A two-dimensional matrix Padé-type approximation in the inner product space

By introducing a bivariate matrix-valued linear functional on the scalar polynomial space, a general two-dimensional (2-D) matrix Padé-type approximant (BMPTA) in the inner product space is defined in this paper. The coefficients of its denominator polynomials are determined by taking the direct inner product of matrices. The remainder formula is developed and an algorithm for the numerator polynomials is presented when the generating polynomials are given in advance. By means of the Hankel-like coefficient matrix, a determinantal expression of BMPTA is presented. Moreover, to avoid the computation of the determinants, two efficient recursive algorithms are proposed. At the end the method of BMPTA is applied to partial realization problems of 2-D linear systems.     

Spectral methods for some singularly perturbed third order ordinary differential equations

Spectral methods with interface point are presented to deal with some singularly perturbed third order boundary value problems of reaction-diffusion and convection-diffusion types. First, linear equations are considered and then non-linear equations. To solve non-linear equations, Newton’s method of quasi-linearization is applied. The problem is reduced to two systems of ordinary differential equations. And, then, each system is solved using spectral collocation methods. Our numerical experiments show that the proposed methods are produce highly accurate solutions in little computer time when compared with the other methods available in the literature.      

Reconstruction of the shape of object with near field measurements in a half-plane

We consider a mathematical problem modelling some characteristics of near field optical microscope.We take a monofrequency line source to illuminate a sample with constant index of refraction and use the scattered field data measured near the sample to reconstruct the shape of it. Mixed reciprocity relation and factorization method are applied to solve our problem.Some numerical examples to show the feasibility of the method are presented.     

A fundamental solution to the Cauchy problem for a fourth-order pseudoparabolic equation

The Cauchy problem for a fourth-order pseudoparabolic equation describing liquid filtration problems in fissured media, moisture transfer in soil, etc., is studied. Under certain summability and boundedness conditions imposed on the coefficients, the operator of this problem and its adjoint operator are proved to be homeomorphism between certain pairs of Banach spaces. Introduced under the same conditions, the concept of a θ-fundamental solution is introduced, which naturally generalizes the concept of the Riemann function to the equations with discontinuous coefficients; the new concept makes it possible to find an integral form of the solution to a nonhomogeneous problem.     

On the Majorant Method for the Cauchy--Kovalevskaya Problem

We present a theory which allows us to justify the existence theorems and derive majorant estimates for solutions of the Cauchy problem for a countable system of partial differential equations. Our results also allow to estimate the maximum existence interval for a solution.     

新疆纺织品出口中的问题与对策

在对新疆纺织行业出口状况调研的基础上，分析了纺织品外贸的现状及存在的问题，并提出了解决问题的算法和意见，新疆是一个具有纺织资源、劳动力资源优势的地区，抓住“入世”机遇，对发展新疆纺织业具有重要的现实和战略意义。     

Decidability of finite quasivarieties generated by certain transformation semigroups

No Abstract. Received January 2, 2000; accepted in final form August 28, 2000.     

Positivity of third order linear recurrence sequences

It is shown that the Positivity Problem for a sequence satisfying a third order linear recurrence with integer coefficients, i.e., the problem whether each element of this sequence is nonnegative, is decidable.     

限位排序的若干结果

In this paper,we first consider the position restriction scheduling problems on a single machine.The problems have been solved in certain special cases,especially for those obtained by restricting the processing time pj=1.We introduce the bipartite matching algorithm to provide some polynomial-time algorithms to solve them.Then we further consider a problem on unrelated processors.     

一类部分信息的随机控制问题的极值原理

在本文中,我们证明了一类部分信息的随机控制问题的极值原理的一个充分条件和一个必要条件.其中,随机控制问题的控制系统是一个由鞅和Brown运动趋动的随机偏微分方程.