Beyond Topology

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Beyond Topology

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Author : FrŽdŽric Mynard
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-05-15

Beyond Topology written by FrŽdŽric Mynard 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 2009-05-15 with Mathematics categories.

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.

Advances In Quantum Chemical Topology Beyond Qtaim

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Author : Juan I. Rodriguez
language : en
Publisher: Elsevier
Release Date : 2022-12-06

Advances In Quantum Chemical Topology Beyond Qtaim written by Juan I. Rodriguez and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-06 with Science categories.

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

Geometry And Topology Of Manifolds Surfaces And Beyond

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Author : Vicente Muñoz
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-10-21

Geometry And Topology Of Manifolds Surfaces And Beyond written by Vicente Muñoz 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 2020-10-21 with Education categories.

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.

Beyond Spacetime

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Author : Nick Huggett
language : en
Publisher: Cambridge University Press
Release Date : 2020-05-14

Beyond Spacetime written by Nick Huggett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-14 with Philosophy categories.

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.

Beyond Orbiting Satellites The Future Of Satellite Communication

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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-07-17

Beyond Orbiting Satellites The Future Of Satellite Communication written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-17 with Technology & Engineering categories.

In a world increasingly reliant on seamless communication and global connectivity, satellite communication has emerged as a transformative force. This comprehensive book delves into the captivating realm of satellite communication, unraveling its intricate technologies, diverse applications, and profound impact on society. From the pioneering days of Sputnik 1 to the cutting-edge advancements of today, this book traces the captivating journey of satellite communication. It explores the fundamental principles of satellite orbits, link design, and network architectures, providing readers with a solid understanding of the underlying mechanisms that enable satellite communication. Venturing beyond theoretical concepts, the book delves into the practical applications of satellite communication, showcasing its vital role in broadcasting, telecommunications, internet access, navigation, and disaster management. It examines the various types of satellite communication systems, including geostationary, medium earth orbit, and low earth orbit satellites, highlighting their unique advantages and applications. The book also explores the emerging frontiers of satellite communication, shedding light on the integration of satellite networks with terrestrial networks, the development of high-throughput satellites, and the convergence of satellite communication with technologies like 5G and artificial intelligence. It discusses the challenges and opportunities presented by these advancements, providing readers with a glimpse into the future of satellite communication. With its comprehensive coverage, engaging writing style, and insightful analysis, this book is an invaluable resource for students, researchers, professionals, and anyone seeking to gain a deeper understanding of satellite communication. It offers a panoramic view of this dynamic field, providing readers with the knowledge and insights they need to navigate the ever-changing landscape of satellite communication. Whether you are a seasoned expert or a curious novice, this book will captivate your imagination and leave you with a newfound appreciation for the remarkable achievements and boundless potential of satellite communication. If you like this book, write a review!

Analysis And Beyond An Introduction With Examples And Exercises

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Author : Shigeru Kanemitsu
language : en
Publisher: World Scientific
Release Date : 2021-01-13

Analysis And Beyond An Introduction With Examples And Exercises written by Shigeru Kanemitsu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-13 with Mathematics categories.

This volume aims to bridge between elementary textbooks on calculus and established books on advanced analysis. It provides elucidation of the reversible process of differentiation and integration through two featured principles: the chain rule and its inverse — the change of variable — as well as the Leibniz rule and its inverse — the integration by parts. The chain rule or differentiation of composite functions is ubiquitous since almost all (a.a.) functions are composite functions of (elementary) functions and with the change of variable method as its reverse process. The Leibniz rule or differentiation of the product of two functions is essential since it makes differentiation nonlinear and with the method of integration by parts as its reverse process.Readers will find numerous worked-out examples and exercises in this volume. Detailed solutions are provided for most of the common exercises so that readers remain enthusiastically motivated in solving and understanding the concepts better.The intention of this volume is to lead the reader into the rich fields of advanced analysis and to obtain a much better view of useful mathematics.

Photons In Fock Space And Beyond In 3 Volumes

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Author : Reinhard Honegger
language : en
Publisher: World Scientific
Release Date : 2015-04-22

Photons In Fock Space And Beyond In 3 Volumes written by Reinhard Honegger and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-22 with Science categories.

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.

Beyond The Triangle Brownian Motion Ito Calculus And Fokker Planck Equation Fractional Generalizations

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Author : Sabir Umarov
language : en
Publisher: World Scientific
Release Date : 2018-02-13

Beyond The Triangle Brownian Motion Ito Calculus And Fokker Planck Equation Fractional Generalizations written by Sabir Umarov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-13 with Mathematics categories.

The book is devoted to the fundamental relationship between three objects: a stochastic process, stochastic differential equations driven by that process and their associated Fokker-Planck-Kolmogorov equations. This book discusses wide fractional generalizations of this fundamental triple relationship, where the driving process represents a time-changed stochastic process; the Fokker-Planck-Kolmogorov equation involves time-fractional order derivatives and spatial pseudo-differential operators; and the associated stochastic differential equation describes the stochastic behavior of the solution process. It contains recent results obtained in this direction.This book is important since the latest developments in the field, including the role of driving processes and their scaling limits, the forms of corresponding stochastic differential equations, and associated FPK equations, are systematically presented. Examples and important applications to various scientific, engineering, and economics problems make the book attractive for all interested researchers, educators, and graduate students.

Convex Analysis And Beyond

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Author : Boris S. Mordukhovich
language : en
Publisher: Springer Nature
Release Date : 2022-04-24

Convex Analysis And Beyond written by Boris S. Mordukhovich and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-24 with Mathematics categories.

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.

Theory Beyond Structure And Agency

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Author : Jean-Sébastien Guy
language : en
Publisher: Springer Nature
Release Date : 2019-09-10

Theory Beyond Structure And Agency written by Jean-Sébastien Guy and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-10 with Social Science categories.

This book offers a solution for the problem of structure and agency in sociological theory by developing a new pair of fundamental concepts: metric and nonmetric. Nonmetric forms, arising in a crowd made out of innumerable individuals, correspond to social groups that divide the many individuals in the crowd into insiders and outsiders. Metric forms correspond to congested zones like traffic jams on a highway: individuals are constantly entering and leaving these zones so that they continue to exist, even though the individuals passing through them change. Building from these concepts, we can understand “agency” as a requirement for group identity and group membership, thus associating it with nonmetric forms, and “structure” as a building-up effect following the accumulation of metric forms. This reveals the contradiction between structure and agency to be a case of forced perspective, leaving us victim to an optical illusion.