In this paper we present a problem of Buffon type for a hypercubic lattice \$\mathfrak\{R'\}^\{(n)\}(L,a)\$ obtained by a hypercubic lattice \$\mathfrak\{R\}^\{(n)\}(L,a)\$ consisting of hypercubic obstacles with edges \$2a\$, having as symmetry center the points \$M_\{h_1,h_2,\ldots,h_n\}=(h_1L,h_2L,\ldots,h_nL)\$, \$h_1,h_2,\ldots, h_n\in \mathbb\{Z\}\$ and the faces parallel to the coordinate planes adding the plane portions delimited by the following segments: \$\\{(x_1,h_2L,\ldots, h_nL):x_1\in [h_1L+a,(h_1+1)L-a]\\}\$, \$\\{(x_1h_1,x_2,h_3L,\ldots, h_nL):x_2\in [h_1L+a (h_1+1)L-a]\\}\$,\ldots,\$\\{(h_1x_1,\ldots,h_\{n-1\}x_\{n 1\},x_n):x_n\in [h_1L+a,(h_1+1)L-a]\\}\$, \$h_1,h_2,\ldots, h_n\in \mathbb\{Z\}\$.

Geometric probabilities for hypercubic lattices with hypercubic obstacles in the Euclidean space E_n / Bonanzinga, Vittoria; Sorrenti, L. - In: COMMUNICATIONS IN APPLIED AND INDUSTRIAL MATHEMATICS. - ISSN 2038-0909. - 378:(2011), pp. 1-7. [10.1685]

Geometric probabilities for hypercubic lattices with hypercubic obstacles in the Euclidean space E_n

BONANZINGA, Vittoria;
2011-01-01

Abstract

In this paper we present a problem of Buffon type for a hypercubic lattice \$\mathfrak\{R'\}^\{(n)\}(L,a)\$ obtained by a hypercubic lattice \$\mathfrak\{R\}^\{(n)\}(L,a)\$ consisting of hypercubic obstacles with edges \$2a\$, having as symmetry center the points \$M_\{h_1,h_2,\ldots,h_n\}=(h_1L,h_2L,\ldots,h_nL)\$, \$h_1,h_2,\ldots, h_n\in \mathbb\{Z\}\$ and the faces parallel to the coordinate planes adding the plane portions delimited by the following segments: \$\\{(x_1,h_2L,\ldots, h_nL):x_1\in [h_1L+a,(h_1+1)L-a]\\}\$, \$\\{(x_1h_1,x_2,h_3L,\ldots, h_nL):x_2\in [h_1L+a (h_1+1)L-a]\\}\$,\ldots,\$\\{(h_1x_1,\ldots,h_\{n-1\}x_\{n 1\},x_n):x_n\in [h_1L+a,(h_1+1)L-a]\\}\$, \$h_1,h_2,\ldots, h_n\in \mathbb\{Z\}\$.
2011
geometric probability
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/8069
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