Perturbations

Author : James A. Murdock
Publisher : SIAM
Page : 358 pages
File Size : 50,6 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 1611971098

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Perturbations by James A. Murdock Pdf

Perturbations: Theory and Methods gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations. Unlike most introductory books on the subject, this one distinguishes between formal and rigorous asymptotic validity, which are commonly confused in books that treat perturbation theory as a bag of heuristic tricks with no foundation. The meaning of "uniformity" is carefully explained in a variety of contexts. All standard methods, such as rescaling, multiple scales, averaging, matching, and the WKB method are covered, and the asymptotic validity (in the rigorous sense) of each method is carefully proved. First published in 1991, this book is still useful today because it is an introduction. It combines perturbation results with those known through other methods. Sometimes a geometrical result (such as the existence of a periodic solution) is rigorously deduced from a perturbation result, and at other times a knowledge of the geometry of the solutions is used to aid in the selection of an effective perturbation method. Dr. Murdock's approach differs from other introductory texts because he attempts to present perturbation theory as a natural part of a larger whole, the mathematical theory of differential equations. He explores the meaning of the results and their connections to other ways of studying the same problems.

Author : James A. Murdock
Publisher : SIAM
Page : 513 pages
File Size : 55,5 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 9780898714432

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Perturbations by James A. Murdock Pdf

This book gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations.

Author : V. F. Proskurin
Publisher : Unknown
Page : 16 pages
File Size : 46,5 Mb
Release : 1960
Category : Artificial satellites
ISBN : UIUC:30112106739656

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First-order Perturbations in the Motion of Earth Satellites Due to Oblateness of the Earth by V. F. Proskurin Pdf

Author : Yifeng Xue
Publisher : World Scientific
Page : 305 pages
File Size : 41,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814383608

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Stable Perturbations of Operators and Related Topics by Yifeng Xue Pdf

This book provides a broad introduction to the generalized inverses, MooreOCoPenrose inverses, Drazin inverses and TOCoS outer generalized inverses and their perturbation analyses in the spaces of infinite-dimensional. This subject has many applications in operator theory, operator algebras, global analysis and approximation theory and so on. Stable Perturbations of Operators and Related Topics is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students. It is also suitable for researchers as a reference. The proofs of statements and explanations in the book are detailed enough that interested readers can study it by themselves."

Author : Desineni S. Naidu
Publisher : Unknown
Page : 36 pages
File Size : 42,8 Mb
Release : 1988
Category : Control theory
ISBN : UIUC:30112106606913

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Singular Perturbations and Time Scales in the Design of Digital Flight Control Systems by Desineni S. Naidu Pdf

Author : G. F. Roach
Publisher : Princeton University Press
Page : 304 pages
File Size : 43,8 Mb
Release : 2009-02-09
Category : Science
ISBN : 9781400828166

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Wave Scattering by Time-Dependent Perturbations by G. F. Roach Pdf

This book offers the first comprehensive introduction to wave scattering in nonstationary materials. G. F. Roach's aim is to provide an accessible, self-contained resource for newcomers to this important field of research that has applications across a broad range of areas, including radar, sonar, diagnostics in engineering and manufacturing, geophysical prospecting, and ultrasonic medicine such as sonograms. New methods in recent years have been developed to assess the structure and properties of materials and surfaces. When light, sound, or some other wave energy is directed at the material in question, "imperfections" in the resulting echo can reveal a tremendous amount of valuable diagnostic information. The mathematics behind such analysis is sophisticated and complex. However, while problems involving stationary materials are quite well understood, there is still much to learn about those in which the material is moving or changes over time. These so-called non-autonomous problems are the subject of this fascinating book. Roach develops practical strategies, techniques, and solutions for mathematicians and applied scientists working in or seeking entry into the field of modern scattering theory and its applications. Wave Scattering by Time-Dependent Perturbations is destined to become a classic in this rapidly evolving area of inquiry.

Author : Daniel Oro
Publisher : Oxford University Press, USA
Page : 165 pages
File Size : 49,6 Mb
Release : 2020-03-26
Category : Nature
ISBN : 9780198849834

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Perturbation, Behavioural Feedbacks, and Population Dynamics in Social Animals by Daniel Oro Pdf

This novel, transdisciplinary work explains how perturbations (defined as strong disturbances or deviations to a system) can affect the population dynamics of social animals, including ourselves. Social responses to perturbations, especially dispersal processes, can also generate non-linear population dynamics, including the potential appearance of tipping points and critical population transitions, which can in turn lead to catastrophic shifts and collapses. The book describes the links between social behaviour (mainly the use of social information and social copying), and non-linear population dynamics at different spatial scales (local dynamics and meta-population dynamics), and their ecological and evolutionary consequences. Examples from the natural world illustrate each of the main themes (prospecting, habitat suitability, collective dispersal, and cultural evolution). Human warfare and conflict, referred to in several chapters together with quantitative and qualitative examples, is also viewed as a form of perturbation and represents a paradigmatic example of the rationale behind this book. This applicability to our own species is particularly timely, given increased interest in both ecosystem change, human migration, and the global refugee crisis. Perturbation, Behavioural Feedbacks, and Population Dynamics in Social Animals will appeal to applied, theoretical, and evolutionary ecologists, particularly those working on the population and behavioural ecology of any social animal including humans. Its overlap with the study of complexity will also ensure its relevance and use to scientists from other disciplines such as sociology, anthropology, physics, computational science, economics, and mathematics.

Author : Anatoli V. Skorokhod,Frank C. Hoppensteadt,Habib D. Salehi
Publisher : Springer Science & Business Media
Page : 500 pages
File Size : 49,9 Mb
Release : 2007-06-21
Category : Mathematics
ISBN : 9780387224466

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Random Perturbation Methods with Applications in Science and Engineering by Anatoli V. Skorokhod,Frank C. Hoppensteadt,Habib D. Salehi Pdf

This book develops methods for describing random dynamical systems, and it illustrats how the methods can be used in a variety of applications. Appeals to researchers and graduate students who require tools to investigate stochastic systems.

Author : Petar Kokotovic,Hassan K. Khali,John O'Reilly
Publisher : SIAM
Page : 379 pages
File Size : 40,5 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 9780898714449

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Singular Perturbation Methods in Control by Petar Kokotovic,Hassan K. Khali,John O'Reilly Pdf

This SIAM Classics edition of the 1986 book provides the theoretical foundation for representative control applications.

Author : M. I. Freidlin,A. D. Wentzell
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468401769

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Random Perturbations of Dynamical Systems by M. I. Freidlin,A. D. Wentzell Pdf

Asymptotical problems have always played an important role in probability theory. In classical probability theory dealing mainly with sequences of independent variables, theorems of the type of laws of large numbers, theorems of the type of the central limit theorem, and theorems on large deviations constitute a major part of all investigations. In recent years, when random processes have become the main subject of study, asymptotic investigations have continued to playa major role. We can say that in the theory of random processes such investigations play an even greater role than in classical probability theory, because it is apparently impossible to obtain simple exact formulas in problems connected with large classes of random processes. Asymptotical investigations in the theory of random processes include results of the types of both the laws of large numbers and the central limit theorem and, in the past decade, theorems on large deviations. Of course, all these problems have acquired new aspects and new interpretations in the theory of random processes.

Author : L.S. Frank
Publisher : Elsevier
Page : 554 pages
File Size : 55,5 Mb
Release : 1990-08-16
Category : Mathematics
ISBN : 0080875440

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Singular Perturbations I by L.S. Frank Pdf

Singular perturbations, one of the central topics in asymptotic analysis, also play a special role in describing physical phenomena such as the propagation of waves in media in the presence of small energy dissipations or dispersions, the appearance of boundary or interior layers in fluid and gas dynamics, as well as in elasticity theory, semi-classical asymptotic approximations in quantum mechanics etc. Elliptic and coercive singular perturbations are of special interest for the asymptotic solution of problems which are characterized by boundary layer phenomena, e.g. the theory of thin buckling plates, elastic rods and beams. This first volume deals with linear singular perturbations (on smooth manifolds without boundary) considered as equicontinuous linear mappings between corresponding families of Sobolev-Slobodetski's type spaces of vectorial order.

Author : Grigory I. Shishkin,Lidia P. Shishkina
Publisher : CRC Press
Page : 408 pages
File Size : 48,5 Mb
Release : 2008-09-22
Category : Mathematics
ISBN : 0203492412

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Difference Methods for Singular Perturbation Problems by Grigory I. Shishkin,Lidia P. Shishkina Pdf

Difference Methods for Singular Perturbation Problems focuses on the development of robust difference schemes for wide classes of boundary value problems. It justifies the ε-uniform convergence of these schemes and surveys the latest approaches important for further progress in numerical methods. The first part of the book explores boundary value problems for elliptic and parabolic reaction-diffusion and convection-diffusion equations in n-dimensional domains with smooth and piecewise-smooth boundaries. The authors develop a technique for constructing and justifying ε uniformly convergent difference schemes for boundary value problems with fewer restrictions on the problem data. Containing information published mainly in the last four years, the second section focuses on problems with boundary layers and additional singularities generated by nonsmooth data, unboundedness of the domain, and the perturbation vector parameter. This part also studies both the solution and its derivatives with errors that are independent of the perturbation parameters. Co-authored by the creator of the Shishkin mesh, this book presents a systematic, detailed development of approaches to construct ε uniformly convergent finite difference schemes for broad classes of singularly perturbed boundary value problems.

Author : Ali Akbar Abolhasani,Hassan Firouzjahi,Atsushi Naruko,Misao Sasaki
Publisher : World Scientific
Page : 182 pages
File Size : 45,9 Mb
Release : 2019-01-30
Category : Science
ISBN : 9789813238770

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Delta N Formalism In Cosmological Perturbation Theory by Ali Akbar Abolhasani,Hassan Firouzjahi,Atsushi Naruko,Misao Sasaki Pdf

Early Universe cosmology is an active area of research and cosmic inflation is a pillar of modern cosmology. Among predictions of inflation, observationally the most important one is the generation of cosmological perturbations from quantum vacuum fluctuations that source all inhomogeneous structures in the Universe, not to mention the large-scale structures such as clusters of galaxies.Cosmological perturbation theory is the basic tool to study the perturbations generated from inflation. There are a few different approaches to primordial cosmological perturbations. In the conventional approach one perturbs the field equations and after quantizing the perturbations by the use of the corresponding action, one calculates the power spectrum of cosmological observables. This approach extends to higher order perturbations such as bispectrum etc., but the analysis becomes increasingly difficult.The delta N formalism, the topic of this book, is an alternative approach. The novelty of this approach is that, under the condition that the scale of interest is very large so that the spatial derivatives may be ignored in the dynamics, it can be applied to all orders in perturbation theory and has a rigorous foundation in general relativity. Thanks to the fact that one can evaluate perturbations with only the knowledge of background solutions, it is proved to be much easier than the conventional approach in evaluating higher order effects in many cases.

Author : W. Eckhaus
Publisher : Elsevier
Page : 286 pages
File Size : 43,7 Mb
Release : 2011-08-30
Category : Mathematics
ISBN : 0080875300

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Asymptotic Analysis of Singular Perturbations by W. Eckhaus Pdf

Asymptotic Analysis of Singular Perturbations

Author : Tamir Hazan,George Papandreou,Daniel Tarlow
Publisher : MIT Press
Page : 413 pages
File Size : 48,8 Mb
Release : 2023-12-05
Category : Computers
ISBN : 9780262549943

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Perturbations, Optimization, and Statistics by Tamir Hazan,George Papandreou,Daniel Tarlow Pdf

A description of perturbation-based methods developed in machine learning to augment novel optimization methods with strong statistical guarantees. In nearly all machine learning, decisions must be made given current knowledge. Surprisingly, making what is believed to be the best decision is not always the best strategy, even when learning in a supervised learning setting. An emerging body of work on learning under different rules applies perturbations to decision and learning procedures. These methods provide simple and highly efficient learning rules with improved theoretical guarantees. This book describes perturbation-based methods developed in machine learning to augment novel optimization methods with strong statistical guarantees, offering readers a state-of-the-art overview. Chapters address recent modeling ideas that have arisen within the perturbations framework, including Perturb & MAP, herding, and the use of neural networks to map generic noise to distribution over highly structured data. They describe new learning procedures for perturbation models, including an improved EM algorithm and a learning algorithm that aims to match moments of model samples to moments of data. They discuss understanding the relation of perturbation models to their traditional counterparts, with one chapter showing that the perturbations viewpoint can lead to new algorithms in the traditional setting. And they consider perturbation-based regularization in neural networks, offering a more complete understanding of dropout and studying perturbations in the context of deep neural networks.