泛灰线性方程组的白化求解方法与应用

在概述泛灰数的概念与泛灰行列式运算的基础上 ,介绍了泛灰线性方法程组的泛灰解法 .由于泛灰行列式运算复杂 ,根据泛灰的性质 ,提出了泛灰线性方程组的白化解法 .理论证明这种求解方法的正确性 .并给出了算例 .     

灰色TSP问题的研究

在确定型TSP问题的基础上,融合灰色系统的思想提出了灰色TSP问题,构建了灰色TSP问题的动态规划模型,结合动态规划方法利用可能度及排序方法给出了求解灰色TSP问题的算法,并结合数值实例,对算法进行了说明.     

灰色双矩阵博弈模型及其均衡解

在支付矩阵和约束条件都是灰色的情况下,给出灰双矩阵博弈的一般形式,并且定义了灰双矩阵博弈的均衡解,证明灰双矩阵博弈的均衡解可由求解一个非线性规划问题得到.     

自乘零化灰阵有关定理及证明的改进

本文对文［１］中有关自乘零化灰阵的定理及其证明给出了改进，并得出了传递矩阵的计算方法     

灰色数学的新分支——灰群

给出灰子半群、强灰子半群、灰子幺半群、强灰子幺半群、灰子群和强灰子群的定义和有关定理，在此基础上，讨论灰子群一模糊子群、一般子群的关系。并且研究了灰正规子群。     

灰色系统理论中的有界灰矩阵

本文详细地讨论了灰色理论中的有界灰矩阵的运算，给出了若干基本性质，指出有界灰矩阵的定义和运算在形式上是实矩阵相应概念的直接推广，但在运算性质上有极大差异，修正了文献「３」中的几个错误。     

含灰气体激波沿平壁传播时诱导的边界层流动*

本文研究合灰气体激波沿平直壁面传播过程中在壁面附近形成的层流边界层流动。我们依照双连续介质双向耦合模型处理含灰气体激波的波后流动及其诱导的边界层问题,控制方程采用有限差分方法数值求解,给出了激波下游两相流场特性并考虑了含灰气体激波的松弛结构对边界层流动的影响。     

灰拓扑空间的连通性

研究灰拓扑空间的连通性,给出了灰拓扑空间连通定义和有关定理,并且研究了灰连通分支。     

求解变系数非齐次亥姆霍茨方程的边界单元法

本文利用拉普拉斯方程的基本解作为权函数，给出求解交系数非齐次亥姆霍茨方程的迭代格式，进而得到求解这类方程的边界元迭代法．文中给出了算例．最后，把本文给出的边界元迭代法与作者早些时候提出的边界元耦合法进行了比较．     

基于灰色系统的模糊综合评判在产险公司偿付能力评价中的应用

本文将灰色系统中的灰关联分析理论和模糊数学中模糊综合评判法引入保险公司偿付能力的综合评价排序中。通过案例分析，对2005年我国八家主要财产保险公司（以下简称产险公司）的偿付能力作了判断比较，给出了综合排序。     

Nash Equilibria for the Multiobjective Control of Linear Partial Differential Equations

This article is concerned with the numerical solution of multiobjective control problems associated with linear partial differential equations. More precisely, for such problems, we look for the Nash equilibrium, which is the solution to a noncooperative game. First, we study the continuous case. Then, to compute the solution of the problem, we combine finite-difference methods for the time discretization, finite-element methods for the space discretization, and conjugate-gradient algorithms for the iterative solution of the discrete control problems. Finally, we apply the above methodology to the solution of several tests problems.     

Sensitivity Analysis for Vector Equilibrium Problems under Functional Perturbations

This article is devoted to sensitivity analysis for vector equilibrium problems under functional perturbations. We show that the solution mapping is upper semicontinuous. Sufficient conditions for lower semicontinuity and Hölder continuity of the solution mapping are established. Finally, we derive some corollaries for special cases of vector equilibrium problems as examples.     

A computational comparison of some non-linear programs

This article deals mainly with a comparison of certain computational techniques used for the solution of non-linear constrained mathematical programming problems.     

A new method to build confidence regions for solutions of stochastic variational inequalities

Stochastic variational inequalities model a large class of equilibrium problems subject to data uncertainty. The true solution to such a problem is usually estimated by a solution to its sample average approximation (SAA) problem. This article proposed a new method to build asymptotically exact confidence regions for the true solution that are computable from the SAA solution.     

Dynamic pickup and delivery problems

In the last decade, there has been an increasing body of research in dynamic vehicle routing problems. This article surveys the subclass of those problems called dynamic pickup and delivery problems, in which objects or people have to be collected and delivered in real-time. It discusses some general issues as well as solution strategies.     

Pointwise Control of the Burgers Equation and Related Nash Equilibrium Problems: Computational Approach

This article is concerned with the numerical solution of multiobjective control problems associated with nonlinear partial differential equations and more precisely the Burgers equation. For this kind of problems, we look for the Nash equilibrium, which is the solution to a noncooperative game. To compute the solution of the problem, we use a combination of finite-difference methods for the time discretization, finite-element methods for the space discretization, and a quasi-Newton BFGS algorithm for the iterative solution of the discrete control problem. Finally, we apply the above methodology to the solution of several tests problems. To be able to compare our results with existing results in the literature, we discuss first a single-objective control problem, already investigated by other authors. Finally, we discuss the multiobjective case.     

A generalized conditional gradient method and its connection to an iterative shrinkage method

This article combines techniques from two fields of applied mathematics: optimization theory and inverse problems. We investigate a generalized conditional gradient method and its connection to an iterative shrinkage method, which has been recently proposed for solving inverse problems. The iterative shrinkage method aims at the solution of non-quadratic minimization problems where the solution is expected to have a sparse representation in a known basis. We show that it can be interpreted as a generalized conditional gradient method. We prove the convergence of this generalized method for general class of functionals, which includes non-convex functionals. This also gives a deeper understanding of the iterative shrinkage method.     

Case-based reasoning for repetitive combinatorial optimization problems, part I: Framework

This article presents a case-based reasoning approach for the development of learning heuristics for solving repetitive operations research problems. We first define the subset of problems we will consider in this work: repetitive combinatorial optimization problems. We then present several general forms that can be used to select previously solved problems that might aid in the solution of the current problem, and several different techniques for actually using this information to derive a solution for the current problem. We describe both fixed forms and forms that have the ability to change as we solve more problems. A simple example for the 0–1 knapsack problem is presented.     

一类二阶拟线性方程边值问题解的存在性

文献[1]讨论了二阶拟线性常微分方程两点边值问题的 正解的存在性,但它限制了0<α<1<β.本文则对方程 证明了正解的存在性.     

Modified equation based mesh adaptation algorithm for evolutionary scalar partial differential equations

It is well known that on uniform mesh classical higher order schemes for evolutionary problems yield an oscillatory approximation of the solution containing discontinuity or boundary layers. In this article, an entirely new approach for constructing locally adaptive mesh is given to compute nonoscillatory solution by representative “second” order schemes. This is done using modified equation analysis and a notion of data dependent stability of schemes to identify the solution regions for local mesh adaptation. The proposed algorithm is applied on scalar problems to compute the solution with discontinuity or boundary layer. Presented numerical results show underlying second order schemes approximate discontinuities and boundary layers without spurious oscillations.