Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Functions consistent with real numbers, and global extrema of functions
  in exponential Takagi class   The functions of the Takagi exponential class are similar in construction to
the continuous, nowhere differentiable Takagi function described in 1901. They
have one real parameter $v\in (-1;1)$ and at points $x\in{\mathbb R}$ are
defined by the series $T_v(x) = \sum_{n=0}^\infty v^n T_0(2^nx)$, where
$T_0(x)$ is the distance between $x$ and the nearest integer point. If $v=1/2$
then $T_v$ coincides with Takagi's function. In this paper, for different
values of the parameter $v$, we study the global extremes of the functions
$T_v$, as well as the sets of extreme points. All functions of $T_v$ have a
period of $1$, so they are investigated only on the segment $[0;1]$. This study
is based on the properties of consistent and anti-consistent polynomials and
series, which the first half of the work is devoted to.

16
The categories of this paper are: stat
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin