Algebra with Quadratic Commutation Relations for an Axially Perturbed Coulomb–Dirac Field

The motion of a particle in the field of an electromagnetic monopole (in the Coulomb–Dirac field) perturbed by an axially symmetric potential after quantum averaging is described by an integrable system. Its Hamiltonian can be written in terms of the generators of an algebra with quadratic commutation relations. We construct the irreducible representations of this algebra in terms of second-order differential operators; we also construct its hypergeometric coherent states. We use these states in the first-order approximation with respect to the perturbing field to obtain the integral representation of the eigenfunctions of the original problem in terms of solutions of the model Heun-type second-order ordinary differential equation and present the asymptotic approximation of the corresponding eigenvalues.     

Crystal Structure and Excimer Fluorescence of Some Benzoylacetonatoboron Difluorides: Stacking Factor

The comparative study of the crystal structures of benzoylacetonato- (1), p-toluylacetonato- (2) and p-ethylbenzoylacetonatoboron (3) difluoride was carried out. Correlation of the luminescence properties of the complexes 1–3 and their crystal structures was revealed. The excimer formation in these compounds occurred the most efficiently for the complexes 1 characterized by the formation of stacks of molecules, unlike the complex 3, where individual dimers behaved as excimer-forming centers. The maximal fluorescence intensity was observed for the complex 2, which had the highest structural ordering.     

Logarithmic corrections in a quantization rule. The polaron spectrum

A nonlinear integrodifferential equation that arises in polaron theory is considered. The integral nonlinearity is given by a convolution with the Coulomb potential. Radially symmetric solutions are sought. In the semiclassical limit, an equation for the self-consistent potential is found and studied. The potential has a logarithmic singularity at the origin, and also a turning point at 1. The phase shifts at these points are determined. The quantization rule that takes into account the logarithmic corrections gives a simple asymptotic formula for the polaron spectrum. Global semiclassical solutions of the original nonlinear equation are constructed.Moscow Institute of Electronic Engineering; Moscow Power Institute. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No. 1, pp. 78–93, October, 1993.     

Partitions of a Polytope and Mappings of a Point Set to Facets

Three theorems of this paper generalize previous results of the author on conjectures of A. Bezdek and V.V. Proizvolov. They show the existence of mappings from a given point set to the set of facets of a given polytope that satistfy some special conditions. Developing the same technique, some results on convex polytope partitions are presented, two of them dealing with partitions with prescribed measures of parts. Then we prove a corollary on the existence of a possibly nonconvex polytope with a given set of vertices, containing given points in its interior. We also consider problems of the following type: find an assignment of vectors from a given set to the parts of a given convex partition of ℝⁿ so that the shifts of the parts by their corresponding vectors either do not intersect by interior points or cover ℝⁿ     

Infrared reflection spectra in contactless nondestructive measurements of the electron density and mobility in indium phosphide

On the basis of numerical calculations and experimental studies we analyze the possibilities of measuring the electrophysical parameters of indium phosphide by means of infrared reflection spectra at wavelengths ranging from 5 to 200 m. We demonstrate that contactless nondestructive measurements of the electron density in the range 10¹⁶–10²⁰ cm^–3 can be made with a relative error not exceeding 15%, and of mobility with a relative error not exceeding 25%. A nomogram method is presented for rapid conversion of data from infrared reflection spectra into the parameters being measured.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 22–27, January, 1988.     

Methodology of using expert systems for structure elucidation of organic molecules by their spectra

Major axioms underlying structure elucidation of molecules by their characteristic spectral data are considered. The amount of information obtained by solving the problem on structure elucidation of molecules serves as a basis to evaluate the quality of solution. Conditions for computer-aided solution of problems using expert systems (ES) are analyzed. Reasons for incorrect or zero solutions and for inconsistencies leading to negative results are examined. The role of additional information as a necessary condition for correct solution is discussed. On the basis of this analysis, a general strategy for structure elucidation of molecules by their spectra using ES is suggested. The principal idea is to use the iteration method, gradually increasing the rigidity of constraints. Strategies named ARCHEOLOGIST and SCULPTOR are discussed. Examples are given. Russian Scientific Research Institute of Organic Synthesis. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 3, pp. 548–558, May–June, 1995. Translated by L. Smolina     

Photochemical behavior of polymer complexes based on Eu(III) acrylato(bisdibenzoylmethanate)

The photochemical behavior of monomer and polymer complexes of Eu³⁺ that are based on dibenzoylmethane and acrylic acid has been studied. It has been shown that these complexes differ from their low-molecular-mass analogs by properties: in the course of photolysis, the intensity of luminescence of the studied Eu³⁺ complexes increases by a factor of 1.3 to 2.5. The mechanism describind the effect of the composition of polymer formulation on the rate of photodegradation is discussed.     

Crystal structure of boron difluoride 3-phenylthiopentane-2,4-dionate. π stacking interactions and luminescence of boron difluoride acetyl acetonates

The crystal structure of boron difluoride 3-phenylthiopentane-2,4-dionate was determined. The relationship between the structure and luminescent properties is traced in the series of boron difluoride acetyl acetonates (acetyl acetonate, phenylacetyl acetonate, and phenylthioacetyl acetonate). The presence of the π stacking interactions in boron difluoride phenylthioacetyl acetonate crystals leads to increased intensity and bathochromic shift of the fluorescence band.     

Fluorescence properties of mixed-ligand europium carboxylates

Mixed-ligand binuclear and mononuclear europium carboxylate complexes with nitrogen-and phosphorus-containing neutral ligands have been studied by luminescence and X-ray photoelectron spectroscopy. The coordination of neutral ligands through the nitrogen donor atom leads to an increase in electron density at the Eu³⁺ atom. In groups of carboxylates of the same type, the coordination of neutral donor ligands leads to an increase in the relative intensity of the ⁵ D ₀-⁷ F ₄ electric dipole transition. Analysis of the luminescence excitation spectra points to the presence of two excitation energy transfer channels for mixed-ligand europium trifluoroacetate and toluate complexes and of one channel for europium cinnamate complexes with neutral ligands.