In this paper we present solutions for problems of Buffon type for a cubic lattice R(L, a) consisting of cubic obstacles with edges 2a, having as symmetry center the points Mh,k,l = (hL, kL, lL), h, k, l ∈ Z and the faces parallel to the coordinate planes and the lattice R0(L, a) obtained by R(L, a) adding the plane portions delimited by the following segments: {(x, kL, lL) : x ∈ [hL+a, (h+1)L−a]}, {(hL, y, lL) : y ∈ [hL+a, (h+1)L−a]}, {(hL, kL, z) : z ∈ [hL + a, (h + 1)L − a]}, h, k, l ∈ Z.

Geometric probabilities for cubic lattices with cubic obstacles

BONANZINGA, Vittoria;
2009-01-01

Abstract

In this paper we present solutions for problems of Buffon type for a cubic lattice R(L, a) consisting of cubic obstacles with edges 2a, having as symmetry center the points Mh,k,l = (hL, kL, lL), h, k, l ∈ Z and the faces parallel to the coordinate planes and the lattice R0(L, a) obtained by R(L, a) adding the plane portions delimited by the following segments: {(x, kL, lL) : x ∈ [hL+a, (h+1)L−a]}, {(hL, y, lL) : y ∈ [hL+a, (h+1)L−a]}, {(hL, kL, z) : z ∈ [hL + a, (h + 1)L − a]}, h, k, l ∈ Z.
2009
stochastic geometry; integral geometry; geometric probability
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/6438
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