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Theory Of Dimensioning
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Book Synopsis Theory of Dimensioning by : Vijay Srinivasan
Download or read book Theory of Dimensioning written by Vijay Srinivasan and published by CRC Press. This book was released on 2004 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a theory of dimensioning synthesized from several areas of geometry, starting from the works of Euclid and culminating in some recent results in classification of continuous symmetry groups. Features numerous examples and illustrations for better understanding of concepts.
Book Synopsis Dimension Theory by : Michael G. Charalambous
Download or read book Dimension Theory written by Michael G. Charalambous and published by Springer Nature. This book was released on 2019-10-08 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the fundamental results of the dimension theory of metrizable spaces, especially in the separable case. Its distinctive feature is the emphasis on the negative results for more general spaces, presenting a readable account of numerous counterexamples to well-known conjectures that have not been discussed in existing books. Moreover, it includes three new general methods for constructing spaces: Mrowka's psi-spaces, van Douwen's technique of assigning limit points to carefully selected sequences, and Fedorchuk's method of resolutions. Accessible to readers familiar with the standard facts of general topology, the book is written in a reader-friendly style suitable for self-study. It contains enough material for one or more graduate courses in dimension theory and/or general topology. More than half of the contents do not appear in existing books, making it also a good reference for libraries and researchers.
Book Synopsis Dimension Theory in Dynamical Systems by : Yakov B. Pesin
Download or read book Dimension Theory in Dynamical Systems written by Yakov B. Pesin and published by University of Chicago Press. This book was released on 2008-04-15 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principles of symmetry and self-similarity structure nature's most beautiful creations. For example, they are expressed in fractals, famous for their beautiful but complicated geometric structure, which is the subject of study in dimension theory. And in dynamics the presence of invariant fractals often results in unstable "turbulent-like" motions and is associated with "chaotic" behavior. In this book, Yakov Pesin introduces a new area of research that has recently appeared in the interface between dimension theory and the theory of dynamical systems. Focusing on invariant fractals and their influence on stochastic properties of systems, Pesin provides a comprehensive and systematic treatment of modern dimension theory in dynamical systems, summarizes the current state of research, and describes the most important accomplishments of this field. Pesin's synthesis of these subjects of broad current research interest will be appreciated both by advanced mathematicians and by a wide range of scientists who depend upon mathematical modeling of dynamical processes.
Book Synopsis Modern Dimension Theory by : Jun-Iti Nagata
Download or read book Modern Dimension Theory written by Jun-Iti Nagata and published by Elsevier. This book was released on 2014-05-12 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bibliotheca Mathematica, Volume 6: Modern Dimension Theory provides a brief account of dimension theory as it has been developed since 1941, including the principal results of the classical theory for separable metric spaces. This book discusses the decomposition theorem, Baire's zero-dimensional spaces, dimension of separable metric spaces, and characterization of dimension by a sequence of coverings. The imbedding of countable-dimensional spaces, sum theorem for strong inductive dimension, and cohomology group of a topological space are also elaborated. This text likewise covers the uniformly zero-dimensional mappings, theorems in euclidean space, transfinite inductive dimension, and dimension of non-metrizable spaces. This volume is recommended to students and specialists researching on dimension theory.
Book Synopsis Dimensions of Ring Theory by : C. Nastasescu
Download or read book Dimensions of Ring Theory written by C. Nastasescu and published by Springer Science & Business Media. This book was released on 1987-04-30 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Gad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of s9phistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Book Synopsis General Topology I by : A.V. Arkhangel'skii
Download or read book General Topology I written by A.V. Arkhangel'skii and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of the encyclopaedia volumes devoted to general topology. It has two parts. The first outlines the basic concepts and constructions of general topology, including several topics which have not previously been covered in English language texts. The second part presents a survey of dimension theory, from the very beginnings to the most important recent developments. The principal ideas and methods are treated in detail, and the main results are provided with sketches of proofs. The authors have suceeded admirably in the difficult task of writing a book which will not only be accessible to the general scientist and the undergraduate, but will also appeal to the professional mathematician. The authors' efforts to detail the relationship between more specialized topics and the central themes of topology give the book a broad scholarly appeal which far transcends narrow disciplinary lines.
Book Synopsis Conformal Dimension by : John M. Mackay
Download or read book Conformal Dimension written by John M. Mackay and published by American Mathematical Soc.. This book was released on 2010 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conformal dimension measures the extent to which the Hausdorff dimension of a metric space can be lowered by quasisymmetric deformations. Introduced by Pansu in 1989, this concept has proved extremely fruitful in a diverse range of areas, including geometric function theory, conformal dynamics, and geometric group theory. This survey leads the reader from the definitions and basic theory through to active research applications in geometric function theory, Gromov hyperbolic geometry, and the dynamics of rational maps, amongst other areas. It reviews the theory of dimension in metric spaces and of deformations of metric spaces. It summarizes the basic tools for estimating conformal dimension and illustrates their application to concrete problems of independent interest. Numerous examples and proofs are provided. Working from basic definitions through to current research areas, this book can be used as a guide for graduate students interested in this field, or as a helpful survey for experts. Background needed for a potential reader of the book consists of a working knowledge of real and complex analysis on the level of first- and second-year graduate courses.
Book Synopsis The Theory of Gauge Fields in Four Dimensions by : H. Blaine Lawson
Download or read book The Theory of Gauge Fields in Four Dimensions written by H. Blaine Lawson and published by American Mathematical Soc.. This book was released on 1985 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an examination of the work of Simon Donaldson. This book offers foundation work in gauge theory (Uhlenbeck, Taubes, Atiyah, Hitchin, Singer, et al.) which underlies Donaldson's work. It is suitable for geometric topologists and differential geometers.
Book Synopsis Thermodynamic Formalism and Applications to Dimension Theory by : Luis Barreira
Download or read book Thermodynamic Formalism and Applications to Dimension Theory written by Luis Barreira and published by Springer Science & Business Media. This book was released on 2011-08-24 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained monograph presents a unified exposition of the thermodynamic formalism and some of its main extensions, with emphasis on the relation to dimension theory and multifractal analysis of dynamical systems. In particular, the book considers three different flavors of the thermodynamic formalism, namely nonadditive, subadditive, and almost additive, and provides a detailed discussion of some of the most significant results in the area, some of them quite recent. It also includes a discussion of the most substantial applications of these flavors of the thermodynamic formalism to dimension theory and multifractal analysis of dynamical systems.
Book Synopsis Theory of Dimensions, Finite and Infinite by : Ryszard Engelking
Download or read book Theory of Dimensions, Finite and Infinite written by Ryszard Engelking and published by . This book was released on 1995 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Function Theory in Higher Dimension by : Filippo Bracci
Download or read book Geometric Function Theory in Higher Dimension written by Filippo Bracci and published by Springer. This book was released on 2018-03-24 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book collects the most relevant outcomes from the INdAM Workshop “Geometric Function Theory in Higher Dimension” held in Cortona on September 5-9, 2016. The Workshop was mainly devoted to discussions of basic open problems in the area, and this volume follows the same line. In particular, it offers a selection of original contributions on Loewner theory in one and higher dimensions, semigroups theory, iteration theory and related topics. Written by experts in geometric function theory in one and several complex variables, it focuses on new research frontiers in this area and on challenging open problems. The book is intended for graduate students and researchers working in complex analysis, several complex variables and geometric function theory.
Book Synopsis Topics in Groups and Geometry by : Tullio Ceccherini-Silberstein
Download or read book Topics in Groups and Geometry written by Tullio Ceccherini-Silberstein and published by Springer Nature. This book was released on 2022-01-01 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.
Book Synopsis Ergodic Theory, Hyperbolic Dynamics and Dimension Theory by : Luís Barreira
Download or read book Ergodic Theory, Hyperbolic Dynamics and Dimension Theory written by Luís Barreira and published by Springer Science & Business Media. This book was released on 2012-04-28 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last two decades, the dimension theory of dynamical systems has progressively developed into an independent and extremely active field of research. The main aim of this volume is to offer a unified, self-contained introduction to the interplay of these three main areas of research: ergodic theory, hyperbolic dynamics, and dimension theory. It starts with the basic notions of the first two topics and ends with a sufficiently high-level introduction to the third. Furthermore, it includes an introduction to the thermodynamic formalism, which is an important tool in dimension theory. The volume is primarily intended for graduate students interested in dynamical systems, as well as researchers in other areas who wish to learn about ergodic theory, thermodynamic formalism, or dimension theory of hyperbolic dynamics at an intermediate level in a sufficiently detailed manner. In particular, it can be used as a basis for graduate courses on any of these three subjects. The text can also be used for self-study: it is self-contained, and with the exception of some well-known basic facts from other areas, all statements include detailed proofs.
Book Synopsis String Theory For Dummies by : Andrew Zimmerman Jones
Download or read book String Theory For Dummies written by Andrew Zimmerman Jones and published by John Wiley & Sons. This book was released on 2009-11-16 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear, plain-English guide to this complex scientific theory String theory is the hottest topic in physics right now, with books on the subject (pro and con) flying out of the stores. String Theory For Dummies offers an accessible introduction to this highly mathematical "theory of everything," which posits ten or more dimensions in an attempt to explain the basic nature of matter and energy. Written for both students and people interested in science, this guide explains concepts, discusses the string theory's hypotheses and predictions, and presents the math in an approachable manner. It features in-depth examples and an easy-to-understand style so that readers can understand this controversial, cutting-edge theory.
Download or read book Galileo Unbound written by David D. Nolte and published by Oxford University Press. This book was released on 2018-07-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.
Book Synopsis The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory by : Brian Greene
Download or read book The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory written by Brian Greene and published by W. W. Norton & Company. This book was released on 2003-09-30 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces the superstring theory that attempts to unite general relativity and quantum mechanics.
Book Synopsis The World in Eleven Dimensions by : M.J Duff
Download or read book The World in Eleven Dimensions written by M.J Duff and published by CRC Press. This book was released on 1999-01-01 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified theory embracing all physical phenomena is a major goal of theoretical physics. In the early 1980s, many physicists looked to eleven-dimensional supergravity in the hope that it might provide that elusive superunified theory. In 1984 supergravity was knocked off its pedestal by ten-dimensional superstrings, one-dimensional objects whose v
