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41.
E.R. Liflyand A.G. Ramm A.I. Zaslavsky 《Journal of Fourier Analysis and Applications》1995,2(3):287-301
Estimates from below for the norms of linear means of multiple Fourier series are obtained. These means are given by some
function λ and generalize the well-known Bochner-Riesz means. Sharpness of these estimates is established. The assumptions
on λ are rather weak and of local character. Our results contain as particular
cases a number of earlier published results. Proofs are based on the authors' new results on asymptotics of the Fourier transform
of piecewise-smooth functions. Some applications of the results obtained are given, namely, orders of growth of the Lebesgue
constants for "ovals" and "hyperbolic crosses" are evaluated and sharp conditions on the modulus of smoothness of a function
are given, for this function to be approximated by the linear means. 相似文献
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Ray dynamics in waveguide media exhibits chaotic motion. For a finite length of propagation, the large distance asymptotics is not uniform and represents a complicated combination of bunches of rays with different intermediate asymptotics. The origin of the phenomena that we call "chaotic transmission," lies in the nonuniformity of the phase space with sticky domains near the boundary of islands. We demonstrate different fractal properties of ray propagation using underwater acoustics as an example. The phenomenon of the kind of Levy flights can occur and it can be used as a mechanism of cooling of signals when the width of spatial spectra dispersion is significantly reduced. (c) 1997 American Institute of Physics. 相似文献
45.
Abubakirov E. B. Vikharev A. A. Ginzburg N. S. Denisenko A.N. Zaslavsky V.Yu. Krapivnitskaya T. O. Kuzikov S. V. Peskov N. Yu. Savilov A.V. 《Radiophysics and Quantum Electronics》2019,62(7-8):520-527
Radiophysics and Quantum Electronics - The concept of Compton-type free-electron lasers (FELs) operating in short wavelength ranges with a high efficiency and power level is currently underway at... 相似文献
46.
Acoustical Physics - A finite element method is used for three-dimensional numerical simulation of hydro- and seismoacoustic waves in shallow water, generated by harmonically oscillating sources.... 相似文献
47.
Mock threshold graphs are a simple generalization of threshold graphs that, like threshold graphs, are perfect graphs. Our main theorem is a characterization of mock threshold graphs by forbidden induced subgraphs. Other theorems characterize mock threshold graphs that are claw-free and that are line graphs. We also discuss relations with chordality and well-quasi-ordering as well as algorithmic aspects. 相似文献
48.
Zaslavsky GM 《Chaos (Woodbury, N.Y.)》1994,4(3):589-591
Exponentially small splitting of the separatrix has been calculated for a high frequency large amplitude perturbation and the correspondent correction to the width of the stochastic layer is obtained. The result can be applied to the large amplitude perturbation. 相似文献
49.
We study how the chaotic ray motion manifests itself at a finite wavelength at long-range sound propagation in the ocean. The problem is investigated using a model of an underwater acoustic waveguide with a periodic range dependence. It is assumed that the sound propagation is governed by the parabolic equation, similar to the Schrodinger equation. When investigating the sound energy distribution in the time-depth plane, it has been found that the coexistence of chaotic and regular rays can cause a "focusing" of acoustic energy within a small temporal interval. It has been shown that this effect is a manifestation of the so-called stickiness, that is, the presence of such parts of the chaotic trajectory where the latter exhibit an almost regular behavior. Another issue considered in this paper is the range variation of the modal structure of the wave field. In a numerical simulation, it has been shown that the energy distribution over normal modes exhibits surprising periodicity. This occurs even for a mode formed by contributions from predominantly chaotic rays. The phenomenon is interpreted from the viewpoint of mode-medium resonance. For some modes, the following effect has been observed. Although an initially excited mode due to scattering at the inhomogeneity breaks up into a group of modes its amplitude at some range points almost restores the starting value. At these ranges, almost all acoustic energy gathers again in the initial mode and the coarse-grained Wigner function concentrates within a comparatively small area of the phase plane. 相似文献
50.