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."     

Explicit traveling wave solutions of five kinds of nonlinear evolution equations

First of all, by using Bernoulli equations, we develop some technical lemmas. Then, we establish the explicit traveling wave solutions of five kinds of nonlinear evolution equations: nonlinear convection diffusion equations (including Burgers equations), nonlinear dispersive wave equations (including Korteweg-de Vries equations), nonlinear dissipative dispersive wave equations (including Ginzburg-Landau equation, Korteweg-de Vries-Burgers equation and Benjamin-Bona-Mahony-Burgers equation), nonlinear hyperbolic equations (including Sine-Gordon equation) and nonlinear reaction diffusion equations (including Belousov-Zhabotinskii system of reaction diffusion equations).     

An examination of the homentropic Euler equations with averaged characteristics

This paper examines the properties of the homentropic Euler equations when the characteristics of the equations have been spatially averaged. The new equations are referred to as the characteristically averaged homentropic Euler (CAHE) equations. An existence and uniqueness proof for the modified equations is given. The speed of shocks for the CAHE equations are determined. The Riemann problem is examined and a general form of the solutions is presented. Finally, numerically simulations on the homentropic Euler and CAHE equations are conducted and the behaviors of the two sets of equations are compared.     

Differential Equations of Fractional Order: Methods,Results and Problems. II

The article, being a continuation of the first one [A.A. Kilbas and J.J. Trujillo (2001). Differential equations of fractional order. Methods, results and problems, I. Applicable Analysis , 78 (1-2), 153-192.], deals with the so-called differential equations of fractional order in which an unknown function is contained under the operation of a derivative of fractional order. The methods and the results in the theory of such fractional differential equations are presented including the Dirichlet-type problem for ordinary fractional differential equations, studying such equations in spaces of generalized functions, partial fractional differential equations and more general abstract equations, and treatment of numerical methods for ordinary and partial fractional differential equations. Problems and new trends of research are discussed.     

Invariant Simultaneous Solutions of Evolution Equations of Integrable Hierarchies

We construct classical point symmetry groups for joint pairs of evolution equations (systems of equations) of integrable hierarchies related to the auxiliary equation of the method of the inverse problem of second order. For the two cases: the hierarchy of Korteweg--de Vries (KdV) equations and of the systems of Kaup equations, we construct simultaneous solutions invariant with respect to the symmetry group. The problem of the construction of these solutions can be reduced, respectively, to the first and second Painlevé equations depending on a parameter. The Painlevé equations are supplemented by the linear evolution equations defining the deformation of the solution of the corresponding Painlevé equation.     

Construction of solutions to quasilinear partial differential equations

We propose a method for constructing solutions to a class of quasilinear parabolic partial differential equations (PDEs) basing on a new property of these equations. The method applies to quasilinear hyperbolic and elliptic equations as well. The results of this article broaden the class of exact solutions to the quasilinear equations, in particular, to the nonlinear heat equations, the equations of chemical kinetics and mathematical biology.     

Travelling wave solutions of some classes of nonlinear evolution equations in (1+1) and (2+1) dimensions

The tanh method is proposed to find travelling wave solutions in (1+1) and (2+1) dimensional wave equations. It can be extended to solve a whole family of modified Korteweg–de Vries type of equations, higher dimensional wave equations and nonlinear evolution equations.     

A new semi-analytical collocation method for solving multi-term fractional partial differential equations with time variable coefficients

The aim of this paper is to present a new numerical method for solving a wide class of fractional partial differential equations (FPDEs) such as wave-diffusion equations, modified anomalous fractional sub-diffusion equations, time-fractional telegraph equations. The proposed method is based on the Fourier series expansion along the spatial coordinate which transforms the original equation into a sequence of multi-term fractional ordinary differential equations (ODEs). These fractional equations are solved by the use of a new efficient numerical technique – the backward substitution method. The numerical examples confirm the high accuracy and efficiency of the proposed numerical scheme in solving FPDEs with variable in time coefficients.     

Existence of solutions and Gevrey class regularity for Leray-alpha equations

In this paper we consider some equations similar to Navier-Stokes equations, the three-dimensional Leray-alpha equations with space periodic boundary conditions. We establish the regularity of the equations by using the classical Faedo-Galerkin method. Our argument shows that there exist an unique weak solution and an unique strong solution for all the time for the Leray-alpha equations, furthermore, the strong solutions are analytic in time with values in the Gevrey class of functions (for the space variable). The relations between the Leray-alpha equations and the Navier-Stokes equations are also considered.     

The Cauchy Problem for Partial Difference Equations

We want to discuss partial difference equations, first of all with respect to the existence and uniqueness of their solution. These equations are considered with solutions on arbitrary subsets of the n-dimensional grid Zn. The basic theorem enables one to formulate the Cauchy problem for such equations. The solution is proven to be recursively computable for partial difference equations under very mild restrictions. (Variable coefficients for linear equations, systems of equations as well as nonlinear equations are not excluded.) The construction of solutions presented here also allows for some qualitative conclusions, such as boundedness of solutions.     

球壳轴对称弯曲问题精确的挠度微分方程及其奇异摄动解

本文提出了球壳轴对称弯曲问题精确的挠度(ω)微分方程和精确的转角(dω/da)微分方程.本文重点研究了挠度微分方程的精度,基本思路是:首先假设边缘效应时经线中面位移u=0,从而建立挠度微分方程,然后再精确地证明挠度微分方程与原来微分方程内力解答完全相同.再精确地证明边缘效应时经线中面位移u=0是精确解.本文给出了挠度微分方程的奇异摄动解,最后验算了平衡条件,证明摄动解求出的内力和外荷载是完全平衡的.这一方面表明摄动解的计算是正确的;另一方面也再二次表明挠度微分方程是精确的微分方程.新微分方程的优点是:1.新微分方程和原来微分方程精度完全相同;2.新微分方程满足的边界条件非常简单;3.新微分方程便于使用摄动解;4.新微分方程可以得到挠度(ω)和转角(dω/da)的表达式.新微分方程使球壳的计算得到很大的简化.本文采用的符号与徐芝纶《弹性力学》第二版下册相同[1].