Optimal control for semilinear evolutionary variational bilateral problem

This paper is concerned with an optimal control problem for some semilinear evolutionary variational inequalities associated with bilateral constraints. The control domain is a general separable metric space and has no algebraic structure, in particular, it is not necessarily convex. Existence and optimality conditions of optimal pairs are established.     

Control of a hybrid conditionally linear Gaussian process

A control problem is considered where the coefficients of the linear dynamics are functions of a noisily observed Markov chain. The approximation introduced is to consider these coefficients as functions of the filtered estimate of the state of the chain; this gives rise to a finite-dimensional conditional Kalman filter. A minimum principle and a new equation for an adjoint process are obtained.This research was partially supported by NSERC under Grant A-7964, by the US Air Force Office of Scientific Research under Contract AFOSR-86-0332, and by the US Army Research Office under Contract DAAL03-87-0102.The authors obtained these results during a visit to UCSD by the first author in January 1990. This author wishes to thank Professor D. D. Sworder and his department for their hospitality.     

剖析博彩弹子机的赢钱原理

介绍了博彩弹子机 ,运用数学建模法剖析了它的赢钱原理 ,强调了一般博彩业主永远是赢家的道理     

-混合序列的不变原理

给出一类较广泛的ρ-混合序列 ,并证明了在一定的矩条件下 ,ρ-混合序列的不变原理成立     

四阶非线性边值问题解的存在性与上下解方法

该文讨论四阶常微分方程边值问题u^(4)(t)=f(t,u,u″), t∈［0,1］,u(0)=u(1)=u″(0)=u″(1)=0解的存在性, 其中f(t,u,v):［0,1］×R×R→R为Carathéodory函数. 在不限制f关于u,v的增长阶, 不假定f关于u,v的单调性的一般情形下, 用上下解方法获得了解的存在性结果,并讨论了单调迭代求解的有效性.     

横观各向同性多孔超弹性矩形板的单向拉伸

利用横观各向同性超弹性材料的广义neo-Hookean应变能函数研究了含有多个微孔的超弹性矩形板在单向拉伸作用下的有限变形和受力分析.给出了含有某种对称性分布的多个微孔的矩形板的变形模式,通过求解该变形模式满足的微分方程,将它用两个参数表示出来.可应用最小势能原理导出变分近似解,从而得到矩形板的变形和应力分布的解析解.分析了板中微孔的增长及微孔边缘应力的分布情况,讨论了板的各向异性程度及微孔的大小和孔间距离的影响,得到了单个、三个及五个微孔板中微孔的增长变形和孔边应力分布的一些基本规律规律,并进行了相互比较.     

奇异非线性二阶三点边值问题正解的存在唯一性

本文研究了一类奇异非线性二阶三点边值问题，通过摄动技巧和比较原理获得了所论问题正解的存在唯一性。     

Maximum norm stability of difference schemes for parabolic equations on overset nonmatching space-time grids

In this paper, theoretical results are described on the maximum norm stability and accuracy of finite difference discretizations of parabolic equations on overset nonmatching space-time grids. We consider parabolic equations containing a linear reaction term on a space-time domain which is decomposed into an overlapping collection of cylindrical subregions of the form , for . Each of the space-time domains are assumed to be independently grided (in parallel) according to the local geometry and space-time regularity of the solution, yielding space-time grids with mesh parameters and . In particular, the different space-time grids need not match on the regions of overlap, and the time steps can differ from one grid to the next. We discretize the parabolic equation on each local grid by employing an explicit or implicit -scheme in time and a finite difference scheme in space satisfying a discrete maximum principle. The local discretizations are coupled together, without the use of Lagrange multipliers, by requiring the boundary values on each space-time grid to match a suitable interpolation of the solution on adjacent grids. The resulting global discretization yields a large system of coupled equations which can be solved by a parallel Schwarz iterative procedure requiring some communication between adjacent subregions. Our analysis employs a contraction mapping argument.

Applications of the results are briefly indicated for reaction-diffusion equations with contractive terms and heterogeneous hyperbolic-parabolic approximations of parabolic equations.

     

我国普通高等教育人力资源发展水平的统计分析

本文综合运用主成分分析和因子分析两种综合评价方法 ,对我国各地区高等教育人力资源的发展水平进行排序和分类 ,为规划和发展各地区的高等教育事业提供了一定的科学依据。两种综合评价方法的综合运用克服了单一评价方法的片面性 ,评价结果较为全面、客观