有理函数

There exists one and only one solution with rank not greater than j to the rational interpolation problem with j interpolating points, which has at least one complementary solution The Welch-Berlekamp algorithm is a iterative algorithm.

本文的主要结果是： 1。利用初等的数学方法研究了有理函数插值问题的性质，证明了Welch-Berlekamp算法的有效性。

This paper points out the relationship between the coefficient of Laurent series and that of the sum of partial fractions for rational functions.

笔者在此指出了罗朗级数的系数与有理函数分解的部分分式之和的系数之间的关系，并举出应用实例。

This book reviews the many areas of numerical analysis, including the configuration polynomial, finite difference, factorial polynomials, summation, Newton formula, operator and configuration polynomial, Cheung section, close polynomials, TaylM more item type, interpolation, numerical differentiation, numerical integration, and with the series, differential equations, differential equations, least squares polynomial approximation, minimax polynomial approximation, rational function approximation, triangular approximation, non-linear algebra, linear equations, linear programming, boundary value problems, MonteCarIo methods and so on.

本书综述了数值分析领域的诸多内容，包括配置多项式、有限差分、阶乘多项式、求和法、Newton公式、算子与配置多项式、祥条、密切多项式、TaylM多项式、插值、数值微分、数值积分、和与级数、差分方程、微分方程、最小二乘多项式逼近、极小化极大多项式逼近、有理函数逼近、三角逼近、非线性代数、线性方程组、线性规划、边值问题、MonteCarIo方法等内容。本书的特色主要表现在利用例题及大量详细的题解来透彻地阐明所述内容的内涵，同时附有大量的补充题以便读者进一步巩固和深化从书中获得的数值分析知识。

The element stiffness matrix of this variable section beam is derived based on principle of virtual displacement.

对圆锥形变截面梁单元进行了分析，采用有理函数的位移模式，利用虚位移原理，推导出该变截面梁单元的刚度矩阵

Let〓be a meromorphic function of finite order and〓z,where qis rational and pis a polynomial.Then every cycle of Bakerdomains of f contains a singularity of〓.

推论3.4设q是一个有理函数，p是一个多项式，m，n是满足〓的两个正整数，又设f是一个满足如下微分方程的亚纯函数〓（3.2）则f的每一个Baker域循环一定含有〓的奇异点。

In chapter 4, the factorization and cascade decomposition for first order singular systems have been discussed, the if and only if conditions have been obtained, the invariaty of minimality under factoiization and cascade decomposition has been proved.

第四章，讨论了一阶奇异系统的因子分解和级联分解，给出了其具有上述分解的充要条件，证明了极小性在分解下的不变性；对具有一阶奇异系统实现的有理函数矩阵，给出了判定其为正实函数的充要条件，推广了著名的正实引理。

Results show that the energy function is Lyapunov stable and the network can be used for finding the minimum covering sphere of a polytope.

第七章 利用有理函数逼近的许多优良特性，构造了一种新的有理连分式链神经网络，给出了网络的一般拓扑结构图和学习算法。

After discussing the structural conditions of the existence of the active network solutions, the state equations in normal form over F of electrical network which are suited for studying the character of network structure are derived. If there is no loop containing only capacitor and independent voltage sources, and if there is no cut-set containing only inductors and independent current-sources, both matrix A and B in ?

在探讨了有源网络解存在的结构条件下，推导了适合研究网络结构特征的多元有理函数域上电网络的范式状态方程：如果不存在仅由独立电压源和电容器构成的回路，且不存在仅由独立电流源和电感器组成的割集，则无论是有源网络还是无源网络，在网络的范式状态方程？

The ill-conditioned normal equations bring numerical problems in construction of macromodel in time domain for power distribution networking using rational function approximation.

摘要有理函数逼近法方程组病态条件数为构建电源分配网络时域宏模型带来了数值问题。

In numerical mathematics, it is interesting and of importance to study the theory of algebraic functions and its applications.

古典代数函数论的研究对象，是以代数关系式 f=0 (1)联系着的两个变量的有理函数φ。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。