Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The modulus of the Fourier transform on a sphere determines
  3-dimensional convex polytopes   Let $\mathcal{P}$ and $\mathcal{P}'$ be $3$-dimensional convex polytopes in
$\mathbb{R}^3$ and $S \subseteq \mathbb{R}^3$ be a non-empty intersection of an
open set with a sphere. As a consequence of a somewhat more general result it
is proved that $\mathcal{P}$ and $\mathcal{P}'$ coincide up to translation
and/or reflection in a point if $|\int_{\mathcal{P}}
e^{-i\mathbf{s}\cdot\mathbf{x}} \,\mathbf{dx}| = |\int_{\mathcal{P}'}
e^{-i\mathbf{s}\cdot\mathbf{x}} \,\mathbf{dx}|$ for all $\mathbf{s} \in S$.
This can be applied to the field of crystallography regarding the question
whether a nanoparticle modelled as a convex polytope is uniquely determined by
the intensities of its X-ray diffraction pattern on the Ewald sphere.

10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga