A numerical analysis of chaotic behaviour in Bianchi IX models

In this paper we investigate the chaotic behaviour of the Bianchi IX cosmological models using techniques developed in the study of dynamical systems and chaotic behaviour. We numerically calculate the Lyapunov exponent, , and show that instead of converging to a constant value, it decreases steadily. We study this effect further by studying the Lyapunov exponent using short-time averages. We show that the usual method of calculating is invalid in the case of a cosmological model.     

Boson realization of YangiansY(sl(2)) andY(sl(3))

Studying the algebraic structure of the YangiansY(sl(2)), andY(sl(3)) we present their boson realizations. In the case ofY(sl(2)) we give the realization by using 1-canonical boson pair and two parameters and in theY(sl(3)) with 2-canonical boson pairs, two parameters and subalgebrasl(2). Substituting the realization ofU(sl(2)), we can obtain the pure boson realization by 3-canonical pairs and three parameters.Presented at the 4th Colloquium Quantum Groups and Integrable Systems, Prague, 22–24 June 1995.     

Stability of certain one-dimensional unsteady gas motions

This paper studies the stability of the adiabatic unsteady motions of a perfect gas for which the velocity is proportional to the distance to the center of symmetry. The solutions of the gas dynamic equations of such a form and their physical interpretation are considered in [1]. The stability of one of the solutions, which corresponds to the pulsations of uniform gravitating spheres, was studied in paper [2]. The stability of the other solutions (gas motions in the absence of Newtonian gravitation, nonperiodic motions of gravitating gas) has not previously been investigated. The stability of such solutions is investigated in this paper and it is shown that the motions in which gas compression occurs are, as a rule, unstable.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 120–127, November–December, 1985.     

Highest-weight representations ofsl(2, ℂ) andsl(3, ℂ) via canonical realizations

The infinite-dimensional representations of thesl(n+1, ) Lie algebras (maximal representations) constructed in our previous paper are studied on the two simplest examplesn = 1,2. The sufficient condition for irreducibility of the maximal representations is proved to be also necessary in these cases. It is further shown, that our method allows us to construct other set of infinite-dimensional highest-weight representations ofsl(3, ), so calledmixed representations which are irreducible in some cases when the maximal as well as the standard highest-weight representations (Verma modules) are reducible.Dedicated to the 25th anniversary of the Joint Institute for Nuclear Research.The authors are grateful to Prof. A. A. Kirillov, Dr. A. U. Klimyk, Dr. W. Lassner and Prof. D. P. Zhelobenko for stimulating discussions.     

One-dimensional unsteady motions of a viscous heat-conducting gas with a linear velocity distribution with respect to the coordinate

The one-dimensional motions of a perfect gas are considered in cases of spherical, cylindrical and plane symmetry, when the velocity is proportional to the distance to the center of symmetry. The solutions obtained are an extension of the known solutions of Sedov [1, 2] to the case of a viscous heat-conducting gas with a power-law temperature dependence of the coefficient of viscosity and thermal conductivity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 130–133, March–April, 1987.The author is grateful to L. I. Sedov for his interest in the work and to A. G. Kulikovskii for useful discussions.     

A class of solutions of the boundary layer equations

Exact solutions of the boundary layer equations can be obtained in closed form only in rare cases. These generally involve self-similar solutions for which the corresponding ordinary differential equation can be integrated exactly. In this paper solutions of more general form, containing additive functions of the longitudinal x coordinate in the expression's for the stream function and the self-similar variable, are considered in relation to two-dimensional steady boundary layers. This makes it possible to enlarge the class of problems whose solutions are analytic expressions and in a number of cases can be obtained in the form of expressions containing arbitrary functions of x, which makes possible various interpretations of the solution. In order to introduce arbitrary functions into the solutions of the equations of the axisymmetric boundary layer the problem is reduced to an overdetermined system of ordinary differential equations. This method is also capable of being applied more widely.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 45–51, March–April, 1990.     

Developments in studio design

The acoustic characteristics of studios have always been of even greater importance than the characteristics of live auditoria because the listener is divorced from the visual cues which can aid concentration and the direction of attention. Background noise acquires a much enhanced ability to mask the desired sounds, while imbalances in the frequency response can create unnatural sensations and the acoustic perspective created may even conflict with the general aim of the programme.Probably because of the early appreciation of the requirements of acoustic design, dramatic changes in recent years have not been necessary and the emphasis has rested more on the economic provision of acceptable conditions in small spaces.