Applying simulated annealing to location-planning models

Simulated annealing is a computational approach that simulates an annealing schedule used in producing glass and metals. Originally developed by Metropolis et al. in 1953, it has since been applied to a number of integer programming problems, including the p-median location-allocation problem. However, previously reported results by Golden and Skiscim in 1986 were less than encouraging. This article addresses the design of a simulated-annealing approach for the p-median and maximal covering location problems. This design has produced very good solutions in modest amounts of computer time. Comparisons with an interchange heuristic demonstrate that simulated annealing has potential as a solution technique for solving location-planning problems and further research should be encouraged.     

非线性伪双曲方程初边值问题整体广义解

本文证明了一类非线性伪双曲方程初边值问题整体广义解的存在唯一性．     

关于一类半线性退化椭圆方程的存在性结果

本文研究下列半线性退化椭圆Ｄｉｒｉｃｈｌｅｔ问题：这里Ｘ＝｛Ｘ１，…，Ｘｍ｝是一组满足Ｈｏｒｍａｎｄｅｒ条件的实光滑向量场．假设它们在区域的边界附近还满足一些附加条件，以及ｆ∈Ｃ∞〔Ω×Ｒ×Ｒｍ），并且　ｚｆ（ｘ，ｚ，ξ）≥０，ｓｉｇｎＸｆ（ｘ，ｚ，０）≥μ＞－∞，ｃ（ｘ）≥ｃ０＞０和ｆ（ｘ，ｚ，ξ）关于变量ξ满足一定的增长条件．我们证明了当边界是无穷可微时，上述岸线性Ｄｉｒｉｃｈｌｅｔ问题的光滑解的存在性和唯一性．     

对线性规划单纯形法的注记

为了更有效地应用单纯形算法求解线性规划问题,本文提出了以下几点注记。(1)人工变量列不必参与数值计算,也不占存储空间,从而可大量节省计算量和存储量;(2)使用基变量指标集来判断人工变量是否离基,可避免舍人误差的影响;(3)虚设人工变量的最终非零值对于修改存在矛盾的数学模型将起着关键性作用;(4)可将大M法与两阶段法统一处理,且M可不取具体的数值,也不参与数值计算;(5)实际计算中宜将Dantzig算法与Bland算法结合起来使用,既可对一般问题达到快速收敛的目的,又可避免退化问题可能产生的循环现象,而且在软件设计与实现上要比字典序方法等简单容易;(6)对于大型稀疏矩阵的计算机数据录入,建议采用二元数组的数据结构逐行录入,则可节省三分之一的录入工作量。     

两点边值问题解的存在性

本文讨论两点边值问题解的存在性,在没有孤立性条件下,获得了不动点定理,作为应用实例,给出了反应扩散方程稳态解的存在性证明。     

关于混合型多项式Hammerstein积分方程正解迭代求法

本文给出了混合型多项式Ｈａｍｍｅｒｓｔｅｉｎ积分方程正解的迭代求法，并将所得结果应用到二阶非线性常微分方程的边值问题     

一类重特征方程柯西问题的存在唯一性

讨论了一类高维重特征方程栖西问题存在唯一性中的离散现象，证明发池方程的参数取某些值时存在唯一性有离散现象发生。并建立了存在唯一性与黎曼问题的联系。     

B-CONVERGENCE PROPERTIES OF GENERAL LINEAR METHODS

In this paper, for general linear methods applied to strictly dissipative initial value problem in Hilbert spaces, we prove that algebraic stability implies B-convergence, which extends and improves the existing results on Runge-Kutta methods. Specializing our results for the case of multi-step Runge-Kutta methods, a series of B-convergence results are obtained.     

MULTIDIMENSIONAL GOURSAT PROBLEM FOR SEMILINEAR HYPERBOLIC EQUATIONS

In this paper we study the Goursat problem for semilinear hyperbolicequations with zero boundary condition where the boundary is the characteristic conefor hyperbolic operator. Our result shows that the solution is Lipschitz and is smoothaway from the characteristic cone.     

关于对偶问题及对偶性质

本文考虑非可微凸规划的一个对偶问题，它使用目标函数的扰动函数的次微分及外法向量锥，它不同于已知结果．我们给出相应的对偶性质．