一些组合地图新算法的实现

本文主要讨论组合地图列举问题.刘的一部专著中提出了一个判定两个地图是否同构的算法.该算法的时间复杂度为O(m2),其中m为下图的规模.在此基础上,本文给出一个用于地图列举以及进而计算任意连通下图的地图亏格分布的通用算法.本文所得结果比之前文献中所给结果更优.     

运用新课程的理念提高数学复习课的课堂效率

如何提高数学复习课的教学效率?这是当前数学教学中值得研究的问题."复习",如果只是基础知识的简单罗列,难免使学生厌倦;如果只是习题解法的演示,又会令学生深陷题海无所适从……,对复习课的目标和功能的认识,决定了复习课内容的选择、教学的模式和教学的效果.     

最小填充问题的可分解性

起源于稀疏矩阵计算和其它应用领域的图G的最小填充问题是在图G中寻求一个内含边数最小的边集F使得G F是弦图.这里最小值|F|称为图G的填充数,表示为f(G).作为NP-困难问题,该问题的降维性质已被研究,其中包括它的可分解性.基本的可分解定理是:如果图G的一个点割集S是一个团,则G经由S是可分解的.作为推广,如果S是一个"近似"团(即只有极少数边丢失的团),则G经由S是可分解的.本文首先给出基本分解定理的另外一个推广:如果S是G的一个极小点割集且G-S含有至少|S|个分支,则G经由S是可分解的;其次,给出了这个新推广定理的一些应用.     

自由群的直积的检验元素的注记

本文研究了自由群的直积的检验元素,通过对直积的自同态的分解,得到了直积中的元素为检验元素的充分必要条件,改进了O'neill和Turner的结果.此外,构造了两类具体的检验元素.     

一个基于复制变异准则的蛋白质作用网络的构建模型

本文主要根据生物学的复制和变异的基本原理,提出了具有反偏爱复制特性的一个蛋白质作用网络的新的演化模型.通过计算,发现所得的网络与实测的蛋白质作用网络的某些拓扑性质能够很好的吻合.生成的网络不仅是稀疏的,而且具有小世界性和无标度(scale-free)性质.     

例谈题目“提示”信息的有效利用

解题的一个重要环节是"审题",审题的目的就是希望从题目中提取有用的解题信息.一些创新性的试题,常在题干中设置了明显的"提示"信息,而对于解题者而言,如何利用好题目的这些"提示"信息,将是成功解题的关键.     

在向量解题中强化学生的解题意识

向量在近几年高考中越来越重要,其工具性作用已渗透以数学的各个分支.解答题中主要是以向量为载体的综合问题,体现向量"搭台",其他知识"唱戏"的特点.近年来高考中小题综合化的特点,已被大家所共识.选填题中对向量知识的考查更加灵活多变,对学生能力要求较高,可是只要是题型新颖一点或能力要求高点的题就成为学生得分的"事故多发地带".……     

员工配置资源行为的优化研究:自适应组织的视角

组织目标必须通过约束体系规范员工行为得以实现.进行组织约束下员工行为的定量研究,这对保证组织健康稳定发展非常必要.员工自身适应组织目标,服从组织的约束体系,配置好自有的资源,使得自身行为得以优化的研究较少.本文简要回顾了经济学理论、组织行为学、人力资源管理等方面对员工配置资源行为优化的研究及应用.界定了组织资源,并将其分为三种类型.在约束体系给出的基础上,将组织对员工行为的控制、要求或激励转为员工在之上或之下的运行约束;认为约束体系具有离散、悬河效应的特点;得出了评价组织约束体系的两种算法.讨论了员工资源及行为.尝试构造了基于员工适应组织约束下,员工的多目标、非线性,既有连续又有离散约束条件的配置资源行为优化的定量模型,并在基于员工利益最大化的前提下,对模型求解最优解的几种情况进行了研究.希望能够填补员工自身适应组织目标,行为优化定量模型这方面研究的空白.     

简议数列综合题的求解策略

数列在中学数学中占有极为重要的地位,它不仅广泛应用于实际,而且还融于高中数学的各个章节构成精彩纷呈的综合题,因此数列的综合题是高考中久考不衰的热点,且常考常新,并以此为压轴题者也屡见不鲜.本文拟就数列的几类主要综合题求解的基本策略简议如下:……     

让我们的课堂充满探索与交流——一个定值问题的诱思教学实录

新课程倡导"数学学习过程应该表现为一个探索与交流的过程--在探索的过程中形成自己对数学的理解,并在与他人的交流过程中逐渐完善自己的想法."     

搭接焊缝内的准确应力分布

本文给出了受弯矩M作用的搭接焊缝内的准确应力分布,结合前文[1]所给出的受集中力P作用的搭接焊缝内的应力分布准确解,使搭接焊缝的设计可以建立在准确的理论解基础之上。     

Optimal design by a homotopy method

An optimal design problem is formulated as a system of nonlinear equations rather than the extremum of a functional. Based on a new homotopy method, an algorithm is developed for solving the nonlinear system which is globally convergent with probability one. Since no convexity is required, the nonlinear system may have more than one solution. The algorithm will produce an optimal design solution for a given starting point. For most engineering problems, the initial prototype design is already well conceived and close to the global optimal solution. Such a starting point usually leads to the optimal design by the homotopy method, even though Newton's method may diverge from that starting point. A simple example is given.     

A simultaneous bus route design and frequency setting problem for Tin Shui Wai,Hong Kong

A bus network design problem for Tin Shui Wai, a suburban residential area in Hong Kong, is investigated, which considers the bus services from the origins inside this suburban area to the destinations in the urban areas. The problem aims to improve the existing bus services by reducing the number of transfers and the total travel time of the users. This has been achieved by the proposed integrated solution method which can solve the route design and frequency setting problems simultaneously. In the proposed solution method, a genetic algorithm, which tackles the route design problem, is hybridized with a neighborhood search heuristic, which tackles the frequency setting problem. A new solution representation scheme and specific genetic operators are developed so that the genetic algorithm can search all possible route structures, rather than selecting routes from the predefined set. To avoid premature convergence, a diversity control mechanism is incorporated in the solution method based on a new definition of hamming distance. To illustrate the robustness and quality of solutions obtained, computational experiments are performed based on 1000 perturbed demand matrices. The t-test results show that the design obtained by the proposed solution method is robust under demand uncertainty, and the design is better than both the current design and the design obtained by solving the route design problem and the frequency setting problem sequentially. Compared with the current bus network design, the proposed method can generate a design which can simultaneously reduce the number of transfers and total travel time at least by 20.9% and 22.7% respectively. Numerical studies are also performed to illustrate the effectiveness of the diversity control mechanism introduced and the effects of weights on the two objective values.     

梁的弹性最优设计*

本文根据最小余能原理建立了弹性梁最优强度设计问题的数学形式,它为一个具有等式和不等式约束的泛函极值问题。进而应用拉格朗日乘子法得到了极值的必要条件,并由此导出最优解所必须满足的一组关系式,这组关系式可以用来检验等强度设计或任一可行弹性设计的最优性。当等强度设计不是最优设计时文中还建议了一个迭代寻优的数值解法。     

Parametric optimal design

Two algorithms for the solution of a parametric optimal design problem are developed and applied to example problems from diverse fields, such as finite allocation problems, optimal design of dynamical systems, and Chebyshev approximation. Sensitivity analysis gives rise to a first-order feedback law, which contains a compensating term for any error in the nominal solution, as well as sensitivity of the solution with respect to design parameters. The compensating term, when used alone, leads to a new second-order method of maximization for a linearly-constrained nonlinear programming problem.This paper is based on the PhD Thesis of the first author.     

逐步区间删失Weibull分布的Bayesian稳健设计

逐步区间删失是获取高可靠性产品相关信息的一种重要方法.文章研究了产品寿命服从Weibull分布,带有随机移除逐步区间删失寿命试验的最优设计问题.采用极大似然方法获取模型参数的估计及其信息矩阵.利用Bayesian方法处理模型参数未知情况下设计准则对模型参数的依赖问题,获得了模型参数估计的Bayesian稳健设计准则.在考虑试验费用有限制的条件下,给出了获得最优稳健设计非线性混合整数算法.同时对先验选取及约束参数设定的敏感性做了分析.数值结果表明文章提出的方法是有效可行的.     

AN APPROACH TO DESIGN OBSERVER FOR A CLASS OF DISCRETE CONTROL SYSTEMS WITH TIME-DELAY

The design of functional observer for a class of discrete systems with time-delay is concerned. The solution to Sylvester function is given. An improved method for the functional observer design is proposed by the condition of linear matrix inequality. In the end,an example is given to illustrate the feasibility of the method.     

单源模糊数的模糊随机有限元方程的解法

在工程实际情况下,有时候可以利用单源模糊数的运算法则,来减少模糊随机有限元方程的计算量.通过推导证明,其计算量仅相当于求解普通的随机有限元方程.为了更好地适应现代工程设计的需要,还提出用模糊随机有限元方程计算结果求结构模糊失效概率的近似方法.     

A dual local search framework for combinatorial optimization problems with TSP application

In practice, solving realistically sized combinatorial optimization problems to optimality is often too time-consuming to be affordable; therefore, heuristics are typically implemented within most applications software. A specific category of heuristics has attracted considerable attention, namely local search methods. Most local search methods are primal in nature; that is, they start the search with a feasible solution and explore the feasible space for better feasible solutions. In this research, we propose a dual local search method and customize it to solve the traveling salesman problem (TSP); that is, a search method that starts with an infeasible solution, explores the dual space—each time reducing infeasibility, and lands in the primal space to deliver a feasible solution. The proposed design aims to replicate the designs of optimal solution methodologies in a heuristic way. To be more specific, we solve a combinatorial relaxation of a TSP formulation, design a neighborhood structure to repair such an infeasible starting solution, and improve components of intermediate dual solutions locally. Sample-based evidence along with statistically significant t-tests support the superiority of this dual design compared to its primal design counterpart.     

Integrated supply chain planning under uncertainty using an improved stochastic approach

This paper proposes an integrated model and a modified solution method for solving supply chain network design problems under uncertainty. The stochastic supply chain network design model is provided as a two-stage stochastic program where the two stages in the decision-making process correspond to the strategic and tactical decisions. The uncertainties are mostly found in the tactical stage because most tactical parameters are not fully known when the strategic decisions have to be made. The main uncertain parameters are the operational costs, the customer demand and capacity of the facilities. In the improved solution method, the sample average approximation technique is integrated with the accelerated Benders’ decomposition approach to improvement of the mixed integer linear programming solution phase. The surrogate constraints method will be utilized to acceleration of the decomposition algorithm. A computational study on randomly generated data sets is presented to highlight the efficiency of the proposed solution method. The computational results show that the modified sample average approximation method effectively expedites the computational procedure in comparison with the original approach.