In recent years, mathematicians have detailed simpler proofs of known theorems, have identified new applications of the method of averaging, and have obtained many new results of these applications. Encompassing these novel aspects, Method of Averaging of the Infinite Interval: Theory and Applications rigorously explains the modern theory of the me
The book is devoted to the study of the correlation effects in many-particle systems. It presents the advanced methods of quantum statistical mechanics (equilibrium and nonequilibrium), and shows their effectiveness and operational ability in applications to problems of quantum solid-state theory, quantum theory of magnetism and the kinetic theory. The book includes description of the fundamental concepts and techniques of analysis following the approach of N N Bogoliubov's school, including recent developments. It provides an overview that introduces the main notions of quantum many-particle physics with the emphasis on concepts and models.This book combines the features of textbook and research monograph. For many topics the aim is to start from the beginning and to guide the reader to the threshold of advanced researches. Many chapters include also additional information and discuss many complex research areas which are not often discussed in other places. The book is useful for established researchers to organize and present the advanced material disseminated in the literature. The book contains also an extensive bibliography.The book serves undergraduate, graduate and postgraduate students, as well as researchers who have had prior experience with the subject matter at a more elementary level or have used other many-particle techniques.
In recent years, mathematicians have detailed simpler proofs of known theorems, have identified new applications of the method of averaging, and have obtained many new results of these applications. Encompassing these novel aspects, Method of Averaging of the Infinite Interval: Theory and Applications rigorously explains the modern theory of the method of averaging and provides a solid understanding of the results obtained when applying this theory. The book starts with the less complicated theory of averaging linear differential equations (LDEs), focusing on almost periodic functions. It describes stability theory and Shtokalo's method, and examines various applications, including parametric resonance and the construction of asymptotics. After establishing this foundation, the author goes on to explore nonlinear equations. He studies standard form systems in which the right-hand side of a system is proportional to a small parameter and proves theorems similar to Banfi's theorem. The final chapters are devoted to systems with a rapidly rotating phase. Covering an important asymptotic method of differential equations, this book provides a thorough understanding of the method of averaging theory and its resulting applications.
Data Analysis Methods in Physical Oceanography is a practical referenceguide to established and modern data analysis techniques in earth and oceansciences. This second and revised edition is even more comprehensive with numerous updates, and an additional appendix on 'Convolution and Fourier transforms'. Intended for both students and established scientists, the fivemajor chapters of the book cover data acquisition and recording, dataprocessing and presentation, statistical methods and error handling,analysis of spatial data fields, and time series analysis methods. Chapter 5on time series analysis is a book in itself, spanning a wide diversity oftopics from stochastic processes and stationarity, coherence functions,Fourier analysis, tidal harmonic analysis, spectral and cross-spectralanalysis, wavelet and other related methods for processing nonstationarydata series, digital filters, and fractals. The seven appendices includeunit conversions, approximation methods and nondimensional numbers used ingeophysical fluid dynamics, presentations on convolution, statisticalterminology, and distribution functions, and a number of importantstatistical tables. Twenty pages are devoted to references. Featuring:• An in-depth presentation of modern techniques for the analysis of temporal and spatial data sets collected in oceanography, geophysics, and other disciplines in earth and ocean sciences.• A detailed overview of oceanographic instrumentation and sensors - old and new - used to collect oceanographic data.• 7 appendices especially applicable to earth and ocean sciences ranging from conversion of units, through statistical tables, to terminology and non-dimensional parameters. In praise of the first edition: "(...)This is a very practical guide to the various statistical analysis methods used for obtaining information from geophysical data, with particular reference to oceanography(...)The book provides both a text for advanced students of the geophysical sciences and a useful reference volume for researchers." Aslib Book Guide Vol 63, No. 9, 1998 "(...)This is an excellent book that I recommend highly and will definitely use for my own research and teaching." EOS Transactions, D.A. Jay, 1999 "(...)In summary, this book is the most comprehensive and practical source of information on data analysis methods available to the physical oceanographer. The reader gets the benefit of extremely broad coverage and an excellent set of examples drawn from geographical observations." Oceanography, Vol. 12, No. 3, A. Plueddemann, 1999 "(...)Data Analysis Methods in Physical Oceanography is highly recommended for a wide range of readers, from the relative novice to the experienced researcher. It would be appropriate for academic and special libraries." E-Streams, Vol. 2, No. 8, P. Mofjelf, August 1999
Hierarchic Electrodynamics and Free Electron Lasers: Concepts, Calculations, and Practical Applications presents intriguing new fundamental concepts in the phenomenon of hierarchical electrodynamics as a new direction in physics. Concentrating on the key theory of hierarchic oscillations and waves, this book focuses on the numerous applications of nonlinear theory in different types of high-current Free Electron Lasers (FEL), including their primary function in the calculation methods used to analyze various multi-resonant, multi-frequency nonlinear FEL models. This is considered the first book to: Completely and systematically describe the foundation of hierarchical electrodynamics as a new direction of physics Fully represent the physics of high-current FEL—and associated models—from the hierarchic oscillation wave perspective Cover the multi-harmonic nonlinear theory of new types of electronic devices, such as plasma-beam and two-stream FEL Formulate and substantiate the concept of cluster femtosecond FEL Analyze practical prospects for a new generation of a global "Star Wars" strategic defense systems These subjects involve a wide range of disciplines. Using numerous real-world examples to illustrate information and concepts, the book offers a mathematical foundation to explore FEL applications as well as analyze hierarchic plasma-like electrodynamic systems and femto-second clusters of electromagnetic energy. Assembling fragmented concepts from existing literature, the author re-examines classic approaches in order to develop new insights and achieve scientific breakthroughs.
Mechanics Today, Volume 3 provides the advances in the fields of solid and fluid mechanics and applied mathematics. This volume is divided into six chapters that discuss the fundamentals and analytical and experimental results of dynamic behavior of linear and nonlinear systems. Chapter I provides a formulation of the effective stiffness theory with equations of motion and boundary conditions presented for the case of plain strain motion. Chapter II summarizes some of the analytical results that have been obtained in an effort to improve understanding of elastodynamic fracture processes. Chapter III presents the matrix difference equations used to formulate problems related to random vibration of periodic and almost periodic structures, taking advantage of the identical construction of the interconnecting units. Chapter IV describes a basic approach to the Oseen problem through the use of integral representations of the velocity and pressure fields. Chapter V deals with an analysis of nonlinear gyroscopic systems and the motions of high-order nongyroscopic systems. Chapter VI focuses on the application of the WKB perturbation method in the study of static deformation, vibration, wave propagation, and instability of elastic bodies. This volume is of great value to solid and fluid mechanics specialists and also to non-specialists with sufficient background of the field.
Calculus: Single Variable, 12th Edition, offers students a rigorous and intuitive treatment of single variable calculus, including the differentiation and integration of one variable. Using the Rule of Four, the authors present mathematical concepts from verbal, algebraic, visual, and numerical points of view. The book includes numerous exercises, applications, and examples that help readers learn and retain the concepts discussed within, and discusses polynomials, rational functions, exponentials, logarithms, and trigonometric functions late in the text.
