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Farafonov V.G.,St. Petersburg State University of Aerospace Instrumentation | Ustimov V.I.,St. Petersburg State University of Aerospace Instrumentation
Optics and Spectroscopy (English translation of Optika i Spektroskopiya) | Year: 2017

In the problem of light scattering by small axisymmetric particles, we have constructed the Rayleigh approximation in which the polarizability of particles is determined by the generalized separation of variables method (GSVM). In this case, electric-field strengths are gradients of scalar potentials, which are represented as expansions in term of eigenfunctions of the Laplace operator in the spherical coordinate system. By virtue of the fact that the separation of variables in the boundary conditions is incomplete, the initial problem is reduced to infinite systems of linear algebraic equations (ISLAEs) with respect to unknown expansion coefficients. We have examined the asymptotic behavior of ISLAE elements at large values of indices. It has been shown that the necessary condition of the solvability of the ISLAE coincides with the condition of correct application of the extended boundary conditions method (ЕВСМ). We have performed numerical calculations for Chebyshev particles with one maximum (also known as Pascal’s snails or limaçons of Pascal). The obtained numerical results for the asymptotics of ISLAE elements and for the matrix support theoretical inferences. We have shown that the scattering and absorption cross sections of examined particles can be calculated in a wide range of variation of parameters with an error of about 1–2% using the spheroidal model. This model is also applicable in the case in which the solvability condition of the ISLAE for nonconvex particles is violated; in this case, the SVM should be considered as an approximate method, which frequently ensures obtaining results with an error less than 0.1–0.5%. © 2017, Pleiades Publishing, Ltd.

Dubard P.,University of Burgundy | Matveev V.B.,University of Burgundy | Matveev V.B.,St. Petersburg State University of Aerospace Instrumentation
Nonlinearity | Year: 2013

Our discovery of multi-rogue wave (MRW) solutions in 2010 completely changed the viewpoint on the links between the theory of rogue waves and integrable systems, and helped explain many phenomena which were never understood before. It is enough to mention the famous Three Sister waves observed in oceans, the creation of a regular approach to studying higher Peregrine breathers, and the new understanding of 2 + 1 dimensional rogue waves via the NLS-KP correspondence. This article continues the study of the MRW solutions of the NLS equation and their links with the KP-I equation started in a previous series of articles (Dubard et al 2010 Eur. Phys. J. 185 247-58, Dubard and Matveev 2011 Natural Hazards Earth Syst. Sci. 11 667-72, Matveev and Dubard 2010 Proc. Int. Conf. FNP-2010 (Novgorod, St Petersburg) pp 100-101, Dubard 2010 PhD Thesis). In particular, it contains a discussion of the large parametric asymptotics of these solutions, which has never been studied before. © 2013 IOP Publishing Ltd & London Mathematical Society.

Il'in V.B.,Saint Petersburg State University | Farafonov V.G.,St. Petersburg State University of Aerospace Instrumentation
Optics Letters | Year: 2011

The Rayleigh approximation is known to be designed only for small ellipsoidal scatterers. We suggest an approach that allows one to find a simple, often analytical, long-wavelength approximation for nonellipsoidal particles. We apply the approach to axisymmetric scatterers and utilize Chebyshev particles to study the main properties of the obtained approximation. To a certain degree, it can be considered as an extension of the Rayleigh approximation to nonspheroidal scatterers. © 2011 Optical Society of America.

Fedorenko S.V.,St. Petersburg State University of Aerospace Instrumentation
IEEE Signal Processing Letters | Year: 2016

A novel method for computing the discrete Fourier transform (DFT) over a finite field based on the Goertzel-Blahut algorithm is described. The novel method is currently the best one for computing the DFT over even extensions of the characteristic two finite field, in terms of multiplicative complexity. © 2016 IEEE.

Sergeev A.M.,St. Petersburg State University of Aerospace Instrumentation
Automatic Control and Computer Sciences | Year: 2014

Properties of generalized Hadamard matrices and a conjecture on the existence of Mersenne matrices included into the former are discussed. A new classification of few-level quasi-orthogonal matrices, including matrices of even and odd orders, is presented. Matrices of Euler, Mersenne, and Hadamard are considered. The fundamental differences between the matrices of Mersenne and Fermat, which explain the failure of the proof of the Hadamard conjecture, are shown. © 2014 Allerton Press, Inc.

Blagoveshchenskii D.V.,St. Petersburg State University of Aerospace Instrumentation
Geomagnetism and Aeronomy | Year: 2013

The result of the effect of magnetospheric storms and substorms on the ionosphere (the so-called main effect) has been studied. The effect consists in that the critical frequency and altitude of the F region vary specifically during a disturbance. The critical frequency first increases before the storm (substorm) active phase, then decreases during the active phase, and increases again after this phase. On the contrary, the F region altitude increases during the active phase and decreases after this phase. An approach to the short-term (2-3 h) prediction of the development of storms (substorms) as the main disturbed space weather elements has been proposed. © 2013 Pleiades Publishing, Ltd.

Fedorenko S.V.,St. Petersburg State University of Aerospace Instrumentation
IEEE International Symposium on Information Theory - Proceedings | Year: 2011

A novel method for computation of the discrete Fourier transform over a finite field with reduced multiplicative complexity is described. The theorem about the multiplicative complexity coincidence of the Goertzel and cyclotomic algorithms is proved. © 2011 IEEE.

Kazakov V.I.,St. Petersburg State University of Aerospace Instrumentation
Proceedings of SPIE - The International Society for Optical Engineering | Year: 2016

Two-lens optical scheme as a system of the optical information processing and transmission is considered. On the basis of applying radio-optics methods, the theory of linear systems and system approach a mathematical model describing the transformation of the optical wave beam in this system is proposed. Input-output ratio of the system in the form of a general spatial impulse response of all linear units included in the system is established. The problem of energy losses of the optical radiation in such a system is considered. As the input and output of system of the single-mode optical fiber is used. The equations defining the minimum possible level of energy losses caused by the diffraction of beam is obtained. The analysis showed that the losses depend explicitly on several parameters: the radiation wavelength, the distance between the end of fiber and the aperture, and the ratio of the diameter of fiber and lens aperture. With the help of computer simulation in Matlab system the losses depending on the parameters mentioned above is presented. © 2016 SPIE.

Fedorenko S.V.,St. Petersburg State University of Aerospace Instrumentation
IEEE Transactions on Signal Processing | Year: 2015

A normalized cyclic convolution is a cyclic convolution when one of its factors is a fixed polynomial. Herein, a novel method for constructing a normalized cyclic convolution over a finite field is introduced. This novel method is the first constructive and best known method for even lengths. This method can be applied for computing discrete Fourier transforms over finite fields. © 2015 IEEE.

Smirnov A.O.,St. Petersburg State University of Aerospace Instrumentation
Theoretical and Mathematical Physics | Year: 2012

We construct a family of two-gap solutions of the focusing nonlinear Schrödinger equation and derive a condition under which the solutions behave as the so-called freak waves located at the nodes of a two-dimensional lattice. We also study how the lattice parameters depend on the parameters of the spectral curve. © 2012 Pleiades Publishing, Ltd.

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