelle — Vincent Acary. N° 0321 20 Juin 2006. ISSN 0249-0803. apport technique. ISRN INRIA/RT--0321--FR+ENG. Thème NUM.

(3)

(4) 

(5)  

(6) !#"#%$&(')"*,+#-"# . / 0%.-%$213"45+"6'7 $98:<;3=7>:*%?) "#@' >BA #+C"# DEF%#%?C "#@"4C@+"6'"*G+#-'H<;3-$' EI' 

(7) 8 / 13> J=CEI @ KMLONQPRLOSUTVXWY[Z\VXS]S]V ^_!` WPaVXWcbed

(8) PaLOfQZ g=hji*kmln<oqpsrutRv[wyxzi*kmlQw%{R|jkm}Q~€‚a|jlQw ƒ?~z„† yl#xU‡@ˆ‰ƒ@Šqƒ ‹UŒŽj„X~x=xzlQ‘6hj{j‚a|jl-{O’C“X”X•[–ru•Ž“m—Ž|j˜{™•†“X“Žšrœ›R Œ†žŽlŸw ∗. †.  e¡C¢Q£*¤I¥j¦Ž£Ž§ nU|jkmlQ~€‚‘*ŒŽ¨©w˜k |©¨˜Œ†x€˜„Ž{m˜wªŒ-«ŽlQv l*¨˜l*kmlQ{Xx?˜{mx€h©l<¬[lQw€˜žŽ{m„†­l*¨˜lQ‘#x€~z„Ž{j‚‘%‘#˜~6‘#|j®xzwQ¯C°<|jžŽl l*±O„X~x6wª²@l*~zl¬[l*³X„†x€lŸ¬mx€„´®x=˜{x€hjlM©ŒŽwx%”Ž“0vŽlQŒŽ~zw5Œ†¨˜¨®„I²%˜{jž x€„0­µ|j¨®¨˜v¶Ol*{jl*·jx=­µ~€„XkHx€hjlMO„Xwzw˜¶j˜¨®®x€˜lQw ©~€„I³R‚¬[lQ¬e¶av‘#˜~z‘*|j®xzw%Œ†{¬‘*„Žkm„X{jl*{ax6w@­¸Œ†¶j~z˜‘QŒIxz®„X{exzlQ‘6hj{j„X¨®„XžŽ˜lQwQ¯ ¹ x€hj~zlQw€hj„X¨˜¬B˜{:xzhjlºwh©~€˜{j«R®{©ž»„†­0‘*„ŽkmO„Ž{jlQ{Xx6we²=ŒŽwl#¼j‘*l*lQ¬jlQ¬FxzhjlQw€l½¨‚ŒŽwxvXlQŒŽ~zwQ¯¾‡@lŸw‚¬[lQw xzhjl´„aw®x€˜³Žl0l#±\lQ‘4xM„Ž{¿x€hjl0®{ax€lQžŽ~6ŒIxz®„X{À„†­?­µ|j{‘4x€˜„Ž{w<˜{ax€„!Œew€®{jžX¨®l0‘6hj®JŒ†{©¬™„Ž{Àxzhjl0lQ¨®lQkml*{axzŒŽ~€v O„I²@l*~‘#„X{©w€|jkm[x€˜„Ž{cÁ={jlQžXŒ†x€˜³Žl!l#±\lQ‘#xzweŒŽjOlQŒ†~ŒŽwml*¨˜lQ‘#x€~z˜‘QŒ†¨UŒ†~6ŒŽw€Âxz˜‘jhjlQ{j„ŽkmlQ{©ŒÃj~zl*³R®„X|©w€¨®v {©l*žŽ¨˜lQ‘#x€lŸ¬¯3tR˜k |j¨‚ŒIxz®„X{©weŒŽ~€l!xzhjl*~zl#­µ„X~€l™k0|©‘6hB¨˜„Ž{jžXl*~e¬[lŸw©Âxzl™x€h©l¿˜{©‘#~zlQŒXwlŸ¬ÄOl*~€­µ„Ž~zk

(9) Œ†{©‘*lQw

(10) „Ž­ ‘*„Žkmj|[xzl*~6w<¶OlQ‘QŒ†|©w€l lQ¨®lQkml*{axzŒŽ~€vÀ‘#„Xkm„X{jl*{axzwqkm„[¬[l*¨‚wŒ†~zl km„Ž~zl ‘#„Xkmj¨®l*¼¿Œ†{©¬Àx€hjl

(11) ‘#„Xkm„X{jl*{axzw ‘*„Ž|j{ax%˜{©‘#~zlQŒXwlŸw*¯ ˆ‰{Jx€h©˜w-~zl*O„Ž~€xQÁ)²5lmj~zlQw€l*{axŒ†{Jhj‚wyxz„Ž~zvÀ„†­@x€hjl

(12) km„[¬[l*¨‚w-Œ†{¬½ŒŽ¨®žX„Ž~zÂxzhjk

(13) w<xzh©ŒIx ŒŽ~€l

(14) ‘*¨˜ŒXw€w€˜‘QŒ†¨˜¨®v |wlŸ¬

(15) x€„´w˜k |©¨˜Œ†x€lŒ ‘#˜~6‘#|j®x=Œ†x5xzhjlMl*¨˜lQ‘4xz~€‚‘*ŒŽ¨¨˜l*³Xl*¨]¯Åg=hjl*~zlQŒ†­Æx€l*~ŸÁa²5lq®{ax€~z„[¬[|©‘*l<xzhjlMw€„†Ç‰‘*ŒŽ¨®¨˜lQ¬m{©„Ž{[Ç w€km„R„†x€h

(16) ‘*¨˜ŒXw€wńŽ­k´„[¬[lQ¨˜wªŒ†{©¬

(17) ŒŽ¨®žX„Ž~zÂxzhjk

(18) wÅwyxz|©¬[˜lQ¬

(19) ŒIxªx€hjlUˆynq‹%ˆ ¹ ÁaŒŽwŲ@l*¨˜¨ŒXwx€h©l%·©~6wyxª~zlQw€|j¨®xzwxzh©ŒIx xzhjl*v!vR˜l*¨‚¬[lQ¬À˜{™xzhjl0w€˜k |j¨‚ŒIxz®„X{™„†­ªw€®kmj¨˜l0‘*®~6‘#|©Âx6w*¯Mg=hjl0{©„Ž{[ljwkm„R„†xzh™Œ†j©~€„aŒŽ‘6hÀwlQl*k

(20) w<x€„e¶Ol0Œ ©~€„Xk´‚w€®{jžmw€„Ž¨˜|[x€˜„Ž{­µ„Ž~=xzhjl-¨˜ŒŽ~€žXlMwz‘*ŒŽ¨®llQ¨®lŸ‘4x€~z‚‘*Œ†¨cw€˜k |j¨‚ŒIxz®„X{c¯ ÈÀÉaÊ\ËzÌ Í ¤IÎC¢Ž§ l*¨˜lQ‘4xz~€„X{j‚‘ ‘#˜~6‘#|j®xQÁ{©ŒŽ{j„†xzlQ‘6hj{©„Ž¨˜„ŽžŽ˜lQwQÁO{a|©k´lQ~€‚‘*ŒŽ¨Cw€˜k |j¨‚ŒIxz®„X{cÁ{j„Ž{jÇÏw€km„a„Žx€h¿w€v[wyÇ xzl*k!Á©ÐÑ5ƒ. ∗ †. ÒOÓyÔ¸Õ]ÖØ×4Ù´Ú4ÛÝÜ#ޟÖØÙß4à4à4á Òâ©ã ÖØÙÝÕåääyã6ÓyÙ*æ‚ç ìè ç í ÓyÙÝä ׀ã é#Ô¸éÝÓ æØêCæ ӀÖØêCÙÝÔ¸ÖØÖÙÝãŸÔ¸ç Öë ãŸÔ ç ë Ô. Unité de recherche INRIA Rhône-Alpes 655, avenue de l’Europe, 38334 Montbonnot Saint Ismier (France) Téléphone : +33 4 76 61 52 00 — Télécopie +33 4 76 61 52 52.

(21)  -C

(22)    j%.+#"=-#"´+ % (#('"*G+#"# 9$%' @"45+"6'"# 0

(23) % .- % ' @ $  % #%ª) "´ +G$!+"#')' @ >BA*+"* $%' '"*G+#%+C' $@"4C@+"6'% #%?C "m +%' A='. + D

(24) $, m8 / 13> -"*$  ¢  § Ð)Œqw˜k |j¨‚ŒIxz®„X{{R|jkm}*~z˜a|jl@lQwx|j{0¬[lŸw)}Q¨®}Qkml*{axzwÇϑ*¨®}Ÿw¬©Œ†{©wC¨‚Œ<‘#„X{©‘#lQ[x€˜„Ž{´¬[lQwC‘#˜~6‘#|j®xzw }Q¨®lŸ‘4xz~€„X{j˜a|jlŸw*¯CÐclŸwªl*±O„X~x6w?˜k´O„Ž~€xzŒŽ{axzwªa|jv

(25) w„X{Xx@‘#„Ž{w€ŒX‘#~z}QwŬ[lQj|j‚w5”X“Œ†{©wª„Ž{axc y|©wza|  ˜‘*Ol*~zkm˜w ¬jl™x€˜~zl*~j¨®lQ®{©l*kml*{ax!©Œ†~€x€¬[lQwO„Xwzw˜¶j˜¨®®x€}Ÿw„Ž±OlQ~xzlQwe©Œ†~¨®lŸwxzlQ‘6hj{©„Ž¨˜„ŽžŽ˜lQw¬[l½­¸Œ†¶j~z˜‘QŒIxz®„X{:¬[lQw ‘*®~6‘#|©Âx6w=l#x<‘#„Xkm„aw€ŒŽ{Xx6w*¯ Ñ5lŸw%¬[l*~z{j˜i*~zlQw%Œ†{©{j}*lŸw*Á[|j{!w€l*|j˜¨)Œ´}#xz}q­µ~6Œ†{‘6hjc¬jŒ†{w=¨˜Œ´km®{©˜Œ†x€|j~z˜wzŒIxz®„X{c¯ªŠq|[x€~zl¨  l#±\l#xUO„Xw€®x€®­ w€|j~?¨ ®{ax€}QžŽ~6ŒIxz®„X{´¬[lŸwÅ­µ„X{©‘4xz®„X{©w?¬jŒŽ{©w?|j{‘*®~6‘#|©Âx?|j{©˜a|jlUl*x5w€|j~ª¨˜lQw?‘*„Ž{©w€„Žkmk

(26) ŒIxz®„X{©w}*¨˜}*kmlQ{Xx6Œ†˜~€lŸw*Á ¬jlQw?l*±Ol*xzwª{j}*žaŒIx€®­¸wªŒŽj©ŒŽ~zŒŽ˜wzwlQ{axő*„ŽkmkmlU¨‚ŒkmŒŽ{j®­µlQwxzŒIxz®„X{¬[lUjh©}*{j„Xk´iQ{jlQwª}*¨˜lQ‘#x€~z˜a|jlŸw?©ŒŽ~zŒXw®x€lŸw ŒŽ|[x€~zl#­µ„X˜w@{j}QžŽ¨˜®žX}QwQ¯ÅÐclQw%w€˜k |j¨‚ŒIxz®„X{©w%w„X{ax=ŒŽ®{©w€¶OlQŒ†|‘#„Ž|©©¨®|©w=¨˜„Ž{©žŽ|jlŸw=l*{!¬[}*j®x<¬[lŸw=k´lQ®¨˜¨˜l*|j~zlQw Ol*~€­µ„Ž~zk

(27) Œ†{©‘*lQwq¬[lQwM„Ž~6¬[˜{©ŒIxzl*|j~6w<‘QŒ†~M¨®lŸw<km„[¬[iQ¨®lŸwM¬jl´‘*„Žkm„aw€ŒŽ{axzwU}Q¨®}Qkml*{axzŒŽ®~zlQwMwl´‘#„Xk´©¨®l*¼R®·©lQ{Xx l*xU¨®l{j„Xk ¶j~zl-¬[l‘#lŸw%‘#„Xk´O„XwzŒ†{ax6w@w  ŒŽ‘*‘*~€„XÂxŸ¯ n<„Ž|©w5j~z}Qw€l*{ax€„X{©w?¬jŒŽ{©w5‘*lU~6Œ†jO„Ž~€xª|j{h©˜wx€„X~€‚a|jl<¬[lŸwªkm„[¬[i*¨˜lQwªl#x%¬[lQw5Œ†¨˜žŽ„X~€®x€hjkmlŸw?‘#¨‚ŒŽwzw‚a|jl#Ç kmlQ{Xx%|[xz®¨˜‚w}Ÿw%„X|j~Uw€®k0|j¨®lQ~=|j{À‘#˜~z‘*|jÂxUŒŽ|{j˜³ŽlŸŒ†|}*¨˜lQ‘#x€~z˜a|jlX¯ ª{©w|©ÂxzlŽÁj{j„X|©w%Œ†¶O„Ž~6¬[„X{©w@¨˜Œm‘#¨‚ŒŽwzw€l ¬jlkm„R¬ji*¨˜lQw-l*x0¬  Œ†¨˜žŽ„Ž~z®x€hjkmlQw ¬[Âx6w{j„X{[ÇÏ~€}QžŽ|j¨˜®lQ~zwM}*x€|©¬[˜}Qw À¨  ˆynq‹%ˆ ¹ l#x0¨®lŸwj~zl*km˜l*~6w-~€}Ÿw|©¨Âx6ŒIxzw ¬jlw€˜k |j¨‚ŒIxz®„X{¬[l-‘#˜~6‘#|j®xzw@}*¨˜}*kmlQ{Xx6Œ†˜~€lŸw=X|  ˜¨˜w=„X{ax@Ol*~zkm˜w%¬  „Ž¶jx€l*{©®~Ÿ¯?Ð  Œ†j©~€„[‘6hjlq{j„Ž{[ÇÏ~z}*žŽ|©¨®˜i*~zl ŒŽj©ŒŽ~zŒŽÂx%‘#„Xk´kml|j{jlw€„Ž¨˜|[xz®„X{j~z„Žkml*xx€lQ|©w€lMO„Ž|©~%¨˜Œ

(28) w€®k0|j¨‚ŒIx€˜„Ž{}*¨˜lQ‘#x€~z˜a|jl ´žŽ~6Œ†{¬[lq}Ÿ‘6hjl*¨˜¨˜lŽ¯ 3Í £Ÿ¢ Ë "¦ !  ¢J§ ‘*®~6‘#|©Âx-}*¨˜lQ‘#x€~z„Ž{j‚a|jlŽÁ){©Œ†{j„Žx€lŸ‘6hj{j„Ž¨˜„ŽžX®lŸw*Áw€®k0|j¨‚ŒIx€˜„Ž{J{R|jkm}*~z˜a|jlXÁ)w€vRwx€iQkml´{©„Ž{[Ç ~z}*žX|j¨˜®lQ~QÁ[ÐCÑ5ƒ.

(29) ”.  

(30)  

(31)   !"$#&%('*)+ ,- .$/0( 1,2(. 3. 46587:9;587+<. = >@ £Q¤ Í Î

(32) C¦†£

(33) A Í @ ? CED £Q¥[£ ÉXËzÍF¸Ë £HG ÉXË ¥[¤Ý£

(34) £HA. B. J É Î Í »I¥ A @ É ! É ¦Ž£*¤ A¸¦X¥ !=H¢ A !¸¥[£ Í ¤I¢ •j¯®– ª ¨®lŸ‘4x€~z‚‘*Œ†¨km„[¬[lQ¨˜w ¯-¯¯-¯¯-¯¯-¯-¯M¯-¯¯-¯¯-¯-¯¯-¯¯-¯M¯-¯¯-¯-¯¯-¯¯-¯¯-¯-¯M¯-¯ K •j¯ • ™p l#x€h©„R¬©w=­µ„Ž~Uw€l#x€x€˜{jžm|jx€hjl-lŸX|ŒIx€˜„Ž{we¯-¯¯-¯-¯¯-¯¯-¯M¯-¯¯-¯-¯¯-¯¯-¯¯-¯-¯M¯-¯ L •j¯ •j¯®– g=hjltR©Œ†~6w€lgCŒ†¶©¨®lŸŒ†| ¹ jj~z„XŒX‘6Nh M]t[g P¹ O ¯¯-¯¯-¯M¯-¯¯-¯-¯¯-¯¯-¯¯-¯-¯M¯-¯ L •j¯ •j¯ • g=hjl-pÀ„[¬[·lQ¬!nU„[¬jŒŽ¨ ¹ {©ŒŽ¨®v[w€˜Qw Måp™n P¹ O ¯-¯¯-¯M¯-¯¯-¯-¯¯-¯¯-¯¯-¯-¯M¯-¯–X– •j¯ ” n<|jkml*~z˜‘QŒ†¨cŒŽ¨®žX„Ž~zÂxzhjk

(35) w ¯¯-¯¯-¯-¯M¯-¯¯-¯¯-¯-¯¯-¯¯-¯M¯-¯¯-¯-¯¯-¯¯-¯¯-¯-¯M¯-¯–Ý• •j¯ ”©¯®– tR„Ž¨˜³R®{jž´xzhjSl RÑ:j~z„Ž¶j¨˜l*k9¯M¯-¯¯-¯¯-¯-¯¯-¯¯-¯M¯-¯¯-¯-¯¯-¯¯-¯¯-¯-¯M¯-¯–Ÿ” •j¯ ”©¯ • nU|jkml*~z‚‘*Œ†¨˜{ax€lQžŽ~6ŒIx€˜„Ž{„†­Å¬[®±OlQ~€lQ{Xxz˜ŒŽ¨cŒ†¨˜žŽlQ¶j~zŒŽ˜‘<lQa|©Œ†x€˜„Ž{©w¯¯-¯¯-¯-¯M¯-¯–Ÿš É F ¥j¢Q£H¢ A !¸¥jH£ A Í @ Í F !¸¥j¤ W É ¦ Aµ¤I"¦ XAµ£Ÿ¢ T É ¦ É @ £mI¥ UVUC¤ Í ¥j¦ G É ¢

(36) £ Í

(37) £ G  =J YEZ G É @ Í @ Ë ¢  ÍcÍ H£ GÄ$¥ UXU¤ Í ¥j¦ G C[= ›¯®–2g=h©l-kmŒ†x€hjlQk

(38) ŒIx€‚‘*ŒŽ¨\­µ~zŒŽkml*²@„Ž~z«´„Ž­xzhjl-{j„X{[ÇÏw€km„R„†x€h!Œ†©j~€„aŒŽ‘6hB¯-¯¯-¯¯-¯¯-¯-¯M¯-¯œ•j– ›¯ • t[®k0|j¨˜Œ†x€˜„Ž{~€lŸw|©¨Âx6w%Œ†{©¬!‘#„Xkm©Œ†~z˜w€„Ž{]w \ „I²@l*~5l*¨˜lQ‘#x€~z„Ž{j‚‘*w

(39) ¯-¯¯-¯-¯¯-¯¯-¯¯-¯-¯M¯-¯œ•Ž” ›¯ •j¯®– g=hjll#¼jŒ†kmj¨˜l„†­Cx€hjl‹UÐ^Ñ R ‘#˜~6‘#|j®x2¯-¯¯-¯¯-¯M¯-¯¯-¯-¯¯-¯¯-¯¯-¯-¯M¯-¯œ•Ž” ›¯ •j¯ • R<˜„[¬[lQw=¶j~z‚¬[žŽl-‘#˜~6‘#|j®x<w˜k |©¨˜Œ†x€˜„Ž{¯¯-¯-¯¯-¯¯-¯M¯-¯¯-¯-¯¯-¯¯-¯¯-¯-¯M¯-¯œ•Žš ›¯ •j¯ ” ƒC„I²@l*~%‘*„Ž{R³ŽlQ~xzl*~6wB¯-¯¯-¯-¯M¯-¯¯-¯¯-¯-¯¯-¯¯-¯M¯-¯¯-¯-¯¯-¯¯-¯¯-¯-¯M¯-¯œ•Žš ›¯ ” t[®k0|j¨˜Œ†x€˜„Ž{~€lŸw|©¨Âx6w%Œ†{©¬!‘#„Xkm©Œ†~z˜w€„Ž{]w \ p½Št´xz~zŒŽ{©w‚wx€„Ž~6w=Œ†{©¬˜{a³Xl*~€x€lQ~zw ¯¯-¯-¯M¯-¯ ”a• ›¯ ”©¯®– ƒ?®lŸ‘#lQ²%˜w€l¨®˜{jlQŒŽ~%km„R¬jl*¨c„Ž­CŒmp½Štex€~6Œ†{©w€‚wyxz„Ž~¯M¯-¯¯-¯-¯¯-¯¯-¯¯-¯-¯M¯-¯ ”a• ›¯ ”©¯ • ˆ‰{a³Xl*~€x€lQ~=‘6hŒ†˜{ ¯-¯¯-¯¯-¯-¯M¯-¯¯-¯¯-¯-¯¯-¯¯-¯M¯-¯¯-¯-¯¯-¯¯-¯¯-¯-¯M¯-¯ ”Xš BE_ Í @ ¦ ! CH¢ A Í @ Y*=. `IaÙ(b©à c4ߟÚ.

(40) ›. # ] /]]/-/

(41) *,-   (. X`. í.

(42) .  

(43)  

(44)   !"$#&%('*)+ ,- .$/0( 1,2(.  

(45) 587:4 7  4 5. ª¨®lŸ‘4x€~z„Ž{©˜‘‘#˜~z‘*|jÂx6wÇ-lQÂxzhjl*~´®{axzl*žŽ~6ŒIxzlQ¬Ã„X{Č¿w€˜{jžŽ¨˜lw€|j¶©wx€~6ŒIxzle„Ž~´ŒŽw´Œ¿w€l#xm„†­<‘*„Žkm„X{jl*{ax6w „X{. Œ¶O„XŒ†~6¬ÀÇUŒŽ~€l0³Žl*~zvÀ„†­Æxzl*{JŒ‘*„Žkmj¨˜l#¼¿ŒXw€w€l*k0¶j¨®v!„Ž­5Œ¨®„ŽxM„Ž­5¶©ŒXw‚‘ ‘*„Žkm„X{jl*{ax6wq²%®x€hJ{j„X{½¨˜®{©lQŒ†~ ‘6hŒ†~6ŒŽ‘4xzl*~z˜wx€‚‘*wQ¯ RqlQw€®žX{jl*~6w%„Ž­lQ¨®lŸ‘4xz~€„X{j˜‘©~€„[¬[|©‘#xzwUŒŽ~€l-~zl*¨˜vR®{©ž

(46) „Ž{!³IŒ†~z®„X|©wU‘6hjlŸ‘6«a˜{jžw€„†­Æxy²=Œ†~zlQw=Œ†km„X{jž

(47) ²%hj‚‘6h lQ¨®lŸ‘4xz~€‚‘*ŒŽ¨?x€˜kml¬j„Žk

(48) Œ†˜{»w˜k |©¨˜Œ†x€„Ž~6w²@l*~zl

(49) xzhjl·©~6wx x€„½¶l¬[l*³Xl*¨˜„ŽOlQ¬º˜{ºxzhjllŸŒ†~z¨®v H– L KI“Xw*¯™g=hjl t[ƒ?ˆ€Ñ ¾•¿w˜k |j¨‚ŒIxz„Ž~ MåtR˜k |j¨‚ŒIxz®„X{»ƒ?~z„ŽžX~zŒŽks²%®x€h ˆ‰{axzl*žŽ~6ŒIxzlQ¬ Ñ5˜~z‘*|j®x ?kmjh©ŒXw‚w O ²=ŒŽw~zl*¨˜lQŒXwlŸ¬ ˜{ H– L KŽÀ¶RvÃx€h©l!‡@lQ~€«Xl*¨˜l*vÃ|j{j˜³ŽlQ~zw€Âxyv»ŒXwmŒ™­µ~zl*lÀw€„†­Æxy²=Œ†~zlŽ¯ºˆÏxŒ†¨˜¨®„I²Uw0xz„½h©ŒÝ³Xl˜{©w€®žXhax´˜{ax€„Jx€hjl lQ³Ž„X¨®|[xz®„X{„Ž­C³X„Ž¨®xzŒŽžŽlQw%ŒŽ{©¬!‘#|j~z~zl*{axzw=˜{ÀŒ

(50) ‘#˜~z‘*|jÂxUkm„[¬[lQ¨®¨˜lQ¬ÀŒXw%Œ†{ÀŒŽwzwlQk ¶j¨˜v„Ž­¬[˜O„Ž¨˜lQwQ¯@tR„Xk´l-„Ž­ xzhjlmŒ†¨˜žŽ„Ž~z®x€hjk

(51) wql*k ¶OlQ¬©¬[lQ¬½®{ÃtRƒ?ˆ€Ñ  l*³X„Ž¨˜³ŽlQ¬™®{Ñ#„Xk´kmlQ~z‘*˜ŒŽ¨³Xl*~6w˜„Ž{©wQÁO¶j|[xx€hjl´k

(52) Œ†˜{½„X~€˜žŽ˜{©ŒŽ¨ ­µlŸŒIxz|j~€lŸw²@l*~zl«ŽlQ[Hx \m|©w€le„Ž­<wkm„R„†xzhºkm„R¬jl*¨‚w0ŒŽ{©¬»w€„Ž¨˜³a˜{jž¿Œ¿wl*x0„†­U{©„Ž{º¨˜®{jlŸŒ†~´lQa|©Œ†x€˜„Ž{©w-²%®x€h n<l*²=xz„Ž{[lj‹UŒ†©h©w„X{½ŒŽ¨®žX„Ž~zÂxzhjkœ„Ž~®xzw-³IŒŽ~€‚Œ†{axzwQ¯

(53) g=hjlmkm„R¬jl*¨‚w-„†­=¬[l*³R‚‘#lQw-ŒŽ{©¬JlQw€lŸ‘#‚Œ†¨˜¨®v¿„†­@pJŠt xz~zŒŽ{©w€˜wx€„X~zw=­µ„X¨®¨˜„I²@lQ¬x€h©l0˜{©‘#~zlQŒXw˜{jž~z„Ž¨˜l„Ž­?©Œ†~6ŒŽw€Âxz˜‘l#±\lQ‘4x6w¬[|jlxz„ežXl*„Žkml*x€~z®lŸw<w€hj~€˜{j«IŒ†žXl Œ†{¬ w€Ol*lQ¬  w=˜{©‘#~zlQŒXwlX¯ ‡@lQw€‚¬[lQw@xzhj˜w<”Ž“´vŽlŸŒ†~6w@wx€„X~€vXÁRl*¨˜lQ‘4xz~€„X{j‚‘*w%‘#˜~6‘#|j®xzw=lQ³Ž„Ž¨˜³ŽlŸ[¬ \

(54) £ G É >]@ £ É W©¤I¥[£ É Î _ Aµ¤I"¦ XAµ£Ÿ ¢  >H_ £ É ¦ G @ Í ! Í WA É ¢ {j„I²BŒ†¨˜¨®„I² xz„ ˜{Xxzl*žX~zŒ†x€l%hR|j{©¬[~zlQ¬©w?„†­ckm˜¨®¨˜˜„Ž{©w „†­x€~6Œ†{w‚wyxz„Ž~6w%w²%®xz‘6h©®{jžŒ†x ° -­µ~zlQa|jlQ{©‘#˜lQwU„Ž{ÀŒ¬[˜l-„†­ 1 cm ¯@ˆÏx<‚wU„Ž|jxU„†­?a|jlQwx€˜„Ž{x€„ w˜k |©¨˜Œ†x€l%Œ<²%h©„Ž¨˜l@w€|©‘6h´ˆ€Ñò%®x€hmŒMtRƒªˆ€Ñ Ãw€˜k |j¨‚ŒIxz„Ž~ŸÁIl*³ŽlQ{ ²%®x€h0x€„[¬jŒÝv  wC‘*„Žkmj|[xzl*~6w Cg=hR|©w ¬[l*³Xl*¨˜„ŽOl*~6w-k

(55) Œ†˜{j¨˜v½~zl*¨˜v½„X{»Œx€hj„X~€„X|jžŽh»tRƒªˆ€Ñ  w€®k0|j¨˜Œ†x€˜„Ž{Ć­Uw€k

(56) Œ†¨˜¨5w€|j¶©w€l#xzw „†­U‘#˜~6‘#|j®xzw Mµ¨˜„ŽžX˜‘5žXŒ†x€lQw O ©~€„I³R‚¬[®{©žqŒ<‘*„XŒŽ~zw€l?km„[¬[l*¨[„Ž­©lQŒX‘6h w|©¶©wl*xxzh©ŒIx²%˜¨®¨R¶Ol@|wlŸ¬˜{0Œq¨®lŸw€wCŒŽ‘Q‘#|j~6ŒIxzl w˜k |©¨˜Œ†x€„ŽS~ M¸¨®„XžŽ‚‘w˜k |j¨‚ŒIxz„Ž~ O ¯ nUlQ³Žl*~€x€h©l*¨˜lQwzw*ÁCw„Xk´l

(57) Œ†~6ŒŽw€Âxz˜‘´l#±\lQ‘#xzwx€h©Œ†x0‘*ŒŽ{Ãwx€~z„Ž{©žŽ¨˜v¿ŒI±\lQ‘#x-x€hjl„XlQ~zŒ†x€˜„Ž{ M¸‘*~€„aw€wxzŒŽ¨®« ¶l*xy²5lQl*{F¨˜®{jlŸw*Á%w€®žX{©Œ†¨%˜{ax€lQžŽ~zÂxyvXÁªO„I²5lQ~¬[˜wx€~z˜¶j|[x€˜„Ž{ O h©ŒÝ³Žlx€„º¶Ol™‘*ŒŽ~€l*­µ|j¨˜¨®v ‘*„Ž{©w€‚¬[l*~zlQ¬¯ tR„ŽkmlU„Ž­\x€hjlŸwlUlQ³ŽlQ{

(58) ~€lŸX|©®~zlUŒ-jhRv[w‚‘*ŒŽ¨jkm„[¬[l*¨©x€„¶Ol<j~z„ŽOl*~z¨˜v0‘6h©ŒŽ~zŒX‘4x€lQ~€! *lŸ¬ M¸å¯ l<Œw€|j~€­¸ŒŽ‘*l „Ž~³X„Ž¨˜|jkmlkm„[¬[l*¨5va˜l*¨‚¬[˜{jž™Œ™w€l#x „Ž­%©Œ†~€x€‚Œ†¨ª¬j±\l*~zl*{ax€‚Œ†¨ªlQa|©ŒIxz®„X{©w O #¯ "BÂxzh Œ†{ºlQ¨®lŸ‘4x€~z‚‘*Œ†¨ w˜k |©¨˜Œ†x€„Ž~M¨˜®«XlmtRƒªˆ€Ñ UÁc®xM‚w-wyxz®¨˜¨„aw€w€˜¶j¨®l0x€„!wx€|©¬[v™x€hjlQ®~l#±\lQ‘#xzwQ¯ ‡@|[xŒe¨˜„ŽžX˜‘0w˜k |©¨˜Œ†x€„Ž~ |©w€lQ¬À­µ„X~-Œ²%hj„X¨®lm‘6hj˜¿w˜k |©¨˜Œ†x€˜„Ž{½‘QŒ†{j{©„†xqhŒ†{©¬[¨˜l´j~€„XlQ~€¨˜vx€hjlŸwl´l#±\lQ‘#xzwQ¯g=hR|©wUxzhjl*~zl´˜w 2. `IaÙ(b©à c4ߟÚ.

(59) š. # ] /]]/-/

(60) *,-   (. x€„[¬jŒÝvŒM{jlQlQ¬ ­µ„Ž~Ōq­¸ŒŽwxCxz®kml%¬[„XkmŒŽ®{0l*¨˜lQ‘#x€~z˜‘QŒ†¨[w˜k |©¨˜Œ†x€„Ž~Cxzh©ŒIxŲ%˜¨®¨jŒŽ¨®¨˜„I²ºx€h©l*˜~?w˜k |j¨‚ŒIxz®„X{ ²%ÂxzhÀŒ†{ÀŒŽ‘Q‘#|j~6ŒŽ‘*vmŒXw%‘#¨˜„Xw€l-ŒŽw=O„Xwzw˜¶j¨˜lqxz„etRƒ?ˆ€Ñ UÁŒ†{©¬k |‘6he­¸ŒXwyxzl*~Ÿ¯ A É Î Ë H¢ A1W @ ¥ !5¦ Aµ¤I¦ VA¸£Q¢m¥ @ Î U ÍRÌ É ¤ É ! É ¦Ž£*¤ Í @ A¸¦X¢Ž§ x€hjlŸwl‘#˜~6‘#|j®xzw@˜{a³X„Ž¨˜³ŽlU˜{ax€lQ~zŒX‘4x€˜{jžmŒ†{©ŒŽ¨®„Xž Œ†{©¬Ã¬[˜žŽ®xzŒŽ¨Å©Œ†~€xzwQ¯ R<|jlmxz„!x€hjl

(61) ‘*„Žkmj¨˜l#¼[Âxyv¿„†­@x€hjl

(62) ¬[˜žŽ®xzŒŽ¨Å©Œ†~€xQÁCŒ!t[ƒ?ˆ€Ñ w˜k |j¨‚ŒIxz®„X{½„Ž­ x€hjl²%hj„X¨®lM‚w5„Ž­Æx€lQ{exz„a„´¨˜„Ž{jž¯g=hR|©w@Ol*„Xj¨®lMh©ŒÝ³XlUx€„m|©w€lw˜k |j¨‚ŒIxz„Ž~6wª²%®x€hxy²@„ «ŽlQ~€{©l*¨‚]w \C„Ž{jl l*³Xl*{axÇ‰¬[~z®³Xl*{»Œ†{¬º·©{j®x€l*ÇÏwxzŒ†x€l³ÝŒŽ¨®|©lQw0«Žl*~z{jlQ¨ª­µ„X~ xzhjl¬j®žXÂx6Œ†¨@©Œ†~€x´ŒŽ{©¬»ŒÀxz®kml*ÇÏwx€lQcÁ?~zlQŒ†¨ ³IŒ†¨˜|jlQw5«ŽlQ~€{jlQ¨w€„Ž¨˜³R®{jž0¬[±\l*~zl*{axz˜ŒŽ¨lŸX|ŒIx€˜„Ž{w?­µ„X~?x€h©lMŒŽ{©Œ†¨˜„Žž-©ŒŽ~xŸ¯Åg=hjl<¨˜®{©«´¶Ol#xy²@l*lQ{e¶O„†xzh «ŽlQ~€{jlQ¨˜w?~€lQ¨®˜lQwª„Ž{Œ-w€l#xª„Ž­c~€|j¨˜lQwÅx€„j~z„I³R˜¬jlUwvR{©‘6hj~z„Ž{© ŸŒIx€˜„Ž{´¶Ol#xy²@l*l*{mxzhjl*k!¯?g=hjlqŒŽ‘*‘*|j~6ŒŽ‘#v „†­M~€lŸw|j¨®xzwm‘QŒ†{ ¶Ol!®km©ŒŽ®~zlQ¬Ä¶RvÃx€hjl!km„Ž~zl!Œ†¶©wx€~6ŒŽ‘#x0km„[¬[l*¨˜®{©žJ„Ž­<xzhjl!¨®„XžŽ‚‘©ŒŽ~xŒ†{¬ºx€„ l*~z~€„X~zwU¨®˜{j«ŽlŸ¬!x€„x€hjlmwvR{©‘6h©~€„X{j ŸŒIxz®„X{~z|j¨˜lQwQ¯<g=hR|©w<Œ­¸ŒŽwx<xz®kml0¬j„Žk

(63) Œ†˜{¿w€®k0|j¨˜Œ†x€„X~U˜wMŒ†¨‚w€„ ~€lŸa|j®~zlQ¬ex€„mj~z„ŽOl*~z¨˜veŒ†{©ŒŽ¨®v Ql<xzhj˜wU«a˜{©¬„†­‘#˜~z‘*|j®xQ¯ ˆ‰{Ãxzhj˜w ~€lQ„X~xŸÁ²@l²%˜¨®¨ª·©~6wyx~zl*³R˜l*² x€hjl¶ŒŽw€˜‘

(64) ©~€˜{©‘#˜j¨˜lQw-„Ž­=x€hjlewxzŒ†x€l*Ç]„Ž­ÆÇåxzhjl#ljŒ†~€xx€˜k´l¬[„†Ç k

(65) ŒŽ®{

(66) w€®k0|j¨˜Œ†x€„X~zwQÁ†Œ†{©¬mw€|jkmk

(67) Œ†~z Ql=x€hjl=­µlŸŒIx€|©~€lŸwń†­Ox€hjl%¨‚ŒIxzlQwxª‘#„Xk´kmlQ~z‘*˜ŒŽ¨jw˜k |j¨‚ŒIxz„Ž~6wő*ŒŽ¨®¨˜lQ¬ ‰­¸ŒXwyx t[ƒ?ˆ€Ñ  4¯cg=hjl*{J²5l´²%˜¨®¨?¬[lŸw€‘*~€˜¶Ol xzhjlm{j„Ž{[ljw€k´„R„Žx€h¿ŒŽjj~z„XŒŽ‘6h¿®{Jkm„R¬jl*¨˜¨®˜{jž!Œ†{©¬½w˜k |j¨‚ŒIxz®{©ž¬[vaÇ {Œ†km˜‘QŒ†¨wv[wx€lQkmwQÁŒe~zlQw€lQŒŽ~z‘6h!·l*¨‚¬™„†­ªx€hjlm‡@ˆ‰ƒ@Šqƒ:xzlQŒ†kœŒ†xMˆynq‹%ˆ ¹ ‹%h Ž{©l#Ç ¹ ¨˜lŸw*¯ "Jl0²%˜¨˜¨w€l*l xzh©ŒIx-xzhj‚wŒ†j©~€„aŒŽ‘6h½ŒŽ¨®~zlQŒX¬[vÀvR®lQ¨˜¬©w-®{axzl*~zlQwx€˜{jž!~€lŸw|j¨®xzw²%h©l*{ÃÂx0˜w-ŒŽjj¨˜®lŸ¬¿xz„Àl*¨˜lQ‘#x€~z„Ž{j‚‘*wQÁ)Œ†{¬ xzh©ŒIxMÂx-‘#„X|j¨‚¬À¶lŸ‘#„Xk´lmŒ†{½Œ†¨®x€l*~z{©Œ†x€l-xz„wxzŒIxzl#Çτ†­ÆÇ]x€hjl*ÇόŽ~xMw˜k |j¨‚ŒIxz„Ž~6w*ÁOl*{Œ†¶j¨˜®{©ž

(68) x€hjlmŒ†{Œ†¨˜vRw€‚wU„†­ªŒ ¨‚Œ†~zžŽlQ~5{R|jk0¶lQ~U„†­Cl*¨˜l*kml*{ax6Œ†~zve¬[l*³R‚‘#lŸw*¯ . . . . X`. í.

(69)  

(70)  

(71)   !"$#&%('*)+ ,- .$/0( 1,2(. K.  .  7 7:9 4 7 9   7 7

(72) 9 9  7   < 

(73)   

(74)  7 4 + < 9.  4   5. g=h©l-t[ƒ?ˆ€Ñ :w˜k |©¨˜Œ†x€„Ž~QM nqŒ†ž KŽ O ˜w=¶©ŒXwlŸ¬e„X{x€hjl­µ„X¨®¨˜„I²%®{©ž0km„[¬[l*¨‚wUŒŽ{©¬w€„Ž¨˜³ŽlQ~zwQ¯  >:*%?)"#@F

(75) $%#' ¹ {lQ¨®lŸ‘4xz~€‚‘*ŒŽ¨Okm„[¬[lQ¨„†­Œm‘#˜~6‘#|j®x@‚w=¶©ŒXwlŸ¬„Ž{!Œ†{ŒŽwzwlQk ¶j¨˜v

(76) „†­Cl*¨˜l*kml*{ax6Œ†~zvm‘*„ŽkmO„Ž{jlQ{Xx6w Mµ³Ž„X¨Âx6Œ†žXl „X~@‘*|j~z~€lQ{Xx=w„X|j~6‘#lŽÁa~zlQw€˜wx€„X~QÁR‘*ŒŽ©ŒŽ‘*Âxz„Ž~ŸÁŽxz~zŒŽ{©w‚wx€„Ž~Ÿ¯*¯Q¯ O ¯g=hjl-‘#„X{j{jlŸ‘4x€˜„Ž{e„X®{axzw=ŒŽ~€lM‘*Œ†¨˜¨˜lQ¬  /  4¯ o<{j¨˜®«XlUjhRv[w‚‘*ŒŽ¨©km„[¬[l*¨‚w?xzh©ŒIx@®{R³X„Ž¨˜³ŽlUŒxzhj„Ž~z„Ž|jžXhwl*x5„Ž­‘*„Žkmj¨˜l#¼

(77) ©ŒŽ~xz˜ŒŽ¨©¬[®±OlQ~€lQ{Xxz˜ŒŽ¨lŸa|©ŒIxz®„X{©w*Á lQ¨®lŸ‘4xz~€‚‘*ŒŽ¨Okm„[¬[lQ¨˜wUŒŽ®k7ŒIx<¬[lŸw€‘*~€˜¶j˜{jž xzhjl-~zlQw€„X{©wl„Ž­CŒm¬[l*³R‚‘#lxzhj~€„X|jžŽ*h \  Œmwk

(78) Œ†¨˜¨c{R|jk0¶lQ~%„†­³IŒŽ~€‚Œ†¶j¨˜lQQw M¸„X¨®lŸw=„Žx€lQ{Xxz˜ŒŽ¨˜w%ŒŽ{©¬¶j~6Œ†{©‘6h‘#|j~z~€lQ{axzw O  Œ y~zlQŒXw„X{©Œ†¶j¨˜l <{R|jk0¶lQ~%„†­©Œ†~6Œ†kml*x€l*~6w  ¨®Œ˜{j¬[«R®±O˜{jlQžm~€lQx€{ahjx€lŸ‚Œ†wl¨©ŒŽ³I¨®Œ†žX~zl*‚¶jŒ†¶j~6Œ†¨˜lQ‚‘@w=lQŒ†a{|©¬ŒIxz®Œ†„X~6{

(79) Œ†kmŒŽwzl#wxz„[l*‘#~6‚w ŒIxzlQ¬0²%Âxzhmx€hjlqwyx6ŒIx€‚‘%Œ†{¬

(80) ¬[vR{©Œ†km‚‘%‘6h©Œ†~6ŒŽ‘#x€l*~z‚wyxz˜‘Qw ©„Ž~<˜{©wxzŒŽ{©‘#lXÁjx€h©ll*¨˜lQ‘#x€~z˜‘QŒ†¨ckm„[¬[l*¨„†­?Œ¬[˜„[¬[l‚wUŒ”

(81) ¬[˜O„Ž¨˜lQw<ŒXw€w€l*k0¶j¨˜vŒŽw<whj„I²%{!˜{C®žX|j~zl •j¯®–Ž¯ żj‘#lQ[xU­µ„X~=x€hjl~zlQw€‚wyxz„Ž~ŸÁRx€hjl-„Žx€hjlQ~U©Œ†~€xzQw M¸³Ž„X¨Âx6Œ†žŽl*Çϑ*„Ž{ax€~z„Ž¨˜¨˜lQ¬e‘*|j~z~€lQ{XxUw€„Ž|j~6‘#l-ŒŽ{©¬³Ž„Ž¨®xzŒŽžŽl*Ç ‘*„Ž{ax€~z„Ž¨˜¨˜lQ¬e‘QŒ†©ŒX‘#®x€„X~ O ®kmj¨˜vŒm{©„Ž{j¨˜®{©lQŒ†~%‘6h©ŒŽ~zŒX‘4xzl*~z˜wx€‚‘†¯g=hjlwxzŒIxz˜‘‘6h©ŒŽ~zŒX‘4xzl*~z˜wx€‚‘ I(V ) „†­Cx€hjl ‘*|j~z~€lQ{Xx%w€„Ž|j~6‘#l‚w%¬[lQwz‘#~z®¶OlQ¬¶RvtRh©„R‘6«R¨˜l*v  w5¨‚ŒÝQ² \ ²%hjlQ{ V > −5.N. k.T I = I .(e − 1) . . S. q.V N.k.T. I = −IS. `IaÙ(b©à c4ߟÚ. ²%hjl*{. q. V < −5.N.. k.T q.

(82) # ] /]]/-/

(83) *,-   (. ²%®x€h V,I IS q k T N. ³Ž„Ž¨®xzŒŽžŽlŒŽ‘*~€„aw€wªx€hjlw€„Ž|©~z‘*lŒŽ{©¬‘#|j~z~€lQ{ax@xzhj~z„Ž|jžXhexzhjl-w„X|j~z‘*l w€Œ†x€|j~6ŒIxz®„X{‘#|©~€~zl*{axQÁj¬jl#­¸Œ†|©¨ÂxU³IŒ†¨˜|jl 10 ¹ l*¨˜lQ‘4xz~€„X{‘6hŒ†~zžŽl 1.6 10 Ñ ‡5„X¨Âx *k

(84) Œ†{©{‘*„Ž{©wxzŒŽ{Xx x€l*kmOl*~6ŒIxz|j~€l˜{  1.38 10 J.K l*km˜wzw€®„X{‘*„al ‘#˜l*{ax −14. −19. −23. −1.  .  .  ˜žŽ|©~€l•[¯˜–\ ?¨˜lQ‘#x€~z˜‘QŒ†¨km„[¬[l*¨)„†­CŒ

(85) ¬j®„[¬[l g~zŒŽ{©w€˜wx€„X~zwMŒ†~zl

(86) Œ†¨‚w„km„R¬jl*¨˜¨®lŸ¬JŒXwŒ†{̎wzwlQk ¶j¨˜v™„†­=w„X|j~6‘#lQwQÁ~zlQw€˜wx€„X~zwQÁc‘*ŒŽ©ŒŽ‘*Âxz„Ž~6w<²%®x€hÃ{j„X{ ¨˜˜{jlQŒŽ~´‘6h©ŒŽ~zŒX‘4xzl*~z˜wx€‚‘*wQ¯ ¹ x0xzhjl!l*{©¬Áªx€hjll*¨˜lQ‘#x€~z˜‘QŒ†¨=km„[¬[l*¨=„†­MŒ¿²%hj„X¨®l!‘#˜~6‘#|j®x´‚w0x€hR|©w

(87) Œ¿¨˜ŒŽ~€žXl ŒXw€w€l*k0¶j¨˜v

(88) „†­l*¨˜l*kml*{axzŒŽ~€v¬j®O„Ž¨˜lQwQ¯ RqlQw€j®x€lmx€h©l

(89) ~€lQ¨˜Œ†x€˜³Žlmw˜kmj¨®‚‘#®xyv¿„Ž­5lQ¨®lŸ‘4x€~z‚‘*Œ†¨km„[¬[l*¨‚w‘*„Žkm©Œ†~zlQ¬™x€„!jhRv[w‚‘*ŒŽ¨Åkm„R¬jl*¨‚w*Áckm„[¬RÇ lQ¨®¨˜˜{jž0w€lŸ‘#‚Œ†¨˜˜wxzw5xz~€v´x€„´j~z„I³R˜¬[lMŒ žX„R„R¬eŒŽ‘*‘*|j~6ŒŽ‘#v´l*³Xl*{²%h©l*{‘*„Žkmj¨˜l#¼kmlQ‘6hŒ†{j‚wk

(90) w5h©ŒÝ³Žl<x€„´¶l x6Œ†«Xl*{À˜{Xxz„ŒX‘*‘#„X|j{axQ¯Ug=hj‚wq˜wq²%hRvexzhjl lQ¨®lŸ‘4x€~z‚‘*Œ†¨km„R¬jl*¨‚w<„Ž­ªp½Štx€~6Œ†{w‚wyxz„Ž~6w=®{R³X„Ž¨˜³Žl{j„I² xzl*{©w „Ž­©Œ†~6Œ†kml#xzl*~6w*¯Cg=hjlU˜{©‘#~zlQŒXw˜{jž-{R|jk0¶lQ~?„†­©ŒŽ~zŒŽk´l*x€lQ~zwÅ‚w?{©„†xª„X{j¨®vmŒk

(91) ŒIx€x€l*~5„†­ 3 „X~ 4 „Ž~6¬[l*~ ŒX‘*‘*|j~zŒX‘#v \MÂx~z l ©lŸ‘4x6wMx€hjlm˜{©‘#~zlQŒXw˜{jž©Œ†~€x-„†­=l#±\lQ‘4x6wx€hŒIx-|©w€lQ¬½x€„!¶Ol‘#„Ž{w‚¬[l*~zlQ¬JŒŽwM©ŒŽ~zŒXw®x€‚‘*w ¶©|[x%x€h©Œ†xU{j„I² hŒÝ³Žl 1 „Ž~6¬[l*~=³IŒ†¨˜|jlQwQ¯ É »¥[¤

(92) =         -  ( ]/  ! ,2 /I H /  (    S / ,2,-  .$/0&,- -  ].$,- ] rd. th. st. ] 1 N -  ,  ]   S] ,( 1, S( /  .$ .$ ( ,2]/ Q .$/0   Q !,-  ] ,]/ &,-   !  ] &     ,-(.$ &  /-/0   (/

(93) ,-    ].  !,2 !   P      -  (  ,- .$/0( (  "   !#$%#'&$)(X !,-/ - 

(94)    +*,-,-.0/  - +&,2]/  .    

(95) ]/ S 2143 " !(I ,  ( 2 ] 5       .$] 1,2( I = f (V , V ) V ]  f    76  8 Q 9(,2(   -  V , V /0( ( ( !,-   ] ,  ]DS/'$;:  ] GS ,- DS .$/0( 1,2(I   .$,-    ,< ] I (   GS  ]DS ,( 1,2(  H( -$ ,-=   .$  !,2 >  ] Q,- 1H(.    "7? " % 1A@ B@ 

(96) ]/  ? ]C /  .$, ]  ,-  D1E1A, H /(  #  ,-/ , F &N,-  ](  I   !, 6 ],2/  $      ]  

(97) ]/  " "$#G#=..* !1H1I*-* )DJ 0#$LK &  M  (/ ]   <,  ( ] , N ] ] !,2 ],-/ ,-  ,-  ]   .$/ 1,-= Q   I  ,2 (/ 

(98)   " "I#G#.-.* )OJ B#$LK &   (  H( -$,-  .$] 1,2(I " 1H1I*-* &$ : +&,-/-/   Q/  Q I(  Q  

(99)   

(100)     ]/  Q  (  ,- .$/0 !,2P  &,- -    ,  ]/  ( N   !,- . (.  (Q .$/ !, / .    .$  !,2  $ X`. í.

(101)  

(102)  

(103)   !"$#&%('*)+ ,- .$/0( 1,2(. L. @

(104) $' EI-7'@c"# .(+e9  m+"# '    g=h©lM˜{jj|jxzw%„Ž­Œmw€®k0|j¨˜Œ†x€„X~=‘*„Ž{©w€‚wyx%¶©ŒXw‚‘*ŒŽ¨®¨˜v„†­ \  ­µŒ„Ž¨®|j˜¶j{~6¬[Œ†~€~zvv-„Ž·©~%¨˜l<¬[lŸ‘#w„X˜{ažŽxz{jŒ†lQ˜~ {j˜{jž©Œ†~6Œ†kml*x€l*~6wC­µ„Ž~ŶŒŽw€˜‘%‘*„Žkm„X{jl*{ax6wōj~z„I³a‚¬[lŸ¬ ¶Rv0Œ-w€l*km‚‘#„X{©¬[|©‘#x€„Ž~  {jŒl#{jxzl*¨®‚x€w¨˜xz˜wwx=„†­‘*„Žkm„X{jl*{ax6w?¶j|j˜¨®x=O„Xwzw€®¶j¨˜vm®{Œhj˜l*~6Œ†~6‘6hj‚‘*Œ†¨©²@ŒÝvm¶Rvm®{©wxzŒŽ{ax€‚ŒIx€˜„Ž{e„†­)w€kmŒŽ¨®¨˜l*~ ©~€„Xk x€h©lQw€lM˜{jj|jxzwQÁjx€h©lw˜k |j¨‚ŒIxz„Ž~%‚¬[l*{axz·©lŸw@x€hjl0wl*x=„Ž­C|©{j«R{j„I²%{©w@x€„

(105) ¶Ol‘#„Xkmj|[x€lŸ¬!ŒIxUlQŒX‘6h xz®kmlÀwx€l*FŒ†{¬ w€„Žkml#xz®kmlQwmŒ†~€x€®x€˜„Ž{©w0x€h©l*k,˜{ax€„Ãw|j¶wl*xzw´x€„ÃŒ†©j¨®vČ¿¶j¨˜„[‘6«aÇ]¶©ŒXwlŸ¬»Œ†¨˜žŽ„X~€®x€h©k¯ Rq|j~z®{©žºx€hjlÃw€®k0|j¨˜Œ†x€˜„Ž{cÁ%k

(106) Œ†x€~z˜‘*lQweŒŽ~€l½ŒŽwzwlQk ¶j¨˜lQ¬ xz„»x€~6Œ†{wy­µ„X~€k x€hjlJŒ†{©ŒŽ¨®vaxz˜‘!­µ„X~€k0|j¨‚ŒIx€˜„Ž{B„Ž­ ¬j±\l*~zl*{ax€‚Œ†¨cŒŽ¨®žXl*¶j~6Œ†‚‘qlQa|©ŒIxz®„X{©w=˜{Xxz„Œ

(107) wl*xU„†­C¨®˜{jlQŒŽ~UlQa|©Œ†x€˜„Ž{©wQ¯ żj‘#lQ[xU˜{xzhjl Mµ~6Œ†~zl O ‘QŒŽw€lM„Ž­Œ ¨˜˜{jlQŒŽ~U‘#„Ž{wyx6Œ†{ax=‘*®~6‘#|©ÂxŸÁjk

(108) ŒIx€~z®¼ŒŽwzwlQk ¶j¨˜v

(109) ‚wU¬[„Ž{©lw€l*³Xl*~6Œ†¨Ox€˜kmlQw%Ol*~=xz®kmlwx€lQc¯ "Jl

(110) ²%®¨˜¨Å{j„I² ~zl*³R˜l*²xzhjlmk

(111) Œ†˜{JŒŽjj~z„XŒŽ‘6h©lQw%xz„x€hj‚wk

(112) ŒIx€~z®¼¿ŒŽwzwlQk ¶j¨˜v \<xzhjltR©Œ†~6w€l´gCŒ†¶j¨˜lQŒŽ| ¹ jj~z„XŒX‘6h0Œ†{¬xzhjlUpÀ„[¬[®·©lQ¬mnU„[¬jŒŽ¨ ¹ {©ŒŽ¨®v[w€˜wQ¯g=h©l%|j{©¬[lQ~€¨˜vR®{jžqx€h©l*„Ž~zv²%˜¨®¨©¶l=l#¼[j¨‚Œ†˜{jlŸ¬xzh©Œ†{j«[w xz„

(113) x€h©ll#¼jŒ†kmj¨˜l„Ž­ÅŒe‘#˜~z‘*|jÂxM‘#„Ž{w‚wyxz®{©ž

(114) „†­?Œ†{™ÐÑ:„aw€‘*®¨˜¨‚ŒIx€„X~Uw|©jj¨˜va˜{jžeŒ¨®„aŒŽ¬~€lŸw‚wx€„Ž~Ux€hj~z„Ž|jžXh Œ´h©ŒŽ¨Â­ÆÇϲ=ŒÝ³ŽlM~€lŸ‘4x€®·©lQ~ MåwlQl C®žX|j~€l•j¯ • O ¯ v1. iC. vC. . iR. iL. . `. vR. vL v2 iD. vD. C˜žŽ|j~zl•[¯Ø•$\ ?¨˜lQ‘#x€~z˜‘QŒ†¨„Xwz‘#˜¨˜¨˜Œ†x€„Ž~=²%®x€h!h©ŒŽ¨Â­ÆÇϲ@ŒÝ³Xlq~zlQ‘#x€®·©l*~  .

(115)     "!#%$&'( *)+ ,!.-. ˆ‰{xzhj˜w=kml*x€hj„[¬ M  °<‡ SKR– O Á[x€h©l-³ÝŒŽ~€‚Œ†¶©¨®lŸw@ŒŽ~€l\  Œ†¨˜¨c{j„[¬[lO„†x€lQ{ax€‚Œ†¨‚w=²%Âxzh~zlQw€OlQ‘4x%xz„

(116) Œ´‘*„Žkmkm„Ž{~€l*­µl*~zl*{©‘*l  Œ†¨˜¨c¶j~6Œ†{©‘6h³Ž„X¨Âx6Œ†žŽlŸw `IaÙ(b©à c4ߟÚ.

(117) –Ÿ“. # ] /]]/-/

(118) *,-   (.  Œ†¨˜¨c¶j~6Œ†{©‘6h‘#|j~z~zl*{axzw ˆ‰{Œkm„Ž~zl<žXl*{jlQ~zŒŽ¨©­µ„X~€k0|j¨‚ŒIx€˜„Ž{)ÁX„X{jlM‘QŒ†{eŒŽ¨˜w€„ |wlMl*¨˜lQ‘#x€~z˜‘q‘6h©Œ†~zžŽl<ŒŽ{©¬k

(119) ŒŽžŽ{jl*x€‚‘ ©|[¼˜{©wx€lŸŒŽ¬„Ž­ ‘*|j~z~€lQ{Xx=„Ž~%³X„Ž¨®xzŒŽžŽlq­µ„Ž~Uw€„Žkml-‘#„ŽkmO„Ž{jlQ{axzwQMµlX¯ ž

(120) ‘QŒ†©ŒX‘#®x€„Ž~ŸÁR®{¬[|©‘4xz„Ž~ O ¯ g=hjl-lŸa|©ŒIxz®„X{©w%Œ†~zlq¶ŒŽw€lQ¬„Ž{ \  x€‚Œ†®~6¨‚w‘6hjhj„Ž±  w5³Ž„X¨Âx6Œ†žŽl<¨˜ŒÝ²Fxzh©ŒIx%w˜kmj¨˜v

(121) ~€lQ¨˜Œ†x€lQw5¶j~6Œ†{©‘6he³Ž„Ž¨®xzŒŽžŽlŸwx€„m‘#„X{j{jlQ‘#x€lŸ¬{j„[¬[lŸwªO„†xzl*{[Ç  Œ´®{j~6„[‘6hj¬[hjl-„Ž˜±w *w%l*‘*~z„|j~€~zl*{ax%¨‚ŒÝ² wxzŒIxz®{©ž0xzh©ŒIx%xzhjlw€|jk „Ž­‘*|j~€~zl*{ax6w=„†­CŒŽ¨®¨)¶j~zŒŽ{©‘6hjlŸw@‘*„Ž{R³ŽlQ~€žX®{©žx€„  x€hjl-¶©~zŒŽ{©‘6h‘*„Ž{©wx€®x€|jx€˜³ŽllQa|©Œ†x€˜„Ž{©w@xzh©ŒIxUkm„[¬[l*¨\xzhjl-¶Ol*h©ŒÝ³R˜„Ž~%„†­‘#„Xk´O„Ž{©l*{axzw "Jl-„Ž¶[x6Œ†˜{exzhjl*{!xzhjlM­µ„Ž¨˜¨®„I²%˜{jžmlQa|©Œ†x€˜„Ž{­µ„Ž~=xzhjl-l#¼jŒ†kmj¨˜l„†­ ˜žŽ|©~€l•[¯Ø• \ ‘*ŒŽ©ŒŽ‘*Âxz„Ž~=³Ž„X¨Âx6Œ†žŽl v Q ‘ Œ†©ŒX‘#®x€„X~=‘*|j~z~€lQ{Xx i ˜  {©¬[|‘4x€„X~%³Ž„X¨Âx6Œ†žŽl v ®   { ¬[|©‘4xz„Ž~<‘*|j~z~€lQ{Xx i z ~ lQw€‚wyxz„Ž~=³Ž„X¨Âx6Œ†žŽl v z ~ Q l w€˜wx€„X~=‘*|j~z~€lQ{Xx i ¬[˜„[¬[l³Ž„X¨Âx6Œ†žŽl v [ ¬ ®„[¬[l‘*|j~z~€lQ{Xx i j { [ „ [ ¬

(122) l –O„†x€lQ{ax€‚Œ†¨ v j { [ „ [ ¬. l 0 • O„†x€lQ{ax€‚Œ†¨ v ˜~z‘6h©hj„†±  w=³Ž„Ž¨®xzŒŽžŽlM¨˜ŒÝ² ˜w=²%~z®xx€lQ{ \ C. C. L. L. R. R. D. D 1 2. ˜~z‘6h©hj„†±  w%‘#|j~z~€lQ{ax=¨‚ŒÝ². ‚w=²%~zÂx€x€l*{*\. vC − v 1 = 0 vL − v 1 = 0 vR − v 1 + v 2 = 0 vD − v 2 = 0. iC + i L + i R = 0 iR − i D = 0. ŒŽ{©¬x€hjl-¶j~6Œ†{‘6h‘#„X{©wx€®x€|[xz®³Xl-lQa|©ŒIxz®„X{©w5­µ„Ž¨˜¨®„I²Q\. 0 CvC − iC = 0 0 LiL − vL = 0 vR − RiR = 0 iD − f (vD ) = 0. ²%h©l*~zl f ‚wªŒŽ{

(123) l#¼[„X{jl*{axz˜ŒŽ¨*MåtRh©„R‘6«R¨˜l*v  wŨ˜ŒÝ² O C¯ g=h©l<¬[vR{©Œ†km‚‘=¶lQh©ŒÝ³R®„X~?„†­\xzhjl<¬[˜„[¬[lU‚wÅ{jl*žX¨®lŸ‘4xzlQ¬¯ X`. í.

(124) –X–.  

(125)  

(126)   !"$#&%('*)+ ,- .$/0( 1,2(. "B®x€h™ŒŽ{l*¼axzl*{©¬jlQ¬k

(127) ŒIx€~z®¼­µ„Ž~zk |j¨‚ŒIxz®„X{NMµx€„

(128) h©ŒŽ{©¬[¨˜lM{©„Ž{j¨˜®{©lQŒ†~z®xyv„†­x€hjl¬[˜„[¬[l O Áj„Ž{©lMžXl#x6w]\ . .        +       . 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 −1 0 0 0 0 0 −1 0 0 0 0 0 0 1 0 0 0 0 0. 0 0 0 0 0 0 C 0 0 0. 0 0 0 0 0 0 0 0 0 0. 0 0 0 0 0  0 0 0 0 0   0 0 0 0 0   0 0 0 0 0   0 0 0 0 0   0 0 0 0 0   0 0 0 0 0   0 L 0 0 0   0 0 0 0 0 0 0 0 0 0   0 0 0 −1 0  0 0 0 −1 0     0 0 0 −1 1     0 1 0 0 −1     1 0 0 0 0  ·  1 0 −1 0 0     0 0 0 0 0     0 0 0 0 0    −R 0 0 0 0   0 0 1 0 0. 0 0 0 0 0 0 0 0 0 0 vC iC vL iL vR iR vD iD v1 v2.   0 0 vC  i0 0    C0  0    v0L  0    iL0  0   ·  v0R  0    iR  0 0    v0D  0    iD 0   v10 0 v20  0   0     0     0     0 +   0     0     0     0 −f (vD ) 0 0 0 0 0 0 0 0 0 0 .                .                . =0. xzha|wŒ!¬[±\l*~zl*{axz˜ŒŽ¨?Œ†¨˜žŽl*¶©~zŒŽ˜‘ lQa|©ŒIxz®„X{½²%®x€hÃw€©Œ†~6wl´k

(129) ŒIxz~€‚‘#lŸw-Œ†{©¬JŒ{j„Ž{j¨˜˜{jlQŒŽ~qxzl*~zk!¯mg=h©˜w kml*x€hj„[¬ |©w€lQw

(130) ŒJ¨®„Žx

(131) „†­|j{j«R{j„I²%{©wQÁª~zlQw€|j¨®x€˜{jžÃ®{Äx€hjlÀ¨‚Œ†~zžŽl!w€ Ql!ŒŽ{©¬FwŒ†~6w®xyvº„†­qx€hjlÀk

(132) ŒIxz~€‚‘#lŸw*¯ ª³Žl*{­CÂx%‚w@³Žl*~zv

(133) žŽlQ{jl*~6Œ†¨\Œ†{¬eŒ†¨˜¨˜„I²Uw5Œ´wyxz~zŒŽ®žXhax­µ„Ž~z²=Œ†~6¬´w€l#x€x€˜{jžm„†­)lŸa|©ŒIxz®„X{©w*Á[ŒŽ{j„†xzhjl*~@kml#x€h©„R¬ ¬jlQŒ†¨˜˜{jžÀ²%Âxzh»k |‘6hº¨®lŸw€w |j{j«R{j„I²%{©w-²=ŒŽwj~€l*­µl*~z~€lŸ¬½­µ„Ž~xzhjlewxzŒ†x€l#Çτ†­ÆÇ]x€h©l#ljŒ†~€x w˜k |j¨‚ŒIxz„Ž~0t[ƒ?ˆ€Ñ  \ xzhjlpÀ„[¬[®·©lQ¬!n<„R¬©Œ†¨ ¹ {Œ†¨˜vRw€‚w*¯ 

(134)   $  . $   ! 

(135)      ) !.g=h©l<·©~6wx@³Xl*~6w˜„Ž{

(136) „Ž­){j„[¬jŒ†¨ŒŽ{©Œ†¨˜v[w‚w5‘*„Ž{©w€‚¬[l*~zlQ¬

(137) „X{j¨˜v

(138) {j„[¬[lqO„†xzl*{ax€‚Œ†¨‚w=ŒŽw5|j{j«R{j„I²%{©w@Œ†{¬ew€l#x=x€hjl lŸa|©ŒIxz®„X{©w@¶av \  ­µ„Ž~mlQŒX‘6h ¶j~6Œ†{‘6hcÁÅx€h©l!‘*„Ž{©wx€®x€|jx€˜³ŽllQa|©ŒIxz®„X{ „Ž­<x€h©l!¬j®O„Ž¨˜l‚wm²%~zÂx€x€l*{ ˜{»x€h©l­µ„X~€k i = Y · (V − V )  ­µ„Ž~%lŸŒŽ‘6h{j„[¬[lŽÁ[xzhj5l ˜~z‘6hjh©„†±  w=‘*|j~€~zl*{ax%¨‚ŒÝ² ‚w%Œ†jj¨˜˜lQ[¬ \ P i = 0 vR˜l*¨‚¬[˜{jžÀx€h©l*{Ȏ{»lQa|©Œ†x€˜„Ž{º„Ž­%x€hjle­µ„Ž~zk ²%®x€h Œ™³ŽlQ‘#x€„X~ „†­<“™„Ž~0‘*|j~z~€lQ{Xx´w„X|j~z‘*lQw ³IŒŽ¨®|jlŸw*Á V Œ´³XlQ‘4xz„Ž~=„†­C|j{j«R{j„I²%{!{j„[¬[lO„†x€IlQ{a=x€‚Œ†Y¨‚w%·Œ†V{©¬ Y x€hjlI ŒX¬[kmÂx€xzŒŽ{©‘#lk

(139) ŒIxz~€®¼¯ g=hjl{j„[¬jŒ†¨@Œ†{©ŒŽ¨®v[w€˜wh©ŒŽ¬»Œ¿wlQ~€˜„Ž|©w ¬[~zŒÝ²%¶ŒŽ‘6« \ ®x0²=ŒŽwŒXw€w€|jkmlQ¬Jxzh©ŒIx0x€hjl‘#|j~z~zl*{ax˜w0žŽ˜³ŽlQ{ l*¼[j¨®‚‘#®x€¨˜vî{ lQŒŽ‘6hº¶©~zŒŽ{©‘6höavºŒ™w€„Ž|©~z‘*l

(140) x€lQ~€k „Ž~0¶avºŒÀ~zl*¨‚ŒIxz®„X{º„†­%xzhjlxyvROl i = f (U, U ) ¯JtR„ ˜{©¬[|‘4x€„X~zwQÁ³Ž„X¨Âx6Œ†žXl0w€„Ž|j~6‘#lŸwqŒŽ{©¬½w€l*³Xl*~6Œ†¨C„†xzhjl*~-wxzŒ†{¬jŒ†~6¬™lQ¨®lŸ‘4x€~z‚‘*Œ†¨km„[¬[l*¨‚w‘#„X|j¨˜¬½{j„Žx¶Olm|©w€lQ¬¯ 1. 2. 0. `IaÙ(b©à c4ߟÚ.

(141) –Ý•. # ] /]]/-/

(142) *,-   (. © „Ž~5x€hjlŸwlM~zlQŒŽw€„Ž{w*ÁXÂx=²@ŒXwªkm„[¬[®·©lQ¬NM  °<‹U‡ KŽ  O ¶Rvm¶©ŒŽw€‚‘*Œ†¨˜¨˜vmŒX¬j¬[˜{jž ˜{xzhjl³ŽlŸ‘4x€„X~ª„Ž­)|j{j«R{j„I²%{©w w€„Žkml¶©~zŒŽ{©‘6hÀ‘#|j~z~€lQ{axzwSMµ­µ„Ž~<˜{©wxzŒŽ{©‘#lXÁ©xzhjl ³X„Ž¨®xzŒ†žXl-w„X|j~z‘*l„Ž~<®{©¬j|©‘4xz„Ž~q‘*|j~z~€lQ{Xx6w O Œ†{©¬ÀŒX¬j¬[˜{jž˜{ xzhjl

(143) ³ŽlŸ‘4xz„Ž~„†­=¬jŒIx6ŒÀw„Xk´lm«R{j„I²%{½³Ž„Ž¨®xzŒŽžŽlŸw*¯mg=hjlp™n ¹ ˜w-²%‚¬[lQ¨®v™|wlŸ¬Jw€˜{©‘#lm®x˜wxzhjlmkml#x€h©„R¬ xzh©ŒIx?²=ŒŽwª‘6hj„Xw€l*{0­µ„Ž~ÅxzhjlqtRƒªˆ€Ñ »w˜k |j¨‚ŒIxz„Ž~?¬[lQ³ŽlQ¨®„XlŸ¬´Œ†xª‡@l*~z«Žl*¨˜l*v0oU{j˜³ŽlQ~zw€Âxyv ®{mxzhjlH– LXšŽ“  wŒ†{¬

(144) – L K†“  w*ÁRŒ†{©¬xzh©ŒIxU~zl*k

(145) Œ†˜{©w5x€h©lwyx6Œ†{©¬jŒŽ~z¬e­µ„Ž~=xz®kml¬[„Xk

(146) Œ†˜{ŒŽ{©Œ†¨˜v[w‚w@„†­Å‘#˜~z‘*|jÂx6w*¯ "Jlò%®¨˜¨-‘#„Ž{w‚¬[l*~{j„I²œhj„I² xzhjlÑ#˜~z‘*|jÂx™•[¯Ø•º‚wwl*x˜{ax€„ lQa|©ŒIxz®„X{©w²%Âxzh:x€h©lJp™n ¹ ¯Ug=hjl |©{j«R{j„I²%{©w%Œ†~zl \ {j„[¬[l

(147) –O„†x€lQ{ax€‚Œ†¨ v {j„[¬[l •0O„†x€lQ{ax€‚Œ†¨ v ®  {¬[|©‘4xz„Ž~<‘*|j~z~€lQ{Xx i g²5„lQa|©Œ†x€˜„Ž{©wM‘#„Xkml­µ~z„Žk x€h©l ˜~z‘6h©hj„†±º‘#|j~z~zl*{axq¨‚ŒÝ²²%~€®xxzl*{JŒIx{j„[¬[lQw´–mŒ†{©¬¿•jÁcŒ†{©¬™x€hjl xzhj˜~z¬lQa|©Œ†x€˜„Ž{˜w%~zl*¨‚ŒIxzlQ¬ex€„´x€h©l-®{©¬j|©‘4xz„Ž~%¶j~6Œ†{©‘6h!‘#„X{©wx€®x€|[xz®³XlMlŸa|©ŒIxz®„X{c¯ "½l-žXl#x=x€h©l*{ \ 1 2. L. . C  0 0.   0   1 − R1 0 0 v1 R 1 0     − R1 0 0 v2 · + R 0 0 L iL −1 0.      1 v1 0 0  ·  v2  +  −f (v2 )  = 0 iL 0 0. xzhR|©w%Œmk |©‘6hkm„Ž~zl-‘#„Žkm©ŒX‘4x=­µ„Ž~zk xzh©Œ†{!²%®x€hx€hjl tjg ¹ kml#xzhj„[¬¯   +="#@»*.-"6!' ˆ‰{mxzhjl<©~€lQ³a˜„Ž|w?wlŸ‘4xz®„X{©w*Áa²@l<w€ŒÝ² hj„I² x€„0wl*x5|jmxzhjl<lŸX|ŒIx€˜„Ž{wÅ®{Œ†{Œ†{Œ†¨˜vXxz˜‘%­µ„Ž~zk¯g=h©ŒŽ{j«[wÅx€„ xzhjl0w€km„R„†x€h¿{©ŒIxz|j~€l0„†­Åxzhjl0km„[¬[lQ¨˜wQÁOx€hjl0lQa|©ŒIxz®„X{©wMŒ†~zl ¬[®±OlQ~€lQ{Xxz˜ŒŽ¨CŒŽ¨®žXl*¶j~6Œ†‚‘lQa|©Œ†x€˜„Ž{©w M2R ¹  O ²%®x€h!km„Xwx%„†­Cx€hjlxz®kml-{j„X{j¨˜®{jlŸŒ†~=©ŒŽ~x6Qw Mµ¨˜®«Xlqxzhjl¬[˜„[¬[l I(V ) ‘6h©ŒŽ~zŒX‘4x€lQ~€‚wx€‚‘ O Á . f (x0 , x, t) = 0. ²%h©˜‘6h!‘*ŒŽ{¶Ol-„†­Æxzl*{!²%~€®xxzl*{!˜{xzhjl­µ„Ž~zk \ ²%®x€h A Œ´k

(148) ŒIx€~z®¼Œ†{©¬ S(t) ®{¬[l*Ol*{©¬jl*{axqw€„Ž|j~6‘#lŸw A · x + g(x) = S(t) ˆÏ­ ¹ ˜w%w€˜{jžŽ|j¨‚Œ†~ŸÁR²%hj‚‘6h‚w@x€hjl‘QŒŽw€lq²%®x€h!„X|j~=l#¼jŒ†kmj¨˜l-wl*x=|©²%®x€hxzhjl-p™n ¹ Áj²5lh©ŒÝ³XlMŒ R ¹ U¯ ˆÏ­=Œ†¨˜¨|j{j«R{j„I²%{©w¬[lQ~€˜³IŒIx€˜³ŽlŸwqŒŽ~€l´|©w€lQ¬ M ¹ ®{R³Xl*~€x€˜¶j¨®l O Á²@l0žXl#xŒ†{ºPŠ R  M]Šq~6¬[˜{©Œ†~zvR<®±\l*~zl*{ax€‚Œ†¨ 5X|ŒIx€˜„Ž{ O ¯ g=hjlq‘*Œ†|w€ŒŽ¨®®xyvj~z®{‘#˜j¨®l%˜kmj¨˜®lŸwÅx€hŒIxª²@lU¬[lQŒŽ¨j²%®x€hŒ†{m˜{j®x€‚Œ†¨©³IŒŽ¨®|jl%©~€„X¶j¨®lQk \)®xª˜wª{jlQ‘*lQwzw€ŒŽ~€v xz„q©~€„I³R‚¬[lªŒM‘#„Ž{w‚wyxzl*{ax˜{j®x€‚Œ†¨R³IŒ†¨˜|jl5­µ„Ž~Œ†¨˜¨X|j{©«a{©„I²%{©wC„†­[x€h©l R ¹ U¯Ig=hj‚wC³ÝŒŽ¨®|©l5k

(149) ŒÝv¶l@„Ž¶jxzŒ†˜{jlŸ¬ ¶RvMŒ†{lQwx€˜k

(150) ŒIx€˜„Ž{)ÁŸ¶RvMw€ŒŽk´©¨®˜{jžUŒ=j~zl*³R˜„Ž|©ww€®k0|j¨‚ŒIx€˜„Ž{-Œ†xŒ=žŽ˜³ŽlQ{M˜{©wxzŒŽ{XxŸÁQ„X~QÁŸkm„Xwxc„†­Rx€h©lÅx€˜kmlŽÁÝÂx ‚wª‘*„Žkmj|[xzlQ¬

(151) ŒXwªŒ†{mlŸX|©®¨˜®¶©~€˜|jkH„X®{ax Må‘*ŒŽ¨®¨˜lQ ¬ R-Ñ O ‘*„Ž{©w€˜¬jl*~z®{jžxzh©ŒIx@Œ†¨˜¨¬[lQ~€˜³IŒIx€˜³ŽlŸw?Œ†~zl%˜{jÂxz˜ŒŽ¨®¨˜v Ql*~z„´"JŒŽlÀ{©¬j~zx€lQh©w€Œ†l*xU{ax´w„Xh©|jl*~z~z‘*llMxzx€hjl*~zl!k

(152) {Rw=|j²%km®l*¨˜¨c~z˜¨‚‘QŒIŒ†xz¨Ul*~%w€„Žj¨˜~z|[„Ix€³R˜„Ž˜¬[{©lqw´x€|©h©w€llQ¬ ¬[vRx€{©„ºŒ†kmw€„Ž‚¨˜‘*³ŽwQl¯ x€hjl R ¹ U¯ C˜~zwx

(153) „†­Œ†¨˜¨åÁ5²5l!²%˜¨®¨ ‘*„Ž{©w€‚¬[l*~@hj„I²Bxz„´w€„Ž¨˜³Žl<x€hjQl R-Ñ Mµ]¯ lM‘*„Ž{©wxzŒŽ{Xx=³IŒ†¨˜|jlQw O j~€„X¶j¨˜l*k!Á[Œ†{©¬wlQlq¨‚ŒIxzl*~@hj„I²BxzhjlMx€~6Œ†{©w€®lQ{ax ŒŽ{©Œ†¨˜v[w‚w MÆxz®kml-³IŒ†~zvR®{jžm³IŒ†¨˜|jlŸw O ‚w%h©Œ†{¬[¨®lŸ¬¯ 0. . X`. í.

(154) –Ÿ”.  

(155)  

(156)   !"$#&%('*)+ ,- .$/0( 1,2(. 

(157) % %$   g=h©lPR-ÑFj~z„Ž¶©¨®lQk¾‚w=w˜kmj¨˜·©lŸ¬xz„ xzhjlMlQa|©ŒIxz®„X{ f (0, x, 0) = 0 ²%®x€h f ¶Ol*˜{jž´k´„awyx=„†­)x€hjlqx€˜kml Œm{©„Ž{j¨˜®{©lQŒ†~=­µ|©{©‘4xz®„X{ R −→ R ¯=p™Œ†˜{j¨˜vxy²@„mŒŽjj~z„XŒX‘6hjlQw@h©ŒÝ³XlM¶Ol*lQ{À|©w€lQ¬®{™wxzŒ†x€l*Ç]„Ž­ÆÇåxzhjl#ljŒ†~€x w€˜k |j¨‚ŒIxz„Ž~6wCx€„ w€„Ž¨˜³Žl%®Hx \x€hjlMnUlQ²=x€„Ž{jÇϋUŒŽjh©w€„Ž{mŒ†¨˜žŽ„X~€®x€hjk¾Œ†j©¨®˜lQ¬´xz„-x€hjl<²%hj„Ž¨˜l<w€l#xª„Ž­\lŸa|©ŒIxz®„X{©w*Á ŒŽ{©¬Œ0~zl*¨‚ŒI¼jŒ†x€˜„Ž{ekml*x€hj„[¬!w„X¨®³R˜{jžmlQŒX‘6helQa|©Œ†x€˜„Ž{„Ž{jlŒ†­Æx€lQ~=x€hjl-„Žx€hjlQ~Q¯ Z G É ÀÉaÌ £ Í @ Ë  I¥ UXGC¢ Í @ ¥ !2W Í ¤ A¸H£ G g=h©˜w

(158) ‘*¨˜ŒXw€w€˜‘QŒ†¨=®x€l*~6ŒIxz®³Xl!k´l*x€hj„[¬Ä·©{©¬©wmx€hjl Ql*~z„ Måw|©j„awlŸ¬Äx€„ölÀl*¼[˜wx€˜{jžºŒ†{©¬ |j{©˜a|jl O „†­MŒ ‘*„Ž{ax€˜{R|j„Ž|w¨˜v¬[l*~z˜³ÝŒŽ¶j¨˜lq­µ|©{©‘4xz®„X{ f : R −→ R ¶Rv \ –Ž¯UtaxzŒŽ~xU²%®x€hÀŒŽ{˜{j®x€‚Œ†¨cžX|jlQwzw x •[¯<Ñ5„Žkmj|[xzlx€hjl—aŒŽ‘*„Ž¶j‚Œ†{„†­ f Œ†x=lŸwyxz®k

(159) Œ†x€l x \  . $&. . .

(160). n. n. . n. n. 0. k. .  Jf (xk ) = . ”j¯<Ñ5„Žkmj|[xzlŒ´{jl*² lQwx€˜k

(161) ŒIx€l\. ¯¯. ∂f1 k ∂x1 (x ) ∂fn k ∂x1 (x ). ¯¯¯. ... .... ¯¯. ∂f1 k ∂xn (x ) ∂fn k ∂xn (x ).   . xk+1 = xk − Jf (xk )−1 · f (xk ). ›©¯<Ñ5„Žkmj|[xzl kx − x k = max (|x − x |) Œ†{©¬À‘6h©lQ‘6«­µ„Ž~qŒŽ¶©w€„Ž¨˜|[x€l„X~<~zl*¨‚ŒIxz®³Xl ‘#„X{a³Xl*~zžŽlQ{©‘#l-¶Rv!‘#„Žkm©ŒŽ~€‚w€„Ž{!²%Âxzh™žŽ˜³ŽlQ{!x€hj~zlQw€hj„X¨˜¬jwQ¯<g„ŒÝ³X„Ž‚¬Œ

(162) ­¸Œ†¨‚wl´‘#„Ž{R³Xl*~zžŽl*{‘#lŽÁ©ÂxM˜w Œ†¨‚w„m{jlŸ‘#lŸw€wzŒ†~zvmx€„

(163) ‘6hjlŸ‘6«

(164) ­µ„Ž~ kf (x )k ¯ ˆ‰{F­¸ŒX‘4xŸÁ5xzhjl¿—aŒŽ‘*„Ž¶j‚Œ†{ k

(165) ŒIx€~z®¼ {jlQlQ¬ {j„Žxe¶l¿®{R³ŽlQ~zw€lQ¬ \Àx€hjl¿{jl*² lQwx€˜k

(166) ŒIxzl x whŒ†¨˜¨U¶l¿x€hjl w€„Ž¨˜|[xz®„X{„Ž­)x€h©l-¨®˜{jlQŒŽ~Uwv[wx€lQk k+1. k. ∞. i=1···n. k+1. k+1 i. k i. ∞. k+1. Jf (xk ) · xk+1 = Jf (xk ) · xk − f (xk ). xzh©ŒIx<‘QŒ†{¶l-„X¶[xzŒŽ®{©lQ¬ex€hj~z„Ž|jžXhwxzŒŽ{©¬jŒŽ~z¬e¨®˜{jlQŒŽ~UŒ†¨˜žŽlQ¶j~zŒ´Œ†¨˜žŽ„X~€®x€h©kmwH\  R<˜~zlQ‘4xUkml*x€hj„[¬jw%¨˜˜«Žl-Ð)o ­¸ŒX‘4x€„X~€! QŒ†x€˜„Ž{  ˆ‰M{©l*¬[{j˜~€lQlŸ~z‘4ŒŽx ¨®! *kmlŸ¬l*x€p™hj„[®¬j{jw˜k

(167) M Œ†¨)Œ†‹U|lQw€ww€Ç‰˜¬[t[|l*‚Œ†¬[¨]l*¯®¯˜¨]¯ ÁCO tRxz|h©‘*ŒI‘#xUlŸw€w€w€lQ˜Œ†³Ž~6l‘6heŠq®³Žx€lQlQ~~zŒ†‹%x€˜l*³Ž¨‚lQŒI¨®¼jv

(168) Œ†xzx€hj˜„Žl{cw€ÁC„Ž‡5¨˜|[µx€Ñ5˜„Ž„Ž{ {† y|jžXŒ†x€l M~6ŒŽ¬[˜l*{axQÁ g=h©l¿„Ž~z˜žŽ˜{©Œ†¨qt[ƒ?ˆ€Ñ 7w€®k0|j¨‚ŒIx€„X~­µ~z„Žk‡@l*~z«Žl*¨˜l*v |©w€lQwx€hjlÃnUlQ²=x€„Ž{jÇϋUŒŽjh©w€„Ž{:ŒŽ¨®žX„Ž~zÂxzhjk!Á@²%®x€h w€l*³Xl*~6Œ†¨\l*{©h©Œ†{©‘*l*kml*{ax6w@x€h©Œ†x=²@l*~zl-¬[„Ž{©lMlQÂxzhjl*~<¶av‡5lQ~€«Xl*¨˜l*v

(169) „X~%¶av‘#„Žkmkml*~6‘#‚Œ†¨w€„†­Æxy²=Œ†~zl<xzlQŒŽkmwQ¯. `IaÙ(b©à c4ߟÚ.

(170) –Q›. # ] /]]/-/

(171) *,-   (. É @ É D £ÉU Z G. É !å¥ c¥[£

(172) A Í @ ¥ !2W Í ¤Aµ£

(173) G

(174) . g=h©˜wUŒŽ¨®žX„Ž~zÂxzhjk ²=ŒŽwUj~€lŸwlQ{ax€lQ¬˜{!x€hjl0Œ†~€x€‚‘#¨˜l °Mt©Ñ ϯ=ˆÏx<~zl*j¨‚ŒŽ‘*lQw=xzhjlžŽ¨˜„Ž¶Œ†¨cw€„Ž¨˜³a˜{jž

(175) „Ž­ÅŒ

(176) w€l#x „Ž­{j„X{j¨˜®{jlŸŒ†~%lŸX|ŒIx€˜„Ž{w5¶RvŒŒŽ|©wzwyÇytRl*‚¬[lQ¨¨®˜«Žl®x€l*~6ŒIxz®„X{ \ –Ž¯UtaxzŒŽ~xU²%®x€hÀŒŽ{˜{j®x€‚Œ†¨cžX|jlQwzw x •[¯

(177) j„X~%lQŒŽ‘6h„†­Cx€h©l i = 1, · · · n lŸa|©ŒIxz®„X{©w*Ájw€„Ž¨˜³ŽlM¶RvxzhjlwlŸ‘*ŒŽ{Xx=kml#xzhj„[¬x€hjl i lŸX|ŒIx€˜„Ž{*\ 0. th. k+1 fi (xk+1 , · · · , xk+1 , xki+1 , · · · , xkn ) = 0 1 i−1 , xi. %² Âxzh!~€lŸwOlQ‘#x%x€„´x€hjlw€˜{jžŽ¨˜l|j{j«R{j„I²%{ x ¯ ”j¯<Ñ5hjlQ‘6«­µ„Ž~U‘#„X{R³Žl*~zžŽlQ{©‘#lq„Ž{ x lQwx€˜k

(178) ŒIxzl k+1 i. k+1.   ) - P)  + 3  ,- .$/    ( 1 ]    ,2 , 8     N -$,   /   ,-  )$ _ Í @ É ¤W É @ ¦ É CU ¤ Í ¡ ! É »¢ Ì Aµ£HGB¢Q£HA ¦ GC¥[¤I¥j¦†£ É ¤Aå¢*£

(179) A¸¦Ž¢e¦ Í  U Í @ É @ Q£ ¢. g=h©l-l#¼[„X{jl*{axz˜ŒŽ¨)‘6h©Œ†~6ŒŽ‘#x€lQ~€‚wyxz˜‘q„†­xzhjl¬[˜„R¬jl Mµ„X~%x€hjla|©ŒX¬[~6ŒIx€‚‘~zlQw€„X{©wl„Ž­Œ

(180) p½Štxz~zŒŽ{©w€˜wx€„X~ xz„ V ²%hjlQ{ ®x´žX„alŸw­µ~z„Žk xzhjl²@lQŒŽ«Ã®{R³ŽlQ~zw€˜„Ž{º~zl*žŽ˜„Ž{Ãxz„¿xzhjl!wyxz~€„X{jž™˜{a³Xl*~6w˜„Ž{º~zl*žX®„X{ O k

(181) ŒÝv ‘QŒ†|©w€lU‘#„X{R³Žl*~zžŽlQ{©‘#l@j~z„Ž¶j¨˜l*k

(182) w²%hjlQ{ŒQRÑȎ{©Œ†¨˜v[w‚wCx€~z®lŸwÅxz„·©{©¬

(183) Œ†{mlŸX|©®¨˜®¶©~€˜|jk¾„X®{axª¶Ol*¨˜„Ž{jžX®{©ž xz„ Œ-~zl*žX®„X{¬[±\l*~zl*{ax?­µ~z„Žk¾xzhjl<˜{j®x€‚Œ†¨©žX|jlQwzwQÁX„X~?²%hjl*{Œx€~6Œ†{©w€˜l*{ax5Œ†{Œ†¨˜vRw€‚wx€~z®lŸwÅxz„0‘#„Xkmj|[x€l<x€hjl lQ³Ž„X¨®|[xz®„X{e„Ž­xzhjl¬[l*³R‚‘#l  w%‘*|j~€~zl*{axUŒŽ‘*~€„aw€wªxy²@„´~zl*žX®„X{©wQ¯ g=hj‚wC²%®¨˜¨R¶l@˜¨®¨˜|©wx€~6ŒIx€lŸ¬˜{xzhjl@‘QŒŽw€lª„Ž­[x€hjl=¬[˜„R¬jl5²%hjlQ{xzhjl@n<l*²=xz„Ž{[lj‹UŒ†©h©w„X{ Œ†¨˜žŽ„X~€®x€h©k xz~€˜lQw xz„

(184) ·©{©¬xy²@„ew€|©‘*‘*lQwzw˜³Žl-O„Ž¨‚Œ†~z! QŒIxz®„X{O„Ž˜{axzw<„†­ªŒ

(185) ‘#˜~6‘#|j®x<²%®x€h¿Œ

(186) ³X„Ž¨®xzŒŽžŽlw€„Ž|j~6‘#l E(t) ÁŒ

(187) ~€lŸw‚wx€„Ž~ Œ†{©¬!Œm¬[˜„R¬jl D MåwlQl C˜žŽ|j~zl•[¯ ”0­µ„Ž~U‘#˜~6‘#|j®x  w%¬[lQwz‘#~z˜[x€˜„Ž{!Œ†{©¬ C˜žŽ|j~zl•[¯ › ­µ„X~UŒ†¨˜žŽ„Ž~z®x€hjk O ¯ R GS. I. UR E(t) UD. C ®žX|j~€l•j¯ ” \Cƒ„X¨˜ŒŽ~€!QŒ†x€˜„Ž{e„Ž­CŒ

(188) ¬[˜„[¬[l g=hjl=j~z„[‘#lŸw€w)­µ„Ž~·©{©¬[˜{jžMx€h©l5{jlQ² O„Ž¨‚Œ†~z ŸŒIxz®„X{-„X®{ax?ŒIxCx€˜kml t+h wxzŒŽ~x6w)²%®x€hmŒŽw®{©Âxz˜ŒŽ¨[žŽ|jlŸw€w x€h©l-„X¨˜ŒŽ~€!QŒ†x€˜„Ž{eO„Ž˜{axU„Ž¶[x6Œ†˜{jlQ¬­µ„X~=x€˜k´l \ ¯ªg=h©l·©~zwxU®x€l*~6ŒIxzl ‚w U žX®³Xl*(t{À+¶Rvh)x€hjl0®{ax€lQ~zw€lQ‘#x€˜„Ž{À¶Ol#xy²@l*lQ{Àx€hjl xzŒŽ{jžŽlQ{Xx<x€„xzhjtl0¬jU®„[¬[(t)l  wq‘6h©Œ†~6ŒŽ‘#x€l*~z‚wyxz˜‘-ŒŽ{©¬Ux€hj(tlmw€+„Ž|jh)~6‘#l*Ç ~zlQw€‚wyxz„Ž~ª‘6h©ŒŽ~zŒX‘4xzl*~z˜wx€‚‘†*¯ Rq|jl<x€„xzhjlqwx€®±\{jlQwzw?„Ž­x€hjlM¬[®„[¬[l  w5‘6h©Œ†~6ŒŽ‘#x€lQ~€‚wyxz˜‘ŽÁIx€h©˜w5³IŒ†¨˜|jl U (t + h) ²%˜¨˜¨c~€lŸw|©¨Âx%˜{!Œ´{R|jkml*~z‚‘*Œ†¨\„I³Xl*~ ©„I²:¬[|j~z®{©žmx€hjl-‘#„Xkmj|[xzŒ†x€˜„Ž{!„†­x€hjl-{©l#¼RxUÂxzl*~6ŒIxzl U (t + h) ¯ 0 D. D. 1 D. 2 D. 1 D. X`. í.

(189) –ݝ. E(t)−UD R. E(t+h)−UD R. I. UD0 (t + h) = UD (t). I(UD ). UD1 (t + h). Numerical overflow !. UD.  

(190)  

(191)   !"$#&%('*)+ ,- .$/0( 1,2(. C˜žŽ|j~zl•[¯ › \ÅnUlQ²=x€„X{[Çϋ<Œ†jh©w€„Ž{Œ†¨˜žŽ„X~€®x€hjk7wlŸŒ†~6‘6hj®{©ž­µ„Ž~UŒm{©l*² O„Ž¨‚Œ†~z!QŒIxz®„X{ `IaÙ(b©à c4ߟÚ.

(192) –Ÿš. # ] /]]/-/

(193) *,-   (. tRlQ³ŽlQ~zŒŽ¨cw„X¨®|[xz®„X{©w=xz~€vex€„

(194) „I³ŽlQ~z‘*„Žkmlqx€hjlŸwl©~€„X¶j¨®lQk

Références

Documents relatifs

1) La recherche des victimations dans les établissements scolaires, à commencer par la Martinique et la Guadeloupe (territoires français d’Amérique), puis sur les

Repérer les signes, les traces et les discours de la commande au sein des espaces de l’édition professionnelle, comme nous l’avons fait pour le cas particulier des éditions du

Dans ce contexte, afin de venir en aide aux différentes parties prenantes présentes sur le terrain de la collabora- tion et afin d’appuyer les décideurs dans leur

can observe that it is composed of three layers: (i) service instance layer, which represents the services, denoted by a service instance; (ii) network slice instance layer,

Les deux indicateurs précédents (encadrés 1 et 2) donnent la synthèse des asymétries existant entre les structures d’exportation, par branche et par destination, d’un PECO et

dant, il décrit les utilisateurs de covoiturage comme des personnes « militantes » ou « associatives » et leur pratique du covoiturage s’apparente plus à la mise en commun

Para um diagnóstico preliminar do nível de resíduos presentes nos frutos de mamão comercializados no atacado de São Paulo se montou uma parceria entre os projetos “Otimização

34 Although the radical cyclization route was a useful approach for the synthesis of helicenes due to the facile preparation of the stilbene-type starting material and