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255 results on '"Ostrovsky L"'

4. Monadic second-order properties of very sparse random graphs

Author

Ostrovsky, L. B. and Zhukovskii, M. E.

Subjects
Mathematics - Combinatorics
Abstract

We study asymptotical probabilities of first order and monadic second order properties of Erdos-Renyi random graph G(n,n^{-a}). The random graph obeys FO (MSO) zero-one k-law if for any first order (monadic second order) formulae it is true for G(n,n^{-a}) with probability tending to 0 or to 1. Zero-one k-laws are well studied only for the first order language and a < 1. We obtain new zero-one k-laws (both for first order and monadic second order languages) when a > 1. Proofs of these results are based on the existed study of first order equivalence classes and our study of monadic second order equivalence classes. The respective results are of interest by themselves.

Published
2016

6. Localized wave structures: Solitons and beyond.

Author

Ostrovsky, L., Pelinovsky, E., Shrira, V., and Stepanyants, Y.

Subjects
*SHEAR flow, *SOLITONS, *STRUCTURAL analysis (Engineering), *NONLINEAR theories, *ROGUE waves
Abstract

The review is concerned with solitary waves and other localized structures in the systems described by a variety of generalizations of the Korteweg–de Vries (KdV) equation. Among the topics we focus upon are "radiating solitons," the generic structures made of soliton-like pulses, and oscillating tails. We also review the properties of solitary waves in the generalized KdV equations with the modular and "sublinear" nonlinearities. Such equations have an interesting class of solutions, called compactons, solitary waves defined on a finite spatial interval. Both the properties of single solitons and the interactions between them are discussed. We show that even minor non-elastic effects in the soliton–soliton collisions can accumulate and result in a qualitatively different asymptotic behavior. A statistical description of soliton ensembles ("soliton gas"), which emerges as a major theme, has been discussed for several models. We briefly outline the recent progress in studies of ring solitons and lumps within the framework of the cylindrical KdV equation and its two-dimensional extension. Ring solitons and lumps (2D solitons) are of particular interest since they have many features in common with classical solitons and yet are qualitatively different. Particular attention is paid to interactions between the objects of different geometries, such as the interaction of ring solitons and shear flows, ring solitons and lumps, and lumps and line solitons. We conclude our review with views of the future developments of the selected lines of studies of localized wave structures in the theory of weakly nonlinear, weakly dispersive waves. [ABSTRACT FROM AUTHOR]

Published
2024
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7. Boundedness of Operators in Bilateral Grand Bebesgue Spaces with Exact and Weakly Exact Constant Calculation

Author

Sirota, E. Ostrovsky L.

Subjects
Mathematics - Functional Analysis
Abstract

In this article we investigate an action of some operators (not necessary to be linear or sublinear) in the so-called (Bilateral) Grand Lebesgue Spaces (GLS), in particular, double weight Fourier operators, maximal operators, imbedding operators etc. We intend to calculate an exact or at least weak exact values for correspondent imbedding constant. We obtain also interpolation theorems for GLS spaces.We construct several examples to show the exactness of offered estimations. In two last sections we introduce anisotropic Grand Lebesgue Spaces, obtain some estimates for Fourier two-weight inequalities and calculate Boyd's multidimensional indices for this spaces.

Published
2011

8. Adaptive optimal regularization of the linear ill posed integral equations

Author

Sirota, E. Ostrovsky L.

Subjects
Mathematics - Numerical Analysis, Mathematics - Statistics Theory
Abstract

We construct an adaptive asymptotically optimal in order in the $ L(2) $ sense a solution (estimation) of an integral linear equation of a first kind and energy of this solution with the confidence region building, also adaptive.

Published
2010

29. Professor Valerian Ill’ich Tatarskii – an appreciation

Author

Brown, G., primary, Charnotskii, M., additional, Churnside, J., additional, Ishimaru, A., additional, Freilikher, V., additional, Fuks, I., additional, Hill, R., additional, Irisov, V., additional, Kravtsov, Y., additional, Lataitis, R., additional, Mudaliar, S., additional, Ostashev, V., additional, Ostrovsky, L., additional, Rino, C., additional, Voronovich, A., additional, and Zavorotny, Valery, additional

Published
2019
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34. Professor Valerian Ill'ich Tatarskii – an appreciation.

Author

Brown, G., Charnotskii, M., Churnside, J., Ishimaru, A., Freilikher, V., Fuks, I., Hill, R., Irisov, V., Kravtsov, Y., Lataitis, R., Mudaliar, S., Ostashev, V., Ostrovsky, L., Rino, C., Voronovich, A., and Zavorotny, Valery

Subjects
ACADEMIC achievement, SCIENCE, COLLEGE teachers, THEORY of wave motion, PHYSICAL sciences, PHYSICISTS
Abstract

On October 13, 2019 is the ninetieth birthday of the renowned physicist Professor Valerian I. Tatarskii. He is one of the founders of the international journal Waves in Random and Complex Media and its Associate Editor from 1991 to 1998. Outstanding seminal works of Professor V. I. Tatarskii made a global impact on physical science. The article describes main milestones of his life in science and his achievements in the theory of wave propagation in random media. [ABSTRACT FROM AUTHOR]

Published
2020
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