Basic Analysis IV: Measure Theory and Integration introduces students to concepts from measure theory and continues their training in the abstract way of looking at the world. This is a most important skill to have when your life's work will involve quantitative modeling to gain insight into the real world. This text generalizes the notion of integration to a very abstract setting in a variety of ways. We generalize the notion of the length of an interval to the measure of a set and learn how to construct the usual ideas from integration using measures. We discuss carefully the many notions of convergence that measure theory provides. Features • Can be used as a traditional textbook as well as for self-study • Suitable for advanced students in mathematics and associated disciplines • Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions
This concise, yet thorough, book is enhanced with simulations and graphs to build the intuition of readers Models for Probability and Statistical Inference was written over a five-year period and serves as a comprehensive treatment of the fundamentals of probability and statistical inference. With detailed theoretical coverage found throughout the book, readers acquire the fundamentals needed to advance to more specialized topics, such as sampling, linear models, design of experiments, statistical computing, survival analysis, and bootstrapping. Ideal as a textbook for a two-semester sequence on probability and statistical inference, early chapters provide coverage on probability and include discussions of: discrete models and random variables; discrete distributions including binomial, hypergeometric, geometric, and Poisson; continuous, normal, gamma, and conditional distributions; and limit theory. Since limit theory is usually the most difficult topic for readers to master, the author thoroughly discusses modes of convergence of sequences of random variables, with special attention to convergence in distribution. The second half of the book addresses statistical inference, beginning with a discussion on point estimation and followed by coverage of consistency and confidence intervals. Further areas of exploration include: distributions defined in terms of the multivariate normal, chi-square, t, and F (central and non-central); the one- and two-sample Wilcoxon test, together with methods of estimation based on both; linear models with a linear space-projection approach; and logistic regression. Each section contains a set of problems ranging in difficulty from simple to more complex, and selected answers as well as proofs to almost all statements are provided. An abundant amount of figures in addition to helpful simulations and graphs produced by the statistical package S-Plus(r) are included to help build the intuition of readers.
Ten years have passed since It Hooft and Polyakov demonstrat ed that superheavy magnetic monopoles were a natural consequence of any Grand Unified Theory (GUT) in which the unifying group contains a U(l) factor as a subgroup. An analysis of these GUTs in an expanding, cooling universe yields a phase transition at an energy ~l015 GeV and at a cosmic time ~lO-35 seconds after the big bang. The general consequences of GUTs and this phase transition are the prediction of proton decay, the production of superheavy magnetic monopoles, and an understanding of the observed excess of matter over anti-matter in the universe. Attempts to provide experimental verification of GUTs has led to valiant experimental efforts in recent years to observe nucleon decay in massive underground detectors. Experiments to search for superheavy monopoles may eventually require similar efforts. Since the unification scale is unreachable in the laboratory, monopole detectors must search for relics of the big bang. Much theoretical groundwork has been accomplished in recent years with the development of GUTs. In Part I of this book, Erick Weinberg gives a theoretical overview of the role of magnetic monopoles in the various unification schemes. Monopoles in the context of the newly revived Kaluza-Klein theories are presented by several authors and are summarized by Qaisar Shafi. Mike Turner begins Part II with a discussion of monopoles in standard big bang cosmology. Paul Steinhardt follows with his perspectives on the inflationary universe; C.
This book treats the theory of global attractors, a recent development in the theory of partial differential equations, in a way that also includes much of the traditional elements of the subject. As such it gives a quick but directed introduction to some fundamental concepts, and by the end proceeds to current research problems. Since the subject is relatively new, this is the first book to attempt to treat these various topics in a unified and didactic way. It is intended to be suitable for first year graduate students.
In this second edition of Interferometry and Synthesis in Radio Astronomy, three leading figures in the development of large imaging arrays, including very-long-baseline interferometry (VLBI), describe and explain the technology that provides images of the universe with an angular resolution as fine as 1/20,000 of an arcsecond. This comprehensive volume begins with a historical review followed by detailed coverage of the theory of interferometry and synthesis imaging, analysis of interferometer response, geometrical relationships, polarimetry, antennas, and arrays. Discussion of the receiving system continues with analysis of the response to signals and noise, analog design requirements, and digital signal processing. The authors detail special requirements of VLBI including atomic frequency standards, broadband recording systems, and antennas in orbit. Further major topics include: Calibration of data and synthesis of images Image enhancement using nonlinear algorithms Techniques for astrometry and geodesy Propagation in the neutral atmosphere and ionized media Radio interference Related techniques: intensity interferometry, moon occultations, antenna holography, and optical interferometry ”This edition meets current demands by providing a comprehensive account of the techniques used today.“ (La Doc STI) [...] The up-to-date edition of Thompson [...] with its exhaustive bibliography, becomes the indispensable source of background for those already in, or considering, radio astronomy.“ (The Observatory)
The Ricci flow uses methods from analysis to study the geometry and topology of manifolds. With the third part of their volume on techniques and applications of the theory, the authors give a presentation of Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject, with an emphasis on the geometric and analytic aspects. The topics include Perelman's entropy functional, point picking methods, aspects of Perelman's theory of $\kappa$-solutions including the $\kappa$-gap theorem, compactness theorem and derivative estimates, Perelman's pseudolocality theorem, and aspects of the heat equation with respect to static and evolving metrics related to Ricci flow. In the appendices, we review metric and Riemannian geometry including the space of points at infinity and Sharafutdinov retraction for complete noncompact manifolds with nonnegative sectional curvature. As in the previous volumes, the authors have endeavored, as much as possible, to make the chapters independent of each other. The book makes advanced material accessible to graduate students and nonexperts. It includes a rigorous introduction to some of Perelman's work and explains some technical aspects of Ricci flow useful for singularity analysis. The authors give the appropriate references so that the reader may further pursue the statements and proofs of the various results.
Sechs erfahrene Autoren beschreiben in diesem Band ein Spezialgebiet der neuronalen Netze mit Anwendungen in der Signalsteuerung, Signalverarbeitung und Zeitreihenanalyse. Ein zeitgemäßer Beitrag zur Behandlung nichtlinear-dynamischer Systeme!
An introduction to key concepts and techniques in probabilistic machine learning for civil engineering students and professionals; with many step-by-step examples, illustrations, and exercises. This book introduces probabilistic machine learning concepts to civil engineering students and professionals, presenting key approaches and techniques in a way that is accessible to readers without a specialized background in statistics or computer science. It presents different methods clearly and directly, through step-by-step examples, illustrations, and exercises. Having mastered the material, readers will be able to understand the more advanced machine learning literature from which this book draws. The book presents key approaches in the three subfields of probabilistic machine learning: supervised learning, unsupervised learning, and reinforcement learning. It first covers the background knowledge required to understand machine learning, including linear algebra and probability theory. It goes on to present Bayesian estimation, which is behind the formulation of both supervised and unsupervised learning methods, and Markov chain Monte Carlo methods, which enable Bayesian estimation in certain complex cases. The book then covers approaches associated with supervised learning, including regression methods and classification methods, and notions associated with unsupervised learning, including clustering, dimensionality reduction, Bayesian networks, state-space models, and model calibration. Finally, the book introduces fundamental concepts of rational decisions in uncertain contexts and rational decision-making in uncertain and sequential contexts. Building on this, the book describes the basics of reinforcement learning, whereby a virtual agent learns how to make optimal decisions through trial and error while interacting with its environment.
This book provides a self-study program on how mathematics, computer science and science can be usefully and seamlessly intertwined. Learning to use ideas from mathematics and computation is essential for understanding approaches to cognitive and biological science. As such the book covers calculus on one variable and two variables and works through a number of interesting first-order ODE models. It clearly uses MatLab in computational exercises where the models cannot be solved by hand, and also helps readers to understand that approximations cause errors – a fact that must always be kept in mind.
Perturbation theory and in particular normal form theory has shown strong growth in recent decades. This book is a drastic revision of the first edition of the averaging book. The updated chapters represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are survey appendices on invariant manifolds. One of the most striking features of the book is the collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with illuminating diagrams.
To the eyes of the average person and the trained scientist, the night sky is dark, even though the universe is populated by myriads of bright galaxies. Why this happens is a question commonly called Olbers' Paradox, and dates from at least 1823. How dark is the night sky is a question which preoccupies astrophysicists at the present. The answer to both questions tells us about the origin of the universe and the nature of its contents ? luminous galaxies like the Milky Way, plus the dark matter between them and the mysterious dark energy which appears to be pushing everything apart. In this book, the fascinating history of Olbers' Paradox is reviewed, and the intricate physics of the light/dark universe is examined in detail. The fact that the night sky is dark (a basic astronomical observation that anybody can make) turns out to be connected with the finite age of the universe, thereby confirming some event like the Big Bang. But the space between the galaxies is not perfectly black, and data on its murkiness at various wavelengths can be used to constrain and identify its unseen constituents.
To the eyes of the average person and the trained scientist, the night sky is dark, even though the universe is populated by myriads of bright galaxies. Why this happens is a question commonly called Olbers' Paradox, and dates from at least 1823. How dark is the night sky is a question which preoccupies astrophysicists at the present. The answer to both questions tells us about the origin of the universe and the nature of its contents — luminous galaxies like the Milky Way, plus the dark matter between them and the mysterious dark energy which appears to be pushing everything apart. In this book, the fascinating history of Olbers' Paradox is reviewed, and the intricate physics of the light/dark universe is examined in detail. The fact that the night sky is dark (a basic astronomical observation that anybody can make) turns out to be connected with the finite age of the universe, thereby confirming some event like the Big Bang. But the space between the galaxies is not perfectly black, and data on its murkiness at various wavelengths can be used to constrain and identify its unseen constituents.
When Mary R. Haas died in 1996, she left behind several thousand pages of notes and texts in the Creek (Muskogee) language collected in Oklahoma from 1936 to 1940. The majority of the texts come from the unpublished writings of James H. Hill of Eufaula, an especially knowledgeable elder who composed texts for Dr. Haas using the standard Creek alphabet. Twelve other speakers served as sources for dictated texts.
This second edition continues to emphasise learning by doing and the development of students' ability to use mathematics with understanding to solve engineering problems. Extensive treatment of some advanced engineering topics, particularly as tools for computer-based system modelling, analysis and design. *Follow on text from Modern Engineering Mathematics, 2E - over 20,000 copies sold *Changing student needs catered for by some easier examples and exercises plus new introductory sections on matrix algebra and vector spaces *New chapter on Numerical Solution of Ordinary Differential Equations *Engineering applications covered in specific sections in each chapter *The increasing importance of digital techniques and statistics is recognised throughout
An authoritative guide to the most up-to-date information on power system dynamics The revised third edition of Power System Dynamics and Stability contains a comprehensive, state-of-the-art review of information on the topic. The third edition continues the successful approach of the first and second editions by progressing from simplicity to complexity. It places the emphasis first on understanding the underlying physical principles before proceeding to more complex models and algorithms. The book is illustrated by a large number of diagrams and examples. The third edition of Power System Dynamics and Stability explores the influence of wind farms and virtual power plants, power plants inertia and control strategy on power system stability. The authors—noted experts on the topic—cover a range of new and expanded topics including: Wide-area monitoring and control systems. Improvement of power system stability by optimization of control systems parameters. Impact of renewable energy sources on power system dynamics. The role of power system stability in planning of power system operation and transmission network expansion. Real regulators of synchronous generators and field tests. Selectivity of power system protections at power swings in power system. Criteria for switching operations in transmission networks. Influence of automatic control of a tap changing step-up transformer on the power capability area of the generating unit. Mathematical models of power system components such as HVDC links, wind and photovoltaic power plants. Data of sample (benchmark) test systems. Power System Dynamics: Stability and Control, Third Edition is an essential resource for students of electrical engineering and for practicing engineers and researchers who need the most current information available on the topic.
COACH THE 3-5-3 DEFENSE This bountiful volume of resources is for any novice or veteran coach looking to implement the 3-5-3 defense. This aggressive, attacking and disciplined defense is the defense to use, especially for youth football. This comprehensive book contains: ? 9 elements of the VICTORY system for developing the foundation for success ? 7 reasons to use the 3-5-3 defense for youth football ? 9 keys to a successful 3-5-3 defense ? Basic alignments for the 3-5-3 defense with adjustments for youth and middle school ? Specific responsibilities in the 3-5-3 defense ? Basic fundamentals for each position in the 3-5-3 defense ? 38 skills and drills for a successful 3-5-3 defense ? 30 basic 3-5-3 defensive plays ? 3 essentials to make it fun for players ? Game day plays and adjustments using the 3-5-3 defense ? 7 necessary basics for a simple football program ? And much more!
Focusing on fundamental principles, Hydro-Environmental Analysis: Freshwater Environments presents in-depth information about freshwater environments and how they are influenced by regulation. It provides a holistic approach, exploring the factors that impact water quality and quantity, and the regulations, policy and management methods that are necessary to maintain this vital resource. It offers a historical viewpoint as well as an overview and foundation of the physical, chemical, and biological characteristics affecting the management of freshwater environments. The book concentrates on broad and general concepts, providing an interdisciplinary foundation. The author covers the methods of measurement and classification; chemical, physical, and biological characteristics; indicators of ecological health; and management and restoration. He also considers common indicators of environmental health; characteristics and operations of regulatory control structures; applicable laws and regulations; and restoration methods. The text delves into rivers and streams in the first half and lakes and reservoirs in the second half. Each section centers on the characteristics of those systems and methods of classification, and then moves on to discuss the physical, chemical, and biological characteristics of each. In the section on lakes and reservoirs, it examines the characteristics and operations of regulatory structures, and presents the methods commonly used to assess the environmental health or integrity of these water bodies. It also introduces considerations for restoration, and presents two unique aquatic environments: wetlands and reservoir tailwaters. Written from an engineering perspective, the book is an ideal introduction to the aquatic and limnological sciences for students of environmental science, as well as students of environmental engineering. It also serves as a reference for engineers and scientists involved in the management, regulation, or restoration of freshwater environments.
How one of the greatest miscarriages of justice in the United States continues to haunt the nation’s racial psyche In 1931, nine black youths were charged with raping two white women in Scottsboro, Alabama. Despite meager and contradictory evidence, all nine were found guilty and eight of the defendants were sentenced to death—making Scottsboro one of the worst travesties of justice to take place in the post-Reconstruction South. Remembering Scottsboro explores how this case has embedded itself into the fabric of American memory and become a lens for perceptions of race, class, sexual politics, and justice. James Miller draws upon the archives of the Communist International and NAACP, contemporary journalistic accounts, as well as poetry, drama, fiction, and film, to document the impact of Scottsboro on American culture. The book reveals how the Communist Party, NAACP, and media shaped early images of Scottsboro; looks at how the case influenced authors including Langston Hughes, Richard Wright, and Harper Lee; shows how politicians and Hollywood filmmakers invoked the case in the ensuing decades; and examines the defiant, sensitive, and savvy correspondence of Haywood Patterson—one of the accused, who fled the Alabama justice system. Miller considers how Scottsboro persists as a point of reference in contemporary American life and suggests that the Civil Rights movement begins much earlier than the Montgomery Bus Boycott of 1955. Remembering Scottsboro demonstrates how one compelling, provocative, and tragic case still haunts the American racial imagination.
Dorf’s Introduction to Electric Circuits, Global Edition, is designed for a one- to -three term course in electric circuits or linear circuit analysis. The book endeavors to help students who are being exposed to electric circuits for the first time and prepares them to solve realistic problems involving these circuits. Abundant design examples, design problems, and the How Can We Check feature illustrate the text’s focus on design. The Global Edition continues the expanded use of problem-solving software such as PSpice and MATLAB.
Fundamental Biomechanics of Sport and Exercise is an engaging and comprehensive introductory textbook that explains biomechanical concepts from first principles, showing clearly how the science relates to real sport and exercise situations. The book is divided into two parts. The first provides a clear and detailed introduction to the structure and function of the human musculoskeletal system and its structural adaptations, essential for a thorough understanding of human movement. The second part focuses on the biomechanics of movement, describing the forces that act on the human body and the effects of those forces on the movement of the body. Every chapter includes numerous applied examples from sport and exercise, helping the student to understand how mechanical concepts describe both simple and complex movements, from running and jumping to pole-vaulting or kicking a football. In addition, innovative worksheets for field and laboratory work are included that contain clear objectives, a description of method, data recording sheets, plus a set of exemplary data and worked analysis. Alongside these useful features are definitions of key terms plus review questions to aid student learning, with detailed solutions provided for all numerical questions. No other textbook offers such a clear, easy-to-understand introduction to the fundamentals of biomechanics. This is an essential textbook for any biomechanics course taken as part of degree programme in sport and exercise science, kinesiology, physical therapy, sports coaching or athletic training.
Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in heal
In many respects, biology is the new frontier for applied mathematicians. This book demonstrates the important role mathematics plays in the study of some biological problems. It introduces mathematicians to the biological sciences and provides enough mathematics for bioscientists to appreciate the utility of the modelling approach. The book presents a number of diverse topics, such as neurophysiology, cell biology, immunology, and human genetics. It examines how research is done, what mathematics is used, what the outstanding questions are, and how to enter the field. Also given is a brief historical survey of each topic, putting current research into perspective. The book is suitable for mathematicians and biologists interested in mathematical methods in biology.
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