Modules over Operator Algebras and Its Module Maps

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具有奇异值分解性质的代数

设F为一个域,R为一个带有对合的F-代数,如果R上每一个矩阵都有奇异值分解(简称SVD),则称R为一个有SVD性质的F-代数.本文指出:R为一个有SVD性质的F-代数的充要条件是:R同构于R~+,或R~+上二次扩域,或R~+上四元数体((-1,-1)/R~+),其中R~+为R的对称元集合,并且R~+为一个Galois序闭域.     

THE RADICALS OF HOPF MODULE ALGEBRAS

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Topological Simplicity of a Certain LF-Algebra

We show that the LF-algebra considered by Akkar and Nacir in [1] is topologically simple.     

Interpolation of positive operators

We study problems of interpolation of positive linear operators in couples of ordered Banach spaces. From this viewpoint, we study couples of noncommutative spaces L ₁, L _∞ associated with weights and traces on von Neumann algebras.     

在可交换四元数空间中的双曲方程的特征边值问题

讨论了一阶和二阶双曲复方程的特征边值问题.对其中两种线性方程,分别在不同的情况下获得通解和可解条件.而对于拟线性的二阶双曲复方程,证明了解的存在性和唯一性.     

A parametric representation of linguistic hedges in Zadeh’s fuzzy logic

This paper proposes a model for the parametric representation of linguistic hedges in Zadeh’s fuzzy logic. In this model each linguistic truth-value, which is generated from a primary term of the linguistic truth variable, is identified by a real number r depending on the primary term. It is shown that the model yields a method of efficiently computing linguistic truth expressions accompanied with a rich algebraic structure of the linguistic truth domain, namely De Morgan algebra. Also, a fuzzy logic based on the parametric representation of linguistic truth-values is introduced.     

Dual Characterizations of Set Containments with Strict Convex Inequalities

Characterizations of the containment of a convex set either in an arbitrary convex set or in the complement of a finite union of convex sets (i.e., the set, described by reverse-convex inequalities) are given. These characterizations provide ways of verifying the containments either by comparing their corresponding dual cones or by checking the consistency of suitable associated systems. The convex sets considered in this paper are the solution sets of an arbitrary number of convex inequalities, which can be either weak or strict inequalities. Particular cases of dual characterizations of set containments have played key roles in solving large scale knowledge-based data classification problems where they are used to describe the containments as inequality constraints in optimization problems. The idea of evenly convex set (intersection of open half spaces), which was introduced by W. Fenchel in 1952, is used to derive the dual conditions, characterizing the set containments.     

求解通信网节点间全部路由的逻辑代数化算法

经典的D IJKSTRA和BELLM AN-F LOYD通信网络路由算法,只能根据特定网络参数得到最佳路由,却无法获得网络存在的全部可用路由,而通信网理论研究及网络管理等方面,往往需要获得节点之间的全部可用路由.研究出一种路由新算法,遵循逻辑代数运算规则、采用关联矩阵中行与行之间整合与删除方式计算,N个节点的网络只需N-1次整合及删除运算,就能得到源节点到任意节点两点之间全部路由结果.详细论证了算法的正确性与合理性,简介了算法的并行运算可行性及与经典路由算法的兼容性等问题.通过算例详细说明算法的计算过程,并验证其正确性.     

New Matrix Lie Algebra, a Powerful Tool for Constructing Multi-component C-KdV Equation Hierarchy

A set of new multi-component matrix Lie algebra is constructed, which is devoted to obtaining a new loop algebra A-2M. It follows that an isospectral problem is established. By making use of Tu scheme, a Liouville integrable multi-component hierarchy of soliton equations is generated, which possesses the multi-component Hamiltonian structures. As its reduction cases, the multi-component C-KdV hierarchy is given. Finally, the multi-component integrable coupling system of C-KdV hierarchy is presented through enlarging matrix spectral problem.