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.     

Traveling Waves in Porous Media Combustion: Uniqueness of Waves for Small Thermal Diffusivity

We study traveling wave solutions arising in Sivashinsky’s model of subsonic detonation which describes combustion processes in inert porous media. Subsonic (shockless) detonation waves tend to assume the form of a reaction front propagating with a well defined speed. It is known that traveling waves exist for any value of thermal diffusivity [5]. Moreover, it has been shown that, when the thermal diffusivity is neglected, the traveling wave is unique. The question of whether the wave is unique in the presence of thermal diffusivity has remained open. For the subsonic regime, the underlying physics might suggest that the effect of small thermal diffusivity is insignificant. We analytically prove the uniqueness of the wave in the presence of non-zero diffusivity through applying geometric singular perturbation theory. Dedicated to Mr. Brunovsky in honor of his 70th birthday.     

On a Class of Weakly Hyperbolic Operators

The paper considers Cauchy problem in the Gevre type multianisotropic spaces. Necessary and sufficient conditions for unique solvability of this problem are obtained and the properties of operators (polynomials) that are hyperbolic with a specified weight are investigated.     

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.     

On almost hypoelliptic polynomials increasing at infinity

It is proved that a polynomial (the symbol of a differential operator), the Newton polygon of which is a rectangular parallelepiped with a vertex at the origin, is almost hypoelliptic if and only if it is regular. Also some algebraic conditions of almost hypoellipticity are obtained for nonregular polynomials increasing at infinity. The results are unimprovable for polynomials of two variables.     

Synthesis of novel 1,3‐substituted 1H‐[1,2,4]‐triazole‐3‐thiol derivatives

By means of regioselective S‐alkylation of 1H‐1,2,4‐triazole‐3‐thiol ( 1 ), a series of S‐substituted derivatives 2a‐j were synthesized. In certain conditions, the reaction of 2 with arylsulfochlorides, arylisocyanates, and quaternary ammonium salts of azines corresponding compounds were obtained 1‐arylsulfonyl‐ (3a‐d) , 1‐arylcarbonamido‐ ( 4a,b ), and 1‐azinyl‐1,2,4‐ ( 6a‐p ) triazoles. Structures of compounds were confirmed by ¹H NMR and elemental analyses. © 2010 Wiley Periodicals, Inc. Heteroatom Chem 20:405–410, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20565