积分的

The characteristic function of the probability density function of response variable is obtained by the high efficient multidimensional numerical integration method or convolution integral based on response surface method. Then the discrete probability density function of response variable is calculated using the fast Fourier inverse transform technique, at last the cumulative distribution function of the response variable can be quantitatively determined.

首先利用高效多维数值积分方法或基于响应面法的卷积积分求解功能函数的分布函数的特征函数，也就是进行Fourier正变换；然后利用快速Fourier逆变换数值求解功能函数的概率密度函数，进而求得失效概率。

The so called indirect integral operation means that Eular angles can be gotten from the direction cosine matrix which is received by the integral operation of quaternions or direction cosine.

飞行器导航中，姿态角的获取可以通过直接或间接的积分运算求得的，所谓间接获取即是指通过四元数或方向余弦的积分运算求得姿态矩阵，再从姿态矩阵中提取姿态角。

In order to meet the required simulation precision and meet the real-time simulation in ballistic simulation calculation,this paper analyzes the selection method of the simulation step,and then introduces variable step integration methods in Runge-Kutta to Adams and educes Adams variable step integral formulas,and then put forwards a method by seeking zero of condition function in discontinuous nonlinear system of the ballistic simulation.

在弹道仿真计算中，为了既达到要求的仿真精度又能满足实时仿真，分析了仿真步长的选择方法，然后在龙格－库塔转阿当姆斯法中引入变步长积分方法，推导了阿当姆斯变步长积分公式，同时对弹道仿真中的间断非线性系统提出条件函数求零的方法来解算弹道。

The ellipsoidal coordinates and the square root characteristics of the displacement jumps across the crack surface are cleverly used in the hypersingular integral equations for an arbitrary planar crack embedded into the infinite three dimensional homogeneous elastic solid.

对无限大三维均质弹性体中任意平片裂纹的超奇异积分方程，巧妙地引入椭球坐标系和利用裂纹表面位移间断具有平方根的特性，获得了受任意方向均布内压力作用下椭圆平片裂纹问题的超奇异积分方程的解析解。

In this paper, the analytic solution for scattering of SH-wave by elliptic cylinder in anisotropic medium is given by the method of separation of variables in elliptic coodi- nates and Mathieu functions.

对于这一课题的研究，介质为各向同性时，有些学者采用波函数益加〔，积分方程技术田和Fourier积分方法⑧；介质为各向异性时，有些学者则利用复变函数构造解的完备函数序列，把间题转化为对一组无穷型的代数方程的求解〔魂，〔5，。

In the paper, we use the same idea to solve the variational equation,which equivalent to the Fredholm integral equation of the first kind with constraint.

这个积分方程的解只能确定到相差一个与边界的法向量成比例的向量，且在边界上的积分必须为零。

In the last chap-ter,the natural integral equation and natural boundary element method forharmonic problem on exterior elliptic domain are introduced.Then,based onthis,the natural boundary reduction method for a kind of exterior problem ofanisotropic constant coefficients elliptic equation is discussed, the natural inte-gral equation and its solving method on circular boundary and elliptic bound-ary are obtained.These results can be directly applied in coupled methodand DDM for exterior boundary value problem.

最后，讨论了椭圆外区域调和问题的自然积分算子即D-N算子及自然边界元方法，并基于此研究了一类各向异性常系数椭圆型方程外问题的自然边界归化方法，首次得到其在圆周边界及椭圆边界上的自然积分方程及其求解方法，并将这些结果直接应用于外边值问题的耦合算法。

In chapter 3, we introduce a new family of functions with negative coefficients T,...

第五章根据α螺旋形函数的定义及算子D~λ定义一族新的解析函数类S_α，导出族中函数的积分表达式；研究了S_α中函数的某种积分运算及卷积定理。

First, the physical models associated with dislocations and cracks are respectively converted to mixed boundary value problems in mathematics. Secondly, by using the Fourier transform, a dual integral equation for a crack and an algebraic equation for a dislocation can be derived from the boundary conditions relating with a crack and a dislocation, respectively. Solving these equations, exact analytical solutions can be obtained in terms of Bessel functions in close-form.

先把位错和裂纹的物理模型写成与它们相关的边值问题，然后，利用Fourier变换将这些边值问题化成一个对偶积分方程(对位错而言，得到一个代数方程)，求解此对偶积分方程，可以获得以Bessel函数给出的封闭形式的分析解。

Because many practical problems could been changed to the boundary value problems for holomorphic function or singular integral equations in the mechanics, physics and the engineering technology.

因为力学、物理学、工程技术中的许多实际问题往往可化为这类问题或者化为奇异积分方程，而奇异积分方程又与解析函数的边值问题有着紧密的联系，所以研究这类问题有着重要的实际意义，从而吸引了很多科研工作者从事这方面的研究。

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。