Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derivations and linear functions along rational functions   The main purpose of this paper is to give characterization theorems on
derivations as well as on linear functions. Among others the following problem
will be investigated: Let $n\in\mathbb{Z}$, $f, g\colon\mathbb{R}\to\mathbb{R}$
be additive functions, $<{array}{cc} a&b c&d
{array}>\in\mathbf{GL}_{2}(\mathbb{Q})$ be arbitrarily fixed, and let us assume
that the mapping \[
  \phi(x)=g<\frac{ax^{n}+b}{cx^{n}+d}>-\frac{x^{n-1}f(x)}{(cx^{n}+d)^{2}} \quad
<x\in\mathbb{R}, cx^{n}+d\neq 0> \] satisfies some regularity on its domain
(e.g. (locally) boundedness, continuity, measurability). Is it true that in
this case the above functions can be represented as a sum of a derivation and a
linear function? Analogous statements ensuring linearity will also be
presented.

0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat