We prove that a harmonic quasiconformal mapping defined on finitely connected domain in the plane, all of whose boundary components are either points or quasicircles, admits extension to whole plane if its Schwarzian derivative is small. also make observation univalence criterion for mappings holds uniform domains.

We study the relation between the centro-affine geometry of starshaped planar curves and the projective geometry of parametrized maps into RP. We show that projectivization induces a map between differential invariants and a bi-Poisson map between Hamiltonian structures. We also show that a Hamiltonian evolution equation for closed star-shaped planar curves, discovered by Pinkall, has the Schwa...

In this note, we present a method of computing monodromies of projective structures on a once-punctured torus. This leads to an algorithm numerically visualizing the shape of the Bers embedding of a one-dimensional Teichmüller space. As a by-product, the value of the accessory parameter of a four-times punctured sphere will be calculated in a numerical way as well as the generators of a Fuchsia...

Theorems due to Nehari and Ahlfors give sufficient conditions for the univalence of an analytic function in relation to the growth of its Schwarzian derivative. Nehari's theorem is for the unit disc and was generalized by Ahifors to any simply-connected domain bounded by a quasiconformal circle. In both cases the growth is measured in terms of the hyperbolic metric of the domain. In this paper ...

A synthetic route to magnesium guanidinate compounds that avoids ligand redistribution is reported; selected derivatives are active pre-catalysts in the dimerization of aldehydes.

Pre-queuosine or queuine (preQ1) is a guanine derivative that is involved in the biosynthetic pathway of the hypermodified tRNA nucleoside queuosine (Que). The core structure of preQ1 is represented by 7-(aminomethyl)-7-deazaguanine (preQ1 base). Here, we report the synthesis of three preQ1 base derivatives with complementary (15)N-labeling patterns, utilizing [(15)N]-KCN, [(15)N]-phthalimide, ...