Quanta of Maths


Book Description

The work of Alain Connes has cut a wide swath across several areas of mathematics and physics. Reflecting its broad spectrum and profound impact on the contemporary mathematical landscape, this collection of articles covers a wealth of topics at the forefront of research in operator algebras, analysis, noncommutative geometry, topology, number theory and physics. Specific themes covered by the articles are as follows: entropy in operator algebras, regular $C^*$-algebras of integral domains, properly infinite $C^*$-algebras, representations of free groups and 1-cohomology, Leibniz seminorms and quantum metric spaces; von Neumann algebras, fundamental Group of $\mathrm{II}_1$ factors, subfactors and planar algebras; Baum-Connes conjecture and property T, equivariant K-homology, Hermitian K-theory; cyclic cohomology, local index formula and twisted spectral triples, tangent groupoid and the index theorem; noncommutative geometry and space-time, spectral action principle, quantum gravity, noncommutative ADHM and instantons, non-compact spectral triples of finite volume, noncommutative coordinate algebras; Hopf algebras, Vinberg algebras, renormalization and combinatorics, motivic renormalization and singularities; cyclotomy and analytic geometry over $F_1$, quantum modular forms; differential K-theory, cyclic theory and S-cohomology.




Euler's Gem


Book Description

Leonhard Euler's polyhedron formula describes the structure of many objects--from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea. From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V - E + F =2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.




Understanding Electric Power Systems


Book Description

A COMPREHENSIVE LOOK IN LAYMAN'S TERMS AT THE MANY ASPECTS OF THE PROVISION OF ELECTRIC POWER, BY TWO VETERAN EXECUTIVES AND RESPECTED EXPERTS Technological advances and changes in government policy and regulation have altered the electric power industry in recent years and will continue to impact it for quite some time. Fully updated with the latest changes to regulation, structure, and technology, this new edition of Understanding Electric Power Systems offers a real-world view of the industry, explaining how it operates, how it is structured, and how electricity is regulated and priced. It includes extensive references for the reader and will be especially useful to lawyers, government officials, regulators, engineers, and students, as well as the general public. The book explains the physical functioning of electric power systems, the electric power business in today's environment, and the related institutions, including recent changes in the roles of the Federal Energy Regulatory Commission and the North American Reliability Company. Significant changes that are affecting the industry are covered in this new edition, including: The expanded role of the federal government in the planning and operation of the nation's electric utilities New energy laws and a large number of FERC regulations implementing these laws Concerns over global warming and potential impacts on the electric industry Pressures for expansion of the electric grid and the implementation of "smart-grid" technologies The growing importance of various energy-storage technologies and renewable energy sources New nuclear generation technologies The 2009 economic stimulus package




Protective Relaying for Power Generation Systems


Book Description

Power outages have considerable social and economic impacts, and effective protection schemes are crucial to avoiding them. While most textbooks focus on the transmission and distribution aspects of protective relays, Protective Relaying for Power Generation Systems is the first to focus on protection of motors and generators from a power generation perspective. It also includes workbook constructions that allow students to perform protection-related calculations in Mathcad® and Excel®. This text provides both a general overview and in-depth discussion of each topic, making it easy to tailor the material to students' needs. It also covers topics not found in other texts on the subject, including detailed time decrement generator fault calculations and minimum excitation limit. The author clearly explains the potential for damage and damaging mechanisms related to each protection function and includes thorough derivations of complex system interactions. Such derivations underlie the various rule-of-thumb setting criteria, provide insight into why the rules-of-thumb work and when they are not appropriate, and are useful for post-incident analysis. The book's flexible approach combines theoretical discussions with example settings that offer quick how-to information. Protective Relaying for Power Generation Systems integrates fundamental knowledge with practical tools to ensure students have a thorough understanding of protection schemes and issues that arise during or after abnormal operation.




Handbook of Electrical Design Details


Book Description

A COMPREHENSIVE SOURCE OF TECHNICAL DETAILS ON ELECTRICALPOWER FROM GENERATION TO PRACTICAL APPLICATIONS Reliable, low-cost electric power is a fundamental requirement for modern society, making possible such vital services as lighting, HVAC, transportation, communication, and data processing, in addition to driving motors of all sizes. A mainstay of industrial productivity and economic prosperity, it is also essential for safeguarding human life and health. This handbook is a valuable information resource on electric power for everyone from technical professionals to students and laypeople. This compact, user-friendly edition updates and expands on the earlier edition. Its core content of power generation, distribution, lighting, wiring, motors, and project planning has been supplemented by new topics: * CAD for preparing electrical drawings and estimates * Basic switch and receptacle circuit wiring * Structured wiring for multimedia * Swimming pool and low-voltage lighting * Electrical surge protection An easy-to-read style makes complex topics understandable. It’s a must-have reference for those with a need or desire to get up to speed on the entire subject of electric power or just familiarize themselves with the latest advances--regardless of their formal education or training. Reader-helpful features in this edition include: * Up-front chapter summaries to save time in finding topics of interest. * References to related articles in the National Electrical Code. * A bibliography identifying additional sources for digging deeper. * Approximately 300 illustrations




The Calculus of Friendship


Book Description

The Calculus of Friendship is the story of an extraordinary connection between a teacher and a student, as chronicled through more than thirty years of letters between them. What makes their relationship unique is that it is based almost entirely on a shared love of calculus. For them, calculus is more than a branch of mathematics; it is a game they love playing together, a constant when all else is in flux. The teacher goes from the prime of his career to retirement, competes in whitewater kayaking at the international level, and loses a son. The student matures from high school math whiz to Ivy League professor, suffers the sudden death of a parent, and blunders into a marriage destined to fail. Yet through it all they take refuge in the haven of calculus--until a day comes when calculus is no longer enough. Like calculus itself, The Calculus of Friendship is an exploration of change. It's about the transformation that takes place in a student's heart, as he and his teacher reverse roles, as they age, as they are buffeted by life itself. Written by a renowned teacher and communicator of mathematics, The Calculus of Friendship is warm, intimate, and deeply moving. The most inspiring ideas of calculus, differential equations, and chaos theory are explained through metaphors, images, and anecdotes in a way that all readers will find beautiful, and even poignant. Math enthusiasts, from high school students to professionals, will delight in the offbeat problems and lucid explanations in the letters. For anyone whose life has been changed by a mentor, The Calculus of Friendship will be an unforgettable journey.




Practical Power System Protection


Book Description

Designed to increase understanding on a practical and theoretical basis, this invaluable resource provides engineers, plant operators, electricians and technicians with a thorough grounding in the principles and practicalities behind power system protection. Coverage of the fundamental knowledge needed to specify, use and maintain power protection systems is included, helping readers to increase plant efficiency, performance and safety. Consideration is also given to the practical techniques and engineering challenges encountered on a day-to-day basis, making this an essential resource for all.




Electrical Power Engineering Reference & Applications Handbook


Book Description

SOME UNIQUE FEATURES Special thrust on energy conservation, pollution control and space saving in consonance with the latest global requirements • Special Coverage on earthquake engineering and tsunami Seismic testing of critical machines . In all there are 32 Chapters and 2 Appendices. Each chapter is very interesting and full of rare Information . The book contains 5 parts and each part is a mini-encyclopedia on the subjects covered • Many topics are research work of the author and may have rare information not available in most works available in the market. Tables of all relevant and equivalent Standards IEC, BS, ANSI, NEMA, IEEE and IS at the end of each chapter is a rare feature APPLICATIONS OF THE HANDBOOK For professionals and practising engineers: As a reference handbook for all professionals and practising engineers associated with design, engineering, production, quality assurance, protection and testing. • Project engineering, project design and project Implementation A very useful book for every industry for selection, Installation and maintenance of electrical machines. . For practising engineers. It would be like keeping a gospel by their sides. For Inhouse training programmes: . Unique handbook for inhouse training courses for Industries, power generating, transmission and distribution organizations For students and research scholars : As a reference textbook for all electrical engineering students in the classrooms and during practical training. It can bridge the gap between the theory of the classroom and the practice in the field. A highly recommended book for all engineering colleges worldwide, right from 1st year through final year. It will prove to be a good guide during higher studies and research activities Subjects like Earthquake Engineering, Intelligent Switchgears, SCADA Power Systems, Surges. Temporary Over Voltage, Surge Protection, Reactive Power Control and Bus Systems etc. are some pertinent topics that can form the basis of their higher studies and research work . The book shall help in technological and product development and give a fresh Impetus to R&D.




Randomness and Recurrence in Dynamical Systems: A Real Analysis Approach


Book Description

Randomness and Recurrence in Dynamical Systems aims to bridge a gap between undergraduate teaching and the research level in mathematical analysis. It makes ideas on averaging, randomness, and recurrence, which traditionally require measure theory, accessible at the undergraduate and lower graduate level. The author develops new techniques of proof and adapts known proofs to make the material accessible to students with only a background in elementary real analysis. Over 60 figures are used to explain proofs, provide alternative viewpoints and elaborate on the main text. The book explains further developments in terms of measure theory. The results are presented in the context of dynamical systems, and the quantitative results are related to the underlying qualitative phenomena—chaos, randomness, recurrence and order. The final part of the book introduces and motivates measure theory and the notion of a measurable set, and describes the relationship of Birkhoff's Individual Ergodic Theorem to the preceding ideas. Developments in other dynamical systems are indicated, in particular Lévy's result on the frequency of occurence of a given digit in the partial fractions expansion of a number.