除环上的矩阵方程AXB=D

先建立除环上的矩阵范畴,并证明这个范畴是Ａｂｅｌ范畴,然后利用范畴论中的结论给出除环上矩阵方程ＡＸＢ＝Ｄ有解的条件。     

Metapositive Semidefinite Solutions to the Matrix Equation AXB＝C over a Strong p－Division Ring

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集对代数软代数的集对表示

指出文[1]中的软代数表示定理（定理2．2）的错误,给出修改后的软代数表示定理。另外,讨论了集对代数的理想、同余关系和同余理想。     

中心代数上一矩阵方程的中心对称与中心斜对称解

Let Ω be a finite dimensional central algebra and chart Ω≠2 .The matrix equation AXB-CXD=E over Ω is considered.Necessary and sufficient conditions for the existence of centro(skew)symmetric solutions of the matrix equation are given.As a particular case ,the matrix equation X-AXB=C over Ω is also considered.     

中心代数上的矩阵方程组

设Ω是一个特征非2的具有对合反自同构的有限维中心代数.本文研究Ω上的两个矩阵方程组,分别给出了其有一般解和次(斜)自共轭解的充要条件.     

Ranks of Solutions of the Matrix Equation AXB = C

The purpose of this article is to solve two problems related to solutions of a consistent complex matrix equation AXB = C : (I) the maximal and minimal ranks of solution to AXB = C , and (II) the maximal and minimal ranks of two real matrices X ₀ and X ₁ in solution X = X ₀ + iX ₁ to AXB = C . As applications, the maximal and minimal ranks of two real matrices C and D in generalized inverse (A + iB)^- = C + iD of a complex matrix A + iB are also examined.     

基于空间分解变换的模糊错误矩阵方程求解

模糊错误逻辑对现实世界的对象用(u,x)表示为((U,S(t),■T(t),L(t)),(x(t)=f((u(t),■),GU(t)),GU(t)),用模糊错误变换矩阵可以表示分解、相似、增加、置换、毁灭、单位变换等6种变换方法,本论文基于求解方程XA′=B,针对■的分解,研究了基于空间分解变换的错误矩阵方程求解。以期从矩阵方程求解的角度对错误转化规律进行探索研究。     

Ranks of Solutions of the Matrix Equation AXB = C

The purpose of this article is to solve two problems related to solutions of a consistent complex matrix equation AXB = C : (I) the maximal and minimal ranks of solution to AXB = C , and (II) the maximal and minimal ranks of two real matrices X₀ and X₁ in solution X = X₀ + iX₁ to AXB = C . As applications, the maximal and minimal ranks of two real matrices C and D in generalized inverse (A + iB)^- = C + iD of a complex matrix A + iB are also examined.     

模糊概念的EI代数分解

应用 AFS结构 [6] 上的 EI代数[6] 分析模糊概念的数学结构 ,证明有限集上任意一个模糊概念都是一类极其简单的模糊概念的 EI代数分解。     

模糊错误二类1矩阵方程实解的存在性及其解法

本文在文（７）的基础上研究了模糊错误二类１矩阵方程实解的存在性和它的基本求解方法。     

Algebra word problem solving approaches in a chemistry context: Equation worked examples versus text editing

Text editing directs students’ attention to the problem structure as they classify whether the texts of word problems contain sufficient, missing or irrelevant information for working out a solution. Equation worked examples emphasize the formation of a coherent problem structure to generate a solution. Its focus is on the construction of three equation steps each of which comprises essential units of relevant information. In an experiment, students were randomly assigned to either text editing or equation worked examples condition in a regular classroom setting to learn how to solve algebra word problems in a chemistry context. The equation worked examples group outperformed the text editing group for molarity problems, which were more difficult than dilution problems. Empirical evidence supports the theoretical rationale in using equation worked examples to facilitate students’ construction of a coherent problem structure so as to develop problem skills and expertise to solve molarity problems.     

完全域上矩阵多项式方程的可解性

本文利用一般域上的λ-矩阵理论，研究了矩阵多项式方程的可解性，证明了完全域上矩阵多项式方程有解的充要条件，这些条件同时提供了解此类矩阵方程的方法。     

The Identities and the Central Polynomials of the Infinite Dimensional Unitary Grassmann Algebra Over a Finite Field

We describe the T-ideal of identities and the T-space of central polynomials for the infinite dimensional unitary Grassmann algebra over a finite field.     

外代数上有线性周期自由分解的不可分解模的表示矩阵

本文主要是受了Eisenbud的启发,在其研究的基础上进一步研究了外代数上有线性周期自由分解的不可分解模的表示矩阵,并给出了其表示矩阵的几个较好的形式.     

Z／（p^e）上分裂环的结构

本文研究了环ｚ／（ｐｅ）上多项式的性质和分裂环的结构．主要分析了分裂环中元素的极小多项式，零化理想的结构，和分裂环子环性质．     

有限维中心代数上矩阵方程组的广对称解与斜广对称解

设Ω是一个具有对合反自同构的有限维中心代数且charΩ≠2.本文在Ω上定义了广对称矩阵和斜广对称矩阵,在Ω[λ]上考虑了三个矩阵方程组,分别给出了其有广对称解和斜广对称的充要条件.作为特例,得到了某些矩阵方程相应的结果.     

量子环面李代数的自同构群, 泛中心扩张与导子

C_q:=C_q[x^±1₁, x^±1₂] 为复数域上的量子环面, 其中q≠ 0是一个非单位根, D(C_q) 为C_q的导子李代数. 记L_q 为C_q ㈩ D(C_q)的导出子代数. 该文研究李代数L_q的自同构群, 泛中心扩张和导子李代数.     

Matrix graphs and MRD codes over finite principal ideal rings

Let R be a finite principal ideal ring and $m,n,d$ positive integers. In this paper, we study the matrix graph over R which is the graph whose vertices are $m\times n$ matrices over R and two matrices A and B are adjacent if and only if $0<\mathrm{rank}(A-B)<d$. We show that this graph is a connected vertex transitive graph. The distance, diameter, independence number, clique number and chromatic number of this graph are also determined. This graph can be applied to study MRD codes over R. We obtain that a maximal independent set of the matrix graph is a maximum rank distance (MRD) code and vice versa. Moreover, we show the existence of linear MRD codes over R.     

量子环面李代数的自同构群,泛中心扩张与导子

Cq=Cq[x1^&#177;1,x2^&#177;1]为复数域上的量子环面，其中q≠0是一个非单位根，D（Cq）为Cq的导子李代数．记Lq为Cq＋D（Cq）的导出子代数．该文研究李代数Lq的自同构群，泛中心扩张和导子李代数．