IRIS PubliCatt
PubliCatt è il repository istituzionale ad accesso aperto dell'Università Cattolica del Sacro Cuore, dove gli utenti autorizzati afferenti all'Ateneo provvedono direttamente e autonomamente a depositare e a rendere visibili le proprie pubblicazioni, inserendo i dati descrittivi del documento stesso ("metadati", quali il titolo, autore, abstract, etc.) e, laddove possibile, il testo della pubblicazione stessa (full-text).
PubliCatt utilizza la piattaforma IRIS (Institutional Research Information System) sviluppata da CINECA.
EnglishWe deal with the question of uniqueness, namely to decide when an unknown finite set of points in $\mathbb{Z}^2$ is uniquely determined by its $X$-rays corresponding to a given set $S$ of lattice directions. In \cite{Ha} L. Hajdu proved that for any fixed rectangle $\mathcal{A}$ in $\mathbb{Z}^2$ there exists a valid set $S$ of four lattice directions (at least when $\mathcal{A}$ is not too ``small''), depending only on the size of $\mathcal{A}$, such that any two subsets of $\mathcal{A}$ can be distinguished by means of their $X$-rays taken in the directions in $S$. The proof was given by explicitly constructing a suitable set $S$ in any possible case. We improve this result by showing that in fact, for any fixed rectangle $\mathcal{A}$ in $\mathbb{Z}^2$, whole families of suitable sets of four directions can be found, for which we provide a complete characterization. Moreover this characterization permits to easily solve some relevant related problems.
Peri, C., Brunetti, S., Dulio, P., Discrete tomography determination of bounded lattice sets from four X-rays, <<DISCRETE APPLIED MATHEMATICS>>, 2012; 2012 (N/A): N/A-N/A. [doi:10.1016/j.dam.2012.09.010] [http://hdl.handle.net/10807/36704]
| Autori: | ||
| Titolo: | Discrete tomography determination of bounded lattice sets from four X-rays | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.dam.2012.09.010 | |
| Data di pubblicazione: | 2012 | |
| Abstract: | We deal with the question of uniqueness, namely to decide when an unknown finite set of points in $\mathbb{Z}^2$ is uniquely determined by its $X$-rays corresponding to a given set $S$ of lattice directions. In \cite{Ha} L. Hajdu proved that for any fixed rectangle $\mathcal{A}$ in $\mathbb{Z}^2$ there exists a valid set $S$ of four lattice directions (at least when $\mathcal{A}$ is not too ``small''), depending only on the size of $\mathcal{A}$, such that any two subsets of $\mathcal{A}$ can be distinguished by means of their $X$-rays taken in the directions in $S$. The proof was given by explicitly constructing a suitable set $S$ in any possible case. We improve this result by showing that in fact, for any fixed rectangle $\mathcal{A}$ in $\mathbb{Z}^2$, whole families of suitable sets of four directions can be found, for which we provide a complete characterization. Moreover this characterization permits to easily solve some relevant related problems. | |
| Lingua: | Inglese | |
| Rivista: | ||
| Citazione: | Peri, C., Brunetti, S., Dulio, P., Discrete tomography determination of bounded lattice sets from four X-rays, <<DISCRETE APPLIED MATHEMATICS>>, 2012; 2012 (N/A): N/A-N/A. [doi:10.1016/j.dam.2012.09.010] [http://hdl.handle.net/10807/36704] | |
| Appare nelle tipologie: | Articolo in rivista, Nota a sentenza |
File in questo prodotto:
Copyright © 2021