A System of Four Matrix Equations over von Neumann Regular Rings and Its Applications

We consider the system of four linear matrix equations A1X = C1, XB2=C2, A3XB3=C3 and A4XB4 = C4 over h, an arbitrary von Neumann regular ring with identity. A necessary and sufficient condition for the existence and the expression of the general solution to the system are derived. As applications, necessary and sufficient conditions are given for the system of matrix equations A1X = C1 and A3X=C3 to have a bisymmetric solution, the system of matrix equations A1X = C1 and A3XB3 = C3 to have a perselfconjugate solution over h with an involution and char h≠2, respectively. The representations of such solutions are also presented. Moreover, some auxiliary resultson other systems over h are obtained. The previous known results on some systems of matrix equations are special cases of the new results.     

体上一矩阵方程组的再研究

Let F,Qand Q be an arbitrary skew field,a skew field with an involutorial antiautomorphism,a strong p-division ring,respectively.This paper is sequel to [1].A practical method of finding the general solution of the system of matrix equations over F is presented.The necessary and sufficient conditions for the existence of and the explicit expressions for the self-conjugate matrix solution over Q,the positive semidefinite self-conjugate matrix solution over Q of the system are derived.     

一类带有Holling Ⅱ类功能性反应和相互干扰及脉冲效应的捕食系统

A kind of predator-prey system of Holling typeⅡand interaction perturbation with impulsive effect is presented.By using Floquet theory and small amplitude perturbations skills,the locally asymptotical stability of prey-eradication periodic solution and the permanence of the system are discussed and the corresponding threshold conditions are given respectively.Finally,the existence of positive periodic solution is investigated by the bifurcation theory.     

ON MONOTONE METHOD FOR NONLINEAR REACTION-DIFFUSION SYSTEM

If we knew the existence of upper and lower solutions u, v of a coupled reaction-diffusion system with quasi-monotone nonlinear reaction functions, then we can prove the existence of a solution ω of the same system such that u<ω相似文献   

THE EXISTENCE, UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTION FOR A CLASS OF NONLINEAR SYSTEM

In this paper, we study the problems on the existence, uniqueness and stability of almost periodic solution for a class of nonlinear system. Using fixed point theorem and Lyapunov functional, the sufficient conditions are given which guarantee the existence, uniqueness and stability of almost periodic solution for the system.     

THE EXISTENCE OF GLOBAL SOLUTION AND "BLOW UP" PHENOMENON FOR A SYSTEM OF MULTI DIMENSIONAL SYMMETRIC REGULARIZED WAVE EQUATIONS

The existence and uniqueness of the global smooth solution to the initial-boundary valueproblem of a system of multi-dimensions SRWE are proved. The sufficient conditions of "blowingup" of the solution are given.     

关于非线性矩阵方程$X^s-A^*X^{-t}A=Q$的Hermitian正定解及其扰动估计

In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X^s - A^＊X^-tA = Q are studied, where Q is a Hermitian positive definite matrix, s and t are positive integers. The existence of a Hermitian positive definite solution is proved. A sufficient condition for the equation to have a unique Hermitian positive definite solution is given. Some estimates of the Hermitian positive definite solutions are obtained. Moreover, two perturbation bounds for the Hermitian positive definite solutions are derived and the results are illustrated by some numerical examples.     

HGAH矩阵的逆特征值问题

In this paper, the inverse eigenvalue problem of Hermitian generalized anti-Hamihonian matrices and relevant optimal approximate problem are considered. The necessary and sufficient conditions of the solvability for inverse eigenvalue problem and an expression of the general solution of the problem are derived. The solution of the relevant optimal approximate problem is given.     

Chemotaxis-fluild 系统的全局弱解

We investigate the existence of the global weak solution to the coupled Chemotaxisfluid system ■in a bounded smooth domain ??R~2. Here, r≥0 and μ 0 are given constants,?Φ∈L~∞(?) and g∈L~2((0, T); L_σ~2(?)) are prescribed functions. We obtain the local existence of the weak solution of the system by using the Schauder fixed point theorem. Furthermore, we study the regularity estimate of this system. Utilizing the regularity estimates, we obtain that the coupled Chemotaxis-fluid system with the initial-boundary value problem possesses a global weak solution.     

解线性方程组的预条件迭代方法

In this paper,we study the preconditioning iterative methods for the solution of the linear system and provide a convergence theorem of this method,it improves some recent results,We prove that if all parameters are in [0,1],the convergence rates for the MGS (Modified Gauss-Seidel)type methods are better than those of the corresponding SOR type methods.     

On a System of Martix Equations over an Arbitrary Skew Field

ＯｎａＳｙｓｔｅｍｏｆＭａｒｔｉｘＥｑｕａｔｉｏｎｓｏｖｅｒａｎＡｒｂｉｔｒａｒｙＳｋｅｗＦｉｅｌｄ￥ＷａｎｇＱｉｎｇｗｅｎ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＣｈａｎｇｗｅｉＴｅａｃｈｅｒｓＣｏｌｌｅｙｅ，Ｗｅｉｆａｎｇ，Ｗｅｉｆａｎｇ，２６１０４３）Ａｂ...     

Roth定理在任意体上的推广

本文给出了任意体上的矩阵方程ＡＸ—ＹＢ＝Ｃ相容的两个充要条件，并给出了其一般解的表达式，从而推广了域上的Ｗ．Ｅ．Ｒｏｔｈ定理．     

除环上左线性方程组的反问题

推广并改进了实数域上线性方程组的反问题及其一系列结果，解决了除环上左线性方程组更具广泛性的一类反问题，给出了此类反问题有（斜）自共轭解及（半）正定自共轭解的充要条件及其解集结构．     

广义逆理论中一个定理的拓广

给出了广义逆理论一个定理的推广,解决了体上相容矩阵方程AX=H解的最简表达式问题.     

体上右线性方程组的反问题

设Ｆ，Ｋ，Ω分别表示一个任意的体、一个具有对合反自同构的体和一个实四元数体，Ｆ^ｎ表示Ｆ上的ｎ维右向量空间．本文推广和改进了实线性方程组的反问题及一系列结果，解决了Ｆ上右线性方程组更具一般性的反问题（简称ＩＰＳ）：给定ｂ∈Ｆ^s和α_ｉ∈Ｆ^ｎ（ｉ＝１，…，ｍ≤ｎ）满足ｒａｎｋ［α₁，…，α_m］＝ｍ，求所有的ｓ×ｎ矩阵Ａ使Ａα_ｉ＝ｂ（ｉ＝１，…，ｍ）．当ｓ＝ｎ时     

模糊矩阵三种广义逆的判定定理

给出模糊矩阵存在广义{1,3}逆,广义{1,4}逆和Moore-Penrose广义逆的判定定理.     

Factoring matrices into the product of two matrices

Linear algebra of factoring a matrix into the product of two matrices with special properties is developed. This is accomplished in terms of the so-called inverse of a matrix subspace which yields an extended notion for the invertibility of a matrix. The product of two matrix subspaces gives rise to a natural generalization of the concept of matrix subspace. Extensions of these ideas are outlined. Several examples on factoring are presented. AMS subject classification (2000)  15A23, 65F30     

在两循环矩阵类中求解线性方程组反问题的快速算法

本文利用多项式最大公因式 ,给出了线性方程组的反问题在 r-循环矩阵类和对称 r-循环矩阵类中有唯一解的充要条件 ,进而得到线性方程组在 r循环矩阵类和对称 r-循环矩阵类中的反问题求唯一解的算法 .最后给出了应用该算法的数值例子 .     

任意体上的矩阵方程［X_（nn）A_（ns），X_（nn）B_（nt）］＝［A_

本文研究了任意体上的矩阵方程［Ｘ（ｎｎ）Ａ（ｎｓ），Ｘ（ｎｎ）Ｂ（ｎｔ）］＝［Ａ（ｎｓ），０］（１）给出了（１）相容的充要条件、通解的表达式、解的性质及其实用解法．