Cauchy problem and averaging in Fock space

We investigate a Cauchy problem in the Fock space for a system consisting of a two-level atom, a quantum field, and a classical field. A solution estimate is obtained for the Cauchy problem with initial data from a special class. This class is invariant with respect to the dynamic semigroup of the system. We propose an averaging method for solving the Cauchy problem in the case where the Hamiltonian parameters differ greatly in the order of magnitude. An estimate of the averaging error is obtained. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 1, pp. 92–106, October, 1998.     

Photodiffraction in InGaAs/InGaAsP multiple quantum wells enclosed in a microcavity

We report new results on the diffraction properties of photoinduced gratings in InGaAs/InGaAsP MQW structures. The original feature of this device is that the QWs are enclosed in an asymmetric Fabry–Perot microcavity in order to increase the diffraction efficiency. We observe oscillations in the diffraction efficiency due to resonant effects in the microcavity. The experimental spectra are compared with theory. Diffraction efficiency at 1.55 μm attains a maximum value of 2.7% at a write beam fluence of 260 μ J cm⁻², and then decreases at higher fluences. We explain this phenomenon by an absorption saturation at high excitation.     

Roughness of layer interfaces and phase diagram of magnetic multilayer structures

The dependence of the type of magnetic ordering in multilayer structures on the magnitude of the exchange interaction between the magnetic layers and on the degree of roughness of the interfaces between the layers is investigated. In the case of a three-layer system the regions of existence of the domain structure, of noncollinear ordering of the homogeneous magnetic layers, and of the collinear ferromagnetic phase and collinear antiferromagnetic phase are found. Fiz. Tverd. Tela (St. Petersburg) 39, 1244–1247 (July 1997)     

The Modeling of Velocity Enhancement in Polymer Flooding

In single-phase polymer flooding experiments it has repeatedly been observed that the average velocity of the polymer molecules is higher than the average velocity of the water molecules. This effect is incorporated in many conventional Enhanced Oil Recovery (EOR) simulators by the introduction of a constant velocity enhancement factor. In this paper we show that, in absence of dispersion, a constant enhancement factor in the mathematical model for two-phase polymer flow (Buckley--Leverett displacement) leads to ill-posedness of the model equations. We propose a saturation dependent enhancement factor, derived from a model based on percolation concepts, for which this problem does not occur.     

Free Groups from Fields

In the nineteenth century, field theory brilliantly resolveda number of questions that had taxed mathematicians for centuries;for example, ‘The circle cannot be squared’ by straightedge and compass, and solving polynomial equations by radicalsis not always possible. These successes have continued to beheld up as superb examples of the power of mathematical thought,and are demonstrated at an undergraduate level. The purposeof this article is to provide another such natural example whichleads to a concrete realisation of the free group on 2 generators.     

New method for the synthesis of 6-amino-4-aryl-3,5-dicyano-3,4-dihydropyridine-2(1H)-thiones by recyclization of 4-aryl-2,6-diamino-4H-thiopyranes

Ammonium 6-amino-4-aryl-3,5-dicyano-1,4-dihydropyridine-2-thiolates were synthesized by recyclization of 4-aryl-2,6-diamino-3,5-dicyano-4H-thiopyranes in the presence of organic bases. On acidification of the products, the corresponding substituted 3,4-dihydropyridine-2(1H)-thiones were obtained which were used in the synthesis of 2-alkylthio-1,4-dihydropyridines, bis-(pyridyl-2)disulfides and thieno[2,3-b]pyridines.Deceased.T. G. Shevchenko Lugansk State Pedagogical Institute, Lugansk 348011. N. D. Zelinskii Institute of Organic Chemistry, Russian Academy of Sciences, Moscow 117913. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, pp. 909–914, July, 1997.     

Reaction of 3,5-diamino-4-nitropyrazole with electrophilic reagents

The interaction of 3,5-diamino-4-nitropyrazole with such electrophilic reagents as acetic anhydride, dimethylformamide acetal, orthoformic ester, and ketones has been studied. Derivatives of pyrazolol[1,5-a]pyrimidines were formed on reaction with 1,3-diketones and some of their properties have been studied.Center for Drug Chemistry, All-Russian Chemical and Pharmaceutical Research Institute (VNIKhFI), Moscow 119815. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 329–335, March, 1997.     

An application of radon inversion to diffraction tomography

Basic equations of linear computer tomography are considered; a connection of the mathermatical formulation of problems of computer tomography with problems of integral geometry is indicated; the properties of the Radon transform for even- and odd-dimensional spaces are analyzed, and applications of Radon inversion to problems of diffraction tomography are presented. Bibliography: 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 230, 1995, pp. 264–277. Translated by V. N. Troyan.