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  • 101.
    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, Russia.
    Il’inski, Anatolij
    Moscow MV Lomonosov State University, Moscow, Russia.
    Recent Progress in the Analysis of Mode Spectrum in Waveguides with Inclusions2015Inngår i: 2015 1st URSI Atlantic Radio Science Conference (URSI AT-RASC) / [ed] IEEE, New York: Institute of Electrical and Electronics Engineers (IEEE), 2015Konferansepaper (Fagfellevurdert)
  • 102.
    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.
    Kuzmina, Ekaterina
    Moscow State Technical University of Radio Engineering, Electronics and Automation, Moscow, Russia.
    Mathematical Aspects of the Theory of Wave Propagation in Metal-Dielectric Waveguides2014Inngår i: General Assembly and Scientific Symposium (URSI GASS), 2014 XXXIth URSI: Beijing, China,  August 16–23, 2014, IEEE Press, 2014Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We consider fundamental issues of the mathematical theory of the wave propagation in waveguides with inclusions. Analysis is performed in terms of a boundary eigenvalue problem for the Maxwell equations which is reduced to an eigenvalue problem for an operator pencil. We prove that the spectrum of normal waves forms a nonempty set of isolated points localized in a strip with at most finitely many real points. We show the importance of these results for the theory of wave propagation in open guiding structures and consider in more detail the surface wave spectrum of the Goubau line.

  • 103.
    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.
    Smolkin, Eugene
    Penza State University, Russia.
    New Propagation Regimes of Symmetric Hybrid Waves in a Nonlinear Metal-Dielectric Waveguide2018Inngår i: IET Conference Publications 2018, Piscataway, New Jersey, USA: IEEE, 2018, Vol. CP741, artikkel-id 1570402136Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The propagation of monochromatic nonlinear symmetric hybrid waves in a cylindrical nonlinear metal-dielectric waveguide is considered. The physical setting is reduced to a transmission eigenvalue problem for a system of ordinary differential equations which is new type of nonlinear eigenvalue problem where spectral parameters are the wave propagation constants. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

  • 104.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smith, Paul
    Macquarie University, Sydney, Australia.
    Vinogradova, Elena
    Macquarie University, Sydney, Australia.
    The effect of inserts upon propagation modes in a waveguide2018Inngår i: Proceedings of 2018 International Conference on Electromagnetics in Advanced Application (ICEAA), Piscataway, New Jersey, USA: IEEE, 2018, s. 315-318, artikkel-id 8520404Konferansepaper (Fagfellevurdert)
    Abstract [en]

    When a perfectly electrically conducting (PEC) waveguide is perturbed by the insertion of a PEC structure aligned with its axis, its propagation constants are perturbed. The underlying boundary value problem may be converted to a homogeneous Fredholm matrix equation in which the propagation constants are found from the roots of the determinant of the matrix; stable and numerically efficient processes may be employed to find the propagation constants. There is no constraint on the size or shape of the inserts. As well as determining the empty waveguide parameters, this approach provides an estimate of the perturbation to the propagation constants of the empty waveguide.

  • 105.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smolkin, Eugene
    Penza State University, Russia.
    Kuzmina, Ekaterina
    Moscow Technologiical University MIREA, Moscow, Russia.
    Spectra of Nonselfadjoint Eigenvalue Problems for Elliptic Systems in Mathematical Models of the Wave Propagation in Open Waveguides2018Inngår i: Lobachevskii Journal of Mathematics, ISSN 1995-0802, E-ISSN 1818-9962, Vol. 39, nr 8, s. 1117-1129Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Statements and analysis are presented of nonselfadjoint eigenvalue problems for ellipticequations and systems, including singular Sturm–Liouville problems on the line, that arise inmathematical models of the wave propagation in open metal-dielectric waveguides. Existence ofreal and complex spectra are proved and their distribution is investigated for canonical structurespossessing circular symmetry of boundary contours.

  • 106.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smolkin, Eugene
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russia.
    Snegur, M.
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russia.
    TE-polarized Wave Diffraction by a Cylinder Covered with Nonlinear Dielectric Layer2018Inngår i: Proceedings of 2018 IEEE Asia-Pacific Conference on Antennas and Propagation (APCAP), 2018, s. 321-322Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The problem of diffraction of TE polarized EM waves by an open dielectric waveguide with a nonlinear inhomogeneous filling is under consideration. In such problems a nonlinear eigenvalue problem for a system of differential equations is arised. For the numerical solution a method based on the solution of the auxillary Cauchy problem is proposed. Numerical results are presented.

  • 107.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smolkin, Eugene
    Penza State University, Russia.
    Snegur, Maxim
    Penza State University, Russia.
    Numerical Study of Multilayer Nonlinear Inhomogeneous Goubau Lines2018Inngår i: Proceedings of the 2018 International Conference on Electromagnetics in Advanced Application (ICEAA), Piscataway, New Jersey, USA: IEEE conference proceedings, 2018, s. 126-129, artikkel-id 8520464Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We consider propagation of surface TE waves in a circular metal-dielectric waveguide filled with nonlinear (Kerr nonlinearity) multilayered inhomogeneous medium. Analysis is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation; eigenvalues of the problem correspond to propagation constants of the waveguide. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

  • 108.
    Shestopalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Recent advances in the spectral theory of open structures: Existence and distribution of the spectra of running waves for a class of open waveguides2016Inngår i: Proceedings of the 2016 18th International Conference on Electromagnetics in Advanced Applications, ICEAA 2016, 2016, s. 370-373, artikkel-id 7731402Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We give a general description of mathematical background and a resume of the results about existence and distribution of the spectra of running waves in open waveguides, including metal-dielectric waveguides with arbitrary cylindrical in-homogeneities, layered concentric dielectric waveguides of circular cross section and Goubau lines with layered dielectric covers. The newly obtained results are reported concerning singularities (resonant states) of the transmission coefficient in the problems of the wave scattering by parallel-plate dielectric slabs in a waveguide and free space. The findings are based on recent advances in the spectral theory of open structures.

  • 109.
    Shestopalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Resonant states in waveguide transmission problems2015Inngår i: Progress in Electromagnetics Research B, ISSN 1937-6472, E-ISSN 1937-6472, Vol. 64, nr 1, s. 119-143Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove the existence of complex eigenfrequencies of open waveguide resonators in the form of parallel-plate waveguides and waveguides of rectangular crosssection containing layered dielectric inclusions. It is shown that complex eigenfrequencies are finite-multiplicity poles of the analytical continuation of the operator of the initial diffraction problem and its Green's function to a multi-sheet Riemann surface, and also of the transmission coefficient extended to the complex plane of some of the problem parameters. The eigenfrequencies are associated with resonant states (RSs) and eigenvalues of distinct families of Sturm-Liouville problems on the line; they form countable sets of points in the complex plane with the only accumulation point at infinity and depend continuously on the problem parameters. The set of complex eigenfrequencies is similar in its structure to the set of eigenvalues of a Laplacian in a rectangle. The presence of a resonance domain in the form of a parallel-plane layered dielectric insert removes the continuous frequency spectrum and gives rise to a discrete set of points shifted to (upper half of) the complex plane.

  • 110.
    Shestopalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Resonant states in waveguide transmission problems2015Inngår i: 2015 1st URSI Atlantic Radio Science Conference (URSI AT-RASC), New York: Institute of Electrical and Electronics Engineers (IEEE), 2015Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We prove the existence of complex eigenfrequencies of open waveguide resonators in the form of parallel-plate waveguides and waveguides of rectangular crosssection containing layered dielectric inclusions. It is shown that complex eigenfrequencies are finite-multiplicity poles of the analytical continuation of the operator of the initial diffraction problem and its Green's function to a multi-sheet Riemann surface, and also of the transmission coefficient extended to the complex plane of some of the problem parameters. The eigenfrequencies are associated with resonant states (RSs) and eigenvalues of distinct families of Sturm-Liouville problems on the line; they form countable sets of points in the complex plane with the only accumulation point at infinity and depend continuously on the problem parameters. The set of complex eigenfrequencies is similar in its structure to the set of eigenvalues of a Laplacian in a rectangle. The presence of a resonance domain in the form of a parallel-plane layered dielectric insert removes the continuous frequency spectrum and gives rise to a discrete set of points shifted to (upper half of) the complex plane.

  • 111.
    Shestopalov, Yury V.
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Podlipenko, Yuri
    T. Shevchenko Kyiv National University, Kyiv, Ukraine.
    Nakonechnyi, Olexandr
    T. Shevchenko Kyiv National University, Kyiv, Ukraine.
    Estimation of Parameters of Boundary Value Problems for Linear Ordinary Differential Equations with Uncertain Data2014Inngår i: Advances in Pure Mathematics, ISSN 2160-0368, E-ISSN 2160-0384, Vol. 4, nr 4, s. 118-146Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed here that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax mean square or guaranteed estimates. We establish that the minimax mean square estimates are expressed via solutions of some systems of differential equations of special type and determine estimation errors.

  • 112.
    Shestopalov, Yury V.
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smirnov, Yu.G.
    Penza State University, Penza, Russia.
    Derevyanchuk, E. D.
    Penza State University, Penza, Russia.
    Tensor permittivity reconstruction of multi-sectional diaphragm in a rectangular waveguide2016Inngår i: Proceedings of the 2016 18th International Conference on Electromagnetics in Advanced Applications, ICEAA 2016, 2016, s. 407-409, artikkel-id 7731412Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This work is devoted to the development of a numerical-analytical method for solving the inverse problem of reconstructing tensor permittivity of a multi-sectional diaphragm in a rectangular waveguide. Numerical results are presented that confirm the efficiency of the proposed technique.

  • 113.
    Shestopalov, Yury V.
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smirnov, Yurij G.
    Penza State University, Penza, Russian Federation.
    Derevyanchuk, E. D.
    Penza State University, Penza, Russian Federation.
    Numerical-analytical method for reconstructing tensor permittivity and permeability of a diaphragm in a rectangular waveguide2016Inngår i: 2016 Progress In Electromagnetics Research Symposium, PIERS 2016 - Proceedings, 2016, s. 217-221, artikkel-id 7734296Konferansepaper (Fagfellevurdert)
    Abstract [en]

    A numerical-analytical method is developed for reconstructing tensor permittivity and permeability of a dielectric diaphragm in a rectangular waveguide. The techniques and obtained solutions can be implemented in practical measurements for the investigation of new artificial materials and media and can be applied in optics, nanotechnology, and design of microwave devices.

  • 114.
    Sjölander, Caroline
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Programmering i matematikundervisningen: En kvalitativ studie kring lärares syn på hur programmering bör implementeras i matematikundervisningen i grundskolan2018Independent thesis Advanced level (professional degree), 20 poäng / 30 hpOppgave
    Abstract [sv]

    Syftet med studien var att se hur programmering på ett framgångsrikt sätt kan implementeras i matematikundervisningen i grundskolan. För att besvara frågeställningarna genomfördes semistrukturerade intervjuer där nio lärare med erfarenhet av programmering deltog. Resultaten visar att lärarna anser att programmering bör användas för att utveckla matematiken och att det går att koppla arbetet till samtliga matematikområden i kursplanen. Vidare anser de också att samtliga av de fem förmågorna som ligger till grund för kunskapskraven går att bedöma i arbetet med programmering. Den progression som går att utläsa ur respondenternas svar stämmer relativt väl överens med den progression som kan ses i läroplanen för grundskolan både gällande typ av programmeringsmiljö och hur programmering används. Avslutningsvis kan nämnas att lärarna belyser ett antal aspekter som avgörande för att implementeringen ska bli framgångsrik, bland annat att läraren har tillräckliga kunskaper inom området och att det finns tillgång till digitala resurser på skolorna.

  • 115.
    Smirnov, A. P.
    et al.
    Lomonosov Moscow State University, Russia.
    Semenov, A. N.
    Lomonosov Moscow State University, Russia.
    Sheina, E. A.
    Lomonosov Moscow State University, Russia.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Absorbing boundary conditions for FDTD analysis of rectangular waveguide with non-uniform dielectric inclusions2015Inngår i: 2015 1st URSI Atlantic Radio Science Conference (URSI AT-RASC), New York: Institute of Electrical and Electronics Engineers (IEEE), 2015Konferansepaper (Fagfellevurdert)
    Abstract [en]

    When the finite-difference time-domain method is used for analysis of waveguide structures, incident waves are needed for calculating electromagnetic parameters and effective absorbing boundary conditions are required for terminating open waveguide structures.

  • 116. Smirnov, A. P.
    et al.
    Semenov, A. N.
    Shestoplalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Numerical analyze of waveguide transmission coefficient with non-uniform dielectric slab2014Inngår i: Progress in Electromagnetics Research Symposium, Electromagnetics Academy , 2014, s. 2619-2621Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Propagation in the time domain of electromagnetic waves in a rectangular waveguide with a non-uniform dielectric slab is considered. Electromagnetic field components are computed and investigation of energy transport in the guide is performed by using Finite Difference Time Domain (FDTD) method in different frequency ranges. Parallel high performance FDTD solver, based on Maxwell equations approximation in integral form on Yee lattice and developed by the paper authors is used. A method for calculating the transmission coefficient with respect to all the problem parameters is proposed. The method is based on the analysis of the amplitude of the scattered wave derived from FDTD numerical solution. The pure scattered field method is proposed to specify the waveguide mode with respect to numerical dispersion. Computations for nonstationary Maxwell equations system are performed for the H10-mode scattering from a dielectric slab placed in the waveguide. Multiple numerical computations for the corresponding large-scale problems have been performed on Lomonosov Moscow State University IBM BlueGene/P supercomputer. Using the methods described above, we compute the values of the waveguide transmission, attenuation and propagation factors in a wide range of permittivity and different positions of the dielectric slab inclusions. Continuous curves on the complex plane describing the dependence of the transmission coefficient on the dielectric constant are obtained. The comparison of the transmission coefficient calculated by the present approach and the volume integral equation method is performed.

  • 117.
    Smirnov, A. P.
    et al.
    Lomonosov Moscow State University, Russian Federation .
    Sheina, E. A.
    Lomonosov Moscow State University, Russian Federation .
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Semenov, A. N.
    Lomonosov Moscow State University, Russian Federation .
    Numerical simulation of a nonuniform dielectric inclusion in a waveguide aimed at reconstructing its permittivity2015Inngår i: Proceedings of the 2015 International Conference on Electromagnetics in Advanced Applications: ICEAA 2015, IEEE Press, 2015, s. 419-421Konferansepaper (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 nonstationary Maxwell’s equations with perfectly matched layer (PML) absorbing boundary conditions using the Berenger layout and estimate parameter ranges providing the prescribed accuracy for solving forward and inverse scattering problems for waveguides with inclusions.

  • 118.
    Smirnov, Yury
    et al.
    Penza State University, Penza, Ryssland.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Derevyanchuk, Ekaterina
    Penza State University, Penza, Russia.
    Frequency-Dependent Complex Permittivity Reconstruction of Layered Diaphragm in a Rectangular Waveguide : Comparison with Experiment2014Inngår i: Proceedings of the 16th Seminar Computer Modeling in Microwave Power Engineering: Multiphysics Models and Material Properties: Karlsruhe, Germany, May 10-14, 2014 / [ed] V. Yakovlev, 2014, s. 48-51Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This study employs the technique developed in the earlier studies of the authors aimed atcomplex 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. The permittivity is assumed to be a function of frequency. We develop a numerical-analytical method of solution to this problem which guarantees accuracy of the result and can be easily implemented in view of practical measurements.Numerical results are presented for different types of materials.

  • 119.
    Smirnov, Yury
    et al.
    Penza State University, Penza, Ryssland.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Derevyanchuk, Ekaterina
    Penza State University, Penza, Russia.
    Inverse problem method for complex permittivity reconstruction of layered media in a rectangular waveguide2014Inngår i: Physica Status Solidi. C, Current topics in solid state physics, ISSN 1610-1634, E-ISSN 1610-1642, Vol. 11, nr 5-6, s. 969-974Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We solve the inverse problem of finding frequency-dependent complex permittivity of a multi-sectional dielectric diaphragm in a waveguide of rectangular cross section from the transmission coefficient measured at different frequencies. Based on the developed recursive method we perform a detailed analysis for one-, two- and three sectional diaphragms

  • 120.
    Smirnov, Yury
    et al.
    Penza State University, Penza, Ryssland.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Derevyanchuk, Ekaterina
    Penza State University, Penza, Russia.
    Solution to the Inverse Problem of Reconstructing Permittivity of an n-Sectional Diaphragm in a Rectangular Waveguide2014Inngår i: Algebra, Geometry and Mathematical Physics: AGMP, Mulhouse, France, October 2011, Springer Berlin/Heidelberg, 2014, Vol 85, s. 555-566Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We have developed a numerical-analytical method of solution to the inverse problem of reconstructing permittivities ofn-sectional diaphragms in a waveguide of rectangular cross section. For a one-sectional diaphragm, a solution in the closed form is obtained and the uniqueness is proved.

  • 121.
    Smirnov, Yury
    et al.
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russia.
    Smolkin, Eugene
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russia.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    On the existence of non-polarized azimuthal-symmetric electromagnetic waves in circular metal-dielectric waveguide filled with nonlinear radially inhomogeneous medium2018Inngår i: Journal Electromagnetic Waves and Applications, ISSN 0920-5071, E-ISSN 1569-3937, Vol. 32, nr 11, s. 1389-1408Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Propagation of monochromatic nonlinear symmetric hybrid waves in a cylindrical nonlinear inhomogeneous metal–dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations where spectral parameters are the wave propagation constants. The setting under study is reduced to a new type of nonlinear eigenvalue problem. An analytical method for solving this problem is elaborated. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

  • 122.
    Smith, P. D.
    et al.
    Macquarie University, Sydney, Australia.
    Vinogradova, E. D.
    Macquarie University, Sydney, Australia.
    Shestopalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    A regularized approach to the calculation of the propagation modes in a perturbed waveguide2017Inngår i: 2017 International Conference on Electromagnetics in Advanced Applications (ICEAA), 2017, s. 1727-1730, artikkel-id 8065627Konferansepaper (Fagfellevurdert)
    Abstract [en]

    When a perfectly electrically conducting (PEC) waveguide is perturbed by the insertion of a PEC structure aligned with its axis, its propagation constants are perturbed. Two complementary approaches to the determination of change induced by the insert are described. The first provides an analytic estimate when the insert is a small flat strip. The second approach converts the underlying boundary value problem to a homogeneous Fredholm matrix equation in which the propagation constants are found from the roots of the determinant of the matrix and stable numerical processes may be employed to find the propagation constants. The second approach is not constrained by the size or shape of the inserts, and thus provides an independent estimate of the accuracy of the analytic estimate of perturbation to the propagation constants of the empty waveguide; it also determines the empty waveguide parameters themselves.

  • 123.
    Smolkin, E.
    et al.
    Penza State University, Penza, Russian Federation.
    Snegur, M.
    Penza State University, Penza, Russian Federation.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Numerical method for electromagnetic wave propagation problem in a cylindrical anisotropic inhomogeneous waveguide with longitudinal magnetization2017Inngår i: 2017 Progress In Electromagnetics Research Symposium - Fall (PIERS - FALL), Electromagnetics Academy , 2017, s. 299-305Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The propagation of monochromatic electromagnetic waves in a cylindrical anisotropic inhomogeneous waveguide with longitudinal magnetization is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. Numerical results are obtained using a modification of the projecting methods. The comparison with known exact solutions (for particular values of parameters) are made. © 2018 Electromagnetics Academy. All rights reserved.

  • 124.
    Smolkin, Eugene
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Goubau line filled with nonlinear medium: Numerical study of TM-polarized waves2015Inngår i: Proceedings of the 2015 International Conference on Electromagnetics in Advanced Applications: ICEAA 2015, IEEE Press, 2015, s. 1572-1575Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The propagation of monochromatic electromagnetic TM waves in the Goubau line (conducting cylinder covered by a concentric dielectric layer) filled with nonlinear inhomogeneous medium is considered. Two types of nonlinearity are studied. A physical problem is reduced to solving a nonlinear transmission eigenvalue problem for a system of ordinary differential equations. Eigenvalues of the problem correspond to propagation constants of the waveguide. A method is proposed for finding approximate eigenvalues of the nonlinear problem based on solving an auxiliary Cauchy problem (by the shooting method). The existence of eigenvalues that correspond to a new propagation regime is predicted. A comparison with the linear case is given.

  • 125.
    Smolkin, Eugene
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Numerical method for electromagnetic wave propagation problem in a cylindrical anisotropic inhomogeneous metal-dielectric waveguide2017Inngår i: Progress in Electromagnetics Research Symposium, Electromagnetics Academy , 2017, s. 3201-3208Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The propagation of monochromatic electromagnetic waves in a cylindrical anisotropic metal-dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. Numerical results are found with a projection method.

  • 126.
    Smolkin, Eugene
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    The azimuthal symmetric hybrid waves in nonlinear cylindrical waveguide2017Inngår i: Progress in Electromagnetics Research Symposium, Electromagnetics Academy , 2017, s. 348-353Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The propagation of monochromatic nonlinear symmetric hybrid waves in a cylindrical nonlinear dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. Numerical results are found with the modification of the shooting method. The method allows us to determine approximate eigenvalues with any prescribed accuracy. The comparison with known exact solutions (for particular values of parameters) are made. The approach described in this paper can be applied to other problems, e.g., to multilayered inhomogeneous waveguides.

  • 127.
    Smolkin, Eugene
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Nonlinear Goubau line: analytical-numerical approaches and new propagation regimes2017Inngår i: Journal Electromagnetic Waves and Applications, ISSN 0920-5071, E-ISSN 1569-3937, Vol. 31, nr 8, s. 781-797Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider propagation of surface TE waves in the Goubau line (GL) assuming that the dielectric cover is non-linear and inhomogeneous. The problem at hand is reduced to a non-linear 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 TE waves for the chosen nonlinearity (Kerr law) is proved by the method of contraction. Conditions under which several higher-order waves can propagate are obtained, and the intervals of the corresponding propagation constants are determined. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. In numerical experiment two types of nonlinearities are considered and compared: Kerr nonlinearity and nonlinearity with saturation. New propagation modes are found.

  • 128.
    Smolkin, Eugene
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Numerical study of multilayered nonlinear inhomogeneous waveguides in the case of TE polarization2016Inngår i: 2016 10th European Conference on Antennas and Propagation: EuCAP 2016, Institute of Electrical and Electronics Engineers (IEEE), 2016, artikkel-id 7481782Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We consider propagation of surface TE waves in a circular dielectric waveguide filled with nonlinear (Kerr non-linearity) multilayered inhomogeneous medium. Each layer is characterized by a specific value of the nonlinearity coefficient α. Analysis is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation; eigenvalues of the problem correspond to propagation constants of the waveguide. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

  • 129.
    Smolkin, Eugene
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Numerical study of multilayered nonlinear inhomogeneous waveguides in the case of TM polarization2016Inngår i: 2016 URSI International Symposium on Electromagnetic Theory (EMTS), IEEE conference proceedings, 2016, s. 247-250Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We consider propagation of surface TM waves in a circular dielectric waveguide filled with nonlinear (Kerr nonlinearity) multilayered inhomogeneous medium. Each layer is characterized by a specific value of the nonlinearity coefficient α. Analysis is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation; eigenvalues of the problem correspond to propagation constants of the waveguide. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

  • 130.
    Smolkin, Eugene
    et al.
    Penza State University, Penza, Russia.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Snegur, Maxim
    Penza State University, Penza, Russia.
    Diffraction of TM polarized electromagnetic waves by a nonlinear inhomogeneous metal-dielectric waveguide2017Inngår i: 2017 International Conference on Electromagnetics in Advanced Applications (ICEAA), 2017, s. 1288-1291, artikkel-id 8065508Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this work, we consider the diffraction of TM waves by an open metal-dielectric waveguide, a Goubau line (GL), with a nonlinear inhomogeneous dielectric cover. Numerical experiments are carried out for the nonlinearity with saturation. The physical problem is reduced to solving a nonlinear boundary value problem for a system of ordinary differential equations. Numerical results are obtained using a modification of the shooting method which makes it possible to determine and plot the amplitude of the reflected field with respect to the amplitude of the incident field. Comparison between the nonlinear problem and the corresponding linear setting is performed.

  • 131.
    Smolkin, Eugene
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Shestopalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Nonlinear coupled TE-TM waves in Goubau line2016Inngår i: Proceedings of the 2016 18th International Conference on Electromagnetics in Advanced Applications, ICEAA 2016, 2016, s. 356-359, artikkel-id 7731397Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Nonlinear coupled electromagnetic TE-TM wave propagation in the Goubau line (a conducting cylinder covered by a concentric dielectric layer) filled with nonlinear inhomogeneous medium is considered. Nonlinearity inside the GL is described by the Kerr law. The physical problem is reduced to a nonlinear two-parameter eigenvalue problem for a system of (nonlinear) ordinary differential equations. For the numerical solution, a method based on solving an auxiliary Cauchy problem (the shooting method) is proposed. The coupled TE-TM waves propagating in GL are determined numerically. Whether these mathematically predicted propagation regime really exist is a hypothesis that can be proved or disproved in an experiment.

  • 132.
    Smolkin, Eugene
    et al.
    Penza State University, Penza, Russia.
    Shestopalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Numerical analysis of electromagnetic wave propagation in metal-dielectric waveguides filled with nonlinear medium2016Inngår i: 2016 Progress In Electromagnetics Research Symposium, PIERS 2016 - Proceedings, 2016, s. 222-226, artikkel-id 7734297Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The propagation of monochromatic electromagnetic waves in metal-dielectric waveguides of simple geometry (circular cylindrical) filled with nonlinear inhomogeneous medium is considered. The Kerr nonlinearity is studied. A physical problem is reduced to solving a nonlinear transmission eigenvalue problem for a system of ordinary differential equations. Eigenvalues of the problem correspond to propagation constants of the waveguide. A method is proposed for finding approximate eigenvalues of the nonlinear problem based on solving an auxiliary Cauchy problem (by the shooting method). The existence of eigenvalues that correspond to a new propagation regime is predicted. A comparison with the linear case is given. 

  • 133.
    Smolkin, Eugene
    et al.
    Penza State University, Penza, Russia.
    Snegur, Maxim
    Penza State University, Penza, Russia.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Diffraction of TM Polarized EM Waves by a Nonlinear Inhomogeneous Dielectric Cylinder2018Inngår i: 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 2018, s. 66-70Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this work, we consider the diffraction of TM waves by a nonlinear inhomogeneous dielectric cylinder. Numerical experiments are carried out for the nonlinearity with saturation. The physical problem is reduced to solving a nonlinear boundary value problem for a system of ordinary differential equations. Numerical results are obtained using a modification of the shooting method which makes it possible to determine and plot the amplitude of the reflected field with respect to the amplitude of the incident field. Comparison between the nonlinear problem and the corresponding linear setting is performed.

  • 134.
    Smolkin, Eugene
    et al.
    Penza State University, Penza, Russia.
    Snegur, Maxim
    Penza State University, Penza, Russia.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Nonlinear Hybrid Waves in a Cylindrical Anisotropic Metal-Dielectric Waveguide2018Inngår i: 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 2018, s. 1948-1954Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The propagation of hybrid waves in a cylindrical anisotropic nonlinear metal-dielectric waveguide is considered. The physical setting is reduced to a transmission eigenvalue problem for a system of ordinary differential equations which is new type of nonlinear eigenvalue problem where spectral parameters are the wave propagation constants. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

  • 135.
    Smolkin, Eugene
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Tsupak, A. A.
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russian Federation.
    Galerkin method for solving scalar problems of diffraction by a partially shielded inhomogeneous body2016Inngår i: Proceedings of the 2016 18th International Conference on Electromagnetics in Advanced Applications, ICEAA 2016, 2016, s. 360-363, artikkel-id 7731398Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The scalar problem of diffraction by an inhomogeneous partially shielded body is considered. The boundary value problem leads to a system of integral equations on two- and three-dimensional manifolds with boundary. The equivalence of the integral and differential formulations of the problem is established; the Fredholm property and invertibility of the matrix operator are proved. Galerkin method for numerical solving of the integral equations is proposed. The approximation property for compactly supported basis functions as well as the convergence of Galerkin method in proper Sobolev spaces is proved. Numerical results are provided.

  • 136. Smolkin, Eugene Y.
    et al.
    Shestopalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Nonlinear goubau line: Numerical study of te-polarized waves2015Inngår i: PIERS 2015 Prague: Progress in Electromagnetics Research Symposium : Proceedings, Cambridge, MA: The Electromagnetics Academy , 2015, s. 1513-1517Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The propagation of monochromatic electromagnetic TE waves in the Goubau line (conducting cylinder covered by a concentric dielectric layer) filled with nonlinear inhomogeneous medium is considered. Two types of nonlinearity are studied. A physical problem is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation. Eigenvalues of the problem correspond to propagation constants of the waveguide. A method is proposed for finding approximate eigenvalues of the nonlinear problem based on solving an auxiliary Cauchy problem (by the shooting method). The existence of eigenvalues that correspond to a new propagation regime is predicted. A comparison with the linear case is given.

  • 137.
    Sundgren, David
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Discrete Second-order Probability Distributions that Factor into Marginals2011Inngår i: Proceedings of the Seventh International Symposium on Imprecise Probabilities: Theories and Applications / [ed] Frank Coolen, Gert de Cooman, Thomas Fetz, Michael Oberguggenberger, SIPTA , 2011, s. 335-342Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In realistic decision problems there is more often than not uncertainty in the background information. As for representation of uncertain or imprecise probability values, second-order probability, i.e. probability distributions over probabilities, offers an option. With a subjective view of probability second-order probability would seem to be impractical since it is hard for a person to construct a second-order distributions that reflects his or her beliefs. From the perspective of probability as relative frequency the task of constructing or updating a second-order probability distribution from data is somewhat easier. Here a very simple model for updating lower bounds of probabilities is employed. But the difficulties in choosing second-order distributions may be further alleviated if structural properties are considered. Either some of the probability values are dependent in some way, e.g. that they are known to be almost equal, or they are not dependent in any other way than what follows from that the values sum to one. In this work we present the unique family of discrete second-order probability distributions that correspond to the case where dependence is limited. These distributions are shown to have the property that the joint distributions are equal to normalised products of marginal distributions. The distribution family introduced here is a generalisation of a special case of the multivariate Pólya distribution and is shown to be conjugate prior to a compound hypergeometric distribution.

  • 138.
    Sundgren, David
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Expected Utility from Multinomial Second-order Probability Distributions2010Inngår i: Polibits, ISSN 1870-9044, nr 42, s. 71-75Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider the problem of maximizing expected utility when utilities and probabilities are given by discrete probability dis- tributions so that expected utility is a discrete stochastic variable. As for discrete second-order distributions, that is probability distributions where the variables are themselves probabilities, the multinomial family is a reasonable choice at least if first-order probabilities are interpreted as relative frequencies. We suggest a decision rule that reflects the uncertainty present in distribution-based probabilities and utilities and we show an example of this rule in action with multinomial second-order distributions.

     

  • 139.
    Sundgren, David
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    The Apparent Arbitrariness of Second-Order Probability Distributions2011Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Adequate representation of imprecise probabilities is a crucial and non-trivial problem in decision analysis. Second-order probability distributions is the model for imprecise probabilitoes whose merits are discussed in this thesis.

    That imprecise probabilities may be represented by second-order probability distributions is well known but there has been little attention to specific distributions. Since different probability distributions have different properties, the study of the desired properties of models of imprecise probabilities with respect to second-order models require analysis of particular second-order distributions.

    An often held objection to second-order probabilities is the apparent arbitrarines in the choice of distribution. We find some evidence that the structure of second-order distributions is an important factor that prohibits arbitrary choice of distributions. In particular, the properties of two second-order distributions are investigated; the uniform joint distribution and a variant of the Dirichlet distribution that has the property of being the normalised product of its own marginal distributions.

    The joint uniform distribution is in this thesis shown to have marginal distributions that belie the supposed non-informativeness of a uniform distribution. On the other hand, the modified Dirichlet distribution  discovered here has its information content evenly divided among the joint and marginal distributions in that the total correlation of the variables is minimal.

    It is also argued in the thesis that discrete distributions, as opposed to the continuous distributions mentioned above, would have the advantage of providing a natural setting for updating of lower bounds, and computation of expected utility is made more efficient.

  • 140.
    Svanstedt, Nils
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Homogenization of parabolic operators1992Rapport (Annet vitenskapelig)
  • 141.
    Söderlund, Karin
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Mer grit i undervisningen: Matematikinlärning i klassrummet2018Independent thesis Advanced level (professional degree), 20 poäng / 30 hpOppgave
  • 142.
    Tinglöf, Mimmi
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Laborativ matematik i grundskolan: Ur ett lärarperspektiv2018Independent thesis Advanced level (professional degree), 20 poäng / 30 hpOppgave
    Abstract [sv]

    Syftet med denna studie är undersöka hur lärare arbetar med laborativt material, vilken inställning de har till arbete med laborativt material och i vilket syfte de använder det. Studien utgår från två frågeställningar; Hur arbetar lärare med laborativt material inom matematikämnet i grundskolan?  På vilket sätt anser lärare att laborativt material främjar inlärningen i och förståelsen för ämnet?   I denna studie har två datainsamlingsmetoder använts för att undersöka mina frågeställningar, metoderna är enkäter och intervjuer. Denna studie har visat att lärare i hög grad arbetar med laborativt material av olika slag och att de har en positiv inställning till undervisning med laborativt material. Utifrån resultat i denna studie kan vi se att en betydande del av respondenterna använder laborativt material till de elever som uppvisar svårigheter vilket är ett vanligt fenomen enligt tidigare forskning men som också har lett till låg status bland eleverna att behöva arbeta med laborativt material. 

  • 143.
    Tomasek, P.
    et al.
    Tomas Bata University in Zlin, Zlin, Czech Republic .
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Kresalek, V.
    Tomas Bata University in Zlin, Zlin, Czech Republic .
    Comparison of selected evolutionary techniques used in reconstruction of permittivity2015Inngår i: Proceedings of the 2015 International Conference on Electromagnetics in Advanced Applications: ICEAA 2015, IEEE conference proceedings, 2015, s. 614-617, artikkel-id 7297189Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This work aims at comparison of some traditional evolutionary algorithms (GA, DE, PSO) used in the computation and optimization of transmission coefficients of waveguide filters and in the estimation of the permittivity formed by multi-sectional diaphragms in a waveguide of rectangular cross-section.

  • 144.
    Tomasek, P.
    et al.
    Tomas Bata University in Zlin, Zlin, Czech Republic .
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Kresalek, V.
    Tomas Bata University in Zlin, Zlin, Czech Republic .
    Reconstruction of permittivity of multiple layers in free space2015Inngår i: Proceedings of the 2015 International Conference on Electromagnetics in Advanced Applications: ICEAA 2015, IEEE conference proceedings, 2015, s. 610-613Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The goal of this theoretical study is the improvement of the techniques of determining electromagnetic permittivity. However, it may be developed and applied for the reconstruction of other parameters. The work is aimed at the preliminary design and implementation of a system solving inverse problem of reconstruction permittivities of materials consisting of several dielectric layers based on real measurements of the transmission and reflection coefficients in free space.

  • 145.
    Tomasek, Pavel
    et al.
    Tomas Bata University, Zlin, Czech Republic .
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Verification of computational model of transmission coefficients of waveguide filters2015Inngår i: PIERS 2015 Prague: Progress in Electromagnetics Research Symposium : Proceedings, Cambridge, MA: The Electromagnetics Academy , 2015, s. 1538-1541Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Owing to the recent research a method of estimating transmission coefficients for a waveguide of rectangular cross-section loaded with multi-layered parallel-plane dielectrics is found. Consequently, the analysis of the transmitted and reflected fields in terms of the scattering matrix formalism can be performed explicitly. This article is mainly based on comparisons between real measured and computed transmission coefficients of a waveguide filter. the computation employs analysis of closed-form solutions and numerical multi-parameter optimization. the presented waveguide filter is formed by multi-sectional diaphragms placed in a waveguide of rectangular cross-section. Comparison of the computed and measured transmission coefficients demonstrates that the difference is very low, rather marginal and thus the output of the work is considerably promising.

  • 146.
    Tossavainen, Timo
    et al.
    University of Eastern Finland.
    Attorps, Iiris
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Väisänen, Pertti
    University of Eastern Finland.
    On mathematics students' understanding of the equation concept2011Inngår i: Far East Journal of Mathematical Education, ISSN 0973-5631, Vol. 6, nr 2, s. 127-147Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We analyze data on mathematics students’ understanding of the concept of equation. A majority of the participants (N = 128) studies in teacher education programs in Finland, Sweden and South Africa. The data reveals a variety of fundamentally different concept definitions of equation, of which only a half can be seen to be correct. In the students’ concept image of equation, it is commonly assumed that every equation must possess the truth value ‘true’ in spite of the fact that any considerations related to the truth value only rarely appear in their concept definitions. Also the presence of a variable is regularly assumed in the participants’ concept images. Both a chain of equations and a pair of equivalent equations are surprisingly often seen being a single equation. Finally, the incomplete understanding of the reflexive and symmetric properties of equality often hindersstudents from identifying equations. The study is based on both phenomenographic andquantitative analyses of the students’ answers to a questionnaire.

    .

  • 147.
    Tossavainen, Timo
    et al.
    University of Eastern Finland.
    Attorps, Iiris
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Väisänen, Pertti
    University of Eastern Finland.
    Some South African mathematics teachers' concept images of the equation concept2012Inngår i: African Journal of Research in Mathematics, Science and Technology Education, ISSN 18117295, Vol. 16, nr 3, s. 376-389Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we examine the concept definitions a group of South African upper secondary school mathematics teachers (N = 47) express and how their understanding of the truth value, the role of variable and the syntax of expression appear in the participants' explanations for their assessment of examples and non-examples of equations. We use content analysis and standard quantitative methods. The data consists of the participants' answers to a questionnaire reflecting both teachers' concept definitions of equation and their skills in classifying examples and non-examples of equation. Altogether 27 participants were able to give a correct definition of the equation concept. Ten participants' definition was slightly ambiguous yet meaningful and ten participants failed in this task. In general, the participants had very high confidence in the sufficiency of their skills in classifying examples and non-examples of equations. Nevertheless, on average, they only succeeded in correctly identifying an equation in 13 of 24 items, with most of the equations being quite simple and none beyond the upper secondary school level. The findings of this study also reveal a common and dominant conception that equations should always possess the truth value 'true' although truth value is discussed only in one participant's concept definition. Secondly, the participants are quite careless about the syntax and the involved binary relation in particular despite the fact that the correct form of equations and the equality relation were regularly mentioned in their concept definitions of equation. Finally, some participants seem to think that there is only one equation related to each algebraic problem.

  • 148.
    Viirman, Olov
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Discourses of functions: University mathematics teaching through a commognitive lens2011Inngår i: Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education / [ed] Marta Pytlak, Tim Rowland, Ewa Swoboda, Rzeszow, Poland, 2011, s. 2103-2112Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This paper reports on an ongoing study focusing on the teaching of functions in undergraduate courses in mathematics at three Swedish universities. In this paper excerpts from the lectures of three teachers at one university are analysed, using commognitive theory. Characteristic features of the teachers’ discourses about functions are presented. Definitions are found to be the central type of narrative, while theorems and proofs are largely absent, despite the fact that the teaching is of a traditional type, often connected to the “definition-theorem-proof” format. Three main categories of routines are found: substantiation, construction and motivation routines. It is also seen that the teachers are more concerned with questions of “why” to do things than “when” to do them. 

  • 149.
    Viirman, Olov
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Discursive practices of two university teachers on the concept of 'linear transformation'2011Inngår i: Developing Mathematical Thinking: Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4 / [ed] Behiye Ubuz, Ankara: PME , 2011, s. 313-320Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This paper reports on an ongoing study focusing on the teaching of functions in undergraduate courses in mathematics at three Swedish universities. In this paper two excerpts of lectures on linear transformations are analysed, using commognitive theory. The two teachers' discursive uses of the terms 'linearity' and 'linear transformation' are described, and potential consequences for student learning are presented. One lecture displays a strong mathematical content while lacking contextualization, while the other is well grounded in everyday experience, but with a lack of attention to mathematical detail potentially detrimental to student learning.

  • 150.
    Viirman, Olov
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik. Karlstads universitet, Institutionen för matematik och datavetenskap.
    The function concept and university mathematics teaching2014Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This thesis concerns the teaching of mathematics at university level, with a particular focus on the teaching of the function concept. The main aim of the thesis is describing and analysing the teaching practices of university mathematics teachers regarding the function concept, and how this concept is constituted through these practices. To this end, video recordings of lectures by seven mathematics teachers at three Swedish universities were analysed using a discursive perspective, Sfard’s commognitive framework. The observed teaching was traditional in form, with teachers using “chalk talk” – simultaneously talking and writing on the board. The results show that the teaching practices of the teachers belong to two distinct but intertwined discourses – a mathematical discourse, and a discourse of mathematics teaching. Classifications of important aspects of these discourses are presented, and it is found that the teachers’ discursive practices, while sharing overall form, still display considerable differences. Other results include an analysis of the levels of objectification displayed by the teachers in their discursive constitution of the function concept. The study contributes to a small but growing body of empirical research on university mathematics teaching practice.

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