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     

Some remarks on metaplectic cusp forms and the correspondences of Shimura and Waldspurger

The simple relation between representations of the covering groups of SL₂ and GL₂ makes it possible to fuse and extend the recent metaplectic results of Shimura, Waldspurger, Flicker, and ourselves. By giving a new (purely local andL-function theoretic) treatment of the Waldspurger-Shintani correspondence, we also simplify some of Waldspurger’s original results.     

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.     

Existence and Stability for Spherical Crystals Growing in a Supersaturated Solution

We consider the growth of a spherical crystal in a supersaturatedsolution. In the first part, existence and uniqueness resultsfor radially symmetric growth are obtained, provided that thesupersaturation is not too large; conversely, when the far-fieldsupersaturation exceeds a critical value, it is shown that theradially symmetric solution ceases to exist in finite time.In the second part, we examine the linear stability of a radiallysymmetric similarity solution (in which the radius grows ast?) to shape perturbations. The results are compared with previousquasi-static analyses, and, in particular, the critical radiusat which the crystal becomes unstable is found to be largerfor small supersaturations, but smaller for large supersaturations,than those predicted by the quasi-static analysis