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We study the existence of normalized homeomorphic solutions for the degenerate Beltrami equation fz = μ(z )f in the whole complex plane C , assuming that its measurable coefficient μ(z ), | μ(z )

Here we consider the classes of mappings of metric spaces that distort the modulus of families of paths similarly to Poletsky inequality. For domains, which are not locally connected at the boundaries, we obtain results on the boundary extension of the indicated mappings. We also investigate the local and global behaviorof mappings in the context of the equicontinuity of their families. The main statements of the article are proved under the condition that the majorant responsible for the distortion of the modulus of the families of paths has a finite mean oscillation at the corresponding points. The results are applicable to well-known classes of conformal and quasiconformal mappings as well as mappings with a finite distortion.

It has been discussed the optimization of the valence force field model for non-ideal III-nitrides wurtzite materials. To describe the static and dynamical lattice properties of nitrides within the same model, the anisotropy of the wurtzite structure and additional second-nearest-neighbor atomic interaction terms are included in the lattice strain energy expression. The sets of the force constants have been optimized through an iterative scheme in which calculated lattice properties are fitted to experimentally reported data. The model has been applied to the binary wurtzite compounds (GaN, InN) and random InxGa1-xN alloys. The calculated phonon dispersions, elastic constants and internal strain parameters of GaN and InN are in reasonable agreement with the experimental/ab initio values.