共查询到20条相似文献,搜索用时 78 毫秒
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非绝对积分概论(连载一)许东福,潘杰(厦门集美高等师范专科学校)(合肥工业大学)[编者按]正H一积分是一种新的积分,它统一了黎曼积分与勒贝格积分,用这种观点介功贝格积分可完全lff开利度.在国外对这种积分的研究非常活跃,而国内在李秉课教授的田明下也有... 相似文献
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该文在Rπ空间中定义了一种Denjoy型非绝对积分,证明了这种Denjoy型积分与B-积分等价,从而给出了B-积分的Denjoy形式. 相似文献
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定义在Cn中具有逐块光滑边界的有界域上光滑函数的一种积分表示,这种积分表示的特点是积分式中含有局部的全纯核,且含有可供任意选择的实参数p,2≤p+∝.利用这个公式,我们可获得有界域上方程的局部解和证明在含参数局部意义下存在一致估计. 相似文献
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该文用Lebesgue-Stieltjes积分给出一个双曲型方程组广义解的新定义,在这个意义下证明了Cauchy问题整体广义解的存在性.这种解自然地包含了δ-激波. 相似文献
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一类广义积分的简便算法钱士茹(安徽化工职工大学,合肥230001)一、引言应用留数定理计算在实轴上有奇点的广义积分,通常是选取环形积分围道(见图1).这种围道是由CR、Cε和两条线段[-R,-ε]、[ε,R]所组成.作小圆Cε的目的是要避开求积函数在... 相似文献
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1.引言由于对积分算子方程来说,配置法比Galerkin法具计算量小的优点(少算一重积分),故配置法更受人们重视.但已有的文献几乎都是将配置空间取作非连续的分片多项式样条空间,以得到某种超收敛结果(如[1,2]).这种方法存在下列不足:(a)光滑核Volterra积分方程与光滑核Fredholm积分方程具完全不同的收敛性质[1],且需用不同的方法获得其加速收敛结果(比较[31与[4]),尽管Volterra积分方程在理论上被看作是Fredholm积分方程的特殊情形;(b)光滑核Volterra积分方程的配置解不具任何超收敛性,其迭代配置解也只在结点… 相似文献
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广义模糊数值Choquet积分的自连续性与其结构特征的保持 总被引:11,自引:1,他引:10
在一般模糊测度空间的任一子集上,针对给定的μ-可积数模糊数值函数,定义所谓广义的模糊数值Choquet积分,并将这种积分整体看成可测空间上的模糊数值集函数.进而讨论并研究它的上(下)自连续性,逆上(下)自连续性,一致自连续性和一致逆自连续性等结构特征. 相似文献
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John T. Conway 《Integral Transforms and Special Functions》2017,28(6):488-503
A method developed recently for obtaining indefinite integrals of functions obeying inhomogeneous second-order linear differential equations has been applied to obtain integrals with respect to the modulus of the complete elliptic integral of the third kind. A formula is derived which gives an integral involving the complete integral of the third kind for every known integral for the complete elliptic integral of the second kind. The formula requires only differentiation and can therefore be applied for any such integral, and it is applied here to almost all such integrals given in the literature. Some additional integrals are derived using the recurrence relations for the complete elliptic integrals. This gives a total of 27 integrals for the complete integral of the third kind, including the single integral given in the literature. Some typographical errors in a previous related paper are corrected. 相似文献
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本文在K-拟可加模糊测度空间上建立了K-拟可加模糊数值积分,利用其积分转换定理和诱导算子的性质,将这种积分整体看成可测空间上取值于模糊值和集函数,从而使得这种模糊积分不仅具有自连续性,而且也满足逆自连续性。这些特性能更好地描述模糊值可测函数列和K-拟可加模糊数值积分序列的收敛性。 相似文献
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模糊积分变换与模糊Choquet积分的一致连续性 总被引:2,自引:0,他引:2
在一般非负单调函数空间 m[0 ,a]上引入模糊积分变换与距离的概念 ,证明了这种模糊积分变换与模糊 Choquet积分在 m[0 ,a]上关于这种距离是一致连续的 ,从而说明当 m[0 ,a]上两个函数变化不大时 ,不会使相应的模糊积分变换与模糊 Choquet积分产生较大的变化 . 相似文献
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E. Babolian A. Arzhang Hajikandi 《Journal of Computational and Applied Mathematics》2011,235(5):1148-1159
A method for finding the numerical solution of a weakly singular Fredholm integral equation of the second kind is presented. The Taylor series is used to remove singularity and Legendre polynomials are used as a basis. Furthermore, the Legendre function of the second kind is used to remove singularity in the Cauchy type integral equation. The integrals that appear in this method are computed in terms of gamma and beta functions and some of these integrals are computed in the Cauchy principal value sense without using numerical quadratures. Four examples are given to show the accuracy of the method. 相似文献
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John T. Conway 《Integral Transforms and Special Functions》2016,27(8):667-682
A substantial number of new indefinite integrals involving the incomplete elliptic integral of the third kind are presented, together with a few integrals for the other two kinds of incomplete elliptic integral. These have been derived using a Lagrangian method which is based on the differential equations which these functions satisfy. Techniques for obtaining new integrals are discussed, together with transformations of the governing differential equations. Integrals involving products combining elliptic integrals of different kinds are also presented. 相似文献
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一类核密度含高阶奇性Cauchy型积分的边值定理 总被引:2,自引:0,他引:2
本文推广「1」,「6」中的结果,讨论了一类开口弧核密度含高阶奇且情形更一般的Cauchy型积分的边值定理,积分号下求导及H连续性。 相似文献
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Computable lower and upper bounds for the symmetric elliptic integrals and for Legendre's incomplete integral of the first kind are obtained. New bounds are sharper than those known earlier. Several inequalities involving integrals under discussion are derived. 相似文献
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在拟可加测度空间上通过引入拟乘算子重新定义广义Sugeno积分,针对依拟可加测度收敛的函数列,应用诱导算子和拟乘算子的运算性质讨论和分析广义Sugeno积分的收敛性,进而获得了这种广义Sugeno积分的单调增收敛定理. 相似文献
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Rui-Sheng Wang 《Journal of Applied Mathematics and Computing》2011,35(1-2):305-321
Fuzzy measure (or non-additive measure), which has been comprehensively investigated, is a generalization of additive probability measure. Several important kinds of non-additive integrals have been built on it. Integral inequalities play important roles in classical probability and measure theory. In this paper, we discuss some of these inequalities for one kind of non-additive integrals—Choquet integral, including Markov type inequality, Jensen type inequality, Hölder type inequality and Minkowski type inequality. As applications of these inequalities, we also present several convergence concepts and convergence theorems as complements to Choquet integral theory. 相似文献