The Dynamical Yang Baxter Equation Representation Theory And Quantum Integrable Systems
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The Dynamical Yang Baxter Equation Representation Theory And Quantum Integrable Systems
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Author : Pavel Etingof
language : en
Publisher: OUP Oxford
Release Date : 2005-03-24
The Dynamical Yang Baxter Equation Representation Theory And Quantum Integrable Systems written by Pavel Etingof and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03-24 with Mathematics categories.
The text is based on an established graduate course given at MIT that provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in representation theory and quantum groups. The book, which contains many detailed proofs and explicit calculations, will be accessible to graduate students of mathematics, who are familiar with the basics of representation theory of semisimple Lie algebras.
The Dynamical Yang Baxter Equation Representation Theory And Quantum Integrable Systems
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Author : P. I. Etingof
language : en
Publisher:
Release Date : 2005
The Dynamical Yang Baxter Equation Representation Theory And Quantum Integrable Systems written by P. I. Etingof and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Yang Baxter Equation In Integrable Systems
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Author : Michio Jimbo
language : ja
Publisher: World Scientific
Release Date : 1990
Yang Baxter Equation In Integrable Systems written by Michio Jimbo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Science categories.
This volume will be the first reference book devoted specially to the Yang-Baxter equation. The subject relates to broad areas including solvable models in statistical mechanics, factorized S matrices, quantum inverse scattering method, quantum groups, knot theory and conformal field theory. The articles assembled here cover major works from the pioneering papers to classical Yang-Baxter equation, its quantization, variety of solutions, constructions and recent generalizations to higher genus solutions.
Quantum Groups And Lie Theory
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Author : Andrew Pressley
language : en
Publisher: Cambridge University Press
Release Date : 2002-01-17
Quantum Groups And Lie Theory written by Andrew Pressley and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-17 with Mathematics categories.
Since its genesis in the early 1980s, the subject of quantum groups has grown rapidly. By the late 1990s most of the foundational issues had been resolved and many of the outstanding problems clearly formulated. To take stock and to discuss the most fruitful directions for future research many of the world's leading figures in this area met at the Durham Symposium on Quantum Groups in the summer of 1999, and this volume provides an excellent overview of the material presented there. It includes important surveys of both cyclotomic Hecke algebras and the dynamical Yang-Baxter equation. Plus contributions which treat the construction and classification of quantum groups or the associated solutions of the quantum Yang-Baxter equation. The representation theory of quantum groups is discussed, as is the function algebra approach to quantum groups, and there is a new look at the origins of quantum groups in the theory of integrable systems.
Hopf Algebras And Generalizations
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Author : Louis H. Kauffman
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Hopf Algebras And Generalizations written by Louis H. Kauffman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Hopf algebras have proved to be very interesting structures with deep connections to various areas of mathematics, particularly through quantum groups. Indeed, the study of Hopf algebras, their representations, their generalizations, and the categories related to all these objects has an interdisciplinary nature. It finds methods, relationships, motivations and applications throughout algebra, category theory, topology, geometry, quantum field theory, quantum gravity, and also combinatorics, logic, and theoretical computer science. This volume portrays the vitality of contemporary research in Hopf algebras. Altogether, the articles in the volume explore essential aspects of Hopf algebras and some of their best-known generalizations by means of a variety of approaches and perspectives. They make use of quite different techniques that are already consolidated in the area of quantum algebra. This volume demonstrates the diversity and richness of its subject. Most of its papers introduce the reader to their respective contexts and structures through very expository preliminary sections.
Hypergeometry Integrability And Lie Theory
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Author : Erik Koelink
language : en
Publisher: American Mathematical Soc.
Release Date : 2022-08-30
Hypergeometry Integrability And Lie Theory written by Erik Koelink and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-30 with Education categories.
This volume contains the proceedings of the virtual conference on Hypergeometry, Integrability and Lie Theory, held from December 7–11, 2020, which was dedicated to the 50th birthday of Jasper Stokman. The papers represent recent developments in the areas of representation theory, quantum integrable systems and special functions of hypergeometric type.
Smoothing And Decay Estimates For Nonlinear Diffusion Equations
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Author : Juan Luis Vázquez
language : en
Publisher: OUP Oxford
Release Date : 2006-08-03
Smoothing And Decay Estimates For Nonlinear Diffusion Equations written by Juan Luis Vázquez and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-03 with Mathematics categories.
This text is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the classical heat equation. They appear as mathematical models in different branches of Physics, Chemistry, Biology, and Engineering, and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on estimates and functional analysis. Concentrating on a class of equations with nonlinearities of power type that lead to degenerate or singular parabolicity ("equations of porous medium type"), the aim of this text is to obtain sharp a priori estimates and decay rates for general classes of solutions in terms of estimates of particular problems. These estimates are the building blocks in understanding the qualitative theory, and the decay rates pave the way to the fine study of asymptotics. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including time decay, smoothing, extinction in finite time, and delayed regularity.
Graph Theory As I Have Known It
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Author : W. T. Tutte
language : en
Publisher: Oxford University Press
Release Date : 2012-05-24
Graph Theory As I Have Known It written by W. T. Tutte and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-24 with Mathematics categories.
A unique introduction to graph theory, written by one of the founding fathers. Professor William Tutte, codebreaker and mathematician, details his experiences in the area and provides a fascinating insight into the processes leading to his proofs.
The Factorization Method For Inverse Problems
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Author : Andreas Kirsch
language : en
Publisher: OUP Oxford
Release Date : 2007-12-13
The Factorization Method For Inverse Problems written by Andreas Kirsch and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-13 with Mathematics categories.
The factorization method is a relatively new method for solving certain types of inverse scattering problems and problems in tomography. Aimed at students and researchers in Applied Mathematics, Physics and Engineering, this text introduces the reader to this promising approach for solving important classes of inverse problems. The wide applicability of this method is discussed by choosing typical examples, such as inverse scattering problems for the scalar Helmholtz equation, a scattering problem for Maxwell's equation, and a problem in impedance and optical tomography. The last section of the book compares the Factorization Method to established sampling methods (the Linear Sampling Method, the Singular Source Method, and the Probe Method).
Mathematical Geophysics
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Author : Jean-Yves Chemin
language : en
Publisher: Clarendon Press
Release Date : 2006-04-13
Mathematical Geophysics written by Jean-Yves Chemin and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-13 with Science categories.
Aimed at graduate students, researchers and academics in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The text is divided into four parts, with the first part providing the physical background of the geophysical models to be analysed. Part II is devoted to a self contained proof of the existence of weak (or strong) solutions to the incompressible Navier-Stokes equations. Part III deals with the rapidly rotating Navier-Stokes equations, first in the whole space, where dispersion effects are considered. The case where the domain has periodic boundary conditions is then analysed, and finally rotating Navier-Stokes equations between two plates are studied, both in the case of periodic horizontal coordinates and those in R2. In Part IV the stability of Ekman boundary layers, and boundary layer effects in magnetohydrodynamics and quasigeostrophic equations are discussed. The boundary layers which appear near vertical walls are presented and formally linked with the classical Prandlt equations. Finally spherical layers are introduced, whose study is completely open.