df ( x )= df ( x )= f ( x ) ;f ( x ) y ( x ;u ) y ( x ;u ) x (0)= x y t> 0 x (0)= x y t> 0 x Ix u 2 U U x 1 ;x 2 2 M h =[ h :::h ] x 2 M y = h ( x )1 • i • p x _ = f ( x )+ g ( x ) u X y =[ y :::y ] m u =[ u :::u ] p
4
0
0
Testo completo
(2) "!$#% '&)(* '&)(,+- ".0/21%354767+-89&;:<&;=;:<&)>?+- "@A!5+B.%!53C676<+-D% A+B474<35:FE;&;G% "@" H6JIK8L3M:N A47 "476<35(, A.%+B. @"8 ".%+B "3O!J&)#%:7\] QPS ".*RT6J U&)@"@' "3(,>? H+;6< ':7&;(*(,&^+V4<+;&).%@"@"+_+W35474<678%19:7D%35 "47+*4< LD9 L U4747 " "47476<67353M(,(, L UD%.% L+B.%.X+B@"4F "6<.%:73M+_&; ":7.` U67 "3M. :735>?47+B4<:F3;(WPa&,RbD%+B.% Y47!5 "+BD9.Z356<:7:7 '+;&)@"(,@'+A+ [ &;@"@"+B:<&c1%. 4< "4F6<35.%(*3M@"&d@'&e(_>?+;1%:7@H(*6< HE;&A&;f :7 '&)G% "@"3!5+B. m ".%=;:7354<47 u = [u . . . u ] 3 p 1%47!M H673 y = [y . . . y ] x˙ = f (x) + g (x)u g R]P"hji R]PlkBi y = h (x) 1 ≤ i ≤ p g D%oK+O 'EZ&)3(*h+0 '=.% "p5[h '&;@"(,. .35..`h673^] &;@"\W!51%@'.%& 3q(*D%&;3Cr98%.%89 "& pM ":7+;3M.9=; Q+BP @'&;:F3WD%3M@"@Qm 1%47!M H6<&XD%35@n47 "476<35(*& 3 x ∈ M P st`u<vnw*vQxzyq{9|*}C~;~ x1, x2 ∈ M }$-;< ) ".%D% "4F6< ".%=B1% "G% "@" ,{Z}CQ;* d"d )~; J ) )%~<| )J jT];%e)0~~" }J}CxQ5Ix T 7 }O|C|J)K )9{ |C j 7;| 9eJ9 )|$9 ~Q< )' u^∈%;U$~Q<W|,JB ); ' *U }$~)A~}C W|$W9|dQ`;|C'| y ^%;t$~Q><|00Z)' ,}C~;~ W% Q;"| _ | F C | ; j { ) | % C | x(0) = x x(0) = x }O ) *QZ|C9~QJ%|^|$ ' )< W`y )e9Q Vt ;>a`0|QN9 j|M @Q m 1%35:,=B19EZ&;35=B:7@" H 'r9&)!M.%&;pO:7&X3 D%@Qm35 "@".%@"3VD% "D%4F6<1% ".%3V=B1%1%47 "!5G% H "6<@"3 H6JID% D%1%3 4F6J&)6< \ D%1%.%/`1%3 .%3M!5354<4<&;:7 "+EZ35:7 Hr9!M&;:73 :7 "!5+B:747+*&;=B@" ¢476<:F19(,35.Z6< D%35@"@Qm &;@"=B35G%y(x:<&0D%, u)£ "3B3 P y(x , u)Pd 35:_>?&;:73V!5 "¡cG% "47+B=B.9& >Q&):73 1. m. T. p. 1. m X. i. i. i=1. i. p. 1. 1. i. T. 2. 1. 1. 2. 2. 1. 2. st`u<vnw*v'¤yq{9|¥J{2 )9 f (x), f (x) }C;QJ ) ¦ ".%D% "835.%D%3M.Z6< W}O| J );|C~Q~ )$ | df (x) = O} ) _) 9|CZ|C9~Qn{2eL{A%~ , _{AA}C|C*| df (x) = hBhBh 1. ∂ f1 ∂x. 2. ∂ f2 ∂x. 1. 2.
(3) W§ ¨a©*ªMª5«`¬O%®%¯ °?±Q°²M³ ´µ¶9·;¸¹<º"»M¼;½'·;¸7¾;¿ ¶¾5¸KÀZ¾5¸7ºHÁ9»M·;¸7¾0½Q Ã%Ä;Ã9·;ÄB½"º'·;µ%ÅM·VÆ%ºNÆ%Ã%¾eÇ?Ã%µ%ÅMº"¼;µ%ºNº"µ¼BÄBµ%º º"È7¹J·)µ`¹<¾ t¿ Ç?É Ã%È7µ%ÃAÅ5Ê*º"¼B»Mµ%º"º¢¾5µZÈ<¼;¹<¾0µ9¼0»5¼BÇÃ%µAµ9Ç?¸7Å5¼;º"µ`¼B¹Jµ%·)º ¸7·;¾0µ9ºY·;½"ÀBºH·)¹<º"½"»J¼BÌ%¸7º ¾jÍJÆ%Înº Ï]¹<ÃA¼O¹7ÀZ¹<¾-¾eÈJ½"·)¾0¸<Ð ½"¼B¸7¼Æ%¾5¸7ºHÀ;·)¹<¾0º"µ t = 0 Ë È7¾0½"¾0Æ%Ã%¾ yi (0) = hi (x0 ) P P i i i y˙i (0) = ∂h x˙ |0 = ∂h f (x) + j ∂h g (x)uj |0 = Lf hi (x0 ) + j Lgj hi uj (0) ∂x ∂x ∂x j y¨i (0) = . = P P P Lf Lf hi + j Lf Lgj hi uj (0) + j Lgj Lf hi uj (0) + j Lgj Lgj hi uj (0) + . . .. Ñ º ¶%Ã%Ò0Á9µÆL·0¼;¸<·0¾Mµ`Ã%µ%»5º'·;¸7¾qÃ%µ9·0¶%¸7º"Ó*·0Æ%¾5Á9µ%º"Å5º"¼Bµ%¾-Æ9º¢¼BÈ7È<¾5¸FÀ;·)Ô%º"½'ºH¹<ÐAÕ Ö «`×<¨a§W¨'ØÚÙÛÜCÙ'ÜCÝÞCß,àáeâOÜJÜMÞCã$ä)àZåCÙÛ'Þ-ÜMÞ x Ix ÙßSæÛÙç<àçJè9Þ x = x é ´Æ%µ ¾5½"½"¸7¾ ¾M·;»5½H¼B¹Jµ%ÐXÆ%È<º"ÅMº'·)º"¼;Ó*µ%¼cº9Æ%º"µ`º9¹7¸<¾M·)¸7µ%¾5ÄBÈ7¼qÈJ·jÈ<¹<Ã*ºTÓ*·c·jÆ9¹<·)¸7¸7º"¾V»5ºQÎëÃ%µ9ê ·c¾5¸NÆ%ÇQ¾C·;Á9¸7¾ìµ9º"»MÅ5º"º"Òq¼Bµ%Æ%¾V¼BÔ%Æ%Ô%ºbº'·;¼BÓ,È7È7¼q¾M¸¶À;·;¾5¸7Ô%Ò^º"½"ºH·;¹J»5ÐX»5¼B¹<µ`¸F¼O¹7À;¾MµZ·;¹Jµ%·;Æ%¸¼ í »5·;ºYµ%»JÆ9Ì%ºY¾0»5¼B½'·µ%Æ%Æ%º"¾CÅ5Á9º"¼Bµ%µ%º"ºUÅ5º"À;¼B·;µ%½"¾0º"Æ%Æ%¾eºN½"¼`º"µ%»MÆ%·;º"½"È7Ó,¹7º"¾5µ%µ`ÄB¹<Ã%¾;º"¿Ô%¹<º"¸<½"ºH·j¹J¹7Ð ¹J·;µ%ÆLÆ%·V¼BÈ7º"ºYµZÆ%¹<¾MºYµ%È<Æ%º"ÈF¾5¹<¸7¾5È7Ó*ºNº"ºYµµ%¼BÈ7¾5µcµ%È<½"º"¼µ%¾M½"¼`·;¸7»OºQ·)ÎK½"¾Bî]¿¢½"»M½"¼;¼;¸<µ2· í È7º"Æ%¾M¸<·)µ%Æ%¼ »Mº"¼ É È7¼B½"¼ »5¼BµZ¹<¸7¼;½'½"ºS¹J·)½"ºK»JÌ%¾B¿ ¶É ¾M¸V¶%º"»5»5¼B½"º]º"µ`¹<¾5¸FÀ;·;½"½"ºS¹<¾5Ó,¶¼B¸7·;½"ºQ¿Sµ%¼Bµ ÇQÈ7·)¾M»MÄ;»5Ã%º'¾M·;µZµ%¹<¼ï¾q·;Æ%½"¾C½"Á9¼BµZµ%¹Jº"Å5·;º"µ9¼B·;µ%¸F¾q¾cÆ%½"º¢¼ðº"µ9È7¹JÆ%·jº"ÈF¹<¹<¼ º"µ%x(t) ÄBÃ%º"Ô%º"Æ9½"ºH·ð¹JÐAÃ%Î µñº"µ`¹<¼;¸7µ%¼ïÆ%º x ÎòÏ]º'·;Ó,¼ïÆ%Ã%µ%ó`Ã%¾c½'· Öæ9ÞC«`ã,×<â<¨aü;§Wø9Ù¨HôÚç<â)õ-ø9ÝQö9ã<Þâ)ÛÜ$Û"âXÝà)çJÝÙâOÜCxÝà;,ø%xÝÞ ∈ V ⊂ù çJMâ)ø ÜCÙq÷;Ùø2ÙçJÜCâjÙÞCøß*â Þ*º'µ%÷`Æ%Þ$º"Ù ÈF¹<çJº"â)µ%ø9ÄBÝQÃ%ã<º"â)Ô%ÛÛº"Ùì½"ºWà;ùßexß0IxÙ'Ü<ÜCúÙQå5ÙÜOÛÞJÙ û u∈U U ú çJè%Þ*æ9Þ$ß,ã à;ø9ÝÞCø`üZà àXæAÛ"à;Þ0ã$ÜMÝQÙâ)ã<ÛÞKöBý5÷ZÙà)â)Ûø%Û'â-Ù x(t, û < ç ) â 9 ø Ý C Þ 9 ø 2 ö Ý , Þ Ù ø ] û 7 Û þ C Þ ; ä ) â l Û Z ö C ý Ù ) â ø Þ x , u) x(t, x , u) V Ü$Ýà)ÝâqÙø9Ù"ýCÙQà;Û'Þ x(0) = x ÞSÛFþ ÞCä;âjÛöZýCÙâ)øÞ y æ9ÞCã t > 0 y t>0 ÷`àVÞ?ÿëæ%à)ø9ã$Ù"ÝýCÙÙã<â)ÞøÞ÷Zé à;ÛÛ"âXÜCÝà)ÝâcÙø9Ù"ý5Ù?à;Û'Þ x(0) = x ÜOâjøâdÙQ÷`Þ$ø9ÝQÙçJè9ÞVøÞCÛbÛ'âjãJâ÷`â)ßeÙø9Ùâ÷)Ù î]½"¼`½"»O½"·)¼B½"¸<Ó,·_¾MÈ7µZº'·;¹<Ó,¾;Î ¼e¶%¸7¼BµZ¹<º¢·_Æ9·;¸7¾KÃ%µ9·_Æ%¾5Á9µ%º"Å5º"¼Bµ%¾KÆ%º¼BÈ<È7¾5¸FÀ;·;Ô%º"½"ºH¹JÐ_µ%¼BµV½'º"µ%¾M·;¸F¾]À;·;½"º"Æ9· Ö «`×<÷)¨aÙ §W¨ ÙøJÛAçCÜCö2Ù'Ü$Ù'ûaÝÞ$æ9ß*ÞCãVà,â<á]ü;÷`ø%ÞCÙìÝQÝÙâø9ݽ"â)¼2ã$»Mø·;â½"Ó,¾5µ`¹7¾ ¼;È<È7¾M÷;¸Ù À;·;Ô%º"û]½"¾ Û"àXº"µ ã<Þ$xÛ"àOý5ÜOÙÞKâjøÞJÜCÞ Ù'Ü$ÝÞ öAøVÙÙø9ßSÝæâ)ã$ÛÙøç<àâ W V ⊂M x x Ix çJè%Þ x x= x é Þ_ÙÛ¢ÜCÙ'ÜCÝÞCß,àXá_Û'âOç<à;ÛlßWÞCø%ÝÞ,âOÜ<ÜOÞCã$ä)àBå5ÙÛ'Þ æ9ÞCã,â7ü;ø9Ù x û à;ÛÛ'âjã<à á0÷`ÞCÝQÝâ ½"¼`»O·)½"Ó,¾MµZ¹<¾ ¼BÈ7È7¾M¸FÀ;·)Ô%º"½"¾ é ÖçJâ)«`ø%×<ݨaÙQÞC§WøÞ ¨ õ_ÞQÿëø%ÙQà;ß*Þìâ ÝQö2Ñ ÝQ¶9Ý·;ÞTÅ5Û'º"Þì¼0Û'Æ%â)ã<ºâq¼BÈ7÷`È<ÞC¾5ã$¸FÙÀ;äj·;à;Å5ݺ"ÞS¼B÷;µ%Ù¾ ã<Þ<Û'ýCâ_Ùâ)Üæ%øàOà)ý5ÛÙ Ùâe÷;Ù ÛÙ øÙÞ7Þ à;ã<Þ^Ûö2÷;ø`Ù ü`Jâ-ö2Û'ø2Þìý5ÝQÙã7âjà;ø9ÙQÙaÞCÝçJÝè%â Þ ã$ÙÞe÷ZÞCÛÜCÙ'hÜCÝÞC,ß,. .àj.ûì, hçCÙâOá L L . . . L h ûìçJâ)ø x = f, g , g , . . . , g , k = 1, 2, . . . Jé øWæã7à)ÝÙç7à 1. 2. 1. 2. 1. 1. 2. 1. 1. 2. 2. 1. 1. 2. 2. . 0. 0. 1. . 0. 1. 2. 2. 0. . . . 1.
(4) . p. x1. x2. xk j. i. 1. 2. m. . !#"%$&
(5) (' )#*
(6) ,+-)#*#./ %*#". 8&89. λ(x) : <n →. <1. "0# '! )#*1/ 23 4%"'5'!! 6 ". f (x) 7.
(7) O = [h1 , . . . , hp , Lf h 1 , . . . , L f h p , ... Lfn−1 h1 , . . . , Lfn−1 hp , Lg1 h1 , . . . Lg1 hp , . . . , Lgm Lgm−1 hp , . . .] :<;>=?=@ A ;%B CED?FGD?HICE;KJLHICEHNMGD?HPOKMGHIQSRETL;GJL;,U(VWULU(;,=?;,XYVECEFGD?HICEDPAE;G=?=?HNJLU @#U(HNMZE;K@3RER @3D?H3CEH CE;>=?=?;NVEJLM>D-UL;I[QSHI=-U(D?RE=?D?M>@
(8) U(;NR\;GTK=?;<XYVECEFGD?HICED\AE;G]I=?D\D?CE]IT/;>JLJLD!^`_CaRET(@
(9) U(D?M>@b=?HcJLR @3FGD?HcAED HIJLJ(;GT/d3@3FGD?HICE;eMGHID?CEMGD?AE; MGHICS=?HfJLR @3FGD?HfAE;G=?=?;ed3@
(10) TLD@3FGD?HICEDEAE;G=?=;eVEJLM>D-UL; MGHITLTLD?JLR\H3C AE;GCgU(D @3AhD?CE]ITL;GJLJ(D0MGHIJ/U @3CgU(Di@jU(T(@
(11) ULULDiAED0RED?MGM>H3=@kAEVET(@
(12) U @^alHnmoEp>qGr!sut3rNsm m>v%wx
(13) pgy%r{z|r{}~ M>H3CPU(D?;GCE;U(VWULU(;u=?;XYVECEF>D?H3CED. h(x). ;u=?;u=H3TLHAE;GTLD-d3@
(14) U(;uAED<HI]3CED<HITLAED?CE;3[ M>@3=?MGHI=@#U(;. =?VEC ]3HS=?;1U(T(@
(15) D?;GULULHITLD?;fAE;G=J(D?J/U(;GQ@^. j P(,cvY0 rYp3sSz?pjMGHAED?J/U(TLD?EVEFGD?HICE;fAEDHIJ(JL;GT/d3@3ED?=?D-U . dO = span ∂Lgm hp ,... ∂x. h. i. dO . s#v>. ∂Lg1 hp ∂Lf hp ∂Lg1 h1 p ∂Lf h1 gm h 1 ∂h1 , . . . , ∂h , ∂x , . . . , ∂x , ∂x , . . . , ∂x , . . . , ∂L∂x ,..., ∂x ∂x. = span[dλ(x), λ ∈ O]. p
(16) r!v%wLp1o\r{ . s#NoEp
(17) }!}p#. dO(q) = span[dH(q)|H ∈ O], q ∈ M iCPVECEMGD@3QSHH3T(@NVECU(;GHIT/;>Q@NM ZE;KM>DPA&<VEC @NMGHICEAED?FGD?HICE;KJ(VE=?=5 HIJLJL;>T/d3@
(18) ED?=?D-U Y=?HPM>@3=?; JLX{TLVWULU @3CEAEH=@uAE;%B C D?FGD?HICE;AEDKMGHPAED?JLU(TLD?EVEFGD?HICE;AEDKHIJLJL;>T/d3@
(19) ED?=?D-U @3RER\;GC @XYHIT/C D-U(@W^ . H3QS;bOb=?;GM>D-U(H@
(20) U/U(;>CEAE;GTLJLD5[ U(T(@
(21) ULU(@3CEAEHJLD?J/U(;>QSDCEHICu=?D?CE;>@3TLD5[&=5 H3J(JL;>TdI@
(22) ED?=?D-U S=?HM>@3=?;. CEHICkDQSRE=?D?M>@=5 HIJLJ(;GT/d3@3ED?=?D-U ]3=?HI @3=?;3^. . P¡&¢ £¥¤§¦¨/¡\©>©G P¢ªE¤E«¬Y®Y¬¯°¥®{¡±3¤&®{ E²¥³&r5pµ´¶m%rm%}v%Spµ´z|}5r{x
(23) p
(24) wr5pgyGr{z?v r{·3w(v(m m%r. u = [u1 . . . um ]T. v. p. ´gm . r{}v. y = [y1 . . . yp ]. x˙ = f (x) +. m X. ¸vz{z?p<¹Gs
(25) wpI. s# . m. gi (x)ui. i=1. º5»¼½¾
(26) ¿#»º!À½iÁKÂÃÄ-Å Æ Ç{Æ<È Ä|Ã!ÂÉÄ?ÊË3ÆÌ ÂKÈ Ä. λ(x). Ì ÍËGÎGÊ. f (x). ÏÐ Ñ%Ò. ½/Ó!ÔÕ» Ñ. ¿#½. n. Lf λ(x) =. X ∂λ ∂λ f (x) = fi (x) ∂x ∂xi i=1. Ü Ô ½ ½ÓÔ Õ/» ¿#½\Ôº!º À»ÔݼÞ#¿
(27) ßGÞ#½\Ô%¼`Þ#¿
(28) Ôà?Þ#¿#Õ/» ¿#½\º!À/Ô ÔÓ5½\½\Ô¼0Þ#¿iÀ/Ôá ½ã5ã Ï Ñ Ò Ñ Ñ Ñ Ï Ò3ÑÝâ à?Þ#¿#Õ/» # ¿ ½eº5À/Ô Ô Ó!½ Ô¼½/Ó5» Ô ãÔN¼» Ó!½/Õ/» ¿
(29) Ô ½Kå Ó!» ½ã!» æ#» ½%ç¼Þ#¿
(30) ßGÞ#½ ½/Ó0½/º5½/á Ñ Ï Øeä â Ñ Ï Ò Ï Ò Ò ¼½/Ó!» Ô(ãÔ ¼» â λ(x) Ï Þ#¿#è Ñ f (x) ½iº5Þ
(31) ÀÀ½Lº!ºY» â Ô á ½/¿Gã!½ Ï Þ#¿#è Ñ g(x) º5» Ñ ã5ã!» ½/¿#½ Ï ÔK¿>Þ. Lg Lf λ(x) =. ∂(Lf λ(x)) g(x) ∂x. Ö×ÙØ Ú%Û. ». Ó!»Ô Ñ Ñ. Ñ(â. ç. Ï. ½&Þ#¿
(32) Ô¿>Þ. Ñ(â. Ó5½/¿
(33) ¼½/¿
(34) ¼. Ò Ôià?Þ#¿#Õ/». Ñ. ¿#½%é. ÑNÏ. Ô Ô. Ö×ÙØ êGÛ. ¦&¦ë.
(35) ìíiîï>ïGðPñòEóEôõYö5õ÷>ø. yi = hi (x) 1 ≤ i ≤ p. . ùPú#û3ü. h = [h1 . . . hp ]T. ü. . ýbþ?ÿ. ÿ. ü Pú. Eÿ. . þ-ÿ.
(36) . ücùgü. þ{þ.
(37)
(38) . ùPü. ÿ. þ. dO = n. ü. ÿ. ü. x∈M. . !#"%$ ?;@ <;:;A
(39) CBD . &
(40)
(41) (' )+*-,' /.10+23. )434 .1576 ,8 ' .:9 ;: <;&= <;> E F== <;>E E ;> x0 7 <;> ;
(42) E; <EG x0
(43)
(44) 3
(45) H . 'I*,J43) 0 *1K L 0 K 0NM K 0+2 ) 4 )%', 2 ) 6 ,' O, = k < n M K 0 2 ) 4 0 O)%',QP 5 R2S $T 0 ) 0UM )434 , ) . 4 *1' K .-57. ',V' )<*-,' . )%434 .1576 ,dO 8 ' R2S ÿ3þ{þ. ú. Lÿ. Lÿ. ü. {þ. û. úú. ÿSý. iÿ. þ. ú. ù. {þ ù. WXWY. ü. ý. ü. ú. ü. ü. ú. ý.
(46)
Documenti correlati
Cilia R, Tunesi S, Marotta G, Cereda E, Siri C, Tesei S, Zecchinelli AL, Canesi M, Mariani CB, Meucci N, Sacilotto G, Zini M, Barichella M, Magnani C, Duga S, Asselta R, Soldà
Ciprandi G, Agostinis F, Amoroso S, Ariano R, Barbato A, Bassi M, Cadario G, Campi P, Cardinale F, Romano C, Incorvaia C, Danneo R, Dal Bo S, Di Gioacchino M, Fiocchi A, Galimberti
(a) Per risolvere gli integrali di funzioni razionali, occorre anzitutto che il grado del numeratore sia strettamente inferiore al grado del denominatore... Si tratta dell’integrale
So, the concentration of Fe(III) ions in a solution can be determined by titration with the ligand H 3 L even in the presence of Fe(II) ions — the ligand is added to the solution
Given the surface tensions for the other interfaces you can calculate energy change to make the water touch the walls instead of air, but this turns out to be negligible:
[r]
onde in una dimensione; partendo dalla formula di d'Alemb ert,
(ii) dimostrare l'unicit a della soluzione dell'equazione di Laplace
