We study the Steiner Tree problem on unit disk graphs. Given a n vertex graph G, subset $$R\subseteq V(G)$$ of t vertices and positive integer k, objective is to decide if there exists tree T in G that spans over all R uses at most k from $$V\setminus R$$ . The are referred as terminals $$V(G)\setminus vertices. First, we show NP-hard. Next, prove graphs can be solved $$n^{O(\sqrt{t+k})}$$ time...

In this paper, we examine the boundary behaviour of generic power series $f$ with coefficients chosen from a fixed bounded set $\Lambda$ in sense Baire category. Notably, prove that for any open subset $U$ unit disk $D$ non-real point on circle, $f(U)$ is dense $\CC$. As it demonstrated, conclusion does not necessarily hold arbitrary sets accumulating to circle. To complement these results, cha...

Surface parameterizations have been widely used in computer graphics and geometry processing. In particular, as simply-connected open surfaces are conformally equivalent to the unit disk, it is desirable to compute the disk conformal parameterizations of the surfaces. In this paper, we propose a novel algorithm for the conformal parameterization of a simply-connected open surface onto the unit ...

in this paper, we consider a new class of analytic functions in the unit disk using polynomials of order alpha. we give some sufficient conditions for functions belonging to this class.