doi: 10.1685/journal.caim.378

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

Loredana Sorrenti, Vittoria Bonanzinga


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,$\{(h_1x_1,\ldots,h_{n-1}x_{n 1},x_n):x_n\in [h_1L+a,(h_1+1)L-a]\}$, $h_1,h_2,\ldots, h_n\in \mathbb{Z}$.

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Communications in Applied and Industrial Mathematics
ISSN: 2038-0909