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Exceptional Lie Algebras (Lecture Notes in Pure and Applied Mathematics #1)
by N. JacobsonThis volume presents a set of models for the exceptional Lie algebras over algebraically closed fieldsof characteristic O and over the field of real numbers. The models given are based on the algebras ofCayley numbers (octonions) and on exceptional Jordan algebras. They are also valid forcharacteristics p * 2. The book also provides an introduction to the problem of forms of exceptionalsimple Lie algebras, especially the exceptional D4 's, � 6 's, and � 7 's. These are studied by means ofconcrete realizations of the automorphism groups.Exceptional Lie Algebras is a useful tool for the mathematical public in general-especially thoseinterested in the classification of Lie algebras or groups-and for theoretical physicists.
Exceptional Lie groups (Lecture Notes in Mathematics #2369)
by Ichiro YokotaThis book provides a concrete description of the identity connected components of the real and complex exceptional Lie groups. The constructions are elementary and improve on those of H. Freudenthal. The complex simple Lie algebras were classified into classical (An, Bn, Cn, Dn) and exceptional (G2, F4, E6, E7, E8) types at the end of the 19th century by W. Killing and É. Cartan. These simple Lie algebras and the corresponding compact simple Lie groups arise in many settings in mathematics and physics. The exceptional Lie groups form an especially interesting class of objects that have attracted the attention of numerous mathematicians. Requiring no prior knowledge of composition algebras or Jordan algebras, the book will be valuable to anyone who wants to learn about the structure and realizations of these fascinating groups.
Exceptional Lifespans (Demographic Research Monographs)
by James W. Vaupel Heiner Maier Bernard JeuneHow long can humans live? This open access book documents, verifies and brings to life the advance of the frontier of human survival. It carefully validates data on supercentenarians, aged 110+, and semi-supercentenarians, aged 105-109, stored in the International Database on Longevity (IDL). The chapters in this book contribute substantial advances in rigorously checked facts about exceptional lifespans and in the application of state-of-the-art analytical strategies to understand trends and patterns in these rare lifespans. The book includes detailed accounts of extreme long-livers and how their long lifespans were documented, as well as reports on the causes of death at the oldest ages. Its key finding, based on the analysis of 1,219 validated supercentenarians, is that the annual probability of death is constant at 50% after age 110. In contrast to previous assertions about a ceiling on the human lifespan, evidence presented in this book suggests that lifespan records in specific countries and globally will be broken again and again as more people survive to become supercentenarians.
Exchange-Rate Dynamics (Princeton Series in International Economics)
by Martin D. EvansA comprehensive and in-depth look at exchange-rate dynamicsVariations in the foreign exchange market influence all aspects of the world economy, and understanding these dynamics is one of the great challenges of international economics. This book provides a new, comprehensive, and in-depth examination of the standard theories and latest research in exchange-rate economics. Covering a vast swath of theoretical and empirical work, the book explores established theories of exchange-rate determination using macroeconomic fundamentals, and presents unique microbased approaches that combine the insights of microstructure models with the macroeconomic forces driving currency trading.Macroeconomic models have long assumed that agents—households, firms, financial institutions, and central banks—all have the same information about the structure of the economy and therefore hold the same expectations and uncertainties regarding foreign currency returns. Microbased models, however, look at how heterogeneous information influences the trading decisions of agents and becomes embedded in exchange rates. Replicating key features of actual currency markets, these microbased models generate a rich array of empirical predictions concerning trading patterns and exchange-rate dynamics that are strongly supported by data. The models also show how changing macroeconomic conditions exert an influence on short-term exchange-rate dynamics via their impact on currency trading.Designed for graduate courses in international macroeconomics, international finance, and finance, and as a go-to reference for researchers in international economics, Exchange-Rate Dynamics guides readers through a range of literature on exchange-rate determination, offering fresh insights for further reading and research.Comprehensive and in-depth examination of the latest research in exchange-rate economicsOutlines theoretical and empirical research across the spectrum of modeling approachesPresents new results on the importance of currency trading in exchange-rate determinationProvides new perspectives on long-standing puzzles in exchange-rate economicsEnd-of-chapter questions cement key ideas
Excursions In Modern Mathematics
by Peter TannenbaumExcursions in Modern Mathematics introduces you to the power of math by exploring applications like social choice and management science, showing that math is more than a set of formulas. Ideal for an applied liberal arts math course, Tannenbaum's text is known for its clear, accessible writing style and its unique exercise sets that build in complexity from basic to more challenging. The Eighth Edition offers more real data and applications to connect with today's readesr, expanded coverage of applications like growth, and revised exercise sets.
Excursions in Harmonic Analysis, Volume 1
by Radu Balan Wojciech Czaja Travis D Andrews John J. Benedetto Kasso A. OkoudjouThe Norbert Wiener Center for Harmonic Analysis and Applications provides a state-of-the-art research venue for the broad emerging area of mathematical engineering in the context of harmonic analysis. This two-volume set consists of contributions from speakers at the February Fourier Talks (FFT) from 2006-2011. The FFT are organized by the Norbert Wiener Center in the Department of Mathematics at the University of Maryland, College Park. These volumes span a large spectrum of harmonic analysis and its applications. They are divided into the following parts: Volume I · Sampling Theory · Remote Sensing · Mathematics of Data Processing · Applications of Data Processing Volume II · Measure Theory · Filtering · Operator Theory · Biomathematics Each part provides state-of-the-art results, with contributions from an impressive array of mathematicians, engineers, and scientists in academia, industry, and government. Excursions in Harmonic Analysis: The February Fourier Talks at the Norbert Wiener Center is an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics.
Excursions in Harmonic Analysis, Volume 2
by Radu Balan Wojciech Czaja Travis D Andrews John J. Benedetto Kasso A. OkoudjouThe Norbert Wiener Center for Harmonic Analysis and Applications provides a state-of-the-art research venue for the broad emerging area of mathematical engineering in the context of harmonic analysis.<P><P> This two-volume set consists of contributions from speakers at the February Fourier Talks (FFT) from 2006-2011. The FFT are organized by the Norbert Wiener Center in the Department of Mathematics at the University of Maryland, College Park. These volumes span a large spectrum of harmonic analysis and its applications. They are divided into the following parts:<P> Volume I<P> · Sampling Theory<P> · Remote Sensing<P> · Mathematics of Data Processing<P> · Applications of Data Processing<P> Volume II<P> · Measure Theory<P> · Filtering<P> · Operator Theory<P> · Biomathematics<P> Each part provides state-of-the-art results, with contributions from an impressive array of mathematicians, engineers, and scientists in academia, industry, and government.<P> Excursions in Harmonic Analysis: The February Fourier Talks at the Norbert Wiener Center is an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics.
Excursions in Harmonic Analysis, Volume 3
by Radu Balan Wojciech Czaja John J. Benedetto Kasso A. Okoudjou Matthew J. BeguéThis volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 - 2013. Containing cutting-edge results by an impressive array of mathematicians, engineers, and scientists in academia, industry, and government, it will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, physics, and engineering. Topics covered include #65533; spectral analysis and correlation; #65533; radar and communications: design, theory, and applications; #65533; sparsity #65533; special topics in harmonic analysis. The February Fourier Talks are held annually at the Norbert Wiener Center for Harmonic Analysis and Applications. Located at the University of Maryland, College Park, the Norbert Wiener Center provides a state-of- the-art research venue for the broad emerging area of mathematical engineering.
Excursions in Harmonic Analysis, Volume 4
by Radu Balan Wojciech Czaja John J. Benedetto Kasso A. Okoudjou Matthew BeguéThis volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 - 2013. Containing cutting-edge results by an impressive array of mathematicians, engineers and scientists in academia, industry and government, it will be an excellent reference for graduate students, researchers and professionals in pure and applied mathematics, physics and engineering. Topics covered include: Special Topics in Harmonic Analysis Applications and Algorithms in the Physical Sciences Gabor Theory RADAR and Communications: Design, Theory, and Applications The February Fourier Talks are held annually at the Norbert Wiener Center for Harmonic Analysis and Applications. Located at the University of Maryland, College Park, the Norbert Wiener Center provides a state-of- the-art research venue for the broad emerging area of mathematical engineering.
Excursions in Harmonic Analysis, Volume 5
by Radu Balan Wojciech Czaja John J. Benedetto Kasso A. Okoudjou Matthew DellatorreThis volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 - 2016. Containing cutting-edge results by an impressive array of mathematicians, engineers, and scientists in academia, industry and government, it will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, physics, and engineering. Topics covered include: Theoretical harmonic analysis Image and signal processing Quantization Algorithms and representations The February Fourier Talks are held annually at the Norbert Wiener Center for Harmonic Analysis and Applications. Located at the University of Maryland, College Park, the Norbert Wiener Center provides a state-of- the-art research venue for the broad emerging area of mathematical engineering.
Excursions in Harmonic Analysis, Volume 6: In Honor of John Benedetto’s 80th Birthday (Applied and Numerical Harmonic Analysis)
by Kasso A. Okoudjou Matthew Hirn Shidong Li Sandra Saliani Özgür YilmazJohn J. Benedetto has had a profound influence not only on the direction of harmonic analysis and its applications, but also on the entire community of people involved in the field. The chapters in this volume – compiled on the occasion of his 80th birthday – are written by leading researchers in the field and pay tribute to John’s many significant and lasting achievements. Covering a wide range of topics in harmonic analysis and related areas, these chapters are organized into four main parts: harmonic analysis, wavelets and frames, sampling and signal processing, and compressed sensing and optimization. An introductory chapter also provides a brief overview of John’s life and mathematical career. This volume will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics.
Excursions in Ill-Condensed Quantum Matter: From Amorphous Topological Insulators to Fractional Spins (Springer Theses)
by Adhip AgarwalaImpurities, disorder or amorphous systems – ill-condensed matter – are mostly considered inconveniences in the study of materials, which is otherwise heavily based on idealized perfect crystals. The Kondo effect and the scaling theory of localization are among the fundamental and early discoveries which revealed the novelty hidden in impure or disordered systems. Recent advances in condensed matter physics have emphasized the role of topology, spin-orbit coupling, and certain discrete symmetries such as time reversal in many physical phenomena. These have irreversibly transformed the essential ideas and purview of condensed matter physics, both in theoretical and experimental directions. However, many of these recent developments and their implications are limited to, or by, ideas that pertain to clean systems. This thesis deals with various aspects of these new developments, but in the case of unclean systems. The author introduces new ideas such as amorphous topological insulators, fractalized metals and fractionalized spins.
Excursions into Mathematics: The Millennium Edition
by Anatole Beck Michael N. Bleicher Donald W. CroweSince it was first published three decades ago, Excursions Into Mathematics has been one of the most popular mathematical books written for a general audience. Taking the reader for short "excursions" into several specific disciplines of mathematics, it makes mathematical concepts accessible to a wide audience. The Millennium Edition is updated with current research and new solutions to outstanding problems that have been discovered since the last edition was printed, such as the solution to the well-known "four-color problem." Excursions Into Mathematics: The Millennium Edition is an exciting revision of the original, much-loved classic. Everyone with an interest in mathematics should read this book.
Executive Power and Soviet Politics (Contemporary Soviet - Post-soviet Politics Ser.)
by Eugene HuskeyEver since the behavioral revolution reached Communist studies more than 2 decades ago, Western scholarship has tended to ignore the powerful and unwieldy institutional structure of the Soviet government. Today, suddenly, it is clear that the dramatic political and legislative reforms of the Gorbachev years will remain incomplete as long as the issues of state bureaucratic power and executive prerogative are unresolved. This volume, brings together original studies of the Soviet executive under Gorbachev by specialists including Barbara Chotiner, Stephen Fortescue, Brnda Horrigan, Ellen Jones, Wayne Limberg, T.H. Rigby and Louise Shelley. Among the topics covered are the major economic, national security and law enforcement ministries, the presidency, the cabinet and questions of presidential-ministerial, presidential-presidential, legislative-executive and party-state relations.
Exemplary Practices for Secondary Math Teachers
by Alfred S. Posamentier Stephen Krulik Daniel JayeEvery year new secondary mathematics teachers take up positions in middle and high schools. The luckiest novices receive assistance from a coach or mentor: a master mathematics teacher who makes constructive comments, models effective approaches, and illuminates other practical aspects of teaching secondary math. But many new teachers don t have this advantage and must further their development on their own. If you are one of these teachers, this is the book you need. <p><p> In these pages, veteran mathematics educators Alfred S. Posamentier, Daniel Jaye, and Stephen Krulik present a treasure chest of ideas to guide new secondary math teachers through the challenging first few months and also provide more experienced teachers with interesting alternatives to familiar methods.
Exercise Book of Statistical Inference (UNITEXT #173)
by Anna Maria Paganoni Francesca Ieva Francesca GasperoniThis book was created with the goal of helping students transition from the theoretical and methodological concepts of statistical inference to their implementation on a computer. The first part of the book is primarily focused on exercises to be solved with pen and paper, so that students can apply knowledge derived from lemmas and theorems; while the second part consists of labs, which involve both the manual implementation of algorithms and the learning of built-in tools for efficient analysis of datasets derived from real-world problems. To optimize the understanding of the topics developed and to guide the reader through their studies, the book is organized into chapters, each of which includes an introductory section that reviews the theoretical foundations of statistical inference, followed by a second part with exercises, each accompanied by a comprehensive solution on paper and, when appropriate, using software. This book is aimed at undergraduate students in Statistics, Mathematics, Engineering, and for graduate-level courses in Data Science.
Exercises and Problems in Mathematical Methods of Physics (Undergraduate Lecture Notes in Physics)
by Giampaolo CicognaThis book is the second edition, whose original mission was to offer a new approach for students wishing to better understand the mathematical tenets that underlie the study of physics. This mission is retained in this book.The structure of the book is one that keeps pedagogical principles in mind at every level. Not only are the chapters sequenced in such a way as to guide the reader down a clear path that stretches throughout the book, but all individual sections and subsections are also laid out so that the material they address becomes progressively more complex along with the reader's ability to comprehend it. This book not only improves upon the first in many details, but it also fills in some gaps that were left open by this and other books on similar topics. The 350 problems presented here are accompanied by answers which now include a greater amount of detail and additional guidance for arriving at the solutions. In this way, the mathematical underpinnings of the relevant physics topics are made as easy to absorb as possible.
Exercises and Solutions in Biostatistical Theory (Chapman & Hall/CRC Texts in Statistical Science)
by Lawrence Kupper Brian Neelon Sean M. O'BrienDrawn from nearly four decades of Lawrence L. Kupper's teaching experiences as a distinguished professor in the Department of Biostatistics at the University of North Carolina, Exercises and Solutions in Biostatistical Theory presents theoretical statistical concepts, numerous exercises, and detailed solutions that span topics from basic probabilit
Exercises and Solutions in Statistical Theory (Chapman & Hall/CRC Texts in Statistical Science)
by Lawrence L. Kupper Sean M. O'Brien Brian. H NeelonExercises and Solutions in Statistical Theory helps students and scientists obtain an in-depth understanding of statistical theory by working on and reviewing solutions to interesting and challenging exercises of practical importance. Unlike similar books, this text incorporates many exercises that apply to real-world settings and provides much mor
Exercises in Algebra (Algebra, Logic and Applications)
by Alexandra I. KostrikinThis book is a collection of exercises for courses in higher algebra, linear algebra and geometry. It is helpful for postgraduate students in checking the solutions and answers to the exercises.
Exercises in Algebra: A Collection of Exercises, in Algebra, Linear Algebra and Geometry
by AlexandraI. KostrikinThis text contains more than 2000 exercises in algebra. These exercises are currently used in teaching a fundamental course in algebra in the Department of Mechanics and Mathematics at Moscow State University. The text is divided into three parts, which correspond to three semesters of study. Each section contains not only standard exercises, but also more difficult exercises at the end of some sections, these more challenging exercises being marked with asterisks. At the end of the book, results of calculations, a list of notations and basic definitions are given.
Exercises in Analysis
by Leszek Gasińksi Nikolaos S. PapageorgiouExercises in Analysis will be published in two volumes. This first volume covers problems in five core topics of mathematical analysis: metric spaces; topological spaces; measure, integration and Martingales; measure and topology and functional analysis. Each of five topics correspond to a different chapter with inclusion of the basic theory and accompanying main definitions and results, followed by suitable comments and remarks for better understanding of the material. At least 170 exercises/problems are presented for each topic, with solutions available at the end of each chapter. The entire collection of exercises offers a balanced and useful picture for the application surrounding each topic. This nearly encyclopedic coverage of exercises in mathematical analysis is the first of its kind and is accessible to a wide readership. Graduate students will find the collection of problems valuable in preparation for their preliminary or qualifying exams as well as for testing their deeper understanding of the material. Exercises are denoted by degree of difficulty. Instructors teaching courses that include one or all of the above-mentioned topics will find the exercises of great help in course preparation. Researchers in analysis may find this Work useful as a summary of analytic theories published in one accessible volume.
Exercises in Applied Mathematics: With a View toward Information Theory, Machine Learning, Wavelets, and Statistical Physics (Chapman Mathematical Notes)
by Daniel AlpayThis text presents a collection of mathematical exercises with the aim of guiding readers to study topics in statistical physics, equilibrium thermodynamics, information theory, and their various connections. It explores essential tools from linear algebra, elementary functional analysis, and probability theory in detail and demonstrates their applications in topics such as entropy, machine learning, error-correcting codes, and quantum channels. The theory of communication and signal theory are also in the background, and many exercises have been chosen from the theory of wavelets and machine learning. Exercises are selected from a number of different domains, both theoretical and more applied. Notes and other remarks provide motivation for the exercises, and hints and full solutions are given for many. For senior undergraduate and beginning graduate students majoring in mathematics, physics, or engineering, this text will serve as a valuable guide as theymove on to more advanced work.
Exercises in Cellular Automata and Groups (Springer Monographs in Mathematics)
by Tullio Ceccherini-Silberstein Michel CoornaertThis book complements the authors’ monograph Cellular Automata and Groups [CAG] (Springer Monographs in Mathematics). It consists of more than 600 fully solved exercises in symbolic dynamics and geometric group theory with connections to geometry and topology, ring and module theory, automata theory and theoretical computer science. Each solution is detailed and entirely self-contained, in the sense that it only requires a standard undergraduate-level background in abstract algebra and general topology, together with results established in [CAG] and in previous exercises. It includes a wealth of gradually worked out examples and counterexamples presented here for the first time in textbook form. Additional comments provide some historical and bibliographical information, including an account of related recent developments and suggestions for further reading. The eight-chapter division from [CAG] is maintained. Each chapter begins with a summary of the main definitions and results contained in the corresponding chapter of [CAG]. The book is suitable either for classroom or individual use.Foreword by Rostislav I. Grigorchuk
Exercises in Computational Mathematics with MATLAB
by Tom Lyche Jean-Louis MerrienDesigned to provide tools for independent study, this book contains student-tested mathematical exercises joined with MATLAB programming exercises. Most chapters open with a review followed by theoretical and programming exercises, with detailed solutions provided for all problems including programs. Many of the MATLAB exercises are presented as Russian dolls: each question improves and completes the previous program and results are provided to validate the intermediate programs. The book offers useful MATLAB commands, advice on tables, vectors, matrices and basic commands for plotting. It contains material on eigenvalues and eigenvectors and important norms of vectors and matrices including perturbation theory; iterative methods for solving nonlinear and linear equations; polynomial and piecewise polynomial interpolation; Bézier curves; approximations of functions and integrals and more. The last two chapters considers ordinary differential equations including two point boundary value problems, and deal with finite difference methods for some partial differential equations. The format is designed to assist students working alone, with concise Review paragraphs, Math Hint footnotes on the mathematical aspects of a problem and MATLAB Hint footnotes with tips on programming.