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Approximation by finitely supported measures

Benoît Kloeckner — 2012

ESAIM: Control, Optimisation and Calculus of Variations

We consider the problem of approximating a probability measure defined on a metric space by a measure supported on a finite number of points. More specifically we seek the asymptotic behavior of the minimal Wasserstein distance to an approximation when the number of points goes to infinity. The main result gives an equivalent when the space is a Riemannian manifold and the approximated measure is absolutely continuous and compactly supported.

Approximation by finitely supported measures

Benoît Kloeckner — 2012

ESAIM: Control, Optimisation and Calculus of Variations

We consider the problem of approximating a probability measure defined on a metric space by a measure supported on a finite number of points. More specifically we seek the asymptotic behavior of the minimal Wasserstein distance to an approximation when the number of points goes to infinity. The main result gives an equivalent when the space is a Riemannian manifold and the approximated measure is absolutely continuous and compactly supported.

Perturbation singulière en dimension trois : canards en un point pseudo-singulier nœud

Éric Benoît — 2001

Bulletin de la Société Mathématique de France

On étudie les systèmes différentiels singulièrement perturbés de dimension 3 du type { x ˙ = f ( x , y , z , ε ) , y ˙ = g ( x , y , z , ε ) , ε z ˙ = h ( x , y , z , ε ) , f , g , h sont analytiques quelconques. Les travaux antérieurs étudiaient les points réguliers où la surface lente h = 0 est transverse au champ rapide vertical. C’est le domaine d’application du théorème de Tikhonov. Dans d’autres travaux antérieurs, on étudiait les singularités de certains types : plis et fronces de la surface lente, ainsi que certaines singularités plus compliquées, analogues...

An ordinal version of some applications of the classical interpolation theorem

Benoît Bossard — 1997

Fundamenta Mathematicae

Let E be a Banach space with a separable dual. Zippin’s theorem asserts that E embeds in a Banach space E 1 with a shrinking basis, and W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński have shown that E is a quotient of a Banach space E 2 with a shrinking basis. These two results use the interpolation theorem established by W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński. Here, we prove that the Szlenk indices of E 1 and E 2 can be controlled by the Szlenk index of E, where the Szlenk index...

Families of strongly projective graphs

Benoit Larose — 2002

Discussiones Mathematicae Graph Theory

We give several characterisations of strongly projective graphs which generalise in many respects odd cycles and complete graphs [7]. We prove that all known families of projective graphs contain only strongly projective graphs, including complete graphs, odd cycles, Kneser graphs and non-bipartite distance-transitive graphs of diameter d ≥ 3.

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