St. Petersburg State University of Aerospace Instrumentation

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Saint Petersburg, Russia
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Kazakov A.Y.,St. Petersburg State University of Aerospace Instrumentation
Proceedings of the International Conference Days on Diffraction, DD 2016 | Year: 2016

Elementary, gauge and Laplace integral symmetries of confluent Heun equation with single added apparent singularity are under consideration. Symmetries from this collection connect solutions of the same equation with different set of parameters. The derivation of these symmetries is based on usage of corresponding generating systems of the first-order equations, whose reduction to the scalar equation coincides with confluent Heun equation with single added apparent singularity. These symmetries can be expressed in terms of the monodromy group of this equation. © 2016 IEEE.


Balonishnikov A.M.,St. Petersburg State University of Aerospace Instrumentation
Technical Physics | Year: 2016

Based on the semi-empirical model of the transport of the specific rate of turbulence energy dissipation, it has been concluded that the resistance laws are observed for a turbulent Taylor–Couette flow between independently rotating coaxial cylinders for very large Taylor numbers. © 2016, 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.


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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