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Author: Toru Maruyama Publisher: Springer ISBN: 9811327300 Category : Mathematics Languages : en Pages : 413
Book Description
This is the first monograph that discusses in detail the interactions between Fourier analysis and dynamic economic theories, in particular, business cycles.Many economic theories have analyzed cyclical behaviors of economic variables. In this book, the focus is on a couple of trials: (1) the Kaldor theory and (2) the Slutsky effect. The Kaldor theory tries to explain business fluctuations in terms of nonlinear, 2nd-order ordinary differential equations (ODEs). In order to explain periodic behaviors of a solution, the Hopf-bifurcation theorem frequently plays a key role. Slutsky's idea is to look at the periodic movement as an overlapping effect of random shocks. The Slutsky process is a weakly stationary process, the periodic (or almost periodic) behavior of which can be analyzed by the Bochner theorem. The goal of this book is to give a comprehensive and rigorous justification of these ideas. Therefore, the aim is first to give a complete theory that supports the Hopf theorem and to prove the existence of periodic solutions of ODEs; and second to explain the mathematical structure of the Bochner theorem and its relation to periodic (or almost periodic) behaviors of weakly stationary processes.Although these two targets are the principal ones, a large number of results from Fourier analysis must be prepared in order to reach these goals. The basic concepts and results from classical as well as generalized Fourier analysis are provided in a systematic way.Prospective readers are assumed to have sufficient knowledge of real, complex analysis. However, necessary economic concepts are explained in the text, making this book accessible even to readers without a background in economics.
Author: Toru Maruyama Publisher: Springer ISBN: 9811327300 Category : Mathematics Languages : en Pages : 413
Book Description
This is the first monograph that discusses in detail the interactions between Fourier analysis and dynamic economic theories, in particular, business cycles.Many economic theories have analyzed cyclical behaviors of economic variables. In this book, the focus is on a couple of trials: (1) the Kaldor theory and (2) the Slutsky effect. The Kaldor theory tries to explain business fluctuations in terms of nonlinear, 2nd-order ordinary differential equations (ODEs). In order to explain periodic behaviors of a solution, the Hopf-bifurcation theorem frequently plays a key role. Slutsky's idea is to look at the periodic movement as an overlapping effect of random shocks. The Slutsky process is a weakly stationary process, the periodic (or almost periodic) behavior of which can be analyzed by the Bochner theorem. The goal of this book is to give a comprehensive and rigorous justification of these ideas. Therefore, the aim is first to give a complete theory that supports the Hopf theorem and to prove the existence of periodic solutions of ODEs; and second to explain the mathematical structure of the Bochner theorem and its relation to periodic (or almost periodic) behaviors of weakly stationary processes.Although these two targets are the principal ones, a large number of results from Fourier analysis must be prepared in order to reach these goals. The basic concepts and results from classical as well as generalized Fourier analysis are provided in a systematic way.Prospective readers are assumed to have sufficient knowledge of real, complex analysis. However, necessary economic concepts are explained in the text, making this book accessible even to readers without a background in economics.
Author: Gerlind Plonka Publisher: Springer Nature ISBN: 3031350057 Category : Mathematics Languages : en Pages : 676
Book Description
New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods. To address this growing need, this monograph combines mathematical theory and numerical algorithms to offer a unified and self-contained presentation of Fourier analysis. The first four chapters of the text serve as an introduction to classical Fourier analysis in the univariate and multivariate cases, including the discrete Fourier transforms, providing the necessary background for all further chapters. Next, chapters explore the construction and analysis of corresponding fast algorithms in the one- and multidimensional cases. The well-known fast Fourier transforms (FFTs) are discussed, as well as recent results on the construction of the nonequispaced FFTs, high-dimensional FFTs on special lattices, and sparse FFTs. An additional chapter is devoted to discrete trigonometric transforms and Chebyshev expansions. The final two chapters consider various applications of numerical Fourier methods for improved function approximation, including Prony methods for the recovery of structured functions. This new edition has been revised and updated throughout, featuring new material on a new Fourier approach to the ANOVA decomposition of high-dimensional trigonometric polynomials; new research results on the approximation errors of the nonequispaced fast Fourier transform based on special window functions; and the recently developed ESPIRA algorithm for recovery of exponential sums, among others. Numerical Fourier Analysis will be of interest to graduate students and researchers in applied mathematics, physics, computer science, engineering, and other areas where Fourier methods play an important role in applications.
Author: Loukas Grafakos Publisher: Springer Science & Business Media ISBN: 0387094326 Category : Mathematics Languages : en Pages : 494
Book Description
The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. This book is mainly addressed to graduate students in mathematics and is designed to serve for a three-course sequence on the subject. The only prerequisite for understanding the text is satisfactory completion of a course in measure theory, Lebesgue integration, and complex variables. This book is intended to present the selected topics in some depth and stimulate further study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of analysis on the torus. This material is included for historical reasons, as the genesis of Fourier analysis can be found in trigonometric expansions of periodic functions in several variables. While the 1st edition was published as a single volume, the new edition will contain 120 pp of new material, with an additional chapter on time-frequency analysis and other modern topics. As a result, the book is now being published in 2 separate volumes, the first volume containing the classical topics (Lp Spaces, Littlewood-Paley Theory, Smoothness, etc...), the second volume containing the modern topics (weighted inequalities, wavelets, atomic decomposition, etc...). From a review of the first edition: “Grafakos’s book is very user-friendly with numerous examples illustrating the definitions and ideas. It is more suitable for readers who want to get a feel for current research. The treatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises.” - Ken Ross, MAA Online
Author: Thierry Vialar Publisher: Springer Science & Business Media ISBN: 3540859780 Category : Business & Economics Languages : en Pages : 752
Book Description
Complex dynamics constitute a growing and increasingly important area as they offer a strong potential to explain and formalize natural, physical, financial and economic phenomena. This book pursues the ambitious goal to bring together an extensive body of knowledge regarding complex dynamics from various academic disciplines. Beyond its focus on economics and finance, including for instance the evolution of macroeconomic growth models towards nonlinear structures as well as signal processing applications to stock markets, fundamental parts of the book are devoted to the use of nonlinear dynamics in mathematics, statistics, signal theory and processing. Numerous examples and applications, almost 700 illustrations and numerical simulations based on the use of Matlab make the book an essential reference for researchers and students from many different disciplines who are interested in the nonlinear field. An appendix recapitulates the basic mathematical concepts required to use the book.
Author: Vincent Barnett Publisher: Taylor & Francis ISBN: 1136737324 Category : Business & Economics Languages : en Pages : 238
Book Description
E.E. Slutsky is perhaps the Russian/Ukrainian economist most quoted by mainstream economists today. This is the first research monograph to examine the life and work of the internationally-renowned economist and mathematician. It does so from both a ‘history of economics’ perspective and a ‘history of science’ perspective, bringing these two strands together in order to demonstrate Slutsky’s enduring legacy as an innovative researcher and an influential intellectual. It also presents some of Slutsky’s lesser-known (and hitherto-unavailable) works in English translation.
Author: Jeff Austin. Brillinger Publisher: CRC Press ISBN: 9780412742408 Category : Mathematics Languages : en Pages : 764
Book Description
First of an eight-volume set, documenting Tukey's work from the 1940s to the 1980s One of the late 20th Century's leading innovators and influences on data analysis, John W. Tukey's discoveries and methods have greatly impacted the work of statisticians throughout the world. The Collected Works of John W. Tukey begins here, with 14 chapters on time series analysis.
Author: Publisher: Elsevier ISBN: 0444537732 Category : Business & Economics Languages : en Pages : 498
Book Description
Handbook in Environmental Economics, Volume 4, the latest in this ongoing series, highlights new advances in the field, with this new volume presenting timely chapters on Modeling Ecosystems and Economic Systems, Framing Sustainability Policy Questions: Who Leads – Ecology or Economics?, Valuing Natural Capital Within an Integrated Economic Ecological, Developing Economies, Urbanization, Climate Change and Health, Viewing Environmental Policy Instruments for Domestic and International Perspective, Quasi experimental Estimation of Environmental Policies, Environment Macro, The Rules for Formal and Informal Institutions in Managing Environmental Resources, and How Should Uncertainty Be Integrated into the Methods for Policy Evaluation? - Answers key policy questions facing environmental agencies in developed and developing economies - Integrates insights from economics and ecology as part of several key chapters - Presents the latest on efforts to review and evaluate the new literatures on field and quasi experiments in environmental economics - Provides the first substantive review of environmental macro economics
Author: Michael R. Lindeburg Publisher: Simon and Schuster ISBN: 1591265797 Category : Technology & Engineering Languages : en Pages : 2969
Book Description
Michael R. Lindeburg PE’s FE Chemical Review Manual offers complete review for the NCEES FE Chemical exam. This book is intended to guide you through the Chemical Fundamentals of Engineering (FE) examination body of knowledge and the idiosyncrasies of the National Council of Examiners for Engineers and Surveyors (NCEES) FE Reference Handbook (NCEES Handbook). This book is not intended as a reference book, because you cannot use it while taking the FE examination. The only reference you may use is the NCEES Handbook. However, the NCEES Handbook is not intended as a teaching tool, nor is it an easy document to use. The NCEES Handbook was never intended to be something you study or learn from, or to have value as anything other than an examday compilation. Many of its features may distract you because they differ from what you were expecting, were exposed to, or what you currently use. To effectively use the NCEES Handbook, you must become familiar with its features, no matter how odd they may seem. FE Chemical Review Manual will help you become familiar with the format, layout, organization, and odd conventions of the NCEES Handbook. This book, which displays the NCEES Handbook material in blue for easy identification, satisfies two important needs: it is (1) something to learn from, and (2) something to help you become familiar with the NCEES Handbook. Topics Covered Chemical Reaction Engineering Chemistry Computational Tools Engineering Sciences Ethics and Professional Practice Fluid Mechanics/Dynamics Heat Transfer Mass Transfer and Separation Material/Energy Balances Materials Science Mathematics Probability and Statistics Process Control Process Design and Economics Safety, Health, and Environment Thermodynamics Key Features: Complete coverage of all exam knowledge areas. Equations, figures, and tables of the NCEES FE Reference Handbook to familiarize you with the reference you’ll have on exam day. Concise explanations supported by exam-like example problems, with step-by-step solutions to reinforce the theory and application of fundamental concepts. A robust index with thousands of terms to facilitate referencing. Binding: Paperback PPI, A Kaplan Company
Author: Toru Maruyama
Author: Toru Maruyama
Author: Gerlind Plonka
Author: Loukas Grafakos
Author: Thierry Vialar
Author: Vincent Barnett
Author: 
Author: Jeff Austin. Brillinger
Author: 
Author: 
Author: Michael R. Lindeburg