Excited-state dynamics in Yb3+-Ho3+-doped fluoroindate glasses

This work has been partially supported by Gobierno Autonomo de Canarias under contact number 226–265/93.     

Euler decompositions for theta-series of even quadratic forms

For a generating Dirichlet vector series with coefficients equal to the number of representations of a quadratic form by another one we abtain a decomposition into the product of a finite number of Dirichlet L-functions and an infinite number of matrix polynomials. The coefficients of the polynomials are the Eichler-Brandt matrices of the basis double cosets of the local orthogonal Hecke rings. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 212, 1994, pp. 97–113. Translated by N. Yu. Netsvetaev.     

Numerical analysis of dissipative instabilities in toroidal plasma configurations with a noncircular cross-section

Translated from Pryamye i Obratnye Zadachi Matematicheskoi Fiziki, pp. 198–203, 1991.     

Spectral characteristics of a microwave radar signal backscattered by the sea surface at small incidence angles

We present a theoretical analysis of the Doppler-spectrum properties of a microwave radar signal scattered by the sea surface at small incidence angles. The dependences of Doppler-spectrum width and shift on the wind velocity and wave development stage and their azimuthal dependence are analyzed. The case of mixed sea (wind wave plus swell) is also considered. The JONSWAP spectrum model is used to describe sea waves. The study shows that Doppler-spectrum parameters are sensitive to variation of sea-surface state; for example, for the case of developed sea waves, an increase in wind velocity by 1 m/sec leads to increases in the Doppler-spectrum width and shift by 15 Hz and 3 Hz, respectively. It is shown that for the case of a moving radar the Doppler spectrum remains sensitive to variation of sea- surface state with a sufficiently narrow radar directivity pattern. Estimates show that in the case of a single sea- wave system on the surface, using Doppler-spectrum parameters we can, in principle, determine wave type (developing wind wave, developed wind wave, or swell), dominant wavelength, wave propagation direction, and wave height; wind velocity, direction, and acceleration distance can be determined for wind waves.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 5, pp. 517–526, May, 1996.This paper was supported by the Russian Foundation for Fundamental Research (project 93-02-15892).     

Stochastic resonance in perspective

Summary We outline the historical development of stochastic resonance (SR), a phenomenon in which the signal and/or the signal-to-noise ratio in a nonlinear system increase with increasing intensity of noise. We discuss basic theoretical ideas explaining and describing SR, and we review some revealing experimental data that place SR within the wider context of statistical physics. We emphasize the close relationship of SR to some effects that are well known in condensed-matter physics. Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena?, Elba, 5–10 June 1994.     

Noncommutative differential geometry related to the Young-Baxter equation

An analogue of the differential calculus associated with a unitary solution of the quantum Young-Baxter equation is constructed. An example of a ring sheaf is considered in which local solutions of the Young-Baxter quantum equation are defined but there is no global section. Bibliography: 13 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 199, 1992, pp. 51–70. Translated by I. A. Izergina.     

Noncommutative four-dimensional subalgebras of conformal algebra integrable in the space R1,3

D'alambert's equation is used as an example to study the possibilities of a new method of exactly integrating systems of linear differential equations — the method of noncommutative integration (NI). The results confirm that use of the NI is equivalent to complete separation of the variables in the case of four-dimensional subalgebras of conformal algebra. However, the method does simplify determination of the exact solution in this instance.Tomsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 120–124, February, 1995.     

Measurement of Hartmann-Hahn cross-polarization dynamics with quenching of proton T1ρ relaxation dependence

A simple modification of the standard cross-polarization method designed for quenching the proton T_1ρ dependence when studying polarization transfer is presented. It is demonstrated that by using this simple procedure, new and subtle details of cross-polarization dynamics, previously hidden by the T_1ρ(¹H) effect, can be observed in dipolar-coupled spin systems.