| 1. |
- Musonda, John
(författare)
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Orthogonal Polynomials, Operators and Commutation Relations
- 2017
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 2. |
- Lundengård, Karl, 1987-
(författare)
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Generalized Vandermonde matrices and determinants in electromagnetic compatibility
- 2017
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 3. |
- Metri, Prashant G, 1987-
(författare)
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Mathematical Analysis of Forced Convective Flow Due to Stretching Sheet and Instabilities of Natural Convective Flow
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The investigations presented in the thesis are theoretical studies of magnetohydrodynamic flows, heat and mass transfer in Newtonian/non-Newtonian cooling liquids, due to horizontal/vertical stretching sheet. The theoretical studies include the effect of magnetic field, uniform and non-uniform heat source/sink (flow and temperature dependent heat source/sink) effects. The considered problems include flow of viscous fluids in the presence of applied magnetic field and electric field with first order chemical reactions. The viscous incompressible Newtonian fluid flow in porous medium with Darcy-Forchheimmer model, electrically conducting fluid and nanofluid is studied. We introduce innovative techniques for finding solutions of highly nonlinear coupled boundary value problems such as Runge-Kutta method, Perturbation method and Differential Transform Method (DTM). Chapter 1-2 gives a brief introduction. Chapter 3 focuses on Lie group analysis of MHD flow and heat transfer over a stretching sheet. The effects of viscous dissipation, uniform heat source/sink and MHD on heat transfer are addressed. In Chapter 4-6 we examined the laminar flow, thermocapillary flow of a nanoliquid thin film over an unsteady stretching sheet in presence of MHD and thermal Radiation in different situations. An effective medium theory (EMT) based model is used for the thermal conductivity of the nanoliquid. Metal and metal oxide nanoparticles are considered in carboxymethyl cellulose (CMC) - water base liquid. In Chapter 7-9 we analyzed, heat and mass transfer in MHD, mixed convection, viscoelastic fluid flow, non-Darcian flow due to stretching sheet in presence of viscous dissipation, non-uniform heat source/sink and porous media have been investigated in different situations. MHD and viscous dissipation have a significant influence on controlling of the dynamics. In Chapter 10 the linear stability of Maxwell fluid-nanofluid flow in a saturated porous layer is examined theoretically when the walls of the porous layers are subjected to time-periodic temperature modulations. A modified Darcy-Maxwell model is used to describe the fluid motion, and the nanofluid model used includes the effects of the Brownian motion. The thermal conductivity and viscosity are considered to be dependent on the nanoparticle volume fraction.In Chapter 11 we studied MHD flow in a vertical double passage channel taking into account the presence of the first order chemical reactions. The governing equations are solved by using a regular perturbation technique valid for small values of the Brinkman number and a DTM valid for all values of the Brinkman number.
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| 4. |
- Silvestrov, D., et al.
(författare)
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Asymptotic Expansions for Moments of Hitting Times for Nonlinearly Perturbed Semi-Markov Processes
- 2017
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Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - Cham : Springer Nature. - 9783319609881 ; , s. 37-66
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Bokkapitel (refereegranskat)abstract
- In Chapter 3, we introduce a model of perturbed semi-Markov processes, formulate basic perturbation conditions, describe a one-step time-space screening procedure of phase space reduction for perturbed semi-Markov processes, introduce hitting times, and prove an invariant property of them with respect to the procedure of phase space reduction. We, also, present algorithms for re-calculation of asymptotic expansions for transition characteristics of nonlinearly perturbed semi-Markov processes with reduced phase spaces and algorithms for sequential reduction of phase space for semi-Markov processes and construction of Laurent asymptotic expansions, without and with explicit upper bounds for remainders, for power moment of hitting times. © 2017, The Author(s).
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| 5. |
- Silvestrov, D., et al.
(författare)
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Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes
- 2017
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Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - Cham : Springer Nature. - 9783319609881 ; , s. 67-79
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Bokkapitel (refereegranskat)abstract
- In Chapter 4, new algorithms for construction of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces are presented. These algorithms are based on the technique of sequential phase space reduction, which can be applied to processes with an arbitrary asymptotic communicative structure of phase spaces. Asymptotic expansions are given in two forms, without and with explicit upper bounds for remainders. © 2017, The Author(s).
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| 6. |
- Silvestrov, D., et al.
(författare)
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Examples and Survey of Applied Perturbed Stochastic Models
- 2017
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Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - Cham : Springer Nature. - 9783319609881 ; , s. 107-121
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Bokkapitel (refereegranskat)abstract
- In Chapter 6, we present a background for construction of numerical examples for asymptotic results presented in Chapters 2 – 5, some numerical examples as well as a summary survey of applied perturbed stochastic systems. © 2017, The Author(s).
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| 7. |
- Silvestrov, D., et al.
(författare)
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Introduction
- 2017
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Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - Cham : Springer Nature. - 9783319609881 ; , s. 1-15
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- This book is devoted to the study of asymptotic expansions for moment of hitting times, stationary and conditional quasi-stationary distributions, and other functionals, for nonlinearly perturbed semi-Markov processes. The introduction intends to present in informal form the main problems, methods, and algorithms that constitute the content of the book. © 2017, The Author(s).
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| 8. |
- Silvestrov, D., et al.
(författare)
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Laurent Asymptotic Expansions
- 2017
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Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - Cham : Springer Nature. - 9783319609881 ; , s. 17-35
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Bokkapitel (refereegranskat)abstract
- In Chapter 2, we present operational rules for Laurent asymptotic expansions given in two forms, with remainders given in the standard form o(⋅ ) and with explicit power-type upper bounds for remainders. In the former case, such rules should be possibly considered as generally known, while, in the latter case, asymptotic expansions have some novelty aspects. © 2017, The Author(s).
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| 9. |
- Silvestrov, D., et al.
(författare)
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Nonlinearly Perturbed Birth-Death-Type Semi-Markov Processes
- 2017
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Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - Cham : Springer Nature. - 9783319609881 ; , s. 81-106
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Bokkapitel (refereegranskat)abstract
- In Chapter 5, we present asymptotic expansions for stationary and conditional quasi-stationary distributions of nonlinearly perturbed birth-death-type semi-Markov processes, which play an important role in many applications. In this case, the corresponding expansions can be given in a more explicit form. © 2017, The Author(s).
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| 10. |
- Silvestrov, D., et al.
(författare)
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Preface
- 2017
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Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - : Springer Nature. - 9783319609881 ; , s. v-vii
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Bokkapitel (övrigt vetenskapligt/konstnärligt)
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