OSCILLATIONS OF A CLASS OF HIGH-ORDER LINEAR ODE WITH IMPULSES

Oscillation of solutions for a class of nth-order linear differential equation with impulses are considered and some sufficient conditions for oscillation of solutions are obtained, which improve and popularize some results in parts of the relative references.     

THE REGULAR SOLUTIONS OF THE ISENTROPIC EULER EQUATIONS WITH DEGENERATE LINEAR DAMPING

The regular solutions of the isentropic Euler equations with degenerate linear damping for a perfect gas are studied in this paper. And a critical degenerate linear damping coefficient is found, such that if the degenerate linear damping coefficient is larger than it and the gas lies in a compact domain initially, then the regular solution will blow up in finite time; if the degenerate linear damping coefficient is less than it, then under some hypotheses on the initial data, the regular solution exists globally.     

Three Dimensional Interface Problems for Elliptic Equations

The author studies the structure of solutions to the interface problems for second order linear elliptic partial differential equations in three space dimension.The set of singular points consists of some singular lines and some isolated singular points.It is proved that near a singular line or a singular point,each weak solution can be decomposed into two parts,a singular part and a regular part.The singular parts are some finite sum of particular solutions to some simpler equations,and the regular parts are bounded in some norms,which are slightly weaker than that in the Sobolev space H~2.     

ON ALTERNATIVE OPTIMAL SOLUTIONS TO QUASIMONOTONIC PROGRAMMING WITH LINEAR CONSTRAINTS

In this paper, the nonlinear programming problem with quasimonotonic （ both quasiconvex and quasiconcave ）objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, the structure of optimal solution set for the programming problem is depicted. Based on a simplified version of the convex simplex method, the uniqueness condition of optimal solution and the computational procedures to determine all optimal solutions are given, if the uniqueness condition is not satisfied. An illustrative example is also presented.     

BOUNDARY ELEMENT ANALYSIS FOR A CLASS OF MULTI-DIMENSIONAL LINEAR PARABOLIC EQUATIONS

In this paper,by me as of beundary element method,we try to deal with the initial -boundary value problem for a class of linear parunolic equations,which is a linear heat conduction equation. We tresent a boundary integral equation for the solution to the problem and its variational formalation The well-posedness of the variational formulation is proved. And the error estimates for the approsutate solutions are provided. The results of this paper are more general than those of[1]     

任意除环上一矩阵方程组的一般解与中心和反中心对称解

Necessary and sufficient conditions are given for the existence of the general solution, the centrosymmetric solution, and the centroskewsymmetric solution to a system of linear matrix equations over an arbitrary skew field. The representations of such the solutions of the system are also derived.     

Stability Analysis and Application of the Exponential Time Differencing Schemes

Exponential time differencing schemes are time integration methods that can be efficiently combined with spatial spectral approximations to provide very high resolution to the smooth solutions of some linear and nonlinear partial differential equations. We study in this paper the stability properties of some exponential time differencing schemes. We also present their application to the numerical solution of the scalar Allen-Cahn equation in two and three dimensional spaces.     

SPHERICAL SYMMETRIC SOLUTIONS FOR THE MOTION OF RELATIVISTIC MEMBRANES AND NULL MEMBRANES IN THE REISSNER-NORDSTRM SPACE-TIME

In this article, we concern the motion of relativistic membranes and null membranes in the Reissner-Nordstrm space-time. The equation of relativistic membranes moving in the Reissner-Nordstrm space-time is derived and some properties are discussed. Spherical symmetric solutions for the motion are illustrated and some interesting physical phenomena are discovered. The equations of the null membranes are derived and the exact solutions are also given. Spherical symmetric solutions for null membranes are just the two horizons of Reissner-Nordstrm space-time.     

HYPER ORDER OF SOLUTIONS TO SOME LINEAR DIFFERENTIAL EQUATIONS IN THE UNIT DISC

In this paper, we investigate the growth of solutions to some linear diferential equations with analytic coefcients in the unit disc. When the coefcients of these equations have some special properties near a point on the boundary of the unit disc, the order and the hyper order of the solutions to these equations are estimated accurately. Especially, our conditions on the coefcients are more general and the results on the hyper order of the solutions are new to some extent.     

SOLUTION WITH SHOCK-BOUNDARY LAYER AND SHOCK-INTERIOR LAYER TO A CLASS OF NONLINEAR PROBLEMS

In this paper,the shock behaviors of solution to a class of nonlinear singularly perturbed problems are considered.Under some appropriate conditions,the outer and interior solutions to the original problem are constructed.Using the special limit and matching theory,the expressions of solutions with the shock behavior near the boundary and some interior points are given and the domain for boundary values is obtained.     

矩阵方程ATXA=B的对称正交对称解及其最佳逼近

By applying the generalized singular value decomposition of matrices, this paper provides the necessary and sufficient conditions for the existence and the expression of the symmetric ortho-symmetric solutions of the linear matrix equation A^TXA = B. In addition, the expression of the optimal approximation solution to the given matrix is derived.     

对称线性互补问题的并行Schwarz算法

1引言考虑对称线性互补问题:求x∈R~N使得(1) Ax 6≥0,x≥0,x~T(Ax b)=0其中,A是给定的N×N实对称矩阵,b是N×1向量.目前求解该互补问题的迭代算法有很多(如Mangasarian(1977),Mangasarian,Leone (1987),Cottle(1992),曾金平,李董辉(1994)等).区域分解法以其将大问题化为若干子问     

线性流形上一类对称广义中心对称矩阵的最佳逼近问题

<正>1问题的提出为叙述方便起见,首先介绍本文中出现的符号.设SR~(n×n)和OR~(n×n)分别表示所有n阶实对称矩阵和正交矩阵的集合,A~+和‖A‖_F分别表示A的Moore-Penrose广义逆和     

从对称矩阵代数到全矩阵代数的线性群逆保持

设F是一个特征不为2的域,Mn(F)和Sn(F)分别记F上的n×n全矩阵代数和对称矩阵代数.所有的从Sn(F)到Mn(F)的保群逆的线性映射被刻划,作为一个中间步骤,三个矩阵的同时相似标准形也被证明.这个标准形简化了从Sn(F)到Mn(F)的保群逆的线性映射的刻划.     

非线性系统的线性对称结构

非线性系统的线性对称结构洪奕光，程代展（中国科学院系统科学研究所，北京１０００８０）１９９１年１２月２０日收到．１９９３年９月１６日收到压缩稿，一、引言近年来，人们对非线性控制系统对称性问题的研究很感兴趣．这主要是因为现实世界存在着大量的对称现象，而...     

TWO ALGORITHMS FOR SYMMETRIC LINEAR SYSTEMS WITH MULTIPLE RIGHT-HAND SIDES

1　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｍａｎｙａｐｐｌｉｃａｔｉｏｎｓｗｅｎｅｅｄｔｏｓｏｌｖｅｍｕｌｔｉｐｌｅｓｙｓｔｅｍｓｏｆｌｉｎｅａｒｅｑｕａｔｉｏｎｓＡｘ(ｉ) =ｂ(ｉ) ,ｉ=1,… ,ｓ (1)ｗｉｔｈｔｈｅｓａｍｅｎ×ｎｒｅａｌｓｙｍｍｅｔｒｉｃｃｏｅｆｆｉｃｉｅｎｔｍａｔｒｉｘＡ ,ｂｕｔｓｄｉｆｆｅｒｅｎｔｒｉｇｈｔ ｈａｎｄｓｉｄｅｓｂ(ｉ) (ｉ=1,… ,ｓ) .Ｉｆａｌｌｏｆｔｈｅｒｉｇｈｔ ｈａｎｄｓｉｄｅｓａｒｅａｖａｉｌａｂｌｅｓｉｍｕｌｔａｎｅｏｕｓｌｙ ,ｔｈｅｎｔｈｅｓｅｓｌｉｎｅａｒｓｙｓｔｅ…     

对称双正型线性互补问题的多重网格迭代解收敛性理论

多重网格法是七十年代产生并获得迅速发展的快速送代法.八十年代初,此方法开始应用于变分不等式的求解,其中包括一类互补问题,近十年来大量的数值实验证实,算法是成功的,而算法的收敛性理论也正在逐步建立,当A正定对称时的多重网格收敛性可见[3]和[7];[4]讨论了A半正定时的情况·本文考虑A为更广的一类矩阵:对称双正阵(见定义1.1),建立互补问题:     

大型对称不定箭形线性方程组的分解方法

1 引言 首先考虑2×2矩阵 显然当k>1/2时,矩阵K是对称正定的,且K可以分解成Cholesky因子:当k=1/2时,K为奇异矩阵;而当k<1/2时,K为对称不定矩阵,这时K有广义Cholesky分解式:并且这种分解是稳定的,一般地我们给出定义 定义1.1 设有矩阵K∈R~((m+n)×(m+n)),若总存在排列矩阵P∈R~((m+n)×(m+n))和对称正定矩阵H∈R~(m×n)、G∈R(m×m)使得则称矩阵K为对称拟定(Symmetric quasidefinite)矩阵。     

A REGULARIZED CONJUGATE GRADIENT METHOD FOR SYMMETRIC POSITIVE DEFINITE SYSTEM OF LINEAR EQUATIONS

AbstractA class of regularized conjugate gradient methods is presented for solving the large sparse system of linear equations of which the coefficient matrix is an ill-conditioned symmetric positive definite matrix. The convergence properties of these methods are discussed in depth, and the best possible choices of the parameters involved in the new methods are investigated in detail. Numerical computations show that the new methods are more efficient and robust than both classical relaxation methods and classical conjugate direction methods.