解抛物问题的一类新的瀑布型多重网格法

本文推广石钟兹 ,许学军对椭圆问题提出的新的瀑布型多重网格法到抛物问题 ,建立了相应的理论结果 .     

Near-optimal design of Global Positioning System (GPS) networks using the Tabu Search technique

This paper describes an optimization technique based on an heuristic procedure which is applied to analyse and improve the efficiency of the design of Global Positioning System (GPS) surveying networks. GPS is a valuable survey tool because of its ability to increase the accuracy, speed and flexibility of a survey. A GPS network can be defined as a number of stations, which are co-ordinated by a series of sessions, formed by placing receivers on stations. The goal is to select the best order in which these sessions can be organised to give the best possible schedule. Generally, solving large networks to optimality requires impractical computational time. This paper proposes a Tabu Search technique which provides optimal or near-optimal solutions for large networks with an acceptable amount of computational effort. Computational results for several case studies with known and unknown optimal schedules have been presented to assess the performance of the proposed technique.     

奇异微分系统的初值问题及其应用

利用依赖于解的奇异非线性时间变换，把奇异微分系统转换为非奇异的常微系统，建立了奇异微分系统初值问题解的(非)存在性和惟一性及多解的存在性．一阶和二阶奇异微分方程的初值问题的应用结果与Petio(2000)和Agarwal(1999)的结果相比，条件简单容易验证，且结论更详细。     

广义拟变分不等式解集的稳定性及本质连通区的存在性

在赋范线性空间下．讨论广义拟变分不等式解集的稳定性，证明了满足一定连续性和凸性条件的广义拟变分不等式问题构成的空间M中，大多数(在Baire分类意义下)广义拟变分不等式问题的解集是稳定的，并证明了M中每一个广义拟变分不等式的解集至少存在一个本质连通区。     

Natural Operators Lifting Vector Fields to Bundles of Weil Contact Elements

Let A be a Weil algebra. The bijection between all natural operators lifting vector fields from m-manifolds to the bundle functor K ^A of Weil contact elements and the subalgebra of fixed elements SA of the Weil algebra A is determined and the bijection between all natural affinors on K ^A and SA is deduced. Furthermore, the rigidity of the functor K ^A is proved. Requisite results about the structure of SA are obtained by a purely algebraic approach, namely the existence of nontrivial SA is discussed.     

一个反应扩散方程的自由边界问题

该文研究了一个描述原细胞生长的反应扩散方程的自由边界问题.利用非线性分析中的线性化思想和偏微分方程的估计理论,证明了该自由边界问题局部古典解的存在唯一性.     

Nonlinear Diffusion Processes

We study elliptic systems of strongly nonlinear first-order differential equations in complex form on the plane. For such systems we develop the theory of Hilbert boundary value problems which is very much similar to the well-known theory for a holomorphic vector. Systems of nonlinear elliptic equations describe problems of interaction of several nonlinear stationary processes in the diffusive and convective mass and heat transport by hydrodynamic fluid flows.     

Modelling and optimal control of coupled structural acoustic systems with piezoelectric elements

We construct a model of a shell with piezoelectric elements (patches) that take into account the mutual influence of deformations and electric fields. Coupled problems for the shell with piezoelectric patches and an acoustic field, are studied and results on the existence and the uniqueness are obtained. For this system we consider an optimal control problem on noise attenuation and obtain results on the existence, the uniqueness, necessary and sufficient conditions of optimality. Copyright © 2003 John Wiley & Sons, Ltd.     

Identification of nonstationary axisymmetric load distributed along a cylindrical shell

The paper outlines a procedure to identify the space-and time-dependent external nonstationary load acting on a closed circular cylindrical shell of medium thickness. Time-dependent deflections at several points of the shell are used as input data to solve the inverse problem. Examples of numerical identification of various nonstationary loads, including moving ones are presented. The relationship between the external load and the stress-strain state of the shell is described by the Volterra equation of the first kind. The identification problem is solved using Tikhonov's regularization method and Apartsin's h-regularization method __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 91–100, July 2008.