Singularities And Oscillations
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Singularities And Oscillations
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Author : Jeffrey Rauch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Singularities And Oscillations written by Jeffrey Rauch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
This IMA Volume in Mathematics and its Applications SINGULARITIES AND OSCILLATIONS is based on the proceedings of a very successful one-week workshop with the same title, which was an integral part of the 1994-1995 IMA program on "Waves and Scattering. " We would like to thank Joseph Keller, Jeffrey Rauch, and Michael Taylor for their excellent work as organizers of the meeting. We would like to express our further gratitude to Rauch and Taylor, who served as editors of the proceedings. We also take this opportunity to thank the National Science Foun dation (NSF), the Army Research Office (ARO) and the Office of Naval Research (ONR), whose financial support made the workshop possible. Avner Friedman Robert Gulliver v PREFACE Thestudyofsingularitiesand oscillationsofwaves has progressed along several fronts. A key common feature is the presence of a small scale in the solutions. Recent emphasis has been on nonlinear waves. Nonlinear problems are generally less amenable than linear problems to broad unified approaches. As a result there is a justifiable tendency to concentrate on problems of particular geometric or physical interest. This volume con tains a multiplicity of approaches brought to bear on problems varying from the formation ofcaustics and the propagation ofwaves at a boundary to the examination ofviscous boundary layers. There is an examination of the foundations of the theory of high-frequency electromagnetic waves in a dielectric or semiconducting medium. Unifying themes are not entirely absent from nonlinear analysis.
Oscillatory Integrals A Mathematical Symphony
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-07-20
Oscillatory Integrals A Mathematical Symphony written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-20 with Mathematics categories.
"Oscillatory Integrals: A Mathematical Symphony" is an intellectual odyssey into the captivating world of oscillatory analysis, where mathematics and physics converge to create a symphony of beauty and practical relevance. This book unveils the profound significance of oscillatory integrals in shaping our understanding of the universe, revealing their role in governing a vast array of natural and man-made phenomena. From the mesmerizing dance of light waves to the intricate patterns of sound, oscillations permeate our world, dictating the behavior of particles, waves, and fields. By delving into the mathematical framework of oscillatory integrals, this book provides a powerful tool for deciphering the language of oscillations, enabling us to unravel the mysteries of diverse physical phenomena. Through its exploration of foundational principles, recent developments, and open problems, "Oscillatory Integrals: A Mathematical Symphony" offers a comprehensive journey into this fascinating field. It unveils the profound connections between seemingly disparate areas of mathematics, revealing the unifying power of oscillatory phenomena. Along the way, readers encounter a symphony of mathematical concepts, each contributing its unique melody to the harmonic composition of oscillatory analysis. This book is an invitation to immerse oneself in the captivating world of oscillatory phenomena, where mathematics and physics converge to create a symphony of intellectual beauty and practical relevance. It is a journey of discovery, enlightenment, and inspiration, empowering readers to appreciate the profound interconnectedness of mathematics, science, and the natural world. Written in an engaging and accessible style, "Oscillatory Integrals: A Mathematical Symphony" is an ideal resource for mathematicians, physicists, engineers, and anyone seeking a deeper understanding of the mathematical underpinnings of oscillatory phenomena. It is also a valuable asset for students seeking to expand their knowledge of oscillatory analysis and its applications in diverse fields. With its comprehensive coverage, clear explanations, and insightful connections, "Oscillatory Integrals: A Mathematical Symphony" is an essential addition to the libraries of those seeking to explore the fascinating world of oscillatory phenomena and its profound impact on our understanding of the universe. If you like this book, write a review!
Nonlinear Oscillations In Physical Systems
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Author : Chihiro Hayashi
language : en
Publisher: Princeton University Press
Release Date : 2014-07-14
Nonlinear Oscillations In Physical Systems written by Chihiro Hayashi and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Science categories.
This book offers a fundamental explanation of nonlinear oscillations in physical systems. Originally intended for electrical engineers, it remains an important reference for the increasing numbers of researchers studying nonlinear phenomena in physics, chemical engineering, biology, medicine, and other fields. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Singularities Of Differentiable Maps
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Author : V.I. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Singularities Of Differentiable Maps written by V.I. Arnold and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The present. volume is the second volume of the book "Singularities of Differentiable Maps" by V.1. Arnold, A. N. Varchenko and S. M. Gusein-Zade. The first volume, subtitled "Classification of critical points, caustics and wave fronts", was published by Moscow, "Nauka", in 1982. It will be referred to in this text simply as "Volume 1". Whilst the first volume contained the zoology of differentiable maps, that is it was devoted to a description of what, where and how singularities could be encountered, this volume contains the elements of the anatomy and physiology of singularities of differentiable functions. This means that the questions considered in it are about the structure of singularities and how they function. Another distinctive feature of the present volume is that we take a hard look at questions for which it is important to work in the complex domain, where the first volume was devoted to themes for which, on the whole, it was not important which field (real or complex) we were considering. Such topics as, for example, decomposition of singularities, the connection between singularities and Lie algebras and the asymptotic behaviour of different integrals depending on parameters become clearer in the complex domain. The book consists of three parts. In the first part we consider the topological structure of isolated critical points of holomorphic functions. We describe the fundamental topological characteristics of such critical points: vanishing cycles, distinguished bases, intersection matrices, monodromy groups, the variation operator and their interconnections and method of calculation.
Practical Time Frequency Analysis
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Author : Rene Carmona
language : en
Publisher: Academic Press
Release Date : 1998-08-27
Practical Time Frequency Analysis written by Rene Carmona and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-27 with Mathematics categories.
Time frequency analysis has been the object of intense research activity in the last decade. This book gives a self-contained account of methods recently introduced to analyze mathematical functions and signals simultaneously in terms of time and frequency variables. The book gives a detailed presentation of the applications of these transforms to signal processing, emphasizing the continuous transforms and their applications to signal analysis problems, including estimation, denoising, detection, and synthesis. To help the reader perform these analyses, Practical Time-Frequency Analysis provides a set of useful tools in the form of a library of S functions, downloadable from the authors' Web sites in the United States and France. - Detailed presentation of the Wavelet and Gabor transforms - Applications to deterministic and random signal theory - Spectral analysis of nonstationary signals and processes - Numerous practical examples ranging from speech analysis to underwater acoustics, earthquake engineering, internet traffic, radar signal denoising, medical data interpretation, etc - Accompanying software and data sets, freely downloadable from the book's Web page
Analysis Of Singularities For Partial Differential Equations
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Author : Shuxing Chen
language : en
Publisher: World Scientific
Release Date : 2011
Analysis Of Singularities For Partial Differential Equations written by Shuxing Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
The book provides a comprehensive overview on the theory on analysis of singularities for partial differential equations (PDEs). It contains a summarization of the formation, development and main results on this topic. Some of the author's discoveries and original contributions are also included, such as the propagation of singularities of solutions to nonlinear equations, singularity index and formation of shocks.
Progress In Mathematical Relativity Gravitation And Cosmology
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Author : Alfonso García-Parrado
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-26
Progress In Mathematical Relativity Gravitation And Cosmology written by Alfonso García-Parrado and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-26 with Mathematics categories.
This book contains contributions from the Spanish Relativity Meeting, ERE 2012, held in Guimarães, Portugal, September 2012. It features more than 70 papers on a range of topics in general relativity and gravitation, from mathematical cosmology, numerical relativity and black holes to string theory and quantum gravity. Under the title "Progress in Mathematical Relativity, Gravitation and Cosmology," ERE 2012 was attended by an exceptional international list of over a hundred participants from the five continents and over forty countries. ERE is organized every year by one of the Spanish or Portuguese groups working in this area and is supported by the Spanish Society of Gravitation and Relativity (SEGRE). This book will be of interest to researchers in mathematics and physics.
Singularities In Fluids Plasmas And Optics
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Author : Russel Caflisch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Singularities In Fluids Plasmas And Optics written by Russel Caflisch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Singularities in Fluids, Plasmas and Optics, which contains the proceedings of a NATO Workshop held in Heraklion, Greece, in July 1992, provides a survey of the state of the art in the analysis and computation of singularities in physical problems drawn from fluid mechanics, plasma physics and nonlinear optics. The singularities include curvature singularities on fluid interfaces, the onset of turbulence in 3-D inviscid flows, focusing singularities for laser beams, and magnetic reconnection. The highlights of the book include the nonlinear Schrödinger equation for describing laser beam focusing, the method of complex variables for the analysis and computation of singularities on fluid interfaces, and studies of singularities for the 3-D Euler equations. The book is suitable for graduate students and researchers in these areas.
Singularity Theory And Some Problems Of Functional Analysis
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Author : Semen Grigorʹevich Gindikin
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Singularity Theory And Some Problems Of Functional Analysis written by Semen Grigorʹevich Gindikin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
The emergence of singularity theory marks the return of mathematics to the study of the simplest analytical objects: functions, graphs, curves, surfaces. The modern singularity theory for smooth mappings, which is currently undergoing intensive developments, can be thought of as a crossroad where the most abstract topics (such as algebraic and differential geometry and topology, complex analysis, invariant theory, and Lie group theory) meet the most applied topics (such as dynamical systems, mathematical physics, geometrical optics, mathematical economics, and control theory). The papers in this volume include reviews of established areas as well as presentations of recent results in singularity theory. The authors have paid special attention to examples and discussion of results rather than burying the ideas in formalism, notation, and technical details. The aim is to introduce all mathematicians - as well as physicists, engineers, and other consumers of singularity theory - to the world of ideas and methods in this burgeoning area.
Magnetospheric Mhd Oscillations
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Author : Anatoly Leonovich
language : en
Publisher: John Wiley & Sons
Release Date : 2024-03-25
Magnetospheric Mhd Oscillations written by Anatoly Leonovich and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-25 with Science categories.
Magnetospheric MHD Oscillations A groundbreaking new theory of the magnetosphere The magnetosphere is the region around Earth in which our planet’s magnetic field exerts its influence to trap charged particles. Waves in this magnetosphere, known as magnetohydrodynamic (MHD) oscillations, are caused by interactions between these charged particles, Solar wind pulses, and the magnetic field. The predictable interval between these oscillations enables them to serve as tools for understanding the magnetospheric plasma which comprises the field. Magnetospheric MHD Oscillations offers a comprehensive overview of the theory underlying these waves and their periodicity. Emphasizing the spatial structure of the oscillations, it advances a theory of MHD oscillation that promises to have significant ramifications in astronomy and beyond. Magnetospheric MHD Oscillations readers will also find: Theorizing of direct relevance to current satellite missions, such as THEMIS and the Van Allen Probe In-depth discussion of topics including Alfven resonance, waveguides in plasma filaments, and many more Detailed appendices including key calculations and statistical parameters Magnetospheric MDH Oscillations is ideal for plasma physicists, theoretical physicists, applied mathematicians, and advanced graduate students in these and related subfields.