Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reconstruction of polytopes from the modulus of the Fourier transform
  with small wave length   Let $\mathcal{P}$ be an $n$-dimensional convex polytope and $\mathcal{S}$ be
a hypersurface in $\mathbb{R}^n$. This paper investigates potentials to
reconstruct $\mathcal{P}$ or at least to compute significant properties of
$\mathcal{P}$ if the modulus of the Fourier transform of $\mathcal{P}$ on
$\mathcal{S}$ with wave length $\lambda$, i.e., $|\int_{\mathcal{P}}
e^{-i\frac{1}{\lambda}\mathbf{s}\cdot\mathbf{x}} \,\mathbf{dx}|$ for
$\mathbf{s}\in\mathcal{S}$, is given, $\lambda$ is sufficiently small and
$\mathcal{P}$ and $\mathcal{S}$ have some well-defined properties. The main
tool is an asymptotic formula for the Fourier transform of $\mathcal{P}$ with
wave length $\lambda$ when $\lambda \rightarrow 0$. The theory of X-ray
scattering of nanoparticles motivates this study since the modulus of the
Fourier transform of the reflected beam wave vectors are approximately
measurable in experiments.

18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg