几何分析中运用Gromov方法的几个课题

近３０年来Ｇｒｏｍｏｖ对数学的多个领域，其中包括微分几何，拓扑，动力系统，群论和偏微分方程，作出了重要的贡献，本文讨论几何分析中与Ｇｒｏｍｏｖ引进的多种几何不变量有关的几个专题中主要包括Ｇｒｏｍｏｖ几乎平坦流形，极小体积空隙独测，填充黎曼流形，等周不等式，Ｇｒｏｍｏｖ字双曲群，非紧空间和具有界曲率奇异空间上的加权Ｌ＾ｐ上同调。     

高师“高中数学选修课程专题”探索

针对高师开设的“普通高中数学选修课程专题研究”课程,以其中“三等分角与数域扩充”专题为例,通过文献资料、教育实验、访谈调查等方法,从专题目标定位、内容组织、实践探索三个方面展开研究,最终提出包括教学、考核形式在内的改进建议.     

摄动方法在生态学中的应用

本文研究摄动方法在生态学中的应用,得到一个生态方程的渐近解。     

用摄动方法求一类广义振荡积分的值

摄动方法中求定积分所定义的函数的渐进展开式的各种方法被用来求一类广义振荡积分的近似值 ,而且多数情况下得到的是精确值     

《数学实验》课程的实验题材研究

本文通过一个具体的实例对实验题材的选取进行了研究 ,讨论了选取数学实验题材的原则 .     

Infinitely Many Solutions of Nonlocal Kirchhoff-Type Equations via Perturbation Methods

Mathematical Notes - We study the multiplicity of weak solutions to the boundary-value problem $$begin{alignedat}{2} - Mbiggl(iint_{mathbb R^{2N}}|u(x)-u(y)|^2 K(x-y),d x,d ybiggr)mathscr...     

Error of One-leg Methods for Singular Perturbation Problems with Delays

This paper is concerned with the error behaviour of one-leg methods applied to some classes of one-parameter multiple stiff singularly perturbed problems with delays. We derive the global error estimates of A-stable one-leg methods with linear interpolation procedure.     

《数学实验》课程的内容设置与选材

人类社会正处在由工业社会向信息社会过渡的历史性变革时代 ,这个时代所呈现出的两大特征是计算机技术的迅速发展与广泛应用以及由此引发的数学的应用向各个领域更为广泛和深入的渗透。这两个特征无疑对数学教育提出了新的要求。数学建模培训是为国家培养新时代所需的创新性人才的一种新途径 ,从近几年的情况看 ,参加过数学建模培训的学生的数学素质和其它综合素质都有明显提高 .但如何将数学建模的思想和方法贯穿到整个工科数学教学实践中去 ,这便是开设《数学实验》课程的客观背景 .作为国家工科数学教学基地建设单位 ,我校从 1 997年起开…     

一种修正的Laplace-同伦摄动算法

在NDLT-HPM(非线性分布Laplace-同伦摄动算法)的基础上,通过引入参数h,提出了一种修正的NDLT-HPM(简称MNDLT-HPM),参数的引入使得求解更加灵活,且能调节和控制级数解的收敛域,克服了NDLT-HPM在嵌入参数p=1处级数解可能不收敛的局限性,使得级数解可以有效地收敛至精确解,从而获得足够精确的解析近似解,两个数值实例表明了该解法的优越性和精确性.     

Finite-Difference Methods for a Class of Strongly Nonlinear Singular Perturbation Problems

The paper is concerned with strongly nonlinear singularly perturbed bound- ary value problems in one dimension.The problems are solved numerically by finite- difference schemes on special meshes which are dense in the boundary layers.The Bakhvalov mesh and a special piecewise equidistant mesh are analyzed.For the central scheme,error estimates are derived in a discrete L~1 norm.They are of second order and decrease together with the perturbation parameterε.The fourth-order Numerov scheme and the Shishkin mesh are also tested numerically.Numerical results showε-uniform pointwise convergence on the Bakhvalov and Shishkin meshes.     

Stability Analysis of Controlled, Partially-Connected, Distributed-Parameter Systems Through Perturbation Methods

A stability result for locally-controlled, interconnected, distributed-parameter systems (DPS) is developed. Using a special perturbation operator, exponential stability is shown to be a function of both the value of the perturbation operator and the characteristics of the interconnected DPS. Proof of the bound is shown using the expansion of the matrix operator and the solution vector through a set of gauge functions. Each expansion term is power matched and individually bound using stationary phase methods. Special consideration is given to interconnected systems of a structural dynamic nature.     

基于技术预见德尔菲调查的共性技术课题选择方法研究

共性技术是国家技术发展过程中的关键技术,它对提升国家的产业技术能力与国际竞争力具有重要的推动作用.但是,目前世界各国的技术预见实践中,鲜有对共性技术的识别方法提供一套有效的系统方案.基于多属性决策理论,采用德尔菲调查的方法,提供了一种计算技术课题发展优先度的具体方案,并提出了相关建议.     

Finite Deformations of Thin Beams, Asymptotic Analysis by Singular Perturbation Methods

Boundary-value problems for a system of singularly perturbednon-linear ordinary differential equations modelling large deflectionsof thin beams are examined. Using the theory of singularly perturbedboundary value problems we establish the existence of locallyunique solutions and derive asymptotic expansions.     

Solving Nonlinear Delay-Differential-Algebraic Equations with Singular Perturbation via Block Boundary Value Methods

Block boundary value methods (BBVMs) are extended in this paper to obtain the numerical solutions of nonlinear delay-differential-algebraic equations with singular perturbation (DDAESP). It is proved that the extended BBVMs in some suitable conditions are globally stable and can obtain a unique exact solution of the DDAESP. Besides, whenever the classic Lipschitz conditions are satisfied, the extended BBVMs are preconsistent and $p$th order consistent. Moreover, through some numerical examples, the correctness of the theoretical results and computational validity of the extended BBVMs is further confirmed.     

Perturbation in eigenvalues

We study the dependence of the eigenvalues of a tridiagonal matrix upon off-diagonal entries. The change in the eigenvalues when a cross-diagonal product approaches zero or infinity is estimated.     

求解特定线性互补问题的牛顿KKT内点法

利用线性互补问题与二次规划之间的关系,推广了求解二次规划的KKT内点法,并用于线性互补问题,分析了推广算法的全局收敛性和局部收敛性.数值实验表明,算法对求解几类线性互补问题是有效的.