Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Online premeans and their computation complexity   We extend some approach to a family of symmetric means (i.e. symmetric
functions $\mathscr{M} \colon \bigcup_{n=1}^\infty I^n \to I$ with $\min\le
\mathscr{M}\le \max$; $I$ is an interval). Namely, it is known that every
symmetric mean can be written in a form
$\mathscr{M}(x_1,\dots,x_n):=F(f(x_1)+\cdots+f(x_n))$, where $f \colon I \to G$
and $F \colon G \to I$ ($G$ is a commutative semigroup). For $G=\mathbb{R}^k$
or $G=\mathbb{R}^k \times \mathbb{Z}$ ($k \in \mathbb{N}$) and continuous
functions $f$ and $F$ we obtain two series of families (depending on $k$). It
can be treated as a measure of complexity in a family of means (this idea is
inspired by theory of regular languages and algorithmics). As a result we
characterize celebrated families of quasi-arithmetic means ($G=\mathbb{R}\times
\mathbb{Z}$) and Bajraktarevi\'c means ($G=\mathbb{R}^2$ under some additional
assumptions). Moreover, we establish certain estimations of complexity for
several other classical families.

23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg