Let and be two smooth vector fields on a two-dimensional manifold . If and are everywhere linearly independent, then they define a Riemannian metric on (the metric for which they are orthonormal) and they give to the structure of metric space. If and become linearly dependent somewhere on , then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way...
The paper deals with the genericity of domain-dependent spectral properties of the Laplacian-Dirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form a free family. We also show that the spectrum is generically non-resonant.
The results are obtained by applying global perturbations of the domains
and exploiting analytic perturbation properties.
The work is motivated by two applications: an existence result for
the problem of maximizing the rate of...
Soient et deux champs de vecteurs lisses sur globalement asymptotiquement stables à l’origine. Nous donnons des conditions nécessaires et des conditions suffisantes sur la topologie de l’ensemble des points où et sont parallèles pour pouvoir assurer la stabilité asymptotique globale du système contrôlé non linéaire non autonome
où le contrôle est une fonction mesurable arbitraire de dans . Les conditions données ne nécessitent aucune intégration ou construction...
We consider a finite-dimensional model for the motion of
microscopic organisms whose propulsion
exploits
the action of a layer of covering its surface.
The model couples
Newton's laws driving the organism,
considered as
a rigid body, with
Stokes equations governing the surrounding fluid.
The action of the
is described by a set of controlled
velocity fields on the surface of the organism.
The first contribution of the paper is the proof
that such a system
is generically controllable
when...
Download Results (CSV)