函数的积分

Analytical expressions for electromagnetic fields of a vertical or horizontal electric dipole over the finitely conducting plane are derived subject to the boundary conditions; Sommerfeld type integral contained in Hertz potential is expressed as the sum of two parts: zeroth order Hankel function and an absolutely convergent series of spherical Hankel function.

在此边界条件下，推导出有限导电平面上垂直和水平电偶极子电磁场的解析表达式；赫芝位函数中的索末菲型积分被表达成零阶汉克尔函数与绝对收敛的球汉克尔函数级数之和的形式。

By combining the theory of sectionally holomorphic function, the analytical extending method, Cauchy model integral, the analysis of the singularity of complex functions and Riemann boundary problem, analytic relations between the complex potentials were obtained.

研究压电材料在均匀热流作用下螺型位错与圆弧裂纹的相互作用，综合运用复变函数分区全纯理论、解析函数奇性主部分析方法、解析延拓原理、Cauchy型积分以及Riemann边值问题求解方法，获得各复势函数之间的解析关系，进一步得到了特殊情况下所讨论问题的封闭解，并求解出像力随温度梯度和位错位置变化的表达式。

By combining the theory of sectionally holomorphic function,the analytical extending method,Cauchy model integral,the analysis of the singularity of complex functions and Riemann boundary problem,analytic relations between the complex potentials were obtained.

综合运用复变函数分区全纯理论、解析函数奇性主部分析方法、解析延拓原理、Cauchy型积分以及Riemann边值问题求解方法，获得各复势函数之间的解析关系，进一步得到了特殊情况下所讨论问题的封闭解，并求解出像力随温度梯度和位错位置变化的表达式。

By combining the theory of sectionally holomorphic function, the analytical extending method, Cauchy model integral, the analysis of the singularity of complex functions and the method for Riemann boundary problem, analytic relations between the complex potentials are obtained.

综合运用复变函数分区全纯理论、解析函数奇性主部分析方法、解析延拓原理、Cauchy型积分以及Riemann边值问题求解力法，导出各复势函数之间的解析关系，进一步得到特殊情况下所讨论问题的封闭解，并解出像力随温度梯度和位错位置变化的表达式。

In this course we shall develop theoretical methods suitable for the description of the many-body phenomena, such as Hamiltonian second-quantized operator formalism, Greens functions, path integral, functional integral, and the quantum kinetic equation.

在本课程中，我们将会建立一种适合描述多体问题的理论方法，诸如哈密顿二次量子化算子形式、格林函数、路径积分、泛函积分和量子动力方程等。

The shear moduli in two directions were assumed to vary in terms with hyperbolic function .

假设剪切模量沿着梯度方向都按双曲函数变化，采用积分变换-对偶积分方程方法，求得了裂纹尖端应力场和应力强度因子，并研究了材料不均匀参数对应力强度因子的影响。

But , when we changeour trainofthought , we can find that sometimes using mathematical Analysis is a better solution to the linear algebraic problems.In thispaper, use the propertyofcontinuous function andimproper integralof infinite interval and to solve some matrix and quadratic form problems.Algebraic ideas andmethodstosolvemathematical analysisproblems are indicated by several specific examples. Close contactof differentmathematical analysis fields is shown.

该文探讨运用数学分析的有关知识（如：函数连续性、无穷区间的广义积分）和方法解决高等代数中的某些复杂、繁琐的问题；通过具体的实例，阐述高等代数的思想和方法在解决数学分析问题中的作用，揭示不同的数学领域之间的密切联系，例如：二次型与正交变换是代数学的基本内容，其用途十分广泛，而重积分的计算往往存在技术性的困难，若利用"二次型"与"正交变换"的有关理论去解决某些重积分的计算问题是颇有功效的。

After constrcting the perfective space , prove that this space is just the space of lebesgue integratiable function , thus explain that lebesgue integral is the form of the perfective riemann integral

在构造了完备化空间之后，证明了该空间就是勒贝格可积函数空间，从而说明了黎曼积分的完备化形式是勒贝格积分。

Based on Monte Carlo method,four different weighted function moment methods for Pearson Ⅲ distribution which were developed in China are first compared by using the evaluation standard considering unbiasness and effectiveness of parameters and design values.

利用统计试验方法，以参数及设计值不偏性、有效性为评价标准，比较了现行几种权函数参数估计法，结果与以理想样本还原准则为标准所得的结论截然相反，以不偏性、有效性标准的结论是数值积分权函数法，并未对马秀峰权函数法作出改进，还从理论上比较分析以上两种评价标准，结论是理想样本还原为标准来评判估计方法的优劣存在较大缺陷，建议今后尽量不要使用该标

After the sea trial, the control algorithm is further improved by using H〓 integral control and μ-analysis respectively to solve the problem of the adscititious integrator and the selection of weighting functions

海上试验后，为实现样机产品化，分别用H〓积分控制和μ分析对原控制算法进行了改进，以解决原控制算法外加积分器和权函数选择的问题。

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。