Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some spectral properties of Rooms and Passages domains and their
  skeletons   In this paper we investigate spectral properties of Lapla- cians on Rooms and
Passages domains. In the first part, we use Dirichlet- Neumann bracketing
techniques to show that for the Neumann Lapla- cian in certain Rooms and
Passages domains the second term of the asymptotic expansion of the counting
function is of order $\sqrt{\lambda}$. For the Dirichlet Laplacian our methods
only give an upper estimate of the form $\sqrt{\lambda}$. In the second part of
the paper, we consider the relation- ship between Neumann Laplacians on Rooms
and Passages domains and Sturm-Liouville operators on the skeleton.

15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas