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  • 51.
    Kushnin, R.
    et al.
    Riga Technical University, Latvia.
    Semenjako, J.
    Riga Technical University, Latvia.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Viduzs, A.
    Riga Technical University, Latvia.
    Two-Slab High Sensitivity Technique for Measurement of Permittivity of a Dielectric Slab in a Rectangular Waveguide2018Inngår i: 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 2018, s. 176-183Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In the present paper an approach to reduce uncertainty in the measurement of the dielectric constant of a rectangular dielectric slab situated in a rectangular waveguide is discussed. The experimental model under consideration consists of two rectangular full height and full width slabs located in an otherwise empty section of a rectangular waveguide. The dielectric constant of one of these slabs is to be measured, while the dielectric constant of the other slab is known (measured with high accuracy in advance). The slab with known constitutive properties is introduced for the purpose of altering the shape of the curve representing the relationship between the absolute value of the reflection coefficient and the dielectric constant to be measured, since curves having larger steepness in the neighborhood of the actual value of the dielectric constant result in smaller values of uncertainty. Although it is possible to change the shape of the curve by varying sample parameters, an increase in steepness obtained this way is not always sufficient. Furthermore, it is not always possible or convenient to alter dimensions of the sample under test and/or frequency. The results of the present study show that this issue can be overcome by extending the experimental model, i.e., by introducing an auxiliary dielectric slab with known constitutive properties. Additionally, it is shown that under certain conditions it is always possible to increase the steepness of the curve in the range of values in which the value of the dielectric constant is expected to fall, by varying the thickness of the auxiliary slab and distance between the slabs. The efficiency of the proposed approach is confirmed by results of numerical modeling.

  • 52. Kuzmina, E. A.
    et al.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Complex Waves in Multi-Layered Metal-Dielectric Waveguides2018Inngår i: Proceedings of the 2018 International Conference on Electromagnetics in Advanced Applications (ICEAA), 2018, s. 122-125, artikkel-id 8520457Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We consider normal waves in multi-layered dielectric rod and Goubau line that are basic types of open metal-dielectric waveguides. The dispersion equations are analyzed using the notion of generalized cylindrical polynomials and methods of calculating determinants of block-diagonal matrices. Sufficient conditions of the existence of symmetric waves are established.

  • 53.
    Kuzmina, E. A.
    et al.
    Institute of Information Technologies, Moscow Technological University (MIREA), 86 Vernadsky Avenue, Moscow, Russian Federation.
    Shestopalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Complex waves in a dielectric rod and goubau line2017Inngår i: 2017 International Conference on Electromagnetics in Advanced Applications (ICEAA), Institute of Electrical and Electronics Engineers Inc. , 2017, s. 963-966, artikkel-id 8065417Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Existence of complex TM and TE waves in a dielectric waveguide of circular cross section and a Goubau line is proved by analyzing functional properties of the dispersion equations (DEs) using the theory of functions of several complex variables and validating the existence of complex roots of DE. The method proceeds from the analysis of general setting involving hybrid nonsymmetric azimuthally dependent real and complex waves.

  • 54. Kuzmina, E.
    et al.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Higher-order surface modes in the Goubau line2014Inngår i: Progress in Electromagnetics Research Symposium, Electromagnetics Academy , 2014, s. 2605-2609Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Existence of the higher-order surface waves of the Goubau line is proved and their structure is analyzed. An efficient computational approach is proposed based on numerical solution to initial-value problems obtained by the parameter differentiation. Several applications and further research directions are discussed.

  • 55.
    Kuzmina, Ekaterina
    et al.
    Moscow Technical University MIREA, Moscow, Russia.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Symmetric surface complex waves in Goubau Line2018Inngår i: Cogent Engineering, ISSN 2331-1916, Vol. 5, nr 1, artikkel-id 1507083Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Existence of symmetric surface complex waves in a Goubau line—a perfectly conducting cylinder of circular cross-section covered by a concentric dielectric layer—is proved by constructing perturbation of the spectrum of symmetric real waves with respect to the imaginary part of the permittivity of the dielectric cover. Closed-form iteration procedures for calculating the roots of the dispersion equation (DE) in the complex domain supplied with efficient choice of initial approximation are developed. Numerical modeling is performed with the help of a parameter-differentiation method applied to the analytical and numerical solution of DEs.

  • 56.
    Kuzmina, Ekaterina
    et al.
    Moscow State Institute of Radio Engineering, Electronics and Automation, Technical University, Moscow, Russian Federation.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Waves in a lossy Goubau line2016Inngår i: 2016 10th European Conference on Antennas and Propagation: EuCAP 2016, Institute of Electrical and Electronics Engineers (IEEE), 2016, artikkel-id 7481368Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We consider a homogeneous Goubau line (GL) with a lossy cover. We analyze the dispersion equation for symmetric waves with respect to the problem parameters, find radially symmetric complex waves, and examine their behavior. We show that longitudinal wavenumbers of complex waves are regular perturbations of the propagation constants of eigenwaves of lossless GL, weakly depend om the imaginary part of permittivity of the cover, and that attenuation in GL is low at higher losses.

  • 57.
    Källström, Rolf
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    D-modules with finite support are semi-simple2014Inngår i: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 52, nr 2, s. 291-299Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Let (R,m,k) be a regular local k-algebra satisfying the weak Jacobian criterion, and such that kR/k is an algebraic field extension. Let D be the ring of k-linear differential operators of R. We give an explicit decomposition of the DR-module D/Dm^(n+1) as a direct sum of simple modules, all isomorphic to D/Dm, where certain “Pochhammer” differential operators are used to describe generators of the simple components. 

  • 58.
    Källström, Rolf
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Purity of Branch and Critical locus2013Inngår i: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 379, s. 156-178Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    To a dominant morphism $X/S \to Y/S$ of N\oe therian integral $S$-schemes one has the inclusion $C_{X/Y}\subset B_{X/Y}$ of the critical locus in the branch locus of $X/Y$. Starting from the notion of locally complete intersection morphisms, we give conditions on the modules of relative differentials $\Omega_{X/Y}$, $\Omega_{X/S}$, and $\Omega_{Y/S}$ that imply bounds on the codimensions of $ C_{X/Y}$ and $ B_{X/Y}$. These bounds generalise to a wider class of morphisms the classical purity results for finite morphisms by Zariski-Nagata-Auslander, and Faltings and Grothendieck, and van der Waerden's purity for birational morphisms.

  • 59.
    Källström, Rolf
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    The Zariski-Lipman conjecture for complete intersections2011Inngår i: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 337, nr 1, s. 169-180Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The tangential branch locus BX/Yt∩BX/Y is the subset of points in the branch locus where the sheaf of relative vector fields TX/Y fails to be locally free. It was conjectured by Zariski and Lipman that if V/k is a variety over a field k of characteristic 0 and BV/kt=∅, then V/k is smooth (= regular). We prove this conjecture when V/k is a locally complete intersection. We prove also that BV/kt=∅ implies codimXBV/k≤1 in positive characteristic, if V/k is the fibre of a flat morphism satisfying generic smoothness.

  • 60.
    Källström, Rolf
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Tadesse, Yohannes
    Stockholms universitet.
    Hilbert series of modules over Lie algebroids2015Inngår i: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 432, s. 129-184Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider modules M over Lie algebroids gA which are of finite type over a local noetherian ring A. Using ideals J ⊂ A such that gA ·J ⊂ J and the length ℓgA (M/JM) < ∞ we can define in a natural way the Hilbert series of M with respect to the defining ideal J. This notion is in particular studied for modules over the Lie algebroid of k-linear derivations gA = TA(I) that preserve an ideal I ⊂ A, for example when A = On, the ring of convergent power series. Hilbert series over Stanley-Reisner rings are also considered.

  • 61.
    Lagovsky, B. A.
    et al.
    Deptartment of Applied Mathematics, Moscow Technological University, Moscow, Russian Federation.
    Samokhin, A. B.
    Deptartment of Applied Mathematics, Moscow Technological University, Moscow, Russian Federation.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Creating Two-Dimensional Images of Objects with High Angular Resolution2018Inngår i: Proceedings of 2018 IEEE Asia-Pacific Conference on Antennas and Propagation (APCAP), 2018, s. 114-115Konferansepaper (Fagfellevurdert)
    Abstract [en]

    A new method of digital radar signal processing for remote sensing is proposed. The technique allows one to obtain two-dimensional images of objects with super resolution. The method is based on solving a convolution-type two- dimensional linear integral equation of the first kind by algebraic methods.

  • 62.
    Lagovsky, B. A.
    et al.
    Moscow Technological University, Moscow, Russia.
    Samokhin, A. B.
    Moscow Technological University, Moscow, Russia.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Increasing accuracy of angular measurements using UWB signals2017Inngår i: 2017 11th European Conference on Antennas and Propagation, EUCAP 2017, Institute of Electrical and Electronics Engineers (IEEE), 2017, s. 1083-1086Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We show that dispersion characteristics of antenna patterns should be taken into account when developing systems using UWB signals. The accuracy of measurement of angular coordinates of objects using UWB pulses is increased by optimizing their shape based on known characteristics of the antenna system and at least partially known characteristics of the investigated signal source. Optimization algorithms allow to minimize the width of the directional pattern for a given level of the useful signal.

  • 63.
    Lagovsky, B. A.
    et al.
    Moscow State Institute of Radio Engineering and Automation, Technical University, Moscow, Russian Federation.
    Samokhin, A. B.
    Moscow State Institute of Radio Engineering and Automation, Technical University, Moscow, Russian Federation.
    Shestopalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Pulse characteristics of antenna array radiating UWB signals2016Inngår i: 2016 10th European Conference on Antennas and Propagation: EuCAP 2016, Institute of Electrical and Electronics Engineers (IEEE), 2016, artikkel-id 7481624Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Dispersion properties of the mutual impedance of emitters significantly alter the shape and spectrum of ultra-wideband (UWB) signals which must be taken into account when forming the signal. In order to take into consideration mutual coupling of elements we propose to use pulse characteristics in the antenna performance analysis and calculations. This approach allows us to simplify calculations of UWB antenna systems and improve their accuracy.

  • 64.
    Lagovsky, B.
    et al.
    Moscow Technological University (MIREA), Moscow, Russian Federation.
    Samokhin, A.
    Moscow Technological University (MIREA), Moscow, Russian Federation.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Increasing effective angular resolution of measuring systems based on antenna arrays2016Inngår i: 2016 URSI International Symposium on Electromagnetic Theory (EMTS): Conference publications, IEEE conference proceedings, 2016, s. 432-434Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Resolution of goniometric systems on the basis of antenna arrays can be increased due to the secondary digital processing of the accepted signals. Necessary algorithms are created on the basis of solution to inverse problems.

  • 65. Lagovsky, Boris A.
    et al.
    Samokhin, Alexander B.
    Shestopalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Superresolution based on the methods of extrapolation2015Inngår i: PIERS 2015 Prague: Progress in Electromagnetics Research Symposium : Proceedings, Cambridge, MA: The Electromagnetics Academy , 2015, s. 1548-1551Konferansepaper (Fagfellevurdert)
    Abstract [en]

    A new method of signal processing by smart antennas is proposed and justified. It allows to improve the accuracy of angle measurement and to restore the image of the object with superresolution. The method is based on the extrapolation of the signals received by each element of the antenna array, outside the aperture. This allows introducing new virtual elements and thus synthesizing significantly larger antenna array. The method is tested in numerical experiments using a mathematical model and the maximum effective angular resolution is found for different cases and objects. Algorithms based on the method of digital aperture synthesis provide angular superresolution 3-7 times greater than that according to the Rayleigh criterion for a signal/noise ratio of 12-13 dB.

  • 66.
    Ma, Qi
    et al.
    Mathematics Department, Uppsala University, Uppsala, Sweden.
    Johansson, Anders
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik. Mathematics Department, Uppsala University, Uppsala, Sweden.
    Tero, Atsushi
    PRESTO, JST, Kawaguchi, Saitama, Japan.
    Nakagaki, Toshiyuki
    Future University Hakodate, Hakodate, Japan.
    Sumpter, David
    Mathematics Department, Uppsala University, Uppsala, Sweden.
    Current-reinforced random walks for constructing transport networks2013Inngår i: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 10, nr 80, s. 20120864-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Biological systems that build transport networks, such as trail-laying ants and the slime mould Physarum, can be described in terms of reinforced random walks. In a reinforced random walk, the route taken by 'walking' particles depends on the previous routes of other particles. Here, we present a novel form of random walk in which the flow of particles provides this reinforcement. Starting from an analogy between electrical networks and random walks, we show how to include current reinforcement. We demonstrate that current-reinforcement results in particles converging on the optimal solution of shortest path transport problems, and avoids the self-reinforcing loops seen in standard density-based reinforcement models. We further develop a variant of the model that is biologically realistic, in the sense that the particles can be identified as ants and their measured density corresponds to those observed in maze-solving experiments on Argentine ants. For network formation, we identify the importance of nonlinear current reinforcement in producing networks that optimize both network maintenance and travel times. Other than ant trail formation, these random walks are also closely related to other biological systems, such as blood vessels and neuronal networks, which involve the transport of materials or information. We argue that current reinforcement is likely to be a common mechanism in a range of systems where network construction is observed.

  • 67.
    Nakonechny, A. G.
    et al.
    Taras Shevchenko National University of Kyiv, Ukraine.
    Podlipenko, Y. K.
    Taras Shevchenko National University of Kyiv, Ukraine.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Aposteriori estimates in inverse problems for the Helmholtz equation2017Inngår i: 2017 Progress In Electromagnetics Research Symposium - Fall (PIERS - FALL), Electromagnetics Academy , 2017, s. 3526-3531Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We consider the problem of estimation of the right-hand sides of the Helmholtz equation that models electromagnetic and acoustic wave fields when that initial data is uncertain. In the case when measurement errors depend on solutions, we construct algorithms of computation of the optimal estimates which are compatible with the measurement data. It is shown that approximate a posteriori estimates of the right-hand sides are expressed via solutions of linear algebraic equations.

  • 68.
    Nakonechny, Alexander G.
    et al.
    Taras Shevchenko National University of Kyiv, Kyiv, Ukraine.
    Podlipenko, Yuri K.
    Taras Shevchenko National University of Kyiv, Kyiv, Ukraine.
    Shestopalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Guaranteed a posteriori estimates of right-hand sides in transmission problems for Helmholtz equations2017Inngår i: 2017 XXXIIND GENERAL ASSEMBLY AND SCIENTIFIC SYMPOSIUM OF THE INTERNATIONAL UNION OF RADIO SCIENCE (URSI GASS), Institute of Electrical and Electronics Engineers (IEEE), 2017Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this work we describe a method of obtaining guaranteed a posteriori estimates of unknown right-hand sides of the Helmholtz transmission problems from indirect measurements of a solution to this problem. The obtained results can be applied in various models of electromagnetics and acoustics that describe excitation of transparent bodies by sources of different kinds.

  • 69.
    Nakonechny, Alexander
    et al.
    T. Shevchenko Kyiv National University, Kyiv, Ukraine.
    Podlipenko, Yury
    T. Shevchenko Kyiv National University, Kyiv, Ukraine.
    Shestopalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Guaranteed estimation for inverse problems in electromagnetics and acoustics2016Inngår i: Proceedings of the 2016 18th International Conference on Electromagnetics in Advanced Applications, ICEAA 2016, 2016, s. 374-377, artikkel-id 7731403Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The analysis is performed and theorems are formulated concerning general form of guaranteed estimates of linear functionals from unknown data of Helmholtz transmission problems arising in electromagnetics and acoustics of inhomogeneous dielectric media.

  • 70.
    Olsson, Gloria
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Framgångsrik matematikundervisning: Framgångsrika matematiklärares beskrivningar av sina undervisningsstrategier2017Independent thesis Advanced level (professional degree), 20 poäng / 30 hpOppgave
    Abstract [sv]

    Den största påverkansfaktorn på elevers studieprestationer är vad läraren gör i undervisningen. Framgångsrika lärares undervisningsmetoder skiljer sig från andra lärares, och eftersom matematik är det skolämne som tycks vara det svåraste att lära sig så är det viktigt att visa exempel på framgångsrik matematikundervisning. Syftet med detta examensarbete var att ta reda på hur framgångsrika matematiklärare i årskurs 4–6 beskriver sin matematikundervisning, samt att lyfta gemensamma undervisningsstrategier som de använder sig av. Sex framgångsrika matematiklärare intervjuades. Intervjuerna transkriberades och sammanfattades för den beskrivande delen av undersökningen, samt kodades för den analytiska delen. Resultaten visade att de intervjuade matematiklärarna brinner för sitt ämne och de har som mål att eleverna ska tycka att matematik är roligt och att de ska få tilltro till sin egen matematiska förmåga. Lärarna har goda kunskaper i matematik men vill ständigt utvecklas och vågar testa nya saker i undervisningen. De gemensamma undervisningsstrategierna som de använder sig av är: diskussioner och kooperativt lärande, problemlösning, digitala hjälpmedel, formativ bedömning och synligt lärande, elevaktiv undervisning där eleverna lär av varandra samt anpassad och varierad undervisning.

  • 71.
    Olsson Karlsson, Rebecca
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Det är inte svaret som räknas: ett undervisningsmaterial inom matematik med fokus på problemlösning, grupparbete och motivation2018Independent thesis Advanced level (professional degree), 20 poäng / 30 hpOppgave
    Abstract [sv]

    Undervisningsprojektet vilket redovisas i examensarbetet syftar till att skapa ett ökat intresse för ämnet matematik samtidigt som det tränar elevens förmåga att arbeta i grupp och stärker gemenskapen i klassen. I arbetet har författaren använt sig av enkäter, deltagande observationer samt semistrukturerade kvalitativa intervjuer som datainsamlingsmetoder. I resultatredovisningen framkommer att undervisningsmaterialet uppnått de kriterier som presenterades under författarens produktutveckling likaväl som syftet med arbete anses uppnås. Inslagen av spelifierat lärande, den varierade undervisningen, samt elevernas upplevelser av verkliga problem bedöms vara de mest framträdande faktorerna i detta projekt vilket har genererat ett för eleverna roligt och lyckat undervisningsmaterial inom problemlösning.

  • 72.
    Persson, Jessica
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Problemlösning: En studie av lärares val av problemlösningsuppgifter i matematikundervisningen i årskurserna 1-32018Independent thesis Advanced level (professional degree), 20 poäng / 30 hpOppgave
  • 73.
    Podlipenko, Y. K.
    et al.
    Taras Shevchenko National University of Kyiv, Kyiv, Ukraine.
    Nakonechny, A. G.
    Taras Shevchenko National University of Kyiv, Kyiv, Ukraine.
    Shestopalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Guaranteed estimation of solutions to Helmholtz problems from pointwise noisy observations2016Inngår i: Proceedings of the International Conference Days on Diffraction, DD 2016, 2016, s. 336-339, artikkel-id 7756869Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The theorems on a general form of guaranteed estimates of linear functionals from unknown solutions of Helmholtz transmission problems are formulated in the case of pointwise noisy observations of these solutions.

  • 74.
    Podlipenko, Y.
    et al.
    Taras Shevchenko National University, Kyiv, Ukraine.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Guaranteed estimation of solutions to transmission problems for Helmholtz equation with uncertain data from their indirect noisy observations2016Inngår i: 2016 URSI International Symposium on Electromagnetic Theory (EMTS), IEEE conference proceedings, 2016, s. 93-95Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We investigate the estimation problems of linear functionals from solutions to transmission problems for Helmholtz equation with inexact data. The right-hand sides of equations entering the statements of transmission problems and the statistical characteristics of observations errors are supposed to be unknown and belonging to the certain sets. It is shown that the 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.

  • 75.
    Podlipenko, Yu K.
    et al.
    Faculty of Cybernetics, Taras Shevchenko National University of Kyiv, Kiev, Ukraine.
    Shestopalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Guaranteed estimation of solutions to Helmholtz transmission problems with uncertain data from their indirect noisy observations2017Inngår i: Radio Science, ISSN 0048-6604, E-ISSN 1944-799X, Vol. 52, nr 9, s. 1129-1139Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 76.
    Podlipenko, Yuri
    et al.
    T. Shevchenko Kyiv National University, Kyiv, Ukraine.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Mixed variational approach to finding guaranteed estimates from solutions and right-hand sides of the second-order linear elliptic equations under incomplete data2016Inngår i: Minimax Theory and its Applications, ISSN 2199-1413, Vol. 1, nr 2, s. 197-244Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We investigate the problem of guaranteed estimation of values of linear continuous functionals defined on solutions to mixed variational equations generated by linear elliptic problems from indirect noisy observations of these solutions. We assume that right-hand sides of the equations, as well as the second moments of noises in observations are not known; the only available information is that they belong to given bounded sets in the appropriate functional spaces. We are looking for linear with respect to observations optimal estimates of solutions of aforementioned equations called minimax or guaranteed estimates. We develop constructive methods for finding these estimates and estimation errors which are expressed in terms ofsolutions to special mixed variational equations and prove that Galerkin approximations of the obtained variational equations converge to their exact solutions. We study also the problem of guaranteed estimation of right-hand sides of mixed variational equations.

  • 77. Rubin, Donald B.
    et al.
    Wang, Xiaoqin
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Yin, Li
    Zell, Elizabth
    Bayesian casual inference: Appraches to Estimating the Effect of Treating Hospital Type on Cancer Survival in Sweden Using Principal Stratification2010Inngår i: The Oxford handbook of applied bayesian analysis, Oxford University Press , 2010, s. 679-708Kapittel i bok, del av antologi (Fagfellevurdert)
  • 78.
    Samokhin, A. B.
    et al.
    Moscow Technological University (MIREA), Moscow, Russian Federation.
    Samokhina, A. S.
    Institute of Control Sciences, Moscow, Russian Federation.
    Shestopalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Fast algorithms for the solution of volume singular integral equations of electromagnetics2017Inngår i: 2017 International Conference on Electromagnetics in Advanced Applications (ICEAA), Institute of Electrical and Electronics Engineers Inc. , 2017, s. 776-778, artikkel-id 8065364Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Fast algorithms for the solution of volume singular integral equations of electromagnetics are presented. Numerical results are demonstrated that confirm efficiency of the developed fast computational algorithms.

  • 79.
    Samokhin, Alexander
    et al.
    Moscow Technical University MIREA, Moscow, Russia.
    Samokhina, Anna
    Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Discretization Methods for Three-Dimensional Singular Integral Equations of Electromagnetism2018Inngår i: Differential equations, ISSN 0012-2661, E-ISSN 1608-3083, Vol. 54, nr 9, s. 1225-1235Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Theorems providing the convergence of approximate solutions of linear operator equations to the solution of the original equation are proved. The obtained theorems are used to rigorously mathematically justify the possibility of numerical solution of the 3D singular integral equations of electromagnetism by the Galerkin method and the collocation method.

  • 80.
    Sheina, E. A.
    et al.
    Lomonosov Moscow State University, Russian Federation.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smirnov, A. P.
    Lomonosov Moscow State University, Russian Federation.
    Planning and processing of measurements in a waveguide aimed at determination of permittivity of dielectric inclusion2017Inngår i: 2017 Progress In Electromagnetics Research Symposium - Fall (PIERS - FALL), Electromagnetics Academy , 2017, s. 1866-1871Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The methods are developed for reconstructing permittivity of the inclusion in a rectangular waveguide with perfectly conducting walls by comparing the results of multifrequency measurements of the principal waveguide mode transmission coefficient with the data obtained from numerical solution to Maxwell's equations. Optimal schemes for experimentation and processing of the obtained data are proposed on the basis of comparison of experimental data with closed-form solutions for cases of empty waveguide and the waveguide containing a uniform diaphragm.

  • 81.
    Sheina, E. A.
    et al.
    Lomonosov Moscow State University, Russian Federation.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smirnov, A. P.
    Lomonosov Moscow State University, Russian Federation.
    Ufimtsev, M. V.
    Lomonosov Moscow State University, Russian Federation.
    FDTD solution of reconstructing permittivity of a dielectric inclusion in a waveguide taking into account measurement inaccuracy2017Inngår i: Progress in Electromagnetics Research Symposium, Electromagnetics Academy , 2017, s. 3188-3195Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Wave propagation in a rectangular waveguide with perfectly conducting walls containing a parallel-plane dielectric diaphragm and a small inclusion is modeled using a numerical solution to Maxwell's equations. The methods are developed for reconstructing permittivity of the inclusion from the transmission coefficient of the principal waveguide mode taking into account experimental error. The results determined by these methods are compared with experimental data obtained for a homogeneous diaphragm.

  • 82.
    Sheina, E. A.
    et al.
    Lomonosov Moscow State University, Russian Federation.
    Smirnov, A. P.
    Lomonosov Moscow State University, Russian Federation.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Influence of standing waves on the solution of the inverse problem of reconstructing parameters of a dielectric inclusion in a waveguide2016Inngår i: 2016 URSI International Symposium on Electromagnetic Theory (EMTS), IEEE conference proceedings, 2016, s. 643-646Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We consider numerical determination of the dielectric media parameters of inclusions in a waveguide of rectangular cross-section from the transmission coefficient. We develop and apply computer codes implementing the FDTD algorithm for numerical solution of the nonstationary Maxwell equations with perfectly matched layer (PML) absorbing boundary conditions using the Berenger layout. We estimate parameter ranges providing the necessary accuracy for solving forward and inverse scattering problems for waveguides with inclusions. Aposteriori estimate of the amplitude of higher-order evanescent waves is obtained and their influence on the choice of parameters of the numerical method is determined.

  • 83.
    Sheina, E. A.
    et al.
    Lomonosov Moscow State University, Moscow, Russian Federation.
    Smirnov, A. P.
    Lomonosov Moscow State University, Moscow, Russian Federation.
    Shestopalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Optimization of the boundary conditions and computational parameters for the FDTD solution of the inverse problem of reconstructing permittivity of a dielectric inclusion in a waveguide2016Inngår i: 2016 Progress In Electromagnetics Research Symposium, PIERS 2016 - Proceedings, 2016, s. 211-216, artikkel-id 773429Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Wave propagation in a waveguide of rectangular cross section with perfectly conducting wall containing an inhomogeneous dielectric insert in the form of a parallel-plane diaphragm with an inclusion is simulated numerically. The permittivity of the inclusion is a quantity to be restored from as little information about the scattered field as possible using FDTD numerical solution of Maxwell’s equations with nonlocal multimode scattering boundary conditions. The optimal number of higher-order evanescent waves and the size of the computational waveguide domain are found using the series of numerical experiments.

  • 84.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Complex waves in a dielectric waveguide2018Inngår i: Wave motion, ISSN 0165-2125, E-ISSN 1878-433X, Vol. 82, s. 16-19Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Existence of two families of symmetric complex waves in a dielectric waveguide of circular cross section is proved. Eigenvalues of the associated Sturm–Liouville problem on the half-line are determined. 

  • 85.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    How to overcome nonuniqueness of permittivity reconstruction in inverse waveguide problems2018Konferansepaper (Fagfellevurdert)
  • 86.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Methods for verifying solvability of the permittivity reconstruction in canonical waveguide inverse problems2017Inngår i: 2017 XXXIIND GENERAL ASSEMBLY AND SCIENTIFIC SYMPOSIUM OF THE INTERNATIONAL UNION OF RADIO SCIENCE (URSI GASS), Institute of Electrical and Electronics Engineers (IEEE), 2017, s. 1-2Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We present a summary of mathematical methods that enable one to study and reveal the properties of the transmission coefficient as a function of problem parameters aimed at solution to some canonical waveguide inverse problems. The results are based on application of the theory of functions of several complex variables and singularities of differentiable mappings and lead to substantial improvement of the available techniques for permittivity reconstruction of material samples in waveguides.

  • 87.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    On a Perspective of Discovering Wave Interaction in Canonical Open Metal-Dielectric Waveguides2018Inngår i: Proceedings of 2018 International Conference on Electromagnetics in Advanced Application (ICEAA), Piscataway, New Jersey, USA: IEEE conference proceedings, 2018, s. 72-75, artikkel-id 8520368Konferansepaper (Fagfellevurdert)
    Abstract [en]

    A possibility of the wave interaction is demonstrated for canonical types of open metal-dielectric waveguides: a dielectric rod of circular cross section and a perfectly conducting circular cylinder covered by a concentric layer of dielectric, a Goubau line. The results and technique that apply rigorous analysis of dispersion equations and determination of Morse critical points admit extension to other types of guiding structures.

  • 88.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    On a spectrum of complex waves in open metal-dielectric waveguides [О спектре комплексных волн в открытых металлических диэлектрических волноводах]2018Inngår i: Современные методы теории краевых задач: материалы международной конференции, посвящённой 90-летию Владимира Александровича Ильина (2-6 мая 2018 г., Москва): Понтрягинские чтения - XXIX / [ed] Budak Alexander Borisovich [Будак Александр Борисович], Moscow: Moscow State University Press , 2018, s. 243-244Konferansepaper (Fagfellevurdert)
  • 89.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    On unique solvability of multi-parameter waveguide inverse problems2017Inngår i: 2017 International Conference on Electromagnetics in Advanced Applications (ICEAA), Institute of Electrical and Electronics Engineers (IEEE), 2017, s. 372-376, artikkel-id 8065253Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This paper provides an introduction to mathematical methods of analytical-numerical solution to multi-parameter waveguide inverse problems of reconstructing permittivity of layered dielectric inclusions from the values of the transmission and reflection coefficients. Sufficient conditions of the unique solvability for a family of waveguide inverse problems are obtained.

  • 90.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Resonant states in forward and inverse waveguide scattering problems2015Inngår i: Proceedings of the 2015 International Conference on Electromagnetics in Advanced Applications: ICEAA 2015, IEEE Press, 2015, s. 31-34Konferansepaper (Fagfellevurdert)
    Abstract [en]

    It is shown that the transmission coefficient of parallel-plane multi-sectional dielectric diaphragms in a waveguide of rectangular cross section has singularities in the complex plane of the longitudinal wavenumber of each section and the singularities are associated with resonant states of the transmission problem.

  • 91.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Singularities of the transmission coefficient and anomalous scattering by a dielectric slab2018Inngår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 59, nr 3, artikkel-id 033507Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove the existence and describe the distribution on the complex plane of the singularities, resonant states (RSs), of the transmission coefficient in the problem of the plane wave scattering by a parallel-plate dielectric slab in free space. It is shown that the transmission coefficient has isolated poles all with nonzero imaginary parts that form countable sets in the complex plane of the refraction index or permittivity of the slab with the only accumulation point at infinity. The transmission coefficient never vanishes and anomalous scattering, when its modulus exceeds unity, occurs at arbitrarily small loss of the dielectric filling the layer. These results are extended to the cases of scattering by arbitrary multi-layer parallel-plane media. Connections are established between RSs, spectral singularities, eigenvalues of the associated Sturm-Liouville problems on the line, and zeros of the corresponding Jost function.

  • 92.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Kuzmina, Ekaterina
    Russian Technological University MIREA, Moscow, Russia.
    On a rigorous proof of the existence of complex waves in a dielectric waveguide of circular cross section2018Inngår i: Progress in Electromagnetics Research B, ISSN 1937-6472, E-ISSN 1937-6472, Vol. 82, s. 137-164Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Existence of symmetric complex waves in a dielectric rod (DR) - a dielectric waveguide of circular cross section - is proved by analyzing functional properties of the dispersion equations (DEs) using the theory of functions of several complex variables and validating the existence of complex roots of DE. A closed-form iteration procedure for calculating the roots in the complex domain supplied with efficient choice of initial approximation is proposed. Numerical modeling is performed with the help of a parameter-differentiation method applied to the analytical and numerical solution of DEs.

  • 93.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Kuzmina, Ekaterina
    Moscow Technical University MIREA, Moscow, Russia.
    Symmetric surface waves along a metamaterial dielectric waveguide and a perfectly conducting cylinder covered by a metamaterial layer2018Inngår i: Advanced Electromagnetics (AEM), E-ISSN 2119-0275, Vol. 7, nr 2, s. 91-98Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Existence of symmetric complex waves in a metamaterial dielectric rod and a perfectly conducting cylinder of circular cross section covered by a concentric layer of metamaterial, a metamaterial Goubau line, is proved. Analytical investigation and numerical solution of dispersion equations reveal several important properties of running waves inher- ent to open metal-metamaterial waveguides which have not been reported for waveguides filled with standard media.

  • 94.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Kuzmina, Ekaterina
    Moscow State Technical University of Radio Engineering, Electronics and Automation, Moscow, Russia.
    Samokhin, Alexander
    Moscow State Technical University of Radio Engineering, Electronics and Automation, Moscow, Russia.
    On a Mathematical Theory of Open Metal-Dielectric Waveguides2014Inngår i: Forum for Electromagnetic Research Methods and Application Technologies (FERMAT), Vol. 5Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Existence of symmetric waves in open metal--dielectric waveguides, a dielectric rod and the Goubau line, is proven by analyzing the of functional properties of the dispersion equations (DEs) and parameter-differentiation method, applied to the analytical and numerical solution of the DEs. Various limiting cases are investigated. Reduction to singular Sturm--Liouville boundary eigenvalue problemson the half-line is performed. Principal and higher-order surface waves  are investigated

  • 95.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Menshikov, Y.
    Dnepropetrovsk University, Dnepropetrovsk, Ukraine.
    An approach to estimation of solutions to inverse problems of electromagnetics2016Inngår i: 2016 URSI International Symposium on Electromagnetic Theory (EMTS), IEEE conference proceedings, 2016, s. 780-782Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper an approach is proposed which is based on a method of regularization for estimating the solution of inverse problems of electromagnetic with noisy measurements. The constraints on the solution of the inverse problem based on physical assumptions are taken into consideration. The solution is reduced to a nonlinear system with the given interval-type inaccuracy of the right-hand side. The developed approach enables one to take into account inaccuracy of the operator of the inverse problem. The method of the special mathematical model selection is described which improves the accuracy of estimations.

  • 96.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Samokhin, Alexander
    Russian Technological University MIREA.
    Lagovsky, Boris
    Russian Technological University MIREA.
    Increasing the Range of UWB Radars2018Inngår i: IET Conference Publications 2018, Piscataway, New Jersey, USA: IEEE, 2018, Vol. CP741, artikkel-id 1570403971Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The use of UWB radars makes it possible to detect, recognize, and carry out measurements of coordinate and velocities of hardly noticeable radar targets. The variational problems of searching for the maximum range of UWB-radar operation using optimization of the shape and duration of UWB-pulses are justified and solved.

  • 97.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smirnov, Y. G.
    Penza State University, Penza, Russian Federation.
    Derevyanchuk, E. D.
    Penza State University, Penza, Russian Federation.
    Tensor permittivity and permeability reconstruction of a one-sectional diaphragm in a rectangular waveguide2016Inngår i: 2016 URSI International Symposium on Electromagnetic Theory (EMTS), IEEE conference proceedings, 2016, s. 353-355Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This work is devoted to the solution of the inverse problem of reconstructing electromagnetic characteristics of anisotropic parallel-plane dielectric diaphragms. We consider a one-sectional diaphragm in a rectangular waveguide filled with anisotropic media having a diagonal permittivity and permeability tensors and propose a method of reconstructing the permittivity and permeability tensors from the values of the transmission coefficient at different frequencies.

  • 98.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smirnov, Yury
    Penza State University, Penza, Ryssland.
    Advanced mathematical techniques  for the analysis of inverse scattering  in waveguides2014Inngår i: Proceedings of the 7th International Conference Inverse Problems: Modeling and Simulation (IPMS 2014): Ölüdeniz, Fethiye, Turkey, May 22–30,2014 / [ed] A. Hasanov, 2014, s. 32-Konferansepaper (Fagfellevurdert)
  • 99.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smirnov, Yury
    Penza State University, Penza, Ryssland.
    Derevyanchuk, Ekaterina
    Penza State University, Penza, Russia.
    Inverse problem method for permittivity reconstruction of two-layered media: numerical and experimental results2014Inngår i: Progress in Electromagnetics Research Symposium: , Electromagnetics Academy , 2014, s. 2610-2613Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This study employs the technique developed in [1-3] and deals with complex permittivity reconstruction of layered materials in the form of diaphragms (sections) in a single-mode waveguide of rectangular cross section from the transmission coefficient measured at different frequencies.

  • 100.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smirnov, Yury G.
    Penza State University, Russian Federation .
    Derevyanchuk, Ekaterina D.
    Penza State University, Russian Federation .
    Permittivity reconstruction of a diaphragm in a rectangular waveguide: Unique solvability of benchmark inverse problems2015Inngår i: PIERS 2015 Prague: Progress in Electromagnetics Research Symposium : Proceedings, Cambridge, MA: The Electromagnetics Academy , 2015, s. 1528-1532Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This work is devoted to the analysis of inverse problems of permittivity reconstruction of diaphragms loaded in a rectangular waveguide including justification of the solution to a benchmark inverse problem of reconstructing permittivity of a one-sectional diaphragm. We perform comparison of theoretical and numerical results based on the measurement data to validate the efficiency of the proposed technique. The obtained solutions can be implemented in practical measurements for investigation of new artificial materials and media and can be applied in optics, nanotechnology, and design of microwave devices.

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