Exponential Asymptotic Stability of a Repairable System with Two Identical Components

2012 ◽  
Vol 591-593 ◽  
pp. 2428-2431
Author(s):  
Xue Feng ◽  
Ping Zuo ◽  
Hong Tu Hua ◽  
Xiao Yan Qi
Keyword(s):  
Asymptotic Stability ◽  
Compact Operator ◽  
Continuous Semigroup ◽  
Repairable System ◽  
Strongly Continuous Semigroup ◽  
Semi Group ◽  
Positive Contraction ◽  
Spectral Bound ◽  
Exponential Asymptotic Stability ◽  
Stability Of The Solution

The repairable system solution’s exponential asymptotic stability was discussed in this paper, First we prove that the positive contraction strongly continuous semigroup which is generated by the operator corresponding to these equations describing a system with two identical components is a quasi-compact operator. Following the result that 0 is an eigenvalue of the operator with algebraic index one and the strongly continuous semi-group is contraction, we deduce that the spectral bound of the operator is zero. By the above results we obtain easily the exponential asymptotic stability of the solution of the repairable system.

Free E0-Semigroups

1995 ◽  
Vol 47 (4) ◽  
pp. 744-785 ◽  
Author(s):  
Neal J. Fowler
Keyword(s):  
Hilbert Space ◽  
Free Product ◽  
Continuous Semigroup ◽  
Fock Space ◽  
Linear Operators ◽  
Free Flow ◽  
Strongly Continuous Semigroup ◽  
Bounded Linear Operators ◽  
Bounded Linear

AbstractGiven a strongly continuous semigroup of isometries ∪ acting on a Hilbert space ℋ, we construct an E0-semigroup α∪, the free E0-semigroup over ∪, acting on the algebra of all bounded linear operators on full Fock space over ℋ. We show how the semigroup αU⊗V can be regarded as the free product of α∪ and αV. In the case where U is pure of multiplicity n, the semigroup au, called the Free flow of rank n, is shown to be completely spatial with Arveson index +∞. We conclude that each of the free flows is cocycle conjugate to the CAR/CCR flow of rank +∞.

Dilations of one Parameter Semigroups of Positive Contractions on Lp Spaces

1997 ◽  
Vol 49 (4) ◽  
pp. 736-748 ◽  
Author(s):  
Gero Fendler
Keyword(s):  
Continuous Semigroup ◽  
Continuous Group ◽  
Strongly Continuous Semigroup ◽  
Von Neumann ◽  
Lp Spaces ◽  
Discrete Semigroup ◽  
Neumann Type ◽  
Transfer Map

AbstractIt is proved in this note, that a strongly continuous semigroup of (sub)positive contractions acting on an Lp-space, for 1 < p < ∞ p ≠ 2, can be dilated by a strongly continuous group of (sub)positive isometries in a manner analogous to the dilation M. A. Akçoglu and L. Sucheston constructed for a discrete semigroup of (sub)positive contractions. From this an improvement of a von Neumann type estimation, due to R. R.Coifman and G.Weiss, on the transfer map belonging to the semigroup is deduced.

Differentiation of Multiparameter Superadditive Processes

1985 ◽  
Vol 37 (3) ◽  
pp. 385-404
Author(s):  
Doğan Çömez
Keyword(s):  
Continuous Semigroup ◽  
Strongly Continuous Semigroup ◽  
Semigroup Of Operators ◽  
Markovian Semigroup ◽  
Extra Assumption ◽  
Differentiation Theorem

In this article our purpose is to prove a differentiation theorem for multiparameter processes which are strongly superadditive with respect to a strongly continuous semigroup of positive L1 contractions (see Section 1 for definitions).Recently, the differentiation theorem for superadditive processes with respect to a one-parameter semigroup of positive L1-contractions has been proved by D. Feyel [9]. Another proof is given by M. A. Akçoğlu [1]. R. Emilion and B. Hachem [7] also proved the same theorem, but with an extra assumption on the process (see also [1]). The proof of this theorem for superadditive processes with respect to a Markovian semigroup of operators on L1 is given by M. A. Akçoğlu and U. Krengel [4]. Thus [1] and [9] extend the result of [4] to the sub-Markovian setting. Here we will obtain the multiparameter sub-Markovian version of this theorem, namely Theorem 3.17 below

scholarly journals An application of topological degree to the periodic competing species problem

1986 ◽  
Vol 28 (2) ◽  
pp. 202-219 ◽  
Author(s):  
Carlos Alvarez ◽  
Alan C. Lazer
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Lower Bounds ◽  
Topological Degree ◽  
Upper And Lower Bounds ◽  
Species Problem ◽  
Competing Species ◽  
Right Hand ◽  
The Right ◽  
Stability Of The Solution

AbstractWe consider the Volterra-Lotka equations for two competing species in which the right-hand sides are periodic in time. Using topological degree, we show that conditions recently given by K. Gopalsamy, which imply the existence of a periodic solution with positive components, also imply the uniqueness and asymptotic stability of the solution. We also give optimal upper and lower bounds for the components of the solution.

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