Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous Limit of Multiple Gravitational Lens Effect and Average
  Magnification Factor   We show that the gravitational magnification factor averaged over all
configurations of lenses in a locally inhomogeneous universe satisfy a second
order differential equation with redshift $z$ by taking the continuous limit of
multi-plane gravitational lens equation (the number $N$ of lenses $\to\infty$)
and that the gravitationally magnified Dyer-Roeder distance in a clumpy
universe becomes to that of the Friedmann-Lema\^{\i}tre universe for arbitrary
values of the density parameter $\Omega_{0}$ and of a mass fraction
$\bar{\alpha}$ (smoothness parameter).

37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol