渐近非扩张映象不动点的三重迭代法

利用赋范线性空间X的凸性模定义,以及凸性模的单调性及半紧性条件研究了渐近非扩张映射T:D→D不动点的三步迭代法.主要结果将过去一些学者研究的二步迭代推广到三步迭代,并减弱了许多条件.从而推广了同类问题的某些结果.     

Hahn-Banach定理在V-凸性模定义中的应用

先给出了V-凸性模的两个等价定义,并利用Hahn-Banach定理给出了它们的等价性.其次,在V-凸性模定义的基础上引进了广义V-凸性模的概念,并给出了其两个等价定义.     

超凸空间中的选择定理及弱外超凸集的性质

本文利用半序方法,研究具有外超凸集值的带次可加模的集值映象的保不动点集,带相同次可加模的单值选择,获得了这类单值选择的存在性及唯一性条件.且研究了弱外超凸集的一些相交性质.     

随机凸分析(Ⅱ):L~0-准桶的随机局部凸模中的连续性和次可微性定理

本文继续研究随机凸分析.首先,引入L0-准桶模的概念;接着,在赋予局部L0-凸拓扑的随机局部凸模的框架下,为了建立随机局部凸模为L0-准桶模的特征,本文发展了随机对偶理论,尤其是证明用于条件风险度量的模途径中的模型空间LpF(E)是L0-准桶的,这形成本文最困难的部分.最后,本文证明L0-准桶的随机局部凸模上的真下半连续L0-凸函数的连续性和次可微性定理.因此,本文的主要结果可以很好地适用于L0-凸条件风险度量的连续性和次可微性的研究.     

极大代数上有限生成模的凸性

研究极大代数上有限生成模的凸性.基于极大代数上有限生成模的几何形态,运用代数与几何方法,分析空间维数n≤3和生成向量数m≥1的有限生成模的凸性.证明n=1,2的有限生成模是凸集.对于n=3,给出m=2的有限生成模为凸集的一个充分必要条件,以及m≥3的有限生成模为凸集的一个充分条件.此外,对于极大代数上有限生成模的几何形态,发现n=3,m≥3的形态有三种情形.     

基于Ekeland变分原理的一类平衡问题解集的稳定性研究及应用

基于Ekeland变分原理建立的平衡问题,减弱了函数和定义域的凸性要求,减弱了三角不等式条件,函数只有循环反单调性,但其具有良好的性质.一方面,利用非线性分析方法,对非凸紧和非凸非紧的平衡问题研究解的唯一性,在Baire分类意义下,得到基于Ekeland变分原理建立的平衡问题的解具有通有唯一性.另一方面,利用有限理性模...     

随机凸分析(Ⅰ):随机局部凸模中的分离性以及Fenchel-Moreau对偶性

为了给出条件风险度量模途径一个牢固的分析基础,本文的目标是在同时考虑(ε,λ)-拓扑和局部L~0-凸拓扑的条件下,在随机局部凸模上建立完整的随机凸分析.本文致力于研究随机局部凸模中的分离性以及Fenchel-Moreau对偶性.主要结果是给出在这两种拓扑下随机局部凸模的两类随机共轭空间的精确关系,这保证了不但可以彻底解决单点集和一个闭L~0-凸集的分离定理,而且可以在随机局部凸模上建立完整的Fenchel-Moreau对偶表示定理.     

局部T-凸模糊拓扑向量空间

基于T-凸模糊集提出了局部T-凸模糊拓扑向量空间的概念,这里的T是一个三角模,给出了局部T-凸模糊拓扑向量空间的几个例子,研究了局部T-凸模糊拓扑向量空间的性质。此外,利用一族满足T-凸性条件的模糊伪范数刻画了局部T-凸模糊拓扑向量空间。     

特征函数与Banach空间的凸性模,光滑模

本文讨论了Banach空间的特征函数[1]与凸性模及光滑模的关系,从而给出了刻划Banach空间的一致凸性、一致光滑性的另一种方法。     

Gurarii的凸性模与正规结构

本文研究了Gurarii的凸性模与正规结构的联系.利用关于该模的不等式得出了如果存在ε,1≤ε≤2,使得β(ε)＞ε-1.则空间X具有一致正规结构.     

两邻接B样条曲面的G1连续条件

本文得到了非均匀重内节点邻接B样条曲面间G1连续的充要条件 ,给出了一类G1连续的充分条件 ;基于对B样条曲线参数连续性的分析 ,本文着重给出了这类充分条件成立的内在约束 ,即对公共边界控制顶点的约束条件 .     

The classification of self-adjoint boundary conditions of differential operators with two singular endpoints

For general even order linear ordinary differential equations with real coefficients and endpoints which are regular or singular and for arbitrary deficiency index d, the self-adjoint domains are determined by d linearly independent boundary conditions. These conditions are of three types: separated, coupled, and mixed. We give a construction for all conditions of each type and determine the number of conditions of each type possible for a given self-adjoint domain. Our construction gives a direct alternative to the recent construction of Everitt and Markus which uses the theory of symplectic spaces. We believe our construction will prove useful in the spectral analysis of these operators and in obtaining canonical forms of self-adjoint boundary conditions. Such forms are known only in the second order, i.e. Sturm-Liouville, case. Even for regular problems of order four no such forms are available. In the case when all d conditions are separated this construction yields explicit non-real conditions for all orders greater than two. It is well known that no such conditions exist in the second order case.     

Matrix representations of Sturm‐Liouville problems with coupled eigenparameter‐dependent boundary conditions and transmission conditions

We study matrix representations of Sturm‐Liouville problems with coupled eigenparameter‐dependent boundary conditions and transmission conditions. Meanwhile, given any matrix eigenvalue problem with coupled eigenparameter‐dependent boundary conditions and transmission conditions, we construct a class of Sturm‐Liouville problems with given boundary conditions and transmission conditions such that they have the same eigenvalues.     

Duffing型方程组的边界值问题的解的存在性

给出了带Dirichlet边界条件、Neumann边界条件和周期边界条件的Duffing型方程组的两点边界值问题的解的几个存在性定理。     

Ultimate boundedness with respect to part of the variables of solutions of systems of differential equations with partly controlled initial conditions

We introduce the notions of equiultimate boundedness and uniform ultimate boundedness with respect to part of the variables for solutions with partly controlled initial conditions. We obtain sufficient conditions for the equiultimate boundedness and uniform ultimate boundedness with respect to part of the variables of solutions with partly controlled initial conditions. We introduce the notions of equiboundedness and uniform boundedness with respect to part of the variables for solutions of systems with partly controlled initial conditions. We obtain sufficient conditions for the equiboundedness and uniform boundedness with respect to part of the variables of solutions with partly controlled initial conditions.     

Long-time behaviour of absorbing boundary conditions

A new class of computational far-field boundary conditions for hyperbolic partial differential equations was recently introduced by the authors. These boundary conditions combine properties of absorbing conditions for transient solutions and properties of far-field conditions for steady states. This paper analyses the properties of the wave equation coupled with these new boundary conditions: well-posedness, dissipativity and convergence in time.     

全概率公式的推广

首先给出了普通事件在普通条件和Fuzzy条件下的Fuzzy条件概率及Fuzzy事件在普通条件和Fuzzy条件下的Fuzzy条件概率公式,并通过对普通事件的全概率公式进行推广,得到普通事件和Fuzzy事件分别在普通划分和Fuzzy划分下的全概率公式     

On the zeros of solutions of beam equations

Summary We consider extensible beam equations, Timoshenko beam equations and the system of coupled beam equations. We show that, under suitable conditions, there are bounded domains in which every solution satisfying certain end conditions has a zero. End conditions to be considered are hinged ends and hinged-sliding ends. The results are based on the conditions for the nonexistence of positive solutions of ordinary differential inequalities.     

Necessary and sufficient conditions for the existence of shock curves of hyperbolic 1-conservation laws

We present three conditions for the existence of shock curves of hyperbolic 1-conservation laws. If at least two of the conditions hold, then shock curves exist uniquely in the classical sense. We present an example (Example 2, Section 4) for which two of the conditions do not hold and a new kind of singularity occurs. In Remark 1 we present two other conditions similar to the above three conditions which also imply the existence of shock curves.     

Comparison of Two Sets of First-Order Conditions as Bases of Interior-Point Newton Methods for Optimization with Simple Bounds

In this paper, we compare the behavior of two Newton interior-point methods derived from two different first-order necessary conditions for the same nonlinear optimization problem with simple bounds. One set of conditions was proposed by Coleman and Li; the other is the standard KKT set of conditions. We discuss a perturbation of the CL conditions for problems with one-sided bounds and the difficulties involved in extending this to problems with general bounds. We study the numerical behavior of the Newton method applied to the systems of equations associated with the unperturbed and perturbed necessary conditions. Preliminary numerical results for convex quadratic objective functions indicate that, for this class of problems, the Newton method based on the perturbed KKT formulation appears to be the more robust.