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Theory Of Topological Structures
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Book Synopsis Theory of Topological Structures by : Gerhard Preuß
Download or read book Theory of Topological Structures written by Gerhard Preuß and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Book Synopsis Basic Topological Structures of Ordinary Differential Equations by : V.V. Filippov
Download or read book Basic Topological Structures of Ordinary Differential Equations written by V.V. Filippov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is a detailed study of topological effects related to continuity of the dependence of solutions on initial values and parameters. This allows us to develop cheaply a theory which deals easily with equations having singularities and with equations with multivalued right hand sides (differential inclusions). An explicit description of corresponding topological structures expands the theory in the case of equations with continuous right hand sides also. In reality, this is a new science where Ordinary Differential Equations, General Topology, Integration theory and Functional Analysis meet. In what concerns equations with discontinuities and differential inclu sions, we do not restrict the consideration to the Cauchy problem, but we show how to develop an advanced theory whose volume is commensurable with the volume of the existing theory of Ordinary Differential Equations. The level of the account rises in the book step by step from second year student to working scientist.
Book Synopsis Topological Model Theory by : Jörg Flum
Download or read book Topological Model Theory written by Jörg Flum and published by Springer. This book was released on 2006-11-14 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis New Foundations for Physical Geometry by : Tim Maudlin
Download or read book New Foundations for Physical Geometry written by Tim Maudlin and published by . This book was released on 2014-02 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.
Author :Alexander Arhangel’skii Publisher :Springer Science & Business Media ISBN 13 :949121635X Total Pages :794 pages Book Rating :4.4/5 (912 download)
Book Synopsis Topological Groups and Related Structures, An Introduction to Topological Algebra. by : Alexander Arhangel’skii
Download or read book Topological Groups and Related Structures, An Introduction to Topological Algebra. written by Alexander Arhangel’skii and published by Springer Science & Business Media. This book was released on 2008-05-01 with total page 794 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraandtopology,thetwofundamentaldomainsofmathematics,playcomplem- tary roles. Topology studies continuity and convergence and provides a general framework to study the concept of a limit. Much of topology is devoted to handling in?nite sets and in?nity itself; the methods developed are qualitative and, in a certain sense, irrational. - gebra studies all kinds of operations and provides a basis for algorithms and calculations. Very often, the methods here are ?nitistic in nature. Because of this difference in nature, algebra and topology have a strong tendency to develop independently, not in direct contact with each other. However, in applications, in higher level domains of mathematics, such as functional analysis, dynamical systems, representation theory, and others, topology and algebra come in contact most naturally. Many of the most important objects of mathematics represent a blend of algebraic and of topologicalstructures. Topologicalfunctionspacesandlineartopologicalspacesingeneral, topological groups and topological ?elds, transformation groups, topological lattices are objects of this kind. Very often an algebraic structure and a topology come naturally together; this is the case when they are both determined by the nature of the elements of the set considered (a group of transformations is a typical example). The rules that describe the relationship between a topology and an algebraic operation are almost always transparentandnatural—theoperationhastobecontinuous,jointlyorseparately.
Book Synopsis Topological Uniform Structures by : Warren Page
Download or read book Topological Uniform Structures written by Warren Page and published by Courier Dover Publications. This book was released on 1988 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exceptionally smooth, clear, detailed examination of uniform spaces, topological groups, topological vector spaces, topological algebras and abstract harmonic analysis. Also, topological vector-valued measure spaces as well as numerous problems and examples. For advanced undergraduates and beginning graduate students. Bibliography. Index.
Book Synopsis Topological Structure and Analysis of Interconnection Networks by : Junming Xu
Download or read book Topological Structure and Analysis of Interconnection Networks written by Junming Xu and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The advent of very large scale integrated circuit technology has enabled the construction of very complex and large interconnection networks. By most accounts, the next generation of supercomputers will achieve its gains by increasing the number of processing elements, rather than by using faster processors. The most difficult technical problem in constructing a supercom puter will be the design of the interconnection network through which the processors communicate. Selecting an appropriate and adequate topological structure of interconnection networks will become a critical issue, on which many research efforts have been made over the past decade. The book is aimed to attract the readers' attention to such an important research area. Graph theory is a fundamental and powerful mathematical tool for de signing and analyzing interconnection networks, since the topological struc ture of an interconnection network is a graph. This fact has been univer sally accepted by computer scientists and engineers. This book provides the most basic problems, concepts and well-established results on the topological structure and analysis of interconnection networks in the language of graph theory. The material originates from a vast amount of literature, but the theory presented is developed carefully and skillfully. The treatment is gen erally self-contained, and most stated results are proved. No exercises are explicitly exhibited, but there are some stated results whose proofs are left to the reader to consolidate his understanding of the material.
Book Synopsis Elements of Operator Theory by : Carlos S. Kubrusly
Download or read book Elements of Operator Theory written by Carlos S. Kubrusly and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: {\it Elements of Operatory Theory} is aimed at graduate students as well as a new generation of mathematicians and scientists who need to apply operator theory to their field. Written in a user-friendly, motivating style, fundamental topics are presented in a systematic fashion, i.e., set theory, algebraic structures, topological structures, Banach spaces, Hilbert spaces, culminating with the Spectral Theorem, one of the landmarks in the theory of operators on Hilbert spaces. The exposition is concept-driven and as much as possible avoids the formula-computational approach. Key features of this largely self-contained work include: * required background material to each chapter * fully rigorous proofs, over 300 of them, are specially tailored to the presentation and some are new * more than 100 examples and, in several cases, interesting counterexamples that demonstrate the frontiers of an important theorem * over 300 problems, many with hints * both problems and examples underscore further auxiliary results and extensions of the main theory; in this non-traditional framework, the reader is challenged and has a chance to prove the principal theorems anew This work is an excellent text for the classroom as well as a self-study resource for researchers. Prerequisites include an introduction to analysis and to functions of a complex variable, which most first-year graduate students in mathematics, engineering, or another formal science have already acquired. Measure theory and integration theory are required only for the last section of the final chapter.
Book Synopsis Model Theory of Topological Structures by : Steven Chester Garavaglia
Download or read book Model Theory of Topological Structures written by Steven Chester Garavaglia and published by . This book was released on 1976 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Local Structure of Algebraic K-Theory by : Bjørn Ian Dundas
Download or read book The Local Structure of Algebraic K-Theory written by Bjørn Ian Dundas and published by Springer Science & Business Media. This book was released on 2012-09-06 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology.
Book Synopsis Contributions to Extension Theory of Topological Structures by : F. Terpe
Download or read book Contributions to Extension Theory of Topological Structures written by F. Terpe and published by . This book was released on 1969 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theory of Mathematical Structures by : Jiří Adámek
Download or read book Theory of Mathematical Structures written by Jiří Adámek and published by Springer Science & Business Media. This book was released on 1983-11-30 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Contributions to Extension Theory of Topological Structures by : Jürgen Flachsmeyer
Download or read book Contributions to Extension Theory of Topological Structures written by Jürgen Flachsmeyer and published by . This book was released on 1969 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Homogenization and Structural Topology Optimization by : Behrooz Hassani
Download or read book Homogenization and Structural Topology Optimization written by Behrooz Hassani and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Structural topology optimization is a fast growing field that is finding numerous applications in automotive, aerospace and mechanical design processes. Homogenization is a mathematical theory with applications in several engineering problems that are governed by partial differential equations with rapidly oscillating coefficients Homogenization and Structural Topology Optimization brings the two concepts together and successfully bridges the previously overlooked gap between the mathematical theory and the practical implementation of the homogenization method. The book is presented in a unique self-teaching style that includes numerous illustrative examples, figures and detailed explanations of concepts. The text is divided into three parts which maintains the book's reader-friendly appeal.
Book Synopsis Contributions to Extension Theory of Topological Structures by : L. Flachsmeyer
Download or read book Contributions to Extension Theory of Topological Structures written by L. Flachsmeyer and published by . This book was released on 1969-06-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Descriptive Set Theory and Dynamical Systems by : M. Foreman
Download or read book Descriptive Set Theory and Dynamical Systems written by M. Foreman and published by Cambridge University Press. This book was released on 2000-05-25 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, first published in 2000, contains a collection of survey papers providing an introduction for graduate students and researchers in these fields.
Book Synopsis Topology Optimization by : Martin Philip Bendsoe
Download or read book Topology Optimization written by Martin Philip Bendsoe and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topology optimization method solves the basic enginee- ring problem of distributing a limited amount of material in a design space. The first edition of this book has become the standard text on optimal design which is concerned with the optimization of structural topology, shape and material. This edition, has been substantially revised and updated to reflect progress made in modelling and computational procedures. It also encompasses a comprehensive and unified description of the state-of-the-art of the so-called material distribution method, based on the use of mathematical programming and finite elements. Applications treated include not only structures but also materials and MEMS.
