向量优化中有效点的存在性

分别在有pre-order的无线性结构的集合和拓扑空间中，给出了有效点的存在性。作为应用，讨论了向量优化问题中解的存在性。最后给出了紧、弱紧、锥紧、锥半紧、上序紧、下序紧、上序半紧、准上序半紧和准下序半紧等之间的关系。     

Sequential definitions of compactness

A subset F of a topological space is sequentially compact if any sequence of points in F has a convergent subsequence whose limit is in F. We say that a subset F of a topological group X is G-sequentially compact if any sequence of points in F has a convergent subsequence such that where G is an additive function from a subgroup of the group of all sequences of points in X. We investigate the impact of changing the definition of convergence of sequences on the structure of sequentially compactness of sets in the sense of G-sequential compactness. Sequential compactness is a special case of this generalization when G=lim.     

C~k(M)类函数集列紧的充要条件

本文讨论了 Rn中紧集 M上 Ck类函数 ,用构造 ε-网的方法给出了这类函数集列紧的一个充要条件 ,从而推广了著名的 Ascoli-Arzela定理     

Tychonoff products of compact spaces in ZF and closed ultrafilters

Let {(X_i, T_i): i ∈I } be a family of compact spaces and let X be their Tychonoff product. ??(X) denotes the family of all basic non‐trivial closed subsets of X and ??_R(X) denotes the family of all closed subsets H = V × ΠX_i of X, where V is a non‐trivial closed subset of ΠX_i and Q_H is a finite non‐empty subset of I. We show: (i) Every filterbase ?? ? ??_R(X) extends to a ??_R(X)‐ultrafilter ? if and only if every family H ? ??(X) with the finite intersection property (fip for abbreviation) extends to a maximal ??(X) family F with the fip. (ii) The proposition “if every filterbase ?? ? ??_R(X) extends to a ??_R(X)‐ultrafilter ?, then X is compact” is not provable in ZF. (iii) The statement “for every family {(X_i, T_i): i ∈ I } of compact spaces, every filterbase ?? ? ??_R(Y), Y = Π_{i ∈I}Y_i, extends to a ??_R(Y)‐ultrafilter ?” is equivalent to Tychonoff's compactness theorem. (iv) The statement “for every family {(X_i, T_i): i ∈ ω } of compact spaces, every countable filterbase ?? ? ??_R(X), X = Π_{i ∈ω}X_i, extends to a ??_R(X)‐ultrafilter ?” is equivalent to Tychonoff's compactness theorem restricted to countable families. (v) The countable Axiom of Choice is equivalent to the proposition “for every family {(X_i, T_i): i ∈ ω } of compact topological spaces, every countable family ?? ? ??(X) with the fip extends to a maximal ??(X) family ? with the fip” (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

I-模糊拓扑空间中的紧度

In this paper, the concept of degree of compactness is introduced in the general framework of I-fuzzy topological spaces, and its property is discussed. All good compactness are generalized to I-fuzzy topological spaces accordingly.     

Locally α-compact spaces based on continuous valued logic

This paper is a continuation of [1]. That is, it considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies), introduced by Ying [2]. It investigates topological notions defined by means of α-open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by Łukasiewicz logic in [0, 1]). Other characterizations of fuzzifying α-compactness are given, including characterizations in terms of nets and α-subbases. Several characterizations of locally α-compactness in the framework of fuzzifying topology are introduced and the mapping theorems are obtained.     

Almost Fuzzy Compactness in L-fuzzy Top ological Spaces

In this paper, the notion of almost fuzzy compactness is defined in L-fuzzy topological spaces by means of inequality, where L is a completely distributive DeMorgan algebra. Its properties are discusse...     

Existence of a global attractor for the parabolic equation with nonlinear Laplacian principal part in an unbounded domain

In this paper, we study the long-time behavior of solutions for the parabolic equation with non-linear Laplacian principal part in Rn. We prove the existence of a global (L₂(Rn), L_∞(Rn))-attractor when n?p and the existence of a global (L₂(Rn), )-attractor when n>p.     

与一拓扑紧性反例相关的结果

有反例表明一个紧致拓扑空间不一定是序列紧致的拓扑空间 .我们给出了一个与此反例密切相关的分析结果 ,表明由任一非常值的单边连续周期函数 ,都可构造一个这样的反例 .     

A Criterion for Relative Compactness of a Sequence of Measure-Valued Random Processes

A criterion for relative compactness of a sequence of measure-valued processes is proved and exemplified.     

An improvement of the Kolmogorov–Riesz compactness theorem

The purpose of this short note is to provide a new and very short proof of a result by Sudakov (1957), offering an important improvement of the classical result by Kolmogorov–Riesz on compact subsets of Lebesgue spaces.     

Convergence of relaxation schemes to the equations of elastodynamics

We study the effect of approximation matrices to semi-discrete relaxation schemes for the equations of one-dimensional elastodynamics. We consider a semi-discrete relaxation scheme and establish convergence using the theory of compensated compactness. Then we study the convergence of an associated relaxation-diffusion system, inspired by the scheme. Numerical comparisons of fully-discrete schemes are carried out.

     

Local Existence of Bounded Solutions to the Degenerate Stefan Problem with Joule's Heating

This paper deals with the degenerate Stefan problem with Joule's heating, which describes the combined effects of heat and electrical current Rows in a metal. The local existence of a bounded weak solution for the problem in proved. Also a degenerate thermistor problem with continuous conductivity is considered.     

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.     

A Grothendieck compactness principle for the Mackey dual topology

Grothendieck [6] proved that every norm compact subset of a Banach space is contained in the closed convex hull of a norm null sequence. In a recent paper [3], an analogous result for weak compactness in a Banach space is shown to be equivalent to the Schur property. In this article, we obtain a similar type result in the Mackey dual of a Banach space. A related result for weak^? compactness is also obtained.     

A note in approximative compactness and midpoint locally k-uniform rotundity in Banach spaces

In this article, we prove the following results: (1) A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; (2) A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set.     

Compactness Properties, Openness Criteria and Coderivatives

We study the local surjectivity and openness properties of mappings and correspondences by using coderivatives. We recall local criteria but concentrate on point criteria. Our study relies on a compactness condition which is of independent interest, for instance, for the study of the behavior of the injectivity constant of a linear map or of a convex process under stabilization procedures. Several known criteria for openness are shown to be a consequences of this new compactness condition.     

$I$-模糊拓扑空间中的模糊紧度

本文借助不等式给出了$I$-模糊拓扑空间中模糊紧度的概念, 并研究了相关的性质.     

(L,M)-模糊拓扑空间中模糊紧性的测度

本文借助不等式,在(L,M)-拓扑空间中引入了模糊紧性度的概念,并讨论了它的性质.     

全空间上带Hardy-Sobolev项的拟线性椭圆方程解的存在性

讨论了全空间上一类带Hardy-Sobolev项的拟线性椭圆问题,利用集中紧原理和适当的实验函数,得到并验证了(PS)_c条件,从而证明了该问题非平凡解的存在性.