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Is Theory Really Ahead of Measurement? by Lawrence J. Christiano Pdf
In the l93Os, Dunlop and Tarshis observed that the correlation between hours and wages is close to zero. This classic observation has become a litmus test by which macroeconomic models are judged. Existing real business cycle models fail this test dramatically. Based on this result, we argue that technology shocks cannot be the sole impulse driving post-war U.S. business cycles. We modify prototypical real business cycle models by allowing government spending shocks to influence labor market dynamics in a way suggested by Aschauer (1985), Barro (1981, 1987) and Kormendi (1983), This modification can, in principle, bring the models into closer conformity with the data. While the empirical performance of the models is significantly improved, they still fail to account for the Dunlop-Tarshis observation. Accounting for that observation will require further advances in model development. Consequently, we conclude that theory is behind, not ahead of, business cycle measurement.
Measure, Integration & Real Analysis by Sheldon Axler Pdf
This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online. For errata and updates, visit https://measure.axler.net/
Measurement and Probability by Giovanni Battista Rossi Pdf
Measurement plays a fundamental role both in physical and behavioral sciences, as well as in engineering and technology: it is the link between abstract models and empirical reality and is a privileged method of gathering information from the real world. Is it possible to develop a single theory of measurement for the various domains of science and technology in which measurement is involved? This book takes the challenge by addressing the following main issues: What is the meaning of measurement? How do we measure? What can be measured? A theoretical framework that could truly be shared by scientists in different fields, ranging from physics and engineering to psychology is developed. The future in fact will require greater collaboration between science and technology and between different sciences. Measurement, which played a key role in the birth of modern science, can act as an essential interdisciplinary tool and language for this new scenario. A sound theoretical basis for addressing key problems in measurement is provided. These include perceptual measurement, the evaluation of uncertainty, the evaluation of inter-comparisons, the analysis of risks in decision-making and the characterization of dynamical measurement. Currently, increasing attention is paid to these issues due to their scientific, technical, economic and social impact. The book proposes a unified probabilistic approach to them which may allow more rational and effective solutions to be reached. Great care was taken to make the text as accessible as possible in several ways. Firstly, by giving preference to as interdisciplinary a terminology as possible; secondly, by carefully defining and discussing all key terms. This ensures that a wide readership, including people from different mathematical backgrounds and different understandings of measurement can all benefit from this work. Concerning mathematics, all the main results are preceded by intuitive discussions and illustrated by simple examples. Moreover, precise proofs are always included in order to enable the more demanding readers to make conscious and creative use of these ideas, and also to develop new ones. The book demonstrates that measurement, which is commonly understood to be a merely experimental matter, poses theoretical questions which are no less challenging than those arising in other, apparently more theoretical, disciplines.
Theory of Electromagnetic Well Logging by C. Richard Liu Pdf
Theory of Electromagnetic Well Logging provides a much-needed and complete analytical method for electromagnetic well logging technology. The book presents the physics and mathematics behind the effective measurement of rock properties using boreholes, allowing geophysicists, petrophysisists, geologists and engineers to interpret them in a more rigorous way. Starting with the fundamental concepts, the book then moves on to the more classic subject of wireline induction logging, before exploring the subject of LWD logging, concluding with new thoughts on electromagnetic telemetry. Theory of Electromagnetic Well Logging is the only book offering an in-depth discussion of the analytical and numerical techniques needed for expert use of those new logging techniques. Features in-depth analysis of the analytical and numerical techniques needed for expert use of logging techniques Includes software codes, providing a handy tool for understanding logging tool physics and design of new logging tools Provides a detailed glossary of all key terms within the introductory chapter
Quantum Theory and Measurement by John Archibald Wheeler,Wojciech Hubert Zurek Pdf
The forty-nine papers collected here illuminate the meaning of quantum theory as it is disclosed in the measurement process. Together with an introduction and a supplemental annotated bibliography, they discuss issues that make quantum theory, overarching principle of twentieth-century physics, appear to many to prefigure a new revolution in science. Originally published in 1983. 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.
An Introduction to Measure Theory by Terence Tao Pdf
This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.
Open Systems and Measurement in Relativistic Quantum Theory by Heinz-Peter Breuer,Francesco Petruccione Pdf
This book treats modern aspects of open systems, measurement, and decoherence in relativistic quantum theory. It starts with a comprehensive introduction to the problems related to measuring local and nonlocal observables and the constraints imposed by the causality principle. In the articles that follow, the emphasis lies on new theoretical models. Quantum dynamical semigroups and stochastic processes in Hilbert space are introduced, as are dynamical reduction models. Further topics include relativistic generalizations of the continuous spontaneous localization model and of the quantum state diffusion model and decoherence and the dynamical selection of preferred basis sets in the framework of continuous measurement theory and of the decoherent histories approach. Mathematical aspects of quantum measurement theory and dynamical entropies are also studied from the viewpoint of the operational approach to quantum mechanics.
Inverse Methods for Atmospheric Sounding by Clive D Rodgers Pdf
Remote sounding of the atmosphere has proved to be a fruitful method of obtaining global information about the atmospheres of the earth and other planets. This book treats comprehensively the inverse problem of remote sounding, and discusses a wide range of retrieval methods for extracting atmospheric parameters of interest from the quantities (thermal emission, for example) that can be measured remotely. Inverse theory is treated in depth from an estimation-theory point of view, but practical questions are also emphasized, such as designing observing systems to obtain the maximum quantity of information, efficient numerical implementation of algorithms for processing large quantities of data, error analysis and approaches to the validation of the resulting retrievals. The book is targeted at graduate students as well as scientists. Contents:Information AspectsError Analysis and CharacterisationOptimal Linear Inverse MethodsOptimal Methods for Nonlinear Inverse ProblemsApproximations, Short Cuts and Ad-hoc MethodsThe Kalman FilterGlobal Data AssimilationNumerical Methods for Forward Models and JacobiansConstruction and Use of Prior ConstraintsDesigning an Observing SystemTesting and Validating an Observing System Readership: Physicists, applied mathematicians and interdisciplinary scientists. keywords:Atmosphere;Satellites;Sounding;Retrievals;Remote Sensing;Radiation;Radiative Transfer;Infrared;Earth “In this book, the author provides a well-founded background and solution of the inverse problem.” Zentralblatt MATH
Measurement Theory for Engineers by Ilya Gertsbakh Pdf
Well written textbook on industrial applications of Statistical Measurement Theory. It deals with the principal issues of measurement theory, is concise and intelligibly written, and to a wide extent self-contained. Difficult theoretical issues are separated from the mainstream presentation. Each topic starts with an informal introduction followed by an example, the rigorous problem formulation, solution method, and a detailed numerical solution. Chapter are concluded with a set of exercises of increasing difficulty, mostly with solutions. Knowledge of calculus and fundamental probability and statistics is assumed.
This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.
Theory and Practice of Thermal Transient Testing of Electronic Components by Marta Rencz,Gábor Farkas,András Poppe Pdf
This book discusses the significant aspects of thermal transient testing, the most important method of thermal characterization of electronics available today. The book presents the theoretical background of creating structure functions from the measured results with mathematical details. It then shows how the method can be used for thermal qualification, structure integrity testing, determining material parameters, and calibrating simulation models. General practical questions about measurements are discussed to help beginners carry out thermal transient testing. The particular problems and tricks of measuring with various electronic components, such as Si diodes, bipolar transistors, MOS transistors, IGBT devices, resistors, capacitors, wide bandgap materials, and LEDs, are covered in detail with the help of various use cases. This hands-on book will enable readers to accomplish thermal transient testing on any new type of electronics and provides the theoretical details needed to understand the opportunities and limitations offered by the methodology. The book will be an invaluable reference for practicing engineers, students, and researchers.
Financial Crisis and the Failure of Economic Theory by Jorge Turmo Arnal Pdf
The global financial crisis of 2008 was largely unpredicted. If economic theory has a role to play in predicting future catastrophes then the methods we rely on need to change. The authors of this study propose a new theory of economics based on more detailed understanding of how and why people behave as they do within their environment. This anthropological approach uses the strengths of many existing economic theories, including Keynesian and Austrian economics, to present a new framework for anticipating and averting the financial crises of the future.