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Vladikavkaz Mathematical Journal

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April-June, 2003

Volume 5, Issue 2

This Issue is dedicated to the 60th anniversary of Illarion Davidovich Muzaev

Illarion Davidovich Muzaev
(on his 60's anniversary)
T. G. Voynich-Syanozhentskiy, A. G. Kusraev, G. L. Lelishvili,
V. G. Sozanov, Zh. D. Tuaeva, Sh. S. Khubezhty

Article (rus.) - [pdf] [zip-pdf]

On the Neveu Decomposition and Ergodic Type Theorems for Semi-Finite von Neumann Algebras
G. Ya. Grabarnik, A. A. Katz (New York, USA)
UDC 517.98

Some ergodic type theorems are considered for automorphisms of semi-finite von Neumann algebras. The Neveu decomposition is employed for proving stochastic convergence. This work is a generalization of the authors' previous results to the case of semi-finite von Neumann algebras. Article (eng.) - [pdf] [zip-pdf]

Integral Representations of Analytic Functions in Unbounded Domains with Defining Manifolds
Kh. P. Dzebisov (Vladikavkaz)
UDC 517.55

The author continues his research in the theory of integral representations of analytic functions of two complex variables. New integral representations are obtained which are applied to solving the problem of reconstruction of a function in unbounded domains of the two-dimensional complex space from the values of the function and its derivatives set on the defining manifolds.

Article (rus.) - [pdf] [zip-pdf]

Mathematical Modeling of Ground Oscillations
V. B. Zaalishvili, Zh. D. Tuaeva (Vladikavkaz)
UDC 532(075.8)

The topic of this article is a model of oscillations of a ground layer of nonlinear material under intense seismic influence given as various waves. The purpose of this article is a method for determining the shift function. The nonlinear seismic influence is considered of an SH wave on a ground layer with nonlinear properties. The model is based in the nonlinear behavior of the "Hardin–Drnevich" type and presents an initial-boundary problem with various input data. Several solutions are obtained of these initial-boundary problems with various data. Inspection of the results shows that if the nonlinear properties of the grounds are taken into account in the mathematical model of oscillations then the sufficiently large deformations involve secondary peaks for harmonics of the characteristic frequency.

Article (rus.) - [pdf] [zip-pdf]

Air Pollutant Dispersion at Mountain Valleys
E. S. Kamenetsky, A. A. Radionoff (Vladikavkaz)
UDC 001.891.57

The results of numerical modeling of thew variation of the air pollutant dispersion during day-time simulation. The influence is demonstrated of air flow regimes at a valley to near surface pollutant concentration at the bottom of the valley.

Article (rus.) - [pdf] [zip-pdf]

One Property Of the Weak Convergence of Operator Iterations in von Neumann Algebras
A. A. Katz (New York, USA)
UDC 517.98

Some equivalent conditions are given for the *-weak convergence of iterations for of positive operators in the preduals of von Neumann algebras.

Article (eng.) - [pdf] [zip-pdf]

Analytical and numerical solutions of boundary value problems of wave driving in a water basin caused by a collapse–landslip or an avalanche stream
V. G. Sozanov, I. D. Muzaev, S. A. Makarov (Vladikavkaz)

In the narrow gorges of mountain rivers there are created artificial deep (270 - 300 m.) water basins. The arrays of rock and streams frequently interfere in them provoking large superficial gravity waves reducing in acts of nature. This makes actual research into the problems of the wave movements of water in narrow deep not prismatic reservoirs.

Article (rus.) - [pdf] [zip-pdf]

To Numerical Solution of Dirichlet Problem by The Method of Locally Canonical Partition
Sh. S. Khubezhty (Vladikavkaz)
UDC 519.64

We prove a theorem on decomposition of an atomic operator in some special basis of lattice homomrphisms and show that this decomposition is in a sense unique.

Article (rus.) - [pdf] [zip-pdf]

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