singular integral

The Noether Theorem of the Singular Integral Equation with Convolution Kernel

含卷积核的奇异积分方程的Noether定理

The surface Helmholtz integral equation dispersed by quadratic iso_parametric element is used as computation equation. Extensive work has been performed to overcome boundary integral equation in acoustic problems, non_uniqueness of solution and singular integral kernels.

以二次等参元离散的表面Helmholtz积分方程作为计算方程，采用一系列数值处理技术，克服了表面Helmholtz积分方程求解声学问题时出现的解的不唯一性和积分函数奇异性。

The natural BIE only contains the strongly singular integral.

该积分方程仅含强奇异积分。

Integral transforms and dislocation density functions were employed to reduce the problem to Cauchy singular integral equations. The numerical results show the effects of loading combination parameter, material distribution and crack configuration on the fracture behavior.

数值方法为采用积分变换和位错函数法将问题简化为Cauchy奇异积分方程，最后给出数值结果，讨论了载荷耦合参数、材料分布形式和裂纹位置等因素对断裂行为的影响。

The stability of Cauchy kennel singular integral with integral curve of the class

Cauchy核奇异积分关于R类积分曲线的稳定性

Linear Singular Integral Equation of Several Complex Variables

多复变数的线性奇异积分方程

On method of solution in class { α,β} for the dual singular integral equation with Cauchy kernel and convolution kernel in the non-normal type case

{α，β}类中含Cauchy核与卷积核的对偶型奇异积分方程非正则型解法

Hadamard~ [ 13] defined high order singular integrals by the think of the integral for finite part in real analysis.

Hadamard在实分析中是用积分有限部分的思想，定义高阶奇异积分的。

The derivation of impedance matrix is presented in details. The numerical treatment to different singular integral and how to choose the unknown function are also discussed.

给出了新方程对应的阻抗矩阵的推导过程与最终表达式，讨论了积分奇异性的处理和待求函数的选择问题。

A Common Singular Integral Formula from Gamma Function

由伽马函数引出一个较普遍的反常积分公式

Indirect Approximate Solution With Complex Splines for Singular Integral Equations on A Closed Contour

封闭曲线上的奇异积分方程的样条间接逼近解法

The singular integral equation for the unkown crack opening displacement is derived.

求出了以裂纹张开位移为未知量的奇异积分方程.

Singular integral equations on bounded domain in the plane

平面有界域上的一类二维奇异积分方程

The unbound regions are modeled as interface cracks, and a set of singular integral equations derived.

把脱离区看做界面裂纹, 将问题归结为一组奇异积分方程.

This is a singular integral equation with Cauchy kernal, we can find the analytic solution by using Chebyshev polynomial expension.

这是一个带Cauchy核的奇异积分方程，应用Chebyshev多项式展开，求出此方程的解析解。

The Replacement Formula of Singular Integral with Nondegenerate Weil Polyhedron

非退化Weil多面体域奇异积分的置换公式

The high order singular integral operators on domain of complex plane

展布在复平面区域的高阶奇异积分算子

Weighted boundedness of bilinear C-Z singular integral operators on space of homogeneous type

齐型空间上双线性C-Z奇异积分算子的加权有界性

The character of the solution depends on the known function of integral equation, as to the Type ⅰ Fredholm integral equation with logarithm function singular integral kernel.

对于具有对数函数弱奇异性积分核的Fredholm型I类积分方程，解的性质主要取决于方程中已知函数的形式。