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1. |
Record Nr. |
UNINA9910438032603321 |
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Autore |
Haigh John |
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Titolo |
Probability Models / / by John Haigh |
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Pubbl/distr/stampa |
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London : , : Springer London : , : Imprint : Springer, , 2013 |
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ISBN |
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Edizione |
[2nd ed. 2013.] |
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Descrizione fisica |
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1 online resource (XII, 287 p. 17 illus.) |
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Collana |
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Springer Undergraduate Mathematics Series, , 1615-2085 |
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Disciplina |
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Soggetti |
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Probabilities |
Computer simulation |
Mathematical statistics |
Operations research |
Decision making |
Computer science—Mathematics |
Computer science - Mathematics |
Mathematical physics |
Probability Theory and Stochastic Processes |
Simulation and Modeling |
Probability and Statistics in Computer Science |
Operations Research/Decision Theory |
Mathematical Applications in Computer Science |
Mathematical Applications in the Physical Sciences |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Probability Spaces -- Conditional Probability and Independence -- Common Probability Distributions -- Random Variables -- Sums of Random Variables -- Convergence and Limit Theorems -- Stochastic Processes in Discrete Time -- Stochastic Processes in Continuous Time -- Appendix: Common Distributions and Mathematical Facts. |
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Sommario/riassunto |
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The purpose of this book is to provide a sound introduction to the study of real-world phenomena that possess random variation. It describes how to set up and analyse models of real-life phenomena that involve elements of chance. Motivation comes from everyday |
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experiences of probability, such as that of a dice or cards, the idea of fairness in games of chance, and the random ways in which, say, birthdays are shared or particular events arise. Applications include branching processes, random walks, Markov chains, queues, renewal theory, and Brownian motion. This popular second edition textbook contains many worked examples and several chapters have been updated and expanded. Some mathematical knowledge is assumed. The reader should have the ability to work with unions, intersections and complements of sets; a good facility with calculus, including integration, sequences and series; and appreciation of the logical development of an argument. Probability Models< is designed to aid students studying probability as part of an undergraduate course on mathematics or mathematics and statistics. |
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2. |
Record Nr. |
UNINA9910967063403321 |
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Titolo |
Topology and physics : Proceedings of the Nankai International Conference in Memory of Xiao-Song Lin, Tianjin, China, 27-31 July 2007 / / editors, Kevin Lin, Zhenghan Wang, Weiping Zhang |
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Pubbl/distr/stampa |
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Hackensak, N.J., : World Scientific, c2008 |
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ISBN |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (468 p.) |
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Collana |
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Nankai tracts in mathematics ; ; v. 12 |
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Altri autori (Persone) |
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LinXiao-song <1957-2007.> |
LinKevin |
WangZhenghan |
ZhangWeiping <1964-> |
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Disciplina |
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Soggetti |
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Low-dimensional topology |
Quantum field theory |
Algebraic topology |
Field theory (Physics) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Papers from a memorial conference in honor of Xiao-Song Lin, organized by the Chern Institue of Mathematics and held in Tianjin, July |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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Foreword; Preface; Short Biography of Lin; Mathematics of Lin; Organizing Committees; List of Participants; Program; Welcome Speech of Weiping Zhang; Speech of Boju Jiang; CONTENTS; Part A Invited Contributions; The Modified Calabi-Yau Problems for CR-manifolds J. Cao and S.-C. Chang; 0. Introduction; 1. Bounded solutions to d = on manifolds with negative curvature; 2. The modified Calabi-Yau problems for singular spaces and CR-manifolds; A. Sup-harmonic functions on Alexandrov spaces with nonnegative sectional curvature |
B. The generalized Calabi problems for Kahler domains with boundaries C. The Calabi-Escobar type problem for Kahler domains with boundaries; Acknowledgments; References; On Picture (2+1)-TQFTs M. Freedman, C. Nayak, K. Walker and Z. Wang; 1. Introduction; 2. Jones representations; 2.1. Braid statistics; 2.2. Generic Jones representation of the braid groups; 2.3. Unitary Jones representations; 2.4. Uniqueness of Jones-Wenzl projectors; 3. Diagram TQFTs for closed manifolds; 3.1. ""d-isotopy"", local relation, and skein relation; 3.2. Picture classes; 3.3. Skein classes; 3.4. Recoupling theory |
3.5. Handles and S-matrix 3.6. Diagram TQFTs for closed manifolds; 3.7. Boundary conditions for picture TQFTs; 3.8. Jones-Kauffman skein spaces; 4. Morita equivalence and cut-paste topology; 4.1. Bimodules over picture category; 4.2. Cutting and paste as Morita equivalence; 4.3. Annualization and quantum double; 5. Temperley-Lieb-Jones categories; 5.1. Annular Markov trace; 5.2. Representation of Temperley-Lieb-Jones categories; 5.3. Rectangular Tempeley-Lieb-Jones categories for low levels; 5.3.1. Level=1, d2 = 1; 5.3.2. Level=2, d2 = 2; 5.3.3. Level=3, d2 = 1 + d or d2 = 1 |
5.4. Annular Temperley-Lieb-Jones theories for low levels 5.4.1. Level=1, d2 = 1; 5.4.2. Level=2, d2 = 2; 5.4.3. Level=3, d2 = 1 + d or d2 = 1; 5.5. Temperley-Lieb-Jones categories for primitive 4th roots of unity; 5.6. Temperley-Lieb-Jones categories for primitive 2nd root of unity, rodd; 6. The definition of a TQFT; 6.1. Redined labels for TQFTs; 6.2. Anomaly of TQFTs and extended manifolds; 6.3. Axioms for TQFTs; 6.4. More consequences of the axioms; 6.5. Framed link invariants and modular representation; 6.6. Verlinde algebras and Verlinde formulas |
7. Diagram and Jones-Kau man TQFTs 7.1. Diagram TQFTs; 7.2. Jones-Kau man TQFTs; 8. WRT and Turaev-Viro SU(2)-TQFTs; 8.1. Flagged TLJ categories; 8.2. Turaev-Viro Unitary TQFTs; 8.3. WRT Unitary TQFTs; 9. Black-White TQFTs; 9.1. Black-white TLJ categories; 9.2. Labels for black-white theories; 9.2.1. Level=2, d2 = 2; 9.2.2. Level=3; 9.3. BW TQFTs; 10. Classification and Unitarity; 10.1. Classification of diagram local relations; 10.2. Unitary TQFTs; 10.3. Classication and unitarity; Appendix A. Topological phases of matter; Ground states manifolds as modular functors |
Elementary excitations as particles |
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Sommario/riassunto |
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This unique volume, resulting from a conference at the Chern Institute of Mathematics dedicated to the memory of Xiao-Song Lin, presents a broad connection between topology and physics as exemplified by the relationship between low-dimensional topology and quantum field theory.The volume includes works on picture (2+1)-TQFTs and their applications to quantum computing, Berry phase and Yang-Baxterization of the braid relation, finite type invariant of knots, categorification and Khovanov homology, Gromov-Witten type invariants, twisted Alexander polynomials, Faddeev knots, generalized Ricci flo |
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