Two definitions of the notion of a chaotic transformation are compared: sensitivity to initial conditions and sensitivity to perturbations. Only the later is compatible with the idea that information has a

In this paper we propose a new method of determining the stability of queueing systems. We attain it using the absorbing process and introduce the untraceable events method to show the existence of the absorbing process. The advantage of our method is that we are able to discuss the stability of various variables for both discrete and continuous parameters in a general framework with nonstation...

3 4 Cassie Wilson, Mark A. King and Maurice R. Yeadon 5 6 1 Department for Health, University of Bath, Bath, BA2 7AY, UK. 7 2 School of Sport, Exercise and Health Sciences, Loughborough University, 8 Loughborough LE11 3TU, UK. 9 10 11 12

In recent years much progress has been made in applying field-theoretic renormalization-group methods to models of diffusion-limited chemical reactions. One such example was a study by the present authors of the A + B--* ~ annihilation reaction with random initial conditions and equal particle densities. III Our purpose here is to correct a mistake contained in this worked and to revise the con...

Let Z t,z be a R -valued jump diffusion controlled by ν with initial condition Z t,z(t) = z. The aim of this paper is to characterize the set V (t) of initial conditions z such that Z t,z can be driven into a given target at a given time by proving that the function u(, z) = 1 − 1V (t) satisfies, in the viscosity sense, the equation (2) below. As an application, we study the problem of hedging ...

Given an attracting periodic orbit of a system of ordinary differential equations, one can assign an asymptotic phase to any initial condition that approaches such a periodic orbit. All initial conditions with the same asymptotic phase lie on what is known as an isochron. Isochrons foliate the basin of attraction, and may have intriguing geometric properties. We present here two cases of a plan...

Heat equations with memory of Gurtin-Pipkin type (i.e. Eq. (1) with α = 0) have controllability properties which strongly resemble those of the wave equation. Instead, recent counterexamples show that when α > 0 the control properties do not parallel those of the (memoryless) heat equation, in the sense that there are initial conditions in L2(Ω) which cannot be controlled to zero. The proof of ...

This paper presents an elementary and self-contained proof of an existence theorem of nal coalgebras for endofunctors on the category of sets and functions.

where m is a (possibly vector-valued) unknown function of a real "time" variable t and an A-dimensional real vector "space" variable x. Here A is a linear operator, constant2 in t, operating on u, where u is considered a function of x alone (i.e., A acts on elements of a linear space (B and, for each value of t, u{-, ¿)G®). The function/is a known function of x and t. Thus u is to satisfy (1) f...

In this paper, we investigate a specific wave equation which generates the pre-Laguerre system, and prove that the pre-Laguerre system is related to the solution of the partial differential equation with some initial conditions. © 2013 Elsevier Ltd. All rights reserved.