Textrm C Algebras And Finite Dimensional Approximations

Author : Nathanial Patrick Brown,Narutaka Ozawa
Publisher : American Mathematical Soc.
Page : 530 pages
File Size : 44,6 Mb
Release : 2008
Category : C*-algebras
ISBN : 9780821843819

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$\textrm {C}^*$-Algebras and Finite-Dimensional Approximations by Nathanial Patrick Brown,Narutaka Ozawa Pdf

$\textrm{C}*$-approximation theory has provided the foundation for many of the most important conceptual breakthroughs and applications of operator algebras. This book systematically studies (most of) the numerous types of approximation properties that have been important in recent years: nuclearity, exactness, quasidiagonality, local reflexivity, and others. Moreover, it contains user-friendly proofs, insofar as that is possible, of many fundamental results that were previously quite hard to extract from the literature. Indeed, perhaps the most important novelty of the first ten chapters is an earnest attempt to explain some fundamental, but difficult and technical, results as painlessly as possible. The latter half of the book presents related topics and applications--written with researchers and advanced, well-trained students in mind. The authors have tried to meet the needs both of students wishing to learn the basics of an important area of research as well as researchers who desire a fairly comprehensive reference for the theory and applications of $\textrm{C}*$-approximation theory.

Author : V. Dlab,Leonard Scott
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 46,6 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9789401715560

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Finite Dimensional Algebras and Related Topics by V. Dlab,Leonard Scott Pdf

Based on invited lectures at the 1992 Canadian Algebra Seminar, this volume represents an up-to-date and unique report on finite-dimensional algebras as a subject with many serious interactions with other mathematical disciplines, including algebraic groups and Lie theory, automorphic forms, sheaf theory, finite groups, and homological algebra. It will interest mathematicians and graduate students in these and related subjects as an introduction to research in an area of increasing relevance and importance.

Author : Kenneth R. Davidson
Publisher : American Mathematical Soc.
Page : 326 pages
File Size : 52,9 Mb
Release : 1996
Category : C*-algebras
ISBN : 9780821805992

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C*-Algebras by Example by Kenneth R. Davidson Pdf

An introductory graduate level text presenting the basics of the subject through a detailed analysis of several important classes of C*-algebras, those which are the basis of the development of operator algebras. Explains the real examples that researchers use to test their hypotheses, and introduces modern concepts and results such as real rank zero algebras, topological stable rank, and quasidiagonality. Includes chapter exercises with hints. For graduate students with a foundation in functional analysis. Annotation copyright by Book News, Inc., Portland, OR

Author : Edward G. Effros
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 46,5 Mb
Release : 1981
Category : Mathematics
ISBN : 9780821888919

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Dimensions and C*-algebras by Edward G. Effros Pdf

Author : Lloyd N. Trefethen,Mark Embree
Publisher : Princeton University Press
Page : 634 pages
File Size : 53,6 Mb
Release : 2005-08-07
Category : Mathematics
ISBN : 0691119465

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Spectra and Pseudospectra by Lloyd N. Trefethen,Mark Embree Pdf

Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.

Author : Brigitte d'Andréa-Novel,Michel De Lara
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 55,7 Mb
Release : 2013-05-09
Category : Technology & Engineering
ISBN : 9783642343247

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Control Theory for Engineers by Brigitte d'Andréa-Novel,Michel De Lara Pdf

Control Theory is at the heart of information and communication technologies of complex systems. It can contribute to meeting the energy and environmental challenges we are facing. The textbook is organized in the way an engineer classically proceeds to solve a control problem, that is, elaboration of a mathematical model capturing the process behavior, analysis of this model and design of a control to achieve the desired objectives. It is divided into three Parts. The first part of the text addresses modeling aspects through state space and input-output representations. The notion of the internal state of a system (for example mechanical, thermal or electrical), as well as its description using a finite number of variables, is also emphasized. The second part is devoted to the stability analysis of an equilibrium point. The authors present classical tools for stability analysis, such as linearization techniques and Lyapunov functions. Central to Control Theory are the notions of feedback and of closed-loop, and the third part of the textbook describes the linear control synthesis in a continuous and discrete-time framework and also in a probabilistic context. Quadratic optimization and Kalman filtering are presented, as well as the polynomial representation, a convenient approach to reject perturbations on the system without making the control law more complex. Throughout the text, different examples are developed, both in the chapters and in the exercises.

Author : Fernando Albiac,Nigel J. Kalton
Publisher : Springer
Page : 508 pages
File Size : 47,7 Mb
Release : 2016-07-19
Category : Mathematics
ISBN : 9783319315577

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Topics in Banach Space Theory by Fernando Albiac,Nigel J. Kalton Pdf

This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous functions. The authors also stress the use of bases and basic sequences techniques as a tool for understanding the isomorphic structure of Banach spaces. From the reviews of the First Edition: "The authors of the book...succeeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendly... It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated by motivations, explanations and occasional historical comments... I strongly recommend to every graduate student who wants to get acquainted with this exciting part of functional analysis the instructive and pleasant reading of this book..."—Gilles Godefroy, Mathematical Reviews

Author : César Polcino Milies,S.K. Sehgal
Publisher : Springer Science & Business Media
Page : 394 pages
File Size : 49,5 Mb
Release : 2002-01-31
Category : Mathematics
ISBN : 1402002386

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An Introduction to Group Rings by César Polcino Milies,S.K. Sehgal Pdf

to Group Rings by Cesar Polcino Milies Instituto de Matematica e Estatistica, Universidade de sao Paulo, sao Paulo, Brasil and Sudarshan K. Sehgal Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton. Canada SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. A c.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-1-4020-0239-7 ISBN 978-94-010-0405-3 (eBook) DOI 10.1007/978-94-010-0405-3 Printed an acid-free paper AII Rights Reserved (c) 2002 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2002 Softcover reprint ofthe hardcover Ist edition 2002 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, inc1uding photocopying, recording Of by any information storage and retrieval system, without written permis sion from the copyright owner. Contents Preface ix 1 Groups 1 1.1 Basic Concepts . . . . . . . . . . . . 1 1.2 Homomorphisms and Factor Groups 10 1.3 Abelian Groups . 18 1.4 Group Actions, p-groups and Sylow Subgroups 21 1.5 Solvable and Nilpotent Groups 27 1.6 FC Groups .

Author : Volodymyr Nekrashevych
Publisher : American Mathematical Society
Page : 248 pages
File Size : 48,5 Mb
Release : 2024-04-05
Category : Mathematics
ISBN : 9781470476915

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Self-Similar Groups by Volodymyr Nekrashevych Pdf

Self-similar groups (groups generated by automata) appeared initially as examples of groups that are easy to define but that enjoy exotic properties like nontrivial torsion, intermediate growth, etc. The book studies the self-similarity phenomenon in group theory and shows its intimate relation with dynamical systems and more classical self-similar structures, such as fractals, Julia sets, and self-affine tilings. The relation is established through the notions of the iterated monodromy group and the limit space, which are the central topics of the book. A wide variety of examples and different applications of self-similar groups to dynamical systems and vice versa are discussed. It is shown in particular how Julia sets can be reconstructed from the respective iterated monodromy groups and that groups with exotic properties appear now not just as isolated examples but as naturally defined iterated monodromy groups of rational functions. The book is intended to be accessible to a wide mathematical readership, including graduate students interested in group theory and dynamical systems.

Author : Gerald W. Johnson,Michel L. Lapidus
Publisher : Clarendon Press
Page : 790 pages
File Size : 46,5 Mb
Release : 2000-03-16
Category : Mathematics
ISBN : 9780191546266

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The Feynman Integral and Feynman's Operational Calculus by Gerald W. Johnson,Michel L. Lapidus Pdf

This book provides the most comprehensive mathematical treatment to date of the Feynman path integral and Feynman's operational calculus. It is accessible to mathematicians, mathematical physicists and theoretical physicists. Including new results and much material previously only available in the research literature, this book discusses both the mathematics and physics background that motivate the study of the Feynman path integral and Feynman's operational calculus, and also provides more detailed proofs of the central results.

Author : R. Baker Kearfott,V. Kreinovich
Publisher : Boom Koninklijke Uitgevers
Page : 460 pages
File Size : 41,9 Mb
Release : 1996-01-31
Category : Computers
ISBN : 0792338472

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Applications of Interval Computations by R. Baker Kearfott,V. Kreinovich Pdf

Papers from a February 1994 international workshop held in El Paso, Texas, survey industrial applications of numerical analysis with automatic result verification, and of interval representation of data. After an introductory chapter explaining the content of the papers in terminology accessible to mathematically literate graduate students, chapters describe applications such as economic input-output models; quality control in manufacturing design; and medical expert systems, focusing on dealing with problems such as overestimation. Other topics include branch and bound algorithms for global optimization; fuzzy logic; and constraint propagation. For students and researchers interested in automatic result verification. Annotation copyright by Book News, Inc., Portland, OR

Author : Karlheinz Gröchenig
Publisher : Springer Science & Business Media
Page : 367 pages
File Size : 42,6 Mb
Release : 2013-12-01
Category : Technology & Engineering
ISBN : 9781461200031

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Foundations of Time-Frequency Analysis by Karlheinz Gröchenig Pdf

Time-frequency analysis is a modern branch of harmonic analysis. It com prises all those parts of mathematics and its applications that use the struc ture of translations and modulations (or time-frequency shifts) for the anal ysis of functions and operators. Time-frequency analysis is a form of local Fourier analysis that treats time and frequency simultaneously and sym metrically. My goal is a systematic exposition of the foundations of time-frequency analysis, whence the title of the book. The topics range from the elemen tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita tive methods in time-frequency analysis and the theory of pseudodifferential operators. This book is motivated by applications in signal analysis and quantum mechanics, but it is not about these applications. The main ori entation is toward the detailed mathematical investigation of the rich and elegant structures underlying time-frequency analysis. Time-frequency analysis originates in the early development of quantum mechanics by H. Weyl, E. Wigner, and J. von Neumann around 1930, and in the theoretical foundation of information theory and signal analysis by D.

Author : Bob Coecke
Publisher : Springer
Page : 1031 pages
File Size : 41,7 Mb
Release : 2011-01-15
Category : Science
ISBN : 9783642128219

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New Structures for Physics by Bob Coecke Pdf

This volume provides a series of tutorials on mathematical structures which recently have gained prominence in physics, ranging from quantum foundations, via quantum information, to quantum gravity. These include the theory of monoidal categories and corresponding graphical calculi, Girard’s linear logic, Scott domains, lambda calculus and corresponding logics for typing, topos theory, and more general process structures. Most of these structures are very prominent in computer science; the chapters here are tailored towards an audience of physicists.

Author : Blaise Bourdin,Gilles A. Francfort,Jean-Jacques Marigo
Publisher : Springer Science & Business Media
Page : 173 pages
File Size : 41,7 Mb
Release : 2008-04-19
Category : Technology & Engineering
ISBN : 9781402063954

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The Variational Approach to Fracture by Blaise Bourdin,Gilles A. Francfort,Jean-Jacques Marigo Pdf

Presenting original results from both theoretical and numerical viewpoints, this text offers a detailed discussion of the variational approach to brittle fracture. This approach views crack growth as the result of a competition between bulk and surface energy, treating crack evolution from its initiation all the way to the failure of a sample. The authors model crack initiation, crack path, and crack extension for arbitrary geometries and loads.

Author : A. Mani,Gianpiero Cattaneo,Ivo Düntsch
Publisher : Springer
Page : 733 pages
File Size : 52,8 Mb
Release : 2019-01-11
Category : Mathematics
ISBN : 9783030011628

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Algebraic Methods in General Rough Sets by A. Mani,Gianpiero Cattaneo,Ivo Düntsch Pdf

This unique collection of research papers offers a comprehensive and up-to-date guide to algebraic approaches to rough sets and reasoning with vagueness. It bridges important gaps, outlines intriguing future research directions, and connects algebraic approaches to rough sets with those for other forms of approximate reasoning. In addition, the book reworks algebraic approaches to axiomatic granularity. Given its scope, the book offers a valuable resource for researchers and teachers in the areas of rough sets and algebras of rough sets, algebraic logic, non classical logic, fuzzy sets, possibility theory, formal concept analysis, computational learning theory, category theory, and other formal approaches to vagueness and approximate reasoning. Consultants in AI and allied fields will also find the book to be of great practical value.