Read Time: ~4.2 hr

Gröbner Deformations of Hypergeometric Differential Equations

Name: Gröbner Deformations of Hypergeometric Differential Equations
Author: Mutsumi Saito, Bernd Sturmfels, Nobuki Takayama
ISBN: 9783642085345

by Mutsumi Saito, Bernd Sturmfels, Nobuki Takayama (2000)

Read Free Sample Buy on Amazon Audible Free Trial

About this book

In recent years, new algorithms for dealing with rings of differential operators have been discovered and implemented. A main tool is the theory of Gröbner bases, which is reexamined here from the point of view of geometric deformations. Perturbation techniques have a long tradition in analysis; Gröbner deformations of left ideals in the Weyl algebra are the algebraic analogue to classical perturbation techniques. The algorithmic methods introduced in this book are particularly useful for studying the systems of multidimensional hypergeometric partial differentiel equations introduced by Gel'fand, Kapranov and Zelevinsky. The Gröbner deformation of these GKZ hypergeometric systems reduces problems concerning hypergeometric functions to questions about commutative monomial ideals, and thus leads to an unexpected interplay between analysis and combinatorics. This book contains a number of original research results on holonomic systems and hypergeometric functions, and it raises many open problems for future research in this rapidly growing area of computational mathematics '

Setting / LocationGlobal

Story EraContemporary / Future

Protagonist / CoreGröbner Deformations of Hypergeometric Differential Equations Lead Character

Themes & Moods

Science & Technology Combinatorics Mathematics Global analysis (Mathematics)Algorithms Geometry, algebraic Contemporary / Future

Readers who enjoyed this also loved

Bioinformatics

Volker Sperschneider

"There are fundamental principles for problem analysis and algorithm design that are continuously used in bioinformatics. This book concentrates on a clear presentation of these principles, presenting them in a self-contained, mathematically clear and precise manner, and illustrating them with lots of case studies from main fields of bioinformatics. Emphasis is laid on algorithmic "pearls" of bioinformatics, showing that things may get rather simple when taking a proper view into them. The book closes with a thorough bibliography, ranging from classic research results to very recent findings, providing many pointers for future research. Overall, this volume is ideally suited for a senior undergraduate or graduate course on bioinformatics, with a strong focus on its mathematical and computer science background."--Jacket.

Cool careers without college for people who are really good at science & math

Daniel McGuinness

Young adult science and math types learn about jobs that don't need a college education. Each career overview includes tips on career preparation and future prospects. Sidebars offer profiles on specialized jobs or professionals, and each chapter contains annotated career information.

The Geometry of Hamiltonian Systems

Tudor Ratiu

The papers in this volume are an outgrowth of some of the lectures and informal discussions that took place during the workshop on the geometry of Hamiltonian systems, held at the MSRI in Berkeley in June of 1989. The emphasis of all the talks was on Hamiltonian dynamics and its relationship to several aspects of symplectic geometry and topology, mechanics, numerical simulations and dynamical systems in general. The articles are of differing lengths and scopes; some are research announcements while others are surveys of particularly active areas of interest where the results can only be found in scattered research articles and preprints. In- cluded in the book is A.T. Fomenko's survey of the classification of integrable systems.

Introduction to Perturbation Methods

Mark H. Holmes

This introductory graduate text is based on a graduate course the author has taught repeatedly over the last twenty or so years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover more advanced topics such as systems and partial differential equations. Moreover, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas. For this new edition every section has been updated throughout, many only in minor ways, while others have been completely rewritten. New material has also been added. This includes approximations for weakly coupled oscillators, analysis of problems that involve transcendentally small terms, an expanded discussion of Kummer functions, and metastability. Two appendices have been added, one on solving difference equations and another on delay equations. Additional exercises have been included throughout. Review of first edition:"Those familiar with earlier expositions of singular perturbations for ordinary and partial differential equations will find many traditional gems freshly presented, as well as many new topics. Much of the excitement lies in the examples and the more than 250 exercises, which are guaranteed to provoke and challenge readers and learners with various backgrounds and levels of expertise."(SIAM Review, 1996 )