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."     

模糊正则文法的逼近性

为了扩大现有研究的应用范围,基于max-min型模糊正则文法引入了max-*型模糊正则文法(其中*为特定t-模)的概念,讨论了max-*型模糊正则文法可以通过max-min型模糊正则文法在任意给定的逼近精度来逼近.研究表明,当t-模*满足一定的条件时,max-*型模糊正则文法与max-min型模糊正则文法在生成模糊语言能力方面是等价的.     

带两个服务等级的三台机最优在线算法

研究了带服务等级约束的三台平行机在线排序问题.每台机器和每个工件的服务等级为1或者2,工件只能在等级不高于它的机器上加工,即等级为1的工件只能在等级为1的机器上加工,等级为2的工件可在所有机器上加工.每个工件的加工时间为一个单位,目标是极小化所有工件的总完工时间.考虑两种情形:当一台机器等级为1,两台机器等级为2时,给出了竞争比为17/14的最优在线算法;当两台机器等级为1,一台机器等级为2时,给出了竞争比为43/36的最优在线算法.     

Higher-order accurate polyspectral estimation with flat-top lag-windows

Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical estimators with second-order kernels. A simple, data-dependent algorithm for selecting the bandwidth is introduced and is shown to be consistent with estimating the optimal bandwidth. The combination of the specialized family of kernels with the new bandwidth selection algorithm yields a considerably improved polyspectral estimator surpassing the performances of existing estimators using second-order kernels. Bispectral simulations with several standard models are used to demonstrate the enhanced performance with the proposed methodology.     

Homeomorphs and amallamorphs of the Petersen graph

Let P be the Petersen graph. The main results of this paper are the discovery of infinite families of chromatically equivalent pairs of P homeomorphs and the discovery of infinite families of flow equivalent pairs of P amallamorphs. In particular, three families of P homeomorphs with 8 parameters, five families with 7 parameters and many families with fewer parameters are obtained. Also one family of P amallamorphs with 9 parameters, three families with 7 parameters, seven families with 6 parameters and many families with fewer parameters are obtained.     

Four equivalent lot-sizing models

We study the following lot-sizing models that recently appeared in the literature: a lot-sizing model with a remanufacturing option, a lot-sizing model with production time windows, and a lot-sizing model with cumulative capacities. We show the equivalence of these models with a classical model: the lot-sizing model with inventory bounds.     

变厚度圆薄板非对称非线性弯曲问题

首先将直角坐标系中的横向变厚度薄板的大挠度方程,转化到极坐标系中的变厚度圆薄板的非对称大挠度方程·　此方程和极坐标系中径向、切向两个平衡方程联立求解·　将物理方程和中面应变非线性变形方程,代入3个平衡方程,可得用3个变形位移表示的3个非对称非线性方程·　用Fourier级数表示的解代入基本方程,获得相应的基本方程·　在周边夹紧边界条件下,用修正迭代法求解·　作为算例,研究了余弦形式载荷作用下的问题,还给出了载荷与挠度的特征曲线,曲线依据变厚度参数变化而变化,其结果和物理概念完全吻合·     

On active redundancy allocation for coherent systems—from the viewpoint of minimal cut decomposition

This paper deals with coherent systems with one active redundancy. For systems with the subclass of minimal cuts associated with one component covering that of another, assigning the redundancy to the former component is proved to bring forth a more reliable redundant system. As for symmetric systems with lower tail permutation decreasing component lifetimes, allocating the redundancy to the less reliable component results in a longer system lifetime. Several numerical examples are also presented to illustrate the new findings.     

M/G/1一般减量服务单重休假排队系统的随机分解

本文讨论了M/G/1型一般减量服务单重休假排队模型,运用结构分析法得到稳态队长和服务时间的随机分解的母函数和拉式变换,并给出稳态分布成立的条件及其概率含义．     

On time-dependent behavior of cross-ply laminated strips with viscoelastic interfaces

The two-dimensional problem of a simply supported laminated orthotropic strip with viscoelastic interfaces under static loading is studied. State-space formulations are developed based on the exact elasticity equations governing orthotropic media and the Kelvin–Voigt constitutive relation of interfaces. Since the response of the strip is time-dependent, the power series expansion technique is adopted to model the variations of elastic fields with time. Results show that the response of the laminated strip with viscoelastic interfaces changes remarkably with time, which is also significantly different from that of a plate with perfect interfaces or with viscous interfaces. Note that from the present analysis, the response for a laminated plate with spring-like interfaces or with viscous interfaces can be easily obtained because they are just two particular cases of the present Kelvin–Voigt model.     

Hankel operators, the Segal-Bargmann space, and symmetrically-normed ideals

Starting with the Segal-Bargmann space, we investigate the Hankel operators with symbol functions in a certain linear space. Given an appropriate symbol function, we consider the associated Hankel operator together with the Hankel operator associated with that symbol function's complex conjugate. We give a necessary and sufficient condition for the simultaneous membership of these two operators in the symmetrically-normed ideal associated with any given symmetric norming function.