集值映射的伪(*)连续与弱(*)连续性

本文引入了集值映射的伪（＊）连续性与弱（＊）连续性概念的定义,研究了伪（＊）连续、（＊）连续及弱（＊）连续的等价关系,最后研究了乘积空间中的集值映射成为伪（＊）连续和弱（＊）连续的充要条件。     

带迁入超过程的轨道连续性

本文利用鞅测度的方法研究了一类带迁入超过程的轨道连续性问题。给出了这类测度值过程弱连续的一个充要条件，以及在τ－拓扑下连续的充分条件．     

Hardy空间Hp(BN)上的加权复合算子

φ：BN→BN的全纯映射，ψ∈H（BN），其中H（BN）表示BN上全纯函数集合，定义加权复合算子Wφ，ψf=ψ（f φ），f∈H（BN）．本文研究了Hardy空间H^p（BN）上的加权复合算子的有界性、紧性、弱紧性以及完全连续性，给出了有界性、紧性的充要条件以及证明了紧性与弱紧性的等价关系．最后讨论了加权复合算子的完全连续性．     

自然增长的半线性次椭圆方程内部H?lder估计

对于低阶项满足自然增长条件的半线性次椭圆方程有界弱解,通过Moser-Nash迭代和弱Harnack不等式,得到弱解的内部H?lder连续性估计.     

弱紧局部一致凸空间中的度量投影

本文研究了弱紧局部一致凸空间中度量投影的弱连续性,将Ｂ．Ｂ．Ｐａｎｄａ和Ｏ．Ｐ．Ｋａｐｏｏｒ的相应结论推广到更一般的弱紧局部一致凸空间．最后给出了局部一致凸点的一个必要条件．     

弱向量变分不等式解集的连通性

研究拓扑向量空间到连续线性映射空间映射的弱向量变分不等式和与之相关 的纯量型变分不等式解集的关系, 引入弱和强一致连续概念,利用纯量型变分不等式 解集所表征的集值映射的特性给出弱向量变分不等式解集连通的一个充分条件。     

参数广义弱向量拟平衡问题解映射的H-连续性刻画

研究了Hausdorff拓扑向量空间中的一类参数广义弱向量拟平衡问题(PGWVQEP)的稳定性.首先，给出了此问题的参数间隙函数，研究了参数间隙函数的连续性.然后, 提出了一个与参数间隙函数相关的关键假设，讨论了它的连续性，并给出关键假设的等价刻画.最后， 借助于假设，获得了PGWVQEP解映射Hausdorff半连续的充分必要条件.并举例验证了所得结果.     

弱有限元方法简论

本文简述弱有限元方法(weak Galerkin finite element met,hods)的数学基本原理和计算机实现.弱有限元方法对间断函数引入广义弱微分,并将其应用于偏微分方程相应的变分形式进行数值求解,而数值解的弱连续性则通过稳定子或光滑子来实现.弱有限元方法针对广义函数而构建,是经典有限元方法的一种自然拓广,且能够弥补经典有限元方法的某些缺憾,也因此在科学与工程计算领域具有广泛的应用前景.     

非齐次p-调和映射方程组弱驻点解的正则性

讨论非齐次p－调和映射方程组弱驻点解的内部正则性，证明了弱驻点解满足拟单调不等式，得到了弱驻点解梯度的Holder连续性。     

赋范线性空间中包含方程可解性定理的推广及弱切锥的应用

本文首先在一般的赋范线性空间中研究了集值映射F;X→Y的平衡点的存在性问题,证明了包含问题O∈F(X)的三个可解性定理.然后在无穷维空间中研究了弱相依锥T_k^σ(x)的直接像,弱相依导数D^σF(x,y)的一个链式法则以及偏y弱导数D_y^σF(x,y)的弱Lip连续性.最后,作为应用,给出并证明了用弱相依导数D^σF(x,y)及弱P导数P^σF(x,y)判定无穷维     

Weak convergence and weak compactness in the space of almost periodic functions on the real line

We give necessary and sufficient conditions for sequences in the space AP(R) of continuous almost periodic functions on the real line to converge in the weak topology. The abstract results are illustrated by a number of examples which show that weak convergence seems to be a rare phenomenon. We also characterize the weakly compact subsets in AP(R). In particular, earlier statements made in the monograph by Dunford and Schwartz are refined and completed. We close with some open problems.     

半序Menger PM-空间中广义弱压缩映射的最佳逼近点定理

本文利用三个控制函数给出了半序Menger PM-空间中满足特定条件的广义弱压缩映射的最佳逼近点定理,并给出了最佳逼近点唯一的充分条件.进一步地,还给出了主要结果的一些推论.     

Optimality conditions for weak efficiency to vector optimization problems with composed convex functions

We consider a convex optimization problem with a vector valued function as objective function and convex cone inequality constraints. We suppose that each entry of the objective function is the composition of some convex functions. Our aim is to provide necessary and sufficient conditions for the weakly efficient solutions of this vector problem. Moreover, a multiobjective dual treatment is given and weak and strong duality assertions are proved.      

Weak subdifferential/superdifferential,weak exhausters and optimality conditions

In this work, the notion of weak superdifferential is presented. Some calculation rules are given to evaluate weak subdifferential and weak superdifferential of some classes of functions represented by support functions. Moreover, some methods are obtained to calculate weak subdifferential of convex functions. In addition, the concept of weak lower and weak upper exhausters of positively homogeneous functions are introduced by using weak subdifferential and weak superdifferential, respectively. In terms of weak exhausters, some optimality conditions are given to find local or global minimizers/maximizers of some classes of functions.     

弱对称Markov积分半群的表示

本文研究了弱对称Markov积分半群的表示.利用积分的方法,获得了弱对称Markov积分半群的Kendall和Karlin-McGregor表示,推广了转移函数的Kendall和Karlin-McGregor表示.     

Some relationships among quasidifferential,weak subdifferential and exhausters

In this study, some relationships between quasidifferentiability and weakly subdifferentiability of a function are investigated, and some results on calculating the quasidifferential in terms of weak exhausters are presented. Moreover, under some assumptions weak subdifferentiability of a quasidifferentiable function is proved and the weak subdifferential is obtained by using the quasidifferential. Under some assumptions, it is proved that a positively homogeneous and lower semicontinuous function is quasidifferentiable. It is also shown that directional differentiability and weak subdifferentiability imply quasidifferentiability. Furthermore, a method to evaluate the quasidifferential is given by using reduced weak lower exhausters.     

On uniformly convex functions

Non-convex functions that yet satisfy a condition of uniform convexity for non-close points can arise in discrete constructions. We prove that this sort of discrete uniform convexity is inherited by the convex envelope, which is the key to obtain other remarkable properties such as the coercivity. Our techniques allow to retrieve Enflo's uniformly convex renorming of super-reflexive Banach spaces as the regularization of a raw function built from trees. Among other applications, we provide a sharp estimation of the distance of a given function to the set of differences of Lipschitz convex functions. Finally, we prove the equivalence of several possible ways to quantify the super weakly noncompactness of a convex subset of a Banach space.     

Sufficient global optimality conditions for weakly convex minimization problems

In this paper, we present sufficient global optimality conditions for weakly convex minimization problems using abstract convex analysis theory. By introducing (L,X)-subdifferentials of weakly convex functions using a class of quadratic functions, we first obtain some sufficient conditions for global optimization problems with weakly convex objective functions and weakly convex inequality and equality constraints. Some sufficient optimality conditions for problems with additional box constraints and bivalent constraints are then derived.      

弱射影与De Morgan代数的同余关系

本文借助弱射影和弱透视的概念刻划了Ｄｅ Ｍｏｒｇａｎ代数的同余关系,由此得到了Ｋａｌｍａｎ关于Ｄｅ Ｍｏｒｇａｎ代数次直不可约定理的一个新的证明并证明了一个完全分配的Ｄｅ Ｍｏｒｇａｎ代数的同余理想与同余关系一一对应的充要条件是Ｌ为弱可补的。