$G$核开集,$G$核邻域与$G$ 核导集

在拓扑空间中, 在$G$方法意义下以$G$壳与$G$核为基础, 引入$G$壳闭集,$G$核开集,$G$核邻域与$G$核导集的概念, 讨论其相应的一些性质. 特别的, 定义了点式$G$方法, 提供了在此方法下$G$闭集与$G$壳闭集, $G$开集与$G$核开集, $G$邻域与$G$核邻域, $G$导集与$G$核导集的一致性, 丰富了拓扑空间中关于$G$闭集, $G$开集, $G$内部, $G$邻域和$G$导集的一些结果. 同时, 提出一些问题以供进一步研究.     

强W-Gorenstein 复形

对自正交模类$\mathcal{W}$,引入了强$\mathcal{W}$-Gorenstein复形的概念.给出了强$\mathcal{W}$-Gorenstein复形的刻画,并将其应用到强Gorenstein内射复形.     

Entropy solutions for nonlinear elliptic anisotropic problems with homogeneous Neumann boundary condition

This study is about a nonlinear anisotropic problem with homogeneous Neumann boundary condition. We first prove, by using the technic of monotone operators in Banach spaces, the existence of weak solution, and by approximation methods, we achieve a result of existence and uniqueness of entropy solution     

齐型空间上的Morrey空间广义极大算子的有界性

主要讨论了齐型空间上的Morrey空间极大算子的有界性,得到了极大算子Mq与M的一个等价关系,即Mq是Lp,(Ф)(X,μ)到Lp,(Ф)(X ,β)有界的等价M的有界性.     

Global well-posedness for a Boussinesq-Navier-Stokes system with critical dissipation

In this paper we study a fractional diffusion Boussinesq model which couples a Navier-Stokes type equation with fractional diffusion for the velocity and a transport equation for the temperature. We establish global well-posedness results with rough initial data.     

Boundary value problems for the Laplacian in convex and semiconvex domains

We study the fully inhomogeneous Dirichlet problem for the Laplacian in bounded convex domains in Rn, when the size/smoothness of both the data and the solution are measured on scales of Besov and Triebel-Lizorkin spaces. As a preamble, we deal with the Dirichlet and Regularity problems for harmonic functions in convex domains, with optimal nontangential maximal function estimates. As a corollary, sharp estimates for the Green potential are obtained in a variety of contexts, including local Hardy spaces. A substantial part of this analysis applies to bounded semiconvex domains (i.e., Lipschitz domains satisfying a uniform exterior ball condition).     

Hierarchy of Hamilton equations on Banach Lie-Poisson spaces related to restricted Grassmannian

We consider the Banach Lie-Poisson space and its complexification , where the first one of them contains the restricted Grassmannian Grres as a symplectic leaf. Using the Magri method we define an involutive family of Hamiltonians on these Banach Lie-Poisson spaces. The hierarchy of Hamilton equations given by these Hamiltonians is investigated. The operator equations of Ricatti-type are included in this hierarchy. For a few particular cases we give the explicit solutions.     

Relations between some basic results derived from two kinds of topologies for a random locally convex module

The purpose of this paper is to exhibit the relations between some basic results derived from the two kinds of topologies (namely the (ε,λ)-topology and the stronger locally L⁰-convex topology) for a random locally convex module. First, we give an extremely simple proof of the known Hahn-Banach extension theorem for L⁰-linear functions as well as its continuous variant. Then we give the relations between the hyperplane separation theorems in [D. Filipovi?, M. Kupper, N. Vogelpoth, Separation and duality in locally L⁰-convex modules, J. Funct. Anal. 256 (2009) 3996-4029] and a basic strict separation theorem in [T.X. Guo, H.X. Xiao, X.X. Chen, A basic strict separation theorem in random locally convex modules, Nonlinear Anal. 71 (2009) 3794-3804]: in the process we also obtain a very useful fact that a random locally convex module with the countable concatenation property must have the same completeness under the two topologies. As applications of the fact, we prove that most of the previously established principal results of random conjugate spaces of random normed modules under the (ε,λ)-topology are still valid under the locally L⁰-convex topology, which considerably enriches financial applications of random normed modules.     

On p-approximation properties for p-operator spaces

This paper has a two-fold purpose. Let 1<p<∞. We first introduce the p-operator space injective tensor product and study various properties related to this tensor product, including the p-operator space approximation property, for p-operator spaces on Lp-spaces. We then apply these properties to the study of the pseudofunction algebra PFp(G), the pseudomeasure algebra PMp(G), and the Figà-Talamanca-Herz algebra Ap(G) of a locally compact group G. We show that if G is a discrete group, then most of approximation properties for the reduced group C^∗-algebra , the group von Neumann algebra VN(G), and the Fourier algebra A(G) (related to amenability, weak amenability, and approximation property of G) have the natural p-analogues for PFp(G), PMp(G), and Ap(G), respectively. The p-completely bounded multiplier algebra McbAp(G) plays an important role in this work.