函数的积分

Then by matching the traction along the branches and the boundary of the strip, Cauchy singular equations were obtained, in which the point dislocation and the distributed dislocation density served as the unknown function.

根据板条边界和裂纹面上的应力边界条件，建立以集中位错强度和分布位错密度为未知函数的Cauchy型奇异积分方程，利用半开型积分法则将该奇异积分方程化为代数方程求解。

This article is mainly discussed the relation between some important concepts and conclusions about the Limit of Sequence, the Limit, Continuity ,Differentiability, Integrability of Function, the Infinite Series , and the Limit, Continuity, Derivativeness,Differentiability of Multivariable Function ,as well as the Multiple Integral, and Integral with parameter .

本文对数列极限，一元函数的极限、连续性、可微性、可积性，无穷级数，多元函数的极限、连续性、可导性、可微性以及重积分，参变量积分中的一些重要概念和结论之间的关系进行了一些探讨，每一个问题都作了适当说明或举出反例，并对一些相关的内容进行了讨论，得到若干结果。

Furthermore, we show that every generator of a nondegenerate distribution cosine function generates a regularized cosine function.

自然地 ，我们可以考虑一类退化型的分布余弦函数，并讨论该分布余弦函数与二阶 Cauchy问题、积分余弦函数及其其它类型余弦函数的关系。

Differential equations of tile first order in the finite discrete function are established, the solutions of which have very simpler structure.

引入了有限离散函数的微分与积分新概念，它具有与连续函数微分和积分相类似的性质，由它建立的一阶微分方程的解有较简单的代数结构。

The Taylor formula holds the very important status in the differential calculus, especially in solves in some concrete problems to have the extremely important application, for instance the proof inequality, the judgment improper integral collects the divergence, asks the function the limit, asks the function the higher order derivative, determines certain complex progressions to collect the divergence, solves certain differential equation, as well as approximate calculation in and so on application, therefore this article will do the thorough research to these seven aspects.

摘 要：泰勒公式在微分学中占有非常重要地地位，尤其在处理1些具体的茄题中有10分重要的应用，比如证明不等式，判断广义积分的敛散性，求函数的极限，求函数的高阶导数，判定某些复杂级数的敛散性，求解某些微分方程，以及近似计算等中的应用，因此本文将对这七个方面做深入的研究。关键词：泰勒公式；不等式；广义积分；极限；高阶导数；复杂级数；微分方程

Infinite integral is a type of improper integral in calculi,and it is also a difficult point in integral.

无穷限积分是指函数在无限区间上的积分，例如+∫∞afdx型，它属于广义积分的一种。

The fact that the integral variable of the inverse transform appears in the denominator of integrand reduces resolution of the numeral integral and blocks the application of them.

为此构造了一种新型的连续小波变换，不论对积分变量如何剖分，任何一种数值积分方法都具有高分辨特性，且积分变量不出现在被积函数的分母上，进而给出了相应的数值解法。

The discrete velocity ordinate method in the kinetic theory of gases is developed and applied to discretize the correspo

借助非定常时间分裂法和无波动无自由参数的NND耗散格式，建立直接求解微观分子速度分布函数的有限差分数值格式；研究并发展可用于离散速度坐标点选取和离散速度空间宏观取矩的高斯─埃尔米特无穷积分方法、等均间隔的牛顿─柯斯复合积分法、以勒让德多项式的根为积分结点的高斯─勒让德数值积分法，并应用于不同马赫数绕流模拟；通过对不同流域一维激波管问题、二维圆柱绕流问题和三维球体绕流的计算研究，并将计算结果与其他途径得到的研究结果诸如DSMC模拟值、N-S解及有关实验数据进行比较分析，创建了一套能有效模拟稀薄流到连续流不同流域气体流动问题简化的统一数值算法研究框架

Based on the fundamental solution of two perfectly bonded elastic halfspaces, the boundary integral equation method is used to reduce the problem to a hypersingular integral equation in which the unknown function is the crack opening displacem...

首先根据双材料空间的弹性力学基本解，使用边界积分方程方法，在有限部积分的意义下导出了以裂纹面位移间断为未知函数的超奇异积分方程，并为其建立了数值法。

By using integral periodogram to estimate the spectral functions of a stationary time series, the invariance principle for the error process has been demonstrated either for Gaussian or non-Gaussian series.

用积分周期图估计平稳时间序列的谱函数，不论是高斯序列还是非高斯序列，其误差过程的不变原理都已被证明￣（［1］，［3］），许重光￣［5］采用自迥归谱估计的积分估计谱函数也证明了误差过程的不变原理成立。

No clear conclusions can be made about the predictie alidity of specific measures, they found, except for criteria for the underuse of drugs for cardioascular disease.

除了心血管病不合理用药标准外，对于特定评价方法的预测效度没有明确的结论。

The third and last is that almost all of them, being infinite in number, have been impostures, and by idle and crafty brains merely contrived and feigned after the event past.

第三、即最后一点是：几乎所有这些不胜枚举的预言都是欺人之谈，都是在事件过后由无聊而狡猾的脑筋推测与凭空捏造的。