Results 271 to 280 of about 74,849 (301)

Covering convex bodies by translates of convex bodies

Mathematika, 1997
Hadwiger conjectured that the smallest number of translates of a convex body \(K\) required to cover \(K\) is \(2^n\). Here a number of known weaker estimates of the number of required translates, or lattice translates, are obtained as consequences of two simple results.
Rogers, C. A., Zong, C.
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Convex bodies with non‐convex cross‐section bodies

Mathematika, 1999
For \(K\) a convex body in \(\mathbb{R}^d\), the inner \((d-1)\)-quermass at direction \(u\in S^{d-1}\) is defined by \[ m_K(u)= \max_{t\in R}\lambda_{d-1} \bigl( K\cap (u^\perp+ tu)\bigr), \] where \(\lambda_{d-1}\) denotes the \((d-1)\)-dimensional Lebesgue measure. The cross-section body \(CK\) of \(K\), introduced by H.
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Intersections of Convex Bodies

Journal of Mathematical Sciences, 2001
For convex bodies \(K_0,K_1,\dots,K_m \subset\mathbb{R}^n\) and for \(\rho=(r_1, \dots,r_n) \in(\mathbb{R}^n)^m\), let \(\Phi(\rho): =K_0\cap \bigcup^m_{i =1} (K_1+r_i)\) and \(D:=\{\rho: \Phi(\rho) \neq\emptyset\}\). Then \(D\) is convex, and the family \(\{\Phi(\rho)\}_{\rho\in D}\) is concave.
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An Inequality for Convex Bodies

1985
Not ...
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Chasing Convex Bodies and Functions

2016
We consider three related online problems: Online Convex Optimization, Convex Body Chasing, and Lazy Convex Body Chasing. In Online Convex Optimization the input is an online sequence of convex functions over some Euclidean space. In response to a function, the online algorithm can move to any destination point in the Euclidean space.
Antoniadis, Antonios, Barcelo, Neal, Nugent, Michael, Pruhs, Kirk, Schewior, Kevin, Scquizzato, Michele   +5 more
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Convex bodies and convexity on grassmann cones (X): Projection functions of parallel convex bodies

Annali di Matematica Pura ed Applicata, 1965
It is shown that if K is a convex polyhedron or a smooth convex body, then for sufficiently large positive ρ, the body parallel to K at distance ρ has convex projection functions. An example is given of a convex body which does not have this property.
Busemann, H., Shephard, Geoffrey C.
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Projected Area of Convex Bodies

Nature, 1948
IN connexion with photometric determination of specific surface of finely divided material, it is essential to know the relation between the projected area of particles, which is actually measured, and the corresponding surface area. The solution of this problem was first given by A.
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Convex Bodies Associated with a Given Convex Body

Journal of the London Mathematical Society, 1958
Rogers, C. A., Shephard, Geoffrey C.
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Some remarks on convex body domination

Journal of Mathematical Analysis and Applications, 2023
Tuomas Hytönen
exaly  

On the Skeletons of Convex Bodies

Bulletin of the London Mathematical Society, 1978
openaire   +2 more sources