广西师范大学学报(自然科学版) ›› 2014, Vol. 32 ›› Issue (4): 76-83.

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广义生灭矩阵的对偶q-矩阵Q*及最小Q*-函数

赵海霞1, 李扬荣2, 唐生强1   

  1. 1.桂林电子科技大学数学与计算科学学院,广西桂林541004;
    2.西南大学数学与统计学院,重庆400715
  • 收稿日期:2014-02-26 发布日期:2018-09-26
  • 通讯作者: 唐生强(1951-),男,广西桂林人,桂林电子科技大学教授。E-mail:tangsq@guet.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11071199,11361017);桂林电子科技大学创新团队项目

The Dual q-matrix Q* and the Minimal Q*-function of the Generalized Birth-death Matrix

ZHAO Hai-xia1, LI Yang-rong2, TANG Sheng-qiang1   

  1. 1. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin Guangxi 541004, China;
    2. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
  • Received:2014-02-26 Published:2018-09-26

摘要: 本文讨论广义生灭矩阵Q的对偶q-矩阵Q*的基本性质,结合基本性质得出在一定条件下Q*强零入、零出的数字刻画,并由此推出在相应条件下,Q强零入当且仅当Q*零出,Q零出当且仅当Q*强零入,从而找到了Q与Q*在性质上的关联。本文还讨论了最小Q*函数的基本性质,并得出在一定条件下最小Q-函数的对偶恰是最小Q*函数。

关键词: 广义生灭矩阵Q, 对偶q-矩阵, 小Q*函数

Abstract: In this paper, the main properties of the dual q-matrix Q* of the generalized birth-death matrix Q were discussed. According to these properties, the digital descriptions of Q* is strong zero-entrance and zero-exit were found respectively. Following conclusions were got: Q is strong zero-entrance if and only if Q* is zero-exit; Q is zero-exit if and only if Q* is strong zero-entrance. Thus the relation between Q and Q* were found. Besides, the main properties of the minimal Q*-function were discussed, and the following conclusion was got, under certain conditions, the dual of the minimal Q-function is the minimal Q*-function exactly.

Key words: generalized birth-death matrix, dual q-matrix, minimal Q*-function

中图分类号: 

  • O177.2
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