Convex rearrangements of random elements

Y Davydov, R Zitikis - Asymptotic methods in stochastics, 2004 - books.google.com
… of zonotopes Zn such that p (Zn, Z) 0 when n→ 00. For more information on zonotopes, …
the convexification Cn is one half of the boundary of a zonotope in R2 (cf. Koshevoy [40],[41]…

[PDF][PDF] Convexity and geometric probabilities

R Schneider - mathematik.uni-freiburg.de
… Such a body Z is called a zonotope, and a convex body which can be approximated by
zonotopes is called a zonoid. Since the function ψ is continuous, it follows that ψ(K + Z) = ψ(K) for …

[PDF][PDF] Integer convex maximization

J De Loera, R Hemmecke, S Onn, UG Rothblum… - ArXiv Mathematics e …, 2006 - Citeseer
… The zonotope generated by a finite set E ⊂ Rn is the polytope Z := zone(E) := conv{∑e∈E …
Let Z := zone(D) ⊂ Rd be the zonotope generated by D. Since d is fixed, by Proposition 2.2 …

[PDF][PDF] Voronoi L-types and hypermetrics.

M Deza, M Dutour - ISVD, 2007 - poivs.tsput.ru
… Erdahl: a Voronoi polytope V is a zonotope if and only if all edge forms of the closure of its
L-type domain are matrices of rank 1, ie, of the form a T a; then zonotope V is the Minkowski …

Cayley lattices of finite Coxeter groups are bounded

N Caspard, CLC de Poly-Barbut, M Morvan - Advances in Applied …, 2004 - Elsevier
zonotope, associated to the reflection, and the obtained zonotope is still a lattice. It is interesting
to add that the main result of this paper finds expression in terms of zonotope as follows: …

Taylor forms—use and limits

A Neumaier - Reliable computing, 2003 - Springer
This review is a response to recent discussions on the reliable computing mailing list, and to
continuing uncertainties about the properties and merits of Taylor forms, multivariate higher …

[PDF][PDF] 3 次元凸多面体の展開図について: Mathematica を利用した計算実験 (情報科学としての函数解析とその周辺)

並木誠, 島崇弘 - 数理解析研究所講究録, 2003 - repository.kulib.kyoto-u.ac.jp
Zonotope は他の多面体と比較すると展開図が重なり易いと言えるのかも知れない. どの方法で
展開してもも重ならない割合が高々50%である. 図 16 は, 自分自身が重なる Zonotope の展開図 で…

[PDF][PDF] Parallelotopes and Voronoi's conjecture

WM Maciejewski - 2007 - prism.ucalgary.ca
… of the zonotope in our definition. One of the most important facts about zonotopes is that they
are all projections of higher dimensional (affine) cubes. That is, if Z is the zonotope defined …

The order dimension of the poset of regions in a hyperplane arrangement

N Reading - Journal of Combinatorial Theory, Series A, 2003 - Elsevier
zonotopes, and the Hasse diagram of PğA, BŞ is the same as the 1-skeleton of the corresponding
zonotope… to the corresponding vertex of an equivalent zonotope. We show that this can …

[PDF][PDF] On Busemann surface area of the unit ball in Minkowski spaces

Z Mustafaev - Journal of Inequalities in Pure and Applied …, 2006 - emis.dsd.sztaki.hu
… Recall that zonoids are the limits of zonotopes with respect to the Hausdorff metric, and
zonotopes are finite Minkowski sums of centered line segments. For a convex body K in Rd and u …