关于Whitney和Tutte猜想

ｗｈｉｔｎｅｙ和Ｔｕｔｔｅ把平面四色问题化为只与圈上的４染色集有关的问题来研究，从而探讨四色问题的理论证明；提出了一个蕴含着四色定理的猜想。本文研究开集的组合不变性，从而证明Ｗｈｉｔｎｅｙ和Ｔｕｔｔｅ的猜想不成立。     

对称迭层矩形板的平面应力分析

常用的对称迭层板为各向异性板．根据平面应力问题的基本方程精确地用应力函数解法求得了各向异性板的一般解析解．推导出平面内应力和位移的一般公式,其中积分常数由边界条件来决定．一般解包括三角函数和双曲函数组成的解,它能满足4个边为任意边界条件的问题．还有代数多项式解,它能满足4个角的边界条件．因此一般解可用以求解任意边界条件下的平面应力问题．以4边承受均匀法向和切向载荷以及非均匀法向载荷的对称迭层方板为例,进行了计算和分析．     

一类非线性电报方程的多重周期解

本文讨论一类非线性电报方程的周期－Ｄｉｒｉｃｈｌｅｔ边值问题解的多重性，在非线性项满足一定渐近线性条件的情况下，利用Ｌｅｒａｙ－Ｓｃｈａｕｄｅｒ度数理论得到了一个关于此类电报方程的多解定理。     

Optimization over the efficient set: Four special cases

Recently, researchers and practitioners have been increasingly interested in the problem (P) of maximizing a linear function over the efficient set of a multiple objective linear program. Problem (P) is generally a difficult global optimization problem which requires numerically intensive procedures for its solution. In this paper, simple linear programming procedures are described for detecting and solving four special cases of problem (P). When solving instances of problem (P), these procedures can be used as screening devices to detect and solve these four special cases.     

Comparison of metaheuristic algorithms for Examination Timetabling Problem

SA, TS, GA and ACS are four of the main algorithms for solving challenging problems of intelligent systems. In this paper we consider Examination Timetabling Problem that is a common problem for all universities and institutions of higher education. There are many methods to solve this problem, In this paper we use Simulated Annealing, Tabu Search, Genetic Algorithm and Ant Colony System in their basic frameworks for solving this problem and compare results of them with each other.     

Global solution of optimization problems with signomial parts

In this paper a new approach for the global solution of nonconvex MINLP (Mixed Integer NonLinear Programming) problems that contain signomial (generalized geometric) expressions is proposed and illustrated. By applying different variable transformation techniques and a discretization scheme a lower bounding convex MINLP problem can be derived. The convexified MINLP problem can be solved with standard methods. The key element in this approach is that all transformations are applied termwise. In this way all convex parts of the problem are left unaffected by the transformations. The method is illustrated by four example problems.     

An extension result for the Landau-Lifshitz equation with Neumann boundary condition

We establish an extension result of existence and partial regularity for the nonzero Neumann initial-boundary value problem of the Landau-Lifshitz equation with nonpositive anisotropy constants in thre...     

The nurse rostering problem: A critical appraisal of the problem structure

This paper is concerned with the problem of nurse rostering within hospitals. We analyse a class of four benchmark instances from the nurse rostering literature to provide insight into the nature of the problem. By highlighting the structure of the problem we are able to reduce the relevant solution space. A mixed integer linear programme is then able to find optimal solutions to all four instances of this class of benchmark problems, each within half an hour. Our second contribution is to extend current mathematical approaches to nurse rostering to take better account of the practical considerations. We provide a methodology for handling rostering constraints and preferences arising from the continuity from one scheduling period to the next.     

热传导型半导体瞬态问题的迎风有限体积元方法

半导体瞬态问题的数学模型是由四个方程组成的非线性偏微分方程组的初边值问题所决定．其中电子浓度和空穴浓度方程往往是对流占优扩散问题,普通的方法已不适用,为此本文用迎风格式处理对流项部分,提出一种全离散迎风有限体积元方法,并进行收敛性分析,在最一般的情况下得到了一阶精度L2模误差估计结果．     

Initial-boundary value problems for anisotropic Landau-Lifshitz equations in three or four space dimensions

In this paper, we will show the existence of partially regular solutions to the initial-boundary value problem for Landau-Lifshitz equations with nonpositive anisotropy constants in three or four space dimensions. The partial regularity is proved up to the boundary both for the Dirichlet problem and for the Neumann problem. In addition, for the Neumann case, a generalized stability condition which ensures the partial regularity is given. For equations with positive or negative anisotropy coefficients, we will give two results of existence and uniqueness for the solutions corresponding to ground states.     

三维定常流Stokes问题的边界积分方程法

1.解的积分表示及变分公式 考虑如下Stokes方程的Dirichlet问题:设Ω是具有光滑边界Γ的单连通区域,Ω′=R~3-Ω。所求未知量是充满于Ω或Ω′的不可压缩粘性流体的流速u=(u_1,u_2,u_3)和压力p。这里v是运动粘性系数。 已经证明[Nedelec-Communication personnelle]:若u_0∈(H~(1/2)(Γ))~3,且满足     

Zolotarev's conformal mapping and Chebotarev's problem

Consider the Chebotarev problem of finding a continuum S in the complex plane including some given points such that the logarithmic capacity of S is minimal. In this paper, we give a complete solution of this problem for the case of three given points with the help of Zolotarev's conformal mapping using Jacobian elliptic and theta functions. Moreover, for four given points, some special cases can be treated.     

Local Convergence Behavior of Some Projection-Type Methods for Affine Variational Inequalities

In this paper, we study the local convergence behavior of four projection-type methods for the solution of the affine variational inequality (AVI) problem. It is shown that, if the sequence generated by one of the methods converges to a nondegenerate KKT point of the AVI problem, then after a finite number of iterations, some index sets in the dual variables at each iterative point coincide with the index set of the active constraints in the primal variables at the KKT point. As a consequence, we find that, after finitely many iterations, the four methods need not compute projections and their iterative equations are of reduced dimension.     

Investigation of polynomial algorithms for solving the three-index planar assignment problem

Under certain additional conditions imposed on the coefficients of the objective function in the three-index planar assignment problem, a large series of computational experiments aimed at the investigation of four polynomial algorithms for finding an asymptotically optimal solution of this problem is conducted.     

基于Solidarity值的河流水资源分配

河流水资源分配问题可以抽象为图限制下合作对策解的模型.基于图限制下合作对策的Solidarity值对参与者的收益分配进行分析,构造了Solidarity值的结构,给出了该值的分支有效性等四个性质,并利用这四个性质刻画了Solidarity值的唯一性.最后通过一个简单的实例,证明了河流水资源分配问题中,基于Solidarity值的收益分配比Myerson值更优.     

A new model for the asymmetric vehicle routing problem with simultaneous pickup and deliveries

The asymmetric vehicle routing problem with simultaneous pickup and deliveries is considered. This paper develops four new classes of valid inequalities for the problem. We generalize the idea of a no-good cut. Together, these help us solve 45-node randomly generated problem instances more efficiently. We report results on a set of benchmark instances in literature. In this set, we are able to show an order of magnitude improvement in computational times over currently published results in literature.     

Investigation of polynomial algorithms for solving the multicriteria three-index planar assignment problem

Under certain additional conditions imposed on the coefficients of the vector objective function in the three-index planar assignment problem, a large series of computational experiments aimed at the investigation of four polynomial algorithms for finding an asymptotically optimal solution of this problem is carried out.     

Multiple solutions for inhomogeneous critical semilinear elliptic problems

In this paper, we consider the existence of multiple positive solutions for an inhomogeneous critical semilinear elliptic problem. We show that the problem possesses at least four positive solutions.     

Clifford分析中多个未知函数向量的非线性边值问题

设fi（x），1≤i≤p为取值在实2n－1维代数An（R）上的函数．我们称F（x）＝（f1，f2，...，fp）为函数向量，而fi，1≤i≤p为向量F的分量，本文借助于向量值分析的思想，利用积分方程方法、Shauder不动点原理和压缩映射原理研究多个未知函数的函数向量F带位移又带共轭值的四元素非线性过值问题解的存在性和相应线性边值问题解的存在唯一性．     

The variable neighborhood search for the two machine flow shop problem with a passive prefetch

We consider the two machine flow shop scheduling problem with passive loading of the buffer on the second machine. To compute lower bounds for the global optimum, we present four integer linear programming formulations of the problem. Three local search methods with variable neighborhoods are developed for obtaining upper bounds. Some new large neighborhood is designed. Our methods use this neighborhood along with some other well-known neighborhoods. For computational experiments, we present a new class of test instances with known global optima. Computational results indicate a high efficiency of the proposed approach for the new class of instances as well as for other classes of instances of the problem.