Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Delone sets generated by square roots   Delone sets are locally finite point sets, such that (a) any two points are
separated by a given minimum distance, and (b) there is a given radius so that
every ball of that radius contains at least one point. Important examples
include the vertex set of Penrose tilings and other regular model sets, which
serve as a mathematical model for quasicrystals. In this note we show that the
point set given by the values $\sqrt{n} e^{2\pi i \alpha \sqrt{n}}$ with
$n=1,2,3,\ldots$ is a Delone set in the complex plane, for any $\alpha>0$. This
complements Akiyama's recent observation (see arXiv:1904.10815) that $\sqrt{n}
e^{2\pi i \alpha{n}}$ with $n=1,2,3,\ldots$ forms a Delone set, if and only if
$\alpha$ is badly approximated by rationals. A key difference is that our
setting does not require Diophantine conditions on $\alpha$.

11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex