一类可靠性模型的主算子的谱  

On the Spectrum of the Operator Corresponding to a Reliability Model

作　　者：古再力努尔·迪力夏提 艾尼·吾甫尔[1] DILIXIATI Guzelinuer;GUPUR Geni(College of Mathematics and Systems Science,Xinjiang University,Urumqi 830046)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《数学的实践与认识》2020年第10期266-281,共16页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11961062)。

摘　　要：研究一个可靠机器,一个具有无穷容量的缓冲库和一个不可靠机器构成的系统的主算子的谱.当机器1的加工率λ,机器2的加工率μ,部件从机器1成功地传送到机器2的概率η1,机器2成功处理完部件的概率η2满足一定的条件时,证明-μ不是该系统的主算子的特征值.We study spectrum of the operator which corresponds to the system consisting of a reliable machine, a storage buffer with infinite capacity and an unreliable machine, and prove that -μ is not an eigenvalue of the operator if λ, the processing rate of machine 1, μ, the processing rate of machine 2, the probability η1 that a workpiece is transferred successfully from machine 1 to machine 2, the probability η2 that machine 2 processes successfully a workpiece satisfy certain condition.

关 键 词：一个可靠机器 一个具有无穷容量的缓冲库和一个不可靠机器构成的系统 C0-半群 特征值 

分 类 号：O175[理学—数学]