留数

复变函数f（z）在∞点的留数及其应用

The Residue of the Complex Function f at ∞ and It 's Applications

本文给出了求z反变换的另一种围线积分公式及其留数算法。

Another formula for finding Z-inverse transformation and its residue algorithm are presented in this paper .

n级极点留数计算方法的探讨

Discussion on the Calculating Method of n-order Pole Residue

第3步，用补偿留数相位的方法对POD控制器参数进行整定。

And thirdly , the parameters of POD controller are set by compensating the phase angle of residue .

严格Sl（Em）函数类中双边矩阵函数留数插值二、末日意识

The Two-sided Residue Interpolation in the Strict Class S_l ( E_m ) for Matrix Functions

泛Clifford分析中的Laurent展式和留数定理

Laurent Expansion and Residue Theorems in Universal Clifford Analysis

把Prony方法用于不含控制器的系统开环传递函数辨识，以及留数的求取。

Prony 's method is used in open-loop transfer function identification and computation of residues .

采用留数比为指标对TCSCPOD控制器输入信号进行选择，采用补偿留数相位的方法对控制器参数进行整定；

This method chooses the input signal of TCSC POD controller by the residue ratio method and tunes the controller by compensating the residue phase .

本文利用MATLAB求解《复变函数与积分变换》中的留数、有理函数展开、富里叶变换、拉普拉斯变换和线性微分方程组等若干问题。

Here MATLAB is utilized to solve several problems in Complex variable function & integral transform , such as : residue , rational function , Fourier transform , Laplace transform and system of linear differential equations .

利用三角降次公式及留数解决了第一类Dirichlet积分问题，即给出了第一类Dirichlet积分的公式解。

The first Dirichlet s integral is solved by trigonometric power reduced formulas and residue theory , namely , formula solutions have been obtained .

本文对Z逆变换中的留数法合理地给出假设条件，并用复变函数中的罗伦级数、留数理论给出了严谨、简捷的证明。

The assumptive conditions are given reasonably about the residue method of Z inverse Transformation , and a close forthright prove is given by the theory of Laurent series and residues in complex function .

运用并矢法求解广义Helmholtz方程，结合Fourier变换、留数定理等数学处理，给出方程的并矢Green函数解析表达式；

The generalized Helmholtz 's equation is solved by the dyadic method , the analytic expression for dyadic Green 's function of the equation is given combining with Fourier 's transformation , theorem of residues , etc.

积分中值定理在广义Riemann积分中的推广广义留数定理在计算某类广义积分中的应用

An Extension of the First Mean Value Theorems for Generalized Riemann Integration ; The Application of Generalized Residue Theorm in Calculating a Certain Kind of Generalized Integral

基于Dirac-delta函数的积分表示和Cauchy留数定理，导出了压电、压磁和电磁各向异性弹性介质二维问题的Green函数。

Based on the integral representation of Dirac - delta function and Cauchy 's theory of residues , the Green 's function for two-dimensional anisotropic elastic media with piezoelectric , piezomagnetic and magnetoelectric coupling effects is derived .

分析表明广域反馈具有相位稳定的特点，可以根据参与因子和传递函数留数选取广域测量信号，通过模式辨识进行2级PSS控制，抑制区间低频振荡。

The phasor of global feedback is stable . Global measurement signal is selected according to participation factor and residue of transfer function and PSS is configured by mode analysis .

通过求Floquet指数讨论平衡点邻域的稳定性，用复变函数留数理论求出Melnikov函数，可得到该动力学系统发生混沌运动的临界条件。

The stability near the equilibrium point was discussed by solving the Floquet exponent and the critical condition is obtained by using Melnikov function .

由于运用了推广的留数定理和Bertrand型换序公式使本问题及类似问题解法得以简化。

The solutions based on the generalized residue theorem and Bertrand-Poincare formula of singular integrals , which are greatly simplified , can also be used in similar problems .

将函数Laurent展开定理及留数概念应用于有理分式是将有理分式化为部分分式的一种行之有效的方法。

This article approaches an effective method which applies expansion in Laurent theorem and reside concept to rational fraction , and then makes rational fraction partial fraction .

利用Laplace变换和留数法，求解得到了在阶跃功率扰动后，母线电压相角增量传播的时域解，并通过仿真验证了理论的止确性。

Through Laplace transform and residue method , the analytic solutions of bus voltage phase angle increment and active power increment after a step-power disturbance was solved . The simulations prove that the solutions are correct .

应用Titchmarsh留数方法，给出了多点边值条件下Dirac特征值问题的特征展开定理。

The expansion theorem of Dirac operator 's eigenvalue problem with multi-point boundary conditions is given by resorting to the Titchmarsh residue method .

由于是在留数分析的基础上进行RGA计算，因此，这种调制信号选取方法可有效降低计算量和缩短选取进程。

Because the RGA computation is implemented based on the residue analysis , the proposed method can effectively reduce computational complexity and shorten signal selection process .

利用留数定理及轨道积分方法，讨论了2n＋1（n＞1）维Heisenberg群上热核及Green核的渐近性，并给出了更简明的渐近公式，彻底解决了Hueber，H等人遗留的问题。

This paper considers the asymptotic property for some heat kernels and Green kernels on the Heisenberg group by residual theorem and path integral method , and gives simple and explicit formulas . The problem left in [ 1 ] is completely solved .

由轴向运动弦线的矩阵函数计算得到系统的传递函数，然后用留数定理计算传递函数的Laplace逆变换，这样就可以得到时域响应。

The transfer function was derived from the matrix function of axialy moving strings . Then the inverse Laplace transform , with the residue theorem , was employed to calculate the time domain response from the frequency domain response .

用分离变量法、傅氏变换和留数定理求解Helmholtz方程，获得电偶极子激励的Green函数及其场。

The scalar Helmholtz equation in cylindrical coordinate is constructed , using the method of separating variable , and fourier transform , and residue theory , and the Green 's function and field of the transverse electric mode associated with the electric diple are also obtained .

采用算子表示法，在F-K域内将横向各向同性介质中的波动方程进行算子分解，然后利用留数定理求出格林函数的解析解。

With operator method , we factorize the wave equation of transversely isotropic media in F-K domain , aPPly the residual theorem to get the analytical solution of the Green 's Function .

讨论采样定理的实验验证问题，分析采样时间对系统性能的影响，并提出用留数法进行Z变换时应注意的问题。

The problem of experimental verification about sampling theorem is discussed , the influence of the finite duration of sampled signals on the performance of system is analysed , and a problem that should be noticed while using residue theorem to find Z & transform is posed .

该方法不必计算系统传递函数的留数，所需的计算时间较少，而且适用于多种电力系统运行方式，又能满足系统对PSS效率的要求。

Because the residues of system transfer function is not to be calculated in this method , less computation time is required , so this method is suitable to various power system operating modes and the efficiency requirement of power system to PSS can also be satisfied .

采用权重留数法进行燃料元件瞬态热传导分析的RTEMP程序

RTEMP & A Computer Program for the Transient Thermal Transfer Analysis in Nuclear Fuel Elements by Using the Method of Weighted Residuals

结合广义最小留数（GMRES）法，分别对装载在两个简单形体和一架大型飞机模型上的线天线的辐射问题进行了求解。

In conjunction with the generalized minimal residual ( GMRES ) method , the preconditioning technique is applied to solve the radiation problems of the wire antennas mounted on a plate , a sphere and a large plane model , respectively .

目的：使留数计算问题更加简化。

Objective : To make the calculation of residue much easy .