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Metric Embeddings: Bilipschitz and Coarse Embeddings into Banach Spaces, Mikhail I. Ostrovskii


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Автор: Mikhail I. Ostrovskii
Название:  Metric Embeddings: Bilipschitz and Coarse Embeddings into Banach Spaces
ISBN: 9783119166225
Издательство: Walter de Gruyter
Классификация: ISBN-10: 3119166227
Обложка/Формат: Mixed media product
Страницы: 372
Вес: 0.00 кг.
Дата издания: 26.06.2013
Серия: Mathematics
Язык: English
Читательская аудитория: Professional and scholarly
Ключевые слова: COMPUTERS / Computer Science,MATHEMATICS / Discrete Mathematics,MATHEMATICS / Group Theory,MATHEMATICS / Topology
Поставляется из: Германии
Описание: Embeddings of discrete metric spaces into Banach spaces recently became an important tool in computer science and topology. The book will help readers to enter and to work in this very rapidly developing area having many important connections with different parts of mathematics and computer science. The purpose of the book is to present some of the most important techniques and results, mostly on bilipschitz and coarse embeddings. The topics include embeddability of locally finite metric spaces into Banach spaces is finitely determined, constructions of embeddings, distortion in terms of Poincare inequalities, constructions of families of expanders and of families of graphs with unbounded girth and lower bounds on average degrees, Banach spaces which do not admit coarse embeddings of expanders, structure of metric spaces which are not coarsely embeddable into a Hilbert space, applications of Markov chains to embeddability problem, metric characterizations of properties of Banach spaces, and Lipschitz free spaces.

Hardy Operators, Function Spaces and Embeddings

Автор: David E. Edmunds; William D. Evans
Название: Hardy Operators, Function Spaces and Embeddings
ISBN: 3642060277 ISBN-13(EAN): 9783642060274
Издательство: Springer
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Цена: 88500.00 T
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Описание: Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are not only of considerable intrinsic interest but have for many years proved to be indispensible in the study of partial differential equations and variational problems.

Cross-Lingual Word Embeddings

Автор: Sogaard Anders, Vulic Ivan, Ruder Sebastian
Название: Cross-Lingual Word Embeddings
ISBN: 1681735725 ISBN-13(EAN): 9781681735726
Издательство: Mare Nostrum (Eurospan)
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Цена: 82230.00 T
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Описание:

The majority of natural language processing (NLP) is English language processing, and while there is good language technology support for (standard varieties of) English, support for Albanian, Burmese, or Cebuano-and most other languages-remains limited.

Being able to bridge this digital divide is important for scientific and democratic reasons but also represents an enormous growth potential. A key challenge for this to happen is learning to align basic meaning-bearing units of different languages.

In this book, the authors survey and discuss recent and historical work on supervised and unsupervised learning of such alignments. Specifically, the book focuses on so-called cross-lingual word embeddings. The survey is intended to be systematic, using consistent notation and putting the available methods on comparable form, making it easy to compare wildly different approaches. In so doing, the authors establish previously unreported relations between these methods and are able to present a fast-growing literature in a very compact way. Furthermore, the authors discuss how best to evaluate cross-lingual word embedding methods and survey the resources available for students and researchers interested in this topic.


Cross-Lingual Word Embeddings

Автор: Sogaard Anders, Vulic Ivan, Ruder Sebastian
Название: Cross-Lingual Word Embeddings
ISBN: 1681730634 ISBN-13(EAN): 9781681730639
Издательство: Mare Nostrum (Eurospan)
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Цена: 61910.00 T
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Описание:

The majority of natural language processing (NLP) is English language processing, and while there is good language technology support for (standard varieties of) English, support for Albanian, Burmese, or Cebuano-and most other languages-remains limited.

Being able to bridge this digital divide is important for scientific and democratic reasons but also represents an enormous growth potential. A key challenge for this to happen is learning to align basic meaning-bearing units of different languages.

In this book, the authors survey and discuss recent and historical work on supervised and unsupervised learning of such alignments. Specifically, the book focuses on so-called cross-lingual word embeddings. The survey is intended to be systematic, using consistent notation and putting the available methods on comparable form, making it easy to compare wildly different approaches. In so doing, the authors establish previously unreported relations between these methods and are able to present a fast-growing literature in a very compact way. Furthermore, the authors discuss how best to evaluate cross-lingual word embedding methods and survey the resources available for students and researchers interested in this topic.


Geometry of Semilinear Embeddings: Relations to Graphs and Codes

Автор: Pankov Mark
Название: Geometry of Semilinear Embeddings: Relations to Graphs and Codes
ISBN: 9814651079 ISBN-13(EAN): 9789814651073
Издательство: World Scientific Publishing
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Цена: 82370.00 T
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Описание: This volume covers semilinear embeddings of vector spaces over division rings and the associated mappings of Grassmannians.

Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics

Автор: Mahir Can; Zhenheng Li; Benjamin Steinberg; Qiang
Название: Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics
ISBN: 1493909371 ISBN-13(EAN): 9781493909377
Издательство: Springer
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Цена: 111790.00 T
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Описание: "The Fields Institute for Research in the Mathematical Sciences."

Автор: Masahisa Adachi
Название: Embeddings and Immersions
ISBN: 0821891642 ISBN-13(EAN): 9780821891643
Издательство: Mare Nostrum (Eurospan)
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Цена: 89630.00 T
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Описание: This book covers fundamental techniques in the theory of $C^{\infty }$-imbeddings and $C^{\infty }$-immersions, emphasising clear intuitive understanding and containing many figures and diagrams. Adachi starts with an introduction to the work of Whitney and of Haefliger on $C^{\infty }$-imbeddings and $C^{\infty }$-manifolds. The Smale-Hirsch theorem is presented as a generalisation of the classification of $C^{\infty }$-imbeddings by isotopy and is extended by Gromov's work on the subject, including Gromov's convex integration theory. Finally, as an application of Gromov's work, the author introduces Haefliger's classification theorem of foliations on open manifolds. Also described here is the Adachi's work with Landweber on the integrability of almost complex structures on open manifolds. This book would be an excellent text for upper-division undergraduate or graduate courses.

Embeddings and Extensions in Analysis

Автор: J.H. Wells; L.R. Williams
Название: Embeddings and Extensions in Analysis
ISBN: 3642660398 ISBN-13(EAN): 9783642660399
Издательство: Springer
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Цена: 83850.00 T
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Описание: The object of this book is a presentation of the major results relating to two geometrically inspired problems in analysis. One is that of determining which metric spaces can be isometrically embedded in a Hilbert space or, more generally, P in an L space; the other asks for conditions on a pair of metric spaces which will ensure that every contraction or every Lipschitz-Holder map from a subset of X into Y is extendable to a map of the same type from X into Y. The initial work on isometric embedding was begun by K. Menger 1928] with his metric investigations of Euclidean geometries and continued, in its analytical formulation, by I. J. Schoenberg 1935] in a series of papers of classical elegance. The problem of extending Lipschitz-Holder and contraction maps was first treated by E. J. McShane and M. D. Kirszbraun 1934]. Following a period of relative inactivity, attention was again drawn to these two problems by G. Minty's work on non-linear monotone operators in Hilbert space 1962]; by S. Schonbeck's fundamental work in characterizing those pairs (X, Y) of Banach spaces for which extension of contractions is always possible 1966]; and by the generalization of many of Schoenberg's embedding theorems to the P setting of L spaces by Bretagnolle, Dachuna Castelle and Krivine 1966].

Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics

Автор: Mahir Can; Zhenheng Li; Benjamin Steinberg; Qiang
Название: Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics
ISBN: 1493956000 ISBN-13(EAN): 9781493956005
Издательство: Springer
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Цена: 102480.00 T
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Описание: "The Fields Institute for Research in the Mathematical Sciences."

Differential and Complex Geometry: Origins, Abstractions and Embeddings

Автор: Raymond O. Wells, Jr.
Название: Differential and Complex Geometry: Origins, Abstractions and Embeddings
ISBN: 331958183X ISBN-13(EAN): 9783319581835
Издательство: Springer
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Цена: 111790.00 T
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Описание: Differential and complex geometry are two central areas of mathematics with a long and intertwined history. This book, the first to provide a unified historical perspective of both subjects, explores their origins and developments from the sixteenth to the twentieth century.
Providing a detailed examination of the seminal contributions to differential and complex geometry up to the twentieth century embedding theorems, this monograph includes valuable excerpts from the original documents, including works of Descartes, Fermat, Newton, Euler, Huygens, Gauss, Riemann, Abel, and Nash.
Suitable for beginning graduate students interested in differential, algebraic or complex geometry, this book will also appeal to more experienced readers.

Embedding CSR into Corporate Culture

Автор: Swanson Diane L.
Название: Embedding CSR into Corporate Culture
ISBN: 1137300078 ISBN-13(EAN): 9781137300072
Издательство: Springer
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Цена: 83850.00 T
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Описание: Embedding CSR into Corporate Culture demonstrates that a new frontier for corporate social responsibility is possible in theory and practice. The key idea - discovery leadership - enables corporate managers to deal effectively with problems, issues, and value clashes occurring at the corporation-society interface.

Embedding CSR into Corporate Culture

Автор: D. Swanson
Название: Embedding CSR into Corporate Culture
ISBN: 1349453013 ISBN-13(EAN): 9781349453016
Издательство: Springer
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Цена: 81050.00 T
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Описание: 1. A Call for Socially Responsible Corporate Leadership 2. Images of the Self: Toward a Model of CSR Leadership 3. Corporate Social Performance: The Context for CSR Leadership 4. Leading Socially-Neglectful Alienated Organizations 5. Leading Socially-Attuned, Value Cohesive Organizations 6. The Practice of Value-Attuned Discovery Leadership 7. The Road Ahead For Research and Education


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