scholarly journals A Bound on the Ratio between the Packing and Covering Densities of a Convex Body

2000 ◽  
Vol 23 (3) ◽  
pp. 325-331 ◽  
Author(s):  
E. H. Smith
Keyword(s):  
Convex Body ◽  
Packing And Covering

Equation of state for hard convex body fluid mixtures

1998 ◽  
Vol 94 (5) ◽  
pp. 809-814 ◽  
Author(s):  
C. BARRIO ◽  
J.R. SOLANA
Keyword(s):  
Equation Of State ◽  
Convex Body ◽  
Body Fluid ◽  
Fluid Mixtures

Generic rotation sets

2020 ◽  
pp. 1-13
Author(s):  
SEBASTIÁN PAVEZ-MOLINA
Keyword(s):  
Dynamical System ◽  
Convex Body ◽  
Probability Measures ◽  
Topological Dynamical System ◽  
Continuous Vector ◽  
Rotation Set ◽  
Vector Valued Function ◽  
Vector Valued ◽  
Uniquely Ergodic ◽  
Dense Set

Abstract Let $(X,T)$ be a topological dynamical system. Given a continuous vector-valued function $F \in C(X, \mathbb {R}^{d})$ called a potential, we define its rotation set $R(F)$ as the set of integrals of F with respect to all T-invariant probability measures, which is a convex body of $\mathbb {R}^{d}$ . In this paper we study the geometry of rotation sets. We prove that if T is a non-uniquely ergodic topological dynamical system with a dense set of periodic measures, then the map $R(\cdot )$ is open with respect to the uniform topologies. As a consequence, we obtain that the rotation set of a generic potential is strictly convex and has $C^{1}$ boundary. Furthermore, we prove that the map $R(\cdot )$ is surjective, extending a result of Kucherenko and Wolf.

scholarly journals Packing and Covering Balls in Graphs Excluding a Minor

COMBINATORICA ◽  
2021 ◽  
Author(s):  
Nicolas Bousquet ◽  
Wouter Cames Van Batenburg ◽  
Louis Esperet ◽  
Gwenaël Joret ◽  
William Lochet ◽  
...  
Keyword(s):  
Packing And Covering ◽  
A Minor

scholarly journals Bounds on the Lattice Point Enumerator via Slices and Projections

2021 ◽  
Author(s):  
Ansgar Freyer ◽  
Martin Henk
Keyword(s):  
Convex Body ◽  
Lattice Point ◽  
Geometric Mean ◽  
Discrete Analogue ◽  
Lattice Points ◽  
General Context ◽  
General Bound

AbstractGardner et al. posed the problem to find a discrete analogue of Meyer’s inequality bounding from below the volume of a convex body by the geometric mean of the volumes of its slices with the coordinate hyperplanes. Motivated by this problem, for which we provide a first general bound, we study in a more general context the question of bounding the number of lattice points of a convex body in terms of slices, as well as projections.

An extremal property of the hypersphere

1951 ◽  
Vol 47 (1) ◽  
pp. 245-247 ◽  
Author(s):  
A. M. Macbeath
Keyword(s):  
Convex Body ◽  
Extremal Property ◽  
Plane Case ◽  
Simple Application ◽  
Plane Convex ◽  
Plane Convex Body

It was shown by Sas (1) that, if K is a plane convex body, then it is possible to inscribe in K a convex n-gon occupying no less a fraction of its area than the regular n-gon occupies in its circumscribing circle. It is the object of this note to establish the n-dimensional analogue of Sas's result, giving incidentally an independent proof of the plane case. The proof is a simple application of the Steiner method of symmetrization.

Measuring the Surface Area of a Convex Body

1944 ◽  
Vol 45 (4) ◽  
pp. 793 ◽  
Author(s):  
P. A. P. Moran
Keyword(s):  
Convex Body ◽  
Surface Area

Covering a convex body by smaller homothetic copies

1993 ◽  
Vol 45 (1) ◽  
pp. 101-113 ◽  
Author(s):  
Valeriu Soltan ◽  
Éva Vásárhelyi
Keyword(s):  
Convex Body ◽  
Homothetic Copies
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