Topics In Cyclic Theory
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| Author | : Daniel G. Quillen |
| Publisher | : Cambridge University Press |
| Total Pages | : 331 |
| Release | : 2020-07-09 |
| Genre | : Mathematics |
| ISBN | : 1108859550 |
Noncommutative geometry combines themes from algebra, analysis and geometry and has significant applications to physics. This book focuses on cyclic theory, and is based upon the lecture courses by Daniel G. Quillen at the University of Oxford from 1988–92, which developed his own approach to the subject. The basic definitions, examples and exercises provided here allow non-specialists and students with a background in elementary functional analysis, commutative algebra and differential geometry to get to grips with the subject. Quillen's development of cyclic theory emphasizes analogies between commutative and noncommutative theories, in which he reinterpreted classical results of Hamiltonian mechanics, operator algebras and differential graded algebras into a new formalism. In this book, cyclic theory is developed from motivating examples and background towards general results. Themes covered are relevant to current research, including homomorphisms modulo powers of ideals, traces on noncommutative differential forms, quasi-free algebras and Chern characters on connections.
| Author | : Daniel G. Quillen |
| Publisher | : Cambridge University Press |
| Total Pages | : 331 |
| Release | : 2020-07-09 |
| Genre | : Mathematics |
| ISBN | : 1108479618 |
This accessible introduction for Ph.D. students and non-specialists provides Quillen's unique development of cyclic theory.
| Author | : Roger Penrose |
| Publisher | : Vintage |
| Total Pages | : 307 |
| Release | : 2011-09-06 |
| Genre | : Science |
| ISBN | : 0307596745 |
From Nobel prize-winner Roger Penrose, this groundbreaking book is for anyone "who is interested in the world, how it works, and how it got here" (New York Journal of Books). Penrose presents a new perspective on three of cosmology’s essential questions: What came before the Big Bang? What is the source of order in our universe? And what cosmic future awaits us? He shows how the expected fate of our ever-accelerating and expanding universe—heat death or ultimate entropy—can actually be reinterpreted as the conditions that will begin a new “Big Bang.” He details the basic principles beneath our universe, explaining various standard and non-standard cosmological models, the fundamental role of the cosmic microwave background, the paramount significance of black holes, and other basic building blocks of contemporary physics. Intellectually thrilling and widely accessible, Cycles of Time is a welcome new contribution to our understanding of the universe from one of our greatest mathematicians and thinkers.
| Author | : Stephen J. Puetz |
| Publisher | : |
| Total Pages | : 626 |
| Release | : 2011 |
| Genre | : Science |
| ISBN | : 9781432781330 |
These simple statements hold huge implications about how the universe must operate if it was truly infinite rather than finite, as is commonly thought. In one sense, this book, Universal Cycle Theory, may seem radical because it postulates that the universe operates in ways that are dramatically different from what we are taught. Yet, this new theory is conventional in the sense that it closely conforms to virtually all existing laws, equations, and observations. There are only two elements that make the Universal Cycle Theory radical cycles and infinity. Other than that, much of what you read in this book will seem familiar and conventional. Cycles are crucial because they are reflections of how matter behaves in an infinite universe: as vortices and waves. A vortex forms when matter rotates, producing circular cycles. A wave forms when colliding matter compresses and decompresses, producing linear cycles. Infinity is crucial because it explains the extent and structure of the universe. We assume that matter is infinitely divisible in the microscopic direction and infinitely integrable in the macroscopic direction. We assume that time was infinite in the past and will be infinite in the future. This concept of infinity is unique, having never been employed in a model of the universe before. It resolves many of the paradoxes and contradictions currently riddling physics and cosmology.
| Author | : Jean-Louis Loday |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 467 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 3662217392 |
This book is a comprehensive study of cyclic homology theory together with its relationship with Hochschild homology, de Rham cohomology, S1 equivariant homology, the Chern character, Lie algebra homology, algebraic K-theory and non-commutative differential geometry. Though conceived as a basic reference on the subject, many parts of this book are accessible to graduate students.
| Author | : Elly van Gelderen |
| Publisher | : John Benjamins Publishing Company |
| Total Pages | : 439 |
| Release | : 2016-03-09 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 902726743X |
This book presents new data and additional questions regarding the linguistic cycle. The topics discussed are the pronoun, negative, negative existential, analytic-synthetic, distributive, determiner, degree, and future/modal cycles. The papers raise questions about the length of time that cycles take, the interactions between different cycles, the typical stages and their stability, and the areal factors influencing cycles. The languages and language families that are considered in depth are Central Pomo, Cherokee, Chinese, English, French, Gbe, German, Hmong-Mien, Maipurean, Mayan, Mohawk, Mon-Khmer, Niger-Congo, Nupod, Quechuan, Sino-Tibetan, Tai-Kadai , Tuscarora, Ute, and Yoruboid. One paper covers several of the world’s language families. Cyclical change connects linguists working in various frameworks because it is exciting to find a reason behind this fascinating phenomenon.
| Author | : Isaac Woungang |
| Publisher | : World Scientific |
| Total Pages | : 725 |
| Release | : 2010 |
| Genre | : Computers |
| ISBN | : 9812837167 |
The last few years have witnessed rapid advancements in information and coding theory research and applications. This book provides a comprehensive guide to selected topics, both ongoing and emerging, in information and coding theory. Consisting of contributions from well-known and high-profile researchers in their respective specialties, topics that are covered include source coding; channel capacity; linear complexity; code construction, existence and analysis; bounds on codes and designs; space-time coding; LDPC codes; and codes and cryptography.All of the chapters are integrated in a manner that renders the book as a supplementary reference volume or textbook for use in both undergraduate and graduate courses on information and coding theory. As such, it will be a valuable text for students at both undergraduate and graduate levels as well as instructors, researchers, engineers, and practitioners in these fields.Supporting Powerpoint Slides are available upon request for all instructors who adopt this book as a course text.
| Author | : Elly van Gelderen |
| Publisher | : John Benjamins Publishing |
| Total Pages | : 344 |
| Release | : 2009 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 9027255296 |
Linguistic Cycles are ever present in language change and involve a phrase or word that gradually disappears and is replaced by a new linguistic item. The most well-known cycles involve negatives, where an initial single negative, such as "not, " is reinforced by another negative, such as "no thing," and subjects, where full pronouns are reanalyzed as endings on the verb. This book presents new data and insights on the well-known cyclical changes as well as on less well-known ones, such as the preposition, auxiliary, copula, modal, and complementation cycles. Part I covers the negative cycle with chapters looking in great detail at the steps that are typical in this cycle. Part II focuses on pronouns, auxiliaries, and the left periphery. Part III includes work on modals, prepositions, and complementation. The book ends with a psycholinguistic chapter. This book brings together linguists from a variety of theoretical frameworks and contributes to new directions in work on language change.
| Author | : Titus Lucretius Carus |
| Publisher | : Courier Corporation |
| Total Pages | : 262 |
| Release | : 2004-01-01 |
| Genre | : Philosophy |
| ISBN | : 9780486434469 |
The Roman philosopher's didactic poem in 6 parts, De Rerum Natura — On the Nature of Things — theorizes that natural causes are the forces behind earthly phenomena and dismisses divine intervention. Derived from the philosophical materialism of the Greeks, Lucretius' work remains the primary source for contemporary knowledge of Epicurean thought.
| Author | : Paul J. Steinhardt |
| Publisher | : Crown |
| Total Pages | : 306 |
| Release | : 2007-05-29 |
| Genre | : Science |
| ISBN | : 0385523114 |
Two world-renowned scientists present an audacious new vision of the cosmos that “steals the thunder from the Big Bang theory.” —Wall Street Journal The Big Bang theory—widely regarded as the leading explanation for the origin of the universe—posits that space and time sprang into being about 14 billion years ago in a hot, expanding fireball of nearly infinite density. Over the last three decades the theory has been repeatedly revised to address such issues as how galaxies and stars first formed and why the expansion of the universe is speeding up today. Furthermore, an explanation has yet to be found for what caused the Big Bang in the first place. In Endless Universe, Paul J. Steinhardt and Neil Turok, both distinguished theoretical physicists, present a bold new cosmology. Steinhardt and Turok “contend that what we think of as the moment of creation was simply part of an infinite cycle of titanic collisions between our universe and a parallel world” (Discover). They recount the remarkable developments in astronomy, particle physics, and superstring theory that form the basis for their groundbreaking “Cyclic Universe” theory. According to this theory, the Big Bang was not the beginning of time but the bridge to a past filled with endlessly repeating cycles of evolution, each accompanied by the creation of new matter and the formation of new galaxies, stars, and planets. Endless Universe provides answers to longstanding problems with the Big Bang model, while offering a provocative new view of both the past and the future of the cosmos. It is a “theory that could solve the cosmic mystery” (USA Today).
