Yevgen Polulyakh

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math.GN2009

On the realization of graph as invariant of pseudoharmonic functions

Yevgen Polulyakh, Iryna Yurchuk

Necessary and sufficient conditions for a finite connected graph with a strict partial order on vertices to be a combinatorial invariant of pseudoharmonic function are obtained.

math.GN2009

On the conditions of topological equivalence of pseudoharmonic functions defined on disk

Yevgen Polulyakh, Iryna Yurchuk

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 fin…

math.GN2009

On continuous functions on two-dimensional disk which are regular in its interior points

Yevgen Polulyakh

We introduce a class of regular continuous functions on the closed 2-disk and show that each function from this class is topologically conjugate to a linear function defined on a s…