The works from Daniel Bernoulli's youth contained in this first volume of his Collected Works bear witness above all of his versatility; they deal with subjects as different as physiology, formal logic, mathematical analysis, hydrodynamics and positional astronomy. Daniel Bernoulli's contacts with Italian scientists gave rise to several controversies. The present volume documents both sides in each of these debates, which culminated with the publication of Bernoulli's first book Exercitationes mathe- maticae in 1724. The discussions with the renowned mathematician Jacopo Riccati on second-order differential equations and on the Newtonian theory of the out-flow of fluids from vessels deserve particular interest. A third group of texts goes back to the time Bernoulli spent at the newly- founded Academy of Sciences in St. Petersburg, where he had been appointed in 1725. There he worked out two more contributions to physiological research - on muscle movement and on the blind spot in the human eye - as well as his only paper in positional astronomy. This last work - suggested by a prize question of the Paris Académie des Sciences - became the occasion for a vehement conflict; the present volume documents these "Zänkereien" (squabbles) and also reproduces three competing treatises. To complete the documentation of Daniel Bernoulli's work on physiology, the volume also includes his academic ceremonial speech De Vita of 1737, where he sketches for the first time the circulation of the work done by the human heart, and its elaboration by Bernoulli's student Daniel Passavant.
Ellsberg elaborates on "Risk, Ambiguity, and the Savage Axioms" and mounts a powerful challenge to the dominant theory of rational decision in this book.
This work examines in depth the methodological relationships that probability and statistics have maintained with the social sciences from their emergence. It covers both the history of thought and current methods. First it examines in detail the history of the different paradigms and axioms for probability, from their emergence in the seventeenth century up to the most recent developments of the three major concepts: objective, subjective and logicist probability. It shows the statistical inference they permit, different applications to social sciences and the main problems they encounter. On the other side, from social sciences—particularly population sciences—to probability, it shows the different uses they made of probabilistic concepts during their history, from the seventeenth century, according to their paradigms: cross-sectional, longitudinal, hierarchical, contextual and multilevel approaches. While the ties may have seemed loose at times, they have more often been very close: some advances in probability were driven by the search for answers to questions raised by the social sciences; conversely, the latter have made progress thanks to advances in probability. This dual approach sheds new light on the historical development of the social sciences and probability, and on the enduring relevance of their links. It permits also to solve a number of methodological problems encountered all along their history.
For several decades, the orthodox economics approach to understanding choice under risk has been to assume that each individual person maximizes some sort of personal utility function defined over purchasing power. This new volume contests that even the best wisdom from the orthodox theory has not yet been able to do better than supposedly naïve models that use rules of thumb, or that focus on the consumption possibilities and economic constraints facing the individual. The authors assert this by first revisiting the origins of orthodox theory. They then recount decades of failed attempts to obtain meaningful empirical validation or calibration of the theory. Estimated shapes and parameters of the "curves" have varied erratically from domain to domain (e.g., individual choice versus aggregate behavior), from context to context, from one elicitation mechanism to another, and even from the same individual at different time periods, sometimes just minutes apart. This book proposes the return to a simpler sort of scientific theory of risky choice, one that focuses not upon unobservable curves but rather upon the potentially observable opportunities and constraints facing decision makers. It argues that such an opportunities-based model offers superior possibilities for scientific advancement. At the very least, linear utility – in the presence of constraints - is a useful bar for the "curved" alternatives to clear.
A comprehensive resource providing extensive coverage of the state of the art in credit secruritisations, derivatives, and risk management Credit Securitisations and Derivatives is a one-stop resource presenting the very latest thinking and developments in the field of credit risk. Written by leading thinkers from academia, the industry, and the regulatory environment, the book tackles areas such as business cycles; correlation modelling and interactions between financial markets, institutions, and instruments in relation to securitisations and credit derivatives; credit portfolio risk; credit portfolio risk tranching; credit ratings for securitisations; counterparty credit risk and clearing of derivatives contracts and liquidity risk. As well as a thorough analysis of the existing models used in the industry, the book will also draw on real life cases to illustrate model performance under different parameters and the impact that using the wrong risk measures can have.
This is the third in a series of short books on probability theory and random processes for biomedical engineers. This book focuses on standard probability distributions commonly encountered in biomedical engineering. The exponential, Poisson and Gaussian distributions are introduced, as well as important approximations to the Bernoulli PMF and Gaussian CDF. Many important properties of jointly Gaussian random variables are presented. The primary subjects of the final chapter are methods for determining the probability distribution of a function of a random variable. We first evaluate the probability distribution of a function of one random variable using the CDF and then the PDF. Next, the probability distribution for a single random variable is determined from a function of two random variables using the CDF. Then, the joint probability distribution is found from a function of two random variables using the joint PDF and the CDF. The aim of all three books is as an introduction to probability theory. The audience includes students, engineers and researchers presenting applications of this theory to a wide variety of problems—as well as pursuing these topics at a more advanced level. The theory material is presented in a logical manner—developing special mathematical skills as needed. The mathematical background required of the reader is basic knowledge of differential calculus. Pertinent biomedical engineering examples are throughout the text. Drill problems, straightforward exercises designed to reinforce concepts and develop problem solution skills, follow most sections.
With many exciting enhancements and robust online resources, the seventh edition of Anatomy & Physiology for Speech, Language, and Hearing provides a solid foundation in anatomical and physiological principles relevant to the fields of speech-language pathology and audiology. This bestselling text is organized around the five “classic” systems of speech, language and hearing: the respiratory, phonatory, articulatory/resonatory, nervous, and auditory systems. Integrating clinical information with everyday experiences to reveal how anatomy and physiology relate to the speech, language, and hearing systems, the text introduces all the essential anatomy and physiology information in a carefully structured way, helping students to steadily build their knowledge and successfully apply it to clinical practice. Hundreds of dynamic, full-color illustrations and online lessons make the complex material approachable even for students with little or no background in anatomy and physiology. Key Features * 560+ figures and tables provide visual examples of the anatomy, processes, body systems, and data discussed. Photographs of human specimens provide a real-life look at the body parts and functions *Chapter pedagogy includes: *Learning objectives, call outs to related ANAQUEST lessons, bolded key terms, and chapter summaries *Clinical notes boxes relate topics directly to clinical experience to emphasize the importance of anatomy in clinical practice *Margin notes identify important terminology, root words, and definitions, that are highlighted in color throughout each chapter *“To summarize” sections provide a succinct listing of the major topics covered in a chapter or chapter section * Muscle tables describe the origin, course, insertion, innervation, and function of key muscles and muscle groups * Glossary with 2,000+ terms and definitions * Comprehensive bibliography in each chapter with 600+ references throughout the text * Multiple online appendices include an alphabetical listing of anatomical terms, useful combining forms, and listings of sensors and cranial nerves New to the Seventh Edition * Addition of clinical cases related to neurophysiology and hearing * Revised and updated physiology of swallowing includes discussion of postnatal development and aging effects of the swallowing mechanism and function * Brief discussion of the basics of genetics and trait transmission * Overview of prenatal development as it relates to the mechanisms of speech and hearing * Presentation of prenatal and postnatal development for each of the systems of speech and hearing, as well as the effects of aging on each system * Learning objectives have been added to the beginning of each chapter Please note that ancillary content (such as documents, audio, and video, etc.) may not be included as published in the original print version of this book.
Whether you're a student who just needs to know the vital concepts of physics, or you're looking for a basic reference tool, this is a must-have guide. Free of ramp-up and ancillary material, it contains content focused on key topics only, provides discrete explanations of critical concepts taught in an introductory physics course, and provides a perfect reference for parents who need to review critical physics concepts as they help high school students with homework assignments.--
The ability to analyze and interpret enormous amounts of data has become a prerequisite for success in allied healthcare and the health sciences. Now in its 11th edition, Biostatistics: A Foundation for Analysis in the Health Sciences continues to offer in-depth guidance toward biostatistical concepts, techniques, and practical applications in the modern healthcare setting. Comprehensive in scope yet detailed in coverage, this text helps students understand—and appropriately use—probability distributions, sampling distributions, estimation, hypothesis testing, variance analysis, regression, correlation analysis, and other statistical tools fundamental to the science and practice of medicine. Clearly-defined pedagogical tools help students stay up-to-date on new material, and an emphasis on statistical software allows faster, more accurate calculation while putting the focus on the underlying concepts rather than the math. Students develop highly relevant skills in inferential and differential statistical techniques, equipping them with the ability to organize, summarize, and interpret large bodies of data. Suitable for both graduate and advanced undergraduate coursework, this text retains the rigor required for use as a professional reference.
These notes develop a theory of restricted orbit equivalence which has as particular examples Ornstein's isomorphism theorem for Bernoulli processes, Dye's orbit equivalence theorem for ergodic processes and the theory of Kakutani equivalence developed by Feldman, Ornstein, Weiss and Katok. A number of results from the Bernoulli theory are shown to be true for any restricted orbit equivalence.
This book, suitable for numerate biologists and for applied statisticians, provides the foundations of likelihood, Bayesian and MCMC methods in the context of genetic analysis of quantitative traits. Although a number of excellent texts in these areas have become available in recent years, the basic ideas and tools are typically described in a technically demanding style and contain much more detail than necessary. Here, an effort has been made to relate biological to statistical parameters throughout, and the book includes extensive examples that illustrate the developing argument.
This monograph offers a broad investigative tool in ergodic theory and measurable dynamics. The motivation for this work is that one may measure how similar two dynamical systems are by asking how much the time structure of orbits of one system must be distorted for it to become the other. Different restrictions on the allowed distortion will lead to different restricted orbit equivalence theories. These include Ornstein's Isomorphism theory, Kakutani Equivalence theory and a list of others. By putting such restrictions in an axiomatic framework, a general approach is developed that encompasses all of these examples simultaneously and gives insight into how to seek further applications.
There have been many advances in the theory and applications of discrete distributions in recent years. They can be applied to a wide range of problems, particularly in the health sciences, although a good understanding of their properties is very important. Discrete Distributions: Applications in the Health Sciences describes a number of new discrete distributions that arise in the statistical examination of real examples. For each example, an understanding of the issues surrounding the data provides the motivation for the subsequent development of the statistical models. Provides an overview of discrete distributions and their applications in the health sciences. Focuses on real examples, giving readers an insight into the utility of the models. Describes the properties of each distribution, and the methods that led to their development. Presents a range of examples from the health sciences, including cancer, epidemiology, and demography. Features discussion of software implementation – in SAS, Fortran and R – enabling readers to apply the methods to their own problems. Written in an accessible style, suitable for applied statisticians and numerate health scientists. Software and data sets are made available on the Web. Discrete Distributions: Applications in the Health Sciences provides a practical introduction to these powerful statistical tools and their applications, suitable for researchers and graduate students from statistics and biostatistics. The focus on applications, and the accessible style of the book, make it an excellent practical reference source for practitioners from the health sciences.
This book explains the modelling and simulation of thermal power plants, and introduces readers to the equations needed to model a wide range of industrial energy processes. Also featuring a wealth of illustrative, real-world examples, it covers all types of power plants, including nuclear, fossil-fuel, solar and biomass. The book is based on the authors’ expertise and experience in the theory of power plant modelling and simulation, developed over many years of service with EDF. In more than forty examples, they demonstrate the component elements involved in a broad range of energy production systems, with detailed test cases for each chemical, thermodynamic and thermo-hydraulic model. Each of the test cases includes the following information: • component description and parameterization data; • modelling hypotheses and simulation results; • fundamental equations and correlations, with their validity domains; • model validation, and in some cases, experimental validation; and • single-phase flow and two-phase flow modelling equations, which cover all water and steam phases. A practical volume that is intended for a broad readership, from students and researchers, to professional engineers, this book offers the ideal handbook for the modelling and simulation of thermal power plants. It is also a valuable aid in understanding the physical and chemical phenomena that govern the operation of power plants and energy processes.
This is one of the first books that describe all the steps that are needed in order to analyze, design and implement Monte Carlo applications. It discusses the financial theory as well as the mathematical and numerical background that is needed to write flexible and efficient C++ code using state-of-the art design and system patterns, object-oriented and generic programming models in combination with standard libraries and tools. Includes a CD containing the source code for all examples. It is strongly advised that you experiment with the code by compiling it and extending it to suit your needs. Support is offered via a user forum on www.datasimfinancial.com where you can post queries and communicate with other purchasers of the book. This book is for those professionals who design and develop models in computational finance. This book assumes that you have a working knowledge of C ++.
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.
Already one of the leading course texts on aerodynamics in the UK, the sixth edition welcomes a new US-based author team to keep the text current. The sixth edition has been revised to include the latest developments in compressible flow, computational fluid dynamics, and contemporary applications. Computational methods have been expanded and updated to reflect the modern approaches to aerodynamic design and research in the aeronautical industry and elsewhere, and new examples of 'the aerodynamics around you' have been added to link theory to practical understanding. - Expanded coverage of compressible flow - MATLAB(r) exercises throughout, to give students practice is using industry-standard computational tools. m-files available for download from companion website - Contemporary applications and examples help students see the link between everyday physical examples of aerodynamics and the application of aerodynamic principles to aerodynamic design - Additional examples and end of chapter exercises provide more problem-solving practice for students - Improved teaching support with PowerPoint slides, solutions manual, m-files, and other resources to accompany the text
These notes give an exposition of a theory of Kakutani-equivalence that runs parallel to the theory of isomorphism between Bernoulli processes with the same entropy. A reinterpretation of the results yields a theory of isomorphisms between reparametrized flows, and of the relations between flows and their cross section maps. A brief survey is given of the more recent results in the theory.
*Major New York Times Bestseller *More than 2.6 million copies sold *One of The New York Times Book Review's ten best books of the year *Selected by The Wall Street Journal as one of the best nonfiction books of the year *Presidential Medal of Freedom Recipient *Daniel Kahneman's work with Amos Tversky is the subject of Michael Lewis's best-selling The Undoing Project: A Friendship That Changed Our Minds In his mega bestseller, Thinking, Fast and Slow, Daniel Kahneman, world-famous psychologist and winner of the Nobel Prize in Economics, takes us on a groundbreaking tour of the mind and explains the two systems that drive the way we think. System 1 is fast, intuitive, and emotional; System 2 is slower, more deliberative, and more logical. The impact of overconfidence on corporate strategies, the difficulties of predicting what will make us happy in the future, the profound effect of cognitive biases on everything from playing the stock market to planning our next vacation—each of these can be understood only by knowing how the two systems shape our judgments and decisions. Engaging the reader in a lively conversation about how we think, Kahneman reveals where we can and cannot trust our intuitions and how we can tap into the benefits of slow thinking. He offers practical and enlightening insights into how choices are made in both our business and our personal lives—and how we can use different techniques to guard against the mental glitches that often get us into trouble. Topping bestseller lists for almost ten years, Thinking, Fast and Slow is a contemporary classic, an essential book that has changed the lives of millions of readers.
Water Pollution Calculations: Quantifying Pollutant Formation, Transport, Transformation, Fate and Risks provides a comprehensive collection of relevant, real-world water pollution calculations. The book's author explains, in detail, how to measure and assess risks to human populations and ecosystems exposed to water pollutants. The text covers water pollution from a multivariate, systems approach, bringing in hydrogeological, climatological, meteorological processes, health and ecological impacts, and water and wastewater treatment and prevention.After first reviewing the physics, chemistry, and biology of water pollution, the author explores both groundwater and surface waters. This is followed by an in-depth look at water quality indicators, measurements, models, and water engineering. Groundwater remediation, risk assessment, and green engineering round out the text with forward-thinking ideas towards sustainability. This invaluable reference offers a practical tool for those needing a precise and applicable understanding of different types of water pollution calculations. - Includes applications of theory to real-world problems with personalized and customized examples of calculations to prepare exams, guidance documents, and correspondence - Walkthroughs and derivation of equations enhance knowledge so that complex water pollution concepts can be more easily grasped - Explains processes and mechanisms, providing an understanding of how pollutants are formed, transported, transformed, deposited, and stored in the environment
This book, which studies the links between mathematics and philosophy, highlights a reversal. Initially, the (Greek) philosophers were also mathematicians (geometers). Their vision of the world stemmed from their research in this field (rational and irrational numbers, problem of duplicating the cube, trisection of the angle...). Subsequently, mathematicians freed themselves from philosophy (with Analysis, differential Calculus, Algebra, Topology, etc.), but their researches continued to inspire philosophers (Descartes, Leibniz, Hegel, Husserl, etc.). However, from a certain level of complexity, the mathematicians themselves became philosophers (a movement that begins with Wronsky and Clifford, and continues until Grothendieck).
The world we live in presents plenty of tricky, impactful, and hard-tomake decisions to be taken. Sometimes the available options are ample, at other times they are apparently binary, either way, they often confront us with dilemmas, paradoxes, and even denial of values.In the dawn of the age of intelligence, when robots are gradually taking over most decision-making from humans, this book sheds a bit of light on decision rationale. It delves into the limits of these decision processes (for both humans and machines), and it does so by providing a new perspective that is somehow opposed to orthodox economics. All Economics reflections in this book are underlined and linked to Artificial Intelligence.The authors hope that this comprehensive and modern analysis, firmly grounded in the opinions of various groundbreaking Nobel laureate economists, may be helpful to a broad audience interested in how decisions may lead us all to flourishing societies. That is, societies in which economic blunders (caused by over simplification of problems and super estimation of tools) are reduced substantially.
Users of statistics in their professional lives and statistics students will welcome this concise, easy-to-use reference for basic statistics and probability. It contains all of the standardized statistical tables and formulas typically needed plus material on basic statistics topics, such as probability theory and distributions, regression, analysis of variance, nonparametric statistics, and statistical quality control. For each type of distribution the authors supply: ? definitions ? tables ? relationships with other distributions, including limiting forms ? statistical parameters, such as variance and generating functions ? a list of common problems involving the distribution Standard Probability and Statistics: Tables and Formulae also includes discussion of common statistical problems and supplies examples that show readers how to use the tables and formulae to get the solutions they need. With this handy reference, the focus can shift from rote learning and memorization to the concepts needed to use statistics efficiently and effectively.
This book is for students in a first course in ordinary differential equations. The material is organized so that the presentations begin at a reasonably introductory level. Subsequent material is developed from this beginning. As such, readers with little experience can start at a lower level, while those with some experience can use the beginning material as a review, or skip this part to proceed to the next level.The book contains methods of approximation to solutions of various types of differential equations with practical applications, which will serve as a guide to programming so that such differential equations can be solved numerically with the use of a computer. Students who intend to pursue a major in engineering, physical sciences, or mathematics will find this book useful.
Dorothy Maharam Stone's contributions to operators and measure algebras has had a profound influence on this area of research. This volume contains the proceedings of the Conference on Measure and Measurable Dynamics, held in honor of Stone at the University of Rochester in September 1987.
This is the second printing of the book first published in 1988. The first four chapters of the volume are based on lectures given by Stroock at MIT in 1987. They form an introduction to the basic ideas of the theory of large deviations and make a suitable package on which to base a semester-length course for advanced graduate students with a strong background in analysis and some probability theory. A large selection of exercises presents important material and many applications. The last two chapters present various non-uniform results (Chapter 5) and outline the analytic approach that allows one to test and compare techniques used in previous chapters (Chapter 6).
This book covers the basics of modern probability theory. It begins with probability theory on finite and countable sample spaces and then passes from there to a concise course on measure theory, which is followed by some initial applications to probability theory, including independence and conditional expectations. The second half of the book deals with Gaussian random variables, with Markov chains, with a few continuous parameter processes, including Brownian motion, and, finally, with martingales, both discrete and continuous parameter ones. The book is a self-contained introduction to probability theory and the measure theory required to study it.
Through the previous three editions, Handbook of Differential Equations has proven an invaluable reference for anyone working within the field of mathematics, including academics, students, scientists, and professional engineers. The book is a compilation of methods for solving and approximating differential equations. These include the most widely applicable methods for solving and approximating differential equations, as well as numerous methods. Topics include methods for ordinary differential equations, partial differential equations, stochastic differential equations, and systems of such equations. Included for nearly every method are: The types of equations to which the method is applicable The idea behind the method The procedure for carrying out the method At least one simple example of the method Any cautions that should be exercised Notes for more advanced users The fourth edition includes corrections, many supplied by readers, as well as many new methods and techniques. These new and corrected entries make necessary improvements in this edition.
This text provides an introduction to the important physics underpinning current technologies, highlighting key concepts in areas that include linear and rotational motion, energy, work, power, heat, temperature, fluids, waves, and magnetism. This revision reflects the latest technology advances, from smart phones to the Internet of Things, and all kinds of sensors. The author also provides more modern worked examples with useful appendices and laboratories for hands-on practice. There are also two brand new chapters covering sensors as well as electric fields and electromagnetic radiation as applied to current technologies.
Master's Thesis from the year 2016 in the subject Mathematics - Stochastics, grade: 1,7, Technical University of Darmstadt (Forschungsgebiet Stochastik), course: Mathematik - Finanzmathematik, language: English, abstract: In this thesis, we present a stochastic model for stock prices incorporating jump diffusion and shot noise models based on the work of Altmann, Schmidt and Stute ("A Shot Noise Model For Financial Assets") and on its continuation by Schmidt and Stute ("Shot noise processes and the minimal martingale measure"). These papers differ in modeling the decay of the jump effect: Whereas it is deterministic in the first paper, it is stochastic in the last paper. In general, jump effects exist because of overreaction due to news in the press, due to illiquidity or due to incomplete information, i.e. because certain information are available only to few market participants. In financial markets, jump effects fade away as time passes: On the one hand, if the stock price falls, new investors are motivated to buy the stock. On the other hand, a rise of the stock price may lead to profit-taking, i.e. some investors sell the stock in order to lock in gains. Shot noise models are based on Merton's jump diffusion models where the decline of the jump effect after a price jump is neglected. In contrast to jump diffusion models, shot noise models respect the decay of jump effects. In complete markets, the so-called equivalent martingale measure is used to price European options and for hedging. Since stock price models incorporating jumps describe incomplete markets, the equivalent martingale measure cannot be determined uniquely. Hence, in this thesis, we deduce the so-called equivalent minimal martingale measure, both in discrete and continuous time. In contrast to Merton's jump diffusion models and to the well-known pricing model of Black and Scholes, the presented shot noise models are able to reproduce volatility smile effects which can be observed in financial markets.
This is the second printing of the book first published in 1988. The first four chapters of the volume are based on lectures given by Stroock at MIT in 1987. They form an introduction to the basic ideas of the theory of large deviations and make a suitable package on which to base a semester-length course for advanced graduate students with a strong background in analysis and some probability theory. A large selection of exercises presents important material and many applications. The last two chapters present various non-uniform results (Chapter 5) and outline the analytic approach that allows one to test and compare techniques used in previous chapters (Chapter 6).
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