Results 11 to 20 of about 15,809 (305)

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, Martin Böhm 0001, Marek Eliás 0001, Grigorios Koumoutsos, Seeun William Umboh   +4 more
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The curvature entropy inequalities of convex bodies

Open Mathematics
There are many entropy inequalities in geometry, some of them can be seen as the Minkowski inequalities in the form of entropy, which play important roles in convex geometry.
Zhang Deyan
doaj   +2 more sources

A discrete methodology for controlling the sign of curvature and torsion for NURBS [PDF]

, 2009
This paper develops a discrete methodology for approximating the so-called convex domain of a NURBS curve, namely the domain in the ambient space, where a user-specified control point is free to move so that the curvature and torsion retains its sign ...
Karousos, EI, Ginnis, A.I., Kaklis, Panagiotis, Ginnis, AI, Karousos, E.I., Kaklis, PD   +5 more
core   +1 more source

Equilibria of Plane Convex Bodies [PDF]

Journal of Nonlinear Science, 2021
AbstractWe obtain a formula for the number of horizontal equilibria of a planar convex body K with respect to a center of mass O in terms of the winding number of the evolute of $$\partial K$$ ∂ K with respect to O.
Jonas Allemann, Norbert Hungerbühler, Micha Wasem   +2 more
openaire   +4 more sources

A general slicing inequality for measures of convex bodies

Journal of Inequalities and Applications, 2019
We consider the following inequality: μ(L)n−kn≤CkmaxH∈Grn−kμ(L∩H), $$\begin{aligned} \mu (L)^{\frac{n-k}{n}} \leq C^{k}\max_{H\in \mathit{Gr}_{n-k}}\mu (L \cap H), \end{aligned}$$ which is a variant of the notable slicing inequality in convex geometry ...
Yufeng Yu
doaj   +1 more source

Local Stereology of Tensors of Convex Bodies [PDF]

, 2014
In this paper, we present local stereological estimators of Minkowski tensors defined on convex bodies in ℝ d . Special cases cover a number of well-known local stereological estimators of volume and surface area in ℝ3, but the general set-up also ...
Jensen, Eva B. Vedel, Ziegel, Johanna F.
core   +1 more source

On the quermassintegrals of convex bodies [PDF]

Journal of Inequalities and Applications, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhao, C, Cheung, WS
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The Lp chord Minkowski problem

Advanced Nonlinear Studies, 2023
Chord measures are newly discovered translation-invariant geometric measures of convex bodies in Rn{{\mathbb{R}}}^{n}, in addition to Aleksandrov-Fenchel-Jessen’s area measures. They are constructed from chord integrals of convex bodies and random lines.
Xi Dongmeng, Yang Deane, Zhang Gaoyong, Zhao Yiming   +3 more
doaj   +1 more source

Contacts in totally separable packings in the plane and in high dimensions

Journal of Computational Geometry, 2022
We study the contact structure of totally separable packings of translates of a convex body K in Rd, that is, packings where any two touching bodies have a separating hyperplane that does not intersect the interior of any translate in the packing.
Márton Naszódi, Konrad Swanepoel
doaj   +1 more source

Experimental analysis on friction increment of surface textured flexible couples

Journal of Advanced Mechanical Design, Systems, and Manufacturing, 2021
The apparent friction force of spherical convex textured rigid bodies sliding on soft materials was tested and analyzed in order to develop the technology of friction increment for frictional transmission.
Xuli ZHU, Zhongling LIU, Daoxin SUN, Zixin ZHANG, Guirong TENG   +4 more
doaj   +1 more source