Violation of isotopic invariance in strong interactions and mass spectrum of the 1/2+ baryon octet

The ideas developed by Gell-Mann and Okubo in studying violation of unitary symmetry are used to describe violation of isototic invariance in strong interactions. The present consideration is performed for the example of the mass spectrum of the octet formed by baryons of spin-parity 1/2⁺: only for this family are the widths of its particles much less than the scale of the effects being investigated, their masses being known from experiments to a fairly high precision. The Gell-Mann-Okubo formula is generalized in such a way that relations both for the splitting between the isomultiplets of the octet and for the mass splitting within these isomultiplets follow from the new formula. Moreover, a relation between masses that describes their electromagnetic splitting and which coincides in form with the Coleman-Glashow relation also follows from this formula. The relations obtained for the masses of the baryons belonging to the octet in question are satisfied to a precision not poorer than 3%.     

Simulation of time-resolved vibronic spectra and the possibility of analyzing molecules with similar spectral properties

The possibility of using time-resolved vibronic spectroscopy for spectral analysis of mixtures of chemical compounds with similar optical properties, when traditional methods (based on stedy-state spectra) are inefficient, is demonstrated by using the method of computer simulation. The analysis is carried out by the example of molecules of a series of polyenes (butadiene, hexadiene, octatetraene, decapentaene, and decatetraene), their various cis-and trans-rotational isomers, and phenyl-substituted polyenes. Ranges of relative concentrations of molecules similar in their spectral properties, where reliable interpretation of time-resolved spectra of mixtures and both qualitative and quantitative analyses are possible, are determined. The use of computer simulation methods for optimizing full-scale experiments in femtosecond spectroscopy is shown to hold much promise.     

Quasi-hexagonal self-organization of nanoparticles upon the laser-controlled deposition of Ga atoms

A cooperative defect-deformation (DD) mechanism is developed for the nucleation of the quasi-monodisperse ensemble of nanoparticles in the low-temperature deposition of Ga atoms in the presence of laser radiation. A comparison with experiment is carried out, and a good agreement between the theoretical and experimental results has been obtained. In particular, in accordance with the DD model, it has been found that the arrangement of nanoparticles is characterized by a latent hexagonal order, and their shape is quasi-hexagonal. It has been shown that the characteristics of the deposited ensemble of nanoparticles can be controlled with the use of an anisotropic deformation.     

Quark masses from regularized integrals of vector current spectral functions

We give estimates of quark masses from a comparison of two methods of regularizing the coefficient of the Schwinger term. The masses of the first radial excited states of ?, ω, and ? would have to be slightly higher than indicated by the new Orsay data for this method to yield real solutions for the masses of theu, d, ands quarks.     

Functional approach to the theory of two-dimensional quantum Fermi systems in an external periodic field

The behavior of an adsorbed layer of Fermi particles in a weak external field with symmetry of the centered quadratic lattice is investigated. Instability of the weakly inhomogeneous state of the system with respect to small fluctuations in the vicinity ofa ^*=2k _F is established; herea ^* is the magnitude of the vectors of the neighbors closest to the point in the inverse lattice; k_F is the Fermi momentum.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 169, pp. 29–43, 1988.It remains to thank V. N. Popov for constant interest in the work.     

UniversalR-matrix for quantized (super)algebras

For quantum deformations of finite-dimensional contragredient Lie (super)algebras we give an explicit formula for the universalR-matrix. This formula generalizes the analogous formulae for quantized semisimple Lie algebras obtained by M. Rosso, A. N. Kirillov, and N. Reshetikhin, Ya. S. Soibelman, and S. Z. Levendorskii. Our approach is based on careful analysis of quantized rank 1 and 2 (super)algebras, a combinatorial structure of the root systems and algebraic properties ofq-exponential functions. We don't use quantum Weyl group.     

A microeconomic simulation model of reproduction

Translated from Programmnoe Oborudovanie i Voprosy Prinyatiya Reshenii, pp. 152–184, 1989.     

On estimates of the bispectral density of certain models of random processes

Estimates are given for the bispectral densities of stationary random processes. Two models of stationary random processes with discrete time are considered. It is shown that for both models conditions hold under which one can construct a consistent estimate of the bispectral density.Translated fromTeoriya Sluchaínykh Protsessov, Vol. 14, pp. 3–7, 1986.