On representation theory and near-vector spaces

Topics relating to representation theory and near-vector spaces are explored. The general form of finite dimensional near-vector spaces of finite fields is given. We show that a near-vector space can be associated with a particular representation and in the case where F is a finite field, properties of these near-vector spaces are given.     

The decomposition of finite-dimensional near-vector spaces

In this paper, we study the decomposition of certain classes of finite-dimensional near-vector spaces, constructed using a result of van der Walt. We derive a formula for calculating the cardinality of the quasi-kernel for certain constructions and we associate a graph with each near-vector space, the regularity graph.     

On Subspaces and Mappings of Near-vector Spaces

We investigate subspaces and homogeneous and linear mappings of near-vector spaces.     

Linear mappings of near-vector spaces

In this paper we investigate the linear and affine mappings of near-vector spaces.     

Finite-Dimensional Near-Vector Spaces Over Fields of Prime Order

A theory is developed in terms of which all finite-dimensional near-vector spaces over ? _p (p a prime) are characterized.     

度量空间中有限点集的费马点

本文首先对紧致的度量拓扑空间证明了有限点集的费马点是存在的，其次，运用度量几何的经典方法考察了度量空间（包括双曲空间和Ｂａｎａｃｈ空间）中有限点集的费马点的唯一性，此外，还对ｎ维欧氏空间Ｅ＾ｎ中有限点集的费马作了进一步研究。     

Sub-Bergman Hilbert spaces

In this paper we analyze sub-Bergman Hilbert spaces in the unit disk associated with finite Blaschke products. We also analyze their analogues in weighted Bergman spaces.     

Linear operators in finite dimensional probabilistic normed spaces

In this paper, we consider strongly bounded linear operators on a finite dimensional probabilistic normed space and define the topological isomorphism between probabilistic normed spaces. Then we prove that every finite dimensional probabilistic normed space which is a topological vector space is complete.     

Suzuki群Sz(q)和线性空间的自同构群

本文研究了线性空间的几乎单的线传递自同构群.利用有限线性空间上线传递自同构群的经典结论,以及Suzuki群Sz(q)的性质,获得了线性空间上线传递且点本原的自同构群的基柱不是Sz(q)的结果,推广了关于线传递性空间的已有结果.     

Radon空间的非标准表示

证明了在扩大的非标准模型中S-空间可完全表示Radon空间并讨论了S-空间的若干性质.还给出一个有限Borel测度空间为Radon空间的充要条件.最后证明了Radon空间的一个＊-有限表示定理.     

Hybrid Projection Algorithm for Two Finite Families of Asymptotically Quasi ϕ-Nonexpansive Mappings in Reflexive Banach Spaces

In this paper, we introduce a hybrid projection algorithm for two finite families of asymptotically quasi ?-nonexpansive mappings to establish a convergence theorem in smooth, strictly convex, and reflexive Banach spaces. As applications, we state the convergence of hybrid projection algorithm for two finite families of asymptotically quasi-nonexpansive mappings in Hilbert spaces and the convergence for a system of equilibrium problems.     

The finiteness obstruction for loop spaces

For finitely dominated spaces, Wall constructed a finiteness obstruction, which decides whether a space is equivalent to a finite CW-complex or not. It was conjectured that this finiteness obstruction always vanishes for quasi finite H-spaces, that are H-spaces whose homology looks like the homology of a finite CW-complex. In this paper we prove this conjecture for loop spaces. In particular, this shows that every quasi finite loop space is actually homotopy equivalent to a finite CW-complex. Received: March 25, 1999.     

加权Bergman空间上的紧算子

本文讨论了加权Ｂｅｒｇｍａｎ空间上的Ｔｏｅｐｌｉｔｚ算子,证明了Ｔｏｐｌｉｔｚ算子的有限乘积的有限和是紧的当且仅当它的Ｂｅｒｅｚｉｎ变换在边界上趋向于零．     

On the structure of generalized symmetric spaces of SLn𝔽q)

In this paper we extend previous results regarding SL₂(k) over any finite field k by investigating the structure of the symmetric spaces for the family of special linear groups SL_n(k) for any integer n>2. Specifically, we discuss the generalized and extended symmetric spaces of SL_n(k) for all conjugacy classes of involutions over a finite field of odd or even characteristic. We characterize the structure of these spaces and provide an explicit difference set in cases where the two spaces are not equal.     

映像组公共不动点的存在性与稳定性

本文建立乘积距离空间中集值与单值映像组的非线性压缩型公共不动点定理以及集值映像组公共不动点集的稳定性定理.     

Local sampling set conditions in weighted shift-invariant signal spaces

How to represent a continuous signal in terms of a discrete sequence is a fundamental problem in sampling theory. Most of the known results concern global sampling in shift-invariant signal spaces. But in fact, the local reconstruction from local samples is one of the most desirable properties for many applications in signal processing, e.g. for implementing real-time reconstruction numerically. However, the local reconstruction problem has not been given much attention. In this article, we find conditions on a finite sampling set X such that at least in principle a continuous signal on a finite interval is uniquely and stably determined by their sampling value on the finite sampling set X in shift-invariant signal spaces.     

Blow-up of the maximal solution to 3D Boussinesq system in Lei-Lin-Gevrey spaces

For arbitrary initial data in Lei-Lin-Gevrey spaces, we investigate the blow-up phenomena in finite time to the local unique solution of the three-dimensional Boussinesq system. We determine the blow-up profile explicitly as a function of time, and we identify the low frequencies part as a solely responsible of this phenomena. Frequencies decomposition, functional spaces interpolation, and Leray theory are used.     

关于弱MCP空间与弱层空间

本文引入了与已知的一些空间类非常类似的两个概念,我们分别称它们为弱MCP空间与弱层空间.本文主要讨论了这两空间类的等价命题与一些基本性质,及它们与原有空间类的关系.     

Convergence theorems for nonexpansive mappings and feasibility problems

In this paper, we introduce an iteration scheme given by finite nonexpansive mappings in Banach spaces and then prove weak convergence theorems which are connected with the problem of image recovery. Using the results, we consider the problem of finding a common fixed point of finite nonexpansive mappings.