In this paper we study the large time behavior of regular solutions to a nematic liquid crystals system in Sobolev spaces Hm(R3) for m ≥ 0.We obtain optimal decay rates in Hm(R3) spaces, in the sense that the rates coincide with the rates of the underlying linear counterpart. The fluid under consideration has constant density and small initial data.

We study the asymptotic behaviour of positive solutions of the Cauchy problem for the fast diffusion equation as t approaches the extinction time. We find a continuum of rates of convergence to a self-similar profile. These rates depend explicitly on the spatial decay rates of initial data.

X iv :h ep -t h/ 01 10 01 4v 1 1 O ct 2 00 1 THE RARITA-SCHWINGER OPERATOR 1 Bochner-Weitzenböck formulas associated with the Rarita-Schwinger operator Thomas Branson and Oussama Hijazi

The calculation of the ~23 mixing angle from semi-leptonic B-decay depends’ on the mass ratio m,/mb. The energy scales at which the running masses m, and rnb should be taken are determined once terms of order [cys . (mc/mb)] are taken into account. We give an analytic expression for the QCD correction to the decay rate to all orders in the ratio between on-shell masses. We explain how it should...

We investigate the time evolution of the decay (or ionization) probability of a D-dimensional model atom (D = 1, 2, 3) in the presence of a uniform (i.e., static and homogeneous) background field. The model atom consists in a non-relativistic point particle in the presence of a point-like attractive well. It is shown that the model exhibits infinitely many resonances leading to possible deviati...

Holographic gratings in photorefractive crystals that are based on charge redistribution inevitably decay as a result of ionic and electronic conduction. Under certain and restricted conditions these decay times can be acceptably long. Relevant decay rates and transient hologram field expressions are derived with special reference to LiNbO(3). Some experimental data are presented.

Our domain G = (0,L) is an interval of length L. The boundary ∂G = {0,L} are the two endpoints. We consider here as an example the case (DD) of Dirichlet boundary conditions: Dirichlet conditions at x = 0 and x = L. For other boundary conditions (NN), (DN), (ND) one can proceed similarly. In one dimension the Laplace operator is just the second derivative with respect to x: ∆u(x, t) = uxx(x, t)...

We consider stability properties of discrete-time bilinear lters. Simple su cient conditions are given for bounded-input bounded-output stability (with not necessarily zero initial conditions), lp stability, and three other important types of stability. In particular, conditions are given under which asymptotically periodic inputs produce asymptotically periodic outputs with the same period. Re...