留数定理

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 .

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 .

泛Clifford分析中的Laurent展式和留数定理

Laurent Expansion and Residue Theorems in Universal Clifford Analysis

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 .

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 .

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 .

无残留，安全可靠。无界域上的高阶奇异积分与推广留数定理

Singular integrals of high order and the generalized residue theorem in the unbounded domains

引入位错密度函数并应用留数定理计算复杂积分，推导出任一点位移与应力的解析表达式。

Dislocation density function is introduced and the residue theorem is used to calculate the complex integrals .

详细讨论了复变函数的解析延拓方法和留数定理用于简化多光子跃迁几率的计算问题。

A detailed study is given for the simplified calculations of multiphoton transition probability by analytical continuation and residue theorem .

运用拉普拉斯变换和留数定理，给出并证明了分数阶线性定常系统的内部和外部稳定性条件，并讨论了其相互关系。

Internal and external stability conditions for fractional order linear time-invariant systems are given using Laplace transform and residue theorem .

市中心广场有个市集。广义留数定理在计算某类广义积分中的应用

There is a fair in the town square . The Application of Generalized Residue Theorm in Calculating a Certain Kind of Generalized Integral

利用留数定理，可以对任何电驱动信号，解析地求出换能器的运动在时域与频域的暂态函数。

By using the residue principle , the transient functions of the temporal and frequency domains for the transducer are determined analytically for any electrical driving signal .

[2]对于惯导减振支架的多自由度系统等效分析模型，则运用模态叠加法和谱分析理论得到响应的功率谱，根据留数定理推导了系统时域加速度动力响应的数值计算公式。

The dynamic response spectrum of this model is achieved by modal analysis and spectrum theory . The numeric formulas of time-domain response are deduced by residue theorem .

应用留数定理，通过构造被积函数，将一类级数求和问题转化为求留数的计算，得到求解此类问题的一种通法。

Using residue theorem and constructing an integrand , we transform the summation of infinite series into the calculation of residue , and obtain a rather universal approach to calculate this kind of problems .

利用相位噪声转换为阿仑方差的积分公式，根据留数定理推导出直接计算阿仑方差的解析表达式，得到增加伺服环路带宽可以有效抑制振动对原子钟频率稳定度影响的结论；

For computing Allan variance directly from integral equation of phase noise , the several analysis formulas were derived by residue theorem . With increased servo loop bandwidth , vibration effects on frequency stability of the atomic clock can be controlled effectively .