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Maximal Subellipticity
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Book Synopsis Maximal Subellipticity by : Brian Street
Download or read book Maximal Subellipticity written by Brian Street and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-07-03 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maximally subelliptic partial differential equations (PDEs) are a far-reaching generalization of elliptic PDEs. Elliptic PDEs hold a special place: sharp results are known for general linear and even fully nonlinear elliptic PDEs. Over the past half-century, important results for elliptic PDEs have been generalized to maximally subelliptic PDEs. This text presents this theory and generalizes the sharp, interior regularity theory for general linear and fully nonlinear elliptic PDEs to the maximally subelliptic setting.
Book Synopsis An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem by : Luca Capogna
Download or read book An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem written by Luca Capogna and published by Springer Science & Business Media. This book was released on 2007-08-08 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an up-to-date account of progress on Pansu's celebrated problem on the sub-Riemannian isoperimetric profile of the Heisenberg group. It also serves as an introduction to the general field of sub-Riemannian geometric analysis. It develops the methods and tools of sub-Riemannian differential geometry, nonsmooth analysis, and geometric measure theory suitable for attacks on Pansu's problem.
Book Synopsis Partial Differential Equations by : Rainer H. Picard
Download or read book Partial Differential Equations written by Rainer H. Picard and published by Walter de Gruyter. This book was released on 2011 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev Lattice structure, a simple extension of the well established notion of a chain (or scale) of Hilbert spaces. The focus on a Hilbert space (rather than an apparently more general Banach space) setting is not a severe constraint, but rather a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential equations. In contrast to other texts on partial differential equations which consider either specific types of partial differential equations or apply a collection of tools for solving a variety of partial differential equations, this book takes a more global point of view by focussing on the issues involved in determining the appropriate functional analytic setting in which a solution theory can naturally be developed. Applications to many areas of mathematical physics are presented. The book aims to be a largely self-contained. Full proofs to all but the most straightforward results are provided, keeping to a minimum references to other literature for essential material. It is therefore highly suitable as a resource for graduate courses and for researchers, who will find new results for particular evolutionary system from mathematical physics.
Download or read book Mathematical Reviews written by and published by . This book was released on 2005-06 with total page 1108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Gibbs Measures and Phase Transitions by : Hans-Otto Georgii
Download or read book Gibbs Measures and Phase Transitions written by Hans-Otto Georgii and published by Walter de Gruyter. This book was released on 2011-05-31 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is much more than an introduction to the subject of its title. It covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics and as an up to date reference in its chosen topics it is a work of outstanding scholarship. It is in fact one of the author's stated aims that this comprehensive monograph should serve both as an introductory text and as a reference for the expert. In its latter function it informs the reader about the state of the art in several directions. It is introductory in the sense that it does not assume any prior knowledge of statistical mechanics and is accessible to a general readership of mathematicians with a basic knowledge of measure theory and probability. As such it should contribute considerably to the further growth of the already lively interest in statistical mechanics on the part of probabilists and other mathematicians." Fredos Papangelou, Zentralblatt MATH The second edition has been extended by a new section on large deviations and some comments on the more recent developments in the area.
Book Synopsis Reviews in Partial Differential Equations, 1980-86, as Printed in Mathematical Reviews by :
Download or read book Reviews in Partial Differential Equations, 1980-86, as Printed in Mathematical Reviews written by and published by . This book was released on 1988 with total page 832 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integral Representation Theory by : Jaroslav Lukeš
Download or read book Integral Representation Theory written by Jaroslav Lukeš and published by Walter de Gruyter. This book was released on 2010 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the state of the art of convexity, with an emphasis to integral representation. The exposition is focused on Choquet's theory of function spaces with a link to compact convex sets. An important feature of the book is an interplay between various mathematical subjects, such as functional analysis, measure theory, descriptive set theory, Banach spaces theory and potential theory. A substantial part of the material is of fairly recent origin and many results appear in the book form for the first time. The text is self-contained and covers a wide range of applications. From the contents: Geometry of convex sets Choquet theory of function spaces Affine functions on compact convex sets Perfect classes of functions and representation of affine functions Simplicial function spaces Choquet's theory of function cones Topologies on boundaries Several results on function spaces and compact convex sets Continuous and measurable selectors Construction of function spaces Function spaces in potential theory and Dirichlet problem Applications
Book Synopsis Conceptual Design of Crystallization Processes by : Christianto Wibowo
Download or read book Conceptual Design of Crystallization Processes written by Christianto Wibowo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-11-23 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents, in a unified manner, various crystallization design methods. It discusses in detail the geometric framework for representing complex phase behavior involving multiple solutes, enantiomers, hydrates, compounds, polymorphs, and solid solutions through visualization of high-dimensional phase diagrams. It also describes how the impact of transport processes is accounted for using kinetically controlled process paths.
Book Synopsis Quantum Invariants of Knots and 3-Manifolds by : Vladimir G. Turaev
Download or read book Quantum Invariants of Knots and 3-Manifolds written by Vladimir G. Turaev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-07-11 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to the strong appeal and wide use of this monograph, it is now available in its third revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups. The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space. This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. Contents: Invariants of graphs in Euclidean 3-space and of closed 3-manifolds Foundations of topological quantum field theory Three-dimensional topological quantum field theory Two-dimensional modular functors 6j-symbols Simplicial state sums on 3-manifolds Shadows of manifolds and state sums on shadows Constructions of modular categories
Book Synopsis Partial Differential Equations by : Bogdan Bojarski
Download or read book Partial Differential Equations written by Bogdan Bojarski and published by . This book was released on 1992 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book General Topology written by Tom Richmond and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-07-06 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first half of the book provides an introduction to general topology, with ample space given to exercises and carefully selected applications. The second half of the text includes topics in asymmetric topology, a field motivated by applications in computer science. Recurring themes include the interactions of topology with order theory and mathematics designed to model loss-of-resolution situations.
Book Synopsis Introduction to Topology by : Min Yan
Download or read book Introduction to Topology written by Min Yan and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-02-22 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to give a broad introduction of topology to undergraduate students. It covers the most important and useful parts of the point-set as well as the combinatorial topology. The development of the material is from simple to complex, concrete to abstract, and appeals to the intuition of readers. Attention is also paid to how topology is actually used in the other fields of mathematics. Over 150 illustrations, 160 examples and 600 exercises will help readers to practice and fully understand the subject. Contents: Set and Map Metric Space Graph Topology Topological Concepts Complex Topological Properties Surface Topics in Point Set Topology Index
Book Synopsis Metric Embeddings by : Mikhail I. Ostrovskii
Download or read book Metric Embeddings written by Mikhail I. Ostrovskii and published by Walter de Gruyter. This book was released on 2013-06-26 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Embeddings of discrete metric spaces into Banach spaces recently became an important tool in computer science and topology. 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: (1) Embeddability of locally finite metric spaces into Banach spaces is finitely determined; (2) Constructions of embeddings; (3) Distortion in terms of Poincaré inequalities; (4) Constructions of families of expanders and of families of graphs with unbounded girth and lower bounds on average degrees; (5) Banach spaces which do not admit coarse embeddings of expanders; (6) Structure of metric spaces which are not coarsely embeddable into a Hilbert space; (7) Applications of Markov chains to embeddability problems; (8) Metric characterizations of properties of Banach spaces; (9) Lipschitz free spaces. Substantial part of the book is devoted to a detailed presentation of relevant results of Banach space theory and graph theory. The final chapter contains a list of open problems. Extensive bibliography is also included. Each chapter, except the open problems chapter, contains exercises and a notes and remarks section containing references, discussion of related results, and suggestions for further reading. The book will help readers to enter and to work in a very rapidly developing area having many important connections with different parts of mathematics and computer science.
Book Synopsis Algebraic Combinatorics and Coinvariant Spaces by : Francois Bergeron
Download or read book Algebraic Combinatorics and Coinvariant Spaces written by Francois Bergeron and published by CRC Press. This book was released on 2009-07-06 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written for graduate students in mathematics or non-specialist mathematicians who wish to learn the basics about some of the most important current research in the field, this book provides an intensive, yet accessible, introduction to the subject of algebraic combinatorics. After recalling basic notions of combinatorics, representation theory, and
Book Synopsis Algebra in the Stone-Cech Compactification by : Neil Hindman
Download or read book Algebra in the Stone-Cech Compactification written by Neil Hindman and published by Walter de Gruyter. This book was released on 2011-12-23 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second revised and extended edition of the successful book on the algebraic structure of the Stone-Čech compactification of a discrete semigroup and its combinatorial applications, primarily in the field known as Ramsey Theory. There has been very active research in the subject dealt with by the book in the 12 years which is now included in this edition. This book is a self-contained exposition of the theory of compact right semigroups for discrete semigroups and the algebraic properties of these objects. The methods applied in the book constitute a mosaic of infinite combinatorics, algebra, and topology. The reader will find numerous combinatorial applications of the theory, including the central sets theorem, partition regularity of matrices, multidimensional Ramsey theory, and many more.
Book Synopsis X-Ray Structure Analysis by : Theo Siegrist
Download or read book X-Ray Structure Analysis written by Theo Siegrist and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-11-22 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a compact overview on crystallography, symmetry, and applications of symmetry concepts. The author explains the theory behind scattering and diffraction of electromagnetic radiation. X-ray diffraction on single crystals as well as quantitative evaluation of powder patterns are discussed.
Book Synopsis Dissertation Abstracts International by :
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2005 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt:
