This work features the interplay of two main branches of mathematics: topology and real analysis. The material of the book is largely contained in the research publications of the authors and their students from the past 50 years. Parts of analysis are touched upon in a unique way, for example, Lebesgue measurability, Baire classes of functions, differentiability, C ]n and C ]*w functions, the Blumberg theorem, bounded variation in the sense of Cesari, and various theorems on Fourier series and generalized bounded variation of a function.
Set theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly all mathematical concepts and results can be formalized within set theory. This textbook is meant for an upper undergraduate course in set theory. In this text, the fundamentals of abstract sets, including relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers, are developed within the framework of axiomatic set theory. The reader will need to be comfortable reading and writing mathematical proofs. The proofs in this textbook are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Exercises are included at the end of each section in a chapter, with useful suggestions for the more challenging exercises.
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.
Hoping to make the text more accessible to readers not schooled in the probabalistic tradition, Stroock (affiliation unspecified) emphasizes the geometric over the stochastic analysis of differential manifolds. Chapters deconstruct Brownian paths, diffusions in Euclidean space, intrinsic and extrinsic Riemannian geometry, Bocher's identity, and the bundle of orthonormal frames. The volume humbly concludes with an "admission of defeat" in regard to recovering the Li-Yau basic differential inequality. Annotation copyrighted by Book News, Inc., Portland, OR.
Daniel Star presents a novel solution to the problem of reconciling normative ethics with ordinary virtue--for while ethical principles seem worth defending, it is not plausible to suggest that virtuous people in general follow them. He presents a new account of virtue, and rethinks the role that knowledge plays in deliberation and action.
Multilingual Natural Language Processing Applications is the first comprehensive single-source guide to building robust and accurate multilingual NLP systems. Edited by two leading experts, it integrates cutting-edge advances with practical solutions drawn from extensive field experience. Part I introduces the core concepts and theoretical foundations of modern multilingual natural language processing, presenting today’s best practices for understanding word and document structure, analyzing syntax, modeling language, recognizing entailment, and detecting redundancy. Part II thoroughly addresses the practical considerations associated with building real-world applications, including information extraction, machine translation, information retrieval/search, summarization, question answering, distillation, processing pipelines, and more. This book contains important new contributions from leading researchers at IBM, Google, Microsoft, Thomson Reuters, BBN, CMU, University of Edinburgh, University of Washington, University of North Texas, and others. Coverage includes Core NLP problems, and today’s best algorithms for attacking them Processing the diverse morphologies present in the world’s languages Uncovering syntactical structure, parsing semantics, using semantic role labeling, and scoring grammaticality Recognizing inferences, subjectivity, and opinion polarity Managing key algorithmic and design tradeoffs in real-world applications Extracting information via mention detection, coreference resolution, and events Building large-scale systems for machine translation, information retrieval, and summarization Answering complex questions through distillation and other advanced techniques Creating dialog systems that leverage advances in speech recognition, synthesis, and dialog management Constructing common infrastructure for multiple multilingual text processing applications This book will be invaluable for all engineers, software developers, researchers, and graduate students who want to process large quantities of text in multiple languages, in any environment: government, corporate, or academic.
Gauge Field theory in Natural Geometric Language addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a brief, integrated approach that exploits standard and non-standard notions, as well as recent advances, in a natural geometric language in which the role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves. In proposing an original bridge between physics and mathematics, this text will appeal not only to mathematicians who wish to understand some of the basic ideas involved in quantum particle physics, but also to physicists who are not satisfied with the usual mathematical presentations of their field.
The Heisenberg group comes from quantum mechanics and is the simplest non-commutative Lie group. While it belongs to the class of simply connected nilpotent Lie groups, it turns out that its special structure yields many results which (up to now) have not carried over to this larger class. This book is a survey of probabilistic results on the Heisenberg group. The emphasis lies on limit theorems and their relation to Brownian motion. Besides classical probability tools, non-commutative Fourier analysis and functional analysis (operator semigroups) comes in. The book is intended for probabilists and analysts interested in Lie groups, but given the many applications of the Heisenberg group, it will also be useful for theoretical phycisists specialized in quantum mechanics and for engineers.
Die kuns van die lewe is nie so ingewikkeld nie. Die lewe moet net sinvol geleef word. Maar hoe? Met hierdie vraag word daar geworstel. Het ek 'n siel? Wat "e;besiel"e; my? Leef ek besield en sit daar "e;siel"e; in dit wat ek vandag doen?Die boek wil mense se oe oopmaak vir dit wat elke dag binne verhoudinge in elk geval "e;gebeur"e;, en jou help om die netwerk van liefdesintimiteit en 'n besielde lewe te ontdek.
Now more streamlined and focused than ever before, the 6th edition of CT and MRI of the Whole Body is a definitive reference that provides you with an enhanced understanding of advances in CT and MR imaging, delivered by a new team of international associate editors. Perfect for radiologists who need a comprehensive reference while working on difficult cases, it presents a complete yet concise overview of imaging applications, findings, and interpretation in every anatomic area. The new edition of this classic reference — released in its 40th year in print — is a must-have resource, now brought fully up to date for today's radiology practice. - Includes both MR and CT imaging applications, allowing you to view correlated images for all areas of the body. - Coverage of interventional procedures helps you apply image-guided techniques. - Includes clinical manifestations of each disease with cancer staging integrated throughout. - Expert Consult eBook version included with purchase. This enhanced eBook experience allows you to search all of the text, figures, images, and references from the book on a variety of devices. - Over 5,200 high quality CT, MR, and hybrid technology images in one definitive reference. - For the radiologist who needs information on the latest cutting-edge techniques in rapidly changing imaging technologies, such as CT, MRI, and PET/CT, and for the resident who needs a comprehensive resource that gives a broad overview of CT and MRI capabilities. - Brand-new team of new international associate editors provides a unique global perspective on the use of CT and MRI across the world. - Completely revised in a new, more succinct presentation without redundancies for faster access to critical content. - Vastly expanded section on new MRI and CT technology keeps you current with continuously evolving innovations.
This book offers a unified presentation of Fourier theory and corresponding algorithms emerging from new developments in function approximation using Fourier methods. It starts with a detailed discussion of classical Fourier theory to enable readers to grasp the construction and analysis of advanced fast Fourier algorithms introduced in the second part, such as nonequispaced and sparse FFTs in higher dimensions. Lastly, it contains a selection of numerical applications, including recent research results on nonlinear function approximation by exponential sums. The code of most of the presented algorithms is available in the authors’ public domain software packages. Students and researchers alike benefit from this unified presentation of Fourier theory and corresponding algorithms.
Harry Reasoner was one of the most trusted and well-liked journalists of the golden age of network television news. Whether anchoring the evening newscast on CBS in the 1960s or on ABC in the 1970s, providing in-depth reporting on 60 Minutes, or hosting numerous special programs covering civil rights struggles, the Vietnam War, and Watergate, Reasoner had "that almost mystical quality it seems to take for good television reporting, exuding this atmosphere of truth and believability," in the words of Walter Cronkite. Yet his reassuring manner and urbane, often witty, on-air persona masked a man who was far more complex and contradictory. Though gifted with the intelligence and drive to rise to the top of his profession, Reasoner was regarded by many colleagues as lazy and self-indulgent, a man who never achieved his full potential despite his many accomplishments. Harry Reasoner: A Life in the News covers the entire sweep of this enigmatic journalist's life and career. Douglass K. Daniel opens with Reasoner's Depression-era Midwestern upbringing and follows him through his early work in newspapers and radio before he joined CBS in 1956. Focusing on Reasoner's thirty-five-year tenure in television news, Daniel presents fascinating, behind-the-scenes accounts of Reasoner's key role in founding the top-rated newsmagazine 60 Minutes. He also explores Reasoner's highly publicized move to ABC in 1970, where he anchored the nightly newscast, first with Howard K. Smith and later with Barbara Walters—a disastrous pairing from which Reasoner's career never fully recovered. Based on scores of interviews and unpublished letters, memos, and other primary sources, this first biography of the man once rated second in credibility only to Walter Cronkite illuminates an entire era in broadcast journalism, as well as many of the unique personalities, from Andy Rooney to Mike Wallace, who made that era distinctive.
Typically, undergraduates see real analysis as one of the most difficult courses that a mathematics major is required to take. The main reason for this perception is twofold: Students must comprehend new abstract concepts and learn to deal with these concepts on a level of rigor and proof not previously encountered. A key challenge for an instructor of real analysis is to find a way to bridge the gap between a student’s preparation and the mathematical skills that are required to be successful in such a course. Real Analysis: With Proof Strategies provides a resolution to the "bridging-the-gap problem." The book not only presents the fundamental theorems of real analysis, but also shows the reader how to compose and produce the proofs of these theorems. The detail, rigor, and proof strategies offered in this textbook will be appreciated by all readers. Features Explicitly shows the reader how to produce and compose the proofs of the basic theorems in real analysis Suitable for junior or senior undergraduates majoring in mathematics.
What does Heidegger mean by 'Dasein'? What does he say in Being and Time? How does his phenomenology differ to that of his teacher, Husserl? Answering these questions and more, The Heidegger Dictionary provides students with all the tools they need to better understand one of the most influential yet complex philosophers of the 20th century. Easy to use and navigate, this book is divided into four main parts, covering Heidegger's life, ideas and innovative terminology, related thinkers, and published and unpublished works. Updated with significant new material throughout, the 2nd edition has been expanded to engage with the latest Heidegger scholarship, and features: · A new A-Z section on Heidegger's influences, past and contemporary, from Aristotle and Nietzsche to Husserl and Dilthey · Summaries of Heidegger's entire 102-volume Collected Works, including the Black Notebooks · Expanded coverage of Heidegger's thought, with straightforward explanations of his views on modernity, science and more · An updated glossary of Heidegger's key terms, listing all the major translation alternatives alongside his original German Providing a road-map to how Heidegger's ideas developed over his long philosophical career, this is an essential research companion for all students of Heidegger, from beginners to the advanced.
This two-volume text provides a complete overview of the theory of Banach spaces, emphasising its interplay with classical and harmonic analysis (particularly Sidon sets) and probability. The authors give a full exposition of all results, as well as numerous exercises and comments to complement the text and aid graduate students in functional analysis. The book will also be an invaluable reference volume for researchers in analysis. Volume 1 covers the basics of Banach space theory, operatory theory in Banach spaces, harmonic analysis and probability. The authors also provide an annex devoted to compact Abelian groups. Volume 2 focuses on applications of the tools presented in the first volume, including Dvoretzky's theorem, spaces without the approximation property, Gaussian processes, and more. In volume 2, four leading experts also provide surveys outlining major developments in the field since the publication of the original French edition.
This book presents methods for estimating optical flow and scene flow motion with high accuracy, focusing on the practical application of these methods in camera-based driver assistance systems. Clearly and logically structured, the book builds from basic themes to more advanced concepts, culminating in the development of a novel, accurate and robust optic flow method. Features: reviews the major advances in motion estimation and motion analysis, and the latest progress of dense optical flow algorithms; investigates the use of residual images for optical flow; examines methods for deriving motion from stereo image sequences; analyses the error characteristics for motion variables, and derives scene flow metrics for movement likelihood and velocity; introduces a framework for scene flow-based moving object detection and segmentation; includes Appendices on data terms and quadratic optimization, and scene flow implementation using Euler-Lagrange equations, in addition to a helpful Glossary.
Highlights the Progression of Meshing Technologies and Their Applications Finite Element Mesh Generation provides a concise and comprehensive guide to the application of finite element mesh generation over 2D domains, curved surfaces, and 3D space. Organised according to the geometry and dimension of the problem domains, it develops from the basic meshing algorithms to the most advanced schemes to deal with problems with specific requirements such as boundary conformity, adaptive and anisotropic elements, shape qualities, and mesh optimization. It sets out the fundamentals of popular techniques, including: Delaunay triangulation Advancing-front (ADF) approach Quadtree/Octree techniques Refinement and optimization-based strategies From the geometrical and the topological aspects and their associated operations and inter-relationships, each approach is vividly described and illustrated with examples. Beyond the algorithms, the book also explores the practice of using metric tensor and surface curvatures for generating anisotropic meshes on parametric space. It presents results from research including 3D anisotropic meshing, mesh generation over unbounded domains, meshing by means of intersection, re-meshing by Delaunay-ADF approach, mesh refinement and optimization, generation of hexahedral meshes, and large scale and parallel meshing, along with innovative unpublished meshing methods. The author provides illustrations of major meshing algorithms, pseudo codes, and programming codes in C++ or FORTRAN. Geared toward research centers, universities, and engineering companies, Finite Element Mesh Generation describes mesh generation methods and fundamental techniques, and also serves as a valuable reference for laymen and experts alike.
Studies the generic finite simple group of characteristic 2 type whose proper subgroups are of known type. The authors' principal result (the Trichotomy Theorem) asserts that such a group has one of three precisely determined internal structures.
Designed for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to teach mathematical thinking while conveying the beauty and elegance of mathematics. The book contains a large number of exercises of varying difficulty, some of which are designed to help reinforce basic concepts and others of which will challenge virtually all readers. The sole prerequisite for reading this text is high school algebra. Topics covered include: * mathematical induction * modular arithmetic * the Fundamental Theorem of Arithmetic * Fermat's Little Theorem * RSA encryption * the Euclidean algorithm * rational and irrational numbers * complex numbers * cardinality * Euclidean plane geometry * constructibility (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass)* infinite series * higher dimensional spaces. This textbook is suitable for a wide variety of courses and for a broad range of students of mathematics and other subjects. Mathematically inclined senior high school students will also be able to read this book. From the reviews of the first edition: “It is carefully written in a precise but readable and engaging style... I thoroughly enjoyed reading this recent addition to the Springer Undergraduate Texts in Mathematics series and commend this clear, well-organised, unfussy text to its target audiences.” (Nick Lord, The Mathematical Gazette, Vol. 100 (547), 2016) “The book is an introduction to real mathematics and is very readable. ... The book is indeed a joy to read, and would be an excellent text for an ‘appreciation of mathematics’ course, among other possibilities.” (G.A. Heuer, Mathematical Reviews, February, 2015) “Many a benighted book misguidedly addresses the need [to teach mathematical thinking] by framing reasoning, or narrowly, proof, not as pervasive modality but somehow as itself an autonomous mathematical subject. Fortunately, the present book gets it right.... [presenting] well-chosen, basic, conceptual mathematics, suitably accessible after a K-12 education, in a detailed, self-conscious way that emphasizes methodology alongside content and crucially leads to an ultimate clear payoff. ... Summing Up: Recommended. Lower-division undergraduates and two-year technical program students; general readers.” (D.V. Feldman, Choice, Vol. 52 (6), February, 2015)
Cardiovascular and Respiratory Systems: Modeling, Analysis, and Control uses a principle-based modeling approach and analysis of feedback control regulation to elucidate the physiological relationships. Models are arranged around specific questions or conditions, such as exercise or sleep transition, and are generally based on physiological mechanisms rather than on formal descriptions of input-output behavior. The authors ask open questions relevant to medical and clinical applications and clarify underlying themes of physiological control organization. Current problems, key issues, developing trends, and unresolved questions are highlighted. Researchers and graduate students in mathematical biology and biomedical engineering will find this book useful. It will also appeal to researchers in the physiological and life sciences who are interested in mathematical modeling.
The power grid can be considered one of twentieth-century engineering?s greatest achievements, and as grids and populations grow, robustness is a factor that planners must take into account. Power grid robustness is a complex problem for two reasons: the underlying physics is mathematically complex, and modeling is complicated by lack of accurate data. This book sheds light on this complex problem by introducing the engineering details of power grid operations from the basic to the detailed; describing how to use optimization and stochastic modeling, with special focus on the modeling of cascading failures and robustness; providing numerical examples that show ?how things work?; and detailing the application of a number of optimization theories to power grids.?
Elastic waves are used in fields as diverse as the non-destructive evaluation of materials, medicine, seismology and telecommunications. Elastic Waves in Solids 1 presents the different modes of propagation of elastic waves in increasingly complex media and structures. It first studies the propagation in an unlimited solid where only the material properties are taken into account. It then analyzes reflection and transmission phenomena at an interface with a fluid or a second solid. It explains the search for propagation modes on a free surface or at the interface between two media. Finally, it proposes a study of the dispersive propagation of elastic waves guided by a plate or a cylinder. This book is intended for students completing a master’s degree in acoustics, mechanics, geophysics or engineering, as well as teachers and researchers in these disciplines.
This book introduces a quantum-mechanical description of the nuclear fission process from an initial compound state to scission. Issues like the relevant degrees of freedom throughout the process, the way of coupling collective and intrinsic degrees during the fission process, and how a nucleus divides into two separate daughters in a quantum-mechanical description where its wave function can be non-local, are currently being investigated through a variety of theoretical, computational, and experimental techniques. The term “microscopic” in this context refers to an approach that starts from protons, neutrons, and an effective (i.e., in-medium) interaction between them. The form of this interaction is inspired by more fundamental theories of nuclear matter, but still contains parameters that have to be adjusted to data. Thus, this microscopic approach is far from complete, but sufficient progress has been made to warrant taking stock of what has been accomplished so far. The aim is to provide, in a pedagogical and comprehensive manner, one specific approach to the fission problem, originally developed at the CEA Bruyères-le-Châtel Laboratory in France. Intended as a reference for advanced graduate students and researchers in fission theory as well as for practitioners in the field, it includes illustrative examples throughout the text to make it easier for the reader to understand, implement, and verify the formalism presented.
From the reviews of the first edition: "This book exposes the beautiful confluence of deep techniques and ideas from mathematical physics and the topological study of the differentiable structure of compact four-dimensional manifolds, compact spaces locally modeled on the world in which we live and operate... The book is filled with insightful remarks, proofs, and contributions that have never before appeared in print. For anyone attempting to understand the work of Donaldson and the applications of gauge theories to four-dimensional topology, the book is a must." #Science#1 "I would strongly advise the graduate student or working mathematician who wishes to learn the analytic aspects of this subject to begin with Freed and Uhlenbeck's book." #Bulletin of the American Mathematical Society#2
This book contains the extended abstracts presented at the 12th International Conference on Power Series and Algebraic Combinatorics (FPSAC '00) that took place at Moscow State University, June 26-30, 2000. These proceedings cover the most recent trends in algebraic and bijective combinatorics, including classical combinatorics, combinatorial computer algebra, combinatorial identities, combinatorics of classical groups, Lie algebra and quantum groups, enumeration, symmetric functions, young tableaux etc...
In June 1944, U.S. Navy Task Group 22.3, a "hunter-killer" force commanded by Daniel Gallery to track down German submarines, boarded and captured U-505 off the coast of Africa. It was the first time that an enemy ship of war had been captured on the high seas by U.S. Navy sailors since 1815, when the USS Peacock seized HMS Nautilus as part of the War of 1812. The extraordinary feat is described in gripping narrative by Gallery himself, who chronicles the long and arduous battle against the German U-boat under the most hazardous conditions. Once they succeeded in capturing and towing their prize seventeen-hundred miles across the Atlantic Ocean, U-505 proved to be of inestimable value, yielding secrets to radio codes among other things. U-505 is now on exhibit at Chicago's Museum of Science and Industry.
This important book introduces perturbation and qualitative methods for differential equations in terms understandable to students with only a basic knowledge of calculus and ordinary linear differential equations. Theorems are stated clearly with their limitations and restrictions and are applied to solve examples from various disciplines. The writing style is informal and new ideas are introduced gradually via concepts already familiar to the reader.
The classification of the finite simple groups is one of the major feats of contemporary mathematical research, but its proof has never been completely extricated from the journal literature in which it first appeared. This book serves as an introduction to a series devoted to organizing and simplifying the proof. The purpose of the series is to present as direct and coherent a proof as is possible with existing techniques. This first volume, which sets up the structure for the entire series, begins with largely informal discussions of the relationship between the Classification Theorem and the general structure of finite groups, as well as the general strategy to be followed in the series and a comparison with the original proof. Also listed are background results from the literature that will be used in subsequent volumes. Next, the authors formally present the structure of the proof and the plan for the series of volumes in the form of two grids, giving the main case division of the proof as well as the principal milestones in the analysis of each case. Thumbnail sketches are given of the ten or so principal methods underlying the proof. Much of the book is written in an expository style accessible to nonspecialists.
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