Results 1 to 10 of about 12,291 (164)
On asphericity of convex bodies in linear normed spaces [PDF]
Journal of Inequalities and Applications, 2018 In 1960, Dvoretzky proved that in any infinite dimensional Banach space X and for any ϵ>0 $\epsilon> 0$ there exists a subspace L of X of arbitrary large dimension ϵ-iometric to Euclidean space.
Nashat Faried +2 more
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Analytic center cutting plane methods for variational inequalities over convex bodies [PDF]
Journal of Inequalities and Applications, 2018 An analytic center cutting plane method is an iterative algorithm based on the computation of analytic centers. In this paper, we propose some analytic center cutting plane methods for solving quasimonotone or pseudomonotone variational inequalities ...
Renying Zeng
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Order Types of Convex Bodies [PDF]
Order, 2010 We give new bounds on the Erdos-Szekeres theorems for convex bodies of Bisztriczky and Fejes Toth and of Pach and Toth. We derive them from a combinatorial characterization of convex position of a family of planar convex bodies. This characterization confirms that the concept of Order Type for points can be extended to noncrossing families of convex ...
Luis Montejano +2 more
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Discrete & Computational Geometry, 2022 AbstractIn this paper we study the fiber bodies, that is the extension of the notion of fiber polytopes for more general convex bodies. After giving an overview of the properties of the fiber bodies, we focus on three particular classes of convex bodies. First we describe the strict convexity of the fiber bodies of the so called puffed polytopes.
Léo Mathis, Chiara Meroni
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Ellipses surrounding convex bodies
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 If, for a double normal xx* of a convex body K, an ellipse E ∋ x, x* is included in K, we say that E is surrounded by the boundary of K. If, instead, in the plane of E, K is included in the convex hull of E, then we say that E is surrounding K.
Zamfirescu Tudor
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THE CONVEX INTERSECTION BODY OF A CONVEX BODY [PDF]
Glasgow Mathematical Journal, 2011 AbstractLet L be a convex body in n and z an interior point of L. We associate with L and z a new, convex and centrally symmetric, body CI(L, z). This generalizes the classical intersection bodyI(L, z) (whose radial function at u ∈ Sn−1 is the volume of the hyperplane section of L through z, orthogonal to u). CI(L, z) coincides with I(L, z) if and only
Meyer, Mathieu, Reisner, Shlomo
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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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Estimations of Covering Functionals of Convex Bodies Based on Relaxation Algorithm
Mathematics, 2023 Estimating covering functionals of convex bodies is an important part of Chuanming Zong’s program to attack Hadwiger’s covering conjecture, which is a long-standing open problem from convex and discrete geometry.
Man Yu +4 more
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CONVEX BODIES AND GAUSSIAN PROCESSES
Image Analysis and Stereology, 2011 For several decades, the topics of the title have had a fruitful interaction. This survey will describe some of these connections, including the GB/GC classification of convex bodies, Ito-Nisio singularities from a geometric viewpoint, Gaussian ...
Richard A Vitale
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Discrete & Computational Geometry, 1993 Given a metric space \((S,\rho)\), and a sequence of regions \(F_ i\), \(i=1,\dots,n\), say the plane \(R^ 2\) and a sequence of convex sets, one is supposed to design an algorithm producing a path \(x_ i\), \(i=1,\dots,n\), \(x_ i\in F_ i\), minimizing the cost \(\sum^{n- 1}_{i=1}\rho(x_ i,x_{i+1})\).
Joel Friedman, Nathan Linial
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