Results 11 to 20 of about 3,694,682 (291)
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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On the Minimal Convex Shell of a Convex Body
Canadian Mathematical Bulletin, 1993 AbstractFor any convex body C in ℝd we introduce the notion of the convex shell and we prove that there exists a unique "minimal" convex shell, extending the notion of the minimal spherical shell of C. Then we prove that a "typical" convex body touches the boundary of its minimal convex shell in precisely d + 2 points.
Carla Peri
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On Quasi Convex Functions and Hadamard's Inequality [PDF]
, 2003 In this paper we establish some inequalities of Hadamard’s type involving Godunova-Levin functions, P-functions, quasi-convex functions, Jquasi- convex functions, Wright-convex functions and Wright-quasi-convex ...
Yang, Gou-Sheng +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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A convex body with chaotic random convex hull [PDF]
, 2013 The asymptotic behavior of the size of the convex hull of uniformly random points in a convex body in Rd is known for polytopes and smooth convex bodies. These are the lower and the upper bound for a general convex body.
Devillers, Olivier +2 more
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Optimal Divisions of a Convex Body
, 2023 For a convex body C in Rd andadivision of C into convex subsets C1,...,Cn, we can consider max{F(C1),...,F(Cn)} (respectively, min{F(C1),...,F(Cn)}), where F represents one of these classical geometric magnitudes: the diameter, the minimal width, or the ...
Márquez Pérez, Alberto +2 more
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On Some New Inequalities of Hermite-Hadamard-Féjer Type Involving Convex Functions [PDF]
, 2005 In this paper, we establish some inequalities of Hermite-Hadamard- Fejér type for m-convex functions and s-convex ...
Hwang, Shiow-Ru +2 more
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Covering the Boundary of Special Convex Bodies with Smaller Homothetic Copies
Journal of Harbin University of Science and Technology, 2019 For Hadwiger conjecture that the least number c(K) of translates of the interior of K needed to cover K is at most 2n, according to the fact that c(K) equals the least number of smaller homothetic copies of K with the same homothetic ratio needed to ...
JI Dong-hai, Lv De-jing, MA Ze-min
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COMPARATIVE PRECISION OF THE PIVOTAL ESTIMATORS OF PARTICLE SIZE
Image Analysis and Stereology, 2011 The pivotal estimators of the surface area and the volume of a generic "particle" are based on a point sampled test line on an isotropic pivotal plane through a fixed point called the pivotal point.
Luis M Cruz-Orive
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Frontiers in Surgery, 2022 Study DesignRetrospective analysis.ObjectiveTo evaluate bone quality and investigate asymmetrical development of the thoracic vertebral body in adolescent idiopathic scoliosis (AIS) based on Hounsfield unit (HU) measurements obtained from computed ...
Taiqiu Chen +11 more
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