Density,Spread and Character of Spaces of Borel Subsets

Ｄｅｎｓｉｔｙ，ＳｐｒｅａｄａｎｄＣｈａｒａｃｔｅｒｏｆＳｐａｃｅｓｏｆＢｏｒｅｌ　ＳｕｂｓｅｔｓＹａｎｇＸｕ（杨旭）（ＤｅｐｅｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｉｐｉｎｇＮｏｒｍａｌＣｏｌｌｅｇｅ，Ｓｉｐｉｎｇ，１３６０００）ＣａｏＹｅ（曹...     

WELL-BEHAVED BASIS AND LR ARRAYS

ＷＥＬＬ－ＢＥＨＡＶＥＤＢＡＳＩＳＡＮＤＬＲＡＲＲＡＹＳＬＩＮＤＯＮＧＤＡＩ（林东岱）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ...     

ConcerningWeightedStirling－typePairs

ＣｏｎｃｅｒｎｉｎｇＷｅｉｇｈｔｅｄＳｔｉｒｌｉｎｇ－ｔｙｐｅＰａｉｒｓＬｅｅｔｓｃｈＣ．ＨｓｕＹｕＨｏｎｇｑｕａｎ（ＤａｌｉａｎＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｒｙ，Ｄａｌｉａｎ１１６０２４）ＣｏｎｃｅｒｎｉｎｇＷｅｉｇｈｔｅｄＳｔｉｒｌ...     

The Spectral Pictures of Completely Irreducible Operators and Decomposition Theorem Of Hilbert Space Operators

ＴｈｅＳｐｅｃｔｒａｌＰｉｃｔｕｒｅｓｏｆＣｏｍｐｌｅｔｅｌｙＩｒｒｅｄｕｃｉｂｌｅＯｐｅｒａｔｏｒｓａｎｄＤｅｃｏｍｐｏｓｉｔｉｏｎＴｈｅｏｒｅｍｏｆＨｉｌｂｅｒｔＳｐａｃｅＯｐｅｒａｔｏｒｓ￥ＪｉａｎｇＣｈｕｎｌａｎ（蒋春澜）（Ｄｅｐａｒｔｍｅｎ...     

ON GENERALIZATION OF SONAR SEQUENCES AND INTERMODULATION－FREE FREQUENCIES ASSIGNMENT SEQUENCES

ＣＨＥＮＷＥＮＤＥ（陈文德）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅｓ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ１０００８０，ＣｈｉｎａａｎｄＳｔａｔｅＫｅｙＬａｂｒａｒｙｏｆＩｎｆｏｒｍａｔｉｏｎＳｅｃｕｒ...     

The Sufficient and Necessary Conditions for the Space X in －Space（X，）to be a Cohomology Sphere

ＴｈｅＳｕｆｆｉｃｉｅｎｔａｎｄＮｅｃｅｓｓａｒｙＣｏｎｄｉｔｉｏｎｓｆｏｒｔｈｅＳｐａｃｅＸｉｎ－Ｓｐａｃｅ（Ｘ，）ｔｏｂｅａＣｏｈｏｍｏｌｏｇｙＳｐｈｅｒｅＺｈａｎｇＺｅｎｇｘｉ（张增喜）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｃａ...     

The Limit Distribution of Some PP CM Statistics with Enough High Dimensions and Large Sample Size

ＴｈｅＬｉｍｉｔＤｉｓｔｒｉｂｕｔｉｏｎｏｆＳｏｍｅＰＰＣＭＳｔａｔｉｓｔｉｃｓｗｉｔｈＥｎｏｕｇｈＨｉｇｈＤｉｍｅｎｓｉｏｎｓａｎｄＬａｒｇｅＳａｍｐｌｅＳｉｚｅＣｈｅｎｇＰｉｎｇ（成平）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，Ａｃａ...     

Complete Distributivity of the Latice LC（S）ofLatice┐orderedSemigroups

ＣｏｍｐｌｅｔｅＤｉｓｔｒｉｂｕｔｉｖｉｔｙｏｆｔｈｅＬａｔｉｃｅＬＣ（Ｓ）ｏｆＬａｔｉｃｅ┐ｏｒｄｅｒｅｄＳｅｍｉｇｒｏｕｐｓＸｉｅＸｉａｎｇｙｕｎ（谢祥云）＊）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＬａｎｚｈｏｕＵｎｉｖｅｒｓｉｔｙ，...     

Boundary Value Problems for Nonlinear Differential Equations of Second Order inBanach Spaces

ＢａｎａｃｈＳｐａｃｅｓＢｏｕｎｄａｒｙＶａｌｕｅＰｒｏｂｌｅｍｓｆｏｒＮｏｎｌｉｎｅａｒＤｉｆｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎｓｏｆＳｅｃｏｎｄＯｒｄｅｒｉｎＢａｎａｃｈＳｐａｃｅｓＣｕｉＣｈａｎｇｊｕｎＬｉｕＹａｎｓｈｅｎｇ（Ｄｅｐｔ．ｏｆＭａ...     

A Construction of Cartesian Authentication Codes from Vector Space and Dual Authentication Codes

ＡＣｏｎｓｔｒｕｃｔｉｏｎｏｆＣａｒｔｅｓｉａｎＡｕｔｈｅｎｔｉｃａｔｉｏｎＣｏｄｅｓｆｒｏｍＶｅｃｔｏｒＳｐａｃｅａｎｄＤｕａｌＡｕｔｈｅｎｔｉｃａｔｉｏｎＣｏｄｅｓＦｅｎｇＲｏｎｇｑｕａｎ（冯荣权）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ...     

I-fuzzy拓扑空间中的Moore-Smith收敛

用方进明提出的I-fuzzy拟重邻域系研究I-fuzzy拓扑空间中的Moore-Smith收敛性，给出它的应用，并获得了很多重要结论。     

L-模糊化拓扑空间中的Moore-Smith收敛理论

This paper presents a definition of L-fuzzifying nets and the related L-fuzzifying generalized convergence spaces. The Moore-Smith convergence is established in L-fuzzifying topology. It is shown that the category of L-fuzzifying generalized convergence spaces is a cartesianclosed topological category which embeds the category of L-fuzzifying topological spaces as a reflective subcategory.     

Axioms for Sequential Convergence

It is of general knowledge that those (ultra)filter convergence relations coming from a topology can be characterized by two natural axioms. However, the situation changes considerable when moving to sequential spaces. In case of unique limit points Kisyński (Colloq Math 7:205–211, 1959/1960) obtained a result for sequential convergence similar to the one for ultrafilters, but the general case seems more difficult to deal with. Finally, the problem was solved by Koutnik (Closure and topological sequential convergence. In: Convergence Structures 1984 (Bechyně, 1984). Math. Res., vol. 24, pp. 199–204. Akademie-Verlag, Berlin, 1985). In this paper we present an alternative approach to this problem. Our goal is to find a characterization more closely related to the case of ultrafilter convergence. We extend then the result to characterize sequential convergence relations corresponding to Fréchet topologies, as well to those corresponding to pretopological spaces.      

Continuous convergence and functional analysis

The usual setting for Functional Analysis is the category LCS of locally convex topological vector spaces. There are, however, advantages in working in a larger setting, the category CVS of convergence vector spaces—even if one's interest is restricted to LCS. In CVS, one has access to a dual structure, continuous convergence, unavailable in LCS.

We show that theorems such as Grothendieck's completion theorem, Ptak's closed graph and open mapping theorems and the Banach-Steinhaus theorem are transformed from technical results in LCS to transparent and elegant results when examined in CVS with continuous convergence. In the theory of distributions, important bilinear mappings such as evaluations, multiplication and convolution, which are separately continuous when viewed in LCS, become jointly continuous in CVS.     

Convergence on Categories

We introduce and study a concept of a convergence structure on a concrete category. The concept is based on using certain generalized filters for expressing the convergence. Some basic properties of the convergence structures are discussed. In particular, we study convergence separation and convergence compactness and investigate relationships between the convergence structures and the usual closure operators on categories. Dedicated to Professor E. Giuli and Professor G. Preuss on the occasion of their 65th birthdays.     

L-fuzzifying拓扑空间范畴和可延L-fuzzy拓扑空间范畴的Galois联络

在完全分配格的格值环境下,提供了L-fuzzifying拓扑结构和可延L-fuzzy拓扑结构相互转化的方法。还进一步研究了L-fuzzifying拓扑空间范畴和可延L-fuzzy拓扑空间范畴之间的关系。文中结果表明,L-fuzzifying拓扑空间范畴和可延L-fuzzy拓扑空间范畴之间存在Galois联络。     

New criterion of the approximation property

This paper is concerned with the approximation property which is an important property in Banach space theory. We show that a Banach space X has the approximation property if (and only if), for every Banach space Y, the set of finite rank operators from X to Y is dense in the corresponding space of compact operators, in the usual topology of uniform convergence on compact sets.     

On some types of covering rough sets from topological points of view

The concept of coverings is one of the fundamental concepts in topological spaces and plays a big part in the study of topological problems. This motivates the research of covering rough sets from topological points of view. From topological points of view, we can get a good insight into the essence of covering rough sets and make our discussions concise and profound. In this paper, we first construct a type of topology called the topology induced by the covering on a covering approximation space. This notion is indeed in the core of this paper. Then we use it to define the concepts of neighborhoods, closures, connected spaces, and components. Drawing on these concepts, we define several pairs of approximation operators. We not only investigate the relationships among them, but also give clear explanations of the concepts discussed in this paper. For a given covering approximation space, we can use the topology induced by the covering to investigate the topological properties of the space such as separation, connectedness, etc. Finally, a diagram is presented to show that the collection of all the lower and upper approximations considered in this paper constructs a lattice in terms of the inclusion relation ⊆.     

LF拓扑空间中的序列连通性

主要引进了拓扑空间中序列连通的定义,并给出了序列连通的一些刻画和性质研究.     

Convergence in measure of logarithmic means of quadratical partial sums of double Walsh-Fourier series

The main aim of this paper is to prove that the logarithmic means of quadratical partial sums of the double Walsh-Fourier series does not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of LlnL(I²), the set of the functions having logarithmic means of quadratical partial sums of the double Walsh-Fourier series convergent in measure is of first Baire category.