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- Jean-Louis Verger-Gaugry
- Discrete & Computational Geometry
- 2005

We give an explicit upper bound of the minimal number of balls of radius 1/2 which form a covering of a ball of radius T > 1/2 in R, n > 2.

We give an explicit upper bound of the minimal number Î½T,n of balls of radius 1/2 which form a covering of a ball of radius T > 1/2 in R , n > 2. The asymptotic estimates of Î½T,n we deduce when n isâ€¦ (More)

- Gilbert Muraz, Jean-Louis Verger-Gaugry
- Experimental Mathematics
- 2005

We study lower bounds of the packing density of a system of nonoverlapping equal spheres in Rn, n â‰¥ 2, as a function of the maximal circumradius of its Voronoi cells. Our viewpoint is that of Deloneâ€¦ (More)

We prove that for all algebraic number Î² > 1 the strings of zeros in the RÃ©nyi Î²expansion dÎ²(1) of 1 exhibit a lacunarity bounded above by log(s(PÎ²))/ log(Î²), where s(PÎ²) is the size of the minimalâ€¦ (More)

- Avi Elkharrat, Christiane Frougny, Jean-Pierre Gazeau, Jean-Louis Verger-Gaugry
- Theor. Comput. Sci.
- 2004

We present a construction of symmetry plane-groups for quasiperiodic point-sets in the plane, named beta-lattices. The algebraic framework is issued from counting systems called beta-integers,â€¦ (More)

Concentration and equi-distribution, near the unit circle, in Solomyakâ€™s set, of the union of the Galois conjugates and the beta-conjugates of a Parry number Î² are characterized by means of theâ€¦ (More)

â€” The Fourier transform of a weighted Dirac comb of beta-integers is characterized within the framework of the theory of Distributions, in particular its pure point part which corresponds to theâ€¦ (More)

Let Î² > 1 be an algebraic number. A general definition of a beta-conjugate of Î² is proposed with respect to the analytical function fÎ²(z) = âˆ’1 + âˆ‘ iâ‰¥1 tiz i associated with the RÃ©nyi Î²-expansionâ€¦ (More)

The beta-conjugates of a base of numeration Î² > 1, Î² being a Parry number, were introduced by Boyd, in the context of the RÃ©nyi-Parry dynamics of numeration system and the beta-transformation. Theseâ€¦ (More)

- T. Janssen, Joseph L. Birman, +6 authors Vojtech KopskÃ½
- Acta crystallographica. Section A, Foundations ofâ€¦
- 2002

The Second Report of the Subcommittee on the Nomenclature of n-Dimensional Crystallography recommends specific symbols for R-irreducible groups in 4 and higher dimensions (nD), for centrings, forâ€¦ (More)