解析函数

In this thesis, the virtual boundary integral equation is based on double layer potential with the virtual density to be determined on virtual boundary. Since this integral equation related to double layer potential only involves the computation of the normal derivative and second normal derivative of fundamental solution, the exponential integral function is not involved in it, so numerical computation for the exponential integral function is avoid.

本文则基于双层位势，引入虚拟矩密度函数来建立虚边界积分方程，并首先对时间变量进行解析积分，在虚、实边界上采用常单元和等额配点离散，该方程只涉及含基本解的法向导数及其二阶法向导数项的计算，对时间变量进行解析积分后，不会出现对指数积分函数的空间变量的积分计算。

Based on the method that a rectangular function can be expanded into a sum of complex Gaussian functions with finite numbers, the propagation characteristics of a Gaussian beam passing through apertured spatial filter systems are analysed and the corresponding analytical formulae are obtained respectively.

根据矩形函数可以展开为有限复高斯函数之和的方法，从柯林斯衍射积分公式出发，对高斯光束通过受限空间滤波器传输特性进行分析，得到了相应的近似解析式。利用Matlab对其解析式进行数值模拟，得出一组直观的结果。

The solitary wave can be generated considering Goring and Raichlen's movement of a paddle. The proposed original linear solution for the solitary wave generation is expressed in the hypergeometric function. Two disadvantages of the original solution with large trailing wave and skewed wave profile are found by comparing with the theory of solitary wave derived from Boussinesq's equation.

本文并以弱非线性的孤立波造波问题做为解析之对象，由於孤立波造波板速度为一超越函数，造成解析上的困难；本文以 hypergeometric 函数推求常微分方程式之全解，并与理论波形解比较后，发现由於未考虑非线性及分散性过强等问题，使得线性暂态解较理论波形拉长与歪斜，可能无法有效描述孤立波造波问题，故针对线性之分散关系做出修正。

The solitary wave can be generated considering Goring and Raichlen's movement of a paddle. The proposed original linear solution for the solitary wave generation is expressed in the hypergeometric function. Two disadvantages of the original solution with large trailing wave and skewed wave profile are found by comparing with the theory of solitary wave derived from Boussinesq's equation. The difference between the original linear solution and the solitary wave theory results from the nonlinearity and dispersion of generated waves in the flume.

本文并以弱非线性的孤立波造波问题做为解析之对象，由於孤立波造波板速度为一超越函数，造成解析上的困难；本文以 hypergeometric 函数推求常微分方程式之全解，并与理论波形解比较后，发现由於未考虑非线性及分散性过强等问题，使得线性暂态解较理论波形拉长与歪斜，可能无法有效描述孤立波造波问题，故针对线性之分散关系做出修正。

It is possible to insert objects created in one sub-interpreter into a namespace of another sub-interpreter; this should be done with great care to avoid sharing user-defined functions, methods, instances or classes between sub-interpreters, since import operations executed by such objects may affect the wronginterpreter's dictionary of loaded modules.

可能会把一个子解析器创建的对象插入到另一个子解析器的名称空间中；这应该被高度的关注，尽量避免在子解析器之间共享用户定义函数，方法，实例和类，由于这样的对像所执行的导入动作可能会造成被加载模块组成的解析器词典错误。

Three elements should be calculated in first-order circuit, which can synthesise analytical solution. Second-order series RLC and parallel RLC both can be calculated by the general function, which uses the Matlab to calculate differential equations. Generally, second-order and high-order circuits use Laplace transformation to formulate circuit equation, and get analytical solution by using Laplace inverse transform.

一阶电路先计算3要素，后合成解析结果；RLC串联和并联的二阶电路采用自编的通用函数计算，自编函数采用了Matlab求解微分方程的符号运算方法；一般的二阶电路和高阶电路采用拉氏变换列写电路方程，再用拉氏反变换得到解析结果。

Based on the fundamental works done by professor Fan Ky, who was the founder of this direction, the present paper introduces the definitions of the class of meromorphic univalent operator-valued functions with positive operator coefficients on Hilbert space and the argument of the operator-valued functions, improves and extends some problems in classical geometry theory of complex functions to the case of operator-valued functions, and studies them respectively.

基于该方向的首倡者Fan Ky教授关于该理论的奠基性工作，本文引入了一类星形算子值函数的定义以及解析算子值函数辐角的定义，将经典的复变函数几何理论中的一些问题推广到了解析算子值函数的情况，并分别进行了讨论。

Deduced the analytical structure of the Mamdani fuzzy system whose input sets were with generalized linear membership function and manifested that the output of the fuzzy systems were monotonical, decreasing, continuous and bounded.

设计了一种将三角形和梯形隶属函数作为特例的广义线性隶属函数，推导了输入采用广义线性隶属函数的典型Mamdani模糊系统的解析结构，证明了典型模糊系统是单调、递减的有界连续函数；在此基础上证明了该类模糊系统能以任意精度逼近任意连续实函数，最后仿真实例证明了本设计的有效性。

Second, based on the spherical vector wave function in uniaxial anisotropic medium, and the first, second, third and fourth spherical Bessel functions satisfy the same differential equation and recursive formula. The scattering fields in terms of spherical vector wave function from a uniaxial anisotropic spherical shell and an anisotropic uniaxial-coated conducting sphere by a plane wave are derived. The electromagnetic fields in uniaxial anisotropic medium and free space can be expressed in terms of spherical vector wave functions in uniaxial anisotropic media and isotropic medium.

二、在建立均匀各向异性单轴介质球矢量波函数理论的基础上，利用二阶线性偏微分方程的性质和第一、第二、第三和第四类球Bessel函数满足相同的微分方程和递推关系，我们分别研究了单轴介质球壳和单轴介质涂覆导体球对平面波的电磁散射特性，首先给出了各个区域的电磁场用球矢量波函数来表示的解析表达式，进而利用电磁场在边界上满足电磁场切向连续的边界条件和球谐函数的正交性，得出了各向异性单轴介质球结构中电磁场用球矢量波函数表示的系数所满足的矩阵方程。

By constructing a generalized function"helical solitary vortex function", the paper solves the stream function of the helical vortex tube with the help of vortex filament one, and obtains some analytical expressions for large single-vortex core and small multi-vortex core.

通过构造一类特殊的广义函数&螺旋孤涡函数&，解决了利用涡丝流函数求(来源：75AB67C论文网www.abclunwen.com)解涡管流函数问题，导出了大单和小多螺旋涡管流函数的解析解。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失