Download or read book Beyond Topology written by Frdric Mynard and published by American Mathematical Soc.. This book was released on 2009-05-15 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this collection is to guide the non-specialist through the basic theory of various generalizations of topology, starting with clear motivations for their introduction. Structures considered include closure spaces, convergence spaces, proximity spaces, quasi-uniform spaces, merotopic spaces, nearness and filter spaces, semi-uniform convergence spaces, and approach spaces. Each chapter is self-contained and accessible to the graduate student, and focuses on motivations to introduce the generalization of topologies considered, presenting examples where desirable properties are not present in the realm of topologies and the problem is remedied in the more general context. Then, enough material will be covered to prepare the reader for more advanced papers on the topic. While category theory is not the focus of the book, it is a convenient language to study these structures and, while kept as a tool rather than an object of study, will be used throughout the book. For this reason, the book contains an introductory chapter on categorical topology.
Download or read book Advances in Quantum Chemical Topology Beyond QTAIM written by Juan I. Rodriguez and published by Elsevier. This book was released on 2022-12-06 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Quantum Chemical Topology Beyond QTAIM provides a complete overview of the field, starting with traditional methods and then covering key steps to the latest state-of-the-art extensions of QTAIM. The book supports researchers by compiling and reviewing key methods, comparing different algorithms, and providing computational results to show the efficacy of the approaches. Beginning with an introduction to quantum chemistry, QTAIM and key extensions, the book goes on to discuss interacting quantum atoms and related energy properties, explores partitioning methods, and compares algorithms for QTAIM. Partitioning schemes are them compared in more detail before applications are explored and future developments discussed. Drawing together the knowledge of key authorities in the area, this book provides a comprehensive, pedogeological guide to this insightful theory for all those interested in modelling, exploring and understanding molecular properties. Provides a contemporary review of the extensions and application of QTAIM methods Compiles all extensions of QTAIM in one place for easy reference Includes a chapter with an Introduction to Quantum Chemistry Presents complex information at a level accessible to those engaged in theoretical/computational chemistry
Download or read book Geometry and Topology of Manifolds Surfaces and Beyond written by Vicente Muñoz and published by American Mathematical Soc.. This book was released on 2020-10-21 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents a novel approach to differential topology. Its main focus is to give a comprehensive introduction to the classification of manifolds, with special attention paid to the case of surfaces, for which the book provides a complete classification from many points of view: topological, smooth, constant curvature, complex, and conformal. Each chapter briefly revisits basic results usually known to graduate students from an alternative perspective, focusing on surfaces. We provide full proofs of some remarkable results that sometimes are missed in basic courses (e.g., the construction of triangulations on surfaces, the classification of surfaces, the Gauss-Bonnet theorem, the degree-genus formula for complex plane curves, the existence of constant curvature metrics on conformal surfaces), and we give hints to questions about higher dimensional manifolds. Many examples and remarks are scattered through the book. Each chapter ends with an exhaustive collection of problems and a list of topics for further study. The book is primarily addressed to graduate students who did take standard introductory courses on algebraic topology, differential and Riemannian geometry, or algebraic geometry, but have not seen their deep interconnections, which permeate a modern approach to geometry and topology of manifolds.
Download or read book Topologies of Power written by John Allen and published by Routledge. This book was released on 2016-01-13 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topologies of Power amounts to a radical departure in the way that power and space have been understood. It calls into question the very idea that power is simply extended across a given territory or network, and argues that power today has a new found ‘reach’. Topological shifts have subtly altered the reach of power, enabling governments, corporations and NGOs alike to register their presence through quieter, less brash forms of power than domination or overt control. In a world in which proximity and distance increasingly play across one another, topology offers an insight into how power remains continuous under transformation: the same but different in its ability to shape peoples’ lives. Drawing upon a range of political, economic and cultural illustrations, the book sets out a clear and accessible account of the topological workings of power in the contemporary moment. It will be invaluable for both students and academics in human geography, politics, sociology, and cultural studies.
Download or read book Beyond Spacetime written by Nick Huggett and published by Cambridge University Press. This book was released on 2020-05-14 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of essays discussing the philosophy and foundations of quantum gravity. Written by leading philosophers and physicists in the field, chapters cover the important conceptual questions in the search for a quantum theory of gravity, and the current state of understanding among philosophers and physicists.
Download or read book Topology Through Inquiry written by Michael Starbird and published by American Mathematical Soc.. This book was released on 2020-09-10 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology Through Inquiry is a comprehensive introduction to point-set, algebraic, and geometric topology, designed to support inquiry-based learning (IBL) courses for upper-division undergraduate or beginning graduate students. The book presents an enormous amount of topology, allowing an instructor to choose which topics to treat. The point-set material contains many interesting topics well beyond the basic core, including continua and metrizability. Geometric and algebraic topology topics include the classification of 2-manifolds, the fundamental group, covering spaces, and homology (simplicial and singular). A unique feature of the introduction to homology is to convey a clear geometric motivation by starting with mod 2 coefficients. The authors are acknowledged masters of IBL-style teaching. This book gives students joy-filled, manageable challenges that incrementally develop their knowledge and skills. The exposition includes insightful framing of fruitful points of view as well as advice on effective thinking and learning. The text presumes only a modest level of mathematical maturity to begin, but students who work their way through this text will grow from mathematics students into mathematicians. Michael Starbird is a University of Texas Distinguished Teaching Professor of Mathematics. Among his works are two other co-authored books in the Mathematical Association of America's (MAA) Textbook series. Francis Su is the Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College and a past president of the MAA. Both authors are award-winning teachers, including each having received the MAA's Haimo Award for distinguished teaching. Starbird and Su are, jointly and individually, on lifelong missions to make learning—of mathematics and beyond—joyful, effective, and available to everyone. This book invites topology students and teachers to join in the adventure.
Download or read book Topological Insulators written by Ari M. Turner and published by Elsevier Inc. Chapters. This book was released on 2013-11-23 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Photons in Fock Space and Beyond written by Reinhard Honegger and published by World Scientific. This book was released on 2015-04-22 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three-volume major reference “Photons in Fock Space and Beyond” undertakes a new mathematical and conceptual foundation of the theory of light emphasizing mesoscopic radiation systems. The quantum optical notions are generalized beyond Fock representations where the richness of an infinite dimensional quantum field system, with its mathematical difficulties and theoretical possibilities, is fully taken into account. It aims at a microscopic formulation of a mesoscopic model class which covers in principle all stages of the generation and propagation of light within a unified and well-defined conceptual frame. The dynamics of the interacting systems is founded — according to original works of the authors — on convergent perturbation series and describes the developments of the quantized microscopic as well as the classical collective degrees of freedom at the same time. The achieved theoretical unification fits especially to laser and microwave applications inheriting objective information over quantum noise. A special advancement is the incorporation of arbitrary multiply connected cavities where ideal conductor boundary conditions are imposed. From there arises a new category of classical and quantized field parts, apparently not treated in Quantum Electrodynamics before. In combination with gauge theory, the additional “cohomological fields” explain topological quantum effects in superconductivity. Further applications are to be expected for optoelectronic and optomechanical systems. Contents:Volume I: From Classical to Quantized Radiation Systems:Preliminaries on ElectromagnetismClassical Electrodynamics in L2-Hilbert SpacesClassical Electrodynamics in the Smeared Field FormalismStatistical Classical ElectrodynamicsCanonical Quantization and Weyl AlgebrasDeformation QuantizationOptical States, Optical CoherenceVolume II: Quantized Mesoscopic Radiation Models:SqueezingBlack Body RadiationMesoscopic Electronic Matter Algebras and StatesWeakly Inhomogeneous InteractionsQuantized Radiation ModelsVolume III: Mathematics for Photon Fields:Observables and AlgebrasStates and Their Decomposition MeasuresDynamics and Perturbation TheoryGauges and Fiber Bundles Readership: This three-volume series is recommended for graduate students and researchers working in rigorous Electrodynamics, Quantum Optics and Quantum Field Theory in general. Key Features:On the side of Physics, “Photons in Fock Space and Beyond” extends the applicability of quantum optical notions far beyond the usual scope of the quantum optical literature by using more general optical cavities and theoretical ansatzes. By establishing a systematic conceptual frame, many fundamental questions of photon theory are clarified by mathematical argumentsOn the side of Mathematical Physics, certain parts of the theory of vector fields with boundary conditions, of operator algebras, ergodic theory, convexity, measures on dual spaces, perturbation theory and electrodynamic gauge bundles are not only treated in an introductory fashion but also supplemented in an original mannerThe unique feature of that exposition of mathematical disciplines is their integration into a comprehesive line of thought within a deductive physical theoryKeywords:Electrodynamics;Vector Analysis;Statistical Physics;Quantum Optics;Quantum Field Theory;Quantum Statistics;Solid State Physics;Superconductivity;Gauge Theory;Operator Algebras;Convexity;Topological Vector Spaces;Fiber BundlesReviews: “This three volume work on the quantum field theory of radiation combines well presented, competent mathematical foundations with actual physical applications to mesoscopic photonics.” (See Full Review) Professor Ernst Binz Universität Mannheim
Download or read book Convex Analysis and Beyond written by Boris S. Mordukhovich and published by Springer Nature. This book was released on 2022-04-24 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified theory of convex functions, sets, and set-valued mappings in topological vector spaces with its specifications to locally convex, Banach and finite-dimensional settings. These developments and expositions are based on the powerful geometric approach of variational analysis, which resides on set extremality with its characterizations and specifications in the presence of convexity. Using this approach, the text consolidates the device of fundamental facts of generalized differential calculus to obtain novel results for convex sets, functions, and set-valued mappings in finite and infinite dimensions. It also explores topics beyond convexity using the fundamental machinery of convex analysis to develop nonconvex generalized differentiation and its applications. The text utilizes an adaptable framework designed with researchers as well as multiple levels of students in mind. It includes many exercises and figures suited to graduate classes in mathematical sciences that are also accessible to advanced students in economics, engineering, and other applications. In addition, it includes chapters on convex analysis and optimization in finite-dimensional spaces that will be useful to upper undergraduate students, whereas the work as a whole provides an ample resource to mathematicians and applied scientists, particularly experts in convex and variational analysis, optimization, and their applications.
Download or read book Beyond Hyperbolicity written by Mark Hagen and published by Cambridge University Press. This book was released on 2019-07-11 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains expository articles and research papers in geometric group theory focusing on generalisations of Gromov hyperbolicity.
Download or read book Spin Glass Theory And Far Beyond Replica Symmetry Breaking After 40 Years written by Patrick Charbonneau and published by World Scientific. This book was released on 2023-07-26 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt: About sixty years ago, the anomalous magnetic response of certain magnetic alloys drew the attention of theoretical physicists. It soon became clear that understanding these systems, now called spin glasses, would give rise to a new branch of statistical physics. As physical materials, spin glasses were found to be as useless as they were exotic. They have nevertheless been recognized as paradigmatic examples of complex systems with applications to problems as diverse as neural networks, amorphous solids, biological molecules, social and economic interactions, information theory and constraint satisfaction problems.This book presents an encyclopaedic overview of the broad range of these applications. More than 30 contributions are compiled, written by many of the leading researchers who have contributed to these developments over the last few decades. Some timely and cutting-edge applications are also discussed. This collection serves well as an introduction and summary of disordered and glassy systems for advanced undergraduates, graduate students and practitioners interested in the topic.
Download or read book 5G and Beyond written by Xingqin Lin and published by Springer Nature. This book was released on 2021-03-25 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible and comprehensive tutorial on the key enabling technologies for 5G and beyond, covering both the fundamentals and the state-of-the-art 5G standards. The book begins with a historical overview of the evolution of cellular technologies and addresses the questions on why 5G and what is 5G. Following this, six tutorial chapters describe the fundamental technology components for 5G and beyond. These include modern advancements in channel coding, multiple access, massive multiple-input and multiple-output (MIMO), network densification, unmanned aerial vehicle enabled cellular networks, and 6G wireless systems. The second part of this book consists of five chapters that introduce the basics of 5G New Radio (NR) standards developed by 3GPP. These include 5G architecture, protocols, and physical layer aspects. The third part of this book provides an overview of the key 5G NR evolution directions. These directions include ultra-reliable low-latency communication (URLLC) enhancements, operation in unlicensed spectrum, positioning, integrated access and backhaul, air-to-ground communication, and non-terrestrial networks with satellite communication.
Download or read book Helicities in Geophysics Astrophysics and Beyond written by Kirill Kuzanyan and published by John Wiley & Sons. This book was released on 2023-12-12 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Helicities in Geophysics, Astrophysics, and Beyond Helicities play essential roles in numerous geophysical, astrophysical, and magnetohydrodynamic phenomena, thus are studied from various disciplinary viewpoints. Helicities in Geophysics, Astrophysics, and Beyond draws together experts from different research fields to present an interdisciplinary and integrated approach to helicity studies. This synthesis advances understanding of the fundamental physical processes underlying various helicity-related phenomena. Volume highlights include: Concise introduction to fundamental properties of helicities Recent developments and achievements in helicity studies Perspectives from different fields including geophysics, space physics, solar physics, plasma physics, atmospheric and nonlinear sciences A cohesive mathematical, physical, observational, experimental, and numerical strategy for helicity studies A synthesized framework for the application of helicity to real-world problems The American Geophysical Union promotes discovery in Earth and space science for the benefit of humanity. Its publications disseminate scientific knowledge and provide resources for researchers, students, and professionals.
Download or read book Topology written by Stefan Waldmann and published by Springer. This book was released on 2014-08-05 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a concise introduction to topology and is necessary for courses in differential geometry, functional analysis, algebraic topology, etc. Topology is a fundamental tool in most branches of pure mathematics and is also omnipresent in more applied parts of mathematics. Therefore students will need fundamental topological notions already at an early stage in their bachelor programs. While there are already many excellent monographs on general topology, most of them are too large for a first bachelor course. Topology fills this gap and can be either used for self-study or as the basis of a topology course.
Download or read book Open Problems in Topology II written by Elliott M. Pearl and published by Elsevier. This book was released on 2011-08-11 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of surveys of research problems in topology and its applications. The topics covered include general topology, set-theoretic topology, continuum theory, topological algebra, dynamical systems, computational topology and functional analysis. * New surveys of research problems in topology * New perspectives on classic problems * Representative surveys of research groups from all around the world
Download or read book Non Hausdorff Topology and Domain Theory written by Jean Goubault-Larrecq and published by Cambridge University Press. This book was released on 2013-03-28 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces the basic concepts of topology with an emphasis on non-Hausdorff topology, which is crucial for theoretical computer science.
Download or read book Royal Road To Topology A Convergence Of Filters written by Szymon Dolecki and published by World Scientific. This book was released on 2024-01-03 with total page 733 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological spaces are a special case of convergence spaces. This textbook introduces topology within a broader context of convergence theory. The title alludes to advantages of the present approach, which is more gratifying than many traditional ones: you travel more comfortably through mathematical landscapes and you see more.The book is addressed both to those who wish to learn topology and to those who, being already knowledgeable about topology, are curious to review it from a different perspective, which goes well beyond the traditional knowledge.Usual topics of classic courses of set-theoretic topology are treated at an early stage of the book — from a viewpoint of convergence of filters, but in a rather elementary way. Later on, most of these facts reappear as simple consequences of more advanced aspects of convergence theory.The mentioned virtues of the approach stem from the fact that the class of convergences is closed under several natural, essential operations, under which the class of topologies is not! Accordingly, convergence theory complements topology like the field of complex numbers algebraically completes the field of real numbers.Convergence theory is intuitive and operational because of appropriate level of its abstraction, general enough to grasp the underlying laws, but not too much in order not to lose intuitive appeal.
