Surface grating formation and erasing on a-Se films

Surface relief formation at holographic recording on amorphous selenium films was demonstrated and investigated. The presence of this optical phase modulation component is essential for ensuring significant, stable and erasable optical recording in a-Se films at 290–320 K temperatures, where conventional photodarkening was known as insignificant and unstable. Photocrystallization can only be observed in super-exposed a-Se films at the given experimental conditions of hologram recording. Erasing behavior of surface relief gratings under heat treatment was also investigated in order to reveal further details of the mechanism. Photoinduced structural transformations within the amorphous phase, connected to local ordering under the condition of light-induced fluidity, are proposed as an explanation for the relief formation and erasing. The observed reversible optical recording process may be useful for the various optoelectronic applications of photoconductive a-Se layers. Received: 12 June 2000 / Accepted: 6 June 2001 / Published online: 30 August 2001     

Reducing systems of linear differential equations to a passive form

In this paper, an application of the Riquer-Thomas-Janet theory is described for the problem of transforming a system of partial differential equations into a passive form, i.e., to a special form which contains explicitly both the equations of the initial system and all their nontrivial differential consequences. This special representation of a system markedly facilitates the subsequent integration of the corresponding differential equations. In this paper, the modern approach to the indicated problem is presented. This is the approach adopted in the Knuth-Bendix procedure [13] for critical-pair/completion and then Buchberger's algorithm for completion of polynomial ideal bases [13] (or, alternatively, for the construction of Groebner bases for ideals in a differential operator ring [14]). The algorithm of reduction to the passive form for linear system of partial differential equations and its implementation in the algorithmic language REFAL, as well as the capabilities of the corresponding program, are outlined. Examples illustrating the power and efficiency of the system are presented.     

A statistical approach to the solution of ill-posed problems in geophysics

The article surveys the main results of the statistical approach to the solution of ill-posed problems of mathematical physics, in application to specific ill-posed inverse problems in geophysics.Invited paper presented at the International Seminar on Mathematical Foundations of the Interpretation of Geophysical Fields, Moscow, May–June 1972.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 79, pp. 67–81, 1978.     

Organotellurides as a source of organometallics: application in the synthesis of (+/−)-frontalin

A masked lithium homoenolate, generated by tellurium/lithium exchange, was reacted with epoxides. The lithium compound was also converted into other organometallics such as Grignard, and cuprates and the reactivity of those organometallics with epoxides was evaluated. The same building block was employed in the synthesis of (+/−)-frontalin.     

Isotopic families of contact manifolds for elliptic PDE

A test for a function to be a solution of an elliptic PDE is given in terms of extensions, as solutions, from the boundaries inside the domains belonging to an isotopic family. It generalizes a result of Ehrenpreis for spheres moved along a straight line.

     

Mass Power Spectrum in a Universe Dominated by the Chaplygin Gas

The mass power spectrum for a Universe dominated by the Chaplygin gas is evaluated numerically from scales of the order of the Hubble horizon to 100 Mpc. The results are compared with a pure baryonic Universe and a cosmological constant model. In all three cases, the spectrum increases with k, the wavenumber of the perturbations. The slope of the spectrum is higher for the baryonic model and smaller for the cosmological constant model, the Chaplygin gas interpolating these two models. The results are analyzed in terms of the sound velocity of the Chaplygin gas and the moment the Universe begins to accelerate.     

Deformation Quantization for Systems with Fermions

Deformation quantization, which achieves the passage from classical mechanics to quantum mechanics by the replacement of the pointwise multiplication of functions on phase space by the star product, is a powerful tool for treating systems involving bosonic degrees of freedom, both in quantum mechanics and in quantum field theory. In the present paper we show how these methods may be naturally extended to systems involving fermions. In particular we show how supersymmetric quantum mechanics can be formulated in this approach and consider examples involving both non-relativistic and relativistic systems.