Download or read book Minimal Sets written by Walter Helbig Gottschalk and published by . This book was released on 1958 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of some of the results, models, and problems of topological dynamics. For simplicity of presentation, attention is mostly confined to flows.
Download or read book Cantor Minimal Systems written by Ian F. Putnam and published by American Mathematical Soc.. This book was released on 2018-05-15 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within the subject of topological dynamics, there has been considerable recent interest in systems where the underlying topological space is a Cantor set. Such systems have an inherently combinatorial nature, and seminal ideas of Anatoly Vershik allowed for a combinatorial model, called the Bratteli-Vershik model, for such systems with no non-trivial closed invariant subsets. This model led to a construction of an ordered abelian group which is an algebraic invariant of the system providing a complete classification of such systems up to orbit equivalence. The goal of this book is to give a statement of this classification result and to develop ideas and techniques leading to it. Rather than being a comprehensive treatment of the area, this book is aimed at students and researchers trying to learn about some surprising connections between dynamics and algebra. The only background material needed is a basic course in group theory and a basic course in general topology.
Download or read book Fluent Forever written by Gabriel Wyner and published by Harmony. This book was released on 2014-08-05 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: NATIONAL BESTSELLER • For anyone who wants to learn a foreign language, this is the method that will finally make the words stick. “A brilliant and thoroughly modern guide to learning new languages.”—Gary Marcus, cognitive psychologist and author of the New York Times bestseller Guitar Zero At thirty years old, Gabriel Wyner speaks six languages fluently. He didn’t learn them in school—who does? Rather, he learned them in the past few years, working on his own and practicing on the subway, using simple techniques and free online resources—and here he wants to show others what he’s discovered. Starting with pronunciation, you’ll learn how to rewire your ears and turn foreign sounds into familiar sounds. You’ll retrain your tongue to produce those sounds accurately, using tricks from opera singers and actors. Next, you’ll begin to tackle words, and connect sounds and spellings to imagery rather than translations, which will enable you to think in a foreign language. And with the help of sophisticated spaced-repetition techniques, you’ll be able to memorize hundreds of words a month in minutes every day. This is brain hacking at its most exciting, taking what we know about neuroscience and linguistics and using it to create the most efficient and enjoyable way to learn a foreign language in the spare minutes of your day.
Download or read book Minimal Flows and Their Extensions written by J. Auslander and published by Elsevier. This book was released on 1988-07-01 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents developments in the abstract theory of topological dynamics, concentrating on the internal structure of minimal flows (actions of groups on compact Hausdorff spaces for which every orbit is dense) and their homomorphisms (continuous equivariant maps). Various classes of minimal flows (equicontinuous, distal, point distal) are intensively studied, and a general structure theorem is obtained. Another theme is the ``universal'' approach - entire classes of minimal flows are studied, rather than flows in isolation. This leads to the consideration of disjointness of flows, which is a kind of independence condition. Among the topics unique to this book are a proof of the Ellis ``joint continuity theorem'', a characterization of the equicontinuous structure relation, and the aforementioned structure theorem for minimal flows.
Download or read book Minimal Surfaces and Functions of Bounded Variation written by Giusti and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of finding minimal surfaces, i. e. of finding the surface of least area among those bounded by a given curve, was one of the first considered after the foundation of the calculus of variations, and is one which received a satis factory solution only in recent years. Called the problem of Plateau, after the blind physicist who did beautiful experiments with soap films and bubbles, it has resisted the efforts of many mathematicians for more than a century. It was only in the thirties that a solution was given to the problem of Plateau in 3-dimensional Euclidean space, with the papers of Douglas [DJ] and Rado [R T1, 2]. The methods of Douglas and Rado were developed and extended in 3-dimensions by several authors, but none of the results was shown to hold even for minimal hypersurfaces in higher dimension, let alone surfaces of higher dimension and codimension. It was not until thirty years later that the problem of Plateau was successfully attacked in its full generality, by several authors using measure-theoretic methods; in particular see De Giorgi [DG1, 2, 4, 5], Reifenberg [RE], Federer and Fleming [FF] and Almgren [AF1, 2]. Federer and Fleming defined a k-dimensional surface in IR" as a k-current, i. e. a continuous linear functional on k-forms. Their method is treated in full detail in the splendid book of Federer [FH 1].
Download or read book Nonlocal Perimeter Curvature and Minimal Surfaces for Measurable Sets written by José M. Mazón and published by Springer. This book was released on 2019-04-10 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the latest developments in the geometry of measurable sets, presenting them in simple, straightforward terms. It addresses nonlocal notions of perimeter and curvature and studies in detail the minimal surfaces associated with them. These notions of nonlocal perimeter and curvature are defined on the basis of a non-singular kernel. Further, when the kernel is appropriately rescaled, they converge toward the classical perimeter and curvature as the rescaling parameter tends to zero. In this way, the usual notions can be recovered by using the nonlocal ones. In addition, nonlocal heat content is studied and an asymptotic expansion is obtained. Given its scope, the book is intended for undergraduate and graduate students, as well as senior researchers interested in analysis and/or geometry.
Download or read book Rough Sets and Current Trends in Computing written by Shusaku Tsumoto and published by Springer. This book was released on 2004-06-16 with total page 871 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years rough set theory has attracted the attention of many researchers and practitioners all over the world, who have contributed essentially to its development and applications. Weareobservingagrowingresearchinterestinthefoundationsofroughsets, including the various logical, mathematical and philosophical aspects of rough sets. Some relationships have already been established between rough sets and other approaches, and also with a wide range of hybrid systems. As a result, rough sets are linked with decision system modeling and analysis of complex systems, fuzzy sets, neural networks, evolutionary computing, data mining and knowledge discovery, pattern recognition, machine learning, and approximate reasoning. In particular, rough sets are used in probabilistic reasoning, granular computing (including information granule calculi based on rough mereology), intelligent control, intelligent agent modeling, identi?cation of autonomous s- tems, and process speci?cation. Methods based on rough set theory alone or in combination with other - proacheshavebeendiscoveredwith awide rangeofapplicationsinsuchareasas: acoustics, bioinformatics, business and ?nance, chemistry, computer engineering (e.g., data compression, digital image processing, digital signal processing, p- allel and distributed computer systems, sensor fusion, fractal engineering), de- sion analysis and systems, economics, electrical engineering (e.g., control, signal analysis, power systems), environmental studies, informatics, medicine, mole- lar biology, musicology, neurology, robotics, social science, software engineering, spatial visualization, Web engineering, and Web mining.
Download or read book Minimal Cooperation and Shared Agency written by Anika Fiebich and published by Springer Nature. This book was released on 2020-06-23 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume examines minimality in cooperation and shared agency from various angles. It features essays written by top scholars in the philosophy of mind and action. Taken together, the essays provide a genuine contribution to the contemporary joint action debate. The main accounts in this debate present sufficient rather than necessary or minimal criteria for there to be cooperation. Much discussion in the debate deals with robust rather than more attenuate and simple cases of cooperation or shared agency. Focusing on such minimal cases, however, may help to explain how cooperation comes into existence and how minimal cooperation interrelates with more complex cases of cooperation. The contributors discuss minimality in cooperation by focusing on particular aspects. For example, they consider how social roles might deliver minimal cooperation constraints or what the minimal contextual criteria are for cooperation to emerge. Readers will find the answers to these and other questions: What is minimally cooperative behavior? By what steps could full members of a society organized by conventions, norms and institutions be constructed from creatures with minimal social skills and cognitive abilities? What do we experience of actions when we act together with a purpose?
Download or read book Formal Methods for Mining Structured Objects written by Gemma C Garriga and published by Springer. This book was released on 2013-02-26 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the field of knowledge discovery, graphs of concepts are an expressive and versatile modeling technique providing ways to reason about information implicit in a set of data. Interesting examples of this can be found under the mathematical theory of formal concept analysis, dedicated to the construction of a lattice of concepts by defining a Galois connection on a binary relationship. This book present such graph of concepts under the more complex case of data that comes in a set of structured objects; e.g. a set of sequences, trees or graphs. Nodes of this graph will represent patterns in the data and edges will correspond to relationships of specificity. From this combinatorial object results are derived such as a full characterization of logical implications and closed partial orders. The results presented in this book are coupled with examples and empirical experiments that illustrate the derived theoretical contributions.
Download or read book Relativistic Quantum Theory of Atoms and Molecules written by Ian P Grant and published by Springer Science & Business Media. This book was released on 2007-04-15 with total page 813 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for physicists and chemists who need to understand the theory of atomic and molecular structure and processes, and who wish to apply the theory to practical problems. As far as practicable, the book provides a self-contained account of the theory of relativistic atomic and molecular structure, based on the accepted formalism of bound-state Quantum Electrodynamics. The author was elected a Fellow of the Royal Society of London in 1992.
Download or read book Transactions on Rough Sets IV written by James F. Peters and published by Springer. This book was released on 2005-11-15 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume IV of the Transactions on Rough Sets (TRS) introduces a number of new advances in the theory and application of rough sets. Rough sets and - proximationspaceswereintroducedmorethan30yearsagobyZdzis lawPawlak. These advances have profound implications in a number of research areas such as the foundations of rough sets, approximate reasoning, arti?cial intelligence, bioinformatics,computationalintelligence, cognitivescience, intelligentsystems, datamining,machineintelligence,andsecurity. Inaddition,itisevidentfromthe papers included in this volume that the foundations and applications of rough sets is a very active research area worldwide. A total of 16 researchers from 7 countries are represented in this volume, namely, Canada, India, Norway, S- den, Poland, Russia and the United States of America. Evidence of the vigor, breadth and depth of research in the theory and applications of rough sets can be found in the 10 articles in this volume. Prof. Pawlak has contributed a treatise on the philosophical underpinnings of rough sets. In this treatise, observations are made about the Cantor notion of a set, antinomies arising from Cantor sets, the problem of vagueness (es- cially, vague (imprecise) concepts), fuzzy sets, rough sets, fuzzy vs. rough sets as well as logic and rough sets. Among the many vistas and research directions suggested by Prof. Pawlak, one of the most fruitful concerns the model for a rough membership function, which was incarnated in many di?erent forms since its introduction by Pawlakand Skowronin 1994. Recall, here, that Prof.
Download or read book Native Listening written by Anne Cutler and published by MIT Press. This book was released on 2012-07-27 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: An argument that the way we listen to speech is shaped by our experience with our native language. Understanding speech in our native tongue seems natural and effortless; listening to speech in a nonnative language is a different experience. In this book, Anne Cutler argues that listening to speech is a process of native listening because so much of it is exquisitely tailored to the requirements of the native language. Her cross-linguistic study (drawing on experimental work in languages that range from English and Dutch to Chinese and Japanese) documents what is universal and what is language specific in the way we listen to spoken language. Cutler describes the formidable range of mental tasks we carry out, all at once, with astonishing speed and accuracy, when we listen. These include evaluating probabilities arising from the structure of the native vocabulary, tracking information to locate the boundaries between words, paying attention to the way the words are pronounced, and assessing not only the sounds of speech but prosodic information that spans sequences of sounds. She describes infant speech perception, the consequences of language-specific specialization for listening to other languages, the flexibility and adaptability of listening (to our native languages), and how language-specificity and universality fit together in our language processing system. Drawing on her four decades of work as a psycholinguist, Cutler documents the recent growth in our knowledge about how spoken-word recognition works and the role of language structure in this process. Her book is a significant contribution to a vibrant and rapidly developing field.
Download or read book Mathematical Programming The State of the Art written by A. Bachem and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the late forties, Mathematical Programming became a scientific discipline in its own right. Since then it has experienced a tremendous growth. Beginning with economic and military applications, it is now among the most important fields of applied mathematics with extensive use in engineering, natural sciences, economics, and biological sciences. The lively activity in this area is demonstrated by the fact that as early as 1949 the first "Symposium on Mathe matical Programming" took place in Chicago. Since then mathematical programmers from all over the world have gath ered at the intfrnational symposia of the Mathematical Programming Society roughly every three years to present their recent research, to exchange ideas with their colleagues and to learn about the latest developments in their own and related fields. In 1982, the XI. International Symposium on Mathematical Programming was held at the University of Bonn, W. Germany, from August 23 to 27. It was organized by the Institut fUr Okonometrie und Operations Re search of the University of Bonn in collaboration with the Sonderforschungs bereich 21 of the Deutsche Forschungsgemeinschaft. This volume constitutes part of the outgrowth of this symposium and docu ments its scientific activities. Part I of the book contains information about the symposium, welcoming addresses, lists of committees and sponsors and a brief review about the Ful kerson Prize and the Dantzig Prize which were awarded during the opening ceremony.
Download or read book Applied Combinatorics written by Alan Tucker and published by Wiley Global Education. This book was released on 2012-04-13 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Linear Algebra in Action written by Harry Dym and published by American Mathematical Society. This book was released on 2023-07-18 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based largely on courses that the author taught at the Feinberg Graduate School of the Weizmann Institute. It conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade. In short, this is material that the author has found to be useful in his own research and wishes that he had been exposed to as a graduate student. Roughly the first quarter of the book reviews the contents of a basic course in linear algebra, plus a little. The remaining chapters treat singular value decompositions, convexity, special classes of matrices, projections, assorted algorithms, and a number of applications. The applications are drawn from vector calculus, numerical analysis, control theory, complex analysis, convex optimization, and functional analysis. In particular, fixed point theorems, extremal problems, best approximations, matrix equations, zero location and eigenvalue location problems, matrices with nonnegative entries, and reproducing kernels are discussed. This new edition differs significantly from the second edition in both content and style. It includes a number of topics that did not appear in the earlier edition and excludes some that did. Moreover, most of the material that has been adapted from the earlier edition has been extensively rewritten and reorganized.
Download or read book Models of ZF Set Theory written by U. Felgner and published by Springer. This book was released on 2006-11-15 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamics with Chaos and Fractals written by Marat Akhmet and published by Springer Nature. This book was released on 2020-01-01 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is concerned with the concepts of chaos and fractals, which are within the scopes of dynamical systems, geometry, measure theory, topology, and numerical analysis during the last several decades. It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. This is the first time in the literature that the description of chaos is initiated from a single motion. Chaos is now placed on the line of oscillations, and therefore, it is a subject of study in the framework of the theories of dynamical systems and differential equations, as in this book. The techniques introduced in the book make it possible to develop continuous and discrete dynamics which admit fractals as points of trajectories as well as orbits themselves. To provide strong arguments for the genericity of chaos in the real and abstract universe, the concept of abstract similarity is suggested.
