Exponential systems

What are the key aspects to achieving acceptable usability outcomes for information systems being developed? The changing technologies and increased usage across the general population, the impacts of this in our everyday lives, at work and at leisure are exponentially increasing. The interfaces and interaction styles presented as part of these technologies have been challenged to be more intuitive, contextually sensitive, location aware, human centred and aimed at a larger community of stakeholders.

376p runthenight04 02-02-2023 6 2   Download

For diffeomorphisms of smooth compact finite-dimensional manifolds, we consider the problem of how fast the number of periodic points with period n grows as a function of n. In many familiar cases (e.g., Anosov systems) the growth is exponential, but arbitrarily fast growth is possible; in fact, the first author has shown that arbitrarily fast growth is topologically (Baire) generic for C 2 or smoother diffeomorphisms.

83p noel_noel 17-01-2013 43 7   Download

Consider the inverse eigenvalue problem of the Schr¨dinger operator deo fined on a finite interval. We give optimal and almost optimal conditions for a set of eigenvalues to determine the Schr¨dinger operator. These conditions are o simple closedness properties of the exponential system corresponding to the known eigenvalues. The statements contain nearly all former results of this topic. We give also conditions for recovering the Weyl-Titchmarsh m-function from its values m(λn ).

35p noel_noel 17-01-2013 43 6   Download

Exponential decay of correlations for C 4 contact Anosov flows is established. This implies, in particular, exponential decay of correlations for all smooth geodesic flows in strictly negative curvature. 1. Introduction The study of decay of correlations for hyperbolic systems goes back to the work of Sinai [36] and Ruelle [32]. While many results were obtained through the years for maps, some positive results have been established for Anosov flows only recently. Notwithstanding the proof of ergodicity, and mixing, for geodesic flows on manifolds of negative curvature [15], [1], [35], ...

39p tuanloccuoi 04-01-2013 58 6   Download

ASYMPTOTIC ESTIMATES AND EXPONENTIAL STABILITY FOR HIGHER-ORDER MONOTONE DIFFERENCE EQUATIONS ´ EDUARDO LIZ AND MIHALY PITUK Received 21 May 2004 Asymptotic estimates are established for higher-order scalar difference equations and inequalities the right-hand sides of which generate a monotone system with respect to the discrete exponential ordering. It is shown that in some cases the exponential estimates can be replaced with a more precise limit relation.

15p sting12 10-03-2012 59 5   Download

EXPONENTIAL STABILITY OF DYNAMIC EQUATIONS ON TIME SCALES ALLAN C. PETERSON AND YOUSSEF N. RAFFOUL Received 6 July 2004 and in revised form 16 December 2004 We investigate the exponential stability of the zero solution to a system of dynamic equations on time scales. We do this by defining appropriate Lyapunov-type functions and then formulate certain inequalities on these functions. Several examples are given. 1. Introduction This paper considers the exponential stability of the zero solution of the first-order vector dynamic equation x∆ = f (t,x), t ≥ 0. (1.

12p sting12 10-03-2012 44 5   Download

STABILITY FOR DELAYED GENERALIZED 2D DISCRETE LOGISTIC SYSTEMS CHUAN JUN TIAN AND GUANRONG CHEN Received 28 August 2003 and in revised form 19 February 2004 This paper is concerned with delayed generalized 2D discrete logistic systems of the form xm+1,n = f (m,n,xm,n ,xm,n+1 ,xm−σ,n−τ ), where σ and τ are positive integers, f : N2 × R3 → 0 R is a real function, which contains the logistic map as a special case, and m and n are nonnegative integers, where N0 = {0,1,...} and R = (−∞, ∞). Some sufficient conditions for this system to be stable and exponentially stable...

12p sting12 10-03-2012 49 6   Download

As Internet connectivity is reaching the global community, information systems are becoming more and more distributed. Inevitably, this overnight exponential growth has also caused traffic overload at various places in the network. Until recently, it was believed that scaling the Internet was simply an issue of adding more resources, i.e. bandwidth and processing power could be brought to where they were needed.

11p tienvovan 11-09-2010 94 6   Download