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.     

Vector spaces as unions of proper subspaces

In this note, we find a sharp bound for the minimal number (or in general, indexing set) of subspaces of a fixed (finite) codimension needed to cover any vector space V over any field. If V is a finite set, this is related to the problem of partitioning V into subspaces.     

On Convergence Approach Spaces

The extension of two axioms due to Cook and Fischer to the category CAP of convergence approach spaces leads to the study of non-Archimedean approach spaces as well as two versions of regularity appropriate to CAP and related categories.     

关于次可分解算子的不变子空间

In this paper,we prove the Mohebi-Radjabalipour Conjecture under an ad-ditional condition,and obtain an invariant subspace theorem on subdecomposableoperators.     

超积空间及其性质

引进了和内积空间没有相互包含关系的一类新空间:超积空间,进而研究了超积空间的性质.这类新的线性空间具有许多内积空间的重要性质,从而得到了线性空间一类新的度量刻画.     

On simultaneous weakly-Chebyshev subspaces

In this paper, we shall introduce and characterize simultaneous quasi-Chebyshev (and weakly-Chebyshev) subspaces of normed spaces with respect to a bounded set S by using elements of the dual space.     

On separable Banach subspaces

We show that any infinite-dimensional Banach (or more generally, Fréchet) space contains linear subspaces of arbitrarily high Borel complexity which admit separable complete norms giving rise to the inherited Borel structure.     

Vector Hulls of Affine Spaces and Affine Bundles

Every affine space A can be canonically immersed as a hyperplane into a vector space  , which is called the vector hull of A. This immersion satisfies a universal property for affine functions defined on A. In the same way, every affine map between affine spaces has a linear prolongation to their vector hulls. Though not much known, this construction is greatly clarifying, both for affine geometry and for its applications. The goal of this paper is to perform a thorough study of the vector hull functor and to describe its counterpart in the framework of affine bundles. With this respect, it is shown that the vector hull of some interesting affine bundles, and more specifically some jet bundles, can be identified with certain vector bundles.      

Limiting values of the variance and the moments of the dimension of a sum or intersection of random vector subspaces

Let W be an n-dimensional vector space over a field F; for each positive integer m, let the m-tuples (U₁, …, U_m) of vector subspaces of W be uniformly distributed; and consider the statistics X_m,1 dim_F(∑_i=1^m U_i) and X_m,2 dim_F (∩_i=1^m U_i). If F is finite of cardinality q, we determine lim E(X_m,1^k), and lim E(X_m,2^k), and hence, lim var(X_m,1) and lim var(X_m,2), for any k > 0, where the limits are taken as q → ∞ (for fixed n). Further, we determine whether these, and other related, limits are attained monotonically. Analogous issues are also addressed for the case of infinite F.     

On existence subspaces inC(Q)

The property of a space to be an existence subspace is studied for subspacesE ofC(Q) such that eitherE orC(Q)/E is a Lindenstrauss space. For a Chebyshev subspaceL⊂C(Q)₁ an analytic representation of the nearest element in terms of the annihilatorL ^┴ is obtained. Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 726–737, May, 1999.     

Segments in a planar nearring

Suppose (N,+,·) is a finite (left) planar nearring. Define the (line) segment in N with endpoints a and b by

We prove that under many circumstances we have

which is the same phenomenon as in the Euclidean plane.     

On the Reflectivity and Coreflectivity of L-Fuzzifying Topological Spaces in L-Topological Spaces

In this paper it is proved that for all completely distributive lattices L, the category of L-fuzzifying topological spaces can be embedded in the category of L-topological spaces (stratified Chang-Goguen spaces) as a simultaneously bireflective and bicoreflective full subcategory. Received April 2, 1999, Revised January 31, 2000, Accepted February 2, 2000     

两点齐性的Finsler流形

该文证明任何一个两点齐性的Finsler流形一定是黎曼流形．证明过程中作者将泛函分析中经典的Mazur定理推广到不一定是绝对齐次的Minkowski空间上．     

关于射影平坦Finsler空间

本文研究了射影平坦Finsler空间的几何量及其几何性质。证明了射影平坦Finsler空间的Ricci曲率可完全由射影因子简洁地刻画出来。同时还证明了，在射影平坦Finsler空间中，平均Berwald曲率S=0意味着Ricci曲率Ric是二次齐次的。此外，给出了一个射影平坦Finsler空间成为常曲率空间或局部Minkowski空间的充分条件。     

关于一类姜空间

在这篇注记中,利用群的作用我们提供了一类姜空间。     

Vector sampling expansions in shift invariant subspaces

Multi-input multi-output (MIMO) sampling scheme which is motivated by applications in multi-channel deconvolution and multi-source separation has been investigated in many aspects. Common for most of results on MIMO systems is that the input signals are supposed to be band-limited. In this paper, we study vector sampling expansions on general finitely generated shift-invariant subspaces. Necessary and sufficient conditions for a vector sampling theorem to hold are given. We also give several examples to illustrate the main result.     

Subsets and subspaces

Several rules known to be valid within the set theory are revisited and considered from the point of view of the question whether they remain satisfied when sets are replaced with subspaces from C_n,1. It is shown that some of the set relationships hold true upon such a replacement, however, there is also an extensive class of relationships whose validity is no longer guaranteed; in this class the commutativity of the orthogonal projectors onto the involved subspaces proves to play an important role. Some related results inspired by probability theory are established as well.     

关于概率准度量族空间的等距同构

引入了带指标的准度量族空间的概念，讨论了带指标的准度族空间与概率准度量族空间和随机准度量族空间之间的关系，建立了这些空间的一些性质，研究了这些空间的等矩同构．