Analytic Perturbation Theory And Its Applications
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Analytic Perturbation Theory And Its Applications
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Author : Konstantin E. Avrachenkov
language : en
Publisher: SIAM
Release Date : 2013-12-11
Analytic Perturbation Theory And Its Applications written by Konstantin E. Avrachenkov and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
Mathematical models are often used to describe complex phenomena such as climate change dynamics, stock market fluctuations, and the Internet. These models typically depend on estimated values of key parameters that determine system behavior. Hence it is important to know what happens when these values are changed. The study of single-parameter deviations provides a natural starting point for this analysis in many special settings in the sciences, engineering, and economics. The difference between the actual and nominal values of the perturbation parameter is small but unknown, and it is important to understand the asymptotic behavior of the system as the perturbation tends to zero. This is particularly true in applications with an apparent discontinuity in the limiting behavior?the so-called singularly perturbed problems. Analytic Perturbation Theory and Its Applications includes a comprehensive treatment of analytic perturbations of matrices, linear operators, and polynomial systems, particularly the singular perturbation of inverses and generalized inverses. It also offers original applications in Markov chains, Markov decision processes, optimization, and applications to Google PageRank? and the Hamiltonian cycle problem as well as input retrieval in linear control systems and a problem section in every chapter to aid in course preparation.
Analytic Perturbation Theory And Its Applications
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Author : Konstantin Avrachenkov
language : en
Publisher:
Release Date : 1999
Analytic Perturbation Theory And Its Applications written by Konstantin Avrachenkov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Markov processes categories.
Perturbation Theory For Linear Operators
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Author : Aref Jeribi
language : en
Publisher: Springer Nature
Release Date : 2021-07-28
Perturbation Theory For Linear Operators written by Aref Jeribi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-28 with Mathematics categories.
This book discusses the important aspects of spectral theory, in particular, the completeness of generalised eigenvectors, Riesz bases, semigroup theory, families of analytic operators, and Gribov operator acting in the Bargmann space. Recent mathematical developments of perturbed non-self-adjoint operators are discussed with the completeness of the space of generalized eigenvectors, bases on Hilbert and Banach spaces and asymptotic behavior of the eigenvalues of these operators. Most results in the book are motivated by physical problems, such as the perturbation method for sound radiation by a vibrating plate in a light fluid, Gribov operator in Bargmann space and other applications in mathematical physics and mechanics. This book is intended for students, researchers in the field of spectral theory of linear non self-adjoint operators, pure analysts and mathematicians.
Algebraic Analysis Of Singular Perturbation Theory
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Author : Takahiro Kawai
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Algebraic Analysis Of Singular Perturbation Theory written by Takahiro Kawai 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 2005 with Mathematics categories.
The topic of this book is the study of singular perturbations of ordinary differential equations, i.e., perturbations that represent solutions as asymptotic series rather than as analytic functions in a perturbation parameter. The main method used is the so-called WKB (Wentzel-Kramers-Brillouin) method, originally invented for the study of quantum-mechanical systems. The authors describe in detail the WKB method and its applications to the study of monodromy problems for Fuchsian differential equations and to the analysis of Painleve functions. This volume is suitable for graduate students and researchers interested in differential equations and special functions.
Analytic Perturbation Theory For Matrices And Operators
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Author : Hellmut Baumgärtel
language : en
Publisher: Birkhauser
Release Date : 1985-04
Analytic Perturbation Theory For Matrices And Operators written by Hellmut Baumgärtel and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-04 with Linear operators categories.
Perturbation Theory Of Eigenvalue Problems
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Author : Franz Rellich
language : en
Publisher: CRC Press
Release Date : 1969
Perturbation Theory Of Eigenvalue Problems written by Franz Rellich and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.
Perturbation Theory And Its Applications In Quantum Mechanics
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Author : Calvin Hayden Wilcox
language : en
Publisher:
Release Date : 1966
Perturbation Theory And Its Applications In Quantum Mechanics written by Calvin Hayden Wilcox and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Perturbation (Quantum dynamics) categories.
Methods And Applications Of Singular Perturbations
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Author : Ferdinand Verhulst
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-04
Methods And Applications Of Singular Perturbations written by Ferdinand Verhulst 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 2006-06-04 with Mathematics categories.
Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach
Application Of Analytic Perturbation Theory To Quantum Mechanics
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Author : Peter Capstick
language : en
Publisher:
Release Date : 1965
Application Of Analytic Perturbation Theory To Quantum Mechanics written by Peter Capstick and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with categories.
Perturbation Theory
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Author : Giuseppe Gaeta
language : en
Publisher: Springer Nature
Release Date : 2022-12-16
Perturbation Theory written by Giuseppe Gaeta and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-16 with Science categories.
This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare’-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.