Note sur la décomposition d’une forme quadratique à variables en une somme de carrés
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.
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.
On étudie les systèmes différentiels singulièrement perturbés de dimension 3 du type où , , sont analytiques quelconques. Les travaux antérieurs étudiaient les points réguliers où la surface lente 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...
Let E be a Banach space with a separable dual. Zippin’s theorem asserts that E embeds in a Banach space 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 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 and can be controlled by the Szlenk index of E, where the Szlenk index...
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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