Erratum to: Holditch Theorem and Steiner Formula for the Planar Hyperbolic Motions

We give a proof of the Steiner formula based on the theory of random convex bodies. In particular, we make use of laws of large numbers for both random volumes and random convex bodies themselves.

Download Full-text

The generalization of Holditch theorem for closed space curves

ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik ◽

10.1002/zamm.200410073 ◽

2004 ◽

Vol 84 (1) ◽

pp. 60-64 ◽

Cited By ~ 1

Author(s):

M. Düldül ◽

N. Kuruoğlu ◽

A. Tutar

Keyword(s):

Closed Space ◽

Space Curves ◽

Holditch Theorem

Download Full-text

Hyperplans poissoniens et compacts de Steiner

Advances in Applied Probability ◽

10.1017/s0001867800040003 ◽

1974 ◽

Vol 6 (03) ◽

pp. 563-579 ◽

Cited By ~ 4

Author(s):

G. Matheron

Keyword(s):

Stationary Process ◽

Convex Set ◽

Compact Convex ◽

Minkowski Sum ◽

Isotropic Case ◽

Geometrical Properties ◽

Steiner Formula ◽

Compact Convex Set ◽

Finite Sums ◽

Linear Variety

A compact convex set in RN is Steiner if it is a finite Minkowski sum of line segments, or a limit of such finite sums, and then satisfies an extension of the Steiner formula. With each Poisson hyperplane stationary process A is uniquely associated a Steiner set M, and for any linear variety V, the Steiner set associated with is the projection of M on V. The density of the order k network Ak (i.e., the set of the intersections of k hyperplanes belonging to A) is linked with simple geometrical properties of M. In the isotropic case, the expression of the covariance measures associated with Ak is derived and compared with the analogous results obtained for (N — k)-dimensional Poisson flats.

Download Full-text

A Steiner formula in the L Brunn Minkowski theory

Advances in Mathematics ◽

10.1016/j.aim.2019.106772 ◽

2019 ◽

Vol 355 ◽

pp. 106772 ◽

Cited By ~ 1

Author(s):

Kateryna Tatarko ◽

Elisabeth M. Werner

Keyword(s):

Steiner Formula

Download Full-text

A Note on the Steiner k-Diameter of Tensor Product Networks

Parallel Processing Letters ◽

10.1142/s0129626419500087 ◽

2019 ◽

Vol 29 (02) ◽

pp. 1950008

Author(s):

Pranav Arunandhi ◽

Eddie Cheng ◽

Christopher Melekian

Keyword(s):

Tensor Product ◽

Short Note ◽

Minimum Size ◽

Complete Graphs ◽

Maximum Value ◽

Steiner Formula ◽

Connected Subgraphs ◽

Vertex Sets ◽

Distance Formula

Given a graph [Formula: see text] and [Formula: see text], the Steiner distance [Formula: see text] is the minimum size among all connected subgraphs of [Formula: see text] whose vertex sets contain [Formula: see text]. The Steiner [Formula: see text]-diameter [Formula: see text] is the maximum value of [Formula: see text] among all sets of [Formula: see text] vertices. In this short note, we study the Steiner [Formula: see text]-diameters of the tensor product of complete graphs.

Download Full-text