Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structural properties of fractals with positive Lebesgue measures   Small-angle scattering (SAS) data which show a succession of power-law decays
with decreasing values of scattering exponents, can be described in terms of
fractal structures with positive Lebesgue measure (fat fractals). In this work
we present a theoretical model for fat fractals and show how one can extract
structural information about the underlying fractal using SAS method, for the
well known fractals existing in the literature: Vicsek and Menger sponge. We
calculate analytically the fractal structure factor and study its properties in
momentum space. The models allow us to obtain the fractal dimension at each
structural level inside the fractal, the number of particles inside the fractal
and about the most common distances between the center of mass of the
particles.

18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph