Multivariate medians and measure-symmetrization

RA Vitale - Lecture Notes-Monograph Series, 2007 - JSTOR
… A special class of convex bodies are sums of line segments, or zonotopes. The A parallel
body to K is K + AB, where Bd is the … We begin by creating, for every x E Rd, the zonotope

[PDF][PDF] Suppression of the wrapping effect by Taylor model-based verified integrators: Long-term stabilization by shrink wrapping

M Berz, K Makino - Int. J. Diff. Eq. Appl, 2005 - bt.pa.msu.edu
… Shown are enclosures by the zonotope method of various … for the center point reported for
the zonotope method in [2] are … similarity of the m = 15 zonotope enclosure with that of the TM …

Fibre tilings

P McMULLEN - Mathematika, 2003 - cambridge.org
… We also present new results about zonotopes, and reformulate old ones about hyperplane
… as: among the fibre polytopes of a zonotope is a zonotope. To see this, we change notation …

[PDF][PDF] A Symmetric Three-dimensional Model of the Hypercube

L Vörös - Symmetry: Culture and Science, 2006 - geometria.mik.pte.hu
… The model’s construction with the well known sliding-method creates a lattice structure,
whose outer bars equal a zonotope’s edges. This structure keeps the 3-cube’s central symmetry …

Geometric computation for assembly planning with planar toleranced parts

Y Ostrovsky-Berman… - Proceedings of the 2005 …, 2005 - ieeexplore.ieee.org
… The contact zonotope and its contribution to the strong NDBG. Vertices of the zonotope are
shown with their corresponding contacts, in which the parts are slightly translated and rotated …

On the gap between the quadratic integer programming problem and its semidefinite relaxation

U Malik, IM Jaimoukha, GD Halikias… - Mathematical …, 2006 - Springer
Consider the semidefinite relaxation (SDR) of the quadratic integer program (QIP): where Q
is a given symmetric matrix and D is diagonal. We consider the SDR gap We establish the …

Minkowski Addition

I Molchanov - Theory of Random Sets, 2005 - Springer
We systematically write M+ L instead of M⊕ L. This chapter deals with laws of large numbers
and limit theorems for Minkowski sums of random sets. The relevant methods are closely …

[PDF][PDF] Calcul efficace de l'ensemble atteignable des systemes linéaires avec incertitudes

C Le Guernic - Master's thesis, Université Paris, 2005 - arpont.imag.fr
… Minkowski pour les zonotopes se fait en concaténant la liste des générateurs, la taille de la
somme de deux zonotopes est donc égale `a la somme des tailles de ces zonotopes. Ainsi, …

[HTML][HTML] Limit shape of convex lattice polygons with minimal perimeter

MN Prodromou - Discrete mathematics, 2005 - Elsevier
… A zonotope Z ⊂ R 2 is a convex body that is the Minkowski sum … It is known that for a zonotope
Z = ∑ i = 1 k S i , where S i = [ - α i … Since Q ( n k ) is a 0-symmetric zonotope, we have the …

The illumination conjecture and its extensions

K Bezdek - Periodica Mathematica Hungarica, 2006 - Springer
… This class of polytopes is wider than the class of zonotopes moreover, it is easy to see
that any convex body of Ed can be represented as a limit of a covergent sequence of belt …