Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivalence classes of codimension one cut-and-project nets   We prove that in any totally irrational cut-and-project setup with
codimension (internal space dimension) one, it is possible to choose sections
(windows) in non-trivial ways so that the resulting sets are bounded
displacement to lattices. Our proof demonstrates that for any irrational
$\alpha$, regardless of Diophantine type, there is a collection of intervals in
$\mathbb{R}/\mathbb{Z}$ which is closed under translation, contains intervals
of arbitrarily small length, and along which the discrepancy of the sequence
$\{n\alpha\}$ is bounded above uniformly by a constant.

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The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
3
The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin