D.C.隶属函数模糊集及其应用(I)--D.C.隶属函数模糊集基本概念与性质

本文是D.C.隶属函数模糊集及其应用系列研究的第一部分.建立了D.C.隶属函数模糊集的基本概念.探讨了D.C.隶属函数模糊集的基本性质和D.C.隶属函数模糊集对一些常见的重要t模、余模和伪补的封闭性.并以此建立了丰富的模糊数学应用模型.     

群的融合自由积的几种广义Fratttini子群

M.K.Azarian将C.Y.Tang的一个引理推广到了下拟Frattini子群的情况,并且还提出了两个公开问题.为了回答这两个问题,进一步研究了群的融合自由积的一些广义Frattini子群,并且得到了一些结果.     

具有超抛物型极限方程的非线性奇摄动反应扩散问题

讨论了一类具有超抛物型方程的反应扩散问题.首先,证明了比较定理.其次,构造了形式渐近解.然后,利用微分不等式方法,研究了问题解的存在、唯一性和渐近性态.最后得到了原问题解的渐近展开式.     

β混合随机变量序列加权和的收敛性

本文研究了混合随机变量序列加权和的收敛性.利用Utev, S.和Peligrad, M不等式得到了混合随机变量序列加权和的收敛性定理及Hajeck-Rènyi型不等式,推广和改进了W.F,Stout,吴群英,J.Hajeck和A.Rènyi.的相应结论.     

一类具有跳跃层的非线性反应扩散系统的渐近行为

讨论了一类具有跳跃层的反应扩散系统.首先,求出了问题的外部解.其次,引入伸长变量,构造了跳跃层校正项.最后,利用微分不等式理论,得到了原问题解的一致有效的渐近展开式.从而研究了相应问题的解的渐近性态.     

关于z.Ditzian定理

1987年Z.Ditzian提出了反映Bernstein算子收敛阶与所逼近函数光滑模之间关系的一个定理,并在α+β≤2情形下给出了这个定理的证明.对于α+β》2情形,Z.Ditzian给出了猜想.1992年周定轩证明了Z.Ditzian的猜想,完成了Z.Ditzian定理的证明.本文对于Z.Ditzian定理给出了一个新的直接证明,这个证明不需要讨论α,β的情况,而且还将Z.Ditzian定理拓广到Bernstein算子线性组合上.     

利用数学建模为载体 培养医科学生研究性学习能力的探索

分析了在医学数学教学中开展研究性学习的意义.介绍了数学建模与研究性学习的关系.探索了开展研究性学习活动的途径.总结了开展研究性学习活动的效果.     

单节点图的弱最大亏格

单节点图即只有一个点的图.本文讨论了该图类的三种嵌入.并得到了对应的最大亏格.对于这类图的弱嵌入.插值定理是成立的.     

拟信息基,ω-代数Cpo,和SFP domain

G.Sam b in引入了(代数)信息基的概念,并证明了代数Scott D om a in范畴和信息基范畴是等价的.B.R.C.Bedrega l给出了ω-代数cpo和SFP dom a in的刻划.而G.Q.Zhang通过序结构给出了SFP dom a in的刻划.本文将引入了拟信息基的概念并给出了ω-代数cpo和SFP dom a in的刻划.     

不对称柔性壁管道内幂律流体蠕动传输的精确解

在不对称管道内,研究了壁面柔曲性对非Newton流体蠕动流的影响.流变学性质由幂律流体本构方程表征.在数学表达中,采用了长波和低Reynolds数近似.得到了流函数和速度的精确解.给出了流线图及其俘获现象.对所讨论的流动,陈列了关键参数的显著特征,并最后给出了主要结论.     

New fixed point theorems for mixed monotone operators and local existence-uniqueness of positive solutions for nonlinear boundary value problems

In this article we present a new fixed point theorem for a class of general mixed monotone operators, which extends the existing corresponding results. Moreover, we establish some pleasant properties of nonlinear eigenvalue problems for mixed monotone operators. Based on them the local existence-uniqueness of positive solutions for nonlinear boundary value problems which include Neumann boundary value problems, three-point boundary value problems and elliptic boundary value problems for Lane-Emden-Fowler equations is proved. The theorems for nonlinear boundary value problems obtained here are very general.     

Adjoint and self-adjoint boundary value problems on a geometric graph

We consider boundary value problems of arbitrary order for linear differential equations on a geometric graph. Solutions of boundary value problems are coordinated at the interior vertices of the graph and satisfy given conditions at the boundary vertices. For considered boundary value problems, we construct adjoint boundary value problems and obtain a self-adjointness criterion. We describe the structure of the solution set of homogeneous self-adjoint boundary value problems with alternating coefficients of a differential equation and obtain nondegeneracy conditions for these boundary value problems.     

An asymptotic initial value method for second order singular perturbation problems of convection-diffusion type with a discontinuous source term

In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method.     

一类广义解析函数的Riemann边值逆问题

本文给出了一类有关广义解析函数Riemann边值逆问题的数学提法．在将此边值逆问题转化为边值问题的基础上，借助于广义解析函数边值问题的相关理论，分别获得了此边值逆问题在正则型和非正则型情况下的解．     

高阶微分积分方程的单调迭代法及其应用

首先利用上下解方法以及微分不等式理论给出了n阶微分积分方程的初值问题解的存在性及其单调迭代法,然后将所得结果应用到n阶微分方程的两点边值问题,得到了n阶非线性两点边值问题解的存在性及其单调迭代法,所得结果推广了已有的结果．     

一类Dirichlet边值逆问题

给出解析函数的一类Dirichlet边值逆问题的数学提法.依据解析函数Dirichlet边值问题和广义Dirichlet边值问题的理论,讨论了此边值逆问题的可解性.利用解析函数Dirichlet边值问题的Schwarz公式,给出了该边值逆问题的可解条件和解的表示式.     

反应扩散方程的奇摄动

§ 1　 IntroductionThe nonlinearsingularly perturbed problem is a very attractive subjectof study in theinternational academic circles[1 ] .During the past decade many approximate methods havebeen developed and refined,including the method of average,boundary layer method,matched asymptotic expansions,and multiple scales.Recently,many scholars,for example,Bohé[2 ] ,Butuzov and Smurov[3] ,O Malley[4] ,Butuzov,Nefedov and Schneider[5] ,Kelley[6]and so on did a great deal of work.Mo consider…     

Linear and nonlinear degenerate boundary value problems in Besov spaces

The boundary value problems for linear and nonlinear degenerate differential-operator equations in Banach-valued Besov spaces are studied. Several conditions for the separability of linear elliptic problems are given. Moreover, the positivity and the analytic semigroup properties of associated differential operators are obtained. By using these results, the maximal regularity of degenerate boundary value problems for nonlinear differential-operator equations is derived. As applications, boundary value problems for infinite systems of degenerate equations in Besov spaces are studied.     

A reliable treatment of singular Emden-Fowler initial value problems and boundary value problems

In this paper, the variational iteration method (VIM) is used to study the singular Emden-Fowler initial value problems and boundary value problems arising in physics and astrophysics. The VIM overcomes the singularity at the origin. The Lagrange multipliers for all cases of the equations are determined. The work is supported by analyzing few initial value problems and boundary value problems where the convergence of the results is emphasized.     

A CLASS OF NONLOCAL BOUNDARY VALUE PROBLEMS OF NONLINEAR ELLIPTIC SYSTEMS IN UNBOUNDED DOMAINS

We consider the following boundary value problem ill the unbounded donain Liui = fi(x,u, Tu), i = 1, 2,' ! N,x E fl, (1) olLi "i0n Pi(x)t'i = gi(x,u), i = l, 2,',N,x E 0fl, (2) where x = (x i,', x.), u = (u1,' f uN), Th = (T1tti,', TNi'N) and [ n. 1 L, = -- I Z ajk(X)the i0j(X)C], Li,k=1' j=1 J] l Ltti = / K(x,y)ui(y)dy, x E n. jn K(x, y)ui(y)dy, x E n. Q denotes an unbounded dolllain in R", including the exterior of a boullded doinain and 0…