Constructing a model transport equation for a massless bose gas and its analytic solution

A model kinetic equation is constructed for the transport of a massless Bose gas. This equation is applied to solve the boundary value problem for the transport of radiation in the half-space occupied by a dispersive medium that is in local thermal equilibrium with the radiation. It is shown that the difference in temperature between the dispersive medium and the incident radiation substantially depends on the character of the scattering properties of the particles in the medium. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 111, No. 3, pp. 462–472, June, 1997.     

A Method for Establishing Optimality Conditions for a Nonsmooth Vector-Valued Minimax Problem

Using a method of uniform approximations, necessary and sufficient conditions for a nonsmooth constrained vector-valued minimax problem are established in terms of Mordukhovich subdifferentials.     

New method for the synthesis of 6-amino-4-aryl-3,5-dicyano-3,4-dihydropyridine-2(1H)-thiones by recyclization of 4-aryl-2,6-diamino-4H-thiopyranes

Ammonium 6-amino-4-aryl-3,5-dicyano-1,4-dihydropyridine-2-thiolates were synthesized by recyclization of 4-aryl-2,6-diamino-3,5-dicyano-4H-thiopyranes in the presence of organic bases. On acidification of the products, the corresponding substituted 3,4-dihydropyridine-2(1H)-thiones were obtained which were used in the synthesis of 2-alkylthio-1,4-dihydropyridines, bis-(pyridyl-2)disulfides and thieno[2,3-b]pyridines.Deceased.T. G. Shevchenko Lugansk State Pedagogical Institute, Lugansk 348011. N. D. Zelinskii Institute of Organic Chemistry, Russian Academy of Sciences, Moscow 117913. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, pp. 909–914, July, 1997.     

Formation of a bistructure of a solid in a computer experiment

Molecular-dynamics was used to investigate the structural changes occurring in a three-dimensional solid when the solid is transferred from an amorphous into a crystalline state. Crystal cells of a new type — pentadecahedrons with five square lateral faces and ten regular triangular faces at the vertices of a cell — were found for the first time in a computer experiment. It is shown that a bistructure consisting of crystal cells of different types, including cells with five-fold symmetry axes, are stable in the solid. Fiz. Tverd. Tela (St. Petersburg) 40, 1919–1924 (October 1998)