Nonuniformly definite multiparameter spectral problems

We establish theorems about the expansion of nonuniformly right-definite multiparameter problems in generalized eigenfunctions. We also give an abstract criterion of existence of commuting self-adjoint extensions of a family of symmetric operators.To Yurii Makarovich BerezanskiiTranslated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 5, pp. 659–670, May, 1995.This research was supported by the Ukrainian State Committee on Science and Technology.     

Plane electromagnetic wave scattering by transversely magnetized ferrite cylinder

The paper is devoted to the problem of scattering of plane electromagnetic wave by transversely magnetized ferrite cylinder. Exact analytical expressions for all partial cylindrical modes are obtained by solving Maxwell’s equations for transversely magnetized ferrite medium in cylindrical coordinate system. They are represented as the power series expansion and then are used to formulate and to solve the boundary problem. Numerical calculations of scattering patterns are also presented. Particular attention is paid to the possibility to control the scattering pattern by the external magnetic field.     

Galvanomagnetic and thermoelectric properties of multicomponent n-type solid solutions based on Bi and Sb chalcogenides

The galvanomagnetic and thermoelectric properties of n-Bi_2-x Sb_xTe_3-y-z Se_yS_z multicomponent solid solutions with atomic substitutions (Sb → Bi; Se, S → Te) are studied. The principal components of the effective mass tensor (m ₁, m ₂, m ₃) for the isotropic mechanism of charge carrier scattering are determined within a many-valley model of the energy spectrum for compositions 0.08 ≤ x ≤ 0.4 and 0.06 ≤ y = z ≤ 0.15. The effect of a variation in the parameters of the constant-energy surface on the thermoelectric efficiency is analyzed for different compositions and carrier concentrations in solid solutions.     

Dependence of the catalytic activity of organoaluminum compounds and some of their complexes on their composition

The influence of the acidity of organoaluminum compounds and their complexes on the catalytic activity in polymerization of trioxane has been studied. It is found that the catalytic activity of organoaluminum compounds of the type R_nALX_3?n depends on n as well as the nature of R or X. Catalytic activity of the complexes also depends on the type of cocatalyst used. The change of electroconductivity in the course of formation of some initiator complexes has been studied and an attempt has been made to determine the relation between conductivity and polymerization activity.     

Determination of metal traces in tantalum by proton activation analysis

Procedures for determining traces of calcium, titanium, vanadium, chromium, iron, copper, niobium, molybdenum and tungsten in tantalum are described utilizing 11 MeV proton activation. The instrumental method of analysis with the use of a Ge(Li) detector and the radiochemical separation of the corresponding fractions are described. The formula for the calculation of the concentration of traces with the use of thick target yields is given. Experimental data on the thick target yields of radioisotopes⁴⁴Sc,⁵²Mn,⁵⁶Co,⁶⁵Zn,^93mMo,⁹⁶Tc are presented. Based on the experimental data, the detection limits are estimated at 1–10 ppb for the above mentioned metal traces in tantalum. The successful solution of the task of the simultaneous determination of nine elements in tantalum confirms the wide applicability of proton activation analysis.     

New liquid-crystalline homo-and copolymers with phenyl benzoate side groups and a chiral center in a flexible spacer

The phase behavior and structure of liquid-crystalline homo-and copolymers based on structurally isomeric units belonging to the family of phenyl benzoates that differ in orientation of an ester link situated between benzene rings have been studied with X-ray diffraction, scanning calorimetry, and polarization optical microscopy. The orientation of this link in the monomer unit affects the temperature of phase transition, the type of the smectic phase, and the packing mode of side mesogenic groups in smectic layers of homopolymers. When monomer units commensurable with the monomer units of the basic component in terms of geometry but not identical to them in terms of smectogenity are randomly incorporated into macromolecules of the LC polymer, the resulting copolymer is characterized by layered packing not typical of either of the components.     

Synthesis of selenophene-2,5-dicarboxylic acid

Selenophene-2,5-dicarboxylic acid was obtained by liquid-phase oxidation of 2,5-dimethylselenophene with molecular oxygen.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 12, p. 1605, December, 1972.     

First synthesis of α-aminophosphonates from natural porphyrin derivatives by the Kabachnik—Fields reaction

A preparative procedure is proposed for the synthesis of α-aminophosphonates of natural porphyrins by the microwave-assisted Kabachnik—Fields reaction.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 256–259, January, 2005.