Department of plastic surgery, IPGME&R, Kolkata

Abstract

In this paper, we prove that the closure of a bounded pseudoconvex domain, which is spirallike with respect to a globally asymptotic stable holomorphic vector field, is polynomially convex. We also provide a necessary and sufficient condition, in terms of polynomial convexity, on a univalent function defined on a strongly convex domain for embedding it into a filtering Loewner chain. Next, we provide an application of our first result. We show that for any bounded pseudoconvex strictly spirallike domain Ω in C n and given any connected complex manifold Y , there exists a holomorphic map from the unit disc to the space of all holomorphic maps from Ω to Y . This also yields us the existence of O(Ω, Y )-universal map for any generalized translation on Ω, which, in turn, is connected to the hypercyclicity of certain composition operators on the space of manifold valued holomorphic maps.

Synthesis of 2‐Arylquinazolin‐4(3H)‐ones by N‐Aryl Benzamidines with Aromatic Carbonates

“…2-(4-Methoxyphenyl)quinazolin-4(3H)-one (3g) [8,9]. The product was obtained as colorless powder, synthesized by the reaction of N-phenyl-4-methoxybenzamidine 1g (10 mmol) and diphenyl carbonate 2a (10 mmol) in triglyme (20 mL); 83.7% yield; mp 240-242 C; 1 H NMR: ,4.79;N,11.10.…”