On Numerical Solution of Shape Inverse Problems

The new method is proposed for the numerical solution of a class of shape inverse problems. The size and the location of a small opening in the domain of integration of an elliptic equation is identified on the basis of an observation. The observation includes the finite number of shape functionals. The approximation of the shape functionals by using the so-called topological derivatives is used to perform the learning process of an artificial neural network. The results of computations for 2D examples show, that the method allows to determine an approximation of the global solution to the inverse problem, sufficiently closed to the exact solution. The proposed method can be extended to the problems with an opening of general shape and to the identification problems of small inclusions. However, the mathematical theory of the proposed approach still requires futher research. In particular, the proof of global convergence of the method is an open problem.     

对G.Ladas的一个开问题的解答

本文获得了一个高阶非线性差分方程具有无界正解的充分条件，所得结果解决了G.Ladas提出的一个开问题。     

椭圆型问题一类广义差分法的L~2模误差估计

1.引 言 广义差分法作为处理偏微分方程的离散技术,能够保持质量,动量,能量等物理量的守恒.广义差分法（有些文献称为box method[3];finite volume element method[4],[5],[6]）利用在对偶剖分体积单元积分原始方程,并将近似解限制于某一有限元空间而得到离散方程.因此,它在局部区域保持了原始方程的物理守恒性和其他重要特性.从而被广泛地应用于数值求解数学物理方程,特别是计算流体力学和热传导问题[11]. 对广义差分法的研究已有许多文献,专著[10]有详细的介绍.早期的工作主要考虑标准的重心对偶剖分.近年来Cai et,al[4],[5],[6],在某些假定下对较一般的对偶剖分给出了能量模误差估计,Huang and Xi[9]去掉了文献[6]中的这些限制.Chou,Li[8]和Li,     

A result on sets,with applications to vector optimization

In this paper there is stated a result on sets in ordered linear spaces which can be used to show that some properties of the sets are inherited by their convex hulls under suitable conditions. As applications one gives a characterization of weakly efficient points and a duality result for nonconvex vector optimization problems.     

对称正交反对称矩阵反问题解存在的条件

矩阵反问题和矩阵特征值反问题在科学和工程技术中具有广泛的应用,有关它们的研究已取得了许多进展[1,2].[3]和[4]分别研究了反对称矩阵反问题和双反对称矩阵特征值反问题等.本文研究一类更广泛的对称正交反对称矩阵反问题.用Rn×m（Cn×m）表示n×m实（复）矩阵的全体,ASRn×n表示n阶反对称矩阵的全体,ABSRn×n表示n阶双反对称矩阵的全体,ORn×n表示n阶正交矩阵的全体.A+表示矩阵A的Moore-Penrose广义逆.In表示n阶单位矩阵.ei表示n阶单位矩阵的第i列,Sn=[en,en-1,     

The Center Problem for a Linear Center Perturbed by Homogeneous Polynomials

The centers of the polynomial differential systems with homogeneous polynomials have been studied for the degrees s = 2, 3, 4, 5. for s = 2, 3, and partially classified for s = 4, 5. In this paper we recall and we give new centers for s = 6, 7 a linear center perturbed by They are completely classified these results for s = 2, 3, 4, 5,     

非齐次微分方程两点边值问题正解的存在性及多重性

本文考虑一类非齐次微分方程的两点边值问题,得到了一些有关其正解存在性与多重性的精确条件．     

总延误问题顺时安排法的性能比

给定一组工件的加工时间与工期，要求确定这些工件在一台机器上的加．工排列，使相应的总延误达到最小，这就是总延误问题．该问题在近年已被证明是NP困难的．由Wilkermn和Irwin（1971），林勋（1983）等所研究的顺时安排法能得到相邻交换意义下的局部解．在本文中，我们进一步证明该算法能得到前移邻域意义下的局部解，并确定了该算法的性能比．     

气体放电击穿过程的物理和数值研究

本文对低气压（１０＾－２Ｐａ）热阴极气体放电的击穿过程给出了物理描述和相应的双流体数学型，并发展了一种选择和调整未知初始条件的有效算法，可以通过伴随试射法得到对初始条件十分敏感的非线性两点边值常微分方程组的数值解，从而给出这类气体放电中击穿过程的定量描述。     

多目标分数变分问题的对偶性

本文利用参数逼近在函数广义（F，ρ）－凸的条件下，建立了一类多目标式变分问题关于有效解的对偶理论。