Download or read book An Example of the Use of Spherical Harmonic Analysis written by Herbert Hall Turner and published by . This book was released on 1912 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Potential Theory in Gravity and Magnetic Applications written by Richard J. Blakely and published by Cambridge University Press. This book was released on 1996-09-13 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text bridges the gap between the classic texts on potential theory and modern books on applied geophysics. It opens with an introduction to potential theory, emphasising those aspects particularly important to earth scientists, such as Laplace's equation, Newtonian potential, magnetic and electrostatic fields, and conduction of heat. The theory is then applied to the interpretation of gravity and magnetic anomalies, drawing on examples from modern geophysical literature. Topics explored include regional and global fields, forward modeling, inverse methods, depth-to-source estimation, ideal bodies, analytical continuation, and spectral analysis. The book includes numerous exercises and a variety of computer subroutines written in FORTRAN. Graduate students and researchers in geophysics will find this book essential.
Download or read book Spherical Harmonic Analysis written by Paul F. Fougère and published by . This book was released on 1965 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ionospheric Multi Spacecraft Analysis Tools written by Malcolm Wray Dunlop and published by Springer Nature. This book was released on 2019-10-29 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book provides a comprehensive toolbox of analysis techniques for ionospheric multi-satellite missions. The immediate need for this volume was motivated by the ongoing ESA Swarm satellite mission, but the tools that are described are general and can be used for any future ionospheric multi-satellite mission with comparable instrumentation. In addition to researching the immediate plasma environment and its coupling to other regions, such a mission aims to study the Earth’s main magnetic field and its anomalies caused by core, mantle, or crustal sources. The parameters for carrying out this kind of work are examined in these chapters. Besides currents, electric fields, and plasma convection, these parameters include ionospheric conductance, Joule heating, neutral gas densities, and neutral winds.
Download or read book Encyclopedia of Solid Earth Geophysics written by D.E. James and published by Springer Science & Business Media. This book was released on 1989-11-30 with total page 1299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consisting of more than 150 articles written by leading experts, this authoritative reference encompasses the entire field of solid-earth geophysics. It describes in detail the state of current knowledge, including advanced instrumentation and techniques, and focuses on important areas of exploration geophysics. It also offers clear and complete coverage of seismology, geodesy, gravimetry, magnetotellurics and related areas in the adjacent disciplines of physics, geology, oceanography and space science.
Download or read book Numerical Methods for Harmonic Analysis on the Sphere written by Oscar L. Colombo and published by . This book was released on 1981 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report presents some numerical methods for estimating spherical harmonic coefficients from data sampled on the sphere. The data may be given in the form of area means or of point values, and it may be free from errors or affected by measurement 'noise'. The case discussed to greatest length is that of complete, global data sets on regular grids (i.e., lines of latitude and longitude, the latter, at least, separated by constant interval); the case where data are sparsely and irregularly distributed is also considered in some detail. The first section presents some basic properties of spherical harmonics, stressing their relationship to two-dimensional Fourier series. Algorithms for the evaluation of the harmonic coefficients by numerical quadratures are given here, and it is shown that the number of operations is the order of N cubed for equal angular grids, where N is the number of lines of latitude, or 'Nyquist frequency', of the grid. The second section introduces a quadratic measure for the error in the estimation of the coefficients by linear techniques. This is the error measure of least squares collocation, which is a method that can be used for harmonic analysis. Efficient algorithms for implementing collocation on the whole sphere are described. a formal relationship between collocation and least squares adjustment is used to obtain an alternative form of the collocation algorithm that is likely to be stable with dense data sets and, with a minor modification, can be used to implement least squares adjustment as well. The basic principle is that for regular grids the variance-convariance matrix of the data consists of Toeplitz-circulant blocks, so it can be both set up and inverted very efficiently.
Download or read book Applications of the Simplified Spherical Harmonics Equations in Spherical Geometry written by Ely M. Gelbard and published by . This book was released on 1962 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Harmonic Analysis and Approximation on the Unit Sphere written by Kunyang Wang and published by . This book was released on 2000 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Harmonic Function Theory written by Sheldon Axler and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package supplements the text for readers who wish to explore harmonic function theory on a computer.
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.
Download or read book Spherical Harmonic Analysis I written by Paul F. Fougere and published by . This book was released on 1963 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new method for performing a spherical harmonic analysis, using only observed components of the earth's magnetic field, is presented. Essential features of the method involve the use of (1) multidimensional vector spaces to exhibit clearllrand to make use of the coupling amound the X, Y, and Z expansions and to simplify the logic, (2) the Gram-SSHMIDT ORTHOGONALIZATION PROCESS TO SIMPLIFY THE SOLUTION OF THE NORMAL EQUATIONS OF LEAST SQUARES AND, MORE IMPORTANT, TO PROVIDE A SYSTEM OF ORTHOGONAL FUNCTIONS WITH THEIR MANY USEFUL PROPERTIES; AND (3) the variance ration test appaied to each orthogonal function in such a way that the significant functions are used in the final approximation and the insig cificant ones are used to estimate error. The method is verified by applying to to two indepen dent sets of data, both derived by evaluating a given set of Gaussian coefficients. That the method works in the error-free case is proved conclusively by the remarkable agreement between input and output coefficients for both sets of data. (Author).
Download or read book the theory of spherical and ellipsoidal harmonics written by E. W. Hobson and published by CUP Archive. This book was released on with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Harmonic Analysis of Spherical Functions on Real Reductive Groups written by R. A. Gangolli and published by Springer. This book was released on 1988 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis on Symmetric spaces, or more generally, on homogeneous spaces of semisimple Lie groups, is a subject that has undergone a vigorous development in recent years, and has become a central part of contemporary mathematics. This is only to be expected, since homogeneous spaces and group representations arise naturally in diverse contexts ranging from Number theory and Geometry to Particle Physics and Polymer Chemistry. Its explosive growth sometimes makes it difficult to realize that it is actually relatively young as mathematical theories go. The early ideas in the subject (as is the case with many others) go back to Elie Cart an and Hermann Weyl who studied the compact symmetric spaces in the 1930's. However its full development did not begin until the 1950's when Gel'fand and Harish Chandra dared to dream of a theory of representations that included all semisimple Lie groups. Harish-Chandra's theory of spherical functions was essentially complete in the late 1950's, and was to prove to be the forerunner of his monumental work on harmonic analysis on reductive groups that has inspired a whole generation of mathematicians. It is the harmonic analysis of spherical functions on symmetric spaces, that is at the focus of this book. The fundamental questions of harmonic analysis on symmetric spaces involve an interplay of the geometric, analytical, and algebraic aspects of these spaces. They have therefore attracted a great deal of attention, and there have been many excellent expositions of the themes that are characteristic of this subject.
Download or read book The Theory of Spherical and Ellipsoidal Harmonics written by Ernest William Hobson and published by . This book was released on 1965 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Harmonic Analysis on Symmetric Spaces and Applications I written by Audrey Terras and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its beginnings with Fourier (and as far back as the Babylonian astron omers), harmonic analysis has been developed with the goal of unraveling the mysteries of the physical world of quasars, brain tumors, and so forth, as well as the mysteries of the nonphysical, but no less concrete, world of prime numbers, diophantine equations, and zeta functions. Quoting Courant and Hilbert, in the preface to the first German edition of Methods of Mathematical Physics: "Recent trends and fashions have, however, weakened the connection between mathematics and physics. " Such trends are still in evidence, harmful though they may be. My main motivation in writing these notes has been a desire to counteract this tendency towards specialization and describe appli cations of harmonic analysis in such diverse areas as number theory (which happens to be my specialty), statistics, medicine, geophysics, and quantum physics. I remember being quite surprised to learn that the subject is useful. My graduate eduation was that of the 1960s. The standard mathematics graduate course proceeded from Definition 1. 1. 1 to Corollary 14. 5. 59, with no room in between for applications, motivation, history, or references to related work. My aim has been to write a set of notes for a very different sort of course.
Download or read book Face Processing Advanced Modeling and Methods written by Wenyi Zhao and published by Elsevier. This book was released on 2011-07-28 with total page 755 pages. Available in PDF, EPUB and Kindle. Book excerpt: Major strides have been made in face processing in the last ten years due to the fast growing need for security in various locations around the globe. A human eye can discern the details of a specific face with relative ease. It is this level of detail that researchers are striving to create with ever evolving computer technologies that will become our perfect mechanical eyes. The difficulty that confronts researchers stems from turning a 3D object into a 2D image. That subject is covered in depth from several different perspectives in this volume. Face Processing: Advanced Modeling and Methods begins with a comprehensive introductory chapter for those who are new to the field. A compendium of articles follows that is divided into three sections. The first covers basic aspects of face processing from human to computer. The second deals with face modeling from computational and physiological points of view. The third tackles the advanced methods, which include illumination, pose, expression, and more. Editors Zhao and Chellappa have compiled a concise and necessary text for industrial research scientists, students, and professionals working in the area of image and signal processing. Contributions from over 35 leading experts in face detection, recognition and image processing Over 150 informative images with 16 images in FULL COLOR illustrate and offer insight into the most up-to-date advanced face processing methods and techniques Extensive detail makes this a need-to-own book for all involved with image and signal processing
Download or read book Mechanization of Spherical Harmonic Analysis written by B. R. Leaton and published by . This book was released on 1967 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
