Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral residues of second-order differential equations: towards a new
  class of summation identities and inversion formulas   The present article deals with differential equations with spectral parameter
from the point of view of formal power series. The treatment does not make use
of the notion of eigenvalue, but introduces a new idea: the spectral residue.
  The article focuses on second-order, self-adjoint problems. In such a setting
every potential function determines a sequence of spectral residues. This
correspondence is invertible, and gives rise to a combinatorial inversion
formula. Other interesting combinatorial consequences are obtained by
considering spectral residues of exactly-solvable potentials of 1-dimensional
quantum mechanics.
  It is also shown that the Darboux transformation of 1-dimensional potentials
corresponds to a simple negation of the corresponding spectral residues. This
fact leads to another combinatorial inversion formula.
  Finally, there is a brief discussion of applications. The topics considered
are enumeration problems and integrable systems.

30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat