Stability criteria for controlled queueing systems

We give an almost complete classification of ergodicity and transience conditions for a general multi-queue system with the following features: arrivals form Poisson streams and there are various routing schemes for allocating arrivals to queues; the servers can be configured in a variety of ways; completed jobs can feed back into the system; the exponential service times and feedback probabilities depend upon the configuration of the servers (this model includes some types of multi-class queueing system); switching between service regimes is instantaneous. Several different levels of control of the service regimes are considered. Our results for the N-queue system require randomisation of service configurations but we have studied the two queue system in situations where there is less control. We use the semi-martingale methods described in Fayolle, Malyshev and Menshikov [3] and our results generalise Kurkova [8] and complement Foley and McDonald [4] and [5]. AMS 2000 subject classification: Primary: 90B22; Secondary: 60J10 90B15     

A generalized square of the zeta function. Spectral decompositions

The spectral decomposition for the square of the classical Riemann zeta function ζ²(s) is generalized to the case of the product of two such functions ζ(s₁) · ζ(s₂) of different arguments. Bibliography: 6 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 322, 2005, pp. 17–44.     

Numerical Analysis and Simulation Analysis for Space‐Time Data

Spatio temporal dynamics of the positive column of a dc neon glow discharge is studied and investigated experimentally and theoretically. Spatio temporal analysis by means of biorthogonal decomposition method (BOD) gives insights into the mechanism of irregularity and can be employed for characterization of spatio‐ temporal complexity. In the weak nonlinear region, the wave dynamics is approximated by an amplitude equation of the Ginzburg‐Landau equation (CGLE) with complex coefficients and an additional integral term based on a fluid model. In the present work we deal with irregular spatio‐temporal data. A comparison between the numerical analysis of the experimental data and simulation results are studied. A good agreement between the dynamical behaviour for experimental space‐time data and theoretical simulation space‐time results was obtained. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Low-Frequency Parasitic Space-Charge Oscillations in the Helical Electron Beam of a Gyrotron

We developed a medium-power pulsed gyrotron equipped with diagnostic systems for studying low-frequency parasitic space-charge oscillations in the helical electron beam and the energy spectrum of electrons in the collector region. Methods for suppressing parasitic oscillations are proposed and tested. An explanation of the mechanism of suppression of these oscillations is given.     

On Computability of Decaying and Nondecaying States in Quantum Systems with Cantor Spectra

We study Hamiltonians with singular spectra of Cantor type with a constant ratio of dissection. The decay properties of the states in such systems depend on the nature of the dissection rate that can be characterized in terms of the algebraic number theory. We show that in spite of simplicity of the considered model the computational modeling of nondecaying states is in general impossible.     

Compatible Dubrovin–Novikov Hamiltonian Operators,Lie Derivative,and Integrable Systems of Hydrodynamic Type [Erratum]

Correction to the paper published in Vol. 133, No. 2, November, 2002.     

Coherent backscattering of light from saturated atoms

We survey recent progress achieved in understanding the impact of inelastic processes on coherent backscattering of light from cold atoms that are saturated by a powerful laser field.