THE INVERSE PROBLEM FOR PART SYMMETRIC MATRICES ON A SUBSPACE

In this paper, the following two problems are considered:Problem Ⅰ. Given S∈E Rn×p,X,B 6 Rn×m, find A ∈ SRs,n such that AX = B, where SR8,n = {A∈ Rn×n|xT(A - AT) = 0, for all x ∈ R(S)}.Problem Ⅱ. Given A* ∈ Rn×n, find A ∈ SE such that ||A-A*|| = minA∈sE||A-A*||, where SE is the solution set of Problem Ⅰ.The necessary and sufficient conditions for the solvability of and the general form of the solutions of problem Ⅰ are given. For problem Ⅱ, the expression for the solution, a numerical algorithm and a numerical example are provided.     

COMPOSITE-STEP LIKE FILTER METHODS FOR EQUALITY CONSTRAINT PROBLEMS

In a composite-step approach, a step sk is computed as the sum of two components vk and hk. The normal component vk, which is called the vertical step, aims to improve the linearized feasibility, while the tangential component hk, which is also called horizontal step, concentrates on reducing a model of the merit functions. As a filter method, it reduces both the infeasibility and the objective function. This is the same property of these two methods. In this paper, one concerns the composite-step like filter approach. That is, a step is tangential component hk if the infeasibility is reduced. Or else, sk is a compositestep composed of normal component Vk and tangential component hk.     

A NEW SMOOTHING EQUATIONS APPROACH TO THE NONLINEAR COMPLEMENTARITY PROBLEMS

The nonlinear complementarity problem can be reformulated as a nonsmooth equation. In this paper we propose a new smoothing Newton algorithm for the solution of the nonlinear complementarity problem by constructing a new smoothing approximation function. Global and local superlinear convergence results of the algorithm are obtained under suitable conditions. Numerical experiments confirm the good theoretical properties of the algorithm.     

Cauchy Problem for Quasilinear Hyperbolic Systemsd with Higher Order Dissipative Terms

In this paper,the author studies the global existence,singularities and life span of smooth solutions of the Cauchy problem for a class of quasilinear hyperbolic systems with higher order dissipative terms and gives their applications to nonlinear wave equations with higher order dissipative terms.     

等距算子的延拓、逼近及相关问题

本文介绍了等距算子从单位球面、从区域及从保距离1等条件下的各种等距廷拓问题；并介绍了(线性与非线性算子)等距算子的弱扰动、强扰动及渐近等距算子等问题．文中从历史到现状，概括了重要的研究结果，并指出了一些尚未解决的遗留问题．     

用图形法再解一道习题

在文 [1 ]中提出这样一个题目 :设 - 2π <α <β<-π ,求 2α- β的范围 .图 1我们用图形法给出另一种解法 ,并很直观地给出一般情况下的结论 .建立如图 1的坐标系 ,易见α ,β的范围是图 1中的阴影部分 .设 2α- β =t则 β =2α -t表示直线 .由于α ,β的取值范围是图 1中的阴影部分 ,所以π <-t<3π即　 - 3π相似文献   

课本习题的价值在探索中升华--改造我们的数学教学方法

孤立地、片面地解决一个课本习题 ,在数学教学中毫无疑问是低效的教学方法 ,我们必须坚决反对 .相反 ,运用运动变化的观点、普遍联系的观点、辩证唯物的观点去分析、观察、探索一个数学问题 ,寻求课本习题的内在变化规律及习题之间的联系 ,是提高教学效率的一种有效途径 ,我们要坚决拥护 .题目不在做得多 ,开发其价值就行 .如何开发课本习题的价值 ?本文提供四种基本方法 :1 )多题一组 ,构造问题链 ;2 )一题多探 ,推而广之 ;3)一题多解 ,比较解法 ;4)一题多改 ,突而破之 .1　多题一组 ,编拟问题链 ,形成“合力” :加强题与题之间的横向联合…     

拟线性双曲方程组一类广义Riemann问题的整体间断解

对一阶拟线性双曲方程组一类广义Riemann问题，该文在一定条件下证明了，包含一个接触间断和一个中心波以及包含一个接触间断和一个激波的间断解的整体存在性和唯一性.     

三阶常微分方程的某些非线性特征值问题的正解

研究了三阶常微分方程的某些非线性特征值问题. 通过考察非 线性项在有界集上的性质建立了这些问题的正解的存在性与多解性.