模糊树自动机的同余与同态

从代数角度出发研究模糊树自动机的同余与同态,得出模糊树自动机的同态基本定理和同构基本定理,且对模糊树自动机的语言及模糊树自动机的极小化问题进行研究.     

有限模糊树自动机的一些代数性质与相应的语言

将模糊自动机的同态、完全、容许关系等概念引入到模糊树自动机中,从代数的角度研究模糊树自动机的一些代数性质,并探讨了模糊树自动机的语言的相关问题.     

确定权重有限自动机的同余及极小自动机

主要研究对象是强双幺半群上的确定权重有限自动机A.首先给出了A上的同态定理和同构定理;接着,构造了识别φ的一个极小自动机Aφ;最后,证明极小自动机在同构意义下是唯一的.     

格值模糊有限自动机的同态

引入了格值模糊有限自动机的(强)同态的概念,研究了它们的相关性质,得出了同态基本定理。给出了A上容许关系及强同态的核的概念,研究了它们相关性质。     

基于格半群的有限状态自动机的同态

本文研究了格值有限状态自动机(LFSA)的同态和强同态及其性质.利用强同态概念,在格值有限状态自动机的状态集上建立了一种等价关系,得到了格值有限状态自动机的商自动机,证明了商自动机与强同态像自动机同构.     

循环模糊有限自动机的同态性质

讨论了模糊有限自动机(即模糊Mealy机)的同态性质和循环模糊有限自动机的同态性质,证明了每个模糊有限自动机都是有限个循环模糊有限自动机的直和的同态象。     

概率有限自动机的代数性质

研究了概率有限自动机的同态(弱同态)、有效划分等代数性质.首先,提出了完全的、不可约的概率有限自动机,概率有限自动机的并积等概念.然后,讨论了两个概率有限自动机的级联积、圈积、并积的有效划分与其因子的有效划分之间的关系,证明了在一定条件下两个概率有限自动机的级联积(并积)的商概率有限自动机与其因子的商概率有限自动机的级联积(并积)是相等的.最后,得到了概率有限自动机的极大有效划分的一个刻画.     

关于Fuzzy3型文法与Fuzzy有限态自动机的关系

本文首先讨论了确定的Fuzzy有限态自动机与非确定的Fuzzy有限态自动机之间的转换关系,在此基础上研究了Fuzzy 3型文法与Fuzzy有限态自动机的关系问题,得出了两个有实用价值的定理。这两个定理为进一步研究Fuzzy文法的理论及其应用奠定了基础。定理1 设(?)是由一个非确定的Fuzzy有限态自动机FA=(∑,Q,δ,q_0,F)所接受的Fuzzy链集,则有一个能接受(?)的确定的Fuzzy有限态自动机FA′=(∑′,Q′,δ′,     

无穷自动机的几个等价命题

本文证明了具有无穷栈符合的实时确定下推自动机与无穷自动机的等价性，并且将有限状态自动机的Ｍｙｈｉｌｌ－Ｎｅｒｏｄｅ定理推广到了无穷自动机和具有无穷栈符号的实时确定下推自动机。     

输入存贮线性有限自动机的极小化

由输入存贮线性有限自动机的线性系数组成的矩阵得出输入存贮线性有限自动机极小的等价定理,由此定理得出输入存贮线性有限自动机的极小化方法.     

Affine-inscribed and affine-circumscribed polygons and polytopes

Five theorems on polygons and polytopes inscribed in (or circumscribed about) a convex compact set in the plane or space are proved by topological methods. In particular, it is proved that for every interior point O of a convex compact set in ℝ³, there exists a two-dimensional section through O circumscribed about an affine image of a regular octagon. It is also proved that every compact convex set in ℝ³ (except the cases listed below) is circumscribed about an affine image of a cube-octahedron (the convex hull of the midpoints of the edges of a cube). Possible exceptions are provided by the bodies containing a parallelogram P and contained in a cylinder with directrix P. Bibliography: 29 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 286–298. Translated by B. M. Bekker.     

Partitions and pairwise sums and products

A seven cell partition of N is constructed with the property that no infinite set has all of its pairwise sums and products in any one cell. A related Ramsey Theory question is shown to have different answers for two and three cell partitions.     

Linear birth and death models and associated Laguerre and Meixner polynomials

We study birth and death processes with linear rates λ_n = n + α + c + 1, μ_{n + 1} = n + c, n 0 and μ₀ is either zero or c. The spectral measures of both processes are found using generating functions and the integral transforms of Laplace and Stieltjes. The corresponding orthogonal polynomials generalize Laguerre polynomials and the choice μ₀ = c generates the associated Laguerre polynomials of Askey and Wimp. We investigate the orthogonal polynomials in both cases and give alternate proofs of some of the results of Askey and Wimp on the associated Laguerre polynomials. We also identify the spectra of the associated Charlier and Meixner polynomials as zeros of certain transcendental equations.     

Distributive and Multiplication Modules and Rings

We study rings in which every ideal is a finitely generated multiplication right ideal.     

Beliefs and beyond: affect and the teaching and learning of mathematics

The importance of beliefs for the teaching and learning of mathematics is widely recognized among mathematics educators. In this special issue, we explicitly address what we call “beliefs and beyond” to indicate the larger field surrounding beliefs in mathematics education. This is done to broaden the discussion to related concepts (which may not originate in mathematics education) and to consider the interconnectedness of concepts. In particular, we present some new developments at the conceptual level, address different approaches to investigate beliefs, highlight the role of student beliefs in problem-solving activities, and discuss teacher beliefs and their significance for professional development. One specific intention is to consider expertise from colleagues in the fields of educational research and psychology, side by side with perspectives provided by researchers from mathematics education.     

Ritz and harmonic Ritz values and the convergence of FOM and GMRES

The Ritz and harmonic Ritz values are approximate eigenvalues, which can be computed cheaply within the FOM and GMRES Krylov subspace iterative methods for solving non‐symmetric linear systems. They are also the zeros of the residual polynomials of FOM and GMRES, respectively. In this paper we show that the Walker–Zhou interpretation of GMRES enables us to formulate the relation between the harmonic Ritz values and GMRES in the same way as the relation between the Ritz values and FOM. We present an upper bound for the norm of the difference between the matrices from which the Ritz and harmonic Ritz values are computed. The differences between the Ritz and harmonic Ritz values enable us to describe the breakdown of FOM and stagnation of GMRES. Copyright © 1999 John Wiley & Sons, Ltd.