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Spherical Harmonics And Approximations On The Unit Sphere An Introduction
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Book Synopsis Spherical Harmonics and Approximations on the Unit Sphere: An Introduction by : Kendall Atkinson
Download or read book Spherical Harmonics and Approximations on the Unit Sphere: An Introduction written by Kendall Atkinson and published by Springer Science & Business Media. This book was released on 2012-02-17 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well as an overview of classical and recent results on some aspects of the approximation of functions by spherical polynomials and numerical integration over the unit sphere. The notes are intended for graduate students in the mathematical sciences and researchers who are interested in solving problems involving partial differential and integral equations on the unit sphere, especially on the unit sphere in three-dimensional Euclidean space. Some related work for approximation on the unit disk in the plane is also briefly discussed, with results being generalizable to the unit ball in more dimensions.
Book Synopsis Spherical Harmonics and Approximations on the Unit Sphere: An Introduction by : Kendall Atkinson
Download or read book Spherical Harmonics and Approximations on the Unit Sphere: An Introduction written by Kendall Atkinson and published by Springer Science & Business Media. This book was released on 2012-02-17 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well as an overview of classical and recent results on some aspects of the approximation of functions by spherical polynomials and numerical integration over the unit sphere. The notes are intended for graduate students in the mathematical sciences and researchers who are interested in solving problems involving partial differential and integral equations on the unit sphere, especially on the unit sphere in three-dimensional Euclidean space. Some related work for approximation on the unit disk in the plane is also briefly discussed, with results being generalizable to the unit ball in more dimensions.
Book Synopsis Advances in Maritime Technology and Engineering by : Carlos Guedes Soares
Download or read book Advances in Maritime Technology and Engineering written by Carlos Guedes Soares and published by CRC Press. This book was released on 2024-05-08 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Maritime Technology and Engineering comprises a collection of the papers presented at the 7th International Conference on Maritime Technology and Engineering (MARTECH 2024) held in Lisbon, Portugal, on 14-16 May 2024. This Conference has evolved from the series of biannual national conferences in Portugal, which have become an international event, reflecting the internationalization of the maritime sector and its activities. MARTECH 2024 is the seventh of this new series of biannual conferences. This book comprises 142 contributions that were reviewed by an International Scientific Committee. Advances in Maritime Technology and Engineering is dedicated to maritime transportation, ports as well as maritime safety and reliability. It further comprises sections dedicated to ship design, cruise ship design, and to the structural aspects of ship design, such as ultimate strength and composites, subsea structures as pipelines, and to ship building and ship repair. The Proceedings in Marine Technology and Ocean Engineering series is dedicated to the publication of proceedings of peer-reviewed international conferences dealing with various aspects of “Marine Technology and Ocean Engineering”. The series includes the proceedings of the following conferences: the International Maritime Association of the Mediterranean (IMAM) conferences, the Marine Structures (MARSTRUCT) conferences, the Renewable Energies Offshore (RENEW) conferences and the Maritime Technology (MARTECH) conferences. The “Marine Technology and Ocean Engineering” series is also open to new conferences that cover topics on the sustainable exploration of marine resources in various fields, such as maritime transport and ports, usage of the ocean including coastal areas, nautical activities, the exploration and exploitation of mineral resources, the protection of the marine environment and is resources, and risk analysis, safety and reliability. The aim of the series is to stimulate advanced education and training through the wide dissemination of the results of scientific research.
Book Synopsis Wavelet Analysis on the Sphere by : Sabrine Arfaoui
Download or read book Wavelet Analysis on the Sphere written by Sabrine Arfaoui and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-03-20 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this monograph is to develop the theory of wavelet harmonic analysis on the sphere. By starting with orthogonal polynomials and functional Hilbert spaces on the sphere, the foundations are laid for the study of spherical harmonics such as zonal functions. The book also discusses the construction of wavelet bases using special functions, especially Bessel, Hermite, Tchebychev, and Gegenbauer polynomials.
Book Synopsis Spherical Harmonics in p Dimensions by : Costas Efthimiou
Download or read book Spherical Harmonics in p Dimensions written by Costas Efthimiou and published by World Scientific. This book was released on 2014-03-07 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The current book makes several useful topics from the theory of special functions, in particular the theory of spherical harmonics and Legendre polynomials in arbitrary dimensions, available to undergraduates studying physics or mathematics. With this audience in mind, nearly all details of the calculations and proofs are written out, and extensive background material is covered before exploring the main subject matter. Contents:Introduction and MotivationWorking in p DimensionsOrthogonal PolynomialsSpherical Harmonics in p DimensionsSolutions to Problems Readership: Undergraduate and graduate students in mathematical physics and differential equations. Key Features:Accessible to everyone (including undergraduate students who have some knowledge in mathematics)Presents a topic that, although well-studied, is not widely disseminated in booksSolutions to all end-of-chapter problems with all the necessary details are given in the final chapter of the bookKeywords:Spherical Harmonics;Special Functions;Mathematical Physics;Green's Functions;Legendre Polynomials
Book Synopsis Approximation Theory XIV: San Antonio 2013 by : Gregory E. Fasshauer
Download or read book Approximation Theory XIV: San Antonio 2013 written by Gregory E. Fasshauer and published by Springer. This book was released on 2014-06-02 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings were prepared in connection with the 14th International Conference on Approximation Theory, which was held April 7-10, 2013 in San Antonio, Texas. The conference was the fourteenth in a series of meetings in Approximation Theory held at various locations in the United States. The included invited and contributed papers cover diverse areas of approximation theory with a special emphasis on the most current and active areas such as compressed sensing, isogeometric analysis, anisotropic spaces, radial basis functions and splines. Classical and abstract approximation is also included. The book will be of interest to mathematicians, engineers\ and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis and related application areas.
Download or read book Geomathematics written by Volker Michel and published by Cambridge University Press. This book was released on 2022-04-28 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive summary of the fundamental mathematical principles behind key topics in geophysics and geodesy. Each section begins with a problem in gravimetry, geomagnetics or seismology and analyses its mathematical features. With each chapter ending with a series of review questions, this is a valuable reference for students and researchers.
Book Synopsis Approximation Theory and Harmonic Analysis on Spheres and Balls by : Feng Dai
Download or read book Approximation Theory and Harmonic Analysis on Spheres and Balls written by Feng Dai and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area.
Book Synopsis Materials Interaction with Femtosecond Lasers by : Bernd Bauerhenne
Download or read book Materials Interaction with Femtosecond Lasers written by Bernd Bauerhenne and published by Springer Nature. This book was released on 2021-10-25 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified view of the response of materials as a result of femtosecond laser excitation, introducing a general theory that captures both ultrashort-time non-thermal and long-time thermal phenomena. It includes a novel method for performing ultra-large-scale molecular dynamics simulations extending into experimental and technological spatial dimensions with ab-initio precision. For this, it introduces a new class of interatomic potentials, constructed from ab-initio data with the help of a self-learning algorithm, and verified by direct comparison with experiments in two different materials — the semiconductor silicon and the semimetal antimony. In addition to a detailed description of the new concepts introduced, as well as giving a timely review of ultrafast phenomena, the book provides a rigorous introduction to the field of laser–matter interaction and ab-initio description of solids, delivering a complete and self-contained examination of the topic from the very first principles. It explains, step by step from the basic physical principles, the underlying concepts in quantum mechanics, solid-state physics, thermodynamics, statistical mechanics, and electrodynamics, introducing all necessary mathematical theorems as well as their proofs. A collection of appendices provide the reader with an appropriate review of many fundamental mathematical concepts, as well as important analytical and numerical parameters used in the simulations.
Book Synopsis Special Functions of Mathematical (Geo-)Physics by : Willi Freeden
Download or read book Special Functions of Mathematical (Geo-)Physics written by Willi Freeden and published by Springer Science & Business Media. This book was released on 2013-02-15 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understanding of special functions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality. The special functions to be discussed in this monograph vary greatly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.) and on the respective field characteristic (potential field, diffusion field, wave field). The differential equation under consideration determines the type of special functions that are needed in the desired reduction process. Each chapter closes with exercises that reflect significant topics, mostly in computational applications. As a result, readers are not only directly confronted with the specific contents of each chapter, but also with additional knowledge on mathematical fields of research, where special functions are essential to application. All in all, the book is an equally valuable resource for education in geomathematics and the study of applied and harmonic analysis. Students who wish to continue with further studies should consult the literature given as supplements for each topic covered in the exercises.
Book Synopsis Spectral Methods Using Multivariate Polynomials On The Unit Ball by : Kendall Atkinson
Download or read book Spectral Methods Using Multivariate Polynomials On The Unit Ball written by Kendall Atkinson and published by CRC Press. This book was released on 2019-11-11 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral Methods Using Multivariate Polynomials on the Unit Ball is a research level text on a numerical method for the solution of partial differential equations. The authors introduce, illustrate with examples, and analyze 'spectral methods' that are based on multivariate polynomial approximations. The method presented is an alternative to finite element and difference methods for regions that are diffeomorphic to the unit disk, in two dimensions, and the unit ball, in three dimensions. The speed of convergence of spectral methods is usually much higher than that of finite element or finite difference methods. Features Introduces the use of multivariate polynomials for the construction and analysis of spectral methods for linear and nonlinear boundary value problems Suitable for researchers and students in numerical analysis of PDEs, along with anyone interested in applying this method to a particular physical problem One of the few texts to address this area using multivariate orthogonal polynomials, rather than tensor products of univariate polynomials.
Book Synopsis Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics by : Wolfgang Arendt
Download or read book Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics written by Wolfgang Arendt and published by Birkhäuser. This book was released on 2015-12-10 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume originates from a conference held in Herrnhut in June 2013. It provides unique insights into the power of abstract methods and techniques in dealing successfully with numerous applications stemming from classical analysis and mathematical physics. The book features diverse topics in the area of operator semigroups, including partial differential equations, martingale and Hilbert transforms, Banach and von Neumann algebras, Schrödinger operators, maximal regularity and Fourier multipliers, interpolation, operator-theoretical problems (concerning generation, perturbation and dilation, for example), and various qualitative and quantitative Tauberian theorems with a focus on transfinite induction and magics of Cantor. The last fifteen years have seen the dawn of a new era for semigroup theory with the emphasis on applications of abstract results, often unexpected and far removed from traditional ones. The aim of the conference was to bring together prominent experts in the field of modern semigroup theory, harmonic analysis, complex analysis and mathematical physics, and to present the lively interactions between all of those areas and beyond. In addition, the meeting honored the sixtieth anniversary of Prof C. J. K. Batty, whose scientific achievements are an impressive illustration of the conference goal. These proceedings present contributions by prominent scientists at this international conference, which became a landmark event. They will be a valuable and inspiring source of information for graduate students and established researchers.
Book Synopsis Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 by : Jens M. Melenk
Download or read book Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 written by Jens M. Melenk and published by Springer Nature. This book was released on 2023-06-30 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume features high-quality papers based on the presentations at the ICOSAHOM 2020+1 on spectral and high order methods. The carefully reviewed articles cover state of the art topics in high order discretizations of partial differential equations. The volume presents a wide range of topics including the design and analysis of high order methods, the development of fast solvers on modern computer architecture, and the application of these methods in fluid and structural mechanics computations.
Book Synopsis Convex Bodies: The Brunn–Minkowski Theory by : Rolf Schneider
Download or read book Convex Bodies: The Brunn–Minkowski Theory written by Rolf Schneider and published by Cambridge University Press. This book was released on 2014 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete presentation of a central part of convex geometry, from basics for beginners, to the exposition of current research.
Book Synopsis Long-Range Dependence and Self-Similarity by : Vladas Pipiras
Download or read book Long-Range Dependence and Self-Similarity written by Vladas Pipiras and published by Cambridge University Press. This book was released on 2017-04-18 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: This modern and comprehensive guide to long-range dependence and self-similarity starts with rigorous coverage of the basics, then moves on to cover more specialized, up-to-date topics central to current research. These topics concern, but are not limited to, physical models that give rise to long-range dependence and self-similarity; central and non-central limit theorems for long-range dependent series, and the limiting Hermite processes; fractional Brownian motion and its stochastic calculus; several celebrated decompositions of fractional Brownian motion; multidimensional models for long-range dependence and self-similarity; and maximum likelihood estimation methods for long-range dependent time series. Designed for graduate students and researchers, each chapter of the book is supplemented by numerous exercises, some designed to test the reader's understanding, while others invite the reader to consider some of the open research problems in the field today.
Book Synopsis Geometric Regularization in Bioluminescence Tomography by : Kreutzmann, Tim
Download or read book Geometric Regularization in Bioluminescence Tomography written by Kreutzmann, Tim and published by KIT Scientific Publishing. This book was released on 2014-01-16 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bioluminescence tomography is a recent biomedical imaging technique which allows to study molecular and cellular activities in vivo. From a mathematical point of view, it is an ill-posed inverse source problem: the location and the intensity of a photon source inside an organism have to be determined, given the photon count on the organism's surface. To face the ill-posedness of this problem, a geometric regularization approach is introduced, analyzed and numerically verified in this book.
Book Synopsis The method of densities for non-isotropic Boolean models by : Hoerrmann, Julia
Download or read book The method of densities for non-isotropic Boolean models written by Hoerrmann, Julia and published by KIT Scientific Publishing. This book was released on 2015-03-20 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
