Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Hausdorff dimension faithfulness connected with
  $Q_{infty}$-expansion   In this paper, we show that, the family of all possible union of finite
consecutive cylinders of the same rank of $Q_{\infty}$-expansion is faithful
for the Hausdorff dimension calculation. Applying this result, we give the
necessary and sufficient condition for the family of all cylinders of
$Q_{\infty}$-expansion to be faithful for Hausdorff dimension calculation on
the unit interval, this answers the open problem mentioned in a paper of S.
Albeverio et al..

19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th