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Author : Narjess Afzaly,Scott Morrison,David Penneys
Publisher : American Mathematical Society
Page : 94 pages
File Size : 46,8 Mb
Release : 2023-04-07
Category : Mathematics
ISBN : 9781470447120
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Author : NARJESS AFZALY; SCOTT MORRISON; DAVID PENNEYS.
Publisher : Unknown
Page : 0 pages
File Size : 52,9 Mb
Release : 2023
Category : Electronic books
ISBN : 1470474433
Author : Anonim
Publisher : Unknown
Page : 1446 pages
File Size : 48,8 Mb
Release : 1993-02
Category : Science
ISBN : CORNELL:31924058963616
Author : Zhenghan Wang
Publisher : American Mathematical Soc.
Page : 134 pages
File Size : 41,8 Mb
Release : 2010
Category : Computers
ISBN : 9780821849309
Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. In this approach, information is stored in the lowest energy states of many-anyon systems and processed by braiding non-abelian anyons. The computational answer is accessed by bringing anyons together and observing the result. Besides its theoretical esthetic appeal, the practical merit of the topological approach lies in its error-minimizing hypothetical hardware: topological phases of matter are fault-avoiding or deaf to most local noises, and unitary gates are implemented with exponential accuracy. Experimental realizations are pursued in systems such as fractional quantum Hall liquids and topological insulators. This book expands on the author's CBMS lectures on knots and topological quantum computing and is intended as a primer for mathematically inclined graduate students. With an emphasis on introducing basic notions and current research, this book gives the first coherent account of the field, covering a wide range of topics: Temperley-Lieb-Jones theory, the quantum circuit model, ribbon fusion category theory, topological quantum field theory, anyon theory, additive approximation of the Jones polynomial, anyonic quantum computing models, and mathematical models of topological phases of matter.
Author : Masamichi Takesaki
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461261889
Mathematics for infinite dimensional objects is becoming more and more important today both in theory and application. Rings of operators, renamed von Neumann algebras by J. Dixmier, were first introduced by J. von Neumann fifty years ago, 1929, in [254] with his grand aim of giving a sound founda tion to mathematical sciences of infinite nature. J. von Neumann and his collaborator F. J. Murray laid down the foundation for this new field of mathematics, operator algebras, in a series of papers, [240], [241], [242], [257] and [259], during the period of the 1930s and early in the 1940s. In the introduction to this series of investigations, they stated Their solution 1 {to the problems of understanding rings of operators) seems to be essential for the further advance of abstract operator theory in Hilbert space under several aspects. First, the formal calculus with operator-rings leads to them. Second, our attempts to generalize the theory of unitary group-representations essentially beyond their classical frame have always been blocked by the unsolved questions connected with these problems. Third, various aspects of the quantum mechanical formalism suggest strongly the elucidation of this subject. Fourth, the knowledge obtained in these investigations gives an approach to a class of abstract algebras without a finite basis, which seems to differ essentially from all types hitherto investigated. Since then there has appeared a large volume of literature, and a great deal of progress has been achieved by many mathematicians.
Author : Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik
Publisher : American Mathematical Soc.
Page : 344 pages
File Size : 51,7 Mb
Release : 2016-08-05
Category : Algebraic topology
ISBN : 9781470434410
Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
Author : James A. Mingo,Roland Speicher
Publisher : Springer
Page : 336 pages
File Size : 48,8 Mb
Release : 2017-06-24
Category : Mathematics
ISBN : 9781493969425
This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory. The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.
Author : Anonim
Publisher : Unknown
Page : 222 pages
File Size : 46,9 Mb
Release : 1981
Category : Hazardous wastes
ISBN : IND:39000008150497
Author : Irving Kaplansky
Publisher : Unknown
Page : 151 pages
File Size : 54,7 Mb
Release : 1968
Category : Lattice theory
ISBN : LCCN:68008872
Author : Miklós Rédei
Publisher : Springer Science & Business Media
Page : 244 pages
File Size : 48,8 Mb
Release : 2013-03-09
Category : Science
ISBN : 9789401590266
This work has grown out of the lecture notes that were prepared for a series of seminars on some selected topics in quantum logic. The seminars were delivered during the first semester of the 1993/1994 academic year in the Unit for Foundations of Science of the Department of History and Foundations of Mathematics and Science, Faculty of Physics, Utrecht University, The Netherlands, while I was staying in that Unit on a European Community Research Grant, and in the Center for Philosophy of Science, University of Pittsburgh, U. S. A. , where I was staying during the 1994/1995 academic year as a Visiting Fellow on a Fulbright Research Grant, and where I also was supported by the Istvan Szechenyi Scholarship Foundation. The financial support provided by these foundations, by the Center for Philosophy of Science and by the European Community is greatly acknowledged, and I wish to thank D. Dieks, the professor of the Foundations Group in Utrecht and G. Massey, the director of the Center for Philosophy of Science in Pittsburgh for making my stay at the respective institutions possible. I also wish to thank both the members of the Foundations Group in Utrecht, especially D. Dieks, C. Lutz, F. Muller, J. Uffink and P. Vermaas and the participants in the seminars at the Center for Philosophy of Science in Pittsburgh, especially N. Belnap, J. Earman, A. Janis, J. Norton, and J.
Author : Volodymyr Nekrashevych
Publisher : American Mathematical Society
Page : 248 pages
File Size : 46,8 Mb
Release : 2024-04-05
Category : Mathematics
ISBN : 9781470476915
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 : Pierre Roberge
Publisher : McGraw-Hill Prof Med/Tech
Page : 1154 pages
File Size : 52,8 Mb
Release : 1999-09-30
Category : Technology & Engineering
ISBN : 9780070765160
Reduce the enormous economic and environmental impact of corrosion Emphasizing quantitative techniques, this guide provides you with: *Theory essential for understanding aqueous, atmospheric, and high temperature corrosion processes Corrosion resistance data for various materials Management techniques for dealing with corrosion control, including life prediction and cost analysis, information systems, and knowledge re-use Techniques for the detection, analysis, and prevention of corrosion damage, including protective coatings and cathodic protection More
Author : Sirakov Boyan,Souza Paulo Ney De,Viana Marcelo
Publisher : World Scientific
Page : 5396 pages
File Size : 45,6 Mb
Release : 2019-02-27
Category : Mathematics
ISBN : 9789813272897
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Author : Ron Martin,Michael Kitson,Peter Tyler
Publisher : Routledge
Page : 178 pages
File Size : 49,7 Mb
Release : 2012-11-12
Category : Business & Economics
ISBN : 9781136012549
There is now a wide spread interest in regions as a key focus in the organization and governance of economic growth and wealth creation. This important book considers the factors that influence and shape the competitive performance of regions. This is not just an issue of academic interest and debate, but also of increasing policy deliberation and action. However, as the readings in this book make clear, the very idea of regional competitiveness is itself complex and contentious. Many academics and policy makers have used the concept without fully considering what is meant by the term and how it can be measured. Policy formulation has tended to rush ahead of understanding and analysis, and the purpose of this book is to close this important gap in understanding. This book was previously published as a special issue of Regional Studies.
Author : Alan L. Porter,Scott W. Cunningham
Publisher : John Wiley & Sons
Page : 384 pages
File Size : 52,9 Mb
Release : 2004-11-26
Category : Technology & Engineering
ISBN : 9780471698456
Tech Mining makes exploitation of text databases meaningful tothose who can gain from derived knowledge about emergingtechnologies. It begins with the premise that we have theinformation, the tools to exploit it, and the need for theresulting knowledge. The information provided puts new capabilities at the hands oftechnology managers. Using the material present, these managers canidentify and access the most valuable technology informationresources (publications, patents, etc.); search, retrieve, andclean the information on topics of interest; and lower the costsand enhance the benefits of competitive technological intelligenceoperations.