函数的积分

As to its computing methods, this paper synthesizes six kinds, they are: utilizing a general integral method of complex function directly; utilizing Cauchy integral theorem; utilizing Cauchy integral formula; utilizing Cauchy high-level differential coefficient; utilizing Cauchy residue theorem; utilizing the residual of logarithm.

关于周线积分的计算方法，本文综合了六种，它们分别是：直接利用一般的复变函数积分的方法；利用柯西积分定理；利用柯西积分公式；利用柯西高阶导数公式；利用柯西留数定理；利用对数留数。

Secondly,we firstly study the properties of functions with values in a uni-versal Clifford algebra 〓,and we obtain the following very important basictheorems in universal Clifford analysis:Cauchy's integral formula,Cauchy's inte-gral theorem,the mean value theorem,the three versions of the maximum mod-ulus theorem,the Taylor's expansion,the Laurent's expansion and the residuetheorem etc..All of these results generalized the classical results.

第二，本文所讨论的各种函数性质以及所得的结果都在泛Clifford代数〓上所做的工作，它一方面包含了从前在泛Clifford代数〓上所做的工作，所得到的结果更广泛、更漂亮、更自然，另一方面，本文也是迄今为止第一次建立起来了在泛Clifford分析中与经典函数论相对照处基础地位的LR正则函数在特异边界上的Cauchy积分公式、Cauchy积分定理、平均值定理、极大模原理的三种表达形式、Taylor展式、Laurent展式留数定理等深刻的结果。

On the basis of the idea of partition of unity, a discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the displacement interpolation formula to account for discontinuity of the contact surface and stress singularity near the contact surface tip respectively. Governing equations are deduced by virtual work principle and the integral of the discontinuous functions are calculated by Gauss integral through sub-elements cut by discontinuous surface.

该方法基于单位分解思想，在位移插值形式中引入不连续函数和裂尖渐近位移场函数分别反映接触面的不连续性和接触面端点的奇异性；根据虚功原理建立有限元支配方程，接触面不连续函数积分采用分区高斯积分的方法。

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，。

Using this formula ,we get several important inference and prove that when the curve and surface integral of the first kind's integrand is odd function or even function and the integral curve or surface is symmetry.

并且利用这个公式，推导出了当第一型曲线积分或曲面积分的被积函数为奇函数或偶函数，积分曲线或曲面是对称的时的几个重要的推论及证明。

The integral range and the integrand structure are the two key points of the function integral.

积分区域和被积函数结构是函数积分的两个关键点。

Fuzzy Choquet integral is defined for the given nonnegative measurable function on the general fuzzy measurable space. The fuzzy integral is wholly regarded as a set function on the general fuzzy measurable space. And its some elementary properties and convergence are discussed.

在一般模糊测度空间上，针对给定的非负可测函数定义了λ-模糊Choquet积分，并将这种模糊积分整体看作一般模糊测度空间上的集函数，进而讨论了这种模糊积分的一些基本性质和收敛性。

The objective of this study is aimed at the implementation of parallelized numerical quadrature routines. The algorithm we choose for numerical quadrature routines is the so called "Adaptive Romberg Tree integration scheme"(abbr."ARTint") proposed by Lin et. al.[1997]. This numerical quadrature scheme can arrange the function evaluation points adaptively in accordance with characteristic of the trend of variation in integrand function values. When the accuracy of the numerical quadrature value is requested to be increased, a newer and larger set of function evaluation points must be incurred. The main advantage of ARTint method is the inclusion of all function evaluation points used in previous stages. It is this feature of ARTint method that makes it a quadratue scheme with prominent computation efficiency.

本研究在探讨数值积分程式之平行化，所使用的演算法为林聪悟与林佳慧[1997]一书所提出的「Romberg树自动布点数值积分」架构，此一数值积分方法能以适应被积函数值变化情形方式自动安排积分点来进行数值求积计算，在提高阶数以获得更高精度积分值的过程中，此一方法只须再计算新增加积分点的函数值，搭配先前已计算过的函数值的重覆运用即可获得更精确的数值积分估计值，如此将能减少升阶过程中函数求值计算的次数，有效率地完成单重积分的数值计算。

In order to solve the problem that matrix A often occurs irreversible when shape function is calculated by using traditional element free Galerkin method, the orthogonal function with the weight function is utilized in the paper. And partition of unity quadrature technique is employed and so a truly "meshless" method is realized.

针对传统无网格伽辽金方法在构造形函数时，矩阵A容易出现不可逆的弊端，采用带权正交基函数构造形函数，在积分方案上采用单位分解积分方法，从而实现了真正的"无网格"。

In the path integral formalism, we represent the generating functional and Green functions of Φ〓 theory by taking account of that the partial and the functional derivatives commute. Also we discuss the effective action for noncommutative scalar fields, and show how the noncommutative phase factors appear in path integral formalism. We realize that the two approaches (path integral and canonical quantizations) are completely equivalent each other.

在用路径积分方法对非对易标量场进行研究时，我们利用偏微商和泛函微商的可交换性，给出了Φ〓场格林函数和格林函数生成泛函的具体表达形式，得出了非对易相因子在路径积分方法中的具体表现形式，并对连通格林函数和有效作用量等问题做了讨论。

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。