Estimating the Scale Parameter of a Lévy-stable Distribution via the Extreme Value Approach

The characteristic exponent α of a Lévy-stable law S _α (σ, β, μ) was thoroughly studied as the extreme value index of a heavy tailed distribution. For 1 < α < 2, Peng (Statist. Probab. Lett. 52: 255–264, 2001) has proposed, via the extreme value approach, an asymptotically normal estimator for the location parameter μ. In this paper, we derive by the same approach, an estimator for the scale parameter σ and we discuss its limiting behavior.      

Microlocal analysis of seismic inverse scattering in anisotropic elastic media

Seismic data is modeled in the high‐frequency approximation, using the techniques of microlocal analysis. We consider general, anisotropic elastic media. Our methods are designed to allow for the formation of caustics. The data is modeled in two ways. First, we give a microlocal treatment of the Kirchhoff approximation, where the medium is assumed to be piecewise smooth, and reflection and transmission occur at interfaces. Second, we give a refined view on the Born approximation based upon a linearization of the scattering process in the medium parameters around a smooth background medium. The joint formulation of Born and Kirchhoff scattering allows us to take into account general scatterers as well as the nonlinear dependence of reflection coefficients on the medium parameters. The latter allows the treatment of scattering up to grazing angles. The outcome of the analysis is a characterization of the singular part of seismic data. We obtain a set of pseudodifferential operators that annihilate the data. In the process we construct a Fourier integral operator and a reflectivity function such that the data can be represented by this operator acting on the reflectivity function. In our construction this Fourier integral operator becomes invertible. We give the conditions for invertibility for general acquisition geometry. The result is also of interest for inverse scattering in acoustic media. © 2002 John Wiley & Sons, Inc.     

Zinc-Containing Polymers and Their Latexes: Structure and Properties

This work deals with the polymer latexes synthesized using zinc-containing monomers. The effect of the ligand environment of the zinc-containing monomers on the colloidal and rheological properties of the latexes, as well as on mechanical properties of their films is studied. Mixed zinc salts containing the residues of saturated and unsaturated carboxylic acids are shown to be more efficient cross-linking agents than the symmetric salts of this metal.     

Complex backflow dynamics in nematic liquid crystals

Received December 31, 2001 / Published online May 21, 2002     

On Pairs of Diagonal Quintic Forms

We demonstrate that a pair of additive quintic equations in at least 34 variables has a nontrivial integral solution, subject only to an 11-adic solubility hypothesis. This is achieved by an application of the Hardy–Littlewood method, for which we require a sharp estimate for a 33.998th moment of quintic exponential sums. We are able to employ p-adic iteration in a form that allows the estimation of such a mean value over a complete unit square, thereby providing an approach that is technically simpler than those of previous workers and flexible enough to be applied to related problems.     

Hierarchical models of unified theories

A modernized conception of hierarchical structure of reality is proposed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 3–6, December, 1980.