An MX/G/1 queueing system with a setup period and a vacation period

This paper deals with an M^X/G/1 queueing system with a vacation period which comprises an idle period and a random setup period. The server is turned off each time when the system becomes empty. At this point of time the idle period starts. As soon as a customer or a batch of customers arrive, the setup of the service facility begins which is needed before starting each busy period. In this paper we study the steady state behaviour of the queue size distributions at stationary (random) point of time and at departure point of time. One of our findings is that the departure point queue size distribution is the convolution of the distributions of three independent random variables. Also, we drive analytically explicit expressions for the system state probabilities and some performance measures of this queueing system. Finally, we derive the probability generating function of the additional queue size distribution due to the vacation period as the limiting behaviour of the M^X/M/1 type queueing system. This revised version was published online in June 2006 with corrections to the Cover Date.     

N-Methyl Piperidinium Chlorochromate Adsorbed on Alumina: A New and Selective Reagent for the Oxidation of Benzylic Alcohols to their Corresponding Carbonyl Compounds

Summary.  N-Methyl piperidinium chlorochromate adsorbed on alumina oxidizes a wide variety of benzylic alcohols to the corresponding carbonyl compounds. Received May 18, 2000. Accepted (revised) July 4, 2000     

The effects of annealing and rate of deposition on the electrical,optical and structural properties of amorphous GeSi alloy films

The electrical, optical and structural properties of rf-sputtered amorphous GeSi alloy films have been investigated as functions of the rate of deposition between 90 and 360 Å min^?1, and various annealing conditions. The stabilization evidenced in the electrical conductivity, optical absorption and density of these films deposited at higher rates and/or annealing temperatures may be explained in terms of the reduction of imperfections in the as-deposited films.     

Fronts in two-phase porous media flow problems: The effects of hysteresis and dynamic capillarity

In this work, we study the behavior of saturation fronts for two-phase flow through a long homogeneous porous column . In particular, the model includes hysteresis and dynamic effects in the capillary pressure and hysteresis in the permeabilities. The analysis uses traveling wave approximation. Entropy solutions are derived for Riemann problems that are arising in this context. These solutions belong to a much broader class compared to the standard Oleinik solutions, where hysteresis and dynamic effects are neglected. The relevant cases are examined and the corresponding solutions are categorized. They include nonmonotone profiles, multiple shocks, and self-developing stable saturation plateaus. Numerical results are presented that illustrate the mathematical analysis. Finally, we discuss the implication of our findings in the context of available experimental results.     

Enhanced Optical and Electrical Properties of Graphene Oxide-Silver Nanoparticles Nanocomposite Film by Thermal Annealing in the Air

Russian Journal of Applied Chemistry - Here, we report the enhanced optical and electrical properties of graphene oxide-silver nanoparticles (GO-AgNPs) nanocomposite due to thermal annealing in air...     

Eighth power moment of Kloosterman sum,supercharacters, and elliptic curves

The Ramanujan Journal - We here use a supercharacter theory of $${\mathbb {F}}_p^2$$ to express the eighth power moment of Kloosterman sum in terms of traces of Frobenius endomorphism of certain...