Multiscale Potential Theory

Multiscale Potential Theory

Author: Willi Freeden

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 522

ISBN-13: 1461220483

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This self-contained text/reference provides a basic foundation for practitioners, researchers, and students interested in any of the diverse areas of multiscale (geo)potential theory. New mathematical methods are developed enabling the gravitational potential of a planetary body to be modeled using a continuous flow of observations from land or satellite devices. Harmonic wavelets methods are introduced, as well as fast computational schemes and various numerical test examples. Presented are multiscale approaches for numerous geoscientific problems, including geoidal determination, magnetic field reconstruction, deformation analysis, and density variation modelling With exercises at the end of each chapter, the book may be used as a textbook for graduate-level courses in geomathematics, applied mathematics, and geophysics. The work is also an up-to-date reference text for geoscientists, applied mathematicians, and engineers.


Geomathematically Oriented Potential Theory

Geomathematically Oriented Potential Theory

Author: Willi Freeden

Publisher: CRC Press

Published: 2012-10-30

Total Pages: 466

ISBN-13: 1439895430

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As the Earth`s surface deviates from its spherical shape by less than 0.4 percent of its radius and today's satellite missions collect their gravitational and magnetic data on nearly spherical orbits, sphere-oriented mathematical methods and tools play important roles in studying the Earth's gravitational and magnetic field. Geomathematically Orien


Geomathematically Oriented Potential Theory

Geomathematically Oriented Potential Theory

Author: Willi Freeden

Publisher: CRC Press

Published: 2012-10-30

Total Pages: 470

ISBN-13: 1439895422

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As the Earth`s surface deviates from its spherical shape by less than 0.4 percent of its radius and today’s satellite missions collect their gravitational and magnetic data on nearly spherical orbits, sphere-oriented mathematical methods and tools play important roles in studying the Earth’s gravitational and magnetic field. Geomathematically Oriented Potential Theory presents the principles of space and surface potential theory involving Euclidean and spherical concepts. The authors offer new insight on how to mathematically handle gravitation and geomagnetism for the relevant observables and how to solve the resulting potential problems in a systematic, mathematically rigorous framework. The book begins with notational material and the necessary mathematical background. The authors then build the foundation of potential theory in three-dimensional Euclidean space and its application to gravitation and geomagnetism. They also discuss surface potential theory on the unit sphere along with corresponding applications. Focusing on the state of the art, this book breaks new geomathematical grounds in gravitation and geomagnetism. It explores modern sphere-oriented potential theoretic methods as well as classical space potential theory.


Geomathematics

Geomathematics

Author: Volker Michel

Publisher: Cambridge University Press

Published: 2022-04-28

Total Pages: 467

ISBN-13: 1108419445

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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.


Sampling: Theory and Applications

Sampling: Theory and Applications

Author: Stephen D. Casey

Publisher: Springer Nature

Published: 2020-05-20

Total Pages: 210

ISBN-13: 3030362914

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The chapters of this volume are based on talks given at the eleventh international Sampling Theory and Applications conference held in 2015 at American University in Washington, D.C. The papers highlight state-of-the-art advances and trends in sampling theory and related areas of application, such as signal and image processing. Chapters have been written by prominent mathematicians, applied scientists, and engineers with an expertise in sampling theory. Claude Shannon’s 100th birthday is also celebrated, including an introductory essay that highlights Shannon’s profound influence on the field. The topics covered include both theory and applications, such as: • Compressed sensing• Non-uniform and wave sampling• A-to-D conversion• Finite rate of innovation• Time-frequency analysis• Operator theory• Mobile sampling issues Sampling: Theory and Applications is ideal for mathematicians, engineers, and applied scientists working in sampling theory or related areas.


New Trends in Applied Harmonic Analysis

New Trends in Applied Harmonic Analysis

Author: Akram Aldroubi

Publisher: Birkhäuser

Published: 2016-04-21

Total Pages: 356

ISBN-13: 3319278738

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This volume is a selection of written notes corresponding to courses taught at the CIMPA School: "New Trends in Applied Harmonic Analysis: Sparse Representations, Compressed Sensing and Multifractal Analysis". New interactions between harmonic analysis and signal and image processing have seen striking development in the last 10 years, and several technological deadlocks have been solved through the resolution of deep theoretical problems in harmonic analysis. New Trends in Applied Harmonic Analysis focuses on two particularly active areas that are representative of such advances: multifractal analysis, and sparse representation and compressed sensing. The contributions are written by leaders in these areas, and cover both theoretical aspects and applications. This work should prove useful not only to PhD students and postdocs in mathematics and signal and image processing, but also to researchers working in related topics.


Realtime Data Mining

Realtime Data Mining

Author: Alexander Paprotny

Publisher: Springer Science & Business Media

Published: 2013-12-03

Total Pages: 333

ISBN-13: 3319013211

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​​​​Describing novel mathematical concepts for recommendation engines, Realtime Data Mining: Self-Learning Techniques for Recommendation Engines features a sound mathematical framework unifying approaches based on control and learning theories, tensor factorization, and hierarchical methods. Furthermore, it presents promising results of numerous experiments on real-world data.​ The area of realtime data mining is currently developing at an exceptionally dynamic pace, and realtime data mining systems are the counterpart of today's “classic” data mining systems. Whereas the latter learn from historical data and then use it to deduce necessary actions, realtime analytics systems learn and act continuously and autonomously. In the vanguard of these new analytics systems are recommendation engines. They are principally found on the Internet, where all information is available in realtime and an immediate feedback is guaranteed. This monograph appeals to computer scientists and specialists in machine learning, especially from the area of recommender systems, because it conveys a new way of realtime thinking by considering recommendation tasks as control-theoretic problems. Realtime Data Mining: Self-Learning Techniques for Recommendation Engines will also interest application-oriented mathematicians because it consistently combines some of the most promising mathematical areas, namely control theory, multilevel approximation, and tensor factorization.


A Software-Defined GPS and Galileo Receiver

A Software-Defined GPS and Galileo Receiver

Author: Kai Borre

Publisher: Springer Science & Business Media

Published: 2007-08-03

Total Pages: 189

ISBN-13: 0817645403

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This book explore the use of new technologies in the area of satellite navigation receivers. In order to construct a reconfigurable receiver with a wide range of applications, the authors discuss receiver architecture based on software-defined radio techniques. The presentation unfolds in a user-friendly style and goes from the basics to cutting-edge research. The book is aimed at applied mathematicians, electrical engineers, geodesists, and graduate students. It may be used as a textbook in various GPS technology and signal processing courses, or as a self-study reference for anyone working with satellite navigation receivers.


Harmonic Analysis and Applications

Harmonic Analysis and Applications

Author: Christopher Heil

Publisher: Springer Science & Business Media

Published: 2006-07-13

Total Pages: 390

ISBN-13: 0817637788

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This self-contained volume in honor of John J. Benedetto covers a wide range of topics in harmonic analysis and related areas. These include weighted-norm inequalities, frame theory, wavelet theory, time-frequency analysis, and sampling theory. The chapters are clustered by topic to provide authoritative expositions that will be of lasting interest. The original papers collected are written by prominent researchers and professionals in the field. The book pays tribute to John J. Benedetto’s achievements and expresses an appreciation for the mathematical and personal inspiration he has given to so many students, co-authors, and colleagues.