Asymptotic stability of the numerical solution for an integrodifferential reaction-diffusion system

This paper presents the study of the numerical solution of a reaction-diffusion system involving a reaction term of integral type arising from biological models. By means of a monotone approach we introduce upper and lower solutions and then we show the existence and the asymptotic behavior of nonnegative numerical solutions. To this end, we require the positivity of the numerical scheme and so we can use some properties of positive and M-matrices. Finally we give some sufficient conditions to verify the asymptotic stability of the numerical solution.     

Relaxation dynamics of a broadband nanosecond acoustic pulse in a bubbly medium

The first experimental observation of the propagation dynamics of a short broadband acoustic pulse in a resonance medium with gas bubbles is carried out. The probing pulse is generated using the optoacoustic effect. It is shown that the theory of short pulse propagation in media with generalized resonance relaxation adequately and accurately describes the dynamics of short pulse dispersion. A possibility to determine the relaxation and resonance parameters of media by the pulsed testing technique is demonstrated.     

Two-stream-like mechanism of zonal-flow generation by Rossby waves in a shallow rotating fluid

It is shown that the small-scale Rossby waves in a shallow rotating fluid placed in a gravitational field can generate large-scale zonal flows by means of a two-stream-like mechanism. This mechanism is revealed under the conditions when the Lighthill instability criterion is not satisfied. The text was submitted by the authors in English.     

Limiting distributions of the likelihood ratio and estimators from censored samples

Limiting distributions are constructed for the log likelihood ratio of close hypotheses and for estimators from censored samples.Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 95–104, 1986.     

Exact solution of a quasipotential equation that describes a bound state of spinor particles

Theoretical and Mathematical Physics -     

Formal degree and existence of stable arithmetic lattices of cuspidal representations ofp-adic reductive groups

Research at MSRI supported in part by NSF Grant DMS-812079-05     

Certain problems of the approximation of functions in two variables by Fourier-Hermite sums in the space L 2(Γ², e -x ² -y ²)

Summary We give an exact estimate of the deviation of the "triangular" partial sums of the double Fourier-Hermite series of functions of the class L^r₂(D) in the space L₂(Γ2, e^-x2-y2).     

Similarity and the structure of unital matrix quadratic trinomials with pairwise different characteristic roots

The normal form of certain polynomial matrices is found.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 175, pp. 63–68, 1989.