Ellipsoidal Harmonics Theory And Applications Encyclopedia Of Mathematics And Its Applications Book PDF, EPUB Download & Read Online Free


Ellipsoidal Harmonics

Ellipsoidal Harmonics
Author: George Dassios
Publisher: Cambridge University Press
ISBN: 1139510134
Pages:
Year: 2012-07-12
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The sphere is what might be called a perfect shape. Unfortunately nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, originated in the nineteenth century, could only be seriously applied with the kind of computational power available in recent years. This, therefore, is the first book devoted to ellipsoidal harmonics. Topics are drawn from geometry, physics, biosciences and inverse problems. It contains classical results as well as new material, including ellipsoidal bi-harmonic functions, the theory of images in ellipsoidal geometry and vector surface ellipsoidal harmonics, which exhibit an interesting analytical structure. Extended appendices provide everything one needs to solve formally boundary value problems. End-of-chapter problems complement the theory and test the reader's understanding. The book serves as a comprehensive reference for applied mathematicians, physicists, engineers and for anyone who needs to know the current state of the art in this fascinating subject.

Mathematical and Computational Methods in Photonics and Phononics

Mathematical and Computational Methods in Photonics and Phononics
Author: Habib Ammari, Brian Fitzpatrick, Hyeonbae Kang, Matias Ruiz, Sanghyeon Yu, Hai Zhang
Publisher: American Mathematical Soc.
ISBN: 1470448009
Pages: 509
Year: 2018-10-15
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The fields of photonics and phononics encompass the fundamental science of light and sound propagation and interactions in complex structures, as well as its technological applications. This book reviews new and fundamental mathematical tools, computational approaches, and inversion and optimal design methods to address challenging problems in photonics and phononics. An emphasis is placed on analyzing sub-wavelength resonators, super-focusing and super-resolution of electromagnetic and acoustic waves, photonic and phononic crystals, electromagnetic cloaking, and electromagnetic and elastic metamaterials and metasurfaces. Throughout this book, the authors demonstrate the power of layer potential techniques for solving challenging problems in photonics and phononics when they are combined with asymptotic analysis. This book might be of interest to researchers and graduate students working in the fields of applied and computational mathematics, partial differential equations, electromagnetic theory, elasticity, integral equations, and inverse and optimal design problems in photonics and phononics.

The Theory of Partitions

The Theory of Partitions
Author: George E. Andrews
Publisher: Cambridge University Press
ISBN: 052163766X
Pages: 255
Year: 1998-07-28
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Discusses mathematics related to partitions of numbers into sums of positive integers.

Permanents

Permanents
Author: Henryk Minc
Publisher: Cambridge University Press
ISBN: 0521302269
Pages: 224
Year: 1984-12-28
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The purpose of this book, which was first published in 1978, is to give a complete account of the theory of permanents, their history and applications. This volume was the first complete account of the theory of permanents, covering virtually the whole of the subject, a feature that no simple survey of the theory of matrices can even attempt. The work also contains many results stated without formal proofs. This book can be used as a textbook at the advanced undergraduate or graduate level. The only prerequisites are a standard undergraduate course in the theory of matrices and a measure of mathematical maturity.

Matroid Applications

Matroid Applications
Author: Neil White
Publisher: Cambridge University Press
ISBN: 0521381657
Pages: 363
Year: 1992-03-05
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This volume, the third in a sequence that began with The Theory of Matroids and Combinatorial Geometries, concentrates on the applications of matroid theory to a variety of topics from engineering (rigidity and scene analysis), combinatorics (graphs, lattices, codes and designs), topology and operations research (the greedy algorithm).

CRC Concise Encyclopedia of Mathematics, Second Edition

CRC Concise Encyclopedia of Mathematics, Second Edition
Author: Eric W. Weisstein
Publisher: CRC Press
ISBN: 1420035223
Pages: 3252
Year: 2002-12-12
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Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the dedication of author Eric Weisstein to collecting, cataloging, and referencing mathematical facts, formulas, and definitions. He has now updated most of the original entries and expanded the Encyclopedia to include 1000 additional pages of illustrated entries. The accessibility of the Encyclopedia along with its broad coverage and economical price make it attractive to the widest possible range of readers and certainly a must for libraries, from the secondary to the professional and research levels. For mathematical definitions, formulas, figures, tabulations, and references, this is simply the most impressive compendium available.

Non-Associative Normed Algebras : Volume 2, Representation Theory and the Zel'manov Approach

Non-Associative Normed Algebras : Volume 2, Representation Theory and the Zel'manov Approach
Author: Miguel Cabrera García, Ángel Rodríguez Palacios
Publisher: Cambridge University Press
ISBN: 1108631436
Pages: 760
Year: 2018-04-12
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This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This second volume revisits JB*-triples, covers Zel'manov's celebrated work in Jordan theory, proves the unit-free variant of the Vidav–Palmer theorem, and develops the representation theory of alternative C*-algebras and non-commutative JB*-algebras. This completes the work begun in the first volume, which introduced these algebras and discussed the so-called non-associative Gelfand–Naimark and Vidav–Palmer theorems. This book interweaves pure algebra, geometry of normed spaces, and infinite-dimensional complex analysis. Novel proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, and an extensive bibliography.

Model Theory

Model Theory
Author: Wilfrid Hodges
Publisher: Cambridge University Press
ISBN: 0521304423
Pages: 772
Year: 1993-03-11
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Model theory is concerned with the notions of definition, interpretation and structure in a very general setting, and is applied to a wide range of other areas such as set theory, geometry, algebra and computer science. This book provides an integrated introduction to model theory for graduate students.

Multiple Scattering

Multiple Scattering
Author: P. A. Martin
Publisher: Cambridge University Press
ISBN: 0521865549
Pages: 437
Year: 2006-08-03
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First book devoted to subject; an essential reference for applied mathematicians, physicists and engineers.

An Elementary Treatise on Fourier's Series

An Elementary Treatise on Fourier's Series
Author: William Elwood Byerly
Publisher: Courier Corporation
ISBN: 0486159906
Pages: 304
Year: 2014-03-05
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Originally published over a century ago, this work remains among the most useful and practical expositions of Fourier's series, and spherical, cylindrical, and ellipsoidal harmonics. The subsequent growth of science into a diverse range of specialties has enhanced the value of this classic, whose thorough, basic treatment presents material that is assumed in many other studies but seldom available in such concise form. The development of functions, series, and their differential equations receives detailed explanations, and throughout the text, theory is applied to practical problems, with the solutions fully worked out. In addition, 190 problems, many with hints, are included. 1893 edition. Appendix of 6 tables.

Spherical harmonics and tensors for classical field theory

Spherical harmonics and tensors for classical field theory
Author: Michael Norman Jones
Publisher: John Wiley & Sons Inc
ISBN:
Pages: 230
Year: 1985
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Geometric Applications of Fourier Series and Spherical Harmonics

Geometric Applications of Fourier Series and Spherical Harmonics
Author: H. Groemer
Publisher: Cambridge University Press
ISBN: 0521473187
Pages: 329
Year: 1996-09-13
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This book provides a comprehensive presentation of geometric results, primarily from the theory of convex sets, that have been proved by the use of Fourier series or spherical harmonics. An important feature of the book is that all necessary tools from the classical theory of spherical harmonics are presented with full proofs. These tools are used to prove geometric inequalities, stability results, uniqueness results for projections and intersections by hyperplanes or half-spaces and characterisations of rotors in convex polytopes. Again, full proofs are given. To make the treatment as self-contained as possible the book begins with background material in analysis and the geometry of convex sets. This treatise will be welcomed both as an introduction to the subject and as a reference book for pure and applied mathematics.

Geometric Tomography

Geometric Tomography
Author: Richard J. Gardner
Publisher: Cambridge University Press
ISBN: 0521866804
Pages: 492
Year: 2006-06-19
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A comprehensive, rigorous treatment, with 66 unsolved problems, over 70 illustrations, and over 800 references.

Lattice Sums Then and Now

Lattice Sums Then and Now
Author: J. M. Borwein, M. L. Glasser, R. C. McPhedran, J. G. Wan, I. J. Zucker
Publisher: Cambridge University Press
ISBN: 1107435390
Pages: 392
Year: 2013-09-05
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The study of lattice sums began when early investigators wanted to go from mechanical properties of crystals to the properties of the atoms and ions from which they were built (the literature of Madelung's constant). A parallel literature was built around the optical properties of regular lattices of atoms (initiated by Lord Rayleigh, Lorentz and Lorenz). For over a century many famous scientists and mathematicians have delved into the properties of lattices, sometimes unwittingly duplicating the work of their predecessors. Here, at last, is a comprehensive overview of the substantial body of knowledge that exists on lattice sums and their applications. The authors also provide commentaries on open questions, and explain modern techniques which simplify the task of finding new results in this fascinating and ongoing field. Lattice sums in one, two, three, four and higher dimensions are covered.

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