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Nested Convex Bodies are Chaseable [PDF]
Algorithmica, 2018 In the Convex Body Chasing problem, we are given an initial point $v_0$ in $R^d$ and an online sequence of $n$ convex bodies $F_1, ..., F_n$. When we receive $F_i$, we are required to move inside $F_i$. Our goal is to minimize the total distance travelled. This fundamental online problem was first studied by Friedman and Linial (DCG 1993).
Nikhil Bansal 0001 +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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Dual Orlicz geominimal surface area
Journal of Inequalities and Applications, 2016 The L p $L_{p}$ -geominimal surface area was introduced by Lutwak in 1996, which extended the important concept of the geominimal surface area. Recently, Wang and Qi defined the p-dual geominimal surface area, which belongs to the dual Brunn-Minkowski ...
Tongyi Ma, Weidong Wang
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MATHEMATICA SCANDINAVICA, 1990 There are several ways to generalize the classical concept of affine surface area of a sufficiently smooth convex body \(K\) in \(\mathbb{R}^ n\) due to Blaschke to arbitrary convex bodies [see \textit{K. Leichtweiss}, Manuscr. Math. 56, 429-464 (1986; Zbl 0588.52011), \textit{E. Lutwak}, Adv. Math. 85, No. 1, 39-68 (1991; Zbl 0727.53016) and \textit{C.
Werner, Elisabeth, Schütt, Carsten
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Some new Brunn-Minkowski-type inequalities in convex bodies
International Journal of Mathematics and Mathematical Sciences, 2005 We establish some analogues of the Brunn-Minkowski inequalities on convex bodies and the Minkowski inequality and their inverse versions. As an application, we generalize and improve some interrelated results.
Zhao Chang-Jian +2 more
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On Some Results in the Geometry of Convex Bodies and their Applications
Моделирование и анализ информационных систем, 2015 We give a survey of some results in the geometry of convex bodies and their applications.
M. V. Nevskii
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General Blaschke Bodies and the Asymmetric Negative Solutions of Shephard Problem
Mathematics, 2019 In this article, based on the Blaschke combination of convex bodies, we define the general Blaschke bodies and obtain the extremal values of their volume and affine surface area. Further, we study the asymmetric negative solutions of the Shephard problem
Tian Li, Weidong Wang, Yaping Mao
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On the Irreducibility of Convex Bodies [PDF]
Canadian Journal of Mathematics, 1959 We select a Cartesian co-ordinate system in ndimensional Euclidean space Rn with origin 0 and employ the usual pointvector notation.By a lattice Λ in Rn we mean the set of all rational integral combinations of n linearly independent points X1, X2, … , Xn of Rn. The points X1 X2, … , Xn are said to form a basis of Λ.
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Forum of Mathematics, SigmaA spectral convex set is a collection of symmetric matrices whose range of eigenvalues forms a symmetric convex set. Spectral convex sets generalize the Schur-Horn orbitopes studied by Sanyal–Sottile–Sturmfels (2011). We study this class of convex bodies,
Raman Sanyal, James Saunderson
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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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