Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: New Proofs on Properties of an Orthogonal Decomposition of a Hilbert
  Space
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg