Praise for the first edition: Principles of Uncertainty is a profound and mesmerising book on the foundations and principles of subjectivist or behaviouristic Bayesian analysis. ... the book is a pleasure to read. And highly recommended for teaching as it can be used at many different levels. ... A must-read for sure! —Christian Robert, CHANCE It's a lovely book, one that I hope will be widely adopted as a course textbook. —Michael Jordan, University of California, Berkeley, USA Like the prize-winning first edition, Principles of Uncertainty, Second Edition is an accessible, comprehensive text on the theory of Bayesian Statistics written in an appealing, inviting style, and packed with interesting examples. It presents an introduction to the subjective Bayesian approach which has played a pivotal role in game theory, economics, and the recent boom in Markov Chain Monte Carlo methods. This new edition has been updated throughout and features new material on Nonparametric Bayesian Methods, the Dirichlet distribution, a simple proof of the central limit theorem, and new problems. Key Features: First edition won the 2011 DeGroot Prize Well-written introduction to theory of Bayesian statistics Each of the introductory chapters begins by introducing one new concept or assumption Uses "just-in-time mathematics"—the introduction to mathematical ideas just before they are applied
This handbook focuses on some important topics from Number Theory and Discrete Mathematics. These include the sum of divisors function with the many old and new issues on Perfect numbers; Euler's totient and its many facets; the Möbius function along with its generalizations, extensions, and applications; the arithmetic functions related to the divisors or the digits of a number; the Stirling, Bell, Bernoulli, Euler and Eulerian numbers, with connections to various fields of pure or applied mathematics. Each chapter is a survey and can be viewed as an encyclopedia of the considered field, underlining the interconnections of Number Theory with Combinatorics, Numerical mathematics, Algebra, or Probability Theory. This reference work will be useful to specialists in number theory and discrete mathematics as well as mathematicians or scientists who need access to some of these results in other fields of research.
In a certain sense, subnormal operators were introduced too soon because the theory of function algebras and rational approximation was also in its infancy and could not be properly used to examine the class of operators. The progress in the last several years grew out of applying the results of rational approximation." from the Preface. This book is the successor to the author's 1981 book on the same subject. In addition to reflecting the great strides in the development of subnormal operator theory since the first book, the present work is oriented towards rational functions rather than polynomials. Although the book is a research monograph, it has many of the traits of a textbook including exercises. The book requires background in function theory and functional analysis, but is otherwise fairly self-contained. The first few chapters cover the basics about subnormal operator theory and present a study of analytic functions on the unit disk. Other topics included are: some results on hypernormal operators, an exposition of rational approximation interspersed with applications to operator theory, a study of weak-star rational approximation, a set of results that can be termed structure theorems for subnormal operators, and a proof that analytic bounded point evaluations exist.
Sliding mode control is a simple and yet robust control technique, where the system states are made to confine to a selected subset. With the increasing use of computers and discrete-time samplers in controller implementation in the recent past, discrete-time systems and computer based control have become important topics. This monograph presents an output feedback sliding mode control philosophy which can be applied to almost all controllable and observable systems, while at the same time being simple enough as not to tax the computer too much. It is shown that the solution can be found in the synergy of the multirate output sampling concept and the concept of discrete-time sliding mode control.
This book is an up-to-date introduction to univariate spectral analysis at the graduate level, which reflects a new scientific awareness of spectral complexity, as well as the widespread use of spectral analysis on digital computers with considerable computational power. The text provides theoretical and computational guidance on the available techniques, emphasizing those that work in practice. Spectral analysis finds extensive application in the analysis of data arising in many of the physical sciences, ranging from electrical engineering and physics to geophysics and oceanography. A valuable feature of the text is that many examples are given showing the application of spectral analysis to real data sets. Special emphasis is placed on the multitaper technique, because of its practical success in handling spectra with intricate structure, and its power to handle data with or without spectral lines. The text contains a large number of exercises, together with an extensive bibliography.
Advanced algebra in the service of contemporary mathematicalresearch-- a unique introduction. This volume takes an altogether new approach to advanced algebra.Its intriguing title, inspired by the term postmodernism, denotes adeparture from van der Waerden's Modern Algebra--a book that hasdominated the field for nearly seventy years. Post-Modern Algebraoffers a truly up-to-date alternative to the standard approach,explaining topics from an applications-based perspective ratherthan by abstract principles alone. The book broadens the field ofstudy to include algebraic structures and methods used in currentand emerging mathematical research, and describes the powerful yetsubtle techniques of universal algebra and category theory.Classical algebraic areas of groups, rings, fields, and vectorspaces are bolstered by such topics as ordered sets, monoids,monoid actions, quasigroups, loops, lattices, Boolean algebras,categories, and Heyting algebras. The text features: * A clear and concise treatment at an introductory level, tested inuniversity courses. * A wealth of exercises illustrating concepts and their practicalapplication. * Effective techniques for solving research problems in the realworld. * Flexibility of presentation, making it easy to tailor material tospecific needs. * Help with elementary proofs and algebraic notations for studentsof varying abilities. Post-Modern Algebra is an excellent primary or supplementary textfor graduate-level algebra courses. It is also an extremely usefulresource for professionals and researchers in many areas who musttackle abstract, linear, or universal algebra in the course oftheir work.
The book deals with dynamical systems, generated by linear mappings of finite dimensional spaces and their applications. These systems have a relatively simple structure from the point of view of the modern dynamical systems theory. However, for the dynamical systems of this sort, it is possible to obtain explicit answers to specific questions being useful in applications. The considered problems are natural and look rather simple, but in reality in the course of investigation, they confront users with plenty of subtle questions and their detailed analysis needs a substantial effort. The problems arising are related to linear algebra and dynamical systems theory, and therefore, the book can be considered as a natural amplification, refinement and supplement to linear algebra and dynamical systems theory textbooks.
Ordinary Differential Equations: An Introduction to the Fundamentals is a rigorous yet remarkably accessible textbook ideal for an introductory course in ordinary differential equations. Providing a useful resource both in and out of the classroom, the text: Employs a unique expository style that explains the how and why of each topic covered Allows for a flexible presentation based on instructor preference and student ability Supports all claims with clear and solid proofs Includes material rarely found in introductory texts Ordinary Differential Equations: An Introduction to the Fundamentals also includes access to an author-maintained website featuring detailed solutions and a wealth of bonus material. Use of a math software package that can do symbolic calculations, graphing, and so forth, such as MapleTM or Mathematica®, is highly recommended, but not required.
Analysis and Application of Analog Electronic Circuits to Biomedical Instrumentation, Second Edition helps biomedical engineers understand the basic analog electronic circuits used for signal conditioning in biomedical instruments. It explains the function and design of signal conditioning systems using analog ICs-the circuits that enable ECG, EEG,
This book contains comprehensive reviews and reprints on dynamical groups, spectrum generating algebras and spectrum supersymmetries, and their applications in atomic and molecular physics, nuclear physics, particle physics, and condensed matter physics. It is an important source for researchers as well as students who are doing courses on Quantum Mechanics and Advanced Quantum Mechanics.
Designed for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narra
The result of more than ten years of research, A Dictionary of Creek/Muskogee draws on the expertise of a linguist and a native Creek speaker to yield the first modern dictionary of the Creek language of the southeastern United States. The dictionaryøcontains over seven thousand Creek-English entries, over four thousand English-Creek entries, and over four hundred Creek place names in Alabama, Georgia, Florida, and Oklahoma. The volume also includes illustrations, a map, antonyms, dialects, stylistic information, word histories, and other useful reference material. Entries are given in both the traditional Creek spelling and a modern phonemic transcription. A Dictionary of Creek/Muskogee is the standard reference work for the Creek language.
Quantum mechanics transcends and supplants classical mechanics at the atomic and subatomic levels. It provides the underlying framework for many subfields of physics, chemistry and materials science, including condensed matter physics, atomic physics, molecular physics, quantum chemistry, particle physics, and nuclear physics. It is the only way we can understand the structure of materials, from the semiconductors in our computers to the metal in our automobiles. It is also the scaffolding supporting much of nanoscience and nanotechnology. The purpose of this book is to present the fundamentals of quantum theory within a modern perspective, with emphasis on applications to nanoscience and nanotechnology, and information-technology. As the frontiers of science have advanced, the sort of curriculum adequate for students in the sciences and engineering twenty years ago is no longer satisfactory today. Hence, the emphasis on new topics that are not included in older reference texts, such as quantum information theory, decoherence and dissipation, and on applications to nanotechnology, including quantum dots, wires and wells. - This book provides a novel approach to Quantum Mechanics whilst also giving readers the requisite background and training for the scientists and engineers of the 21st Century who need to come to grips with quantum phenomena - The fundamentals of quantum theory are provided within a modern perspective, with emphasis on applications to nanoscience and nanotechnology, and information-technology - Older books on quantum mechanics do not contain the amalgam of ideas, concepts and tools necessary to prepare engineers and scientists to deal with the new facets of quantum mechanics and their application to quantum information science and nanotechnology - As the frontiers of science have advanced, the sort of curriculum adequate for students in the sciences and engineering twenty years ago is no longer satisfactory today - There are many excellent quantum mechanics books available, but none have the emphasis on nanotechnology and quantum information science that this book has
Covering important aspects of the theory of unitary representations of nuclear Lie groups, this self-contained reference presents the general theory of energy representations and addresses various extensions of path groups and algebras.;Requiring only a general knowledge of the theory of unitary representations, topological groups and elementary st
A consistent and near complete survey of the important progress made in the field over the last few years, with the main emphasis on the rigidity method and its applications. Among others, this monograph presents the most successful existence theorems known and construction methods for Galois extensions as well as solutions for embedding problems combined with a collection of the existing Galois realizations.
Vector Partitions, Visible Points and Ramanujan Functions offers a novel theory of Vector Partitions, though very much grounded in the long-established work of others, that could be developed as an extension to the existing theory of Integer Partitions. The book is suitable for graduate students in physics, applied mathematics, number theory and computational mathematics. It takes the reader up to research level, presenting new results alongside known classical results from integer partitions and areas of vector and multipartite partition theory. It also sets forth new directions for research for the more advanced reader. Above all, the intention of the book is to bring new inspiration to others who study mathematics and related areas. It is hoped that some new ideas will be launched to add value and insight into many of the classical and new theories surrounding partitions. The book is an appreciation of the many gifted authors of research into partitions over the past century and before, in the hope that more may come of this for future generations. Features Provides a step-by-step guide through the known literature on Integer and Vector Partitions, and a focus on the not so well-known Visible Point Vector identities Serves as a reference for graduate students and researchers in physics, applied mathematics, number theory and computational mathematics Offers a variety of practical examples as well as sets of exercises suitable for students and researchers Geoffrey B. Campbell completed his PhD at Australian National University in 1998 under the esteemed physicist Professor Rodney Baxter. His affiliation with the Australian National University Mathematical Sciences Institute has continued for over 30 years. Within that time frame, Geoffrey also served eight years as an Honorary Research Fellow at LaTrobe University Mathematics and Statistics Department in Melbourne. Currently he writes ongoing articles for the Australian Mathematical Society Gazette. Within the international scope, Geoffrey currently serves as a PhD external committee member for a mathematics graduate student at Washington State University in America. Geoffrey has built a career within Australian Commonwealth and State government departments, including as an Advisor at the Department of Prime Minister and Cabinet; as Analyst Researcher for a Royal Commission. Geoffrey specializes in complex data, machine learning including data analytics. He is also a published poet in Australian anthologies and literary magazines.
The volume contains papers based on lectures delivered during the school "Per spectives in Control Theory" held in Sielpia, Poland on September 19-24, 1988. The aim of the school was to give the state-of-the-art presentation of recent achievements as weH as perspectives in such fields of control theory as optimal control and optimization, linear systems, and nonlinear systems. Accordingly, the volume includes survey papers together with presentations of some recent results. The special emphasis is put on: - nonlinear systems (algebraic and geometric methods), - optimal control and optimization (general problems, distributed parameter systems), - linear systems (linear-quadratic problem, robust stabilization). An important feature of the school (and consequently of the volume) was its really "international" character since it brought together leading control theoriests from West and East. All together the school was attended by 108 participants from 18 countries. During the school 21 one-hour invited lectures were delivered. Moreover, five half-an-hour talks were given and 30 contributions were presented in frames of poster sessions. The school was organized and supported by: Institute of Mathematics of the Polish Academy of Sciences, Committee of Automatic Control and Robotics of the Polish Academy of Sciences, - Institute of Automatic Control, Warsaw University of Technology (as Co ordinator of the Basic Research Program R.P.I.02 "Theory of Control of Continuous Dynamic Systems and Discrete Processes" ).
From a biomedical engineering perspective, this book takes an analytic, quantitative approach to describing the basic components of physiological regulators and control systems (PRCs). In Endogenous and Exogenous Regulation and Control of Physiological Systems, the author provides grounding in the classical methods of designing linear and nonlinear systems. He also offers state-of-the-art material on the potential of PRCs to treat immune system ailments, most notably AIDS and cancer. The book focuses on certain "wet" physiological regulators, such as those using endocrine hormones as parametric control substances. Endogenous and Exogenous Regulation and Control of Physiological Systems includes simulations that illustrate model validations and the putative control of cancer and HIV proliferation. It explores novel, untried immunotherapies on the cutting-edge of PRC treatment and explores the latest technologies.
Transport Phenomena in Micro- and Nanoscale Functional Materials and Devices offers a pragmatic view on transport phenomena for micro- and nanoscale materials and devices, both as a research tool and as a means to implant new functions in materials. Chapters emphasize transport properties (TP) as a research tool at the micro/nano level and give an experimental view on underlying techniques. The relevance of TP is highlighted through the interplay between a micro/nanocarrier's characteristics and media characteristics: long/short-range order and disorder excitations, couplings, and in energy conversions. Later sections contain case studies on the role of transport properties in functional nanomaterials. This includes transport in thin films and nanostructures, from nanogranular films, to graphene and 2D semiconductors and spintronics, and from read heads, MRAMs and sensors, to nano-oscillators and energy conversion, from figures of merit, micro-coolers and micro-heaters, to spincaloritronics. Presents a pragmatic description of electrical transport phenomena in micro- and nanoscale materials and devices from an experimental viewpoint Provides an in-depth overview of the experimental techniques available to measure transport phenomena in micro- and nanoscale materials Features case studies to illustrate how each technique works Highlights emerging areas of interest in micro- and nanomaterial transport phenomena, including spintronics
Starting with O. Teichmuller's basic concepts, G. Pickert developed an extensive theory of purely inseparable extensions, especially the finite degree case. In these notes are presented an infinite degree theory, especially for the case without exponent.
A twenty-fifth anniversary edition featuring a new preface, invaluable for graduate students and researchers in general relativity and elementary particle theory.
The interdisciplinary field of biomedical engineering requires its practitioners to master not only engineering skills, but also a diversity of material in the biological sciences. This text helps biomedical engineers strengthen their skills in the common network of applied mathematics that ties together these diverse disciplines. Based on the auth
The stories of Kauai's ruling chiefs were passed from generation to generation in songs and narratives recited by trained storytellers either formally at the high chief's court or informally at family gatherings. Their chronology was ordered by a ruler's genealogy, which, in the case of the pua alii (flower of royalty), was illustrious and far reaching and could be traced to one of the four great gods of Polynesia--Käne, Kü, Lono, and Kanaloa. In these legends, Hawaiians of old sought answers to the questions "Who are we?" "Who are our ancestors and where do they come from?" "What lessons can be learned from their conduct?" Nä Pua Alii o Kauai presents the stories of the men and women who ruled the island of Kauai from its first settlement to the final rebellion against Kamehameha I's forces in 1824. Only fragments remain of the nearly two-thousand-year history of the people who inhabited Kauai before the coming of James Cook in 1778. Now scattered in public and private archives and libraries, these pieces of Hawaii's precontact past were recorded in the nineteenth century by such determined individuals as David Malo, Samuel Kamakau, and Abraham Fornander. All known genealogical references to the Kauai alii nui (paramount chiefs) have been gathered here and placed in chronological order and are interspersed with legends of great voyages, bitter wars, courageous heroes, and passionate romances that together form a rich and invaluable resource.
The major histocompatibility complex (Mhc) is one of the few identified gene systems in domestic animals that is associated with quantitative traits such as disease resistance, immune response, growth, and reproduction. As knowledge of this important system increases, we move closer toward the reality of genetic enhancement of animal welfare and production efficiency. This book represents the current state of knowledge on the Mhc of agriculturally important animals and explores the latest advances in technology. For the first time, the unique findings of recent Mhc research are presented in a single source. The Major Histocompatibility Complex Region of Domestic Animal Species begins with a discussion of the evolution of Mhc. The chapters are then organized with respect to specific species, with a chapter devoted to each. The Mhc of mice and humans are used as a common reference for comparisons between diverse species. The text concludes with a look at future strategies and directions in Mhc research. Comparative immunologists and geneticists, veterinarians, animal breeders, researchers, and university and postgraduate students will all benefit from this detailed look at the evolution, structure, and organization of Mhc.
As more applications are found, interest in Hidden Markov Models continues to grow. Following comments and feedback from colleagues, students and other working with Hidden Markov Models the corrected 3rd printing of this volume contains clarifications, improvements and some new material, including results on smoothing for linear Gaussian dynamics. In Chapter 2 the derivation of the basic filters related to the Markov chain are each presented explicitly, rather than as special cases of one general filter. Furthermore, equations for smoothed estimates are given. The dynamics for the Kalman filter are derived as special cases of the authors’ general results and new expressions for a Kalman smoother are given. The Chapters on the control of Hidden Markov Chains are expanded and clarified. The revised Chapter 4 includes state estimation for discrete time Markov processes and Chapter 12 has a new section on robust control.
This volume contains a description of the architecture and inscriptional content of the royal tomb, a catalogue of all artifacts, translation and commentary on inscriptions, publication and analysis of pottery, a bio-anthropological report on the human remains, a paleobotanical report, an elemental analysis of pottery fabrics and an historical analysis.
As relevant today as it was when it was first published 20 years ago, this book is a classic in the field. Nowhere else can you find more complete coverage of radiation and scattering of waves. The chapter: Asympotic Evaluation of Integrals is considered the definitive source for asympotic techniques. This book is essential reading for engineers, physicists and others involved in the fields of electromagnetics and acoustics. It is also an indispensable reference for advanced engineering courses.
Many practical suggestions and tips; the examples are meaningful and the illustrations are effective....Destined to become a classic reference that any serious practitioner of ocean acoustics cannot afford to ignore." Revue de livre Authored by four internationally renowned scientists, this volume covers 20 years of progress in computational ocean acoustics and presents the latest numerical techniques used in solving the wave equation in heterogeneous fluid-solid media. The authors detail various computational schemes and illustrate many of the fundamental propagation features via 2-D color displays.
This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first edition, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible for the talented and hard-working undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings and Eulerian and Hamiltonian cycles. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, and algorithms and complexity. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.
This text presents a general survey of digital signal processing concepts, design methods, and implementation considerations, with an emphasis on digital filters. It includes MATLAB exercises.
Here, the authors strive to change the way logic and discrete math are taught in computer science and mathematics: while many books treat logic simply as another topic of study, this one is unique in its willingness to go one step further. The book traets logic as a basic tool which may be applied in essentially every other area.
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