Quantum system level-band in a strong quasiresonant field with a deep modulation

The dynamics of a level-band quantum system in a strong external quasiresonant laser field with a deep modulation is discussed. It is assumed that the amplitude of the external field considerably exceeds the width of the band. The related Schrödinger equation is reduced to a singular integro-differential equation with a large parameter. Using appropriate asymptotic techniques, the decay of the level population is examined. Bibliography: 12 titles.     

Finite basis for analytic strong n-gaps

We identify the finite list of minimal analytic n-gaps which are not weakly countably separated, and we prove that every analytic n-gap which is not countably separated contains a gap from our finite list     

Quantum corrections to the conductivity of a two-dimensional disordered system in a strong magnetic field

A system of noninteracting electrons moving in a magnetic field and a field of randomly distributed impurities is considered. An exact expression is obtained for the sum of the series of maximally crossed diagrams; it is valid in an arbitrary magnetic field. It is shown that in the two-dimensional case the relative magnitude of the corrections to the conductivity due to this series reaches 60% in the center of the lower Landau sub-band.Physicotechnical Institute of the Urals Branch of the Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 3, pp. 486–495, March, 1993.     

A strong mixing condition for a homogeneous random field

For a homogeneous random field , one obtains a sufficient condition in order to have the relation.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 130, pp. 167–174, 1983.In conclusion, I express my gratitude to I. A. Ibragimov for his help in the preparation of this paper.     

A basis for the Stickelberger ideal and the system of circular units of a cyclotomic field

A basis for the Stickelberger ideal is constructed, along with a system of independent units that, together with-, where =exp(2i/m), m 2, m 2 (mod 4), generate the group of circular units of the field Q(). As an application, it is possible to obtain a representation for the first and second factors of a number of classes of divisors of the field Q() in the form of determinants.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 175, pp. 69–74, 1989.     

Nonequilibrium state of a ferroelectric in a strong magnetic field

Vitebsk Branch of the Institute of Solid-State Physics and Semiconductors, Belorussian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 78, No. 1, pp. 147–153, January, 1989.     

QED2+1 radiation effects in a strong magnetic field

We develop the eigenfunction method for the Dirac operator in a background magnetic field in the (2+1)-dimensional quantum electrodynamics (QED₂₊₁). In the eigenfunction repressentation, we find the exact solutions and the Green's functions of the Dirac equation in a strong constant homogeneous magnetic field in 2+1 dimensions. In the one-loop QED₂₊₁ approximation, we derive the effective Lagrangian, the density of vacuum fermions induced by the field, and the electron mass operator in a homogeneous background magnetic field. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 121, No. 3, pp. 412–423, December, 1999.     

On assigning drivers for a home-delivery system on a performance basis

Consider a firm providing home-delivery of small parcels within a short period of time. The paper proposes a method to estimate the productivity of each driver on any fictitious route using linear regressions. The method separates the trip time in terms of the time spent: with customers, driving, and all other activities. Our tests show that productivity, measured in terms of number of customers visited per hour, vary across drivers. Even more, the same driver’s productivity vary for peak and off-peak demand periods considerably. This methodology should enhance the reliability of the driver scheduling programs, since it reduces the error and bias of the productivity offered by the assigned set of drivers. It shall also improve the reliability of the delivery time promised to the customer.     

Magnetohydrodynamic free convection about a semi-infinite vertical plate in a strong cross field

Summary The magnetohydrodynamic free convection flow of an electrically conducting fluid past a semi-infinite plate in a strong cross-field has been examined. Formulation in terms of a characteristic length has enabled a full numerical solution to be obtained providing details of skin friction and heat transfer at all stations along the plate. An estimate of an indeterminacy in asymptotic solutions allows favourable comparison to be made between series solutions estimates of these quantities and their exact numerical values.

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Zusammenfassung Die magneto-hydrodynamische Strömung mit freier Konvektion in einer elektrisch leitenden Flüssigkeit entlang einer halbunendlichen Platte ist in einem starken Querfeld untersucht worden. Die Einführung einer charakteristischen Länge hat eine vollständige numerische Lösung ermöglicht, die die Reibungskraft und den Wärmeübergang entlang der Platte ergibt. Eine Abschätzung von einer Unbestimmtheit in den asymptotischen Lösungen erlaubt einen Vergleich zwischen den durch Reihelösungen erhaltenen Werten dieser Grössen und ihren exakten numerischen Werten.