On smooth solutions of a class of almost hypoelliptic equations

For a class of non-degenerate (regular) almost hypoelliptic equations, which are partially hypoelliptic with respect to certain variables, infinitely differentiable in a specific strip solutions are extracted.     

Effect of a magnetic impurity on the optical properties of a spherical ZnSe quantum dot

We consider the electron and hole states in a semiconductor ZnSe spherical quantum dot, in the center of which a magnetic impurity atom of manganese is located. In calculations the quantum dot is approximated by a spherical rectangular well with a finite depth. Within the framework of perturbation theory, the effect of exchange spin interaction of an electron and a hole with a magnetic impurity on the band structure of the system is considered. The optical spectrum of the system for different polarizations of the incident light is studied also.     

Glycine glycinium picrate--reinvestigation of the structure and vibrational spectra

The crystal of diglycine picrate (glycine glycinum picrate) has been obtained from an aqueous solution containing stoichiometric quantities of the components. The species crystallizes in the monoclinic system (space group P2(1)/c). The crystal structure was determined with high accuracy, IR and Raman spectra are discussed and compared with previous results, and the molecular structure is presented. It was shown that crystals of diglycine picrate obtained from the solution containing equimolar quantities may contain picric acid as impurity, which is the reason for the previously reported observation of second harmonic generation in this centrosymmetric crystal. With this example we want to point out the risk of misinterpretation of SHG signals in general.     

On weighted hyperbolic polynomials

The results by Görding, Larsson, Cattabriga, Rodino, Calvo on correctness of Cauchy problem for N-hyperbolic equations are generalized. We prove that in the general case where the vector N = (N ₁, …,N _n ) is different from the vector (1, 0, …, 0), for the correctness of the Cauchy problem more stronger condition is required, which we call weighted hyperbolicity condition. We also discuss the properties of polynomials possessing weighted hyperbolicity property.