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We study lower bounds of the packing density of non-overlapping equal spheres in R n , n 2, as a function of the maximal circumradius of its Voronoi cells. Our viewpoint is that of Delone sets which allows to investigate the gap between the upper bounds of Rogers or Kabatjanski ˘ i-Leven˘ stein and the Minkowski-Hlawka type lower bounds for the density of… (More)

We study lower bounds of the packing density of a system of non-overlapping equal spheres in R n , n ≥ 2, as a function of the maximal circumradius of its Voronoi cells. Our viewpoint is that of Delone sets which allows to investigate the gap between the upper bounds of Rogers or Kabatjanski ˘ i-Leven˘ stein and the Minkowski-Hlawka type lower bounds for… (More)

par Gilbert MURAZ et Jean-Louis VERGER-GAUGRY Résumé. On montre que l'ensemble UD r des ensembles de points de R n , n ≥ 1, qui ont la propriété que leur distance interpoint min-imale est plus grande qu'une constante strictement positive r > 0 donnée est muni d'une métrique pour lequel il est compact et tel que la métrique de Hausdorff sur le sous-ensemble… (More)

We investigate, by " ` a la Marcinkiewicz " techniques applied to the (asymptotic) density function, how dense systems of equal spheres of R n , n ≥ 1, can be partitioned at infinity in order to allow the computation of their density as a true limit and not a limsup. The density of a packing of equal balls is the norm 1 of the characteristic function of the… (More)

We give the construction of a metric, invariant by the group of rigid motions of R n , on the set of uniformly discrete point sets of R the property that their minimal interpoint distance is greater than a given strictly positive real number. The corresponding metric space is complete and locally compact. As a consequence , we prove in a non-effective way… (More)

In this note, the authors illustrate how compact embeddings between function spaces can be obtained using wavelet methods. They consider weighted Hölder spaces and obtain optimal growth conditions on the wavelet coefficients for functions in these weighted spaces. These conditions lead to continuous embeddings between weighted Hölder spaces and certain… (More)

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