Complete and ready simulation semantics are not finitely based over BCCSP, even with a singleton alphabet

This note shows that the complete and the ready simulation preorders do not have a finite inequational basis over the language BCCSP when the set of actions is a singleton. Moreover, the equivalences induced by those preorders do not have a finite (in)equational axiomatization either. These results are in contrast with a claim of finite axiomatizability for those semantics in the literature, which was based on the erroneous assumption that they coincide with complete trace semantics in the presence of a singleton set of actions.     

Weak pseudo-Wajsberg and weak pseudo-MV algebras

 We introduce and study a generalization of pseudo-Wajsberg and pseudo-MV algebras. The weakening of the axioms leads to the existence of two lattice structures, and of two multiplicative monoid structures. Some categorical equivalences are established.     

A characterization of computable analysis on unbounded domains using differential equations

The functions of computable analysis are defined by enhancing normal Turing machines to deal with real number inputs. We consider characterizations of these functions using function algebras, known as real recursive functions. Since there are numerous incompatible models of computation over the reals, it is interesting to find that the two very different models we consider can be set up to yield exactly the same functions. Bournez and Hainry used a function algebra to characterize computable analysis, restricted to the twice continuously differentiable functions with compact domains. In our earlier paper, we found a different (and apparently more natural) function algebra that also yields computable analysis, with the same restriction. In this paper we improve earlier work, finding three function algebras characterizing computable analysis, removing the restriction to twice continuously differentiable functions and allowing unbounded domains. One of these function algebras is built upon the widely studied real primitive recursive functions. Furthermore, the proof of this paper uses our previously developed method of approximation, whose applicability is further evidenced by this paper.     

有扭仿射李代数赋值模的某些性质

设g为有限维复单李代数,g^^[σ]为对应的有扭仿射李代数,U1,…,U,为不可约g-模,z1,…,zr为互不相同的非零复数．利用生成函数的方法证明赋值模U1（z1）×…Ur（zr）为g^^[σ]-模范畴E中不可约模并证明其同构定理．     

度量空间的大尺度几何与高指标问题(特约稿)

粗几何上的指标理论是＂非交换几何＂领域近年来非常活跃的研究分支,与几何、拓扑、算子代数、几何群论、Banach空间几何理论等都有密切联系。对该领域的若干思想、主要问题和部分最新研究进展进行综述性介绍。     

一类效应代数中的理想

证明了若I是效应代数（E（Ω）,,⊥,0,1）的一个闭理想,则存在Ω的一个闭的子集S,使得I是所有在S上为零的函数的集合.反之,若S是一个Ω的闭子集,则所有在S上为零的函数之集是效应代数（E（Ω）,,⊥,0,1）的一个闭理想.     

三角代数上的ξ-Lie可导映射

设U=Tri(A,M,B)是含单位元I的三角代数并且φ:U→U是线性映射.利用代数分解的方法,证明了当三角代数U满足适当条件时,如果U,V∈U且UV=VU=I,有φ([U,V]ξ)=[φ(U),V]ξ+[U,φ(V)]ξ(ξ≠±1),则φ是导子.并得到了套代数上ξ-Lie可导映射的一个刻画.     

Lower bounds for the bilinear complexity of associative algebras

Let R(A) denote the bilinear complexity (also called rank) of a finite dimensional associative algebra A.?We prove that if the decomposition of into simple algebras contains only noncommutative factors, that is, the division algebra is noncommutative or . In particular, -matrix multiplication requires at least essential bilinear multiplications. We also derive lower bounds of the form essential bilinear multiplications. We also derive lower bounds of the form for the algebra of upper triangular -matrices and the algebra of truncated bivariate polynomials in the indeterminates X,Y over some field k.?A class of algebras that has received wide attention in this context con-sists of those algebras A for which the Alder—Strassen Bound is sharp, i.e., R(A) = 2dim A—t is the number of maximal twosided ideals in A. These algebras are called algebras of minimal rank. We determine all semisimple algebras of minimal rank over arbitrary fields and all algebras of minimal rank over algebraically closed fields. Received: January 12, 2000.     

N-可分效应代数

引入了N-可分效应代数的定义,证明了N-可分效应代数是区间效应代数且N-可分效应代数可嵌入到可分效应代数中.     

Asymptotic stabilization of planar systems

Sufficient conditions for the existence of a C¹ asymptotically stabilizing feedback control for planar, affine systems are given. The methods are constructive and yield homogeneous feedback controls for homogeneous systems which allow the results to be extended to more general systems.