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  • 1.
    Lagovsky, Boris
    et al.
    Russian Technological University MIREA.
    Samokhin, Alexander
    Russian Technological University MIREA.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Angular superresolution based on a priori information2021In: Radio Science, ISSN 0048-6604, E-ISSN 1944-799X, Vol. 56, no 3, article id e2020RS007100Article in journal (Refereed)
    Abstract [en]

    The results of theoretical studies and mathematical modeling indicate the possibility of obtaining the angular superresolution and its limits by using algebraic methods of imaging. The necessary algorithms are created on the basis of solution to inverse problems. The limiting levels of the achieved angular superresolution are found depending on the signal‐to‐noise ratio for objects of various types. A number of specific advantages of the method are shown as applied to the solution of two‐dimensional problems. Capabilities of the method are illustrated by examples. High performance of the proposed approach allows one to use it in real time when scanning and tracking targets.

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  • 2.
    Podlipenko, Yu K.
    et al.
    Faculty of Cybernetics, Taras Shevchenko National University of Kyiv, Kiev, Ukraine.
    Shestopalov, Yury V.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Guaranteed estimation of solutions to Helmholtz transmission problems with uncertain data from their indirect noisy observations2017In: Radio Science, ISSN 0048-6604, E-ISSN 1944-799X, Vol. 52, no 9, p. 1129-1139Article in journal (Refereed)
    Abstract [en]

    We investigate the guaranteed estimation problem of linear functionals from solutions to transmission problems for the Helmholtz equation with inexact data. The right-hand sides of equations entering the statements of transmission problems and the statistical characteristics of observation errors are supposed to be unknown and belonging to certain sets. It is shown that the optimal linear mean square estimates of the above mentioned functionals and estimation errors are expressed via solutions to the systems of transmission problems of the special type. The results and techniques can be applied in the analysis and estimation of solution to forward and inverse electromagnetic and acoustic problems with uncertain data that arise in mathematical models of the wave diffraction on transparent bodies.

  • 3.
    Sheina, Elena
    et al.
    Lomonosov Moscow State University, Russia.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Smirnov, Alexander
    Lomonosov Moscow State University, Russia.
    Advantages of a multi-frequency experiment for determining the dielectric constant of a layer in a rectangular waveguide and free space2021In: Radio Science, ISSN 0048-6604, E-ISSN 1944-799X, Vol. 56, no 3, article id e2020RS007115Article in journal (Refereed)
    Abstract [en]

    An inverse problem of reconstructing real permittivity of a plane‐parallel layer in a perfectly conducting rectangular waveguide or in free space from experimental data using an explicit expression for the scattering matrix is considered. In general, this problem is improperly posed and may be unsolvable due to inaccuracy of the experimental data, and for a perfect noiseless experiment the solution may be not unique because the scattering coefficients curve has self‐intersection points. It is shown that the traditional multi‐frequency method of measurements applied in vector network analyzers can be justified. The following facts are rigorously proved in the paper: nonuniqueness of the solution can be removed if the frequency resolution is sufficiently small; and an algorithm for processing measurement results using least squares provides an approximate solution to the problem that converges to the exact one when the quality of the experiment improves, the convergence rate depends on the number of frequencies used in the experiment.

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  • 4.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Resonance scattering by a circular dielectric cylinder2021In: Radio Science, ISSN 0048-6604, E-ISSN 1944-799X, Vol. 56, no 6, article id e2020RS007095Article in journal (Refereed)
    Abstract [en]

    A unified approach is developed for the analysis of singularities of the scattered field and vanishing of scattering harmonics. Rigorous proofs are presented of the existence of complex resonance singularities of the solution to the problem of the plane wave scattering by a circular homogeneous dielectric cylinder. The method employs a mathematically correct approach of the spectral theory of open structures involving generalized conditions at infinity when complex resonance frequencies may be considered. The result is obtained by verifying the existence of complex singularities of the series solution coefficients considered as functions of the problem parameters. The recently developed theory of generalized cylindrical polynomials (GCPs) is used that enables one to reduce determination of singularities (resonances) to finding zeros (real or complex) of a particular subfamily of GCPs.

     

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  • 5.
    Smirnov, Yuri
    et al.
    Department of Mathematics and Supercomputing, Penza State University, Russian Federation.
    Smolkin, Eugene
    Department of Mathematics and Supercomputing, Penza State University, Russian Federation.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Diffraction of a TE-Polarized Wave by a Nonlinear Goubau Line2019In: Radio Science, ISSN 0048-6604, E-ISSN 1944-799X, Vol. 54, no 1, p. 151-157Article in journal (Refereed)
    Abstract [en]

    The diffraction of a cylindrical wave by a nonlinear metal-dielectric waveguide filled with nonlinear medium is considered. Two widely used types of nonlinearities (Kerr nonlinearity and nonlinearity with saturation) are considered. The problem is to find amplitudes of the reflected and the transmitted fields when the amplitude of the incident field is known. The analytical and numerical solution techniques are developed. Numerical results are presented. ©2019. American Geophysical Union. All Rights Reserved.

  • 6.
    Smolkin, Eugen
    et al.
    Penza State University, Russia.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Snegur, Maxim
    Penza State University, Russia.
    Surface waves in a nonlinear metamaterial rod2020In: Radio Science, ISSN 0048-6604, E-ISSN 1944-799X, Vol. 55, no 10, p. 1-8, article id e2020RS007101Article in journal (Refereed)
    Abstract [en]

    We consider propagation of surface TE waves in a rod filled with nonlinear metamaterial medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green function of an auxiliary boundary value problem on an interval. The existence of propagating nonlinear surface TE waves for the chosen nonlinearity (Kerr law) is proved using the method of contraction. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. New propagation regimes are discovered.

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