Highly accurate calculation of radial spheroidal functions

A new method for calculating the radial spheroidal functions of the first kind is proposed for the arguments that are greater than unity in modulus. A well-known representation of these functions is refined and used for this purpose. The constructs and the software implementation proposed in the paper provide an efficient tool for the calculation of the functions with a desired accuracy in a wide range of parameters.     

Linear nonstationary optical dimensional resonances in atomic nanostructures

The existence of linear nonstationary optical resonances in a diatomic nanostructural object with a dipole-dipole atomic interaction has been proved. A new solution to the joint system of modified Bloch optical equations and nonlocal field equations is obtained for time intervals much shorter than the times of phase and energy relaxation. Formulas for effective polarizabilities of the object’s atoms, which have a set of dimensional resonances, are derived. The frequencies of these resonances significantly differ from the eigenfrequencies of the object’s atoms, and their properties depend on the interatomic distance, light-pulse duration, initial atomic inversions, and the orientation of the object’s axis relative to the direction of incidence of the external light wave.     

Univariate Ore Polynomial Rings in Computer Algebra

We present some algorithms related to rings of Ore polynomials (or, briefly, Ore rings) and describe a computer algebra library for basic operations in an arbitrary Ore ring. The library can be used as a basis for various algorithms in Ore rings, in particular, in differential, shift, and q-shift rings. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 13, Algebra, 2004.     

Hyperfine structure of a hydrogen-like atom due to orbit-orbit,spin-orbit,and spin-spin interactions

A nonrelativistic model of a hydrogen-like atom is considered. This model is used to calculate corrections to the energy spectrum of the atom. The analysis is based on a Hamiltonian that includes the intratomic fields generated by the electron and the nucleus.     

Synthesis of Oxathiacrown Compounds by the Reactions of Sulfur Dichloride with Unsaturated Compounds and Their Extraction Characteristics. (Review)

Published data of the last 10-15 years on the use of the reactions of sulfur dichloride with various unsaturated compounds for the synthesis of oxathia- and thiacrown compounds and study of their extraction characteristics toward various transition and heavy metals are reviewed. Some previously unpublished results and associated experimental data are also included.     

Nucleophilic substitution in 4-bromo-5-nitrophthalodinitrile: VIII. Synthesis of 4-(benzotriazol-1-yl)-5-[4-(1-methyl-1-phenylethyl)phenoxy]phthalodinitrile and phthalocyanines on its basis

Nucleophilic aromatic substitution of the bromine atom in 4-bromo-5-nitrophthalodinitrile by a 2-aminophenylamine residue followed by conversion of the resulting compound to 4-(1-benzothiazol-1-yl)-5-nitrophthalodinitrile and nucleophilic substitution of the nitro group by a 4-(1-methyl-1-phenylethyl)-phenoxy group gave 4-(benzotriazol-1-yl)-5-[4-(1-methyl-1-phenylethyl)phenoxy]phthalodinitrile. The latter product was reacted with certain metal acetates and chlorides to obtain the corresponding metal complexes of octasubstituted phthalocyanines. Spectral properties of the complexes were studied.     

Synthesis of 3-Aryl[1,2,4]triazolo[3,4-<Emphasis Type="Italic">b</Emphasis>][1,3]benzothiazole-6,7-dicarbonitriles from 5-Aryl-4H-triazole-2-thiols and 5-Bromo-5-nitrophthalonitrile

New 3-aryl-substituted [1,2,4]triazolo][3,4-b][1,3]benzothiazole-6,7-dicarbonitriles have been synthesized by successive interaction of 5-aryl-4H-triazole-2-thiols with 4-bromo-5-nitrophthalonitrile in the presence of K₂CO₃ initially at the bromine atoms and then at the nitro group.__________Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, 270–272, February, 2005.