Results 11 to 20 of about 707 (41)
EXPECTED MEAN WIDTH OF THE RANDOMIZED INTEGER CONVEX HULL
Mathematika, Volume 67, Issue 2, Page 422-433, April 2021., 2021 Abstract Let K⊂Rd be a convex body, and assume that L is a randomly rotated and shifted integer lattice. Let KL be the convex hull of the (random) points K∩L. The mean width W(KL) of KL is investigated. The asymptotic order of the mean width difference W(λK)−W((λK)L) is maximized by the order obtained by polytopes and minimized by the order for smooth ...
Binh Hong Ngoc, Matthias Reitzner
wiley +1 more source
EXPECTED f‐VECTOR OF THE POISSON ZERO POLYTOPE AND RANDOM CONVEX HULLS IN THE HALF‐SPHERE
Mathematika, Volume 66, Issue 4, Page 1028-1053, October 2020., 2020 Abstract We prove an explicit combinatorial formula for the expected number of faces of the zero polytope of the homogeneous and isotropic Poisson hyperplane tessellation in Rd. The expected f‐vector is expressed through the coefficients of the polynomial (1+(d−1)2x2)(1+(d−3)2x2)(1+(d−5)2x2)….Also, we compute explicitly the expected f‐vector and the ...
Zakhar Kabluchko
wiley +1 more source
The General Dual Orlicz Geominimal Surface Area
Journal of Function Spaces, Volume 2020, Issue 1, 2020., 2020 In this paper, we study the general dual Orlicz geominimal surface area by the general dual Orlicz mixed volume which was introduced by Gardner et al. (2019). We find the conditions to the existence of the general dual Orlicz‐Petty body and hence prove the continuity of the general geominimal surface area in the Orlicz setting (2010 Mathematics Subject
Ni Li, Shuang Mou, Alberto Fiorenza
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International Journal of Mathematics and Mathematical Sciences, Volume 1, Issue 1, Page 63-67, 1978., 1977 A new proof of a (slightly extended) geometric version of Tucker′s fundamental result is given.
Abraham Berman, Michael Tarsy
wiley +1 more source
Comments on the floating body and the hyperplane conjecture [PDF]
, 2011 We provide a reformulation of the hyperplane conjecture (the slicing problem) in terms of the floating body and give upper and lower bounds on the logarithmic Hausdorff distance between an arbitrary convex body $K\subset \mathbb{R}^{d}$\ and the convex ...
Fresen, Daniel
core
Approximations of convex bodies by polytopes and by projections of spectrahedra [PDF]
, 2012 We prove that for any compact set B in R^d and for any epsilon >0 there is a finite subset X of B of |X|=d^{O(1/epsilon^2)} points such that the maximum absolute value of any linear function ell: R^d --> R on X approximates the maximum absolute value of ...
Barvinok, Alexander
core +1 more source
New duality results for evenly convex optimization problems. [PDF]
Optimization, 2021 Fajardo MD, Grad SM, Vidal J.
europepmc +1 more source
Diversities and the Generalized Circumradius. [PDF]
Discrete Comput Geom, 2023 Bryant D +3 more
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Approximating orthogonal matrices by permutation matrices
, 2005 Motivated in part by a problem of combinatorial optimization and in part by analogies with quantum computations, we consider approximations of orthogonal matrices U by ``non-commutative convex combinations'' A of permutation matrices of the type A=sum ...
Barvinok, Alexander
core +2 more sources
Inequalities and asymptotics for some moment integrals. [PDF]
J Inequal Appl, 2017 Abi-Khuzam F.
europepmc +1 more source