Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic behavior for the principal eigenvalue of a reinforcement
  problem   In this paper, we consider the asymptotic behavior for the principal
eigenvalue of an elliptic operator with piecewise constant coefficients. This
problem was first studied by Friedman in 1980. We show how the geometric shape
of the interface affects the asymptotic behavior for the principal eigenvalue.
This is a refinement of the result by Friedman.

22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg