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1 Konno, Hitoshi Elliptic Quantum Groups I09584 2020 eBook  
2 Weingartner, Paul A Alternative Logics. Do Sciences Need Them? I11584 2004 eBook  
3 Coecke, Bob Current Research in Operational Quantum Logic I11348 2000 eBook  
4 Pavicic, Mladen Quantum Computation and Quantum Communication I06732 2006 eBook  
5 Rosenberg, Ivo G Algebras and Orders I05135 1993 eBook  
6 Rival, Ivan Ordered Sets I04730 1982 eBook  
7 Goerss, P.G Algebraic K-Theory and Algebraic Topology I02299 1993 eBook  
8 Rival, Ivan Graphs and Order I00228 1985 eBook  
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TitleElliptic Quantum Groups : Representations and Related Geometry
Author(s)Konno, Hitoshi
PublicationSingapore, 1. Imprint: Springer 2. Springer Singapore, 2020.
DescriptionXIII, 131 p. 3 illus : online resource
Abstract NoteThis is the first book on elliptic quantum groups, i.e., quantum groups associated to elliptic solutions of the Yang-Baxter equation. Based on research by the author and his collaborators, the book presents a comprehensive survey on the subject including a brief history of formulations and applications, a detailed formulation of the elliptic quantum group in the Drinfeld realization, explicit construction of both finite and infinite-dimensional representations, and a construction of the vertex operators as intertwining operators of these representations. The vertex operators are important objects in representation theory of quantum groups. In this book, they are used to derive the elliptic q-KZ equations and their elliptic hypergeometric integral solutions. In particular, the so-called elliptic weight functions appear in such solutions. The author???s recent study showed that these elliptic weight functions are identified with Okounkov???s elliptic stable envelopes for certain equivariant elliptic cohomology and play an important role to construct geometric representations of elliptic quantum groups. Okounkov???s geometric approach to quantum integrable systems is a rapidly growing topic in mathematical physics related to the Bethe ansatz, the Alday-Gaiotto-Tachikawa correspondence between 4D SUSY gauge theories and the CFT???s, and the Nekrasov-Shatashvili correspondences between quantum integrable systems and quantum cohomology. To invite the reader to such topics is one of the aims of this book
ISBN,Price9789811573873
Keyword(s)1. ALGEBRA 2. EBOOK 3. EBOOK - SPRINGER 4. GROUP THEORY 5. Group Theory and Generalizations 6. Mathematical Applications in the Physical Sciences 7. MATHEMATICAL PHYSICS 8. Order, Lattices, Ordered Algebraic Structures 9. Ordered algebraic structures
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2.     
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TitleAlternative Logics. Do Sciences Need Them?
Author(s)Weingartner, Paul A
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2004.
DescriptionXVII, 368 p : online resource
Abstract NoteInitially proposed as rivals of classical logic, alternative logics have become increasingly important in sciences such as quantum physics, computer science, and artificial intelligence. The contributions collected in this volume address and explore the question whether the usage of logic in the sciences, especially in modern physics, requires a deviation from classical mathematical logic. The articles in the first part of the book set the scene by describing the context and the dilemma when applying logic in science. In Part II the authors offer several logics that deviate in different ways from classical logics. The twelve papers in Part III investigate in detail specific aspects such as quantum logic, quantum computation, computer-science considerations, praxic logic, and quantum probability. Most of the contributions are revised and partially extended versions of papers presented at a conference of the same title of the Acad??mie Internationale de Philosophie des Sciences held at the Internationales Forschungszentrum Salzburg in May 1999. Others have been added to complete the picture of recent research in alternative logics as they have been developed for applications in the sciences
ISBN,Price9783662056790
Keyword(s)1. ALGEBRA 2. COMPUTERS 3. EBOOK 4. EBOOK - SPRINGER 5. Order, Lattices, Ordered Algebraic Structures 6. Ordered algebraic structures 7. PHILOSOPHY 8. Philosophy, general 9. QUANTUM COMPUTERS 10. Quantum Information Technology, Spintronics 11. QUANTUM PHYSICS 12. SPINTRONICS 13. Theory of Computation
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TitleCurrent Research in Operational Quantum Logic : Algebras, Categories, Languages
Author(s)Coecke, Bob;Moore, David;Wilce, Alexander
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 2000.
DescriptionVII, 325 p : online resource
Abstract NoteThe present volume has its origins in a pair of informal workshops held at the Free University of Brussels, in June of 1998 and May of 1999, named "Current Research 1 in Operational Quantum Logic". These brought together mathematicians and physicists working in operational quantum logic and related areas, as well as a number of interested philosophers of science, for a rare opportunity to discuss recent developments in this field. After some discussion, it was decided that, rather than producing a volume of conference proceedings, we would try to organize the conferees to produce a set of comprehensive survey papers, which would not only report on recent developments in quantum logic, but also provide a tutorial overview of the subject suitable for an interested non-specialist audience. The resulting volume provides an overview of the concepts and methods used in current research in quantum logic, viewed both as a branch of mathemati?? cal physics and as an area of pure mathematics. The first half of the book is concerned with the algebraic side of the subject, and in particular the theory of orthomodular lattices and posets, effect algebras, etc. In the second half of the book, special attention is given to categorical methods and to connections with theoretical computer science. At the 1999 workshop, we were fortunate to hear three excellent lectures by David J. Foulis, represented here by two contributions. Dave's work, spanning 40 years, has helped to define, and continues to reshape, the field of quantum logic
ISBN,Price9789401712019
Keyword(s)1. ALGEBRA 2. Applications of Mathematics 3. APPLIED MATHEMATICS 4. Category theory (Mathematics) 5. Category Theory, Homological Algebra 6. EBOOK 7. EBOOK - SPRINGER 8. ENGINEERING MATHEMATICS 9. GROUP THEORY 10. Group Theory and Generalizations 11. Homological algebra 12. Order, Lattices, Ordered Algebraic Structures 13. Ordered algebraic structures 14. QUANTUM PHYSICS
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TitleQuantum Computation and Quantum Communication : Theory and Experiments
Author(s)Pavicic, Mladen
PublicationNew York, NY, 1. Imprint: Springer 2. Springer US, 2006.
DescriptionXVI, 223 p : online resource
Abstract NoteThe field of quantum computing has experienced rapid development and many different experimental and theoretical groups have emerged worldwide.This book presents the key elements of quantum computation and communication theories and their implementation in an easy-to-read manner for readers coming from physics, mathematics and computer science backgrounds. Integrating both theoretical aspects and experimental verifications of developing quantum computers, the author explains why particular mathematical methods, physical models and realistic implementations might provide critical steps towards achieving the final goal - constructing quantum computers and quantum networks. The book serves as an excellent introduction for new researchers and also provides a useful review for specialists in the field
ISBN,Price9780387289007
Keyword(s)1. ALGEBRA 2. Communications Engineering, Networks 3. Computer science???Mathematics 4. EBOOK 5. EBOOK - SPRINGER 6. ELECTRICAL ENGINEERING 7. Mathematics of Computing 8. Order, Lattices, Ordered Algebraic Structures 9. Ordered algebraic structures 10. QUANTUM COMPUTERS 11. Quantum Information Technology, Spintronics 12. QUANTUM OPTICS 13. QUANTUM PHYSICS 14. SPINTRONICS
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TitleAlgebras and Orders
Author(s)Rosenberg, Ivo G;Sabidussi, Gert
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 1993.
DescriptionXVIII, 558 p : online resource
Abstract NoteIn the summer of 1991 the Department of Mathematics and Statistics of the Universite de Montreal was fortunate to host the NATO Advanced Study Institute "Algebras and Orders" as its 30th Seminaire de mathematiques superieures (SMS), a summer school with a long tradition and well-established reputation. This book contains the contributions of the invited speakers. Universal algebra- which established itself only in the 1930's- grew from traditional algebra (e.g., groups, modules, rings and lattices) and logic (e.g., propositional calculus, model theory and the theory of relations). It started by extending results from these fields but by now it is a well-established and dynamic discipline in its own right. One of the objectives of the ASI was to cover a broad spectrum of topics in this field, and to put in evidence the natural links to, and interactions with, boolean algebra, lattice theory, topology, graphs, relations, automata, theoretical computer science and (partial) orders. The theory of orders is a relatively young and vigorous discipline sharing certain topics as well as many researchers and meetings with universal algebra and lattice theory. W. Taylor surveyed the abstract clone theory which formalizes the process of compos?? ing operations (i.e., the formation of term operations) of an algebra as a special category with countably many objects, and leading naturally to the interpretation and equivalence of varieties
ISBN,Price9789401706971
Keyword(s)1. ALGEBRA 2. Computer science???Mathematics 3. Discrete Mathematics in Computer Science 4. EBOOK 5. EBOOK - SPRINGER 6. MATHEMATICAL LOGIC 7. Mathematical Logic and Foundations 8. NUMBER THEORY 9. Order, Lattices, Ordered Algebraic Structures 10. Ordered algebraic structures 11. TOPOLOGY
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6.     
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TitleOrdered Sets : Proceedings of the NATO Advanced Study Institute held at Banff, Canada, August 28 to September 12, 1981
Author(s)Rival, Ivan
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 1982.
Description978 p : online resource
Abstract NoteThis volume contains all twenty-three of the principal survey papers presented at the Symposium on Ordered Sets held at Banff, Canada from August 28 to September 12, 1981. The Symposium was supported by grants from the NATO Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada, the Canadian Mathematical Society Summer Research Institute programme, and the University of Calgary. tve are very grateful to these Organizations for their considerable interest and support. Over forty years ago on April 15, 1938 the first Symposium on Lattice Theory was held in Charlottesville, U.S.A. in conjunction with a meeting of the American Mathematical Society. The principal addresses on that occasion were Lattices and their applications by G. Birkhoff, On the application of structure theory to groups by O. Ore, and The representation of Boolean algebras by M. H. Stone. The texts of these addresses and three others by R. Baer, H. M. MacNeille, and K. Menger appear in the Bulletin of the American Mathematical Society, Volume 44, 1938. In those days the theory of ordered sets, and especially lattice theory was described as a "vigorous and promising younger brother of group theory." Some early workers hoped that lattice?? theoretic methods would lead to solutions of important problems in group theory
ISBN,Price9789400977983
Keyword(s)1. ALGEBRA 2. Computer science???Mathematics 3. Discrete Mathematics in Computer Science 4. EBOOK 5. EBOOK - SPRINGER 6. Order, Lattices, Ordered Algebraic Structures 7. Ordered algebraic structures
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7.     
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TitleAlgebraic K-Theory and Algebraic Topology
Author(s)Goerss, P.G;Jardine, John F
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 1993.
DescriptionXII, 328 p : online resource
Abstract NoteA NATO Advanced Study Institute entitled "Algebraic K-theory and Algebraic Topology" was held at Chateau Lake Louise, Lake Louise, Alberta, Canada from December 12 to December 16 of 1991. This book is the volume of proceedings for this meeting. The papers that appear here are representative of most of the lectures that were given at the conference, and therefore present a "snapshot" of the state ofthe K-theoretic art at the end of 1991. The underlying objective of the meeting was to discuss recent work related to the Lichtenbaum-Quillen complex of conjectures, fro~ both the algebraic and topological points of view. The papers in this volume deal with a range of topics, including motivic cohomology theories, cyclic homology, intersection homology, higher class field theory, and the former telescope conjecture. This meeting was jointly funded by grants from NATO and the National Science Foun?? dation in the United States. I would like to take this opportunity to thank these agencies for their support. I would also like to thank the other members of the organizing com?? mittee, namely Paul Goerss, Bruno Kahn and Chuck Weibel, for their help in making the conference successful. This was the second NATO Advanced Study Institute to be held in this venue; the first was in 1987. The success of both conferences owes much to the professionalism and helpfulness of the administration and staff of Chateau Lake Louise
ISBN,Price9789401706957
Keyword(s)1. ALGEBRA 2. ALGEBRAIC GEOMETRY 3. ALGEBRAIC TOPOLOGY 4. Associative rings 5. Associative Rings and Algebras 6. EBOOK 7. EBOOK - SPRINGER 8. K-THEORY 9. Order, Lattices, Ordered Algebraic Structures 10. Ordered algebraic structures 11. Rings (Algebra)
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8.    
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TitleGraphs and Order : The Role of Graphs in the Theory of Ordered Sets and Its Applications
Author(s)Rival, Ivan
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 1985.
Description816 p : online resource
Abstract NoteThis volume contains the accounts of the principal survey papers presented at GRAPHS and ORDER, held at Banff, Canada from May 18 to May 31, 1984. This conference was supported by grants from the N.A.T.O. Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada and the University of Calgary. We are grateful for all of this considerable support. Almost fifty years ago the first Symposium on Lattice Theory was held in Charlottesville, U.S.A. On that occasion the principal lectures were delivered by G. Birkhoff, O. Ore and M.H. Stone. In those days the theory of ordered sets was thought to be a vigorous relative of group theory. Some twenty-five years ago the Symposium on Partially Ordered Sets and Lattice Theory was held in Monterey, U.S.A. Among the principal speakers at that meeting were R.P. Dilworth, B. Jonsson, A. Tarski and G. Birkhoff. Lattice theory had turned inward: it was concerned primarily with problems about lattices themselves. As a matter of fact the problems that were then posed have, by now, in many instances, been completely solved
ISBN,Price9789400953154
Keyword(s)1. ALGEBRA 2. Computer science???Mathematics 3. Discrete Mathematics in Computer Science 4. EBOOK 5. EBOOK - SPRINGER 6. Order, Lattices, Ordered Algebraic Structures 7. Ordered algebraic structures
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