Étude sur les transformations homographiques planes.
Nouvelle théorie des diamètres.
Sur les dérivées modulaires des polynômes
Note relative aux points d'intersection des courbes algébriques
Sur la généralisation du rapport anharmonique
Groupes à moitié ordonnés
Convergence towards self-similar asymptotic behavior for the dissipative quasi-geostrophic equations
This work proves the convergence in L¹(ℝ²) towards an Oseen vortex-like solution to the dissipative quasi-geostrophic equations for several sets of initial data with suitable decay at infinity. The relative entropy method applies in a direct way for solving this question in the case of signed initial data and the difficulty lies in showing the existence of unique global solutions for the class of initial data for which all properties needed in the entropy approach are met. However, the estimates...
Approximate roots of a valuation and the Pierce-Birkhoff conjecture
In this paper, we construct an object, called a system of approximate roots of a valuation, centered in a regular local ring, which describes the fine structure of the valuation (namely, its valuation ideals and the graded algebra). We apply this construction to valuations associated to a point of the real spectrum of a regular local ring . We give two versions of the construction: the first, much simpler, in a special case (roughly speaking, that of rank 1 valuations), the second – in the case...
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