The Riemann Hilbert Problem
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The Riemann Hilbert Problem
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Author : D. V. Anosov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
The Riemann Hilbert Problem written by D. V. Anosov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
The Riemann-Hilbert problem (Hilbert's 21st problem) belongs to the theory of linear systems of ordinary differential equations in the complex domain. The problem concerns the existence of a Fuchsian system with prescribed singularities and monodromy. Hilbert was convinced that such a system always exists. However, this turned out to be a rare case of a wrong forecast made by him. In 1989 the second author (A. B.) discovered a counterexample, thus obtaining a negative solution to Hilbert's 21st problem in its original form.
The Riemann Hilbert Problem
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Author : D. V. Anosov
language : en
Publisher:
Release Date : 1994
The Riemann Hilbert Problem written by D. V. Anosov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
Aspects Of Mathematics
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Author :
language : en
Publisher:
Release Date : 1981
Aspects Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Riemann Hilbert Problems Their Numerical Solution And The Computation Of Nonlinear Special Functions
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Author : Thomas Trogdon
language : en
Publisher: SIAM
Release Date : 2015-12-22
Riemann Hilbert Problems Their Numerical Solution And The Computation Of Nonlinear Special Functions written by Thomas Trogdon and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-22 with Mathematics categories.
Riemann?Hilbert problems are fundamental objects of study within complex analysis. Many problems in differential equations and integrable systems, probability and random matrix theory, and asymptotic analysis can be solved by reformulation as a Riemann?Hilbert problem.This book, the most comprehensive one to date on the applied and computational theory of Riemann?Hilbert problems, includes an introduction to computational complex analysis, an introduction to the applied theory of Riemann?Hilbert problems from an analytical and numerical perspective, and a discussion of applications to integrable systems, differential equations, and special function theory. It also includes six fundamental examples and five more sophisticated examples of the analytical and numerical Riemann?Hilbert method, each of mathematical or physical significance or both.
Recent Developments In Integrable Systems And Riemann Hilbert Problems
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Author : Kenneth T-R McLaughlin
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Recent Developments In Integrable Systems And Riemann Hilbert Problems written by Kenneth T-R McLaughlin 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 2003 with Mathematics categories.
This volume is a collection of papers presented at a special session on integrable systems and Riemann-Hilbert problems. The goal of the meeting was to foster new research by bringing together experts from different areas. Their contributions to the volume provide a useful portrait of the breadth and depth of integrable systems. Topics covered include discrete Painleve equations, integrable nonlinear partial differential equations, random matrix theory, Bose-Einstein condensation, spectral and inverse spectral theory, and last passage percolation models. In most of these articles, the Riemann-Hilbert problem approach plays a central role, which is powerful both analytically and algebraically. The book is intended for graduate students and researchers interested in integrable systems and its applications.
The 21st Hilbert Problem For Linear Fuchsian Systems
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Author : A. A. Bolibrukh
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
The 21st Hilbert Problem For Linear Fuchsian Systems written by A. A. Bolibrukh 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 1995 with Mathematics categories.
Bolibrukh presents the negative solution of Hilbert's twenty-first problem for linear Fuchsian systems of differential equations. Methods developed by Bolibrukh in solving this problem are then applied to the study of scalar Fuchsian equations and systems with regular singular points on the Riemmann sphere.
Orthogonal Polynomials And Random Matrices A Riemann Hilbert Approach
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Author : Percy Deift
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Orthogonal Polynomials And Random Matrices A Riemann Hilbert Approach written by Percy Deift 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 2000 with Orthogonal polynomials categories.
This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models. The central question was the following: Why do very general ensembles of random n times n matrices exhibit universal behavior as n > infinity? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems. Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.
Painleve Transcendents
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Author : A. S. Fokas
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Painleve Transcendents written by A. S. Fokas 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 2006 with Mathematics categories.
At the turn of the twentieth century, the French mathematician Paul Painleve and his students classified second order nonlinear ordinary differential equations with the property that the location of possible branch points and essential singularities of their solutions does not depend on initial conditions. It turned out that there are only six such equations (up to natural equivalence), which later became known as Painleve I-VI. Although these equations were initially obtainedanswering a strictly mathematical question, they appeared later in an astonishing (and growing) range of applications, including, e.g., statistical physics, fluid mechanics, random matrices, and orthogonal polynomials. Actually, it is now becoming clear that the Painleve transcendents (i.e., the solutionsof the Painleve equations) play the same role in nonlinear mathematical physics that the classical special functions, such as Airy and Bessel functions, play in linear physics. The explicit formulas relating the asymptotic behaviour of the classical special functions at different critical points, play a crucial role in the applications of these functions. It is shown in this book, that even though the six Painleve equations are nonlinear, it is still possible, using a new technique called theRiemann-Hilbert formalism, to obtain analogous explicit formulas for the Painleve transcendents. This striking fact, apparently unknown to Painleve and his contemporaries, is the key ingredient for the remarkable applicability of these ``nonlinear special functions''. The book describes in detail theRiemann-Hilbert method and emphasizes its close connection to classical monodromy theory of linear equations as well as to modern theory of integrable systems. In addition, the book contains an ample collection of material concerning the asymptotics of the Painleve functions and their various applications, which makes it a good reference source for everyone working in the theory and applications of Painleve equations and related areas.
Bolibrukh The Riemann Hilbert Problem
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Author : D. V. Anosov
language : en
Publisher:
Release Date :
Bolibrukh The Riemann Hilbert Problem written by D. V. Anosov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
The Riemann Hypothesis And Hilbert S Tenth Problem
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Author : Sarvadaman Chowla
language : en
Publisher: CRC Press
Release Date : 1987
The Riemann Hypothesis And Hilbert S Tenth Problem written by Sarvadaman Chowla and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.