关于正规Boole矩阵行空间的的基数

称Ｂｏｏｌｅ矩阵Ａ是正规是，是指Ａ的行秩与列秩相等。本文主要得到两个结果。第一，推广了Ｊ．Ｋｏｎｉｅｃｚｎｙ在Ｓｅｍｉｇｒｏｕｐ ｆＯＲＵＭ，ｖｏｌ．４４（１９９２）发表的论文Ｏｎ ｃａｒｄｉｎａｌｉｔｉｅｓ ｏｆ ｒｏｗ ｓｐａｃｅ ｏｆ Ｂｏｏｌｅａｎ ｍａｔｒｉｃｅｓ的重要结果。第二，若ｎ阶Ｂｏｏｌｅ矩阵的行空间基数大于２＾ｎ－１－２，则Ａ必是正规的。     

Hyperabelian群的Abel子群

本文利用Ｄｉｒｉｃｈｌｅｔ单位定理证明了：设Ｇ是个Ｈｙｐｅｒａｂｅｌｉａｎ群．若Ｇ的亏数２的次正规Ａｂｅｌ子群都是有限生成的，则Ｇ是个多重循环群，且Ｇ的Ｈｉｒｓｃｈ数ｈ（Ｇ）ｎ２＋ｎ，其中ｎ是Ｇ的亏数２的次正规Ａｂｅｌ子群的最大０－秩．这个定理进一步推广了Ｍａｌｃ＇ｅｖ关于多重循环群的著名工作［５］．     

Angles of Norm ed Linear Spaces and Characterizations of Inner Product Spaces

§１．　Ｄｅｆｉｎｉｔｉｏｎｓ，ＬｅｍｍａｓａｎｄＴｈｅｏｒｅｍＤｅｆｉｎｉｔｉｏｎ１［１］　Ｌｅｔ（Ｘ，ｙ·ｙ）ｂｅａｒｅａｌｎｏｒｍｅｄｌｉｎｅａｒｓｐａｃｅｏｆｄｅｍｅｎｓｉｏｎｇｒｅａｔｅｒｔｈａｎ１，ｗｅｄｅｆｉｎｅａｎｇｌｅｓＡｍ，ｎ（ｘ，ｙ）ｂｅｔｗｅｅｎｎｏｎｚｅｒｏｖｅｃｔｏｒｓｘａｎｄｙｉｎＸｂｙＡｍ，ｎ（ｘ，ｙ）＝ｃｏｓ－１ｎｙｘｙｘｙ＋ｙｙｙｙｙ２－ｍｙｘｙｘｙ－ｙｙｙｙｙ２＋２（ｍ－ｎ）２（ｍ＋ｎ），ｈｅｒｅｍａｎｄｎａｒｅｔｗｏｎｏｎ－ｎｅｇｅｎｔｉｖｅｉｎｔｅ－ｇｅ…     

利用导数求cos~n(A/2) cos~n(B/2) cos~n(C/2)的上下限

利用导数求ｃｏｓｎ（Ａ／２）＋ｃｏｓｎ（Ｂ／２）＋ｃｏｓｎ（Ｃ／２）的上下限阚云鹏王岩松（大庆石油化工总厂职工大学１６３０００）数学通报９６年第二期《关于ｃｏｓｎ（Ａ／２）＋ｃｏｓｎ（Ｂ／２）＋ｃｏｓｎ（Ｃ／２）上下限估计》一文，徐宁先生介绍了初等数...     

布尔矩阵行空间基数的存在点

设 Ｂｎ 表示所有的ｎ 阶布尔矩阵的集合, Ｒ（ Ａ）表示 Ａ∈ Ｂｎ 的行空间,｜ Ｒ（ Ａ）｜表示 Ｒ（ Ａ）的基数．设ｍ ,ｎ,ｋ 为正整数,本文证明了当ｎ≥９, ｎ＋ ５２ ≤ｋ≤ｎ－ ３ 时,对任意的 ｍ ,２ｋ≤ｍ ≤２ｋ＋ ２ｎ－ ｋ＋ ２＋ ２ｎ－ ｋ＋ １ ＋ …＋ ２３,存在 Ａ∈ Ｂｎ,使得｜ Ｒ（ Ａ）｜＝ ｍ ．     

cos~n(A/2) cos~n(B/2) cos~n(C/2)的上下确界

ｃｏｓｎＡ２＋ｃｏｓｎＢ２＋ｃｏｓｎＣ２的上下确界杨寅（呼和浩特交通学校０１００２３）设Ａ、Ｂ、Ｃ为三角形的三个内角，题目中的问题久已悬而未决．今用分析方法彻底解决这个问题．定理设Ａ、Ｂ、Ｃ为三角形的三个内角，ｎ２为自然数，则有ｍｉｎ１＋２２２ｎ，...     

On (4p~2q~(2b),2p~2q~(2b)-pq~b,p~2q~(2b)-pq~b) Menon Difference Sets

Ｏｎ（４ｐ２ｑ２ｂ，２ｐ２ｑ２ｂ－ｐｑｂ，ｐ２ｑ２ｂ－ｐｑｂ）ＭｅｎｏｎＤｉｆｅｒｅｎｃｅＳｅｔｓＷａｎＺｈａｏｚｅ（万兆泽）（ＣｏｌｅｇｅｏｆＭａｔｈｅｍａｔｉｃＳｃｉｅｎｃｅ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ，１００８７１）Ａｂｓ...     

A Property of Solutions for Elliptic Equation with Nonstandard Growth Conditions in Unbounded Domain

§０．　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔΩｂｅａｎｕｎｂｏｕｎｄｅｄｄｏｍａｉｎｉｎｔｈｅｎ－ｄｉｍｅｎｓｉｏｎａｌＥｕｃｌｉｄｅａｎｓｐａｃｅＥｎ（ｎ３）．Ｃｏｎｓｉｄｅｒ－ｉｎｇｔｈｅｆｏｌｌｏｗｉｎｇｅｌｌｉｐｔｉｃｅｑｕａｔｉｏｎｗｉｔｈｎｏｎｓｔａｎｄａｒｄｇｒｏｗｔｈｃｏｎｄｉｔｉｏｎｓ：－ｄｉｖＡ（ｘ,ｕ,ｕ）＝Ｂ（ｘ,ｕ,ｕ）（１）ｗｈｅｒｅＡ（ｘ,ｕ,ξ）＝｛Ａｉ（ｘ,ｕ,ξ）,ｉ＝１,２,…,ｎ｝ａｎｄＢ（ｘ,ｕ,ξ）ａｒｅｄｅｆｉｎｅｄｏｎＥｎ×Ｅ１×Ｅｎ,ｃｏｎ－…     

空间折线与其中点折线周长间的一个关系

我们知道，依次连接三角形各边中点所得三角形的周长是原三角形周长的一半．一般地，依次连接折线各边中点所得的折线称为中点折线．那么，任意一条封闭折线（不一定是平面的），它的中点折线的周长与原折线的周长之间有什么关系呢？先给出如下引理引理１　△ＡＢＣ中，ＡＢ＋ＡＣ≤ＢＣ·ｃｓｃＡ２．其中当且仅当ＡＢ＝ＡＣ时取等号．证　在△ＡＢＣ中，ＢＣ２＝ＡＢ２＋ＡＣ２－２·ＡＢ·ＡＣ·ｃｏｓＡ＝（ＡＢ＋ＡＣ）２ｓｉｎ２Ａ２＋（ＡＢ－ＡＣ）２ｃｏｓ２Ａ２≥（ＡＢ＋ＡＣ）２ｓｉｎ２Ａ２，∴ＡＢ＋ＡＣ≤ＢＣ·ｃｓｃＡ２．…     

Hilbert空间上交换本质正规算子组的C_p－类扰动

本文证明了若Ｂ＝（Ｂ１，…，Ｂｎ）是Ｈｉｌｂｅｒｔ空间Ｈ上交换正规算子组，Ａ＝（Ａ１，…，Ａｎ）是Ｈ上交换本质正规算子组，Ｓｐ（Ｂ）Ｓｐｅ（Ａ），且Ｓｐ（Ｂ）的Ｈａｕｓｄｏｒｆｆ维数等于α，则对任意ε＞０及ｐ≥ｍａｘ（α＋ε，１），Ａ模Ｃｐ－近似酉等价于ＡＢ＝（Ａ１Ｂ１，……ＡｎＢｎ）．     

矩阵的初等标准形与线性方程组

指出矩阵的初等标准形理论是线性方程组问题的理论基础     

Some explicit formulas for the polynomial decomposition of the matrix exponential and applications

This paper is devoted to the study of some formulas for polynomial decomposition of the exponential of a square matrix A. More precisely, we suppose that the minimal polynomial M_A(X) of A is known and has degree m. Therefore, e^tA is given in terms of P₀(A),…,P_m−1(A), where the P_j(A) are polynomials in A of degree less than m, and some explicit analytic functions. Examples and applications are given. In particular, the two cases m=5 and m=6 are considered.     

Factoring matrices into the product of two matrices

Linear algebra of factoring a matrix into the product of two matrices with special properties is developed. This is accomplished in terms of the so-called inverse of a matrix subspace which yields an extended notion for the invertibility of a matrix. The product of two matrix subspaces gives rise to a natural generalization of the concept of matrix subspace. Extensions of these ideas are outlined. Several examples on factoring are presented. AMS subject classification (2000)  15A23, 65F30     

模糊矩阵三种广义逆的判定定理

给出模糊矩阵存在广义{1,3}逆,广义{1,4}逆和Moore-Penrose广义逆的判定定理.     

任意除环上一矩阵方程组的一般解与中心和反中心对称解

Necessary and sufficient conditions are given for the existence of the general solution, the centrosymmetric solution, and the centroskewsymmetric solution to a system of linear matrix equations over an arbitrary skew field. The representations of such the solutions of the system are also derived.     

关于矩阵迹的一些不等式

对由Bellman不等式推导的两个关于实正定对称矩阵迹的不等式进行了进一步的推广,并得到了一系列的关于矩阵迹的不等式。     

二阶矩阵的n次方和n次方根

利用Chebyshev多项式讨论了二阶矩阵的n次方的各元素的表达式和其n次方根的存在条件.     

Linear recurrence relations in the algebra of matrices and applications

We study here some linear recurrence relations in the algebra of square matrices. With the aid of the Cayley–Hamilton Theorem, we derive some explicit formulas for Aⁿ (nr) and e^tA for every r×r matrix A, in terms of the coefficients of its characteristic polynomial and matrices A^j, where 0jr−1.     

Weight choosability of graphs

Suppose the edges of a graph G are assigned 3‐element lists of real weights. Is it possible to choose a weight for each edge from its list so that the sums of weights around adjacent vertices were different? We prove that the answer is positive for several classes of graphs, including complete graphs, complete bipartite graphs, and trees (except K₂). The argument is algebraic and uses permanents of matrices and Combinatorial Nullstellensatz. We also consider a directed version of the problem. We prove by an elementary argument that for digraphs the answer to the above question is positive even with lists of size two. © 2008 Wiley Periodicals, Inc. J Graph Theory 60: 242–256, 2009