Randomly switched vector fields sharing a zero on a common invariant face

On a Metric on Translation Invariant Spaces

In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.

A Comparison of the Common Vector and the Discriminative Common Vector Methods for Face Recognition

The Common Vector (CV) method is a successful method which has been originally proposed for isolated word recognition problems in the case where the number of samples for each class is less than or equal to the dimensionality of the sample space. This method suggests elimination of all the features that are in the direction of the eigenvectors corresponding to the nonzero eigenvalues of the cov...

Stabilizing Randomly Switched Systems

This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the system state; it selects, at each instant of time, the active subsystem from a family of systems. Sufficient conditions for stochastic stability (almost sur...

Admissible vector fields and quasi-invariant measures∗

Invariant Hypersurfaces for Positive Characteristic Vector Fields

We show that a generic vector field on an affine space of positive characteristic admits an invariant algebraic hypersurface. This is in sharp contrast with the characteristic zero case where Jouanolou’s Theorem says that a generic vector field on the complex plane does not admit any invariant algebraic curve.