军械物资供应系统中的多目标运输问题

建立了军械物资运输问题的模糊多目标线性规划模型，运用一种解模糊函数和一种基于线性隶属函数的模糊规划算法求其调和解。方法简便、有效，可为部队军械物资的运输供应高效化提供科学依据。     

通过一道最值问题的求解研究其命制原理

对于一道最值问题,分析求解思路,总结了此类问题的两种解法,探究了此类问题的命制原理.     

数学解题中的优化假设举例

在解题教学中注重优化假设的数学思想与方法 ,探索解题的思路和规律 ,能培养学生的直觉思维、发散思维和想象力 .在各类的数学问题中 ,有许多的题目可由条件和结论的特殊性与一般性的辩证关系 ,采用优化假设思想 ,创设新的解题思路 ,优化解题过程 .优化假设通过恰当的假设处理问题 ,优化出新的解题方法与思路 .优化假设是科学的发现、创造的方法之一 ,在优化假设过程中 ,体现了假设、猜想、优化等数学思想 ,渗透了数学其他的方法和思路 ,在高考和数学竞赛题中有许多数学问题能采用此方法给予解决 .1　假设条件特殊化优化解题思路一个命题成…     

对一道存在性问题的探讨

贵刊在2000年11月(下)发表的《先找后定一存在性问题的一种解法思路》一文,提出了有关存在性问题另一种解法思路,这种方法新颖、独特,但所选用的例1,在运用“先找后     

不同思路求解一道立体几何空间角问题

立体几何的空间角相关问题是高中数学的常考内容,其问题具有一定的难度和挑战,对学生的解题思路和知识储备都具有一定要求.掌握常见不同解答立体几何空间角问题的思路和方法,有助于提升解题效率.本文中主要从一道立体几何例题的不同求解思路着手,拓展解题策略和思考角度.     

城市垃圾收运系统中的车辆收运计划问题

将垃圾收运系统中收运小车一天的收运计划问题,分为停车场设在转运站或别处两种情况,以小车行走总距离最小为目标,分别构建了混合整数规划模型.接着提出问题的求解思路:当停车场设在转运站时,可以将问题转化为VRP问题求解;若停车场设在别处,在求解上一问题的基础上设计了最近回路节点插入法将停车场插入离其最近的回路节点即可.最后以实例验证了模型和求解思路的可行性和有效性.     

矩阵方程AX＝B的中心对称解及其最佳逼近

基于一种新的思路,本文将一类约束矩阵方程问题化为无约束矩阵方程问题,从而轻易地获得了简洁且满意的结果.     

例题教学中的"不讲"艺术

有一位教育家说过 :作为教师重要的是懂得什么该讲 ,什么不该讲 .这个看法是正确的 .这是改变讲风大盛的状况 ,优化课堂教学 ,提高教学效益的重要保证 .我们在例题教学中巧妙地运用“不讲”艺术 ,即设置问题解决的环境 ,让学生通过自主以及合作研究的途径加以解决 ,促使学生的主观能动性得到了充分发挥 ,有效地培养了解决实际问题的能力 .1　不讲路子 ,让学生在探索中学会思考解答数学问题的关键是思路 .教学中发现 ,老师直接传授给学生的思路 ,往往容易忘掉 ,碰到具体问题仍是束手无策 .而经过学生自身思维活动得到的思路 ,容易在大脑信息…     

中学数学解题中的思维定势例说

中学生在数学解题思维过程中普遍存在各式各样的思维定势,这些思维定势的特点是：总是按照某种习惯的思路和方法去分析、解决问题,当这种习惯思路与实际问题的解决途径一致时,能产生思维定势的正迁移,有利于问题的顺利解决;反之,若这种习惯思路与实际问题的解决途径相悖或不尽相同时,就会产生思维定势的负迁移,使学生的思路陷入误区．所以,在平时的数学学习过程中,注意突破数学思维定势的束缚就显得尤为重要．     

先定再动,分层突破

在高三复习时,经常遇到含有多个参变量或者多个动点的最值问题,主要以填空题的形式出现,难度较大.这类问题属于学生感觉“不太顺手”的问题,遇到时往往不敢下手,总认为找不准问题的切入点,理不清思路,平时总结的解题经验也用不上来.这类问题的常用思路是先把其中的某个变量视为定量,将问题分层研究,寻求突破.本文将结合几道典型例题,呈现这类问题的常见载体,谈谈如何先定再动,找出题目思路,供大家参考.正如数学大师波利亚在谈审读题意寻找解题思路时说：“如果你不能解决所提出的问题,你能不能想出一个更容易着手的有关问题？你能不能从已知数据导出某些有用的东西？”     

To solving problems of algebra for two-parameter matrices. VII

The paper discusses the method of rank factorization for solving spectral problems for two-parameter polynomial matrices. New forms of rank factorization, which are computed using unimodular matrices only, are suggested. Applications of these factorizations to solving spectral problems for two-parameter polynomial matrices of both general and special forms are presented. In particular, matrices free of the singular spectrum are considered. Conditions sufficient for a matrix to be free of the singular spectrum and also conditions sufficient for a basis matrix of the null-space to have neither the finite regular nor the finite singular spectrum are provided. Bibliography: 3 titles.     

A Heuristic for Vehicle Routeing and Depot Staffing

This paper discusses the approach taken in solving a specific depot staffing and routeing problem. The problem differs from the normal routeing exercise in that the route passes through a number of outlets where monetary collections are made. Owing to the ever increasing risks of carrying money there is a requirement for the money to be deposited at banks along the route. Consequently, the more traditional routeing and scheduling methodologies and software are not easily applied to the problem. This paper details the approach used and highlights some of the good points and the pitfalls in the proposed solution.     

关于函数一致连续的研究性教学

详细介绍函数一致连续的教学模式：先通过几何直观,使学生理解这一概念,随之引导学生认真学习一致连续在积分计算、函数项级数以及含参变量积分问题中的应用,使学生加深对这一概念的认识．同时就这一内容设置一系列探索性问题,进行研究性教学,以培养学生独立思考和解决问题的能力．     

Decision making in a fuzzy environment and its application to multicriteria power engineering problems

This paper presents results of research into the use of the Bellman–Zadeh approach to decision making in a fuzzy environment for solving multicriteria optimization problems. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. The use of the Bellman–Zadeh approach has served as a basis for solving a problem of multicriteria allocation of resources (or their shortages) and developing a corresponding adaptive interactive decision making system (AIDMS1). AIDMS1 includes procedures for considering linguistic variables to reflect conditions that are difficult to formalize as well as procedures for constructing and correcting vectors of importance factors for goals. The use of these procedures permits one to realize an adaptive approach to processing information of a decision maker to provide successive improvment in solution quality. The results of the paper are universally applicable and are already being used to solve power engineering problems. It is illustrated by considering problems of multicriteria power and energy shortage allocation and multicriteria power system operation.     

Performance bounds for hierarchical systems under partial dynamic information

This paper discusses a general approach to obtain optimum performance bounds for (N+1)-person deterministic decision problems,N+1>2, with several levels of hierarchy and under partial dynamic information. Both cooperative and noncooperative modes of decision making are considered at the lower levels of hierarchy; in each case, it is shown that the optimum performance of the decision maker at the top of the hierarchy can be obtained by solving a sequence of open-loop (static) optimization problems. A numerical example included in the paper illustrates the general approach.     

A Reduced Basis Approach for Some Weakly Stochastic Multiscale Problems

In this paper,a multiscale problem arising in material science is considered.The problem involves a random coefficient which is assumed to be a perturbation of a deterministic coefficient,in a sense made precisely in the body of the text.The homogenized limit is then computed by using a perturbation approach.This computation requires repeatedly solving a corrector-like equation for various configurations of the material.For this purpose,the reduced basis approach is employed and adapted to the specific context.The authors perform numerical tests that demonstrate the efficiency of the approach.     

Solving linear programs with multiple right-hand sides: Pricing and ordering schemes

This paper discusses the use of different pricing and ordering schemes when solving many linear programs that differ only in the right-hand sides. This is done in a setting of what has become known as bunching or trickling down. The idea is to collect (bunch) all right-hand sides that have the same optimal basis, and to organize the search for these bases efficiently. We demonstrate that the choice of pricing rule is indeed very important, but we were not able to make conclusions regarding ordering schemes. Numerical results are given.     

Differential-Algebraic Approach to Linear Programming

This paper presents a differential-algebraic approach for solving linear programming problems. The paper shows that the differential-algebraic approach is guaranteed to generate optimal solutions to linear programming problems with a superexponential convergence rate. The paper also shows that the path-following interior-point methods for solving linear programming problems can be viewed as a special case of the differential-algebraic approach. The results in this paper demonstrate that the proposed approach provides a promising alternative for solving linear programming problems.     

Parametric Interval Linear Solver

IntervalComputations‘LinearSystems’ is a Mathematica package supporting tools for solving parametric and nonparametric linear systems involving uncertainties. It includes a variety of functions, implementing different interval techniques, that help in producing sharp and rigorous results in validated interval arithmetic. The package is designed to be easy to use, versatile, to provide a necessary background for further exploration, comparisons and prototyping, and to provide some indispensable tools for solving parametric interval linear systems. This paper presents the functionality, provided by the current version of the package, and briefly discusses the underlying methodology. A new hybrid approach for sharp parametric enclosures, that combines parametric residual iteration, exact bounds, based on monotonicity properties, and refinement by interval subdivision, is outlined.