Generalization of Steiner formula for the homothetic motions on the planar kinematics

2003 ◽  
Vol 24 (8) ◽  
pp. 945-949 ◽  
Author(s):  
N. Kuruoğlu ◽  
M. Düldül ◽  
A. Tutar
Keyword(s):  
Steiner Formula

On the volume of parallel bodies: a probabilistic derivation of the Steiner formula

1995 ◽  
Vol 27 (1) ◽  
pp. 97-101 ◽  
Author(s):  
Richard A. Vitale
Keyword(s):  
Convex Bodies ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Steiner Formula ◽  
Random Convex

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.

Hyperplans poissoniens et compacts de Steiner

1974 ◽  
Vol 6 (03) ◽  
pp. 563-579 ◽  
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.

scholarly journals A Steiner formula in the L Brunn Minkowski theory

2019 ◽  
Vol 355 ◽  
pp. 106772 ◽  
Author(s):  
Kateryna Tatarko ◽  
Elisabeth M. Werner
Keyword(s):  
Steiner Formula

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

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.

On the volume of parallel bodies: a probabilistic derivation of the Steiner formula

1995 ◽  
Vol 27 (01) ◽  
pp. 97-101 ◽  
Author(s):  
Richard A. Vitale
Keyword(s):  
Convex Bodies ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Steiner Formula ◽  
Random Convex

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.

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