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Let G be a finite domain in the complex plane with K-quasicon formal boundary, z0 be an arbitrary fixed point in G and p>0. Let π( z) be the conformal mapping from G onto the disk with radius r0>0 and centered at the origin 0, normalized by ϕ( z0) = 0 and ϕ( z0) = 1. Let us set $$\varphi _p \left( z \right): = \int_{x_0 }^x {\left[ {\phi \left( \zeta \right)} \right]^{2/8} } d\zeta $$ , and let π n,p( z) be the generalized Bieberbach polynomial of degree n for the pair ( G,z0) that minimizes the integral $$\iint\limits_c {\left| {\varphi _p \left( z \right) - P_x^1 (z)} \right|^p d0_x }$$ in the class $$\mathop \prod \limits_n $$ of all polynomials of degree ≤ n and satisfying the conditions P n( z0) = 0 and P′ n( z0) = 1. In this work we prove the uniform convergence of the generalized Bieberbach polynomials π n,p( z) to ϕ p( z) on $$\bar G$$ in case of $$p > 2 - \frac{{K^2 + 1}}{{2K^4 }}$$ . [ABSTRACT FROM AUTHOR]

We report the growth and characterization of a new wide bandgap II-VI alloy, ZnCdMgSe, grown lattice-matched to InP. High quality quaternary layers with bandgaps ranging from 2.4 to 3.1 eV were grown by molecular beam epitaxy. The bandgaps and lattice constants were measured using photoluminescence and single crystal Θ-2Θ scans. Quantum well structures with quaternary barriers and ZnCdSe wells were also grown, entirely lattice matched to InP. Their photoluminescence properties suggest that these materials are suitable for the design of visible semiconductor lasers spanning the blue, green, and yellow regions of the visible range. The absence of strain in these heterostructures is expected to improve the reliability of the materials in device applications. [ABSTRACT FROM AUTHOR]