具有优化调整状态的供应链系统算子的性质
Properties of the System Operator for the Supply Chain System with State of Optimal Adjustment

作者: 冯志瑞 * , 原文志 :太原师范学院数学系,山西 晋中;

关键词: 预解正算子共轭算子增长界共尾谱上界Resolvent Positive Adjoint Operator Growth Bound Cofinal Upper Spectral Bound

摘要:
研究了一类具有优化调整状态的供应链系统。通过选取空间和定义算子将模型方程转化成抽象柯西问题,运用C0半群理论,证明了系统算子是稠密的预解正算子,得出了系统算子的共轭算子及其定义域,并证明了系统算子的增长界为0。最后运用预解正算子中共尾的概念及相关理论证明了系统算子的谱上界也是0。

Abstract: The paper presents a supply chain system with state of optimal adjustment. By choosing space and defining operator of this system, we transfer this model into an abstract Cauchy problem. Using C0 semigroup theory, we first prove the system operator is a densely defined resolvent positive op-erator. We obtain the adjoint operator of the system operator and its domain. Furthermore, we prove that 0 is the growth bound of the system operator. Finally, we show that 0 is also the upper spectral bound of the system operator using the concept of cofinal and relative theory.

文章引用: 冯志瑞 , 原文志 (2017) 具有优化调整状态的供应链系统算子的性质。 理论数学, 7, 482-493. doi: 10.12677/PM.2017.76064

参考文献

[1] 辛玉红, 郑爱华, 胡薇薇. 一个供应链系统的可靠性模型的适定性分析[J]. 数学的实践与认识, 2008, 38(1): 46- 52.

[2] 辛玉红, 朱铁丹, 史祎馨. 基于可靠性的企业优化模型[J]. 数学的实践与认识, 2008, 38(3): 67-72.

[3] 郭丽娜, 王鲜霞, 任杨莉. 一类具有优化调整状态的供应链系统的稳定性分析[J]. 数学的实践与认识, 2012, 42(12): 107-111.

[4] 匡继昌. 实分析与泛函分析[M]. 北京: 高等教育出版社, 2002.

[5] Gupur, G., Li, X.Z. and Zhu, G.T. (2001) Functional Analysis Method in Queueing Theory. Research Information, Hertfordshire.

[6] 方保砚, 周继东, 李医民. 矩阵论[M]. 第2版. 北京: 清华大学出版社, 2013.

[7] Arendt, W. (1987) Resolvent Positive Operators. Proceedings of the London Mathematical Society, 54, 321-349.
https://doi.org/10.1112/plms/s3-54.2.321

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