Fuchsian Reduction
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Fuchsian Reduction
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Author : Satyanad Kichenassamy
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-14
Fuchsian Reduction written by Satyanad Kichenassamy 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 2007-09-14 with Mathematics categories.
This four-part text beautifully interweaves theory and applications in Fuchsian Reduction. Background results in weighted Sobolev and Holder spaces as well as Nash-Moser implicit function theorem are provided. Most chapters contain a problem section and notes with references to the literature. This volume can be used as a text in graduate courses in PDEs and/or Algebra, or as a resource for researchers working with applications to Fuchsian Reduction. The comprehensive approach features the inclusion of problems and bibliographic notes.
Fuchsian Reduction Applications To Geometry Cosmology And Mathematical Physics
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Author : Kichenassamy
language : en
Publisher:
Release Date : 2009-09-01
Fuchsian Reduction Applications To Geometry Cosmology And Mathematical Physics written by Kichenassamy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-01 with categories.
Painlev Equations And Related Topics
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Author : Alexander D. Bruno
language : en
Publisher: Walter de Gruyter
Release Date : 2012-08-31
Painlev Equations And Related Topics written by Alexander D. Bruno and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-31 with Mathematics categories.
This is a proceedings of the international conference "Painlevé Equations and Related Topics" which was taking place at the Euler International Mathematical Institute, a branch of the Saint Petersburg Department of the Steklov Institute of Mathematics of the Russian Academy of Sciences, in Saint Petersburg on June 17 to 23, 2011. The survey articles discuss the following topics: General ordinary differential equations Painlevé equations and their generalizations Painlevé property Discrete Painlevé equations Properties of solutions of all mentioned above equations: – Asymptotic forms and asymptotic expansions – Connections of asymptotic forms of a solution near different points – Convergency and asymptotic character of a formal solution – New types of asymptotic forms and asymptotic expansions – Riemann-Hilbert problems – Isomonodromic deformations of linear systems – Symmetries and transformations of solutions – Algebraic solutions Reductions of PDE to Painlevé equations and their generalizations Ordinary Differential Equations systems equivalent to Painlevé equations and their generalizations Applications of the equations and the solutions
Higher Special Functions
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Author : Wolfgang Lay
language : en
Publisher: Cambridge University Press
Release Date : 2024-05-23
Higher Special Functions written by Wolfgang Lay 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 2024-05-23 with Mathematics categories.
Higher special functions emerge from boundary eigenvalue problems of Fuchsian differential equations with more than three singularities. This detailed reference provides solutions for singular boundary eigenvalue problems of linear ordinary differential equations of second order, exploring previously unknown methods for finding higher special functions. Starting from the fact that it is the singularities of a differential equation that determine the local, as well as the global, behaviour of its solutions, the author develops methods that are both new and efficient and lead to functional relationships that were previously unknown. All the developments discussed are placed within their historical context, allowing the reader to trace the roots of the theory back through the work of many generations of great mathematicians. Particular attention is given to the work of George Cecil Jaffé, who laid the foundation with the calculation of the quantum mechanical energy levels of the hydrogen molecule ion.
Nonlinear Pde S Dynamics And Continuum Physics
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Author : J. L. Bona
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Nonlinear Pde S Dynamics And Continuum Physics written by J. L. Bona 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 Mathematics categories.
This volume contains the refereed proceedings of the conference on Nonlinear Partial Differential Equations, Dynamics and Continuum Physics which was held at Mount Holyoke College in Massachusetts, from July 19th to July 23rd, 1998. Models examined derive from a wide range of applications, including elasticity, thermoviscoelasticity, granular media, fluid dynamics, gas dynamics and conservation laws. Mathematical topics include existence theory and stability/instability of traveling waves, asymptotic behavior of solutions to nonlinear wave equations, effects of dissipation, mechanisms of blow-up, well-posedness and regularity, and fractal solutions. The text will be of interest to graduate students and researchers working in nonlinear partial differential equations and applied mathematics.
Complex Analysis And Dynamical Systems V
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Author : Mark Lʹvovich Agranovskiĭ
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-06-03
Complex Analysis And Dynamical Systems V written by Mark Lʹvovich Agranovskiĭ 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 2013-06-03 with Mathematics categories.
This volume contains the proceedings of the Fifth International Conference on Complex Analysis and Dynamical Systems, held from May 22-27, 2011, in Akko (Acre), Israel. The papers cover a wide variety of topics in complex analysis and partial differential
Elliptic And Parabolic Problems
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Author : Catherine Bandle
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-17
Elliptic And Parabolic Problems written by Catherine Bandle 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 2006-01-17 with Mathematics categories.
Haim Brezis has made significant contributions in the fields of partial differential equations and functional analysis, and this volume collects contributions by his former students and collaborators in honor of his 60th anniversary at a conference in Gaeta. It presents new developments in the theory of partial differential equations with emphasis on elliptic and parabolic problems.
Recent Advances In Mathematical And Statistical Methods
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Author : D. Marc Kilgour
language : en
Publisher: Springer
Release Date : 2018-11-04
Recent Advances In Mathematical And Statistical Methods written by D. Marc Kilgour and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-04 with Computers categories.
This book focuses on the recent development of methodologies and computation methods in mathematical and statistical modelling, computational science and applied mathematics. It emphasizes the development of theories and applications, and promotes interdisciplinary endeavour among mathematicians, statisticians, scientists, engineers and researchers from other disciplines. The book provides ideas, methods and tools in mathematical and statistical modelling that have been developed for a wide range of research fields, including medical, health sciences, biology, environmental science, engineering, physics and chemistry, finance, economics and social sciences. It presents original results addressing real-world problems. The contributions are products of a highly successful meeting held in August 2017 on the main campus of Wilfrid Laurier University, in Waterloo, Canada, the International Conference on Applied Mathematics, Modeling and Computational Science (AMMCS-2017). They make this book a valuable resource for readers interested not only in a broader overview of the methods, ideas and tools in mathematical and statistical approaches, but also in how they can attain valuable insights into problems arising in other disciplines.
On Finiteness In Differential Equations And Diophantine Geometry
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Author : Dana Schlomiuk
language : en
Publisher: American Mathematical Soc.
Release Date :
On Finiteness In Differential Equations And Diophantine Geometry written by Dana Schlomiuk 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 with Mathematics categories.
This book focuses on finiteness conjectures and results in ordinary differential equations (ODEs) and Diophantine geometry. During the past twenty-five years, much progress has been achieved on finiteness conjectures, which are the offspring of the second part of Hilbert's 16th problem. Even in its simplest case, this is one of the very few problems on Hilbert's list which remains unsolved. These results are about existence and estimation of finite bounds for the number of limit cycles occurring in certain families of ODEs. The book describes this progress, the methods used (bifurcation theory, asymptotic expansions, methods of differential algebra, or geometry) and the specific results obtained. The finiteness conjectures on limit cycles are part of a larger picture that also includes finiteness problems in other areas of mathematics, in particular those in Diophantine geometry where remarkable results were proved during the same period of time. There is a chapter devoted to finiteness results in D The volume can be used as an independent study text for advanced undergraduates and graduate students studying ODEs or applications of differential algebra to differential equations and Diophantine geometry. It is also is a good entry point for researchers interested these areas, in particular, in limit cycles of ODEs, and in finiteness problems. Contributors to the volume include Andrey Bolibrukh and Alexandru Buium. Available from the AMS by A. Buium is Arithmetic Differential Equations, as Volume 118 in the Mathematical Surveys and Monographs series.
Basic Modern Theory Of Linear Complex Analytic Q Difference Equations
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Author : Jacques Sauloy
language : en
Publisher: American Mathematical Society
Release Date : 2024-11-06
Basic Modern Theory Of Linear Complex Analytic Q Difference Equations written by Jacques Sauloy and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-06 with Mathematics categories.
The roots of the modern theories of differential and $q$-difference equations go back in part to an article by George D. Birkhoff, published in 1913, dealing with the three ?sister theories? of differential, difference and $q$-difference equations. This book is about $q$-difference equations and focuses on techniques inspired by differential equations, in line with Birkhoff's work, as revived over the last three decades. It follows the approach of the Ramis school, mixing algebraic and analytic methods. While it uses some $q$-calculus and is illustrated by $q$-special functions, these are not its main subjects. After a gentle historical introduction with emphasis on mathematics and a thorough study of basic problems such as elementary $q$-functions, elementary $q$-calculus, and low order equations, a detailed algebraic and analytic study of scalar equations is followed by the usual process of transforming them into systems and back again. The structural algebraic and analytic properties of systems are then described using $q$-difference modules (Newton polygon, filtration by the slopes). The final chapters deal with Fuchsian and irregular equations and systems, including their resolution, classification, Riemann-Hilbert correspondence, and Galois theory. Nine appendices complete the book and aim to help the reader by providing some fundamental yet not universally taught facts. There are 535 exercises of various styles and levels of difficulty. The main prerequisites are general algebra and analysis as taught in the first three years of university. The book will be of interest to expert and non-expert researchers as well as graduate students in mathematics and physics.