Banach空间中的时滞积分微分方程数值方法及其牛顿迭代解的存在唯一性

该文分析了扩展的一般线性方法关于Banach空间中一类时滞积分微分方程数值解的可解性,给出了其方法的解的存在唯一性判据,并探讨了其Newton迭代解的性态.所获结果可应用于扩展的Runge-Kutta方法和扩展的线性多步方法等.     

三人模糊联盟合作博弈的最小核心解

研究了联盟是模糊的合作博弈.利用多维线性扩展的方法定义了模糊联盟最小核心解,并推导出三人模糊联盟合作博弈最小核心的计算公式.研究结果发现,多维线性扩展的模糊联盟合作博弈最小核心解是对清晰联盟合作博弈最小核心解的扩展.最后给出三人模糊联盟合作博弈的一个具体事例,证明了此方法的有效性和适用性.     

基于多维线性扩展的模糊联盟合作对策tau值性质与计算方法

研究模糊联盟合作对策tau值的计算方法及其性质. 利用多维线性扩展方法定义了模糊联盟合作对策的tau值, 证明了其存在性、唯一性等性质, 并推导出基于多维线性扩展凸模糊联盟合作对策tau值的计算公式. 研究结果发现, 基于多维线性扩展的模糊联盟合作对策tau值是对清晰联盟合作对策tau值的扩展, 而清晰联盟合作对策tau值仅是其特例. 特别地, 对于凸模糊联盟合作对策, 利用其tau值计算公式, 可进一步简化求解过程.     

F初始状态下一阶微分方程组的数值解法

本运用模糊数的扩展运算,给出了一阶微分方程组（常系数或变系数,线性或非线性系）当其初始状态具有模糊不确定性,用模糊仿真原理求数值解的方法。     

基于多维线性扩展的模糊联盟合作对策τ值性质与计算方法

研究模糊联盟合作对策τ值的计算方法及其性质.利用多维线性扩展方法定义了模糊联盟合作对策的τ值,证明了其存在性、唯一性等性质,并推导出基于多维线性扩展凸模糊联盟合作对策τ值的计算公式.研究结果发现,基于多维线性扩展的模糊联盟合作对策τ值是对清晰联盟合作对策τ值的扩展,而清晰联盟合作对策τ值仅是其特例,特别地,对于凸模糊联盟合作对策,利用其τ值计算公式,可进一步简化求解过程.     

线性互补问题均衡解的存在形式与识别方法

研究了线性互补问题均衡解的存在形式与判定方法,给出了线性互补问题有解的充要条件,得到了带有几类特殊系数矩阵的线性互补问题的解的性质.在此基础上设计了求解线性互补问题均衡解的直接算法.     

中立型延迟微分方程一般线性方法的非线性稳定性

本文研究一类非线性中立型延迟微分方程一般线性方法的数值稳定性.证明了一般线性方法为(k,p,O)-代数稳定时,在一定的约束条件下,其数值解保持微分方程理论解的稳定性质,特别是证明了在约束网格情形代数靛的-般线性方法能无条件保持解析解的稳定性.     

非预解形式线性微分方程的解

通过几个实例给出解非预解形式线性微分方程的一般方法,并讨论了预解形式的线性微分方程与非预解形式的线性微分方程解集的差别.     

基于时间尺度的中立型时滞细胞神经网络概周期解的动态特征研究

在时间尺度上,通过使用线性动力方程的指数二分法、不动点理论和微积分理论,研究带有泄漏项的中立型时滞细胞神经网络模型,获得了一些使其概周期解存在和全局指数稳定的充分条件,并将以前的结论在时间尺度上做了扩展.     

Jacobi-Davidson方法中的修正方程和对应的精化方法

Jacobi-Davidson方法的核心之一是求解用以合理扩展投影子空间的线性修正方程组,众多文献均认为该方程是自然有解的.本文详细研究了修正方程,证明它可能无解,并给出了解存在的条件.同时,为克服近似特征向量的可能不收敛性,提出了精化的Jacobi-Davidson方法,建立了对应的修正方程.     

Fundamental solutions of uniform loads over triangular elements in a three-dimensional piezoelectric medium

In this paper, fundamental solutions of uniform loads over triangular elements in an infinite transversely isotropic piezoelectric three-dimensional space are derived. The triangle element can be parallel or vertical to the plane of isotropy and the uniform load can be mechanical and electric types, oriented in an arbitrary orientation. The solutions are expressed simply as a linear combination of three kinds of elementary functions – linear, trigonometric and logarithm functions. Three methods of superposition are employed to verify the obtained fundamental solutions. Numerical examples are also presented for the extended displacements and stresses induced by both mechanical and electric loads on the vertical and horizontal triangles.     

Extending and relating different approaches for solving fuzzy quadratic problems

Quadratic programming problems are applied in an increasing variety of practical fields. As ambiguity and vagueness are natural and ever-present in real-life situations requiring solutions, it makes perfect sense to attempt to address them using fuzzy quadratic programming problems. This work presents two methods used to solve linear problems with uncertainties in the set of constraints, which are extended in order to solve fuzzy quadratic programming problems. Also, a new quadratic parametric method is proposed and it is shown that this proposal contains all optimal solutions obtained by the extended approaches with their satisfaction levels. A few numerical examples are presented to illustrate the proposed method.     

Stackelberg solutions for fuzzy random two-level linear programming through probability maximization with possibility

This paper considers Stackelberg solutions for decision making problems in hierarchical organizations under fuzzy random environments. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced into the formulated fuzzy random two-level linear programming problems. On the basis of the possibility and necessity measures that each objective function fulfills the corresponding fuzzy goal, together with the introduction of probability maximization criterion in stochastic programming, we propose new two-level fuzzy random decision making models which maximize the probabilities that the degrees of possibility and necessity are greater than or equal to certain values. Through the proposed models, it is shown that the original two-level linear programming problems with fuzzy random variables can be transformed into deterministic two-level linear fractional programming problems. For the transformed problems, extended concepts of Stackelberg solutions are defined and computational methods are also presented. A numerical example is provided to illustrate the proposed methods.     

A simplex algorithm for piecewise-linear programming II: Finiteness,feasibility and degeneracy

The simplex method for linear programming can be extended to permit the minimization of any convex separable piecewise-linear objective, subject to linear constraints. Part I of this paper has developed a general and direct simplex algorithm for piecewise-linear programming, under convenient assumptions that guarantee a finite number of basic solutions, existence of basic feasible solutions, and nondegeneracy of all such solutions. Part II now shows how these assumptions can be weakened so that they pose no obstacle to effective use of the piecewise-linear simplex algorithm. The theory of piecewise-linear programming is thereby extended, and numerous features of linear programming are generalized or are seen in a new light. An analysis of the algorithm's computational requirements and a survey of applications will be presented in Part III.This research has been supported in part by the National Science Foundation under grant DMS-8217261.     

Linear difference equations mod 2 with applications to nonlinear difference equations1

Known results for linear difference equations mod 2 with T-periodic solutions are extended and compiled for applications to the semicycle analysis of nonlinear difference equations. For the calculation of T, four methods are presented. A further application concerns rational functions in the field of integers mod 2.     

The Bäcklund transformations and abundant explicit exact solutions for the AKNS–SWW equation

The Bäcklund transformations and abundant explicit exact solutions to the AKNS shallow water wave equation are obtained by combining the extended homogeneous balance method with the extended hyperbolic function method. The solutions obtained admit of multiple arbitrary parameters. These solutions include (a) a compound of the rational fractional function and a linear function, (b) a compound of solitary wave solution and a linear function, (c) a compound of the singular travelling wave solutions and a linear function, and (d) a compound of the periodic wave solutions of triangle function and a linear function. In special cases, we can obtain a series of soliton solutions, singular travelling wave solutions, periodic travelling wave solutions, and rational fractional function solution. In addition to re-deriving some known solutions in a systematic way, some brand-new exact solutions are also established.     

Fuzzy costs in quadratic programming problems

Although quadratic programming problems are a special class of nonlinear programming, they can also be seen as general linear programming problems. These quadratic problems are of the utmost importance in an increasing variety of practical fields. As, in addition, ambiguity and vagueness are natural and ever-present in real-life situations requiring operative solutions, it makes perfect sense to address them using fuzzy concepts formulated as quadratic programming problems with uncertainty, i.e., as Fuzzy Quadratic Programming problems. This work proposes two novel fuzzy-sets-based methods to solve a particular class of Fuzzy Quadratic Programming problems which have vagueness coefficients in the objective function. Moreover, two other linear approaches are extended to solve the quadratic case. Finally, it is shown that the solutions reached from the extended approaches may be obtained from two proposed parametric multiobjective approaches.     

Linear decision rules for cash-balancing and inventory problems

Optimal dynamic programming solutions for cash-balancing problems are compared with suboptimal linear decision rule solutions. It can be shown that cost deviations are not larger than 10% for small set-up costs. The comparison is extended to the pure inventory case for which similar results are obtained.     

Decomposition and Dynamic Cut Generation in Integer Linear Programming

Decomposition algorithms such as Lagrangian relaxation and Dantzig-Wolfe decomposition are well-known methods that can be used to generate bounds for mixed-integer linear programming problems. Traditionally, these methods have been viewed as distinct from polyhedral methods, in which bounds are obtained by dynamically generating valid inequalities to strengthen an initial linear programming relaxation. Recently, a number of authors have proposed methods for integrating dynamic cut generation with various decomposition methods to yield further improvement in computed bounds. In this paper, we describe a framework within which most of these methods can be viewed from a common theoretical perspective. We then discuss how the framework can be extended to obtain a decomposition-based separation technique we call decompose and cut. As a by-product, we describe how these methods can take advantage of the fact that solutions with known structure, such as those to a given relaxation, can frequently be separated much more easily than arbitrary real vectors.     

Boundary control problems for quasilinear systems of hyperbolic equations

For quasilinear systems of hyperbolic equations, the nonclassical boundary value problem of controlling solutions with the help of boundary conditions is considered. Previously, this problem was extensively studied in the case of the simplest hyperbolic equations, namely, the scalar wave equation and certain linear systems. The corresponding problem formulations and numerical solution algorithms are extended to nonlinear (quasilinear and conservative) systems of hyperbolic equations. Some numerical (grid-characteristic) methods are considered that were previously used to solve the above problems. They include explicit and implicit conservative difference schemes on compact stencils that are linearizations of Godunov’s method. The numerical algorithms and methods are tested as applied to well-known linear examples.