带有分段常数变元的时滞微分方程解的稳定性和振动性

本文讨论带有分段常数变元的时滞微分方程解的渐性性质。我们利用Ｒａｚｕｍｉｋｈｉｍ方法证明了零解的稳定性，并且改进了文［１］得到的两上振动定理。     

酉辛群上的调和分析Ⅳ-Fourier级数的球求和

本文沿用龚昇[2]中研究酉群上Fourier级数球求和的方法,讨论了酉辛群的同一问题,得到了相应的结果。我们证明了: 酉辛群USp(2n)上任一连续函数的Fourier级数,可以δ次Riesz球求和于它自己,但δ>(n(2n+1)-1)/2; 酉辛群USp(2n)上任一连续函数的Fourier级数,可以按Gauss-Sommerfeld意义的球求和于它自己;     

Searching for counterfeit coins

The well-known counterfeit problem asks for the minimum number of weighings necessary to determine all fake coins in a given set ofn coins. We derive a new upper bound when we know that at mostd coins are defective, improving a previous result of L. Pyber.     

酉辛群上的调和分析Ⅲ——Fourier级数的Abel求和

Abelian Summability may define as the limit case of Cesaro suminability whera α→∞, The kernel of Abelian mean, the so-called Poisson kernel of USp(2n) is.     

一类边值问题的振动准则

本文考虑一类中立型泛函偏微分方程的边值问题。我们的主要工具是平均技巧，利用有关的泛函微分不等式来建立这类边值问题解的振动准则。     

一类PCG迭代的强初值效应

预处理共轭梯度法的大量计算结果都表明,当迭代终止标准要求将余量的模减小某个倍数时,初值的选取对迭代次数仅有微弱影响。然而,本文给出的一类算例却表明,采用零初值或不同的随机初值,迭代次数之间会出现数倍的差别。同一种随机初值对不同参数模型问题的迭代次数也有很大差别。这种强初值效应对于方法的研究和比较是不利的。本文讨论和分析了这种现象。     

Augmented coupling interface method for solving eigenvalue problems with sign-changed coefficients

In this paper, we propose an augmented coupling interface method on a Cartesian grid for solving eigenvalue problems with sign-changed coefficients. The underlying idea of the method is the correct local construction near the interface which incorporates the jump conditions. The method, which is very easy to implement, is based on finite difference discretization. The main ingredients of the proposed method comprise (i) an adaptive-order strategy of using interpolating polynomials of different orders on different sides of interfaces, which avoids the singularity of the local linear system and enables us to handle complex interfaces; (ii) when the interface condition involves the eigenvalue, the original problem is reduced to a quadratic eigenvalue problem by introducing an auxiliary variable and an interfacial operator on the interface; (iii) the auxiliary variable is discretized uniformly on the interface, the rest of variables are discretized on an underlying rectangular grid, and a proper interpolation between these two grids are designed to reduce the number of stencil points. Several examples are tested to show the robustness and accuracy of the schemes.     

以酉辛群为特征边界的双曲空间的调和分析

§1.前言 本文采用四元数体的观点,讨论了以酉辛群USP(2n)为特征边界的双曲空间 {I-Z>0,ZJ=J}(1.1) 的调和函数论,从另一角度建立酉辛群上的Abel收敛定理的出发点。 §2.四元数体上的第一类典型域 华罗庚教授、万哲元教授“典型群”中建立了一般非交换体上方阵行列式理论。 四元数体的工阶方阵表示