THE SOLVABILITY CONDITIONS FOR INVERSE EIGENVALUE PROBLEM OF ANTI-BISYMMETRIC MATRICES

AbstractThis paper is mainly concerned with solving the following two problems: Problem I. Given X Cnxm, A = diag( 1, 2, ..... , m) Cmxm . Find A ABSRnxn such thatAX = XAwhere ABSRnxn is the set of all real n x n anti-bisymmetric matrices. Problem II. Given A RnXn. Find A SE such thatwhere || || is Frobenius norm, and SE denotes the solution set of Problem I.The necessary and sufficient conditions for the solvability of Problem I have been studied. The general form of SB has been given. For Problem II the expression of the solution has been provided.     

Exponential iterated integrals and the relative solvable completion of the fundamental group of a manifold

We develop a class of integrals on a manifold M called exponential iterated integrals, an extension of K.T. Chen's iterated integrals. It is shown that the matrix entries of any upper triangular representation of π₁(M,x) can be expressed via these new integrals. The ring of exponential iterated integrals contains the coordinate rings for a class of universal representations, called the relative solvable completions of π₁(M,x). We consider exponential iterated integrals in the particular case of fibered knot complements, where the fundamental group always has a faithful relative solvable completion.     

一类艾滋病传播的数学模型的定态非负解

利用分歧理论讨论带扩散问题艾滋病传播数学模型定态非负解及全局性质．     

Inverse Eigenvalue Problem in Structural Dynamics Design

1 Introduction Structural dynamics design is to design a structure subject to the dynamic characteristics re- quirement, i.e., determine physical and geometrical parameters such that the structure has the given frequencies and (or) mode shapes. This problem often arises in engineering connected with vibration. Recently, Joseph [1], Li et al. [2,3] converted the structural dynamics design to the following inverse eigenvalue problem. GIEP Let x = (x1, , xm)T , and let A(x) and B(x) be real n…     

含公共开支的两部门内生经济增长模型

本文研究了一个含公共开支的两部门的内生经济增长模型 ,其生产函数具有最一般的形式 .用于两部分的三要素—物质资本 ,人力资本 ,有效劳动的份额正相关 ,产出用于公共开支的份额与用于生产部门的三要素的份额负相关 ,经济增长极大地依赖于生产弹性 .并给出均衡值为正的条件和经济系统沿二维稳定流形收敛于稳定点的条件     

Higher-order spectral analysis and weak asymptotic stability of convex processes

This paper deals with the asymptotic stability analysis of a discrete dynamical inclusion whose right-hand side is a convex process. We provide necessary and sufficient conditions for weak asymptotic stability, and obtain sharp estimates for the asymptotic null-controllability set. These estimates involve not only standard, but also higher-order spectral information on the convex process and its adjoint.     

与波动方程边界控制有关的一类本征值问题

本文在高维空间情形，研究了大型空间结构和柔性机器人的控制中提出的一类新型的包含边界双线性形式的本征值问题，利用Ｐｏｈｏｚａｅｖ恒等式，分析了本征元的边界形态．     

External finite-element approximations of eigenfunctions in the case of multiple eigenvalues

The paper deals with the finite-element analysis of second-order elliptic eigenvalue problems when the approximate domains Ω_h are not subdomains of the original domain . The considerations are restricted to piecewise linear approximations. Special attention is devoted to the convergence of approximate eigenfunctions in the case of multiple exact eigenvalues. As yet the approximate solutions have been compared with linear combinations of exact eigenfunctions with coefficients depending on the mesh parameter h. We avoid this disadvantage.     

Network analysis of eigenvalue problem for multilayer dielectric waveguide consisting of arbitrary number of layers

In this paper, the eigenvalue problem of a multilayer dielectric waveguide consisting of arbitrary number of layers is solved by the microwave network method. A general program with the function of computer graphics has been developed for analyzing the dispersion characteristics and the electromagnetic field distributions of an N layer dielectric waveguide. As examples of practical applications of the program, first, the dispersions and field patterns for the planar waveguides with refractive index of parabolic and exponential profiles are analyzed. Secondly, the procedure of mode conversion and mode separation in dielectric branching waveguides is vividly demonstrated through analyzing the field distributions of asymmetric multilayer dielectric structures and the general rules of mode conversion are discussed. The examples show that the present method possesses the advantages of versatility, rapidity, simplicity and accuracy.