Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the conditions of topological equivalence of pseudoharmonic functions
  defined on disk   Let $D^2 \subset C$ be a closed two-dimensional disk and $f:D^2 \to R$ be a
continuous function such that a restriction of $f$ to $\partial D^2$ is a
continuous function with a finite number of local extrema and $f$ has a finite
number of critical points in $\Int{D^2}$ such that each of them is saddle
(i.e., in its neighborhood the local representation of $f$ is $f = Re z^n +
const$, where $z=x+iy$, $n \geq 2$). This class of functions coincides with
class of pseudoharmonic functions defined on $D^2$.
  First, we will construct an invariant of such functions which contains all
information about them. Then, in terms of such invariant the necessary and
sufficient conditions for pseudoharmonic functions to be topologically
equivalent will be obtained.

29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org