几乎相合性与Bayes相合性

本文包含两个部分，首先我们证明了一个定理，它断言：在唯一的条件“不同参数值对应着不同的分布”之下，必存在一个“几乎相合”的估计，其次，基于这一结果，我们在很一般的条件下证明了当样本量趋于无穹时，一个贝叶斯决策必然是贝叶斯相合的，也就是说，若以Ｒｎ记样本量为ｎ时虫叶斯决策的风叶斯风险，则当ｎ→∞时有Ｒｎ→ｉｎｆＬ（θ０α）这里Ｌ为损失函数，α跑遍行动空间，而θ０为真参数值。     

Fuzzy序列紧性,可数Fuzzy紧性和Fuzzy列紧性

本文引进了Fuzzy序列紧性、可数Fuzzy紧性和Fuzzy列紧性,它们是一般拓扑学中相应概念的“良扩张”(R. Lowen意义下),文中讨论了这些fts的主要性质,以及它们之间的联系。     

高阶泛函微分方程的振动性和渐近性

本文讨论带有强迫项的时滞型泛函微分方程的振动性和渐近性。对于形如和的方程得到了几个振动及渐近性质的判别准则。本文的结论的证明还修正了R.S.Dahiya在讨论线性方程时出现的错误。     

图的不可收缩性和end-正则性

图的半群理论是图的群理论的延伸．图的不可收缩性和end－正则性是其中受到普遍关注的课题．本文揭示了两者之间的内在联系．     

均匀性度量中的密集性偏差与稀疏性偏差

该文根据王元，方开泰［２］的近似偏差（discrepancy）的均匀性准则，定义了理想布点情况下的标准半径，定义了ｍ 维单位子空间Ｃｍ＝［０，１］中两点间的ｆ距离和ｇ距离，由此定义了最大空穴半径和最小空穴半径，提出了均匀性度量的密集性偏差与稀疏性偏差．给出了二维情况 下的计算结果．我们的方法计算量不大，不仅能较好地度量布点的均匀性以及布点在低维投影的均匀性，而且能指导如何调整布点使之尽可能与理想布点接近．     

随机指数系的完备性和极小性

得到了随机指数系在加权Banach空间Cα中完备和极小的充要条件,其中Cα是实直线R上的复连续函数在权α的一致范数下组成的Banach空间.这些结果可以看作是Malliavin经典结果的概率推广.     

线性距离空间的一致凸性与自反性

本文研究了线性距离空间的一致凸性与自反性，同时对吴从Ｘｉｎ等提出的严格缩条件能否去掉的问题给出了肯定的答案。     

二阶拟线性差分方程的振动性与渐近性

This paper is concerned with the oscillatory(and nonoscillatory)behavior of solutions of second oder quasilinear difference equations of the type Δ(g(Δyn-1)) f(n,yn)=0.Some necessary and sufficient conditions are given for the equation to admit oscillatory and nonocillatory solutions with special asymptotic properties.These results generalize and improve some konown results.     

一类偏差分方程解的振动性与渐近性

本培出了一类偏差分方程解的振动性的充分条件。     

算子矩阵代数的自反性和超自反性

本文总假定 H 是可分的 Hilbert 空间;L(H)表示 H 上有界线性算子全体;而 L(?)(H)表示 L(H)上σ-ω算子拓扑连续的线性泛函全体.设(?)L(H)为σ-ω算子拓扑闭的子代数,(?)称为自反的是指(?)=Alg Lat(?)={T∈L(H):TE(?)E (?)E∈Lat(?)},其中 Lat(?)是(?)的不变子空间格.(?)称为超自反的是指存在常数 K>0,使对任意的 T∈L(H)有 d(T,(?))≤K sup{‖P_M~(?)TP_M‖∶M∈Lat(?)}.其中 P_M 是指到 M 上的自伴投影。有关算子代数的超自反性已有一些结果,例如见     

L-拓扑空间中的相对强F紧性与相对超F紧性

In this paper,two concepts of relative compactness-the relative strong fuzzy compactness and the relative ultra-fuzzy compactness are defined in L-topological spaces for an arbitrary L-set.Properties of relative strong fuzzy sets and relative ultra-fuzzy compact sets are studied in detail and some characteristic theorems are given.Some examples are illustrated.     

L-拓扑空间中的几乎超紧L-子集

在L-拓扑空间中定义了L-子集的几乎超紧性,讨论了几乎超紧L-子集的性质以及L-子集的几乎超紧性与超紧性、近似超紧性及几乎良紧性之间的关系,给出了几乎超紧L-子集的网式及滤子刻画并证明了L-拓扑空间的几乎超紧性是几乎紧性的“L-推广”.     

L-拓扑空间的弱局部强F紧性及单点强F紧化

以R.Lowen的强F紧性为基础,定义了L-拓扑空间的弱局部强F紧性及单点强F紧化,推广了有关弱局部紧拓扑空间和拓扑空间的单点紧化的若干结果,证明了L-拓扑空间的弱局部强F紧性是拓扑空间的弱局部紧性的L-推广。     

Compact Hausdorff fuzzy topological spaces are topological

Many examples of compact fuzzy topological spaces which are highly non topological are known [5, 6]. Equally many examples of Hausdorff fuzzy topological spaces which are highly non topological can be given. In this paper we show that the two properties - compact and Hausdorff - combined however necessarily imply that the fuzzy topological space is topological. This at once solves some open questions with regard to the compactification of fuzzy topological spaces [8]. It also emphasizes once more the particular role played by compact Hausdorff topological spaces not only in the category of topological spaces but even in the category of fuzzy topological spaces.     

Compactness for manifolds and integral currents with bounded diameter and volume

By Gromov??s compactness theorem for metric spaces, every uniformly compact sequence of metric spaces admits an isometric embedding into a common compact metric space in which a subsequence converges with respect to the Hausdorff distance. Working in the class of oriented k-dimensional Riemannian manifolds (with boundary) and, more generally, integral currents in metric spaces in the sense of Ambrosio?CKirchheim and replacing the Hausdorff distance with the filling volume or flat distance, we prove an analogous compactness theorem in which however we only assume uniform bounds on volume and diameter.     

Almost compactness in fuzzy topological spaces

We introduce and study almost compactness for fuzzy topological spaces. We show that the almost continuous image of an almost compact fuzzy topological space is almost compact. Moreover, we show that generally almost compactness for fuzzy topological spaces is not product-invariant, but if X and Y are almost fuzzy topological spaces and X is product related to Y, then their fuzzy topological product is almost compact.     

RELATIVE COMPACTNESS AND COMPACTNESS OF GENERAL SUBSETS IN AN I- TOPOLOGICAL SPACE

Abstract

In a previous work, we introduced a form of compactness applicable to general fuzzy sets in an I-topological space. It was shown that many of the standard results for compactness in general topology remain valid in the fuzzy setting. In this paper we continue our investigations into the behaviour of compact fuzzy subsets. We also introduce the notion of a relatively compact fuzzy subset and obtain results very similar to those of general topology. Many of our results are in the setting of fuzzy neighbourhood space and fuzzy uniform spaces. In particular, a number of criteria for compactness, already known for the whole space, are extended to arbitrary fuzzy subsets in a fuzzy neighbourhood space.     

On fuzzy topological spaces

In this paper, a few separation properties and some aspects of subspace fuzzy topology have been studied, where both the crisp and the fuzzy elements have been taken into consideration. Since the conventional definition of compactness is not quite meaningful in Hausdorff fuzzy spaces (as introduced by us), a new more natural definition of proper compactness is given and a few properties resulting from this are established.     

A note on λ-compact spaces

We extend the well-known and important fact that “a topological space X is compact if and only if every ideal in C(X) is fixed”, to more general topological spaces. Some interesting consequences are also observed. In particular, the maximality of compact Hausdorff spaces with respect to the property of compactness is generalized and the topological spaces with this generalized property are characterized.     

Spectrum topology of a residuated lattice

In this paper, given a non-commutative residuated lattice L, a topological space is constructed using certain fuzzy subsets of L. Indeed, we show that the set of all prime fuzzy filters of a non-commutative residuated lattice L forms a topological space. Particularly, we show that this space is compact and a T ₀-space and its certain subspaces are Hausdorff spaces. Finally, we show that the set of all prime filters of L is also a Hausdorff space.