Abstract We show that the components of finite energy solutions to general nonlinear Schrödinger systems have exponential decay at infinity. Our results apply positive or sign-changing components, and cooperative, competitive, mixed-interaction systems. As an application, we use derive upper bound for least possible a solution with prescribed number nonradial components.

La percolation bootstrap constitue une classe étendue d’automates cellulaires aux conditions initiales aléatoires. Dans ce travail on développe des outils pour étudier en toute généralité l’une trois classes « d’universalité » de modèles deux dimensions appelée souscritique. On introduit la nouvelle notion densités critiques qui jouent le rôle difficultés les (Bollobás et al.), mais adaptée sou...

I consider a physical system described by a continuous field theory and enclosed in a large but finite cubical box with periodic boundary conditions. The system is assumed to undergo a continuous phase transition at some critical point. The 4 M theory that is a continuous version of the Ising model is such a system but there are many other examples corresponding to higher spin, higher symmetry ...

We here analyse numerical simulations of supersonic, hypersonic and magnetohydrodynamic turbulence that is free to decay. Our goals are to understand the dynamics of the decay and the characteristic properties of the shock waves produced. This will be useful for interpretation of observations of both motions in molecular clouds and sources of non-thermal radiation. We find that decaying hyperso...

The problem of testing two simple hypotheses in a general probability space is considered. For fixed type-I error probability, the best exponential decay rate type-II investigated. In regular asymptotic cases (i.e., when length observation interval grows without limit) given by Stein’s exponent. paper, for space, some non-asymptotic lower and upper bounds are derived. These represent pure analy...

I consider a physical system described by a continuous field theory and enclosed in a large but finite cubical box with periodic boundary conditions. The system is assumed to undergo a continuous phase transition at some critical point. The 4 M theory that is a continuous version of the Ising model is such a system but there are many other examples corresponding to higher spin, higher symmetry ...