二维各向异性压电介质机电耦合场的基本解

本文研究各向异性压电介质的机电耦台问题．应用平面波分解法和留数定理，首次得到了线力和线电荷作用下一般二维各向异性压电介质机电耦合场的基本解．本文的解适用于平面问题、反平面问题以及平面和反平面相互耦合问题．作为特例，文中给出了横观各向同性压电介质的基本解．     

半无限及含孔无限平面在各种边界条件下的复位势基本解

运用Ｒｉｅｍａｎｎ＿Ｓｃｈｗａｒｚ对称原理和线弹性力学解的叠加原理建立了半无限平面及含孔无限平面在各种边界条件下基本解的一般求解方法，并分别导出边界上受不同荷载以及边界固定等各种边界条件下的复位势基本解·     

求弹性半平面问题基本解的一个直接方法

本文利用镜像法和直接积分导出了弹性半平面问题的基本解。这个推导方法比Gladwell用镜像法和富氏变换要直观。这个基本解对于用边界元法分析半平面域具有任意外形孔洞的应力集中问题将起着十分重要的作用。     

含裂纹平面问题Erdogan基本解的显式表达

基本解是边界元法、基本解法和无网格法等数值方法的重要理论基础.在断裂问题中,采用含裂纹的基本解可以避免将裂纹表面作为边界条件,从而大大简化问题的求解.在复变函数表示的含裂纹平面问题Erdogan基本解的基础上,对Erdogan基本解的使用条件进行了注解,修正了Erdogan基本解的一些错误,并推导出Erdogan基本解中位移函数解答的显式表达形式.编写了基于Erdogan基本解显式表达的样条虚边界元法（spline fictitious boundary element method, SFBEM）计算程序,计算了具有复合边界条件平面问题的位移、应力和应力强度因子.数值算例结果表明了该文提出的Erdogan基本解显式表达形式的正确性.     

带周期裂缝的弹性半平面问题

本文把具有任意形状和个数的周期裂缝的弹性半平面基本问题化为了某种特殊类型的奇异积分方程,证明了其解的存在和唯一。并对带周期共线直裂缝的弹性半平面问题,给出了封闭形式的解。     

各向异性半平面与一各向同性长条的焊接问题

本文利用平面弹性复变方法和解析函数边值问题的基本理论以及积分方程论，研究了各向异性半平面与一各向同性长条的焊接问题，给出了应力分布封闭形式的解。     

各向异性板半无限裂纹平面问题的保角变换解法

本文给出了各向异性板半无限裂纹平面问题的保角变换解.首先,简单介绍了各向异性板平面问题的基本理论.随后采用复变函数的方法,通过引用适当的保角映射研究了各向异性板半无限裂纹平面弹性问题,得到了各向异性板中半无限裂纹在任意面内集中载荷作用下的裂纹尖端的应力强度因子的解析解.最后,作为特例得到了当集中力作用在裂纹表面时的应力强度因子的解析解,依此验证了结果的正确性.结果表明该方法简单实用.     

用“调和函数”表示的压电介质平面问题的通解

本文首先从压电介质平面问题基本方程出发，引入一个位移函数，导出其通解，然后利用推广的Almansi定理，将通解化为简单形式，即通过三个“调和函数”来表示所有的物理量，其次，推导了楔形体顶端受集中力和点电荷作用时有限形式的解，退化可得半无限平面直线边界受集中力和点电荷的解。     

各向异性复合材料的平面周期焊接问题

利用平面弹性复变方法和解析函数边值问题的基本理论,讨论不同材料的各向异性弹性半平面和弹性长条的周期焊接问题,并给出应力分布封闭形式的解     

二维流形的广义Poincaré-Bendixson定理

平面上Poincar-Bendixson环域定理对于讨论平面动力系统的周期解的存在性具有基本意义,这个古典的环域定理只适用于平面上无奇点的双连通区域,这个定理由叶彦谦、马知恩很好地推广到平面上多连通区域上,并且他们还讨论了平面上多连通区域上有有限个奇点的情况,得到了平面系统的广义的环域定理.     

INVERSE SCATTERING BY AN INHOMOGENEOUS PENETRABLE OBSTACLE IN A PIECEWISE HOMOGENEOUS MEDIUM

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using the integral equation method. We then proceed to establish two tools that play important roles for the inverse problem: one is a mixed reciprocity relation and the other is a priori estimates of the solution on some part of the interfaces between the layered media. For the inverse problem, we prove in this paper that both the penetrable interfaces and the possible inside inhomogeneity can be uniquely determined from a knowledge of the far field pattern for incident plane waves.     

一类源于传染病模型的积分方程的正解

利用Krasnosel'skii拓扑方法对一类积分方程给出正解存在唯一的充要条件,并利 用模型参数对阈值作出估计.     

Reduction of three-dimensional dynamical elasticity theory problems with arbitrarily located plane slits to integral equations

By generalizing a method described earlier /1/ for reducing three-dimensional dynamical problems of elasticity theory for a body with a slit to integral equations, integral equations are obtained for an infinite body with arbitrarily located plane slits. The interaction of disc-shaped slits located in one plane is investigated when normal external forces that vary sinusoidally with time (steady vibrations) are given on their surfaces.

Problems of the reduction of dynamical three-dimensional elasticity theory problems to integral equations for an infinite body weakened by a plane slit were examined in /1, 2/. The solution of the initial problem is obtained in /1/ by applying a Laplace integral transform in time to the appropriate equations and constructing the solution in the form of Helmholtz potentials with densities characterizing the opening of the slit during deformation of the body. The problem under consideration is solved in /2/ by using the fundamental Stokes solution /3/ with subsequent construction of the solution in the form of an analogue of the elastic potential of a double layer.     

Approximate solution of a control problem on the basis of the nilpotent approximation

We consider the control problem for deterministic systems described by ordinary differential equations with linear controls. On the basis of the nilpotent approximation method, we construct an algorithm for finding an approximate solution of the control problem for three-dimensional nonlinear systems with two linear controls. The algorithm was implemented in Maple and tested in examples including the control of a mobile robot on a plane and the attitude control of a sphere rolling on a plane.     

Solving real-world linear ordering problems using a primal-dual interior point cutting plane method

Cutting plane methods require the solution of a sequence of linear programs, where the solution to one provides a warm start to the next. A cutting plane algorithm for solving the linear ordering problem is described. This algorithm uses the primaldual interior point method to solve the linear programming relaxations. A point which is a good warm start for a simplex-based cutting plane algorithm is generally not a good starting point for an interior point method. Techniques used to improve the warm start include attempting to identify cutting planes early and storing an old feasible point, which is used to help recenter when cutting planes are added. Computational results are described for some real-world problems; the algorithm appears to be competitive with a simplex-based cutting plane algorithm.Research partially supported by ONR Grant number N00014-90-J-1714.     

对称迭层矩形板的平面应力分析

常用的对称迭层板为各向异性板．根据平面应力问题的基本方程精确地用应力函数解法求得了各向异性板的一般解析解．推导出平面内应力和位移的一般公式，其中积分常数由边界条件来决定．一般解包括三角函数和双曲函数组成的解，它能满足4个边为任意边界条件的问题．还有代数多项式解，它能满足4个角的边界条件．因此一般解可用以求解任意边界条件下的平面应力问题．以4边承受均匀法向和切向载荷以及非均匀法向载荷的对称迭层方板为例，进行了计算和分析．     

矩阵特征值问题的Bendixson定理的改进

任一n×n矩阵A可分解为A=B C,其中B=1/2(A A~H),C=1/2(A-A~H)。Bendixson定理的主要内容是:λ_j(A)(j=1,2,…,n)落在矩形区域F上,而构成F的四个边的直线分别为x=max(λ_j(B)),x=min(λ_j(B)),y=max(-iλ_j(C)),y=min(-iλ_j(C))。本文给出用B,C的特征值和矩阵A的正规性偏离度对A的特征值的进一步估计。     

ON UNIQUENESS OF MEROMORPHIC FUNCTIONS WITH SHARED-SETS IN AN ANGULAR DOMAIN

In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary.     

An asymptotic method of solving transient dynamic contact problems

Using a special approximation in the complex plane of the symbol of the kernel of the contact-problem integral equation, an asymptotic form of its solution is constructed which is the fundamental solution of the transient dynamic plane contact problem of the impact of a rigid punch with an elastic half-plane for short interaction times. The proposed approximation of the kernel symbol enables it to be approximated in the complex plane with any previously specified accuracy. Unlike existing approaches [1, 2, etc.], the approximation of the kernel symbol of the integral equation employed here enables the solution of this problem to be obtained in the form of simple formulae not containing singular quadratures.