Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: On the Bernoulli free boundary problems for the half Laplacian and for
  the spectral half Laplacian
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph