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Engineering Mathematics II : Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization
- 2016
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Editorial collection (peer-reviewed)abstract
- This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most relevant for applications in modern technologies and engineering. It addresses mathematical methods of algebra, applied matrix analysis, operator analysis, probability theory and stochastic processes, geometry and computational methods in network analysis, data classification, ranking and optimisation.The individual chapters cover both theory and applications, and include a wealth of figures, schemes, algorithms, tables and results of data analysis and simulation. Presenting new methods and results, reviews of cutting-edge research, and open problems for future research, they equip readers to develop new mathematical methods and concepts of their own, and to further compare and analyse the methods and results discussed.The book consists of contributed chapters covering research developed as a result of a focused international seminar series on mathematics and applied mathematics and a series of three focused international research workshops on engineering mathematics organised by the Research Environment in Mathematics and Applied Mathematics at Mälardalen University from autumn 2014 to autumn 2015: the International Workshop on Engineering Mathematics for Electromagnetics and Health Technology; the International Workshop on Engineering Mathematics, Algebra, Analysis and Electromagnetics; and the 1st Swedish-Estonian International Workshop on Engineering Mathematics, Algebra, Analysis and Applications.It serves as a source of inspiration for a broad spectrum of researchers and research students in applied mathematics, as well as in the areas of applications of mathematics considered in the book.
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| 3. |
- Muhumuza, Asaph Keikara, 1975-
(author)
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Extreme points of the Vandermonde determinant in numerical approximation, random matrix theory and financial mathematics
- 2020
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Doctoral thesis (other academic/artistic)abstract
- This thesis discusses the extreme points of the Vandermonde determinant on various surfaces, their applications in numerical approximation, random matrix theory and financial mathematics. Some mathematical models that employ these extreme points such as curve fitting, data smoothing, experimental design, electrostatics, risk control in finance and method for finding the extreme points on certain surfaces are demonstrated.The first chapter introduces the theoretical background necessary for later chapters. We review the historical background of the Vandermonde matrix and its determinant, some of its properties that make it more applicable to symmetric polynomials, classical orthogonal polynomials and random matrices.The second chapter discusses the construction of the generalized Vandermonde interpolation polynomial based on divided differences. We explore further, the concept of weighted Fekete points and their connection to zeros of the classical orthogonal polynomials as stable interpolation points.The third chapter discusses some extended results on optimizing the Vandermonde determinant on a few different surfaces defined by univariate polynomials. The coordinates of the extreme points are shown to be given as roots of univariate polynomials.The fourth chapter describes the symmetric group properties of the extreme points of Vandermonde and Schur polynomials as well as application of these extreme points in curve fitting.The fifth chapter discusses the extreme points of Vandermonde determinant to number of mathematical models in random matrix theory where the joint eigenvalue probability density distribution of a Wishart matrix when optimized over surfaces implicitly defined by univariate polynomials.The sixth chapter examines some properties of the extreme points of the joint eigenvalue probability density distribution of the Wishart matrix and application of such in computation of the condition numbers of the Vandermonde and Wishart matrices. The seventh chapter establishes a connection between the extreme points of Vandermonde determinants and minimizing risk measures in financial mathematics. We illustrate this with an application to optimal portfolio selection.The eighth chapter discusses the extension of the Wishart probability distributions in higher dimension based on the symmetric cones in Jordan algebras. The symmetric cones form a basis for the construction of the degenerate and non-degenerate Wishart distributions.The ninth chapter demonstrates the connection between the extreme points of the Vandermonde determinant and Wishart joint eigenvalue probability distributions in higher dimension based on the boundary points of the symmetric cones in Jordan algebras that occur in both the discrete and continuous part of the Gindikin set.
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- Lundengård, Karl, et al.
(author)
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Application of the Marquardt Least Square Method to the Estimation of Pulse Function Parameters
- 2014
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In: 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014Conference date: 15–18 July 2014 Location: Narvik, Norway ISBN: 978-0-7354-1276-7 Editor: Seenith Sivasundaram Volume number: 1637 Published: 10 december 2014. - : AIP Publishing LLC. - 9780735412767 ; , s. 637-646
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Conference paper (peer-reviewed)abstract
- Application of the Marquardt least-squares method (MLSM) to the estimation of non-linear parameters of functionsused for representing various lightning current waveshapes is presented in this paper. Parameters are determined for the Pulse,Heidler’s and DEXP function representing the first positive, first and subsequent negative stroke currents as given in IEC62305-1 Standard Ed.2, and also for some other fast- and slow-decaying lightning current waveshapes. The results prove theability of the MLSM to be used for the estimation of parameters of the functions important in lightning discharge modeling.
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| 5. |
- Lundengård, Karl, et al.
(author)
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Estimation of Pulse Function Parameters for Approximating Measured Lightning Currents Using the Marquardt Least Squares Method
- 2014
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In: IEEE International Symposium on Electromagnetic Compatibility. - 9781479932252 ; , s. 571-576
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Conference paper (peer-reviewed)abstract
- The Marquardt least-squares method is applied in this paper for estimation of the Pulse function’s non-linear parameters in order to approximate measured lightning currents. Such procedure is generalized so it could be used for other pulse functions representing lightning current waveshapes. The obtained results show that this method provides good results for the IEC 62305-1 standard lightning current waveshapes of the first and subsequent return stroke currents, and also for some measured fast- and slow-decaying current waveshapes.
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| 6. |
- Monsefi, Farid, et al.
(author)
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Evaluating Parameters of Approximate Functions for Representation of Sommerfeld Integrals
- 2015
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In: ASMDA 2015 Proceedings. - : ISAST: International Society for the Advancement of Science and Technology. - 9786185180058 ; , s. 711-722
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Conference paper (peer-reviewed)abstract
- Approximate evaluation of Sommerfeld type integrals has been of great interest for researchers in the field of electromagnetics, in particular in the areas of antenna theory and grounding systems analysis. These integrals arise in the expressions describing the electromagnetic field in the surroundings of such structures when they are located above/inside a semi-conducting media. The fact that these integrals don’t have a closed form solution, enticed researchers to approximately evaluate them either by employing a numerical integration technique, or using some kind of procedure that will approximate them and allow their analytical evaluation.A simple procedure for approximate calculation of one type of Sommerfeld integrals occurring in cases of wire conductors buried in semi-conducting ground is proposed. It considers approximation of a part of the integrand using a weighted exponential function with an additional unknown constant complex term. This kind of modification allows the obtained integral to be calculated analytically.
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| 7. |
- Monsefi, Farid, et al.
(author)
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HF Analysis of Thin Horizontal Central-Fed Conductor above Lossy Homogeneous Soil
- 2014
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In: IEEE International Symposium on Electromagnetic Compatibility 20 October 2014. - 9781479932252 ; , s. 916-921
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Conference paper (peer-reviewed)abstract
- In this paper, the authors perform HF analysis of a thin horizontal conductor fed in its center, and arbitrarily positioned above lossy homogeneous ground of known electrical parameters. The approach is based on the electric-field integral equation method, and formulation of the Hallén’s integral equation. This equation is then solved for the current using the point-matching method. The Sommerfeld’s integrals that express the influence of the lossy ground, and that appear in these calculations, are solved approximately. Thorough analysis is performed in order to observe the influence of different parameters of the geometry and the ground on current distribution in the specified frequency range. Furthermore, the verification of the method is done by comparison with the exact model based on the full-wave theory.
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| 8. |
- Monsefi, Farid, et al.
(author)
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Solution of Two-Dimensional Electromagnetic Scattering Problem by FDTD with Optimal Step Size, Based on a Semi-Norm Analysis
- 2014
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In: 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014 Conference date: 15–18 July 2014 Location: Narvik, Norway ISBN: 978-0-7354-1276-7 Editor: Seenith Sivasundaram Volume number: 1637 Published: 10 december 2014. - : American Institute of Physics (AIP). - 9780735412767 ; , s. 683-690
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Conference paper (peer-reviewed)abstract
- To solve the electromagnetic scattering problem in two dimensions, the Finite Difference Time Domain (FDTD)method is used. The order of convergence of the FDTD algorithm, solving the two-dimensional Maxwell’s curl equations,is estimated in two different computer implementations: with and without an obstacle in the numerical domain of the FDTDscheme. This constitutes an electromagnetic scattering problem where a lumped sinusoidal current source, as a source ofelectromagnetic radiation, is included inside the boundary. Confined within the boundary, a specific kind of AbsorbingBoundary Condition (ABC) is chosen and the outside of the boundary is in form of a Perfect Electric Conducting (PEC)surface. Inserted in the computer implementation, a semi-norm has been applied to compare different step sizes in the FDTDscheme. First, the domain of the problem is chosen to be the free-space without any obstacles. In the second part of thecomputer implementations, a PEC surface is included as the obstacle. The numerical instability of the algorithms can berather easily avoided with respect to the Courant stability condition, which is frequently used in applying the general FDTDalgorithm.
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| 9. |
- Monsefi, Farid, et al.
(author)
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Sommerfeld’s integrals and Hallen’s integral equation in Data Analysis for Horizontal Dipole Antenna above Real Ground
- 2014
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In: SMTDA 2014 Proceedings. - : ISAST: International Society for the Advancement of Science and Technology. - 9786188125766 ; , s. 507-518
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Conference paper (peer-reviewed)abstract
- Increase of the radiation power in different frequency bands during the last decades, has called for a study of harmful effects on the living organisms and electronic equipment of the radio frequency energy. An accurate determination of the near field strength, electric as well as magnetic, in the vicinity of higher-power transmitting antennas is necessary for assessing any possible radiation hazard. In that sense, it is of great importance to account for the influence of the finite ground conductivity on the electromagnetic field structure in the surroundings of these emitters. The estimation of this influence has been intensively studied, and a number of approaches has been applied in that sense, ranging from the exact full-wave based ones to different forms of approximate, less time-consuming, ones. Although the approximate methods introduce a certain level of calculation error, their simplicity is of interest in the electomagnetic compatibility (EMC) studies. For that reason, finding an approximate, but satisfyingly accurate method, applicable to wide range of parameters is often a goal of researches done in this field.In this paper, the authors perform an analysis of a thin horizontal dipole antenna (HDA) above real ground of known electrical parameters. The approach is based on the electric-field integral equation method, and formulation of the Hallén’s integral equation (HIE). This equation is then solved for the current, which is assumed in a polynomial form, using the point-matching method (PMM). This way obtained system of linear equations involves improper Sommerfeld’s integrals, which express the influence of the real ground and are here solved approximately using simple, so-called OIA and TIA, approximations (one- and two-image approximations). Both types of approximations are in an exponential form, and therefore are similar to those obtained applying the method of images. It should be kept in mind that the goal of this approach is to develop approximations that have a simple form, whose application yields satisfyingly accurate calculations of the Sommerfeld`s type of integrals, and are widely applicable, i.e. their employment is not restricted by the values of electrical parameters of the ground, or the geometry.Thorough analysis is performed in order to observe the influence of different parameters of the geometry, and the ground, on current distribution and the input impedance/admittance of the HDA in a wide frequency range. Furthermore, the verification of the method is done by comparison to the exact model based on the full-wave theory, and experimental data. Obtained results indicate a possibility of applying the described methodology to inverse problem involving evaluation of electrical parameters of the ground (or detection of ground type change) based on measured input impedance/admittance of the antenna.
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| 10. |
- Peric, Mirjana, et al.
(author)
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Analysis of shielded coupled microstrip line with partial dielectric support
- 2014
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In: 2014 18th International Symposium on Electrical Apparatus and Technologies, SIELA 2014 - Proceedings. - : IEEE conference proceedings. - 9781479958177 ; , s. Article number 6871881-
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Conference paper (peer-reviewed)abstract
- A shielded coupled microstrip line with partial dielectric support is analysed using the hybrid boundary element method (HBEM) and the finite difference method (FDM). The HBEM is a combination of the equivalent electrodes method (EEM) and the boundary element method (BEM). The microstrip line characteristic parameters: the effective relative permittivity and the characteristic impedance are determined. “Odd” and “even” modes are taken into account. The results are compared with corresponding ones found in the literature.
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