图闭模糊映射与闭模糊映射的关系研究

给出图闭模糊映射和闭模糊映射的关系:图闭模糊映射一定是闭模糊映射;若闭模糊映射是上半连续的则它也是图闭模糊映射.     

形式演绎系统L~*中封闭理论的性质及其应用

本文在模糊命题演算的形式演绎系统L~*中引入了封闭理论的概念,讨论了封闭理论的基本性质,并利用封闭理论给出了形式演绎系统L~*的基于公式集的完备性的证明.首先,在形式演绎系统L~*中引入了封闭理论的概念,给出了理论封闭化扩张的方法;其次,在形式演绎系统L~*中引入了完全封闭理论的概念,证明了满足相关条件的完全封闭理论的存在性;第三,对形式演绎系统L~*中的封闭理论确定的同余关系性质进行了讨论,在公式集中引入了强同余关系的概念,给出了封闭理论和强同余关系相互决定的方法;第四,在形式演绎系统L~*中证明了封闭理论型L~*-Lindenbaum代数是R_0代数,并且封闭理论型L~*-Lindenbaum代数是全序的当且仅当封闭理论是完全的;最后,利用完全封闭理论型L~*-Lindenbaum代数完成了形式系统L~*完备性的证明,并改进了原有的结果.     

环的代数封闭性

证明了任一环有代数封闭的扩张环,且实封闭域上的四元数体是代数封闭的,给出了代数封闭环的若干性质.     

AF C*-代数中的Lie理想

本文描述了AF C*-代数中闭Lie理想,证明了如果AF C*-代数A中的线性流形L 是A的闭Lie理想,则存在A的闭结合理想I和A的典型masa D中的闭子代数EI使得[A,I](?)L(?)I EI,并且A中每一个这种形式的闭子空间都是A的闭Lie理想.     

Some properties of graphs of closed operators

In this paper we study some properties of graphs of closed operators in Hilbert spaces. We construct representations of von Neumann algebras induced by graphs of closed operators. We describe some classes of closed operators in terms of their characteristic matrices and study some properties of operations on graphs of closed operators.     

QUantale中的闭滤子

在Quantale中讨论了与Gabriel拓扑密切关联的闭滤子,给出了闭滤子与闭映射之间的相互确定关系．证明了凝聚左侧Quantale Q的闭滤子全体F(Q)在包含序下构成Frame,并且Q的紧闭滤子全体Fc(Q)是F(Q)的子Frame．最后,证明了凝聚双侧交换Quantale的紧闭滤子全体在包含序下构成Coherent Frame．     

局部可分度量空间闭s映象的注记

该文讨论局部可分度量空间闭s映象的分解定理, 证明了正则的Fréchet空间是局部可分度量空间的闭s映象当且仅当满足如下条件: 具有点可数的cs*网, 第一可数的闭子空间是局部可分的, 且Lindelof的闭子空间是可分的.     

Almost Integrally Closed Domains

Abstract

A domain R is called almost integrally closed if R is integrally closed in R _P for each nonzero P ∈ Spec(R). Arbitrary quasilocal domains of (Krull) dimension 1 and arbitrary integrally closed domains are examples of almost integrally closed domains. There are no other examples in the contexts of Noetherian, one-dimensional or pseudo-valuation domains, as a consequence of the fact that any almost integrally closed domain that is not integrally closed has at most one height 1 prime ideal. However, a pullback example shows that a non-integrally closed domain that is almost integrally closed need not be semiquasilocal or of dimension at most 1. By analyzing the behavior of the almost integrally closed property for CPI-extensions, we obtain a characterization of the almost integrally closed locally divided domains. Applications are given to the case of G-domains. It also follows that if a divided domain R is not a field, then R is almost integrally closed if and only if some (resp., each) nonzero P ∈ Spec(R) is such that R _P is almost integrally closed and R is integrally closed in R _P .     

Locally Closed Semirings and Iteration Semirings

Locally closed semirings, iteration semirings and Conway semirings play an important role in the algebraic theory of semirings and theoretical computer science. Z. ésik and W. Kuich showed that a locally closed commutative semiring is an iteration semiring (is also a Conway semiring). By study of polynomial semirings and matrix semirings, we obtain new expressions of certain polynomials and show that all matrix semirings over a locally closed semiring are also locally closed, and so a locally closed semiring (which need not be commutative) is an iteration semiring.     

A universal mapping characterization of the completion by cuts

Closed maps of lattices are defined to be those satisfying the condition that the inverse image of closed ideals are closed ideas. Residuated maps are closed and closed maps are complete-join homomorphisms. The natural embeddingj of a lattice into its completion by cuts is a closed map. For every closed map ϕ from a latticeL into a complete latticeM, there exists a unique closed map φ* from the completion by cutsL intoM such that φ*j=φ. This characterizes the completion by cuts. Presented by R. P. Dilworth.     

Centrally closed hopf module algebras

We introduce a concept of centrally closed Hopf module algebras and show that centrally closed Hopf module algebras inherit all basic properties of centrally closed algebras.     

闭集与闭区间上连续函数的性质

本文首先分析了闭集与闭区间上连续函数的联系,随之在此基础上证明了闭区间上连续函数常用的一些性质     

Locally Closed Semirings and Iteration Semirings

Locally closed semirings, iteration semirings and Conway semirings play an important role in the algebraic theory of semirings and theoretical computer science. Z. ésik and W. Kuich showed that a locally closed commutative semiring is an iteration semiring (is also a Conway semiring). By study of polynomial semirings and matrix semirings, we obtain new expressions of certain polynomials and show that all matrix semirings over a locally closed semiring are also locally closed, and so a locally closed semiring (which need not be commutative) is an iteration semiring.     

The index growth and multiplicity of closed geodesics

In the recent paper [31] of Long and Duan (2009), we classified closed geodesics on Finsler manifolds into rational and irrational two families, and gave a complete understanding on the index growth properties of iterates of rational closed geodesics. This study yields that a rational closed geodesic cannot be the only closed geodesic on every irreversible or reversible (including Riemannian) Finsler sphere, and that there exist at least two distinct closed geodesics on every compact simply connected irreversible or reversible (including Riemannian) Finsler 3-dimensional manifold. In this paper, we study the index growth properties of irrational closed geodesics on Finsler manifolds. This study allows us to extend results in [31] of Long and Duan (2009) on rational, and in [12] of Duan and Long (2007), [39] of Rademacher (2010), and [40] of Rademacher (2008) on completely non-degenerate closed geodesics on spheres and CP² to every compact simply connected Finsler manifold. Then we prove the existence of at least two distinct closed geodesics on every compact simply connected irreversible or reversible (including Riemannian) Finsler 4-dimensional manifold.     

Subspaces of non-commutative spaces

This paper concerns the closed points, closed subspaces, open subspaces, weakly closed and weakly open subspaces, and effective divisors, on a non-commutative space.

     

三维空间型中闭曲面和测地球面的比较

本文建立关于三维空间型中的可定向闭曲面的某些公式.引入积分绝对平均曲率来描述可定向闭曲面的平均弯曲程度.在此意义上,可定向闭曲面可以与作为包含该闭曲面的凸的测地球的边界测地球面进行比较,这种比较能用于说明空间型自身的某些属性     

复合型裂纹应变能释放率逐点闭合的外推逼近研究

提出用外推逼近法计算复合型裂纹的应变能量释放率的新方法,闭合能计算时,采用逐点闭合的方法。避免了某些文献中闭合能计算不能自治的缺点:"当沿经向闭合节点多于两个时,裂纹(脱层)前端节点力乘位移已计算了闭合能,中间点还要重复计算闭合能"。具体计算了DCB(双悬臂梁)试件并与理论解进行了比较,吻合度优于其他方法。同时,又计算了紧凑拉伸试件、三点弯曲试件、单边裂纹试件,均取得满意结果。与理论解比较,误差可控制在1%之内。此方法可以广泛用于类似复合材料脱层裂纹的断裂力学分析。     

Banach空间中闭线性算子广义预解式存在定理

在Banach空间中研究闭线性算子广义逆扰动问题和广义预解式存在性问题.给出了闭线性算子广义逆在T-有界扰动下的一些稳定特征,这些特征推广了在有界线性算子情形、闭线性算子有界扰动情形以及闭线性算子保值域或保核空间情形的一些已知结果.以此为基础,得到了闭线性算子广义预解式存在的一些充要条件及其广义预解式的显式表达式.作为应用,给出了闭Fredholm算子和闭半-Fredholm算子的广义预解式存在性特征.     

Coherence for closed categories with biproducts

A coherence result for symmetric monoidal closed categories with biproducts is shown in this paper. It is also explained how to prove coherence for compact closed categories with biproducts and for dagger compact closed categories with dagger biproducts by using the same technique.