域上无限方阵的分解

讨论了域上无限上三角方阵存在单侧逆方阵的充分条件,证明了域上无限方阵的分解定理。     

除环上无限方阵的逆方阵

本文探讨了除环上无限方阵的逆方阵,得到了除环上无限方阵存在左（或右）逆方阵的充要条件．     

一类特殊无限方阵的逆

研究了除环上一类特殊无限方阵的逆方阵,用紧致性论证给出了除环上无限上三角阵具有左（右）逆和双侧逆方阵的充分条件。     

域上无限方阵的分解

讨论了域上无限上三角方阵存在单侧逆方阵的充分条件 ,证明了域上无限方阵的分解定理     

具有有限周期的无限布尔方阵的传递指数

给出了无限布尔方阵周期的概念,研究了无限布尔方阵伴随有向图的若干性质,研究了有限布尔矩阵幂的图论性质,最后给出了无限布尔方阵传递指数的上、下界估计.     

除环上无限方阵的分解

对除环上无限方阵的逆方阵作了简单讨论,证明了除环上无限方阵的分解定理.     

除环上无限方阵的分解

对除环上无限方阵的逆方阵作了简单讨论,证明了除环上无限方阵的分解定理．     

一类本原无限布尔方阵的本原指数集的刻划

引入了本原无限布尔方阵的概念,给出了无限布尔方阵为本原阵的一个充分必要条件,最后给出了一类本原无限布尔方阵的本原指数集的刻划.     

围长为2的本原无限布尔方阵类的本原指数集

研究了围长为2的无限布尔方阵的本原性,通过无限有向图D（A）的直径给出了这类矩阵的本原指数的上确界,最后证明了直径小于等于d且围长为2的本原无限布尔方阵所构成的矩阵类的本原指数集为Ed^0={2,3,…,3d}．     

Derivations of Rings of Infinite Matrices

For any associative unital ring R we investigate two rings – the ring of all infinite upper triangular matrices and the ring of all infinite matrices with the finite number of nonzero entries in each column. We describe derivations of these rings. We prove that every derivation of any of them is a sum of an inner derivation and a derivation which is induced by some derivation of R.     

非负矩阵的一些算法

本文利用有限图论和齐次有限马尔可夫链理论的有关命题和算法得到了不同于[1]、[3]的算法:(1)有限阶非负矩阵可约性的判别、有限阶可约矩阵化为主对角线上都为不可约子块的分块三角阵的算法;(2)有限阶不可约矩阵的Frobenius表示的算法.对上述二算法本文还分别给出了直观简便的图示法.     

Infinite end-devouring sets of rays with prescribed start vertices

We prove that every end of a graph contains either uncountably many disjoint rays or a set of disjoint rays that meet all rays of the end and start at any prescribed feasible set of start vertices. This confirms a conjecture of Georgakopoulos.     

INFINITE CIRCULANTS AND THEIR PROPERTIES

ＩＮＦＩＮＩＴＥＣＩＲＣＵＬＡＮＴＳＡＮＤＴＨＥＩＲＰＲＯＰＥＲＴＩＥＳＺＨＡＮＧＦＵＪＩ（张福基）ＨＵＡＮＧＱＩＯＮＧＸＩＡＮＧ（黄琼湘）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉｎｊｉａｎｇＵｎｉｖｅｒｓｉｔｙ，Ｕｒｕｍｃｈｉ８３００...     

Infinite versus finite graph domination

We raise the following general problem: Which structural properties of dominating subgraphs in finite graphs remain valid for infinite graphs? Positive and negative results are presented.     

可换对合阵组合的可逆性

先讨论两个可换对合阵P,Q线性组合aP+bQ可逆的充分必要条件及可逆时逆矩阵计算公式,再利用矩阵分解,以两种形式讨论两个可换对合阵P,Q组合aI+bP+cQ+dPQ及三个两两可换对合阵P,Q,R组合aI+bP+cQ+dPQ+eR+fPR+gQR+hPQR可逆的充分必要条件及可逆时分别给出逆矩阵计算公式.     

Intersection Theorems for Infinite Families of Convex Sets in Graphs

We prove several Helly-type theorems for infinite families of geodesically convex sets in infinite graphs. That is, we determine the least cardinal n such that any family of (particular) convex sets in some infinite graph has a nonempty intersection whenever each of its subfamilies of cardinality less than n has a nonempty intersection. We obtain some general compactness theorems, and some particular results for pseudo-modular graphs, strongly dismantlable graphs and ball-Helly graphs.