A System of Four Matrix Equations over von Neumann Regular Rings and Its Applications

We consider the system of four linear matrix equations A1X = C1, XB2=C2, A3XB3=C3 and A4XB4 = C4 over h, an arbitrary von Neumann regular ring with identity. A necessary and sufficient condition for the existence and the expression of the general solution to the system are derived. As applications, necessary and sufficient conditions are given for the system of matrix equations A1X = C1 and A3X=C3 to have a bisymmetric solution, the system of matrix equations A1X = C1 and A3XB3 = C3 to have a perselfconjugate solution over h with an involution and char h≠2, respectively. The representations of such solutions are also presented. Moreover, some auxiliary resultson other systems over h are obtained. The previous known results on some systems of matrix equations are special cases of the new results.     

Semirings which are unions of rings

Sernirings which are a disjoint union of rings form a variety S which contains the variety of all rings and the variety of all idempotent sernirings, and in particular, the variety of distributive lattices. Various structure theorems are established which bring insight into the structure of the lattice of subvarieties of S.``     

Unitary couplings,scattering suboperators and regular factorizations of bounded operator valued functions II

In the paper bilateral shifts are studied which generate factorizations of unitary couplings (in the system theory they play the part of channels). Subspaces of L²(??), reducing the multiplication operator by e^it, are investigated in the channel language. New criteria for regular divisibility of contractive operator functions in the class L^∞ are obtained. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Generators in Ideals of Entire Functions of Finite Order and Type on the Plane

We study ideals in the space of entire functions of finite order and type on the plane. We obtain necessary and sufficient conditions for the ideal of functions vanishing at the common zeros of a system of N functions to be generated by the latter.     

二维广义Ginzburg-Landau方程在Banach空间的指数吸引子

本文应用能量积分和解析半群的有关估计,研究广义二维Ginzburg-Landau方程 在Banach空间LP(Ω)的子空间X-α的指数吸引子.     

强耦合反应扩散方程组的定性分析

本文研究由四个反应扩散方程组成的强耦合方程组，利用算子半群理论，上、下解方法和能量积分等经典分析方法，论证此类方程组的整体解的存在唯一性和有界性。     

Thermodynamics of solutions of iodine and perfluorocarbons in cycloalkanes

The solubilities of iodine from 9 to 30°C were measured in the C₅, C₆, C₇, C₈, and C₁₀ cycloalkanes. The solubilities were found to increase smoothly with ring size and to be greater than these of corresponding n-alkane. The results are analyzed in terms of the solubility parameter version of the regular solution theory and, unlike the n-alkanes, good agreement is found suggesting that the cycloalkanes are good model substances for testing theoretical predictions of the effect of molecular size on the thermodynamics of liquid mixtures and that molecular shape and flexibility need not be considered, at least in equilibrium properties governed by the free energy. A similar analysis of the upper critical solution temperatures of cyloalkane + perfluorotributylamine, cycloalkane + perfluorocyclohexane, and n-alkane + perfluorotributylamine mixtures leads to the same conclusion.     

Conditional measures and operators

A detailed study of the structure of conditional expectations and conditional probability measures is presented. Some characterizations of conditional expectations as a subclass of projection operators on Banach function spaces, and similarly conditional probabilities as a subclass of vector valued measures on such spaces are included. As applications of these results, a representation of Reynolds operators and related unified formulation of ergodic-martingale theorems are given.     

关于重尾随机和大偏差的一个注记

设｛Xκ，κ≥1｝为一列独立同分布的非随机变量，且具有共同的分布函数F。记Sn为序列｛Xκ，κ≥1｝的前n项部分和。在F属于ERV分布族的假定下，文中证明了关于随机和SN(t)的随机中心化的精细大偏差结果。这里N（t）为一个与｛Xκ，κ≥1｝独立的非负整数值的随机过程。