scholarly journals A Semigroup Approach to the System with Primary and Secondary Failures

2010 ◽  
Vol 2010 ◽  
pp. 1-33 ◽  
Author(s):  
Abdukerim Haji
Keyword(s):  
Functional Analysis ◽  
Steady State ◽  
Asymptotic Stability ◽  
Positive Solution ◽  
Steady State Solution ◽  
Linear Operators ◽  
Time Dependent ◽  
Well Posedness ◽  
Semigroup Approach ◽  
Time Dependent Solution

We investigate the solution of a repairable parallel system with primary as well as secondary failures. By using the method of functional analysis, especially, the spectral theory of linear operators and the theory ofC0-semigroups, we prove well-posedness of the system and the existence of positive solution of the system. And then we show that the time-dependent solution strongly converges to steady-state solution, thus we obtain the asymptotic stability of the time-dependent solution.

Stability of the Redundant System with Two Correlated Units

2012 ◽  
Vol 198-199 ◽  
pp. 973-977 ◽  
Author(s):  
Xing Qiao ◽  
Ming Fang
Keyword(s):  
Banach Space ◽  
Functional Analysis ◽  
Steady State ◽  
Semigroup Theory ◽  
Steady State Solution ◽  
Linear Operators ◽  
Well Posedness ◽  
Redundant System ◽  
Bounded Linear ◽  
System Operator

In this paper the qualitative behaviors of the two correlated units redundant system with two types of failure were discussed. By using the method of functional analysis, especially, the semigroup theory of bounded linear operators on Banach space, the well-posedness and the existence of positive solution of the system was obtained. By analyzing the spectra distribution of the system operator, the dynamic solution of the system asymptotically converges to the nonnegative steady-state solution which is the eigenfunction corresponding to eigenvalue 0 of the system operator was proved.

scholarly journals Semigroup Methods for the M/G/1 Queueing Model with Working Vacation and Vacation Interruption

2016 ◽  
Vol 8 (5) ◽  
pp. 56 ◽  
Author(s):  
Ehmet Kasim
Keyword(s):  
Semigroup Theory ◽  
Steady State Solution ◽  
Linear Operators ◽  
Time Dependent ◽  
Queueing Model ◽  
Working Vacation ◽  
Positive Time ◽  
Vacation Interruption ◽  
Vacation Period ◽  
Time Dependent Solution

By using the strong continuous semigroup theory of linear operators we prove that the M/G/1 queueing model with working vacation and vacation interruption has a unique positive time dependent solution which satisfies probability conditions. When the both service completion rate in a working vacation period and in a regular busy period are constant, by investigating the spectral properties of an operator corresponding to the model we obtain that the time-dependent solution of the model strongly converges to its steady-state solution.

The well-Posedness of a Two-Unit Standby Redundant Electronic Equipment System

2013 ◽  
Vol 325-326 ◽  
pp. 315-318
Author(s):  
Xing Qiao ◽  
Yan Wang ◽  
Dan Ma ◽  
Zhuang Liu
Keyword(s):  
Steady State ◽  
Electronic Equipment ◽  
Time Dependent ◽  
Well Posedness ◽  
Reliability Study ◽  
Reliability Indices ◽  
Unique Existence ◽  
Human Failure ◽  
Time Dependent Solution ◽  
Equipment System

In this paper, we deal with a two-unit standby redundant electronic equipment system under human failure. In reliability study, it is ordinary to substitute the steady-state reliability indices for dynamic ones because the time-dependent solution is difficult to get. But this replacement should be based on some conditions in general. Therefore it is important to study the unique existence and the expression of the dynamic solution and it is the same with its stability.

scholarly journals On Asymptotic Behavior of the Time-Dependent Solution of a Reliability Model

2014 ◽  
Vol 2 ◽  
pp. 1-11 ◽  
Author(s):  
Geni Gupur
Keyword(s):  
Asymptotic Behavior ◽  
Steady State ◽  
Steady State Solution ◽  
State Solution ◽  
Time Dependent ◽  
Reliability Model ◽  
Repair Rate ◽  
Lipschitz Continuous ◽  
Time Dependent Solution

On the basis of our previous work we study asymptotic behavior of the time-dependent solution of a reliability model of two identical units and a repairman and prove the following result: If the repair rate μ(x) is Lipschitz continuous and there exist two positive constants μ and μ such that 0 < μ ≤μ(x)≤ μ < ∞, then its time-dependent solution exponentially converges to its steady-state solution.

Dynamic Stability of an Impact System Connected With Rock Drilling

1969 ◽  
Vol 36 (4) ◽  
pp. 743-749 ◽  
Author(s):  
C. C. Fu
Keyword(s):  
Computer Simulation ◽  
Exact Solution ◽  
Steady State ◽  
Asymptotic Stability ◽  
Piecewise Linear ◽  
Steady State Solution ◽  
External Excitation ◽  
Rock Drilling ◽  
Impact System ◽  
Number Of Cycles

This paper deals with asymptotic stability of an analytically derived, synchronous as well as nonsynchronous, steady-state solution of an impact system which exhibits piecewise linear characteristics connected with rock drilling. The exact solution, which assumes one impact for a given number of cycles of the external excitation, is derived, its asymptotic stability is examined, and ranges of parameters are determined for which asymptotic stability is assured. The theoretically predicted stability or instability is verified by a digital computer simulation.

A PREY-PREDATOR MODEL WITH DIFFUSION AND A SUPPLEMENTARY RESOURCE FOR THE PREY IN A TWO‐PATCH ENVIRONMENT

2005 ◽  
Vol 9 (1) ◽  
pp. 9-24 ◽  
Author(s):  
J. Dhar
Keyword(s):  
Steady State ◽  
Asymptotic Stability ◽  
Prey Species ◽  
Steady State Solution ◽  
State Solution ◽  
Prey Population ◽  
Predator Species ◽  
Additional Resource ◽  
Linear And Nonlinear ◽  
Predator Model

In this paper, a prey‐predator dynamics, where the predator species partially depends upon the prey species, in a two patch habitat with diffusion and there is a non‐diffusing additional resource for the prey population, is modeled and analyzed. It is shown, that there exists a positive, monotonic, continuous steady state solution with continuous matching at the interface for both the species separately. Further, we obtain conditions for asymptotic stability for both linear and nonlinear cases. Šiame straipsnyje modeliuojama ir analizuojama plešr‐unu ir auku dinamika, laikant, kad plešr-unu populiacija dalinai priklauso nuo auku skačiaus. Areala sudaro dvi sritys, kuriose vyksta populiaciju individu difuzija, be to, aukoms yra išskirtas nedifunduojantis resursas. Irodyta, kad egzistuoja teigiamas, monotoniškas, tolydus stacionarusis sprendinys, tenkinantis tolydumo salyga abiems populiacijoms atskirai. Gautos asimptotinio stabilumo salygos tiesiniu ir netiesiniu atvejais.

scholarly journals Time-Dependent Solution of a Full Hydrodynamic Model Including Convective Terms and Viscous Effect

VLSI Design ◽  
1998 ◽  
Vol 6 (1-4) ◽  
pp. 173-176 ◽  
Author(s):  
Deyin Xu ◽  
Ting-Wei Tang ◽  
Sergei S. Kucherenko
Keyword(s):  
Steady State ◽  
Hydrodynamic Model ◽  
Plasma Oscillation ◽  
Transient Behavior ◽  
Time Dependent ◽  
Viscous Effect ◽  
Turn On ◽  
Time Dependent Solution

Sub-picosecond turn-on transient behavior of ballistic diodes (N+ - N - N+ structures) is studied by solving a system of time-dependent hydrodynamic (HD) equations. Convective terms as well as viscous effect are included in the study. The simulation result indicates that the diode undergoes approximately one quarter of a plasma oscillation before it relaxes to the steady-state value through collisions.

scholarly journals Time dependence of groundwater pumping from a well near a river

2008 ◽  
Vol 465 (2101) ◽  
pp. 175-192 ◽  
Author(s):  
Stefan G Llewellyn Smith ◽  
Anthony M.J Davis
Keyword(s):  
Steady State ◽  
Mixed Boundary ◽  
Linear Equations ◽  
Mixed Boundary Conditions ◽  
Pressure Head ◽  
Steady State Solution ◽  
Time Dependent ◽  
Governing Equations ◽  
Dependent Flow ◽  
Infinite Set

The time-dependent flow of groundwater through an aquifer, generated from rest by pumping from a well close to a river, is calculated without making Dupuit's approximation. The governing equations reduce to the diffusion equation for the pressure head with mixed boundary conditions at the surface of the aquifer and at the base of the river. Using transform techniques, the problem is reduced to an infinite set of linear equations. The steady-state solution provides a guide to the numerical solution of the time-dependent problem. Results are presented for the flux from the river into the aquifer as well as for the flux from the aquifer into the river and out again. Explicit expressions for these fluxes are obtained in the case of rivers that are narrow compared with the aquifer depth. The steady-state flux is then much smaller than the transient flux. Results are significantly different from those obtained using the Dupuit approximation.

SEMIGROUP METHODS FOR A PARALLEL MAINTENANCE SYSTEM WITH TWO COMPONENTS

2010 ◽  
Vol 08 (04) ◽  
pp. 363-386 ◽  
Author(s):  
ABDUKERIM HAJI ◽  
BILIKIZ YUNUS
Keyword(s):  
Asymptotic Behavior ◽  
Spectral Theory ◽  
Positive Operators ◽  
Time Dependent ◽  
Well Posedness ◽  
Maintenance System ◽  
Time Dependent Solution

By using the theory of C0-semigroups and spectral theory of positive operators, we prove well-posedness of the parallel maintenance system with two components and study the asymptotic behavior of the time-dependent solution.

scholarly journals Stability and solution of the time-dependent Bondi–Parker flow

2020 ◽  
Vol 493 (2) ◽  
pp. 2834-2840
Author(s):  
Eric Keto
Keyword(s):  
Steady State ◽  
Transonic Flow ◽  
Initial Conditions ◽  
Steady State Solution ◽  
State Solution ◽  
Time Dependent ◽  
Hamiltonian Description ◽  
Bernoulli’S Equation ◽  
Wide Range ◽  
Isothermal And Adiabatic Flows

ABSTRACT Bondi and Parker derived a steady-state solution for Bernoulli’s equation in spherical symmetry around a point mass for two cases, respectively, an inward accretion flow and an outward wind. Left unanswered were the stability of the steady-state solution, the solution itself of time-dependent flows, whether the time-dependent flows would evolve to the steady state, and under what conditions a transonic flow would develop. In a Hamiltonian description, we find that the steady-state solution is equivalent to the Lagrangian implying that time-dependent flows evolve to the steady state. We find that the second variation is definite in sign for isothermal and adiabatic flows, implying at least linear stability. We solve the partial differential equation for the time-dependent flow as an initial-value problem and find that a transonic flow develops under a wide range of realistic initial conditions. We present some examples of time-dependent solutions.

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