简介：Inthispaper,wedevelopGaussianquadratureformulasfortheHadamardfi-nitepartintegrals.Inourformulas,theclassicalorthogonalpolynomialssuchasLegendreandChebyshevpolynomialsareusedtoapproximatethedensityfunctionf(x)sothattheGaussianquadratureformulashavedegreen-1.Theerrorestimatesoftheformulasareobtained.Itisfoundfromthenumericalexamplesthattheconvergencerateandtheaccu-racyoftheapproximationresultsaresatisfactory.Moreover,therateandtheaccuracycanbeimprovedbychoosingappropriateweightfunctions.

简介：这篇文章介绍hypersingular积分的近似?abg(x)(x-t)dx并且?abg(x)|x-t|有任意的单个点t的dx(一，b)并且否定部分数字<-1。这些一般扩大对hypersingular积分的一个大范围适用，包括在文学和还没被探讨的另外的重要的讨论的两流行hypersingular积分。相应中间矩形的公式和推测，能以相当直接的方法计算，被调查。数字例子被提供说明数字方法的特征并且验证理论结论。

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简介：单个不可分的操作员

简介：Byusingtheconceptoffinite-partintegral,asetofhypersingularintegro-differentialequationsformultipleinterfacialcracksinathree-dimensionalinfinitebi-materialsubjectedtoarbitraryloadsisderived.Inthenumericalanalysis,unknowndisplacementdiscontinuitiesareapproximatedwiththeproductsofthefundamentalden-sityfunctionsandpowerseries.Thefundamentalfunctionsarechosentoexpressatwo-dimensionalinterfacecrackrigorously.Asillustrativeexamples,thestressintensityfactorsfortworectangularinterfacecracksarecalculatedforvariousspacing,crackshapeandelasticconstants.Itisshownthatthestressintensityfactorsdecreasewiththecrackspacing.