Differentiability and Compactness of Semigroup Generated by k/G:N Redundant System with Finite Repair Time

Ehmet ABLET, Qing Jin CHENG, Jian Jian WANG, Wen ZHANG

Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (3) : 475-488.

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Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (3) : 475-488. DOI: 10.12386/A2022sxxb0039

Differentiability and Compactness of Semigroup Generated by k/G:N Redundant System with Finite Repair Time

  • Ehmet ABLET1, Qing Jin CHENG2, Jian Jian WANG2, Wen ZHANG2
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Abstract

We investigate the differentiability and compactness of the C0-semigroup generated by the k/G:N redundant system with finite repair time. We show that the C0-semigroup is eventually differentiable and eventually compact when the repair time is finite. However, this is not true for the case when the repair time is infinite.

Key words

k/G:N redundant system / eventual differentiability / eventual compactness / C0-semigroup

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Ehmet ABLET, Qing Jin CHENG, Jian Jian WANG, Wen ZHANG. Differentiability and Compactness of Semigroup Generated by k/G:N Redundant System with Finite Repair Time. Acta Mathematica Sinica, Chinese Series, 2022, 65(3): 475-488 https://doi.org/10.12386/A2022sxxb0039

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