Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Sums of norm spheres are norm shells and lower triangle inequalities are
  sharp
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ