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.     

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.     

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.     

Lie group method: A new approach to image matching with arbitrary orientations

In this article, we develop a new method for image matching of any two images with arbitrary orientations. The idea comes from the workpiece localization in machining industry. We first describe an image as a 3D point set other than the common 2D function f(x, y), then, making the sets corresponding to the compared images form solid surfaces, we equivalently translate the matching problem into an optimization problem on the Lie group SE(3). Through developing a kind of steepest descent algorithms on a general Lie group, we present an practical algorithm for matching problem. Simulations of eye detection and face detection are presented to show the feasibility and efficiency of the proposed algorithm. © 2010 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 20, 245–252, 2010.     

基于格值逻辑系统LP(X)的α-归结域的代数结构

首先得到了与g不可α-归结的广义文字的集合D*_α (g)做成了∨-半群且也是一个序滤子;其次研究了由D*_α (g)所确定的一个新的代数结构D^f,D^f做成一个格滤子,并研究了D^f的一些相关性质;最后研究了由D^f所确定的代数结构κ(D),得到了κ(D)构成滤子并研究了κ(D)的结构。     

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.     

On a new class of finite dimensional estimation algebras

We introduce a new class of solvable finite dimensional estimation algebras that contains both the linear and the Bene cases. The condition for finite dimensionality is expressed in terms of two matrices. They play an important role in understanding the structure of estimation algebras.     

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.     

Congruences and ideals in pseudoeffect algebras

This paper is devoted to congruences and ideals in pseudoeffect algebras. Let I be a normal ideal in a pseudoeffect algebra E. We show that: (1) the relation ~ _I induced by I is a congruence if and only if for every a∈E, I∩ [0,a] is upper directed; (2) the relation ~ _I induced by I is a strong congruence if and only if I is a normal weak Riesz ideal in a pseudoeffect algebra E. Moreover, we introduce a stronger concept of congruence—namely Riesz strong congruence—and we prove that, if I is a normal weak Riesz ideal in a pseudoeffect algebra E, then ~ _I is a Riesz strong congruence and, conversely, if ~ is a Riesz strong congruence, then I = [0]_~ is a normal weak Riesz ideal, and ~ _I = ~. This work was supported by the National Natural Science Foundation of China (Grant No. 10271069).