Operating systems do not perform their intended functions as time passes and ultimately fail due the failure of one or more of their parts, units, or components. Failure is caused by many factors such as age, deterioration, wear and tear, leakage, and lack of proper and timely maintenances. Failed components are usually replaced if not expensive or critical; otherwise repaired. Repair can be pe...

Aims. Most of current models of TeV blazars emission assume a Synchrotron Self-Compton mechanism where relativistic particles emit both synchrotron radiation and Inverse Compton photons. For sake of simplicity, these models usually consider only steady state emission. The spectral features are thus only related to the shape of the particle distribution, and do not depend on the timing of observ...

This paper investigates the relations between three different properties, which are of importance in continuous-time optimal control problems: dissipativity of the underlying dynamics with respect to a specific supply rate, optimal operation at steady state, and the turnpike property. We show that dissipativity with respect to a steady state implies optimal operation at this steady state and th...

In this paper we derive a model describing the dynamics of HIV-1 infection in tissue culture where the infection spreads directly from infected cells to healthy cells trough cell-to-cell contact. We assume that the infection rate between healthy and infected cells is a saturating function of cell concentration. Our analysis shows that if the basic reproduction number does not exceed unity then ...

We consider priority fluid queueing systems where high priority class has strict priority access to service. Sample path analysis tools, such as Poisson Counter Driven Stochastic Differential Equation, are employed to study system queueing behavior in steady state. We are able to obtain various analytical results for different fluid traffic models and system configurations. Those results can be...

In this article, single product Cournot oligopolies are considered, where the demand and cost functions are linear. While cost functions are completely known by all firms, they only partially know the demand function, as they misspecify the slope. At any stage of the repeated oligopoly game firms update the slope of their subjective demand functions on the basis of the discrepancy they observe ...

In order to enrich the modelling of uid ows, we investigate in this paper a coupling between two models dedicated to distinct regimes. More precisely, we focus on the in uence of the Mach number as the low Mach case is known to induce theoretical and numerical issues in a compressible framework. A moving interface is introduced to separate a compressible model (Euler with source term) and its l...

This article considers a continuous review perishable (s,S) inventory system in which the demands arrive according to a Markovian arrival process (MAP). The lifetime of items in the stock and the lead time of reorder are assumed to be independently distributed as exponential. Demands that occur during the stock-out periods either enter a pool which has capacity N(<∞) or are lost. Any demand tha...

We prove new enclosures for the spectrum of non-selfadjoint operator matrices associated with second order linear differential equations z̈(t) +Dż(t) +A0z(t) = 0 in a Hilbert space. Our main tool is the quadratic numerical range for which we establish the spectral inclusion property under weak assumptions on the operators involved; in particular, the damping operator only needs to be accretive a...

The growth of tumors can be modeled as a free boundary problem involving partial differential equations. We consider one such model and compute steady-state solutions for this model. These solutions include radially symmetric solutions where the free boundary is a sphere and nonradially symmetric solutions. Linear and nonlinear stability for these solutions are determined numerically.