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• 1.
University Pretoria, South Africa.
University of the Basque Country, Spain. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Common Fixed Points of Generalized Rational Type Cocyclic Mappings in Multiplicative Metric Spaces2015In: Discrete dynamics in nature and society, ISSN 1026-0226, E-ISSN 1607-887X, Vol. 2015, article id 532725Article in journal (Refereed)

The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.

• 2.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
University of Copenhagen.
On the universality of the Epstein zeta functionManuscript (preprint) (Other academic)

We study universality properties of the Epstein zeta function En(L,s) for lattices L of large dimension n and suitable regions of complex numbers s . Our main result is that, as n→∞ , En(L,s) is universal in the right half of the critical strip as L varies over all n -dimensional lattices L . The proof uses an approximation result for Dirichlet polynomials together with a recent result on the distribution of lengths of lattice vectors in a random lattice of large dimension and a strong uniform estimate for the error term in the generalized circle problem. Using the same basic approach we also prove that, as n→∞ , En(L1,s)−En(L2,s) is universal in the full half-plane to the right of the critical line as (L1,L2) varies over all pairs of n -dimensional lattices. Finally, we prove a more classical universality result for En(L,s) in the s -variable valid for almost all lattices L of dimension n . As part of the proof we obtain a strong bound of En(L,s) on the critical line that is subconvex for n≥5 and almost all n -dimensional lattices L.

• 3.
Max Planck Institute for Gravitational Physics (AEI), Am Mühlenberg 1, D-14476 Golm, Germany.
Université de Haute Alsace, Lab. de Mathématiques Informatique et Applications, 4, rue des Frères Lumière, F-68093 Mulhouse, France. Mälardalen University, School of Education, Culture and Communication.
Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras2011In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 52, no 12, p. 123502-Article in journal (Refereed)

As n-ary operations, generalizing Lie and Poisson algebras, arise in many different physical contexts, it is interesting to study general ways of constructing explicit realizations of such multilinear structures. Generically, they describe the dynamics of a physical system, and there is a need of understanding their quantization. Hom-Nambu-Lie algebras provide a framework that might be an appropriate setting in which n-Lie algebras (n-ary Nambu-Lie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)-ary Hom-Nambu-Lie algebras from n-ary Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n + k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3653197]

• 4.
Danderyds Gymnasium, Danderyd, Sweden.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Umeå University, Umeå, Sweden. Uppsala University, Uppsala, Sweden.
Semi-Bloch Functions in Several Complex Variables2016In: Journal of Geometric Analysis, ISSN 1050-6926, E-ISSN 1559-002X, Vol. 26, no 1, p. 463-473Article in journal (Refereed)

Let M be an n-dimensional complex manifold. A holomorphic function f:M→C is said to be semi-Bloch if for every λ∈C the function (Formula presented.) is normal on M. We characterize semi-Bloch functions on infinitesimally Kobayashi non-degenerate M in geometric as well as analytic terms. Moreover, we show that on such manifolds, semi-Bloch functions are normal.

• 5.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
American Option pricing under Mutiscale Model using Monte Carlo and Least-Square approach2017Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

In the finance world, option pricing techniques have become an appealing topic among researchers, especially for pricing American options. Valuing this option involves more factors than pricing the European style one, which makes it more computationally challenging. This is mainly because the holder of American options has the right to exercise at any time up to maturity. There are several approaches that have been proved to be efficient and applicable for maximizing the price of this type of options. A common approach is the Least squares method proposed by Longstaff and Schwartz. The purpose of this thesis is to discuss and analyze the implementation of this approach under the Multiscale Stochastic Volatility model. Since most financial markets show randomly variety of volatility, pricing the option under this model is considered necessary. A numerical study is performed to present that the Least-squares approach is indeed effective and accurate for pricing American options.

• 6.
Mälardalen University, Department of Mathematics and Physics.
Unique characterization of the Bel-Robinson tensor2004In: Classical and Quantum Graviry, ISSN 0264-9381, Vol. 21, no 14, p. 3499-3503Article in journal (Refereed)

We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors.

• 7.
Mälardalen University, School of Education, Culture and Communication.
Introduction to some modes of convergence: Theory and applications2017Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

This thesis aims to provide a brief exposition of some chosen modes of convergence; namely uniform convergence, pointwise convergence and L1 convergence. Theoretical discussion is complemented by simple applications to scientific computing. The latter include solving differential equations with various methods and estimating the convergence, as well as modelling problematic situations to investigate odd behaviors of usually convergent methods.

• 8.
Norwegian University of Science and Technology.
Eilers, SorenUniversity of Copenhagen.Restorff, GunnarUniversity of the Faroe Islands.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication.
Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 20122013Collection (editor) (Refereed)
• 9.
University of Southern Denmark.
Lund University.
On the Exel crossed product of topological covering maps2009In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, ISSN 0167-8019, E-ISSN 1572-9036, ISSN 0167-8019, Vol. 108, no 3, p. 573-583Article in journal (Refereed)

For dynamical systems defined by a covering map of a compact Hausdorff space and the corresponding transfer operator, the associated crossed product C *-algebras C(X)⋊ α,ℒℕintroduced by Exel and Vershik are considered. An important property for homeomorphism dynamical systems is topological freeness. It can be extended in a natural way to in general non-invertible dynamical systems generated by covering maps. In this article, it is shown that the following four properties are equivalent: the dynamical system generated by a covering map is topologically free; the canonical embedding of C(X) into C(X)⋊ α,ℒℕis a maximal abelian C *-subalgebra of C(X)⋊ α,ℒN; any nontrivial two sided ideal of C(X)⋊ α,ℒℕhas non-zero intersection with the embedded copy of C(X); a certain natural representation of C(X)⋊ α,ℒℕis faithful. This result is a generalization to non-invertible dynamics of the corresponding results for crossed product C *-algebras of homeomorphism dynamical systems.

• 10.
Norwegian University of Science and Technology (NTNU), Trondheim, Norway .
Mälardalen University, School of Education, Culture and Communication.
On the K-theory of the C*-algebra associated with a one-sided shift space2010In: Proceedings of the Estonian Academy of Sciences, ISSN 1736-6046, E-ISSN 1736-7530, Vol. 59, no 4, p. 272-279Article in journal (Refereed)

One-sided shift spaces are a special kind of non-invertible topological dynamical system with which one can associate a C*-algebra. We show how to construct the C*-algebra associated with a one-sided shift space as the Cuntz-Pimsner C*-algebra of a C*-correspondence and use this to compute its K-theory.

• 11.
Umeå University.
An equivalence to the Gleason problem2010In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 370, no 2, p. 373-378Article in journal (Refereed)

In this article we study the Gleason problem locally. A new method for solving the Gleason A problem is presented. This is done by showing an equivalent statement to the Gleason A problem. In order to prove this statement, necessary and a sufficient conditions for a bounded domain to have the Gleason A property are found. Also an example of a bounded but not smoothly-bounded domain in Cn is given, which satisfies the sufficient condition at the origin, and hence has the Gleason A property there.

• 12.
University of Missouri.
The University of Iowa. University of Oklahoma. Technische Universität Berlin. Texas A&M University. Institute for Biomathematics and Biometry, Helmholtz Zentrum München. Lousiana State University. University of Colorado at Boulder. Mälardalen University, School of Education, Culture and Communication. University of Central Florida.
Preface2012In: Numerical Functional Analysis and Optimization, ISSN 0163-0563, E-ISSN 1532-2467, Vol. 33, no 7-9, p. 705-707Article in journal (Other academic)
• 13.
University of Tuscia Largo dell’Universita, Italy.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. University of Salerno, Italy. Nanjing University, China.
On the Critical Strip of the Riemann zeta Fractional derivative2017In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 151, p. 459-472Article in journal (Refereed)

The fractional derivative of the Dirichlet eta function is computed in order to investigate the behavior of the fractional derivative of the Riemann zeta function on the critical strip. Its convergence is studied. In particular, its half-plane of convergence gives the possibility to better understand the fractional derivative of the Riemann zeta function and its critical strip. As an application, two signal processing networks, corresponding to the fractional derivative of the eta function and to its Fourier transform, respectively, are shortly described.

• 14.
Leiden University.
Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication.Skau, ChristianNorwegian University of Science and Technology (NTNU), Norway.Tomiyama, JunUniversity of Tokyo, Japan.
Operator structures and dynamical systems2009Conference proceedings (editor) (Refereed)
• 15. Dutkay, Dorin Ervin
Mälardalen University, School of Education, Culture and Communication.
Decomposition of wavelet representations and Martin boundaries2012In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 262, no 3, p. 1043-1061Article in journal (Refereed)

We study a decomposition problem for a class of unitary representations associated with wavelet analysis, wavelet representations, but our framework is wider and has applications to multi-scale expansions arising in dynamical systems theory for non-invertible endomorphisms. Our main results offer a direct integral decomposition for the general wavelet representation, and we solve a question posed by Judith Packer. This entails a direct integral decomposition of the general wavelet representation. We further give a detailed analysis of the measures contributing to the decomposition into irreducible representations. We prove results for associated Martin boundaries, relevant for the understanding of wavelet filters and induced random walks, as well as classes of harmonic functions. Published by Elsevier Inc.

• 16.
University of Central Florida, US.
Texas A and M University, United sTATES. Lund University.
Irreducible wavelet representations and ergodic automorphisms on solenoids2011In: Operators and Matrices, ISSN 1846-3886, E-ISSN 1848-9974, Vol. 5, no 2, p. 201-219Article in journal (Refereed)

We focus on the irreducibility of wavelet representations. We present some connections between the following notions: covariant wavelet representations, ergodic shifts on solenoids, fixed points of transfer (Ruelle) operators and solutions of refinement equations. We investigate the irreducibility of the wavelet representations, in particular the representation associated to the Cantor set, introduced in [13], and we present several equivalent formulations of the problem.

• 17. Dutkay, Dorin Ervin
Mälardalen University, School of Education, Culture and Communication. Lund University.
REDUCIBILITY OF THE WAVELET REPRESENTATION ASSOCIATED TO THE CANTOR SET2011In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 139, no 10, p. 3657-3664Article in journal (Refereed)

We answer a question by Judith Packer about the irreducibility of the wavelet representation associated to the Cantor set. We prove that if the QMF filter does not have constant absolute value, then the wavelet representation is reducible.

• 18. Dutkay, Dorin Ervin
Mälardalen University, School of Education, Culture and Communication.
Wavelet Representations and Their Commutant2012In: Analysis for Science, Engineering and Beyond / [ed] Åström, Kalle; Persson, Lars-Erik; Silvestrov, Sergei D., Springer Berlin/Heidelberg, 2012, Vol. 6, p. 253-265Chapter in book (Refereed)

We study the reducibility of the wavelet representation associated to various QMF filters, including those associated to Cantor sets. We show there are connections between this problem, the harmonic analysis of transfer operators and the ergodic properties of shifts on solenoids. We prove that if the QMF filter does not have constant absolute value, then the wavelet representations is reducible.

• 19.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. University of Salerno, Italy.
Entropy and fractal antennas2016In: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 18, no 3, article id 84Article in journal (Refereed)

The entropies of Shannon, Rényi and Kolmogorov are analyzed and compared together with their main properties. The entropy of some particular antennas with a pre-fractal shape, also called fractal antennas, is studied. In particular, their entropy is linked with the fractal geometrical shape and the physical performance.

• 20.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. University of Salerno, Italy.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
A functional equation for the Riemann zeta fractional derivative2017In: Proceedings of INCPAA 2016, 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences / [ed] Sivasundaram, S, American Institute of Physics (AIP), 2017, Vol. 1798, p. 020063-1-020063-10, article id UNSP 020063Conference paper (Refereed)

In this paper a functional equation for the fractional derivative of the Riemann zeta function is presented. The fractional derivative of the zeta function is computed by a generalization of the Grunwald-Letnikov fractional operator, which satisfies the generalized Leibniz rule. It is applied to the asymmetric functional equation of the Rieman zeta function in order to obtain the result sought. Moreover, further properties of this fractional derivative are proposed and discussed.

• 21.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Fractional Derivative of Riemann zeta function and Main Properties2016Conference paper (Other academic)

The Caputo-Ortigueira fractional derivative provides the fractional derivativeof complex functions. This derivative plays an important role in the number theory, and has been shown suitable for the analysis of the Dirichlet series, Hurwitz zeta function and Riemann zeta function. An integral representation for the fractional derivative of the Riemann zeta function was discovered. Since the Riemann zeta function is widely used in Physics, the unilateral Fourier transform of its fractional derivative is computed to investigate its applications in Quantum Theory and Signal Processing.

• 22.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Fractional-Wavelet Analysis of Positive definite Distributions and Wavelets on D’(C)2016In: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Silvestrov, Sergei; Rančić, Milica, Springer, 2016, p. 337-353Chapter in book (Refereed)

In the following chapter we describe a wavelet expansion theory for positivedefinite distributions over the real line and define a fractional derivative operator for complex functions in the distribution sense. In order to obtain a characterisation of the complex fractional derivative through the distribution theory, the Ortigueira-Caputo fractional derivative operator is rewritten as a convolution product according to the fractional calculus of real distributions. In particular, the fractional derivative of the Gabor-Morlet wavelet is computed together with its plots and main properties.

• 23.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
A spectral analysis of the Weierstrass-Mandelbrot function on the Cantor set2016Conference paper (Other academic)

In this paper, the Weierstrass-Mandelbrot function on the Cantor set is presented with emphasis on possible applications in science and engineering. An asymptotic estimation of its one-sided Fourier transform, in accordance with the simulation results, is analytically derived. Moreover, a time-frequency analysis of the Weierstrass-Mandelbrot function is provided by the numerical computation of its continuous wavelet transform.

• 24.
University of Niš, Faculty of Electronic Engineering, Niš, Serbia.
University of Niš, Faculty of Electronic Engineering, Niš, Serbia. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Modelling of measured lightning discharge currents to tall towers2017In: Conference Proceedings - 2017 17th IEEE International Conference on Environment and Electrical Engineering and 2017 1st IEEE Industrial and Commercial Power Systems Europe, EEEIC / I and CPS Europe 2017, Institute of Electrical and Electronics Engineers Inc. , 2017, article id 7977795Conference paper (Refereed)

Lightning discharge currents and their derivatives have been measured at instrumented tall towers for a few decades already. Results of those measurements are used for lightning research purposes, modelling of lightning discharges and making improvements in lightning protection. Some of the measured lightning currents are represented in this paper by the multi-peaked analytically extended function (MP-AEF). The same function may be used for lightning current derivatives, thus providing their analytical integration.

• 25. Jorgensen, Palle
Mälardalen University, School of Education, Culture and Communication.
Operator algebras and representation theory: frames, wavelets and fractals2011In: Oberwolfach Reports, ISSN 1660-8933, E-ISSN 1660-8941, Vol. 8, no 1, p. 901-978Article in journal (Refereed)

Operator Algebras and Representation Theory: Frames, Wavelets and Fractals

Organized by: Palle E.T. Jorgensen (1), Gitta Kutyniok (2), Gestur Olafsson (3) and Sergei Silvestrov (4)

(1) Department of Mathematics, University of Iowa, IA 52242-1466, IOWA CITY, UNITED STATES(2) Fachbereich Mathematik / Informatik, Universität Osnabrück, Albrechtstr. 28a, 49069, OSNABRÜCK, GERMANY(3) Department of Mathematics, Louisiana State University, LA 70803-4918, BATON ROUGE, UNITED STATES(4) Centre for Mathematical Sciences, Lund University, P.O. Box 118, 22100, LUND, SWEDEN

The central focus of the workshop was Kadison-Singer conjecture and its connection to operator algebras, harmonic analysis, representation theory and the theory of fractals. The program was intrinsically interdisciplinary and represented areas with much recent progress. The workshop includes talks on operator theory, wavelets, shearlets, frames, fractals, representations theory and compressed sensing.

• 26.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Gravitationally self-bound quantum states in unstable potentials2018In: Physical Review A: covering atomic, molecular, and optical physics and quantum information, ISSN 2469-9926, E-ISSN 2469-9934, Vol. 97, no 4, article id 042116Article in journal (Refereed)

Quantum mechanics at present cannot be unified with the theory of gravity at the deepest level, and to guide research towards the solution of this fundamental problem, we need to look for ways to observe or refute predictions originating from attempts to combine quantum theory with gravity. The influence of the gravitational field created by the material density given by the wave function itself gives rise to nontrivial phenomena. In this study I consider the wave function for the center-of-mass coordinate of a spherical mass distribution under the influence of the self-interaction of Newtonian gravity. I solve numerically for the ground state in the presence of an unstable potential and find that the energy of the free-space bound state can be lowered despite the nontrapping character of the potential. The center-of-mass ground state becomes increasingly localized for the used unstable potentials, although only in a limited parameter regime. The feebleness of the energy shift makes the observation of these effects demanding and requires further developments in the cooling of material particles. In addition, the influence of gravitational perturbations that are present in typical laboratory settings necessitates the use of extremely quiet and controlled environments such as those provided by recently proposed space-borne experiments.

• 27.
Uppsala University, Sweden.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Lp-Boundedness of Two Singular Integral Operators of Convolution Type2016In: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016Chapter in book (Refereed)

We investigate boundedness properties of two singular integral operators defined on Lp-spaces (1 < p < ∞) on the real line, both as convolution operators on Lp(R) and on the spaces Lp(w), where w(x) = 1/2cosh πx/2. It is proved that both operators are bounded on these spaces and estimates of the norms are obtained. This is achieved by first proving boundedness for p = 2 and weak boundedness for p = 1, and then using interpolation to obtain boundedness for 1 < p ≤ 2. To obtain boundedness also for 2 ≤ p < ∞, we use duality in the translation invariant case, while the weighted case is partly based on the expositions on the conjugate function operator in [7].

π/2

• 28.
Department of Mathematics Gulbarga University Gulbarga, Karnataka, India.
Department of Mathematics, Gulbarga University, Gulbarga, Karnataka, India, and Department of Engineering, University of Sannio, Benevento, Italy. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Effect of First Order Chemical Reaction on Magneto Convection in a Vertical Double Passage Channel2016In: Engineering Mathematics I: Electromagnetics, Fluid Mechanics, Material Physics and Financial Engineering / [ed] Sergei Silvestrov, Milica Rancic, Springer, 2016, p. 247-279Chapter in book (Refereed)

The objective of this paper is to study magnetohydrodynamic flow in a vertical double passage channel taking into account the presence of the first order chemical reaction. The channel is divided into two passages by means of a thin,perfectly conducting plane baffle and hence the velocity will be individual in each stream. The governing equations are solved by using regular perturbation technique valid for small values of the Brinkman number and differential transform method valid for all values of the Brinkman number. The results are obtained for velocity, temperature and concentration. The effects of various dimensionless parameters such as thermal Grashof number, mass Grashof number, Brinkman number, first order chemical reaction parameter, and Hartman number on the flow variables are discussed and presented graphically for open and short circuits. The validity of solutions obtained by differential transform method and regular perturbation method are in good agreement for small values of the Brinkman number. Further the effects of governing parameters on the volumetric flow rate, species concentration, total heart rate, skin friction and Nusselt number are also observed and tabulated.

• 29.
Stockholm University, Sweden.
Mälardalen University, Department of Mathematics and Physics. Stockholm University, Sweden.
On the inverse scattering problem on branching graphs2002In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, Vol. 35, no 1, p. 101-122Article in journal (Refereed)

The inverse scattering problem on branching graphs is studied. The definition of the Schrödinger operator on such graphs is discussed. The operator is defined with real potentials with finite first momentum and using special boundary conditions connecting values of the functions at the vertices. It is shown that in general the scattering matrix does not determine the topology of the graph, the potentials on the edges and the boundary conditions uniquely.

• 30. Laustsen, Niels Jakob
Lund University.
Heisenberg-Lie commutation relations in Banach algebras2009In: Mathematical Proceedings of the Royal Irish Academy, ISSN 1393-7197, E-ISSN 2009-0021, Vol. 109, no 2, p. 163-186Article in journal (Refereed)
• 31.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Generalized Vandermonde matrices and determinants in electromagnetic compatibility2017Licentiate thesis, comprehensive summary (Other academic)

Matrices whose rows (or columns) consists of monomials of sequential powers are called Vandermonde matrices and can be used to describe several useful concepts and have properties that can be helpful for solving many kinds of problems. In this thesis we will discuss this matrix and some of its properties as well as a generalization of it and how it can be applied to curve fitting discharge current for the purpose of ensuring electromagnetic compatibility.

In the first chapter the basic theory for later chapters is introduced. This includes the Vandermonde matrix and some of its properties, history, applications and generalizations, interpolation and regression problems, optimal experiment design and modelling of electrostatic discharge currents with the purpose to ensure electromagnetic compatibility.

The second chapter focuses on finding the extreme points for the determinant for the Vandermonde matrix on various surfaces including spheres, ellipsoids, cylinders and tori. The extreme points are analysed in three dimensions or more.

The third chapter discusses fitting a particular model called the p-peaked Analytically Extended Function (AEF) to data taken either from a standard for electromagnetic compatibility or experimental measurements. More specifically the AEF will be fitted to discharge currents from the IEC 62305-1 and IEC 61000-4-2 standards for lightning protection and electrostatic discharge immunity as well as some experimentally measured data of similar phenomena.

• 32.
Mälardalen University, School of Education, Culture and Communication.
Mälardalen University, School of Education, Culture and Communication.
Extreme points of the Vandermonde determinant on the sphere and some limits involving the generalized Vandermonde determinant2013Report (Other academic)

The values of the determinant of Vandermonde matrices with real elements are analyzed both visually and analytically over the unit sphere in various dimensions. For three dimensions some generalized Vandermonde matrices are analyzed visually. The extreme points of the ordinary Vandermonde determinant on finite-dimensional unit spheres are given as the roots of rescaled Hermite polynomials and a recursion relation is provided for the polynomial coefficients. Analytical expressions for these roots are also given for dimension three to seven. A transformation of the optimization problem is provided and some relations between the ordinary and generalized Vandermonde matrices involving limits are discussed.

• 33.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Optimization of the determinant of the Vandermonde matrix on the sphere and related surfaces2015In: ASMDA 2015 Proceedings: 16th Applied Stochastic Models and Data Analysis International Conference with 4th Demographics 2015 Workshop / [ed] Christos H Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2015, p. 637-648Conference paper (Refereed)

The value of the Vandermonde determinant is optimized over various surfaces, including the sphere, ellipsoid and torus. Lagrange multipliers are used to find a system of polynomial equations which give the local extreme points in its solutions. Using Gröbner basis and other techniques the extreme points are given either explicitly or as roots of polynomials in one variable. The behavior of the Vandermonde determinant is also presented visually in some interesting cases.

• 34.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Department of Mathematics, Gulbarga University, Gulbarga, Karnataka, India. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
MHD Boundary Layer Flow over a Nonlinear Stretching Sheet in a Nanofluid with Convective Boundary Condition2016In: Engineering Mathematics I: Electromagnetics, Fluid Mechanics, Material Physics and Financial Engineering / [ed] Silvestrov, Sergei; Rancic, Milica, Springer, 2016Chapter in book (Refereed)

We analyzed the boundary layer flow and heat transfer over a stretching sheet due to nanofluids with the effects of magnetic field, Brownian motion, thermophoresis, viscous dissipation and convective boundary conditions. The transport equations used in the analysis took into account the effect of Brownian motion and thermophoresis parameters. The highly nonlinear partial differential equations governing flow and heat transport are simplified using similarity transformation. Resultant ordinary differential equations are solved numerically using the Runge–Kutta–Fehlberg and Newton–Raphson schemes based on the shooting method. The solutions velocity temperature and nanoparticle concentration depend on parameters such as Brownian motion, thermophoresis parameter, magnetic field and viscous dissipation, which have a significant influence on controlling the dynamics of the considered problem. Comparison with known results for certain particular cases shows an excellent agreement.

• 35.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Department of Mathematics, Gulbarga University, Gulbarga, India. Department of Mathematics, Department of Mathematics Bheemanna Khandre Institute of Technology Bidar, India. Department of Physics, Central University of Karnataka Gulbarga, India.
Fluid Flow and Radiative Nonlinear Heat Transfer in a Liquid Film over an UnsteadyStretching Sheet2016Conference paper (Refereed)

A mathematical analysis of the MHD boundary layer flow and heat transfer characteristics of a laminar liquid film over an unsteady stretching sheet in presence of thermal radiation is presented. The effect of thermal radiation using the nonlinear Rosseland approximation is investigated. Similarity solutions are used to transform the governing equations to set of coupled nonlinear ordinary differential equations. Resultant ordinary differential equations are solved numerically using Runge-Kutta-Fehlberg method. A relationship between film thickness β and the unsteadiness parameter S is found; the effects of unsteadiness parameter S, Prandtl number Pr, magnetic parameter Mn, and radiation parameter Nr on the temperature distributions are presented and discussed in detail.

• 36.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Department of Mathematics, PDA college of engineering, Gulbarga, Karnataka, India. Department of Physics, School of physical sciences, Central university of Kalburgi, Karnataka, India. Department of Mathematics, Gulbarga University, Gulbarga, Karnataka, India. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mixed Convection Heat Transfer in MHD Non-Darcian Flow Due to an Exponential Stretching Sheet Embedded in a Porous Medium in Presence of Non-uniform Heat Source/Sink2016In: Engineering Mathematics I: Electromagnetics, Fluid Mechanics, Material Physics and Financial Engineering / [ed] Sergei Silvestrov, Milica Rančić, Springer, 2016, p. 187-201Chapter in book (Refereed)

A mathematical analysis has been carried out to describe mixed convection heat transfer in MHD non-Darcian flow due to an exponential stretching sheet embedded in a porous medium in presence of non-uniform heat source/sink. Approximate analytical similarity solutions of the highly non-linear momentum and energy equations are obtained. The governing system of partial differential equations is first transformed into a system of non-linear ordinary differential equations using similarity transformation. The transformed equations are non-linear coupled differential equations and are solved very efficiently by using fifth order Runge–Kutta–Fehlberg method with shooting technique for various values of the governing parameters. The numerical solutions are obtained by considering an exponential dependent stretching velocity and prescribed boundary temperature on the flow directional coordinate. The computed results are compared with the previously published work on various special cases of the problem and are in good agreement with the earlier studies. The effect of various physical parameters, such as the Prandtl number,the Grashoff number, the Hartmann number, porous parameter, inertia coefficient and internal heat generation on flow and heat transfer characteristics are presented graphically to show some interesting aspects of the physical parameter.

• 37.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Lie group analysis for MHD boundary layer flow and heat transfer over stretching sheet in presence of viscous dissipation and uniform heat source/sink2017In: AIP Conference Proceedings, Volume 1798, American Institute of Physics (AIP), 2017, Vol. 1798, p. 020096-1-020096-10, article id 020096Conference paper (Refereed)

An analysis for the MHD boundary layer flow and heat transfer towards stretching sheet is carried out via symmetry analysis. A steady two-dimensional flow of an electrically conducting incompressible fluid flow over a stretching sheet. The flow permeated by a uniform transverse magnetic field. The governing partial dierential equations are reduced to a system of ordinarydierential equations by the scaling symmetries. The symmetry groups admitted by the corresponding boundary value problem are obtained by using special Lie group transformations. The scaling of group transformations is applied to the governing equations.The system remains invariant due to some relation among the parameters of the transformations. After finding two absolute invariants a third order ordinary dierential equation corresponding to momentum equation and second order dierential equation corresponding to energy equation are derived. The equations along with boundary conditions solved numerically. Numerical solutions of these equations are obtained by using Runge-Kutta-Fehlberg scheme. Further more attention is paid to the eects of some physical parameters magnetic field (Mn), Prandtl number (Pr), Eckert number (Ec) and uniform heat source/sink, on velocity and thermal boundary layer. The results thus obtained are presented graphically and discussed.

• 38.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Department of Physics, Sangameshwar college Solapur, Maharashtra, India. Department of Mathematics, Gulbarga University,Gulbarga, Karnataka, India. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Heat transfer in MHD mixed convection viscoelastic fluid flow over a stretching sheet embedded in a porous medium with viscous dissipation and non-uniform heat source/sink2016In: Procedia Engineering, ISSN 1877-7058, E-ISSN 1877-7058, Vol. 157, p. 309-316Article in journal (Refereed)

A numerical model is developed to study the MHD mixed convective boundary layer viscoelastic fluid flow over a stretching sheet embedded in a porous medium in presence of viscous dissipation and non-uniform heat source have been investigated. The variation of porosity is assumed. The governing partial differential equations are converted into ordinary differential equations by applying suitable similarity transformations. Thenumerical solution of the problem is also obtained by the efficient Runge-Kutta-Fehlberg method with shooting technique. Here two types of different heating processes are considered namely, PST and PHF cases. The effect of various physical parameters such as Prandtl number, Eckert number, magnetic parameter, convection parameter and porous parameter which determine the temperature profiles are shown in several plots.Some important findings reported in this work reveals that the effect of viscous dissipation and non-uniform heat source have significant impact in controlling the rate of heat transfer in the boundary layer region.

• 39.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Department of Mathematics, M. S. Ramaiah University of Applied Sciences, Bangalore, Karnataka, India. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Hypergeometric Steady Solution of Hydromagnetic Nano Liquid Film Flow over an Unsteady Stretching Sheet2017In: AIP Conference Proceedings, Volume 1798 / [ed] Sivasundaram, S, American Institute of Physics (AIP), 2017, Vol. 1798, p. 020097-1-020097-10, article id 020097Conference paper (Refereed)

In this paper, we examine the hydromagnetic boundary layer flow and heat transfer characteristics of a laminar nano liquid film over an unsteady stretching sheet is presented. The highly nonlinear partial dierential equations governing flow and heat transport are simplified using similarity transformation. The analytical solutions of the resulting ODEs are obtained for some special case of nano liquid film using hypergeometric power series functions, and from which the analytical solutions of the original problem are presented. The influence of pertinent parameters such as the magnetic parameter, the solid volume fraction of nanoparticles and the type of nanofluid on the flow, heat transfer, Nusselt number and skin friction coefficient is discussed analytically.

• 40.
Institute of Engineering T.U, Pulchowk Campus, Nepal.
Institute of Engineering T.U, Pulchowk Campus, Nepal. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
A Note on Exploration of Sequence Spaces and Function Spaces on Interval [0,1] for DNA Sequencing2014In: International Journal of Sciences: Basic and Applied Research (IJSBAR), ISSN 2307-4531, Vol. 14, no 1, p. 265-275Article in journal (Refereed)

In [7] authors studied the sequence spaces and function spaces on interval [0,1]. Further they introduced new sequence spaces by using generalized p-summation method and proved these spaces of sequences and functions are Banach spaces. In this paper we extend the results of authors in [7] by introducing a new basis function and strongly p-summation method.

• 41.
Institute of Engineering T.U, Pulchowk Campus, Nepal.
Institute of Engineering T.U, Pulchowk Campus, Nepal. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
New Paranormed Sequence Spaces l(p,λ) , c(p,λ) and c0(p,λ) Generated by an Infinite Matrix2014In: International Journal of Mathematical Trends and Technology (IJMTT), ISSN 2231-5373, Vol. 6, no 2, p. 176-182Article in journal (Refereed)
• 42.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, Busitema University, Kampala, Uganda.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, Makerere University, Kampala, Uganda. Department of Mathematics, Makerere University, Kampala, Uganda.
Extreme points of the Vandermonde determinant on surfaces implicitly determined by a univariate polynomialManuscript (preprint) (Other academic)

In this paper some results on optimising the Vandermonde determinanton a few different surfaces defined by univariate polynomials are discussed. The coordinates of the extreme points are given as roots of polynomials. Applications in curve-fitting and electrostatics are also briefly discussed.

• 43.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, Busitema University, Kampala, Uganda.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. College of Natural Science, Makerere University, Kampala, Uganda. College of Natural Science, Makerere University, Kampala, Uganda.
Optimization of the Wishart Joint Eigenvalue Probability Density Distribution Based on the Vandermonde Determinant.Manuscript (preprint) (Other academic)

A number of models from mathematics, physics, probability theory and statistics can be described in terms of Wishart matrices and their eigenvalues. The most prominent example being the Laguerre ensembles of the spectrum of Wishart matrix. We aim to express extreme points of the joint eigenvalue probability densitydistribution of a Wishart matrix using optimisation techniques for the Vandermondedeterminant over certain surfaces implicitly defined by univariate polynomials.

• 44.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Orthogonal Polynomials, Operators and Commutation Relations2017Licentiate thesis, monograph (Other academic)

Orthogonal polynomials, operators and commutation relations appear in many areas of mathematics, physics and engineering where they play a vital role. For instance, orthogonal functions in general are central to the development of Fourier series and wavelets which are essential to signal processing. In particular, as demonstrated in this thesis, orthogonal polynomials can be used to establish the L2-boundedness of singular integral operators which is a fundamental problem in harmonic analysis and a subject of extensive investigations. The Lp-convergence of Fourier series is closely related to the Lp-boundedness of singular integral operators. Many important relations in physical sciences are represented by operators satisfying various commutation relations. Such commutation relations play key roles in such areas as quantum mechanics, wavelet analysis, representation theory, spectral theory, and many others.

This thesis consists of three main parts. The first part presents a new system of orthogonal polynomials, and establishes its relation to the previously studied systems in the class of Meixner–­Pollaczek polynomials. Boundedness properties of two singular integral operators of convolution type are investigated in the Hilbert spaces related to the relevant orthogonal polynomials. Orthogonal polynomials are used to prove boundedness in the weighted spaces and Fourier analysis is used to prove boundedness in the translation invariant case. It is proved in both cases that the two operators are bounded on L2-spaces, and estimates of the norms are obtained.

The second part extends the investigation of the boundedness properties of the two singular integral operators to Lp-spaces on the real line, both in the weighted and unweighted spaces. It is proved that both operators are bounded on these spaces and estimates of the norms are obtained. This is achieved by first proving boundedness for L2 and weak boundedness for L1, and then using interpolation to obtain boundedness for the intermediate spaces. To obtain boundedness for the remaining spaces, duality is used in the translation invariant case, while the weighted case is partly based on the methods developed by M. Riesz in his paper of 1928 for the conjugate function operator.

The third and final part derives simple and explicit formulas for reordering elements in an algebra with three generators and Lie type relations. Centralizers and centers are computed as an example of an application of the formulas.

• 45.
Mälardalen University, School of Education, Culture and Communication. University of Zambia.
Reordering in Noncommutative Algebras, Orthogonal Polynomials and Operators2018Doctoral thesis, comprehensive summary (Other academic)

The main object studied in this thesis is the multi-parametric family of unital associative complex algebras generated by the element $Q$ and the finite or infinite set $\{S_j\}_{j\in J}$ of elements satisfying the commutation relations $S_jQ=\sigma_j(Q)S_j$, where $\sigma_j$ is a polynomial for all $j\in J$. A concrete representation is given by the operators $Q_x(f)(x)=xf(x)$ and $\alpha_{\sigma_j}(f)(x)=f(\sigma_j(x))$ acting on polynomials or other suitable functions. The main goal is to reorder arbitrary elements in this family and some of its generalizations, and to study properties of operators in some representing operator algebras, including their connections to orthogonal polynomials. For $J=\{1\}$ and $\sigma(x)=x+1$, the above commutation relations reduce to the famous classical Heisenberg--Lie commutation relation $SQ-QS=S$. Reordering an element in $S$ and $Q$ means to bring it, using the commutation relation, into a form where all elements $Q$ stand either to the left or to the right. For example, $SQ^2=Q^2S+2QS+S$. In general, one can use the commutation relation $SQ-QS=S$ successively and transform for any positive integer $n$ the element $SQ^n$ into a form where all elements $Q$ stand to the left. The coefficients which appear upon reordering in this case are the binomial coefficients. General reordering formulas for arbitrary elements in noncommutative algebras defined by commutation relations are important in many research directions, open problems and applications of the algebras and their operator representations. In investigation of the structure, representation theory and applications of noncommutative algebras, an important role is played by the explicit description of suitable normal forms for noncommutative expressions or functions of generators. Further investigation of the operator representations of the commutation relations by difference type operators on Hilbert function spaces leads to interesting connections to functional analysis and orthogonal polynomials.

This thesis consists of two main parts. The first part is devoted to the multi-parametric family of algebras introduced above. General reordering formulas for arbitrary elements in this family are derived, generalizing some well-known results. As an example of an application of the formulas, centralizers and centers are computed. Some operator representations of the above algebras are also described, including considering them in the context of twisted derivations. The second part of this thesis is devoted to a special representation of these algebras by difference operators associated with action by shifts on the complex plane. It is shown that there are three systems of orthogonal polynomials of the class of Meixner--Pollaczek polynomials that are connected by these operators. Boundedness properties of two singular integral operators of convolution type connected to these difference operators are investigated in the Hilbert spaces related to these systems of orthogonal polynomials. Orthogonal polynomials are used to prove boundedness in the weighted spaces and Fourier analysis is used to prove boundedness in the translation invariant case. It is proved in both cases that the two operators are bounded on the $L^2$-spaces and estimates of the norms are obtained. This investigation is also extended to $L^p$-spaces on the real line where it is proved again that the two operators are bounded.

• 46.
Department of Mathematics, M. S. Ramaiah University of Applied Sciences, Bangalore, Karnataka, India.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Thermocapillary flow of a non-Newtonian nanoliquid film over an unsteady stretching sheet2017In: Proceedings of ICNPAA 2016 world congress / [ed] Sivasundaram, S, American Institute of Physics (AIP), 2017, Vol. 1798, p. 020109-1-020109-10, article id 020109Conference paper (Refereed)

The influence of surface tension on the laminar flow of a thin film of a non-Newtonian nano liquid over an unsteady stretching sheet is considered. Surface tension is assumed vary linearly with temperature. An effective medium theory (EMT) based model is used for the thermal conductivity of the nano liquid. Metal and metal oxide nanoparticles are considered in carboxymethyl cellulose (CMC) – water base liquid. The unsteady boundary layer equations are transformed to a system of non-linear ordinary differential equations with the application of similarity transformations. Resultant two-point boundary value problem is solved numerically using a shooting method together with Runge-Kutta-Fehlberg and Newton-Raphson schemes. The effect of surface tension on the dynamics of the considered problem is presented graphically and analyzed in detail. The clear liquid results which form special case of the present study are in excellent agreement with the results reported in the literature

• 47.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, COMSATS Institute of Information Technology.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Linear Classification of data with Support Vector Machines and Generalized Support Vector Machines2016In: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016Chapter in book (Refereed)

In this paper, we study the support vector machine and introduced the notion of generalized support vector machine for classification of data. We showthat the problem of generalized support vector machine is equivalent to the problem of generalized variational inequality and establish various results for the existence of solutions. Moreover, we provide various examples to support our results.

• 48.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, COMSATS Institute of Information Technology.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Common Fixed Point Results for Family of Generalized Multivalued F-contraction Mappings in Ordered Metric Spaces2016In: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016Chapter in book (Refereed)

In this paper, we study the existence of common fixed points of family of multivalued mappings satisfying generalized F-contractive conditions in ordered metric spaces. These results establish some of the general common fixed point theorems for family of multivalued maps.

• 49.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, COMSATS Institute of Information Technology.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, University of Management and Technology, C-II, Johar Town, Lahore, Pakistan and Faculty of Science, Department of Mathematics, King Abdulaziz University, Saudi Arabia.
Common fixed point results of four mappings in ordered partial metric spaces2016In: Waves Wavelets Fractals - Advanced Analysis, ISSN 2449-5557, Vol. 2, no 1, p. 46-63Article in journal (Refereed)

On partially ordered set equipped with a partial metric, we study the sufficient conditions for existence of common fixed points of various mappings satisfying generalized weak contractive conditions. These results unify several comparable results in the existing literature. We also study the existence of nonnegative solution of implicit nonlinear integral equation. Furthermore, we study the fractal of finite family of generalized contraction mappings defined on a partial metric space.

• 50.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. COMSATS Institute of Information Technology, Pakistan.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics and Applied Mathematics, University of Pretoria, South Africa.
Fractals of generalized F-Hutchinson operator2016In: Waves, Wavelets and Fractals. Advanced Analysis, ISSN 2449-5557, Vol. 2, no 1, p. 29-40Article in journal (Refereed)

The aim of this paper is to construct a fractal with the help of a finite family of F−contraction mappings, a class of mappings more general than contraction mappings, defined on a complete metric space. Consequently, we obtain a variety of results for iterated function systems satisfying a different set of contractive conditions. Some examples are presented to support the results proved herein. Our results unify, generalize and extend various results in the existing literature.

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