函数的积分

In this paper,the boundary singular kernel method in Reproducing Kernel Paicle Method has been applied to impose the essential boundary conditions in EFGM by revising the MLS shape function.The stress field and the displacement field are analysed by linear elastic theory.The contour integral method is used to calculate the J-integral,then the stress intensity factors of mixed-mode crack is acquired.The correctness and the validity of the method are validated.

本文将再生核质点方法中的边界奇异权方法引入EFGM中，通过对MLS形函数进行修正实现了本质边界条件在节点处的精确施加；运用线弹性断裂理论分析裂纹板的应力应变场，采用围线积分法计算J积分，给出了复合型裂纹板的应力强度因子的无网格伽辽金方法。

Property 2 (Term-by-Term Integration) Suppose that is the sum of a power series on interval ;that is,Then, if is interior to ,and the radius of convergence of the integrated series is the same as for the orginal series.

性质 2 幂级数的和函数在其收敛域上可积，并有逐项积分公式，，逐项积分后所得到的幂级数和原级数有相同的收敛半径。

The convergence theorem of the neural networks algorithm and the theorem of numerical integration solution and its inferences are presented and proved.

摘要该文提出了一种基于三角基函数神经网络算法求解数值积分的新方法，提出并证明了神经网络算法的收敛定理和数值积分的求解定理及推论。

The deflection pulse response function in the general Duhamel integration is got by using integral transform and the program of corresponding numerical inverse integral is worked out.

采用积分变换的方法，求得了广义Duhamel积分式中的弯沉脉冲响应函数，并编制了相应的数值积分逆变换程序。

The direct method of solution for non-normal type of singular integral equation with Hubert kernel is discussed. Their solution have form of integral and the condition of solution have form of the system of equations.

给出了具有Hilbert核非正则型奇异积分方程的直接解法，对核密度函数k在附加某些条件下，得出了方程积分形式的解和方程组形式的可解条件。

In this paper,the singularity in the integrand of electrical field integral equation for 3-dimensional vector fields scattering is first analyzed.

本文研究了电场积分方程中被积函数奇异性的处理方法，特别是三维矢量散射分析中出现的高阶奇异性，给出了两种解决积分方程奇异性的数值方法。

Dept.of Microwave Eng.,UEST of China,Chengdu 610054,ChinaAbstract:In this paper,the singularity in the integrand of electrical field integral equation for 3-dimensional vector fields scattering is first analyzed.

本文研究了电场积分方程中被积函数奇异性的处理方法，特别是三维矢量散射分析中出现的高阶奇异性，给出了两种解决积分方程奇异性的数值方法。

According to a given function, namely, composite trapezoidal formula using composite Simpson formula Romberg quadrature formula and the variable step-size integration quadrature formula results, and compare the accuracy of points.

详细说明：根据给定的函数，分别用复合梯形公式、复合辛普森公式、龙贝格求积公式和变步长的求积公式计算积分结果，并且比较积分的精确度。

In this dissertation, many works have been done on the basis of the summarization of the merits of all kinds of meshless methods after a large number of relevant references are read and studied. The basic ideas, principles of meshless methods and their development in the recent years are introduced synoptically. Applications of Element-free Galerkin method in elastic foundation plate are studied deeply and some useful conclusions are obtained as follows:(1) Comparisons between numerical solutions and analytical solutions for several different styles of weight functions, including Gaussian weight function, spline weight function and singular weight function etc, are performed. The results show that Gaussian weight function is the best one.(2) Ranges of relevant parameters for Gaussian weight function are given.(3) Influences of nodal distribution schemes and the number of Gaussian integrated dots on computational results are discussed.

在本文中，作者在认真阅读和研究所搜集到的大量参考文献、综合各种无网格法优点的基础上，首先，对无网格法的基本思想、基本原理、发展现状作了概括性的介绍；其次，对无单元Galerkin法在弹性地基板计算中的应用进行了较为深入的探讨：(1)分别对高斯型、样条型、奇异型等不同形式的权函数进行比较分析，数值计算结果与级数解析解的比较表明，高斯型权函数效果较好：(2)对高斯型权函数进行参数研究，得到地基板计算中相关参数的选取范围；(3)对不同节点分布方案和不同高斯积分对计算结果的影响等作了有益的讨论。

What encumbers it most is the integration of density function along rays in field. The method presents in the paper borrowed idea from volume method of ray casting, and greatly improves calculation efficiency.

其中的计算难点是光线在流场中的密度函数积分，文中利用光线投射原理改进原有的光线积分方法，有效地提高计算效率。

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。