一类Z-矩阵的置换结构

利用图论方法并结合Z－矩阵的本身特点，讨论了对角元全为零的Z－矩阵的伴随有向图性质，并由给出了对角元全为零的非奇异Z－矩阵的置换结构。     

广义严格对角占优矩阵的判定

１引言设Ａ＝（ａｉｊ）Ｃｎｘｎ,若对每一ｉＮ＝｛１,２,…,ｎ｝都有则称Ａ为对角占优矩阵,记为ＡＤυ;若（１）式中每一不等号都是严格的,则称Ａ为严格对角占优矩阵,记为ＡＤ．若存在正对角阵Ｘ使ＡＸＤυ（或ＡＸＤ）,则称Ａ为广义（或广义严格）对角占优矩阵;记为ＡＤΥ（或ＡＤ）．广义严格对角占优矩阵的判定在计算数学和矩阵论的研究中占有重要的地位,文［１］和［２］分别定义了α－对角占优矩阵和双对角占优矩阵,讨论了广义严格对角占优矩阵的判定及性质,本文引进了α双对角占优矩阵的概念,得到了广义严格对角占优矩…     

κ-path覆盖α-对角占优矩阵

利用矩阵的有向图引入k-path覆盖α-对角占优矩阵概念,讨论后k-path覆盖α-对角占优矩阵为非奇异H-矩阵(广义严格对角占优矩阵)的充要条件,进而得到了非奇异H-矩阵的新的判定条件.     

实循环矩阵与实对角矩阵相似问题

本文中我们证明了与实对角矩阵相似的每一个实循环矩阵都是对称的．并给出了一个正交变换，使得任意的ｎ×ｎ实循环对称矩阵通过该变换与实对角矩阵相似．     

关于反循环矩阵的对角化问题

反循环矩阵是一种特殊类型的矩阵，它本身有许多重要的性质，而且与矩阵的对角化问题有联系．本文拟探讨反循环矩阵的对角化问题，以及任一ｎ阶方阵Ａ可对角化时，Ａ与反循环矩阵之间的关系．     

矩阵乘法AB＝BA成立的两个充要条件与一个充分条件

矩阵乘法ＡＢ＝ＢＡ成立的两个充要条件与一个充分条件韩锦扬（湖北汽车工业学院）我们知道，矩阵的乘法不满足交换律，即在一般的情况下，ＡＢ／ＢＡ。这就是说，矩阵乘法ＡＢ—ＢＡ成立是有条件的。比如，对于ｎ阶矩阵Ａ、Ｂ中任意一个为ｎ阶单位矩阵Ｅ时，矩阵乘法ＡＥ...     

广义严格对角占优矩阵与非奇M矩阵的判定

１引言Ｍ矩阵是计算数学中应给极其广泛的矩阵类,它出现于经济价值模型矩阵和反网络系统分析的系数矩阵及解某类确定微分方程问题的数值解法中．由于Ｍ矩阵的重要性,讨论Ｍ矩阵及相关的广义对角占优矩阵的判定及性质有着十分重要的意义．本文则是在文［１］～［３］基础上,给出了广义严格对角占优矩阵与非奇Ｍ矩阵几则新的充分条件．拓广了文［１］～［３］的相关结果．２主要结果定义１设Ａ＝（ａｉｊ）,如果存在正对角阵Ｄ,使得ＡＤ为严格对角占优阵,则称Ａ为广义严格对角占优阵．定义２设Ａ＝,Ｍ（Ａ）＝（Ｍｉｊ）,其中,则称Ｓ…     

关于《相似变换矩阵的简单求法》的改进

关于《相似变换矩阵的简单求法》的改进朱广化（安徽教育学院数学系２３００６１）贵刊在１９９３年第９期发表了任化民同志《相似变换矩阵的简单求法》一文［１］，其方法是通过初等变换将矩阵（λＥ—Ａ）与（λＥ—Ｂ）都化成法式，即由求得…＋Ｑ。，然后将矩阵Ｂ代人...     

Lyapunov不等式的最佳解与一般线性方法的可行性

１引言在刚性常微分方程初值问题数值解法理论中,常要求数值方法中的某个系数矩阵Ｂ具有性质：使Ｌｙａｐｕｎｏｖ不等式有对角正定解Ｄ存在,即存在对角正定矩阵Ｄ,使ＤＢ＋ＢＴＤ为正定矩阵·在许多情形,这种解Ｄ是存在的,例如Ｇ－Ｌ-、ＩＡ-和ⅡＡ－ＲＫ方法［３］．然而也存在一些方法,它是Ａ－稳定、Ｌ－稳定,甚至是代数稳定的,但这种Ｄ却不存在．例如ⅢＣ（ｓ≥３）ＲＫ方法［３］和当θ＝１时的块θ－方法［５］（至少对ｒ＝２,３,４是如此）．前者是Ｌ－稳定的,也是代数稳定的,后者也是Ｌ－稳定的．这意味着,可能有不少…     

线性矩阵方程的解

线性矩阵方程的解郝秀梅，杨子胥（山东财政学院基础部２５００１４）在一般的高等代数和线性代数教材中，常有以下结论：当Ａ为非奇异方阵时，矩阵方程ＡＸ＝Ｂ有唯一解为Ｘ＝Ａ－１Ｂ．本文则讨论一般的线性矩阵方程ＡＸ＝Ｂ、ＸＡ＝Ｂ以及ＡＸＢ＝Ｃ（这里矩阵Ａ，Ｂ；...     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

Journal of the Operations Research Society of China Special issue on Operations Research in Healthcare Management

正Guest Editors:Hong Chen,Shanghai Jiao Tong University,Shanghai,China Guohua Wan,Shanghai Jiao Tong University,Shanghai,China David Yao,Columbia University,New York,USA Scope:Healthcare delivery worldwide has been fraught with high cost,low efficiency and poor quality of patient care service.For the field of operations research(OR),healthcare offers some of the biggest challenges as well as best opportunities in     

ANALYSIS IN THEORY AND APPLICATIONS Vol. 30, 2014 CONTENTS

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On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.