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  • 1.
    Abbas, M.
    et al.
    University Pretoria, South Africa.
    De La Sen, M.
    University of the Basque Country, Spain.
    Nazir, Talat
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Common Fixed Points of Generalized Rational Type Cocyclic Mappings in Multiplicative Metric Spaces2015Inngår i: Discrete dynamics in nature and society, ISSN 1026-0226, E-ISSN 1607-887X, Vol. 2015, artikkel-id 532725Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.
    Andersson, Johan
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Anders, Södergren
    University of Copenhagen.
    On the universality of the Epstein zeta functionManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    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.
    Arnlind, Joakim
    et al.
    Max Planck Institute for Gravitational Physics (AEI), Am Mühlenberg 1, D-14476 Golm, Germany.
    Makhlouf, Abdenacer
    Université de Haute Alsace, Lab. de Mathématiques Informatique et Applications, 4, rue des Frères Lumière, F-68093 Mulhouse, France.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras2011Inngår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 52, nr 12, s. 123502-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.
    Backlund, U.
    et al.
    Danderyds Gymnasium, Danderyd, Sweden.
    Carlsson, Linus
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Fällström, A.
    Umeå University, Umeå, Sweden.
    Persson, H.
    Uppsala University, Uppsala, Sweden.
    Semi-Bloch Functions in Several Complex Variables2016Inngår i: Journal of Geometric Analysis, ISSN 1050-6926, E-ISSN 1559-002X, Vol. 26, nr 1, s. 463-473Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.
    Bart Adde, Tiffany
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Puspita, Kadek Maya Sri
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    American Option pricing under Mutiscale Model using Monte Carlo and Least-Square approach2017Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [en]

       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.
    Bergqvist, Göran
    et al.
    Linköpings Universitet, Sweden.
    Lankinen, Paul
    Mälardalens högskola, Institutionen för matematik och fysik.
    Unique characterization of the Bel-Robinson tensor2004Inngår i: Classical and Quantum Graviry, ISSN 0264-9381, Vol. 21, nr 14, s. 3499-3503Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.
    Bolibrzuch, Milosz
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Introduction to some modes of convergence: Theory and applications2017Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [en]

    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.
    Carlsen, Toke M.
    et al.
    Norwegian University of Science and Technology.
    Eilers, SorenUniversity of Copenhagen.Restorff, GunnarUniversity of the Faroe Islands.Silvestrov, SergeiMälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 20122013Collection/Antologi (Fagfellevurdert)
  • 9.
    Carlsen, Toke Meier
    et al.
    University of Southern Denmark.
    Silvestrov, Sergei
    Lund University.
    On the Exel crossed product of topological covering maps2009Inngår i: 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, nr 3, s. 573-583Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.
    Carlsen, Toke Meier
    et al.
    Norwegian University of Science and Technology (NTNU), Trondheim, Norway .
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    On the K-theory of the C*-algebra associated with a one-sided shift space2010Inngår i: Proceedings of the Estonian Academy of Sciences, ISSN 1736-6046, E-ISSN 1736-7530, Vol. 59, nr 4, s. 272-279Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.
    Carlsson, Linus
    Umeå University.
    An equivalence to the Gleason problem2010Inngår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 370, nr 2, s. 373-378Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.
    Casazza, P. G.
    et al.
    University of Missouri.
    Jorgensen, Palle E. T.
    The University of Iowa.
    Kornelson, Keri A.
    University of Oklahoma.
    Kutyniok, Gitta
    Technische Universität Berlin.
    Larson, David R.
    Texas A&M University.
    Massopust, Peter
    Institute for Biomathematics and Biometry, Helmholtz Zentrum München.
    Olafsson, Gestur
    Lousiana State University.
    Packer, Judith A.
    University of Colorado at Boulder.
    Silvestrov, Sergei D.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Sun, Qiyu
    University of Central Florida.
    Preface2012Inngår i: Numerical Functional Analysis and Optimization, ISSN 0163-0563, E-ISSN 1532-2467, Vol. 33, nr 7-9, s. 705-707Artikkel i tidsskrift (Annet vitenskapelig)
  • 13.
    Cattani, Carlo
    et al.
    University of Tuscia Largo dell’Universita, Italy.
    Guariglia, Emanuel
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. University of Salerno, Italy.
    Wang, Shuihua
    Nanjing University, China.
    On the Critical Strip of the Riemann zeta Fractional derivative2017Inngår i: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 151, s. 459-472Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.
    de Jeu, Marcel
    et al.
    Leiden University.
    Silvestrov, SergeiMälardalens högskola, Akademin för utbildning, kultur och kommunikation.Skau, ChristianNorwegian University of Science and Technology (NTNU), Norway.Tomiyama, JunUniversity of Tokyo, Japan.
    Operator structures and dynamical systems2009Konferanseproceedings (Fagfellevurdert)
  • 15. Dutkay, Dorin Ervin
    et al.
    Jorgensen, Palle E. T.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Decomposition of wavelet representations and Martin boundaries2012Inngår i: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 262, nr 3, s. 1043-1061Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.
    Dutkay, Dorin Ervin
    et al.
    University of Central Florida, US.
    Larson, David R.
    Texas A and M University, United sTATES.
    Silvestrov, Sergei
    Lund University.
    Irreducible wavelet representations and ergodic automorphisms on solenoids2011Inngår i: Operators and Matrices, ISSN 1846-3886, E-ISSN 1848-9974, Vol. 5, nr 2, s. 201-219Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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
    et al.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation. Lund University.
    REDUCIBILITY OF THE WAVELET REPRESENTATION ASSOCIATED TO THE CANTOR SET2011Inngår i: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 139, nr 10, s. 3657-3664Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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
    et al.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Wavelet Representations and Their Commutant2012Inngår i: Analysis for Science, Engineering and Beyond / [ed] Åström, Kalle; Persson, Lars-Erik; Silvestrov, Sergei D., Springer Berlin/Heidelberg, 2012, Vol. 6, s. 253-265Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    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.
    Guariglia, Emanuel
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. University of Salerno, Italy.
    Entropy and fractal antennas2016Inngår i: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 18, nr 3, artikkel-id 84Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.
    Guariglia, Emanuel
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. University of Salerno, Italy.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    A functional equation for the Riemann zeta fractional derivative2017Inngår i: 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, s. 020063-1-020063-10, artikkel-id UNSP 020063Konferansepaper (Fagfellevurdert)
    Abstract [en]

    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.
    Guariglia, Emanuel
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Fractional Derivative of Riemann zeta function and Main Properties2016Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    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.
    Guariglia, Emanuel
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Fractional-Wavelet Analysis of Positive definite Distributions and Wavelets on D’(C)2016Inngår i: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Silvestrov, Sergei; Rančić, Milica, Springer, 2016, s. 337-353Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    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.
    Guariglia, Emanuel
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Qi, Xiaomin
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    A spectral analysis of the Weierstrass-Mandelbrot function on the Cantor set2016Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    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.
    Javor, V.
    et al.
    University of Niš, Faculty of Electronic Engineering, Niš, Serbia.
    Javor, D.
    University of Niš, Faculty of Electronic Engineering, Niš, Serbia.
    Lundengård, Karl
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Rancic, Milica
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Modelling of measured lightning discharge currents to tall towers2017Inngår i: 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, artikkel-id 7977795Konferansepaper (Fagfellevurdert)
    Abstract [en]

    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
    et al.
    Kutyniok, Gitta
    Olafsson, Gestur
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Operator algebras and representation theory: frames, wavelets and fractals2011Inngår i: Oberwolfach Reports, ISSN 1660-8933, E-ISSN 1660-8941, Vol. 8, nr 1, s. 901-978Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.
    Jääskeläinen, Markku
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Gravitationally self-bound quantum states in unstable potentials2018Inngår i: Physical Review A: covering atomic, molecular, and optical physics and quantum information, ISSN 2469-9926, E-ISSN 2469-9934, Vol. 97, nr 4, artikkel-id 042116Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.
    Kaijser, Sten
    et al.
    Uppsala University, Sweden.
    Musonda, John
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Lp-Boundedness of Two Singular Integral Operators of Convolution Type2016Inngår i: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    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.
    Kumar, Jada Pratar
    et al.
    Department of Mathematics Gulbarga University Gulbarga, Karnataka, India.
    Umavathi, Jawali C
    Department of Mathematics, Gulbarga University, Gulbarga, Karnataka, India, and Department of Engineering, University of Sannio, Benevento, Italy.
    Metri, Prashant G
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Effect of First Order Chemical Reaction on Magneto Convection in a Vertical Double Passage Channel2016Inngår i: Engineering Mathematics I: Electromagnetics, Fluid Mechanics, Material Physics and Financial Engineering / [ed] Sergei Silvestrov, Milica Rancic, Springer, 2016, s. 247-279Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    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.
    Kurasov, P
    et al.
    Stockholm University, Sweden.
    Stenberg, F
    Mälardalens högskola, Institutionen för matematik och fysik. Stockholm University, Sweden.
    On the inverse scattering problem on branching graphs2002Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, Vol. 35, nr 1, s. 101-122Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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
    et al.
    Silvestrov, S. D.
    Lund University.
    Heisenberg-Lie commutation relations in Banach algebras2009Inngår i: Mathematical Proceedings of the Royal Irish Academy, ISSN 1393-7197, E-ISSN 2009-0021, Vol. 109, nr 2, s. 163-186Artikkel i tidsskrift (Fagfellevurdert)
  • 31.
    Lundengård, Karl
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Generalized Vandermonde matrices and determinants in electromagnetic compatibility2017Licentiatavhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    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.
    Lundengård, Karl
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Österberg, Jonas
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Extreme points of the Vandermonde determinant on the sphere and some limits involving the generalized Vandermonde determinant2013Rapport (Annet vitenskapelig)
    Abstract [en]

    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.
    Lundengård, Karl
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Österberg, Jonas
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Optimization of the determinant of the Vandermonde matrix on the sphere and related surfaces2015Inngår i: 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, s. 637-648Konferansepaper (Fagfellevurdert)
    Abstract [en]

    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.
    Metri, Prashant G
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Abel, Subhas M
    Department of Mathematics, Gulbarga University, Gulbarga, Karnataka, India.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    MHD Boundary Layer Flow over a Nonlinear Stretching Sheet in a Nanofluid with Convective Boundary Condition2016Inngår i: Engineering Mathematics I: Electromagnetics, Fluid Mechanics, Material Physics and Financial Engineering / [ed] Silvestrov, Sergei; Rancic, Milica, Springer, 2016Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    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.
    Metri, Prashant G
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Abel, Subhas
    Department of Mathematics, Gulbarga University, Gulbarga, India.
    Tawade, Jagdish
    Department of Mathematics, Department of Mathematics Bheemanna Khandre Institute of Technology Bidar, India.
    Metri, Pushpanjali M
    Department of Physics, Central University of Karnataka Gulbarga, India.
    Fluid Flow and Radiative Nonlinear Heat Transfer in a Liquid Film over an UnsteadyStretching Sheet2016Konferansepaper (Fagfellevurdert)
    Abstract [en]

    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.
    Metri, Prashant G
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Bablad, Veena M
    Department of Mathematics, PDA college of engineering, Gulbarga, Karnataka, India.
    Metri, Pushpanjali M
    Department of Physics, School of physical sciences, Central university of Kalburgi, Karnataka, India.
    Abel, Subhas M
    Department of Mathematics, Gulbarga University, Gulbarga, Karnataka, India.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    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/Sink2016Inngår i: Engineering Mathematics I: Electromagnetics, Fluid Mechanics, Material Physics and Financial Engineering / [ed] Sergei Silvestrov, Milica Rančić, Springer, 2016, s. 187-201Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    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.
    Metri, Prashant G
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Guariglia, Emanuel
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Lie group analysis for MHD boundary layer flow and heat transfer over stretching sheet in presence of viscous dissipation and uniform heat source/sink2017Inngår i: AIP Conference Proceedings, Volume 1798, American Institute of Physics (AIP), 2017, Vol. 1798, s. 020096-1-020096-10, artikkel-id 020096Konferansepaper (Fagfellevurdert)
    Abstract [en]

    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.
    Metri, Prashant G
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Metri, Pushpanjali G
    Department of Physics, Sangameshwar college Solapur, Maharashtra, India.
    Abel, Subhas
    Department of Mathematics, Gulbarga University,Gulbarga, Karnataka, India.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    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/sink2016Inngår i: Procedia Engineering, ISSN 1877-7058, E-ISSN 1877-7058, Vol. 157, s. 309-316Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.
    Metri, Prashant G
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Narayana, Mahesh
    Department of Mathematics, M. S. Ramaiah University of Applied Sciences, Bangalore, Karnataka, India.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Hypergeometric Steady Solution of Hydromagnetic Nano Liquid Film Flow over an Unsteady Stretching Sheet2017Inngår i: AIP Conference Proceedings, Volume 1798 / [ed] Sivasundaram, S, American Institute of Physics (AIP), 2017, Vol. 1798, s. 020097-1-020097-10, artikkel-id 020097Konferansepaper (Fagfellevurdert)
    Abstract [en]

    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.
    Mishra, Shailendra K.
    et al.
    Institute of Engineering T.U, Pulchowk Campus, Nepal.
    Parajuli, Vinod
    Institute of Engineering T.U, Pulchowk Campus, Nepal.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    A Note on Exploration of Sequence Spaces and Function Spaces on Interval [0,1] for DNA Sequencing2014Inngår i: International Journal of Sciences: Basic and Applied Research (IJSBAR), ISSN 2307-4531, Vol. 14, nr 1, s. 265-275Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.
    Mishra, Shailendra K.
    et al.
    Institute of Engineering T.U, Pulchowk Campus, Nepal.
    Parajuli, Vinod
    Institute of Engineering T.U, Pulchowk Campus, Nepal.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    New Paranormed Sequence Spaces l(p,λ) , c(p,λ) and c0(p,λ) Generated by an Infinite Matrix2014Inngår i: International Journal of Mathematical Trends and Technology (IJMTT), ISSN 2231-5373, Vol. 6, nr 2, s. 176-182Artikkel i tidsskrift (Fagfellevurdert)
  • 42.
    Muhumuza, Asaph Keikara
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, Busitema University, Kampala, Uganda.
    Lundengård, Karl
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Österberg, Jonas
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Mango, John
    Department of Mathematics, Makerere University, Kampala, Uganda.
    Kakuba, Godwin
    Department of Mathematics, Makerere University, Kampala, Uganda.
    Extreme points of the Vandermonde determinant on surfaces implicitly determined by a univariate polynomialManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    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.
    Muhumuza, Asaph Keikara
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, Busitema University, Kampala, Uganda.
    Lundengård, Karl
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Österberg, Jonas
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Mango, John
    College of Natural Science, Makerere University, Kampala, Uganda.
    Kakuba, Goodwin
    College of Natural Science, Makerere University, Kampala, Uganda.
    Optimization of the Wishart Joint Eigenvalue Probability Density Distribution Based on the Vandermonde Determinant.Manuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    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.
    Musonda, John
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Orthogonal Polynomials, Operators and Commutation Relations2017Licentiatavhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    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.
    Musonda, John
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation. University of Zambia.
    Reordering in Noncommutative Algebras, Orthogonal Polynomials and Operators2018Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    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.
    Narayana, Mahesha
    et al.
    Department of Mathematics, M. S. Ramaiah University of Applied Sciences, Bangalore, Karnataka, India.
    Metri, Prashant G
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Thermocapillary flow of a non-Newtonian nanoliquid film over an unsteady stretching sheet2017Inngår i: Proceedings of ICNPAA 2016 world congress / [ed] Sivasundaram, S, American Institute of Physics (AIP), 2017, Vol. 1798, s. 020109-1-020109-10, artikkel-id 020109Konferansepaper (Fagfellevurdert)
    Abstract [en]

    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.
    Nazir, Talat
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, COMSATS Institute of Information Technology.
    Qi, Xiaomin
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Linear Classification of data with Support Vector Machines and Generalized Support Vector Machines2016Inngår i: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    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.
    Nazir, Talat
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, COMSATS Institute of Information Technology.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Common Fixed Point Results for Family of Generalized Multivalued F-contraction Mappings in Ordered Metric Spaces2016Inngår i: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    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.
    Nazir, Talat
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, COMSATS Institute of Information Technology.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Abbas, Mujahid
    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 spaces2016Inngår i: Waves Wavelets Fractals - Advanced Analysis, ISSN 2449-5557, Vol. 2, nr 1, s. 46-63Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.
    Nazir, Talat
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. COMSATS Institute of Information Technology, Pakistan.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Abbas, Mujahid
    Department of Mathematics and Applied Mathematics, University of Pretoria, South Africa.
    Fractals of generalized F-Hutchinson operator2016Inngår i: Waves, Wavelets and Fractals. Advanced Analysis, ISSN 2449-5557, Vol. 2, nr 1, s. 29-40Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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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