Compactness And Contradiction
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Compactness And Contradiction
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Author : Terence Tao
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-03-22
Compactness And Contradiction written by Terence Tao and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-22 with Mathematics categories.
There are many bits and pieces of folklore in mathematics that are passed down from advisor to student, or from collaborator to collaborator, but which are too fuzzy and nonrigorous to be discussed in the formal literature. Traditionally, it was a matter
Nonlinear Problems With Lack Of Compactness
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Author : Giovanni Molica Bisci
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-02-08
Nonlinear Problems With Lack Of Compactness written by Giovanni Molica Bisci and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-08 with Mathematics categories.
This authoritative book presents recent research results on nonlinear problems with lack of compactness. The topics covered include several nonlinear problems in the Euclidean setting as well as variational problems on manifolds. The combination of deep techniques in nonlinear analysis with applications to a variety of problems make this work an essential source of information for researchers and graduate students working in analysis and PDE's.
Compactness And Stability For Nonlinear Elliptic Equations
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Author : Emmanuel Hebey
language : en
Publisher: Erich Schmidt Verlag GmbH & Co. KG
Release Date : 2014
Compactness And Stability For Nonlinear Elliptic Equations written by Emmanuel Hebey and has been published by Erich Schmidt Verlag GmbH & Co. KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Differential equations, Elliptic categories.
The book offers an expanded version of lectures given at ETH Zurich in the framework of a Nachdiplomvorlesung. Compactness and stability for nonlinear elliptic equations in the inhomogeneous context of closed Riemannian manifolds are investigated. This field is presently undergoing great development. The author describes blow-up phenomena and presents the progress made over the past years on the subject, giving an up-to-date description of the new ideas, concepts, methods, and theories in the field. Special attention is devoted to the nonlinear stationary Schrodinger equation and to its critical formulation. Intended to be as self-contained as possible, the book is accessible to a broad audience of readers, including graduate students and researchers.
Compactness On Single Valued Neutrosophic Ideal Topological Spaces
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Author : Fahad Alsharari
language : en
Publisher: Infinite Study
Release Date : 2021-08-01
Compactness On Single Valued Neutrosophic Ideal Topological Spaces written by Fahad Alsharari and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-01 with Mathematics categories.
The theories of r-single-valued neutrosophic compact, r-single-valued neutrosophic ideal compact, r-single-valued neutrosophic quasi H-closed and r-single-valued neutrosophic compact modulo a single-valued neutrosophic ideal ℐ̃ are presented and investigated.
Pseudocompact Topological Spaces
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Author : Michael Hrušák
language : en
Publisher: Springer
Release Date : 2018-07-19
Pseudocompact Topological Spaces written by Michael Hrušák and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-19 with Mathematics categories.
This book, intended for postgraduate students and researchers, presents many results of historical importance on pseudocompact spaces. In 1948, E. Hewitt introduced the concept of pseudocompactness which generalizes a property of compact subsets of the real line. A topological space is pseudocompact if the range of any real-valued, continuous function defined on the space is a bounded subset of the real line. Pseudocompact spaces constitute a natural and fundamental class of objects in General Topology and research into their properties has important repercussions in diverse branches of Mathematics, such as Functional Analysis, Dynamical Systems, Set Theory and Topological-Algebraic structures. The collection of authors of this volume include pioneers in their fields who have written a comprehensive explanation on this subject. In addition, the text examines new lines of research that have been at the forefront of mathematics. There is, as yet, no text that systematically compiles and develops the extensive theory of pseudocompact spaces, making this book an essential asset for anyone in the field of topology.
Spaces Of Dissension
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Author : Julia Lossau
language : en
Publisher: Springer Nature
Release Date : 2020-02-10
Spaces Of Dissension written by Julia Lossau and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-10 with Philosophy categories.
This volume focusses on contradiction as a key concept in the Humanities and Social Sciences. By bringing together theoretical and empirical contributions from a broad disciplinary spectrum, the volume advances research in contradiction and on contradictory phenomena, laying the foundations for a new interdisciplinary field of research: Contradiction Studies. Dealing with linguistic phenomena, urban geographies, business economy, literary writing practices, theory of the social sciences, and language education, the contributions show that contradiction, rather than being a logical exemption in the Aristotelian sense, provides a valuable approach to many fields of socially, culturally, and historically relevant fields of research.
Spectral Theory And Differential Operators
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Author : David Eric Edmunds
language : en
Publisher: Oxford University Press
Release Date : 2018
Spectral Theory And Differential Operators written by David Eric Edmunds and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Mathematics categories.
This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.--
Hilbert S Fifth Problem And Related Topics
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Author : Terence Tao
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-07-18
Hilbert S Fifth Problem And Related Topics written by Terence Tao and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-18 with Mathematics categories.
In the fifth of his famous list of 23 problems, Hilbert asked if every topological group which was locally Euclidean was in fact a Lie group. Through the work of Gleason, Montgomery-Zippin, Yamabe, and others, this question was solved affirmatively; more generally, a satisfactory description of the (mesoscopic) structure of locally compact groups was established. Subsequently, this structure theory was used to prove Gromov's theorem on groups of polynomial growth, and more recently in the work of Hrushovski, Breuillard, Green, and the author on the structure of approximate groups. In this graduate text, all of this material is presented in a unified manner, starting with the analytic structural theory of real Lie groups and Lie algebras (emphasising the role of one-parameter groups and the Baker-Campbell-Hausdorff formula), then presenting a proof of the Gleason-Yamabe structure theorem for locally compact groups (emphasising the role of Gleason metrics), from which the solution to Hilbert's fifth problem follows as a corollary. After reviewing some model-theoretic preliminaries (most notably the theory of ultraproducts), the combinatorial applications of the Gleason-Yamabe theorem to approximate groups and groups of polynomial growth are then given. A large number of relevant exercises and other supplementary material are also provided.
An Invitation To Alexandrov Geometry
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Author : Stephanie Alexander
language : en
Publisher: Springer
Release Date : 2019-05-08
An Invitation To Alexandrov Geometry written by Stephanie Alexander and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-08 with Mathematics categories.
Aimed toward graduate students and research mathematicians, with minimal prerequisites this book provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory. Beginning with an overview of fundamentals, definitions, and conventions, this book quickly moves forward to discuss the Reshetnyak gluing theorem and applies it to the billiards problems. The Hadamard–Cartan globalization theorem is explored and applied to construct exotic aspherical manifolds.
Mathematical Analysis
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Author : Bernd S. W. Schröder
language : en
Publisher: John Wiley & Sons
Release Date : 2008-01-28
Mathematical Analysis written by Bernd S. W. Schröder and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-28 with Mathematics categories.
A self-contained introduction to the fundamentals of mathematical analysis Mathematical Analysis: A Concise Introduction presents the foundations of analysis and illustrates its role in mathematics. By focusing on the essentials, reinforcing learning through exercises, and featuring a unique "learn by doing" approach, the book develops the reader's proof writing skills and establishes fundamental comprehension of analysis that is essential for further exploration of pure and applied mathematics. This book is directly applicable to areas such as differential equations, probability theory, numerical analysis, differential geometry, and functional analysis. Mathematical Analysis is composed of three parts: ?Part One presents the analysis of functions of one variable, including sequences, continuity, differentiation, Riemann integration, series, and the Lebesgue integral. A detailed explanation of proof writing is provided with specific attention devoted to standard proof techniques. To facilitate an efficient transition to more abstract settings, the results for single variable functions are proved using methods that translate to metric spaces. ?Part Two explores the more abstract counterparts of the concepts outlined earlier in the text. The reader is introduced to the fundamental spaces of analysis, including Lp spaces, and the book successfully details how appropriate definitions of integration, continuity, and differentiation lead to a powerful and widely applicable foundation for further study of applied mathematics. The interrelation between measure theory, topology, and differentiation is then examined in the proof of the Multidimensional Substitution Formula. Further areas of coverage in this section include manifolds, Stokes' Theorem, Hilbert spaces, the convergence of Fourier series, and Riesz' Representation Theorem. ?Part Three provides an overview of the motivations for analysis as well as its applications in various subjects. A special focus on ordinary and partial differential equations presents some theoretical and practical challenges that exist in these areas. Topical coverage includes Navier-Stokes equations and the finite element method. Mathematical Analysis: A Concise Introduction includes an extensive index and over 900 exercises ranging in level of difficulty, from conceptual questions and adaptations of proofs to proofs with and without hints. These opportunities for reinforcement, along with the overall concise and well-organized treatment of analysis, make this book essential for readers in upper-undergraduate or beginning graduate mathematics courses who would like to build a solid foundation in analysis for further work in all analysis-based branches of mathematics.
