Fuzzy Systems Engineering

Toward Human-Centric Computing

Author: Witold Pedrycz,Fernando Gomide

Publisher: John Wiley & Sons

ISBN: 9780470168950

Category: Technology & Engineering

Page: 648

View: 9513

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A self-contained treatment of fuzzy systems engineering, offering conceptual fundamentals, design methodologies, development guidelines, and carefully selected illustrative material Forty years have passed since the birth of fuzzy sets, in which time a wealth of theoretical developments, conceptual pursuits, algorithmic environments, and other applications have emerged. Now, this reader-friendly book presents an up-to-date approach to fuzzy systems engineering, covering concepts, design methodologies, and algorithms coupled with interpretation, analysis, and underlying engineering knowledge. The result is a holistic view of fuzzy sets as a fundamental component of computational intelligence and human-centric systems. Throughout the book, the authors emphasize the direct applicability and limitations of the concepts being discussed, and historical and bibliographical notes are included in each chapter to help readers view the developments of fuzzy sets from a broader perspective. A radical departure from current books on the subject, Fuzzy Systems Engineering presents fuzzy sets as an enabling technology whose impact, contributions, and methodology stretch far beyond any specific discipline, making it applicable to researchers and practitioners in engineering, computer science, business, medicine, bioinformatics, and computational biology. Additionally, three appendices and classroom-ready electronic resources make it an ideal textbook for advanced undergraduate- and graduate-level courses in engineering and science.

Applied Combinatorics, 6th Edition

Author: Alan Tucker

Publisher: Wiley Global Education

ISBN: 1118210115

Category: Mathematics

Page: 496

View: 6586

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The new 6th edition of Applied Combinatorics builds on the previous editions with more in depth analysis of computer systems in order to help develop proficiency in basic discrete math problem solving. As one of the most widely used books in combinatorial problems, this edition explains how to reason and model combinatorically while stressing the systematic analysis of different possibilities, exploration of the logical structure of a problem, and ingenuity. Although important uses of combinatorics in computer science, operations research, and finite probability are mentioned, these applications are often used solely for motivation. Numerical examples involving the same concepts use more interesting settings such as poker probabilities or logical games.

Concepts from Tensor Analysis and Differential Geometry

Author: Tracy Y. Thomas

Publisher: Elsevier

ISBN: 1483263711

Category: Mathematics

Page: 128

View: 6594

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Concepts from Tensor Analysis and Differential Geometry discusses coordinate manifolds, scalars, vectors, and tensors. The book explains some interesting formal properties of a skew-symmetric tensor and the curl of a vector in a coordinate manifold of three dimensions. It also explains Riemann spaces, affinely connected spaces, normal coordinates, and the general theory of extension. The book explores differential invariants, transformation groups, Euclidean metric space, and the Frenet formulae. The text describes curves in space, surfaces in space, mixed surfaces, space tensors, including the formulae of Gaus and Weingarten. It presents the equations of two scalars K and Q which can be defined over a regular surface S in a three dimensional Riemannian space R. In the equation, the scalar K, which is an intrinsic differential invariant of the surface S, is known as the total or Gaussian curvature and the scalar U is the mean curvature of the surface. The book also tackles families of parallel surfaces, developable surfaces, asymptotic lines, and orthogonal ennuples. The text is intended for a one-semester course for graduate students of pure mathematics, of applied mathematics covering subjects such as the theory of relativity, fluid mechanics, elasticity, and plasticity theory.

Problems & Solutions in Group Theory for Physicists

Author: Zhong-Qi Ma,Xiao-Yan Gu

Publisher: World Scientific

ISBN: 9789812388339

Category: Science

Page: 464

View: 4981

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This book is aimed at graduate students and young researchers in physics who are studying group theory and its application to physics. It contains a short explanation of the fundamental knowledge and method, and the fundamental exercises for the method, as well as some important conclusions in group theory. This book is also suitable for some graduate students in theoretical chemistry.

Quantum Topology and Global Anomalies

Author: R A Baadhio

Publisher: World Scientific

ISBN: 9814498777

Category: Science

Page: 284

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Anomalies are ubiquitous features in quantum field theories. They can ruin the consistency of such theories and put significant restrictions on their viability, especially in dimensions higher than four. Global gauge and gravitational anomalies are to date, one of the scant powerful and probing tools available to physicists in the pursuit of uniqueness. This monograph is one of the very few that specializes in the study of global anomalies in quantum field theories. A discussion of various issues associated to three dimensional physics — the Chern–Simons–Witten theories — widen the scope of this book. Topics discussed here comprises: the ongoing quest for three-manifolds invariant, the role of the mapping class groups in (a) the detection and cancellation of global anomalies, (b) formulating three-manifolds invariant; the geometric quantization of Chern-Simons-Witten theories; deformation quantization; study of chiral and gravitational anomalies; anomalies and the Atiyah-Patodi-Singer Index theorem; exotic spheres; global gravitational anomalies in some six and ten dimensional supergravity and superstring theories, with an additional case study of Witten SU(2) Global Gauge Anomalies. In addition, five chapters lay out the mathematical basis for a thorough use of the topics above. One chapter focuses on the relationship between Teichmüller spaces, moduli spaces and mapping class groups. Another chapter is devoted to mapping class groups and arithmetic groups. Gauge theories on Riemann surfaces are studies in well over two chapters, the first one centered on the theory of bundles and the second on connections. Many readers will find this a useful book, especially theoretical physicists and mathematicians. The material presented here will be of interest to both the experts who will find complete, detailed and precise descriptions of important topics of current interest in mathematical physics, and to students and newcomers to the field, who will appreciate the vast amount of information provided here, especially on global anomalies. Contents:The Ongoing Quest for Three-Manifold InvariantsMapping Class Groups and 3-Manifold InvariantsTeichmüller Spaces and Mapping Class GroupsMapping Class Groups and Arithmetic GroupsWeil-Petersson Geometry of Teichmüller SpacesGauge Theories on Riemann Surfaces I: BundlesGauge Theories on Riemann Surfaces II: ConnectionsGeometric Quantization of Chern–Simons–Witten TheoriesDeformation QuantizationChiral and Gravitational AnomaliesAnomalies and the Index TheoremGlobal AnomaliesMapping Class Groups and Global AnomaliesExotic Spheres Readership: Mathematicians and physicists. keywords:

Confessions of an American Media Man

Author: Tom Plate

Publisher: Marshall Cavendish

ISBN: 9789812613158

Category: Biography & Autobiography

Page: 352

View: 4204

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For better or for worse, the news media in the United States has huge worldwide influence. And yet little is actually known about its real inner workings, inherent logic and deeply embedded customs. In this revealing and sometimes brutally honest media autobiography, veteran American journalist Tom Plate tells you what it is really like to work inside these corridors of power. The author-a syndicated newspaper columnist as well as a professor at the University of California at Los Angeles (UCLA)-takes you behind the scenes at iconic media institutions such as Time magazine, the Los Angeles Times and New York magazine. There you meet such factors of media life as the reality of the deadline, the speed of the news cycle, the inevitability of office politics, the debilitating impact of political correctness and the occasional great joys of journalism. For young adults who are considering a career in the news media, this compelling book is necessary reading; and for older professionals who in their work have to deal directly with the news media or who are deeply curious about its inner workings, this book will come as a true revelation.

Theories of Integration

The Integrals of Riemann, Lebesgue, Henstock–Kurzweil, and McShane Second Edition

Author: Douglas S Kurtz,Charles W Swartz

Publisher: World Scientific Publishing Company

ISBN: 9813108266

Category: Mathematics

Page: 312

View: 4951

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The book uses classical problems to motivate a historical development of the integration theories of Riemann, Lebesgue, Henstock–Kurzweil and McShane, showing how new theories of integration were developed to solve problems that earlier integration theories could not handle. It develops the basic properties of each integral in detail and provides comparisons of the different integrals. The chapters covering each integral are essentially independent and could be used separately in teaching a portion of an introductory real analysis course. There is a sufficient supply of exercises to make this book useful as a textbook.

Geometrical Quickies & Trickies

Author: Yan Kow Cheong

Publisher: MathPlus Publishing

ISBN: 9810973896

Category: Mathematics

Page: 208

View: 2489

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Are you bored or unchallenged by drill-and-kill geometry questions in your textbooks and workbooks? Are you half-prepared for your coming math contests and competitions? Some benefits of Geometrical Quickies & Trickies are: * Over 200 non-routine geometry questions to separate the nerd of mathletes from the herd of drill-and-kill specialists; * Trick and tricky questions to meet the mathematical needs and wants of students- and teachers-problem solvers; * Twenty enrichment geometry units to promote an appreciation for recreational mathematics; * Hints and solutions, and a reference list for more practice on quickies and tricks. Geometrical Quickies & Trickies is suitable for grades 6-9 problem solvers and mathletes, and for teachers and tutors who desire to challenge (or torture) their students mathematically. Contents 1. What is a Circle? 2. Three Famous (or Notorious) Geometrical Problems 3. Non-Euclidean Geometry for Goondus 4. How Many Regions? 5. That Holy Little Geometry Book 6. Fun with Areas and Perimeters 7. Always a Parallelogram! 8. The Malfatti's Problem 9. The Beauty of Pi 10. The Zero Option 11. The Golden Ratio by Paper Folding 12. The Ubiquity of Phi 13. Matchstick Mathematics 14. The Rolling Circle Question 15. Two Useful Circle Properties 16. Proving the Obvious 17. Sanguku—Japanese Temple Geometry 18. Applications of Pythagorean Theorem 19. Visualizing Infinity 20. Geometrical Idiosyncrasies Answers/Hints/Solutions Bibliography & References

Fourier and Wavelet Analysis

Author: George Bachmann,Lawrence Narici,Edward Beckenstein

Publisher: Springer Science & Business Media

ISBN: 1461205050

Category: Mathematics

Page: 507

View: 8980

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This comprehensive volume develops all of the standard features of Fourier analysis - Fourier series, Fourier transform, Fourier sine and cosine transforms, and wavelets. The books approach emphasizes the role of the "selector" functions, and is not embedded in the usual engineering context, which makes the material more accessible to a wider audience. While there are several publications on the various individual topics, none combine or even include all of the above.

Wavelet Transforms and Their Applications

Author: Lokenath Debnath,Firdous Shah

Publisher: Springer

ISBN: 0817684182

Category: Technology & Engineering

Page: 553

View: 4267

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This textbook is an introduction to wavelet transforms and accessible to a larger audience with diverse backgrounds and interests in mathematics, science, and engineering. Emphasis is placed on the logical development of fundamental ideas and systematic treatment of wavelet analysis and its applications to a wide variety of problems as encountered in various interdisciplinary areas. Topics and Features: * This second edition heavily reworks the chapters on Extensions of Multiresolution Analysis and Newlands’s Harmonic Wavelets and introduces a new chapter containing new applications of wavelet transforms * Uses knowledge of Fourier transforms, some elementary ideas of Hilbert spaces, and orthonormal systems to develop the theory and applications of wavelet analysis * Offers detailed and clear explanations of every concept and method, accompanied by carefully selected worked examples, with special emphasis given to those topics in which students typically experience difficulty * Includes carefully chosen end-of-chapter exercises directly associated with applications or formulated in terms of the mathematical, physical, and engineering context and provides answers to selected exercises for additional help Mathematicians, physicists, computer engineers, and electrical and mechanical engineers will find Wavelet Transforms and Their Applications an exceptionally complete and accessible text and reference. It is also suitable as a self-study or reference guide for practitioners and professionals.

Symmetries of Islamic Geometrical Patterns

Author: S. J. Abas,Amer Shaker Salman

Publisher: World Scientific

ISBN: 9789810217044

Category: Mathematics

Page: 396

View: 5935

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... a major contribution to the world of science and of particular value to the documention of the culture of Islam. N Gedal ... a masterly account of the way in which art and science are combined into aesthetic beauty by the Islamic geometric designs and motifs which decorate much of the Eastern World. M Evans ... This book will allow readers to travel through time and space, from ancient ornaments to the most modern computer graphics patterns. C. Pickover Ever since the discovery of the existence of seventeen space groups in two dimensions by Fedorov in 1891, it has been speculated that all seventeen could be found in Islamic art. But it is in this book that this remarkable fact is for the first time detailed and analysed, with beautiful illustrations. Rarely is there such a thought-provoking blend of esthetics and geometry with abstraction. C N Yang Geometrical form. Here, mathematics combines with art and exhibits clearly its aesthetic appeal Islamic patterns provide a marvellous illustration of symmetry and Drs. Abas and Salman perform a useful service by taking this as their theme and blending it with ideas on computer graphics. Foreword by Michael Atiyah Abas and Salman have assembled a fascinating collection that combines art, history, culture, science, mathematics and philosophy. Their examples range from a 12th-century minaret in Uzbekistan via the Alhambra in Granada to modern computer graphics of Koranic calligraphy on dodecahedrons and tori. They conclude by speculating on the prospect of creating Islamic patterns in virtual reality, where 'a seeker after unity in science and art would be able to submerge himself or herself in exquisite Alhambras of the mind'.Judging by the evidence presented here, it would be an unforgettable experience. New Scien

A Friendly Guide to Wavelets

Author: Gerald Kaiser

Publisher: Springer Science & Business Media

ISBN: 9780817681111

Category: Mathematics

Page: 300

View: 5548

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This volume is designed as a textbook for an introductory course on wavelet analysis and time-frequency analysis aimed at graduate students or advanced undergraduates in science and engineering. It can also be used as a self-study or reference book by practicing researchers in signal analysis and related areas. Since the expected audience is not presumed to have a high level of mathematical background, much of the needed analytical machinery is developed from the beginning. The only prerequisites for the first eight chapters are matrix theory, Fourier series, and Fourier integral transforms. Each of these chapters ends with a set of straightforward exercises designed to drive home the concepts just covered, and the many graphics should further facilitate absorption.

A Guide to Distribution Theory and Fourier Transforms

Author: Robert S. Strichartz

Publisher: World Scientific

ISBN: 9789812384300

Category: Mathematics

Page: 226

View: 5307

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This important book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book.A Guide to Distribution Theory and Fourier Transforms can serve as a textbook for parts of a course on Applied Analysis or Methods of Mathematical Physics, and in fact it is used that way at Cornell.

Numerical Solution of Partial Differential Equations

Author: T. Meis,U. Marcowitz

Publisher: Springer Science & Business Media

ISBN: 1461258855

Category: Mathematics

Page: 556

View: 9454

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This book is the result of two courses of lectures given at the University of Cologne in Germany in 1974/75. The majority of the students were not familiar with partial differential equations and functional analysis. This explains why Sections 1, 2, 4 and 12 contain some basic material and results from these areas. The three parts of the book are largely independent of each other and can be read separately. Their topics are: initial value problems, boundary value problems, solutions of systems of equations. There is much emphasis on theoretical considerations and they are discussed as thoroughly as the algorithms which are presented in full detail and together with the programs. We believe that theoretical and practical applications are equally important for a genuine understa- ing of numerical mathematics. When writing this book, we had considerable help and many discussions with H. W. Branca, R. Esser, W. Hackbusch and H. Multhei. H. Lehmann, B. Muller, H. J. Niemeyer, U. Schulte and B. Thomas helped with the completion of the programs and with several numerical calculations. Springer-Verlag showed a lot of patience and under standing during the course of the production of the book. We would like to use the occasion of this preface to express our thanks to all those who assisted in our sometimes arduous task.

Tensor Calculus with Applications

translated from Russian by Vladislav V Goldberg

Author: Maks A Akivis

Publisher: World Scientific Publishing Company

ISBN: 981310225X

Category: Science

Page: 380

View: 7834

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This textbook presents the foundations of tensor calculus and the elements of tensor analysis. In addition, the authors consider numerous applications of tensors to geometry, mechanics and physics. While developing tensor calculus, the authors emphasize its relationship with linear algebra. Necessary notions and theorems of linear algebra are introduced and proved in connection with the construction of the apparatus of tensor calculus; prior knowledge is not assumed. For simplicity and to enable the reader to visualize concepts more clearly, all exposition is conducted in three-dimensional space. The principal feature of the book is that the authors use mainly orthogonal tensors, since such tensors are important in applications to physics and engineering. With regard to applications, the authors construct the general theory of second-degree surfaces, study the inertia tensor as well as the stress and strain tensors, and consider some problems of crystallophysics. The last chapter introduces the elements of tensor analysis. All notions introduced in the book, and also the obtained results, are illustrated with numerous examples discussed in the text. Each section of the book presents problems (a total over 300 problems are given). Examples and problems are intended to illustrate, reinforce and deepen the presented material. There are answers to most of the problems, as well as hints and solutions to selected problems at the end of the book.