We give an explicit dependence of quasiconformal constant on its boundary function, provided that the mapping is quasiconformal harmonic and maps the unit disk onto a strictly convex domain. This result refines some earlier results obtain by the first author and Pavlović ([11, 27]).

A numerical method for analyzing and parameterizing quadratic surface intersection curves (QSIC) is proposed. This method is based on numerical fractional linear transformations, numerical irreducible decomposition and a numerical version of a classical method for replacing an irreducible QSIC with a numerically birationally equivalent cubic plane curve. Ultimately each component of the QSIC is parameterized by a plane curve of the form $y=u(x)$ or $y^2=u(x)$ where $u(x)$ is a numerical polynomial of degree $3$ or less.

Burst errors are very common in practice. There have been many designs in order to correct or at least detect such errors. Recently, a new kind of burst error which is termed as repeated burst error has been introduced in order to detect or correct errors that occurs in very busy communication channels. In this paper, we extend the definition of repeated burst errors for block and array codes endowed with a homogeneous metric. We also obtain some upper bounds on the number of parity check digits for these codes correcting all repeated burst errors.