Flocking in noisy environments

We consider a perturbed version of the dynamics of a flock introduced by Cucker and Smale ("Emergent behaviour in flocks") and prove, under similar conditions, that nearly-alignment (a concept that is precised in the text) is achieved with a certain probability, bounded from below

Nash functions over real spectra

AbstractIn this note we construct a sheaf of rings over real spectra which generalizes the common sheaf of Nash functions over a Nash set and we use it to get some Nullstellensätze for the geometric case