Characterization of information matrices for balanced two-level fractional factorial designs of odd resolution derived from two-symbol simple arrays

We consider a balanced fractional 2^m factorial design of resolution 2?+1 which permits estimation of all factorial effects up through ?-factor interactions under the situation in which all (?+1)-factor and higher order interactions are to be negligible for an integer satisfying [m/2]<lE;?m, where [x] denotes the greatest integer not exceeding x. This paper investigates algebraic structure of the information matrix of such a design derived from a simple array through that of an atomic array. We obtain an explicit expression for the irreducible matrix representation based on the above design and its algebraic properties. The results in this paper will be useful to characterize the designs under consideration.     

中美线性代数教学方法的对比与分析

线性代数作为理工科院校的公共基础课,随着社会、经济、政治、文化、科学技术的快速发展,越来越受到工程技术人员的重视。本文对中美线性代数教材作了比较分析,并结合国内线性代数课程教学实践,比较了中美线性代数授课过程中的异同,分析了美国现行线性代数教材的优点和授课方法,以期对我国线性代数教材建设和教学改革提供有效的方法。     

Computation of the stationary distribution of a markov chain

Eight algorithms are considered for the computation of the stationary distribution l´ of a finite Markov chain with associated probability transition matrix P. The recommended algorithm is based on solving l´(I—P+eú)=ú, where e is the column vector of ones and u´ is a row vector satisfying u´e ≠0.An error analysis is presented for any such u including the choices ú= e_jP and ú=e´_j where é_j is the jth row of the identity matrix. Computationalcomparisons between five of the algorithms are made based on twenty 8 x 8, twenty 20 x 20, and twenty 40 x 40 transition matrices. The matrix (I—P+eú)^?1 is shown to be a non-singular generalized inverse of I—P when the unit root of P is simple and úe ≠ 0. A simple closed form expression is obtained for the Moore-Penrose inverse of I—P whenI—P has nullity one     

Quadratic subspaces and construction of Bayes invariant quadratic estimators of variance components in mixed linear models

Gnot et al. (J Statist Plann Inference 30(1):223–236, 1992) have presented the formulae for computing Bayes invariant quadratic estimators of variance components in normal mixed linear models of the form where the matrices V _i , 1 ≤ i ≤ k − 1, are symmetric and nonnegative definite and V _k is an identity matrix. These formulae involve a basis of a quadratic subspace containing MV ₁ M,...,MV _k-1 M,M, where M is an orthogonal projector on the null space of X′. In the paper we discuss methods of construction of such a basis. We survey Malley’s algorithms for finding the smallest quadratic subspace including a given set of symmetric matrices of the same order and propose some modifications of these algorithms. We also consider a class of matrices sharing some of the symmetries common to MV ₁ M,...,MV _k-1 M,M. We show that the matrices from this class constitute a quadratic subspace and describe its explicit basis, which can be directly used for computing Bayes invariant quadratic estimators of variance components. This basis can be also used for improving the efficiency of Malley’s algorithms when applied to finding a basis of the smallest quadratic subspace containing the matrices MV ₁ M,...,MV _k-1 M,M. Finally, we present the results of a numerical experiment which confirm the potential usefulness of the proposed methods. Dedicated to the memory of Professor Stanisław Gnot.     

正蕴涵BCI-代数的自同态

给出了BCI-代数X的伴随半群中任一元素σ是X的自同态的充要条件,并得到了m-正蕴涵BCI-代数和广义正蕴涵BCI-代数的一些自同态.     

q—畸变Virasoro代数中心扩张的新途径

本文定义了共形场论中能动量张量算子积展开式的q—畸变形式,由此出发,推导出了含有中心项的q—畸变Virasoro代数,当参数q→1时,就退化为普通的Vira-soro代数;最后,找到了与这种中心扩张相对应的q—畸变雅可比关系式。值得指出的是,利用这种畸变代数可以得出q—畸变的Kdv方程。     

“高等代数试题库”软件的设计与使用

本文介绍了一个用Ｆｏｘｂａｓｅ编写的“高等代数试题库”，详细说明了它的设计思想、特点、功能和它的使用方法     

具有相似群不变的1 1维的高阶微分方程

本文利用李代数在矢量场的实现，得到了具有相似群不变的一般的k阶微分方程,同时许多熟知的1＋1微的可积模型如kdv方程等也被给出。     

一类无限维单李代数

给出了复数域Ｃ上的结合代数Ｃｑ〔Ｘ，Ｙ，Ｘ－１，Ｙ－１〕（ｑｎ≠１，ｎ∈Ｎ）的导子代数Ｌ０，并证明了Ｌ０为一个无限维单完备李代数