Диссертация (1137475), страница 15
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Îñòàëîñü ïðîâåðèòü ïîñëåäíþþòî÷êó ξi = ξj + ε:f (ξj + ε, ξj , u) = 2S 0 (ξj )S 0 (u + ξj )℘1 (ξj + ε − ξj )+000+ S (ξj )S (u+ξj ) −ζ1 (u+ξj +ε)+ζ1 (ξj +ε−ξj )+ζ2 (u+ξj ) −S 0 (ξj )S 0 (u+ξj )℘2 (u+ξj )+000+ S (ξj )S (u + ξj ) −ζ1 (ξj + ε) + ζ1 (ξj + ε − ξj ) + ζ2 (ξj ) − S 0 (ξj )S 0 (u + ξj )℘2 (ξj )++ S 00 (ξj + ε − ξj ) S 0 (ξj + ε)S 0 (u + ξj ) + S 0 (ξj )S 0 (u + ξj + ε) .Çäåñü âêëàä ìîãóò äàòü òîëüêî2S 0 (ξj )S 0 (u + ξj )℘1 (ε) + S 0 (ξj )S 00 (u + ξj )ζ1 (ε) + S 00 (ξj )S 0 (u + ξj )ζ1 (ε)++ S 00 (ε) S 0 (ξj + ε)S 0 (u + ξj ) + S 0 (ξj )S 0 (u + ξj + ε) =111= 2S 0 (ξj )S 0 (u + ξj ) 2 + S 0 (ξj )S 00 (u + ξj ) + S 00 (ξj )S 0 (u + ξj ) −εεεhi1− 2 (S 0 (ξj ) + εS 00 (ξj ))S 0 (u + ξj ) + S 0 (ξj )(S 0 (u + ξj ) + εS 00 (u + ξj )) =ε111= 2S 0 (ξj )S 0 (u + ξj ) 2 + S 0 (ξj )S 00 (u + ξj ) + S 00 (ξj )S 0 (u + ξj ) −εεε1 0111− 2 S (ξj )S 0 (u + ξj ) − 2 εS 00 (ξj )S 0 (u + ξj ) − 2 S 0 (ξj )S 0 (u + ξj ) − 2 εS 0 (ξj )S 00 (u + ξj ) =εεεε111= 2S 0 (ξj )S 0 (u + ξj ) 2 + S 0 (ξj )S 00 (u + ξj ) + S 00 (ξj )S 0 (u + ξj ) −εεε111−2 2 S 0 (ξj )S 0 (u + ξj ) − S 00 (ξj )S 0 (u + ξj ) − S 0 (ξj )S 00 (u + ξj ).εεεÈ òóò îñîáåííîñòè íåò, ñëåäîâàòåëüíî, íè îäèí èç ïîëþñîâ íå ïîäòâåðäèëñÿ, è ôóíêöèÿ ÿâëÿåòñÿ êîíñòàíòîé ïî ξi .
×òîáû íàéòè ýòó êîíñòàíòó, ìû åå îöåíèâàåì â ðåãóëÿðíîé òî÷êå ξi = ξj + 21 . Èìååì:11f (ξj + , ξj , u) = 2S 0 (ξj )S 0 (u + ξj )℘1 ( )+2211000+ S (ξj )S (u+ξj ) −ζ1 (u+ξj + )+ζ1 ( )+ζ2 (u+ξj ) −S 0 (ξj )S 0 (u+ξj )℘2 (u+ξj )+2210411+ S (ξj )S (u + ξj ) −ζ1 (ξj + ) + ζ1 ( ) + ζ2 (ξj ) − S 0 (ξj )S 0 (u + ξj )℘2 (ξj )+221 01 00 1000+ S ( ) S (ξj + )S (u + ξj ) + S (ξj )S (u + ξj + ) =22200000= 2S (ξj )S (u+ξj )℘2 (0)+ S (ξj )S (u+ξj ) −ζ2 (u+ξj )+ζ2 (0)+ζ2 (u+ξj ) −00000−S (ξj )S (u + ξj )℘2 (u + ξj ) + S (ξj )S (u + ξj ) −ζ2 (ξj ) + ζ2 (0) + ζ2 (ξj ) −1 01 0000 1000−S (ξj )S (u+ξj )℘2 (ξj )+ S ( ) S (ξj + )S (u+ξj )+S (ξj )S (u+ξj + ) .222000Ïîëó÷èëè, ÷òîf (ξj + 21 , ξj , u) = 2S 0 (ξj )S 0 (u + ξj )℘2 (0)−−S 0 (ξj )S 0 (u + ξj )℘2 (u + ξj ) − S 0 (ξj )S 0 (u + ξj )℘2 (ξj )++S 00 ( 21 )0S (ξj +102 )S (u00+ ξj ) + S (ξj )S (u + ξj +12)== S 0 (ξj )S 0 (u + ξj ) 2℘2 (0) − ℘2 (u + ξj ) − ℘2 (ξj ) + 011 0S(ξ+)S(u+ξ+1jj22)+ S 00 ( ).+2S 0 (ξj )S 0 (u + ξj )Èñïîëüçóÿ (AI.23), (AI.14) è (AI.15) (èç êîòîðîãî ìû íàõîäèìS 00 ( 12 ) = −π 2 θ32 (0, τ2 )θ42 (0, τ2 )), ìîæíî âèäåòü, ÷òî âûðàæåíèå â êâàäðàòíûõ ñêîáêàõ ðàâíî íóëþ:1 S 0 (ξj + 21 ) S 0 (u + ξj + 21 )℘2 (0)−℘2 (u+ξj )+℘2 (0)−℘2 (ξj )+ S ( )+=2S 0 (ξj )S 0 (u + ξj )00= π 2 θ22 (0)θ32 (0)θ42 (0)−π 2 θ32 (0)θ42 (0)θ1 (−ξj )θ1 (ξj )θ1 (−u − ξj )θ1 (u + ξj ) 2 2+π θ2 (0)θ32 (0)θ42 (0) 2−22θ2 (0)θ2 (u + ξj )θ2 (0)θ22 (ξj )θ1 (ξj )θ1 (u + ξj ) θ1 (u + ξj )1θ1 (ξj )−πθ3 (0)θ4 (0)−=θ2 (ξj ) πθ3 (0)θ4 (0) θ2 (ξj )θ2 (u + ξj ) θ2 (u + ξj )= π 2 θ32 (0)θ42 (0)θ1 (−ξj )θ1 (ξj )θ1 (−u − ξj )θ1 (u + ξj )2 22+πθ(0)θ(0)+34θ22 (u + ξj )θ22 (ξj )+π 2 θ32 (0)θ42 (0)θ12 (ξj )θ12 (u + ξj )2 22+πθ(0)θ(0)=34θ22 (ξj )θ22 (u + ξj )105= −π 2 θ32 (0)θ42 (0)+π 2 θ32 (0)θ42 (0)θ12 (ξj )θ12 (u + ξj )2 22−πθ(0)θ(0)+34θ22 (u + ξj )θ22 (ξj )θ12 (ξj )θ12 (u + ξj )2 22+πθ(0)θ(0)= 0.34θ22 (ξj )θ22 (u + ξj )Ò.å.
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