Additive Adjugate Preservers on the Matrices over Fields

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＳｕｐｐｏｓｅｔｈａｔＦｉｓａｆｉｅｌｄａｎｄＦ＊ｉｔｓｍｕｌｔｉｐｌｉｃａｔｉｖｅｇｒｏｕｐ．ＬｅｔＭｎ（Ｆ）ａｎｄＳｎ（Ｆ）ｂｅｔｈｅｓｐａｃｅｏｆａｌｎ×ｎｍａｔｒｉｃｅｓａｎｄａｌｎ×ｎｓｙｍｍｅｔｒｉｃｍａｔｒ...     

On Rational Bases of Subspaces of F((D))~n

ＯｎＲａｔｉｏｎａｌＢａｓｅｓｏｆＳｕｂｓｐａｃｅｓｏｆＦ（（Ｄ））~ｎＷａｎＺｈｅｘｉａｎ（万哲先）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ，１０００８０ａｎｄＤｅｐａｒ?..     

Saks空间中（A）型相容映射的叠合点及公共不动点（英）

ＣｏｉｎｃｉｄｅｎｃｅＰｏｉｎｔｓａｎｄＣｏｍｍｏｎＦｉｘｅｄＰｏｉｎｔｓｆｏｒＣｏｍｐａｔｉｂｌｅＭａｐｓｏｆＴｙｐｅ（Ａ）ｏｎＳａｋｓＳｐａｃｅｓＰ．Ｐ．Ｍｕｒｔｈｙ，Ｂ．Ｋ．Ｓｈａｒｔｒｉａ，Ｙ．Ｊ．ＣｈｏＣｏｉｎｃｉｄｅｎｃｅＰｏｉｎｔｓａｎ...     

Fuzzy S-Regular Spaces and S-Almost Regular Spaces

ＦｕｚｚｙＳＲｅｇｕｌａｒＳｐａｃｅｓａｎｄＳＡｌｍｏｓｔＲｅｇｕｌａｒＳｐａｃｅｓＦａｎｇＪｉｎｍｉｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＯｃｅａｎＵｎｉｖｅｒｓｉｔｙｏｆＱｉｎｇｄａｏ，Ｑｉｎｇｄａｏ，２６６０...     

Conesin Integrable Vector Valued Function SpacesandAbstractImpulsiveIntegro┐diferentialEquations

ＣｏｎｅｓｉｎＩｎｔｅｇｒａｂｌｅＶｅｃｔｏｒＶａｌｕｅｄＦｕｎｃｔｉｏｎＳｐａｃｅｓａｎｄＡｂｓｔｒａｃｔＩｍｐｕｌｓｉｖｅＩｎｔｅｇｒｏ┐ｄｉｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎｓ＊）ＬｉｕＷｅｉａｎ（刘伟安）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍ...     

Teichmüller Spaces and Function Spaces

ＴｅｉｃｈｍüｌｅｒＳｐａｃｅｓａｎｄＦｕｎｃｔｉｏｎＳｐａｃｅｓＧｕｏＨｕｉ（郭辉）（ＳｃｈｏｌｏｆＭａｔｈｅｍａｔｉｃａｌＳｃｉｅｎｃｅ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ，１００８７１）ＣｏｍｍｕｎｉｃａｔｅｄｂｙＬｉＺｈｏｎｇＲ...     

The Strong Compact-covering ss-images of Metric Spaces

ＴｈｅＳｔｒｏｎｇＣｏｍｐａｃｔ┐ｃｏｖｅｒｉｎｇｓｓ┐ｉｍａｇｅｓｏｆＭｅｔｒｉｃＳｐａｃｅｓＬｉＫｅｄｉａｎ（李克典）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａｎｇｑｉｕＴｅａｃｈｅｒｓ＇Ｃｏｌｅｇｅ，Ｈｅｎａｎ，４７６０００）Ａｂ...     

The U~* -property of Orlicz Spaces

Ａｂｓｔｒａｃｔ：ＦｏｒＯｒｌｉｃｚｓｐａｃｅｓ，ｔｈｅｃｒｉｔｅｒｉａｏｆＵ＊－ｐｒｏｐｅｒｔｙａｒｅｇｉｖｅｎ．Ｋｅｙｗｏｒｄｓ：ＯｒｌｉｃｚＳｐａｃｅｓ；Ｕ－ｐｒｏｐｅｒｔｙ；Ｕ＊－ｐｒｏｐｅｒｔｙ（王廷辅）（计东海）Ｌｅｔ（Ｘ，１１＇１１）ｂ...     

Devil＇s Staircase of K－H Waves in a SeparatingShearLayerwithAcousticExcitation

Ｄｅｖｉｌ＇ｓＳｔａｉｒｃａｓｅｏｆＫ－ＨＷａｖｅｓｉｎａＳｅｐａｒａｔｉｎｇＳｈｅａｒＬａｙｅｒｗｉｔｈＡｃｏｕｓｔｉｃＥｘｃｉｔａｔｉｏｎＹ．Ｆ．ＤＯＮＧ，Ｚ．Ｌ．ＷＥＩａｎｄＣ．ＸＵｆ（Ｄｅｐｔ．ｏｆＭｅｃｈａｎｉｃｓａｎｄＥｎｇｉｎｅｅｒｉｎ...     

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

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

Cleavability in Ordered Spaces

In this paper we study the role of cleavability and divisibility in the topology of generalized ordered (GO-)spaces. We characterize cleavability of a GO-space over the class of metrizable spaces, and over the spaces of irrational and rational numbers. We present a series of examples related to characterizations of cleavability over separable metric spaces and over the space of real numbers.     

Orthogonality spaces and orthogonally additive mappings

Summary An open problem on orthogonality spaces posed by Jürg R?tz in [10] (also cf. [14] is completely solved in this paper, so that orthogonality spaces admitting nonzero even orthogonally additive mappings are completely described. As a by-product, a characterization of real inner product spaces is also given.     

关于随机赋范空间与随机内积空间的某些基本理论(英文)

首先提出随机度量空间定义的另一个提法,这提法不仅等价于原始的定义而且也使随机度量空间自动归入广义度量空间的框架,也考虑了关于拓扑结构的某些新的问题;循着同样的思路,对随机赋范空间的定义也作了新的处理并同时简化了随机赋范模的定义．其次本文也证明了一个Ｅ－范空间的商空间等距同构于一个典型的Ｅ－范空间;进一步,在概率赋范空间的框架下证明了一个概率赋伪范空间是伪内积生成空间的充要条件是它等距同构于一个Ｅ－内积空间,这回答了Ｃ．Ａｌｓｉｎａ与Ｂ．Ｓｃｈｗｅｉｚｅｒ等人新近提出的公开问题．最后,本文转向了它的中心部分──关于随机内积空间的研究,对随机内积空间中的特有且复杂的正交性作较系统的讨论,论证了只有几乎处处正交性才是唯一合理的正交性概念,在此基础上本文尤其将Ｇ．Ｓｔａｍｐａｃｃｈｉａ的在众多学科中都有多种用途的一般投影定理（或称变分不等式解存在性定理）以适当形式推广到完备实随机内积模上．     

Isosceles-orthogonality preserving property and its stability

For real normed spaces, we consider the class of linear operators, preserving approximately the relation of isosceles-orthogonality. We show some general properties of such mappings. Next, we examine whether an approximately orthogonality preserving mapping admits an approximation by an orthogonality preserving one. In regard to this, we generalize some results obtained earlier for inner product spaces with standard orthogonality relation.     

Cleavability in Semigroups

The notion of cleavability (splittability) is observed to apply not only to topological spaces, where it was first developed, but to semigroups also. Several results of the form 'if a semigroup D is cleavable over a class of semigroups each of which has property P, then D also has property P' are derived, and some suggestions for further investigations are put forward.     

Pythagorean euclidean four point properties

Characterizations of real inner product spaces among a class of metric spaces have been obtained based on homogeneity of metric pythagorean orthogonality, a metrization of the concept of pythagorean orthogonality as defined in normed linear spaces. In the present paper a considerable weakening of this hypothesis is shown to characterize real inner product spaces among complete, convex, externally convex metric spaces, generalizing a result of Kapoor and Prasad [9], and providing a connection with the many characterizations of such spaces using euclidean four point properties.     

An orthogonality in normed linear spaces based on angular distance inequality

In this paper, we present a new orthogonality in a normed linear space which is based on an angular distance inequality. Some properties of this orthogonality are discussed. We also find a new approach to the Singer orthogonality in terms of an angular distance inequality. Some related geometric properties of normed linear spaces are discussed. Finally a characterization of inner product spaces is obtained.     

An orthogonality type based on invariant inner products

Aequationes mathematicae - A new orthogonality type in normed linear spaces, which is based on invariant inner products, is introduced. It is shown that this orthogonality has properties of...     

Area orthogonality in normed linear spaces

A new concept of orthogonality in real normed linear spaces is introduced. Typical properties of orthogonality (homogeneity, symmetry, additivity, ...) and relations between this orthogonality and other known orthogonalities (Birkhoff, Boussouis, Unitary-Boussouis and Diminnie) are studied. In particular, some characterizations of inner product spaces are obtained.     

Complements on Diminnie Orthogonality

A new orthogonality relation for normed linear spaces is introduced by C. R. DIMINNIE in [10]. Some interesting properties of such orthogonality and its relationship with Birkhoff orthogonality are studied in the above paper. The first part of this paper begins with a geometrical interpretation of Diminnie-orthogonality which allows us to obtain some other properties of such orthogonality. The second part deals with relationships between Diminnie orthogonality and some other known orthogonalities.