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Book Synopsis The Classification of Subfactors with Index at Most $5 frac {1}{4}$ by : Narjess Afzaly
Download or read book The Classification of Subfactors with Index at Most $5 frac {1}{4}$ written by Narjess Afzaly and published by American Mathematical Society. This book was released on 2023-04-07 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
In this seminal work, published by the C.I.A. itself, produced by Intelligence veteran Richards Heuer discusses three pivotal points. First, human minds are ill-equipped ("poorly wired") to cope effectively with both inherent and induced uncertainty. Second, increased knowledge of our inherent biases tends to be of little assistance to the analyst. And lastly, tools and techniques that apply higher levels of critical thinking can substantially improve analysis on complex problems.
Book Synopsis Psychology of Intelligence Analysis by : Richards J Heuer
Download or read book Psychology of Intelligence Analysis written by Richards J Heuer and published by Pickle Partners Publishing. This book was released on 2020-03-05 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this seminal work, published by the C.I.A. itself, produced by Intelligence veteran Richards Heuer discusses three pivotal points. First, human minds are ill-equipped ("poorly wired") to cope effectively with both inherent and induced uncertainty. Second, increased knowledge of our inherent biases tends to be of little assistance to the analyst. And lastly, tools and techniques that apply higher levels of critical thinking can substantially improve analysis on complex problems.
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.
Book Synopsis Topological Quantum Computation by : Zhenghan Wang
Download or read book Topological Quantum Computation written by Zhenghan Wang and published by American Mathematical Soc.. This book was released on 2010 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Government Reports Announcements & Index by :
Download or read book Government Reports Announcements & Index written by and published by . This book was released on 1993-02 with total page 1446 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Tensor Categories by : Pavel Etingof
Download or read book Tensor Categories written by Pavel Etingof and published by American Mathematical Soc.. This book was released on 2016-08-05 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Book Synopsis Regional Competitiveness by : Ron Martin
Download or read book Regional Competitiveness written by Ron Martin and published by Routledge. This book was released on 2012-11-12 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Book Synopsis Theory of Operator Algebras I by : Masamichi Takesaki
Download or read book Theory of Operator Algebras I written by Masamichi Takesaki and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Book Synopsis Quantum Logic in Algebraic Approach by : Miklós Rédei
Download or read book Quantum Logic in Algebraic Approach written by Miklós Rédei and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Book Synopsis Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by : Sirakov Boyan
Download or read book Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) written by Sirakov Boyan and published by World Scientific. This book was released on 2019-02-27 with total page 5396 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Arguably the oldest form of health care, Ayurveda is often referred to as the "Mother of All Healing." Although there has been considerable scientific research done in this area during the last 50 years, the results of that research have not been adequately disseminated. Meeting the need for an authoritative, evidence-based reference, Scientific Basis for Ayurvedic Therapies is the first book to analyze and synthesize current research supporting Ayurvedic medicine. This book reviews the latest scientific information, evaluates the research data, and presents it in an easy to use format. The editor has carefully selected topics based on the availability of scientific studies and the prevalence of a disease. With contributions from experts in their respective fields, topics include Ayurvedic disease management, panchkarma, Ayurvedic bhasmas, the current status of Ayurveda in India, clinical research design, and evaluation of typical clinical trials of certain diseases, to name just a few. While there are many books devoted to Ayurveda, very few have any in-depth basis in scientific studies. This book provides a critical evaluation of literature, clinical trials, and biochemical and pharmacological studies on major Ayurvedic therapies that demonstrates how they are supported by scientific data. Providing a natural bridge from Ayurveda to Western medicine, Scientific Basis for Ayurvedic Therapies facilitates the integration of these therapies by health care providers.
Book Synopsis Scientific Basis for Ayurvedic Therapies by : Lakshmi C. Mishra
Download or read book Scientific Basis for Ayurvedic Therapies written by Lakshmi C. Mishra and published by CRC Press. This book was released on 2003-09-29 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arguably the oldest form of health care, Ayurveda is often referred to as the "Mother of All Healing." Although there has been considerable scientific research done in this area during the last 50 years, the results of that research have not been adequately disseminated. Meeting the need for an authoritative, evidence-based reference, Scientific Basis for Ayurvedic Therapies is the first book to analyze and synthesize current research supporting Ayurvedic medicine. This book reviews the latest scientific information, evaluates the research data, and presents it in an easy to use format. The editor has carefully selected topics based on the availability of scientific studies and the prevalence of a disease. With contributions from experts in their respective fields, topics include Ayurvedic disease management, panchkarma, Ayurvedic bhasmas, the current status of Ayurveda in India, clinical research design, and evaluation of typical clinical trials of certain diseases, to name just a few. While there are many books devoted to Ayurveda, very few have any in-depth basis in scientific studies. This book provides a critical evaluation of literature, clinical trials, and biochemical and pharmacological studies on major Ayurvedic therapies that demonstrates how they are supported by scientific data. Providing a natural bridge from Ayurveda to Western medicine, Scientific Basis for Ayurvedic Therapies facilitates the integration of these therapies by health care providers.
