Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solution of a uniqueness problem in the discrete tomography of algebraic
  Delone sets   We consider algebraic Delone sets $\varLambda$ in the Euclidean plane and
address the problem of distinguishing convex subsets of $\varLambda$ by X-rays
in prescribed $\varLambda$-directions, i.e., directions parallel to nonzero
interpoint vectors of $\varLambda$. Here, an X-ray in direction $u$ of a finite
set gives the number of points in the set on each line parallel to $u$. It is
shown that for any algebraic Delone set $\varLambda$ there are four prescribed
$\varLambda$-directions such that any two convex subsets of $\varLambda$ can be
distinguished by the corresponding X-rays. We further prove the existence of a
natural number $c_{\varLambda}$ such that any two convex subsets of
$\varLambda$ can be distinguished by their X-rays in any set of
$c_{\varLambda}$ prescribed $\varLambda$-directions. In particular, this
extends a well-known result of Gardner and Gritzmann on the corresponding
problem for planar lattices to nonperiodic cases that are relevant in
quasicrystallography.

32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an