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."     

Creep of polymer concrete in the nonlinear region

Two polyester-based polymer concretes with various volume content of diabase as an extender and aggregate are tested in creep under compression at different stress levels. The phenomenological and structural approaches are both used to analyze the experimental data. Common features of changes in the instantaneous and creep compliances are clarified, and a phenomenological creep model which accounts for the changes in the instantaneous compliance and in the retardation spectrum depending on the stress level is developed. It is shown that the model can be used to describe the experimental results of stress relaxation and creep under repeated loading. Modeling of the composite structure and subsequent solution of the optimization problem confirm the possibility of the existence of an interphase layer more compliant than the binder. A direct correlation between the interphase volume content and the instantaneous compliance of the composite is revealed. It is found that the distinction in nonlinearity of the viscoelastic behavior of the two polymer concretes under investigation can be due to the difference in their porosity. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000.) Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 147–164, 2000.     

Gaussian Versus Optimal Integration of Analytic Functions

We consider error estimates for optimal and Gaussian quadrature formulas if the integrand is analytic and bounded in a certain complex region. First, a simple technique for the derivation of lower bounds for the optimal error constants is presented. This method is applied to Szeg?-type weight functions and ellipses as regions of analyticity. In this situation, the error constants for the Gaussian formulas are close to the obtained lower bounds, which proves the quality of the Gaussian formulas and also of the lower bounds. In the sequel, different regions of analyticity are investigated. It turns out that almost exclusively for ellipses, the Gaussian formulas are near-optimal. For classes of simply connected regions of analyticity, which are additionally symmetric to the real axis, the asymptotic of the worst ratio between the error constants of the Gaussian formulas and the optimal error constants is calculated. As a by-product, we prove explicit lower bounds for the Christoffel-function for the constant weight function and arguments outside the interval of integration. September 7, 1995. Date revised: October 25, 1996.     

Variation of the structure and permeability of tensioned fiber layers during impregnation with a thermoplastic polymer melt

The influence of displacements of tensioned fibers on the impregnation of fibrous layers with a polymer melt and on the final composite structure is studied. Using computer simulation, it is shown that, during impregnation, the structure of tensioned fibrous layers changes considerably depending on the initial arrangement and tensioning of fibers. The consolidated regions formed under the melt front move inside the impregnated layer with the advancing melt front. Displacement of the tensioned fibers as well as the formation of “washouts” favors the impregnation of internal layers, but cause significant inhomogeneity of the polymer structure. The surface (on the side of the melt flow) regions are more saturated with the polymer than the internal ones. A difference in the melt percolation mechanisms at various impregnation regimes is revealed. The effective permeability coefficients of a tensioned fiber layer are not constant but depend on the conditions and regimes of impregnation. Submitted to the 11th Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 259–270, March–April, 2000.     

Asymptotics of the distribution of the integral of the positive part of the Brownian bridge for large arguments

The double Laplace transform of the distribution function of the integral of the positive part of the Brownian bridge was determined by M. Perman and J.A. Wellner, as well as the moments of this distribution. The purpose of the present paper is to determine the asymptotics of this distribution for large values of the argument, and the corresponding asymptotics of the moments.     

The nonlinear and scaled growth of the ottoman and Roman empires

In this work, mathematical models for the growth of the Ottoman and Roman Empires are found. The time interval considered for both cases covers the time from the birth of the empire to the end of the fast expansion period. These empires are assumed to be nonlinearly growing and self-multiplying systems. This approach utilizes the concepts of chaos theory, and scaling. The area governed by the empire is taken as the measure of its growth. It was found that the expansion of each empire on lands, seas, and on both (i.e., lands+seas) can be expressed by power laws. In the Ottoman Empire, the nonlinear growth power of total area is approximately equal to the golden ratio, and the nonlinear growth power of the expansion on lands is approximately equal to the square root of 2. In the case of the Romans, some numbers associated with the golden ratio, or the square root of 2, appear as the power of the nonlinear growth term. The appearance of both the golden ratio and the square root of 2 show that both empires had intention on achieving stability during their growth.     

基于偏序集的PROMETHEE方法优化研究

尽管PROMETHEE是当前最受欢迎的多准则决策方法之一,但在实践应用过程中,模型的应用范围与质量依然受制于指标权重问题。一些常用的赋权方法,不仅没有解决不确定权重问题,反而增加了决策风险。在偏序集相关定理的基础上,给出权重的定性信息即权重次序,由流出矩阵、流入矩阵和净流矩阵等定义,得到了PROMETHEE的偏序集表达形式。当流入和流出之和为常数时,证明了模型存在对偶性质。根据对偶性质,简化了PROMETHEE方法的分析步骤,删减模型冗余信息。应用偏序集表示的PROMETHEE,突破了模型没有具体权重便无法应用的思维定势,解决了模型赋权困难,增强了模型的鲁棒性,拓展了模型处理数据类型的范围。     

Analysis of the Stress State of the Surface Layer of a Polymeric Mass upon Filling of Bulky Compression Molds

The stress state of the surface layer of a polymeric mass during filling of bulky compression molds is analyzed. It is shown that, at particular rheological characteristics of the mass, temperature, and filling rates, cracking of the surface layer occurs, which leads to defects in the finished products. A physical analysis of this process makes it possible to conclude that the cracks arise due to the normal stresses operating in the front region of the moving polymeric mass. It is found that, under certain flow conditions, areas with a pressure lower than the atmospheric one appear on the surface of the polymer. If the tensile stresses arising in these local regions are higher than the tensile strength of the mass, the continuity of the composition is broken in the direction determined by the greatest rate of the normal deformation. To confirm the reliability of the crack-formation mechanism proposed, the distribution of the pressure and normal stresses over the free surface is calculated based on a numerical method. These calculations show that, by comparing the stress level achieved in the front region with the tensile-strength characteristics of the polymeric composition, it is possible to predict, with a sufficient accuracy, the possibility of crack formation in the surface layer of such a mass under given flow conditions and thus to solve the question on flawless manufacturing of products.     

Generalized derivatives and nonsmooth optimization, a finite dimensional tour

During the early 1960’s there was a growing realization that a large number of optimization problems which appeared in applications involved minimization of non-differentiable functions. One of the important areas where such problems appeared was optimal control. The subject of nonsmooth analysis arose out of the need to develop a theory to deal with the minimization of nonsmooth functions. The first impetus in this direction came with the publication of Rockafellar’s seminal work titledConvex Analysis which was published by the Princeton University Press in 1970. It would be impossible to overstate the impact of this book on the development of the theory and methods of optimization. It is also important to note that a large part of convex analysis was already developed by Werner Fenchel nearly twenty years earlier and was circulated through his mimeographed lecture notes titledConvex Cones, Sets and Functions, Princeton University, 1951. In this article we trace the dramatic development of nonsmooth analysis and its applications to optimization in finite dimensions. Beginning with the fundamentals of convex optimization we quickly move over to the path breaking work of Clarke which extends the domain of nonsmooth analysis from convex to locally Lipschitz functions. Clarke was the second doctoral student of R.T. Rockafellar. We discuss the notions of Clarke directional derivative and the Clarke generalized gradient and also the relevant calculus rules and applications to optimization. While discussing locally Lipschitz optimization we also try to blend in the computational aspects of the theory wherever possible. This is followed by a discussion of the geometry of sets with nonsmooth boundaries. The approach to develop the notion of the normal cone to an arbitrary set is sequential in nature. This approach does not rely on the standard techniques of convex analysis. The move away from convexity was pioneered by Mordukhovich and later culminated in the monographVariational Analysis by Rockafellar and Wets. The approach of Mordukhovich relied on a nonconvex separation principle called theextremal principle while that of Rockafellar and Wets relied on various convergence notions developed to suit the needs of optimization. We then move on to a parallel development in nonsmooth optimization due to Demyanov and Rubinov called Quasidifferentiable optimization. They study the class of directionally differentiable functions whose directional derivatives can be represented as a difference of two sublinear functions. On other hand the directional derivative of a convex function and also the Clarke directional derivatives are sublinear functions of the directions. Thus it was thought that the most useful generalizations of directional derivatives must be a sublinear function of the directions. Thus Demyanov and Rubinov made a major conceptual change in nonsmooth optimization. In this section we define the notion of a quasidifferential which is a pair of convex compact sets. We study some calculus rules and their applications to optimality conditions. We also study the interesting notion of Demyanov difference between two sets and their applications to optimization. In the last section of this paper we study some second-order tools used in nonsmooth analysis and try to see their relevance in optimization. In fact it is important to note that unlike the classical case, the second-order theory of nonsmoothness is quite complicated in the sense that there are many approaches to it. However we have chosen to describe those approaches which can be developed from the first order nonsmooth tools discussed here. We shall present three different approaches, highlight the second order calculus rules and their applications to optimization.     

Mario Pieri’s address at the University of Catania

The contributions made by the Italian mathematician Mario Pieri (1860-1913) are well known in the field of geometry. Pieri was a member of the School of Peano at the University of Turin. There he became engaged both by the problems of logic and by the philosophical aspects of Peano’s epistemology. This article was motivated by Pieri’s address given at the University of Catania, at the inauguration of the 1906-1907 academic year. My aim is to identify Pieri’s philosophical premises as found in his works and to present them in the general framework of the historical development of the Peano School.     

Formulations and valid inequalities for the node capacitated graph partitioning problem

We investigate the problem of partitioning the nodes of a graph under capacity restriction on the sum of the node weights in each subset of the partition. The objective is to minimize the sum of the costs of the edges between the subsets of the partition. This problem has a variety of applications, for instance in the design of electronic circuits and devices. We present alternative integer programming formulations for this problem and discuss the links between these formulations. Having chosen to work in the space of edges of the multicut, we investigate the convex hull of incidence vectors of feasible multicuts. In particular, several classes of inequalities are introduced, and their strength and robustness are analyzed as various problem parameters change.