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History of Banach Spaces and Linear Operators
Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. While other historical texts on the subject focus on developments before 1950, this one is mainly devoted to the second half of the 20th century.Banach space theory is presented in a broad mathematical context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, and logic.
Handbook of Spatial Logics
The aim of this handbook is to create, for the first time, a systematic account of the field of spatial logic. The book comprises a general introduction, followed by fourteen chapters by invited authors. Each chapter provides a self-contained overview of its topic, describing the principal results obtained to date, explaining the methods used to obtain them, and listing the most important open problems. Jointly, these contributions constitute a comprehensive survey of this rapidly expanding subject.
Handbook of K-Theory
This handbook offers a compilation of techniques and results in K-theory.Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. The overall intent of this handbook is to offer the interested reader an exposition of our current state of knowledge as well as an implicit blueprint for future research.
Graph-based representations in pattern recognition ; 5th IAPR International Workshop, GbRPR 2005, Poitiers, France, April 11-13, 2005, Proceedings
Many vision problems have to deal with di?erent entities (regions, lines, line junctions, etc.) and their relationships. These entities together with their re- tionships may be encoded using graphs or hypergraphs. The structural inf- mation encoded by graphs allows computer vision algorithms to address both the features of the di?erent entities and the structural or topological relati- ships between them. Moreover, turning a computer vision problem into a graph problem allows one to access the full arsenal of graph algorithms developed in computer science. The Technical Committee (TC15, http://www.iapr.org/tcs.html) of the IAPR (International Association for Pattern Recognition) has been funded in order to federate and to encourage research work in these ?elds. Among its - tivities, TC15 encourages the organization of special graph sessions at many computer vision conferences and organizes the biennial workshop GbR.
Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics
This book explores the foundations of hamiltonian dynamical systems and statistical mechanics, in particular phase transition, from the point of view of geometry and topology. A broad participation of topology in these fields has been lacking and this book will provide a welcome overview of the current research in the area, in which the author himself is a pioneer. Using geometrical thinking to solve fundamental problems in these areas, compared to the purely analytical methods usually used in physics could be highly productive. The author skillfully guides the reader, whether mathematician or physicists through the background needed to understand and use these techniques.
Geometric Topology : Localization, Periodicity and Galois Symmetry : the 1970 MIT notes
The seminal `MIT notes' of Dennis Sullivan were issued in June 1970 and were widely circulated at the time, but only privately. The notes had a major influence on the development of both algebraic and geometric topology, pioneering the localization and completion of spaces in homotopy theory, including P-local, profinite and rational homotopy theory, the Galois action on smooth manifold structures in profinite homotopy theory, and the K-theory orientation of PL manifolds and bundles. This is the first time that this major work has actually been published, and made available to anyone interested in topology.
Geometric Modeling and Algebraic Geometry
The two ?elds of Geometric Modeling and Algebraic Geometry, though closely - lated, are traditionally represented by two almost disjoint scienti?c communities. Both ?elds deal with objects de?ned by algebraic equations, but the objects are studied in different ways. While algebraic geometry has developed impressive - sults for understanding the theoretical nature of these objects, geometric modeling focuses on practical applications of virtual shapes de?ned by algebraic equations. Recently, however, interaction between the two ?elds has stimulated new research. For instance, algorithms for solving intersection problems have bene?ted from c- tributions from the algebraic side.
Geometric and Topological Methods for Quantum Field Theory
This volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is by Christine Lescop on knot invariants and configuration spaces, in which a universal finite-type invariant for knots is constructed as a series of integrals over configuration spaces. This is followed by the contribution of Raimar Wulkenhaar on Euclidean quantum field theory from a statistical point of view. The author also discusses possible renormalization techniques on noncommutative spaces. The third lecture is by Anamaria Font and Stefan Theisen on string compactification with unbroken supersymmetry. The authors show that this requirement leads to internal spaces of special holonomy and describe Calabi-Yau manifolds in detail. The last lecture, by Thierry Fack, is devoted to a K-theory proof of the Atiyah-Singer index theorem and discusses some applications of K-theory to noncommutative geometry. These lectures notes, which are aimed in particular at graduate students in physics and mathematics, start with introductory material before presenting more advanced results. Each chapter is self-contained and can be read independently.
Gene Expression and Regulation
This book offers a comprehensive look into the science of gene expression and regulation. Focusing on topics such as actions of nuclear receptors, RNA processing, and DNA methylation and imprinting, Gene Expression and Regulation is edited by a leading biologist and includes contributions by experts in the field. Presented in the following five sections, this book covers a full spectrum of topics: The History; The Machinery; The Regulators; The Genome; and Special Topics. The Machinery section covers the transcriptional apparatus and general transcription factors. The Regulators section examines selected gene-specific transcription factors important to regulating gene expression. The Genome section covers issues relevant to the behavior of the genome in relation to gene regulation. The Special Topics section discusses several selected topics ranging from bacterial and plant gene expression to DNA topology and interference RNA. The book’s focus is on scientific concepts and issues, rather than specific organisms or experimental approaches.
Functional Properties of Nanostructured Materials
Nanostructured materials are becoming of major significance, and their investigations require a comprehensive approach. The fundamental properties of these materials are remarkably altered as the size of their constituent grains or phases decreases to the nanometer scale. These novel materials made of nanosized building blocks offer unique and entirely different electrical, optical, mechanical, and magnetic properties compared to conventional micro- or millimetre-size materials owing to their distinctive size, shape, topology, surface properties, etc.
Fractals in Biology and Medicine : Beyond Planting Trees
This volume it highlights the potential that fractal geometry offers for elucidating and explaining the complex make-up of cells, tissues and biological organisms either in normal or in pathological conditions, including the structural changes that occur in tumours. It helps develop the concepts, questions and methods required in research on fractal biology and natural phenomena and to evidence the pitfalls of a too simplistic application of these principles in investigating topical subjects of biology and medicine. It discusses present and future applications of fractal geometry, bringing together cellular and molecular biology, engineering, mathematics, physics, medicine and other disciplines and allowing an interdisciplinary vision.
Foundations of Hyperbolic Manifolds
The book is divided into three parts. The first part is concerned with hyperbolic geometry and discrete groups. The main results are the characterization of hyperbolic reflection groups and Euclidean crystallographic groups. The second part is devoted to the theory of hyperbolic manifolds. The main results are Mostow’s rigidity theorem and the determination of the global geometry of hyperbolic manifolds of finite volume. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. The main result is Poincare«s fundamental polyhedron theorem.
Fixed point theory for decomposable sets
This book attempts to show the present stage of "decomposable analysis" from the point of view of fixed point theory. The book is split into three parts, beginning with the background of functional analysis, proceeding to the theory of multifunctions and lastly, the decomposability property.Mathematicians and students working in functional, convex and nonlinear analysis, differential inclusions and optimal control should find this book of interest. A good background in fixed point theory is assumed as is a background in topology.
Essential Topology
Taking a direct route, Essential Topology brings the most important aspects of modern topology within reach of a second-year undergraduate student. Based on courses given at the University of Wales Swansea, it begins with a discussion of continuity and, by way of many examples, leads to the celebrated ""Hairy Ball theorem"" and on to homotopy and homology: the cornerstones of contemporary algebraic topology. While containing all the key results of basic topology, Essential Topology never allows itself to get mired in details. Instead, the focus throughout is on providing interesting examples that clarify the ideas and motivate the student, reflecting the fact that these are often the key examples behind current research.
Espaces vectoriels topologiques : Chapitres 1à 5 = Topological vector spaces : Chapters 1 to 5
The Mathematics Elements of Nicolas BOURBAKI aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations. This book is the fifth of the treatise; it is devoted to the basics of functional analysis. It contains in particular the Hahn-Banach theorem and the Banach-Steinhaus theorem.
Entertainment computing – ICEC 2007 ; 6th International Conference, Shanghai, China, September 15-17, 2007, Proceedings
This book are organized in topical sections on augmented, virtual and mixed reality, computer games, image processing, mesh and modeling, digital storytelling and interactive systems, sound, music and creative environments, video processing, rendering, computer animation and networks, game based interfaces, as well as robots and cyber pets.
Eléments dhistoire des mathématiques = Elements of the history of mathematics
Brings together the historical notes published in the various books of mathematics elements by the author. They therefore concern all the matters covered in this treaty: set theory, algebra, topology, functions of a variable real, topological vector spaces, integration, commutative algebra, groups and Lie algebras. Composed of initially separate studies, this work does not claim to sketch a followed and complete history of development of mathematics. The interweaving of the different themes and the unity of the point of view ensure the deep consistency.
Einstein Manifolds
"[...] an efficient reference book for many fundamental techniques of Riemannian geometry. [...] despite its length, the reader will have no difficulty in getting the feel of its contents and discovering excellent examples of all interaction of geometry with partial differential equations, topology, and Lie groups. Above all, the book provides a clear insight into the scope and diversity of problems posed by its title."
Effective Computational Geometry for Curves and Surfaces
Computational geometry emerged as a discipline in the seventies and has had considerable success in improving the asymptotic complexity of the solutions to basic geometric problems including constructions of data structures,convex hulls, triangulations, Voronoi diagrams and geometric arrangements as well as geometric optimisation. The goal of this book is to take into consideration the multidisciplinary nature of the problem and to provide solid mathematical and algorithmic foundations for effiective computational geometry fo rcurves and surfaces. This book covers two main approaches. In a first part, we discuss exact geometric algorithms for curves and s- faces. We revisit two prominent data structures of computational geometry, namely arrangements (Chap. 1) and Voronoi diagrams (Chap. 2) in order to understand how these structures, which are well-known for linear objects, behave when de?ned on curved objects.
Discrete geometry for computer imagery ; Vol. 3429 ; 12th International Conference, DGCI 2005, Poitiers, France, April 11-13, 2005, Proceedings
This book constitutes the refereed proceedings of the 12th International Conference on Discrete Geometry for Computer Imagery, DGCI 2005, held in Poitiers, France in April 2005. The 36 revised full papers presented together with an invited paper were carefully reviewed and selected from 53 submissions. The papers are organized in topical sections on applications, discrete hierarchical geometry, discrete tomography, discrete topology, object properties, reconstruction and recognition, uncertain geometry, and visualization.
