A theorem of S. Warschawski on the derivative of a holomorphic function mapping conformally the circle onto a simply-connected domain bounded by the piecewise-Lyapunov Jordan curve is extended to domains with a non-Jordan boundary having interior cusps of a certain type. 2000 Mathematics Subject Classification: 3OC35.

We study Koebe orderings of planar graphs: vertex obtained by modelling the graph as intersection pairwise internally-disjoint discs in plane, and ordering vertices non-increasing radii associated discs. prove that for every $d\in \mathbb{N}$, any such has $d$-admissibility bounded $O(d/\ln d)$ weak $d$-coloring number $O(d^4 \ln d)$. This particular shows graphs is d)$, which asymptotically ma...

Since density is considered as one of the most important numerical indices to explain quantitative values of a plant community by affecting on many aspects and activity of ecosystem, on the other hand, awareness about plants distribution pattern in environment is an essential preparation for measurement and study of vegetative cover, therefore, in this research determination of density and dist...

In this paper we start a new approach to the uniformization problem of Riemann surfaces and algebraic curves by means of computational procedures. The following question is studied: Given a compact Riemann surface S described as the quotient of the Poincaré upper half-plane divided by the action of a Fuchsian group, find explicitly the polynomial describing S as an algebraic curve (in some norm...

In this paper, we concerned with positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions by using a result from the theory of fixed...