r模同态的{1}-逆与{2}-逆

本文探讨模同态广义逆在环模理论中的应用．利用模同态的{1}-逆与{2}-逆，分别给出了一类环及一类重要模的特征刻画．     

关于广义逆矩阵A(1,2)T,S的刻画推广

本文通过一类秩等方程给出了A(1,2)T,S、A(2)T,S的一种刻画及一类秩等方程有解的充分必要条件,推广了文献[1]、[4]的结论,并改进了[4]关于矩阵A的Drazin逆Ad的一类刻画的证明.     

保矩阵{1}逆的线性映射

设R是特征为2的主理想整环,Mn(R)表示R上n×n矩阵代数,在本文中我们给出了保Mn(R)中矩阵{1}逆的线性映射的一个刻划.     

Quantale矩阵的广义逆及其正定性

给出Quantale矩阵{1}-广义逆的一种刻划以及存在的条件,给出Quantale矩阵M-P广义逆的定义,讨论Quantale矩阵M-P广义逆的若干性质,得到Quantale矩阵M-P广义逆的具体形式.引入Quantale矩阵正定性的概念,研究交换幂等Quantale上矩阵正定的一些性质,得到交换幂等Quantale上矩阵正定的一些等价刻画.     

关于广义逆矩阵AT，S^（1,2）的刻画推广

本文通过一类秩等方程给出了AT,S^(1,2)、AT,S^(2)的一种刻画及一类秩等方程有解的充分必要条件，推广了文献[1]、[4]的结论，并改进了[4]关于矩阵A的Drazin逆Af的一类刻画的证明。     

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.     

半环上保持矩阵{1}-逆的线性算子

刻画了某类特殊可换无零因子反环上保持矩阵{1}一逆的可逆线性算子,并将此结果推广到此类无零因子反环的任意直积上．推广了某些文献的一些结果．     

{2}广义逆的一种表示及其应用

本文沿用[1]中的术语与记号。 在[2]中我们研究了复矩阵A的一种特殊的扰动与A的{1,2}广义逆类之间的关系。本文进一步研究复矩阵A的一种特殊的扰动与A的{2}广义逆类之间的关系,并给出这些结果的若干应用。     

运用动态规划算法求解集值折扣{0-1}背包问题

针对生产不同类商品需选择不同生产机械和模具的实际问题,提出折扣{0-1}背包问题(D{0-1}KP)的扩展模型,即集值折扣{0-1}背包问题(D{0-1}KPS).首先对该类背包问题进行理论分析,构造D{0-1}KPS的子模型D{0-1}.KPS(k,γ),然后基于D{0-1}KPS(k,γ)得到问题求解的递推公式,并...     

Comments on some recent results concerning {2, 3} and {2, 4}-generalized inverses

We give a comment on some recent results concerning the representations of generalized {2, 3} and {2, 4}-inverses. Shorter proofs of some previous results are presented.     

Sequential Determination of the {1, 4}-Inverse of a Matrix

In this paper, we provide a set of results for the sequential determination of the {1, 4}-generalized inverse of a matrix. This inverse is of importance in areas where the minimal norm solution of a system of algebraic equations is desired.     

二重(r1,r2)-循环矩阵求逆的一种新算法

本文给出了判定任意数域上二重（r1,r2)－循环矩阵非异性的一个充要条件，并提供了求这类矩阵逆的一种新方法。     

环上矩阵方程AXB＋CYD=E的可解性

设Ｒ为一个含幺环，应用矩阵的｛１，２｝－逆（存在的前提下），本文得到Ｒ上矩阵方程ＡＸＢ＋ＣＹＤ＝Ｅ有解的充要条件以及一般解的公式，并且推广了著名的Ｒｏｔｈ等价定理。     

Asymptotic Behavior of a Stochastic Predator-prey Model with Beddington-DeAngelis Functional Response and L\'{e}vy Jumps

A stochastic two-prey-one-predator model with Beddington-DeAngelis functional response and L\''{e}vy jumps is proposed and investigated in this paper. First of all, we prove the existence and uniqueness of the global positive solution, and stochastic ultimate boundedness of the solution. Next, under a simple assumption, by using It\^{o} formula and other important inequalities, some sufficient conditions are established to ensure the extinction and persistence in the mean of the system. The results show that neither strong white noise nor L\''{e}vy noise is conducive to the persistence of the population. Finally, the theoretical results are verified by numerical simulations.     

Asymptotic enumeration of sparse 0-1 matrices with irregular row and column sums

Let s=(s₁,…,s_m) and t=(t₁,…,t_n) be vectors of non-negative integer-valued functions with equal sum . Let N(s,t) be the number of m×n matrices with entries from {0,1} such that the ith row has row sum s_i and the jth column has column sum t_j. Equivalently, N(s,t) is the number of labelled bipartite graphs with degrees of the vertices in one side of the bipartition given by s and the degrees of the vertices in the other side given by t. We give an asymptotic formula for N(s,t) which holds when S→∞ with 1?st=o(S^2/3), where and . This extends a result of McKay and Wang [Linear Algebra Appl. 373 (2003) 273-288] for the semiregular case (when s_i=s for 1?i?m and t_j=t for 1?j?n). The previously strongest result for the non-semiregular case required 1?max{s,t}=o(S^1/4), due to McKay [Enumeration and Design, Academic Press, Canada, 1984, pp. 225-238].