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Search: MSC category 52C07 ( Lattices and convex bodies in $n$ dimensions [See also 11H06, 11H31, 11P21] )

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1. CMB 2009 (vol 52 pp. 361)

Tóth, Gábor Fejes
A Note on Covering by Convex Bodies
A classical theorem of Rogers states that for any convex body $K$ in $n$-dimensional Euclidean space there exists a covering of the space by translates of $K$ with density not exceeding $n\log{n}+n\log\log{n}+5n$. Rogers' theorem does not say anything about the structure of such a covering. We show that for sufficiently large values of $n$ the same bound can be attained by a covering which is the union of $O(\log{n})$ translates of a lattice arrangement of $K$.

Categories:52C07, 52C17

2. CMB 2009 (vol 52 pp. 380)

Henk, Martin; Cifre, Mar\'\i a A. Hernández
Successive Minima and Radii
In this note we present inequalities relating the successive minima of an $o$-symmetric convex body and the successive inner and outer radii of the body. These inequalities join known inequalities involving only either the successive minima or the successive radii.

Keywords:successive minima, inner and outer radii
Categories:52A20, 52C07, 52A40, 52A39

3. CMB 2002 (vol 45 pp. 483)

Baake, Michael
Diffraction of Weighted Lattice Subsets
A Dirac comb of point measures in Euclidean space with bounded complex weights that is supported on a lattice $\varGamma$ inherits certain general properties from the lattice structure. In particular, its autocorrelation admits a factorization into a continuous function and the uniform lattice Dirac comb, and its diffraction measure is periodic, with the dual lattice $\varGamma^*$ as lattice of periods. This statement remains true in the setting of a locally compact Abelian group whose topology has a countable base.

Keywords:diffraction, Dirac combs, lattice subsets, homometric sets
Categories:52C07, 43A25, 52C23, 43A05

4. CMB 2002 (vol 45 pp. 537)


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