Local bases of primitive non-powerful signed digraphs

In 1994, Z. Li, F. Hall and C. Eschenbach extended the concept of the index of convergence from nonnegative matrices to powerful sign pattern matrices. Recently, Jiayu Shao and Lihua You studied the bases of non-powerful irreducible sign pattern matrices. In this paper, the local bases, which are generalizations of the base, of primitive non-powerful signed digraphs are introduced, and sharp bounds for local bases of primitive non-powerful signed digraphs are obtained. Furthermore, extremal digraphs are described.  

Path Decomposition of Graphs with Given Path Length

A path decomposition of a graph G is a list of paths such that each edge appears in exactly onepath in the list.G is said to admit a {P_l}-decomposition if G can be decomposed into some copies of P_l,whereP_l is a path of length l-1.Similarly,G is said to admit a {P_l,P_k}=decomposition if G can be decomposed intosome copies of P_l or P_k.An k-cycle,denoted by C_k,is a cycle with k vertices.An odd tree is a tree of which allvertices have odd degree.In this paper,it is shown that a connected graph G admits a {P_3,P_4}-decompositionif and only if G is neither a 3-cycle nor an odd tree.This result includes the related result of Yan,Xu andMutu.Moreover,two polynomial algorithms are given to find {P_3}-decomposition and {P_3,P_4}-decompositionof graphs,respectively.Hence,{P_3}-decomposition problem and {P_3,P_4}-decomposition problem of graphs aresolved completely.  

半质环的一个交换性条件

定理 设R是半质环,则R是交换环的充分必要条件是: 对任意x,y∈R,存在整数n=n(x)>1,s=s(x)>1及t=t(x)>1(或者n=n(y)>1,s=s(y)>1及t=t(y)>1)使得 (xy)ⁿ-x³y^t∈Z(R). 其中Z(R)是R的中心。  

改进的优劣系数法及其区间数推广

首先,通过指标的优集合,相持集合和劣集合的定义,改进了优劣系数法中的一致性矩阵和不一致性矩阵的定义,定义使得一致性矩阵和不一致性矩阵具有很好的优良性质,进而使得优劣系数法更加简洁,实用.其次,利用区间数的可能度的性质和相离度的概念将优劣系数法推广到区间数决策问题中来.最后给出了两个算例.  

广义Hom-李代数的中心不变量

设L是一个广义Hom-李代数, V 是[L,L]的一个H-Hom-李理想. 本文主要研究了L的中心不变量问题. 利用Hopf代数中的方法, 得到了V 的H-不变量包含在L的中心H-不变量中, 这推广了1994年Cohen和Westreich的主要结论.  

Notes on Automorphisms of Prime Rings

Let Rbe a prime ring, L a noncentral Lie ideal and σ a nontrivial automorphism of Rsuch that usσ(u)ut = 0 for all u ∈ L, where s, t are fixed non-negative integers. If either charR>s+t or charR=0, then...  

The super-bihamiltonian reduction on C(, OSP(|))

In this article, we will show that the super-bihamiltonian structures of the Kuper-KdV equation in [3], the Kuper-CH equation in [17, 18] and the super-HS equation in [11, 16,19] can be obtained by applying a super-bihamiltonian reduction of different super-Poisson pairs defined on the loop algebra of osp(1|2).  

THE SUPER-BIHAMILTONIAN REDUCTION ON C∞（S1,OSP（1｜2））

In this article, we will show that the super-bihamiltonian structures of the Kuper- KdV equation in [3], the Kuper-CH equation in [17, 18] and the super-HS equation in [11, 16, 19] can be obtained by applying a super-bihamiltonian reduction of different super-Poisson pairs defined on the loop algebra of osp（1｜2）.