Wreath Products and Universal Equivalence

We consider the question of preservation of universal equivalence for the cartesian and direct wreath products of lattice-ordered groups and groups. We prove that the basic rank is infinite of the quasivariety of torsion-free nilpotent groups of nilpotence length c (c2)     

A universal property of reflexive hereditarily indecomposable Banach spaces

It is shown that every separable Banach space universal for the class of reflexive Hereditarily Indecomposable space contains isomorphically and hence it is universal for all separable spaces. This result shows the large variety of reflexive H.I. spaces.

     

Dedekind Complete Commutative BCK-algebras

We study Dedekind complete commutative BCK-algebras with the relative cancellation property and their connection with corresponding universal groups. We shall characterize Dedekind orthogonally complete atomic and Archimedean BCK-algebras, generalizing results of Jakubík known for MV-algebras. Finally, we characterize those Dedekind complete and atomic commutative BCK-algebras that are isomorphic to direct products of basic BCK-chains, generalizing a result of Cignoli for MV-algebras.     

Completion of Semiuniform Convergence Spaces

Semiuniform convergence spaces form a common generalization of filter spaces (including symmetric convergence spaces [and thus symmetric topological spaces] as well as Cauchy spaces) and uniform limit spaces (including uniform spaces) with many convenient properties such as cartesian closedness, hereditariness and the fact that products of quotients are quotients. Here, for each semiuniform convergence space a completion is constructed, called the simple completion. This one generalizes Császár's -completion of filter spaces. Thus, filter spaces are characterized as subspaces of convergence spaces. Furthermore, Wyler's completion of separated uniform limit spaces can be easily derived from the simple completion.     

量子纠缠态的普适远程克隆

提出一种任意两粒子纠缠态1→2普适远程克隆方案. 此方案仅需一个特殊的四粒子纠缠态作为量子信道, 就可使处于空间不同位置的两个接收者分别以5/6的保真度得到任意输入态的近似拷贝, 该保真度远高于已有方案中的保真度. 将方案推广到任意两粒子纠缠态1→N(N>2)普适远程克隆的情况, 可使处于不同地点的N个接收者分别以(2N+1)/(3N)的保真度得到输入态的近似拷贝. 另外, 提出一种以上述单个特殊四粒子纠缠态作为量子信道, 在多目标量子比特受控非门和 关键词： 量子纠缠态 普适远程克隆 保真度     

Analytic description of statistics of spectra of quantum graphs

We discuss how to obtain exact and approximate distributions for various statistical characteristics of the spectra of quantum graphs using previously found exact solutions of the spectral problem. We indicate the relation between the appearing spectral decompositions and the theory of weakly dependent random variables and indicate the relation between the known limit theorems for trigonometric sums and the universal statistical properties of the spectra of quantum chaotic systems. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 1, pp. 38–66, July, 2008.     

基于RM型通用门ULM3的对称函数综合

阐述了基本RM型对称函数的定义和性质，给出了任意”变量对称函数在n-1变量基本RM型对称函数完备集中展开系数的计算公式，在此基础上，提出了基于RM型三变量通用逻辑门ULM3的变量数为奇数或偶数的对称函数综合方法，实例验证了上述方法的有效性．     

一类时滞离散动力系统及其截断系统定性行为的研究

研究了一类时滞离散动力系统的一次截断系统,仔细分析其分支行为和混沌性态等定性行为.与原系统进行比较,证明二者主要的定性行为非常相似.最后对未来工作提出几点建议.     

Non-Deterministic Closure Theory and Universal Arrows

Traditional closure theory discusses the closure operations on orders with graph-theoretic methods, or the reflectors on skeletal categories with category-theoretic methods. Both approaches are confined, like most of classical mathematics, to total and deterministic operations. So traditional closure theory makes it possible to define the semantics of the while-do commands only for terminating and deterministic programming. This paper outlines a closure theory for relations which transcend totality and determinism. For the sake of conciseness, the language used is that of graph theory but the methods are category-theoretic and some hints are offered for a possible translation into the language of category theory. Our basic idea is that closure relations consist of universal arrows in the sense of category theory. The new closure theory is appropriate for defining a semantics of the while-do commands both for terminating, deterministic programming and for non-terminating, non-deterministic programming.     

Universal abelian covers of superisolated singularities

We give explicit examples of Gorenstein surface singularities with integral homology sphere link, which are not complete intersections. Their existence was shown by Luengo–Velasco, Melle–Hernández and Némethi, thereby providing counterexamples to the universal abelian covering conjecture of Neumann and Wahl (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)