Fractions continues de matrices,convergence et applications

The aim of this article is to give some property of continued fraction with matrices arguments, about their convergence and others applications. At the end of this work, we present a resolution of the Algebraic Riccati Equation by giving an explicit continued fraction development of its solution. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mathematical study of a bacteria–fish model with level of infection structure

In this paper, we propose a mathematical model to study a bacteria–fish system, based upon the interactions between Clostridium botulinum and tilapia, Oerochromis mossambicus. The fish population is divided into susceptible and infected, and the infected fish population is considered structured by the level of infection. The model is thus a system with the infected fish equation being an evolution equation, while those corresponding to the susceptible fish and bacteria in water are ordinary differential equations. The model is firstly transformed into a system with distributed delay for susceptible fish and bacteria and, further, under some assumptions, into a system with discrete delay. The study of this system gives us some results concerning the existence, uniqueness, positivity and boundedness of solutions; we also discuss the existence and stability of its equilibrium points, including conditions for the appearance of Hopf bifurcation. The theoretical results are illustrated by some numerical simulations.     

Commutativity theorems in rings with involution

In this paper, we investigate commutativity of ring R with involution ? which admits a derivation satisfying certain algebraic identities. Some well-known results characterizing commutativity of prime rings have been generalized. Finally, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.     

A series expansion of fractional Brownian motion

Let B be a fractional Brownian motion with Hurst index H(0,1). Denote by the positive, real zeros of the Bessel function J_–H of the first kind of order –H, and let be the positive zeros of J_1–H. In this paper we prove the series representation where X₁,X₂,... and Y₁,Y₂,... are independent, Gaussian random variables with mean zero and and the constant c_H² is defined by c_H²=^–1(1+2H) sin H. We show that with probability 1, both random series converge absolutely and uniformly in t[0,1], and we investigate the rate of convergence.Mathematics Subject Classification (2000): 60G15, 60G18, 33C10     

Study of the surface state density and potential in MIS diode Schottky using the surface photovoltage method

ABSTRACT

The effects of surface preparation and illumination on electric parameters of Au/GaN/GaAs Schottky diode were investigated. The thin GaN film is realized by nitridation of GaAs substrates with different thicknesses of GaN layers (0.7 – 2.2 nm). In order to study the electrical characteristics under illumination, we use an He-Ne laser of 632 nm wavelength. The I(V) current- voltage, the surface photovltage SPV measurement were plotted and analysed taking into consideration the influence of charge exchange between a continuum of the surface states and the semiconductor. The barrier height Ф_Bn, the serial resistance R_s and the ideality factor n are respectively equal to 0.66 eV, 1980 Ω, 2.75 under dark and to 0.65 eV, 1160 Ω, 2.74 under illumination for simple 1 (GaN theckness of 0.7 nm). The interface states density N_ss in the gap and the excess of concentration δn are determined by fitting the experimental curves of the surface photovltage SPV with the theoretical ones and are equal to 4.5×10¹² eV^?1 cm^?2, 5×10⁷ cm^?3, respectively, for sample 1 and 3.5×10¹² eV^?1 cm^?2, 7×10⁸ cm^?3 for sample 2 (GaN theckness of 2 nm). The results confirm that the surface photovoltage is an efficient method for optical and electrical characterizations.     

Convergence of matrix continued fractions

The aim of this work is to give some criteria on the convergence of matrix continued fractions. We begin by presenting some new results which generalize the links between the convergent elements of real continued fractions. Secondly, we give necessary and sufficient conditions for the convergence of continued fractions of matrix arguments. This paper will be completed by illustrating the theoretical results with some examples.