Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the irrationality measure of certain numbers   The paper presents upper estimates for the irrationality measure and the
non-quadraticity measure for the numbers
$\alpha_k=\sqrt{2k+1}\ln\frac{\sqrt{2k+1}-1}{\sqrt{2k+1}+1}, \ k\in\mathbb N.$

12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph