Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Linear Stability Implies Nonlinear Stability for Faber-Krahn Type
  Inequalities
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol