Results 41 to 50 of about 44,177 (192)
Random Symmetrizations of Convex Bodies [PDF]
Advances in Applied Probability, 2014 In this paper we investigate the asymptotic behavior of sequences of successive Steiner and Minkowski symmetrizations. We state an equivalence result between the convergences of those sequences for Minkowski and Steiner symmetrizations. Moreover, in the case of independent (and not necessarily identically distributed) directions, we prove the almost ...
Coupier, D., Davydov, Yu.
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AIMS Mathematics, 2023 In recent years, numerous scholars have investigated the relationship between symmetry and generalized convexity. Due to this close relationship, generalized convexity and symmetry have become new areas of study in the field of inequalities.
Muhammad Bilal Khan +4 more
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Competitively Chasing Convex Bodies [PDF]
SIAM Journal on Computing, 2019 Let $\mathcal{F}$ be a family of sets in some metric space. In the $\mathcal{F}$-chasing problem, an online algorithm observes a request sequence of sets in $\mathcal{F}$ and responds (online) by giving a sequence of points in these sets. The movement cost is the distance between consecutive such points.
Sébastien Bubeck +3 more
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Ectopic localization of neural crest cells: etiological factor of scoliosis
Хирургия позвоночника, 2015 Objective. To identify cell phenotypes in vertebral body growth plates from patients with idiopathic scoliosis. Material and Methods. Cells were isolated from vertebral body growth plates both on convex and concave sides of the de- formity in 50 ...
Alla M. Zaidman +6 more
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Polytopes and $C^1$-convex bodies [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 The face numbers of simplicial polytopes that approximate $C^1$-convex bodies in the Hausdorff metric is studied. Several structural results about the skeleta of such polytopes are studied and used to derive a lower bound theorem for this class of ...
Karim Adiprasito, José Alejandro Samper
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Existence and Approximation of Densities of Chord Length- and Cross Section Area Distributions
Image Analysis and Stereology, 2023 In various stereological problems a n-dimensional convex body is intersected with an (n−1)-dimensional Isotropic Uniformly Random (IUR) hyperplane. In this paper the cumulative distribution function associated with the (n−1)-dimensional volume of such a ...
Thomas van der Jagt +2 more
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Convex Bodies with Few Faces [PDF]
Proceedings of the American Mathematical Society, 1990 It is proved that if $u_1,\ldots, u_n$ are vectors in ${\Bbb R}^k, k\le n, 1 \le p < \infty$ and $$r = ({1\over k} \sum ^n_1 |u_i|^p)^{1\over p}$$ then the volume of the symmetric convex body whose boundary functionals are $\pm u_1,\ldots, \pm u_n$, is bounded from below as $$|\{ x\in {\Bbb R}^k\colon \ |\langle x,u_i\rangle | \le 1 \ \hbox{for ...
Keith Ball, Alain Pajor
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Polar Duals of Convex Bodies [PDF]
Proceedings of the American Mathematical Society, 1990 A generalizationand the dual version of the following result due to Firey is given: the mixed area of a plane convex body and its polar dual is at least π. We give a sharp upper bound for the product of the dual cross-sectional measure of any index and that of its polar dual.
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ARRANGEMENTS OF HOMOTHETS OF A CONVEX BODY [PDF]
Mathematika, 2017 13 pages, 2 figures.
Naszódi, Márton +2 more
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Floating and Illumination Bodies for Polytopes: Duality results
Discrete Analysis, 2019 Floating and illumination bodies for polytopes: duality results, Discrete Analysis 2019:11, 22 pp. A well-known concept in convex geometry is that of the _floating body_ of a convex body, which is defined as follows.
Elisabeth Werner, Olaf Mordhorst
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