级数的和

Based on the series expansion technology in complex potential theory established by Muskhelishvili the complex stress functions can be estabished. By utilizing the continuity principle of the boundary condition and the characteristics of far field and according to the comparison of the coefficients of the terms on both sides of the equation with the same exponent the present problem can be transformed into solving of linear equation set.

根据Muskhelishvili复势理论的级数展开技术，构造了合适的各区复应力函数；然后，利用边界上位移、力的连续性条件和远场的性态，通过等式两边同次幂指数的系数比较，将问题转化为线性方程组的求解；结合叠加原理，获得混凝土在此情况下环向应力的解析解答。

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。

A new approach based on operator decomposition method has been developed to solve nonlinear Helmholtz equation.The approach is applied to compute the magnetic field and eddy current in nonlinear ferromagnetic materials and it provides an analytical solution.

根据算子分裂法的基本思想提出了一种有效的求解非线性亥姆霍兹方程的逼近解析法，对非线性铁磁材料中的磁场和涡流进行了求解，获得了级数形式的解析解。

Taking discrete Fourier series and Fourier Transform of periodic sequence as an example,this paper expounds how to simplify those abstruse theory by using straightforward mathematical knowledge which students are well-informed.

本文以周期序列的离散傅立叶级数和傅立叶变换的推导为例，就教师如何用简单的或学生所熟悉的数学知识，进行深入浅出的教学进行了探讨。

According to the theory created for the generalized multi-pole technique (in domain of half-analytical method), the center of each circle is determined as a starting point of each variable in a series expansion of the 2D-field solution function, and the arranging blank of the starting points in the generalized multi-pole technique can be filled up owing to the precise variable positioning.

根据为广义多极技术创建的理论体系，这些极点确定了解函数在级数展开式中各变量的起点。正因为这些变量的准确定位，不仅克服了广义多极技术中极，点位置设置的盲目性，而且提高了解的计算效率和计算精度。

This paper provides the analytic method to calculate the value of Green s functions in space domain at the zero distance by the discrete complex image theory,that is ,to express the finite progressional sum of Green.

对此，本文在讨论采用离散复镜象理论计算空间域Green函数时，提出了采用该镜象理论计算空间域Green函数零距离处奇异值的解析方法，即，采用Taylor公式展开镜象理论得到的空间域Green函数的有限级数和形式，并结合特定的分域基函数来得到零距离处Green函数奇异值的解析计算式进行计算。

This paper provides the analytic method to calculate the value of Green"s functions in space domain at the zero distance by the discrete complex image theory,that is ,to express the finite progressional sum of Green"s functions detained with DCIT into Taylor expansion and deduce the analytic expression of the singularities at the zero distance with the help of the specific subdomain base functions.

对此，本文在讨论采用离散复镜象理论计算空间域Green函数时，提出了采用该镜象理论计算空间域Green函数零距离处奇异值的解析方法，即，采用Taylor公式展开镜象理论得到的空间域Green函数的有限级数和形式，并结合特定的分域基函数来得到零距离处Green函数奇异值的解析计算式进行计算。

The intensity of grating diffraction spectrum is obtained by the Fourier series expansion of the transmissivity function. Finally, the design feasibility is analyzed by comparing the minimum signal spectral intensity with the maximal spectral intensity of the background light and the noise intensity.

通过对透射率函数的傅立叶级数展开，得到光栅衍射谱线的强度，对信号光谱线的最小强度、背景光谱线的最大强度和噪声强度的比较，得到设计的可行性。

In order to develop this local property,this paper presents a method,which uses Fourier Series to approximate the boundary shapes of the shafts with periodic boundary of cross section,and uses the conformal mapping in Theory of Function of a Complex Variable to make the complicated boundary shapes of the shafts map a unit circle.Thus elastic theory can analyze...

本文提出一种方法，其实质是：采用富里埃级数来逼近横截面呈周期性变化边界的轴类零件的边界形状；并应用复变函数论中保角映射原理，将零件复杂的边界形状映像成单位圆，从而使弹性理论可以分析和计算复杂边界轴类零件的应力场；再通过留数的求解实现保角映射的反变换。

The influence of initial imperfections on the stability ofcomposite laminated plates was studied by solving the nonlinear governing equations for laminated plates with elastical restraints subject to in-plane loading using the energy variational principle and nonlinear geometric equations incorporating the initial imperfection. The governing equations were solved using generalized Fourier series to obtain the effect of the non-uniform order term.

为深入研究初始缺陷对复合材料层板稳定性的影响，利用能量变分原理和考虑初始缺陷的非线性几何方程，建立了具有弹性约束的层合板在面内载荷作用下的非线性稳定性控制方程组，运用广义傅立叶级数法对其进行求解，并进一步获得了影响非线性稳定性控制方程组的性质的非齐次项。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。