Pad Methods for Painlev Equations

Among them, the Padé method explained in this book provides a simple approach to those equations in both continuous and discrete cases.

Pad   Methods for Painlev   Equations

Pad Methods for Painlev Equations

The isomonodromic deformation equations such as the Painlevé and Garnier systems are an important class of nonlinear differential equations in mathematics and mathematical physics. For discrete analogs of these equations in particular, much progress has been made in recent decades. Various approaches to such isomonodromic equations are known: the Painlevé test/Painlevé property, reduction of integrable hierarchy, the Lax formulation, algebro-geometric methods, and others. Among them, the Padé method explained in this book provides a simple approach to those equations in both continuous and discrete cases. For a given function f(x), the Padé approximation/interpolation supplies the rational functions P(x), Q(x) as approximants such as f(x)~P(x)/Q(x). The basic idea of the Padé method is to consider the linear differential (or difference) equations satisfied by P(x) and f(x)Q(x). In choosing the suitable approximation problem, the linear differential equations give the Lax pair for some isomonodromic equations. Although this relation between the isomonodromic equations and Padé approximations has been known classically, a systematic study including discrete cases has been conducted only recently. By this simple and easy procedure, one can simultaneously obtain various results such as the nonlinear evolution equation, its Lax pair, and their special solutions. In this way, the method is a convenient means of approaching the isomonodromic deformation equations.

Algebraic and Analytic Aspects of Integrable Systems and Painleve Equations

MR2066627(2005h:33004) M. Noumi, S. Tsujimoto, and Y. Yamada, Padé interpolation for elliptic Painlevé equation, Symmetries, integrable systems and ... MR1920282 (2003h:33018) Y. Yamada, Padé method to Painlevé equations, Funkcial.

Algebraic and Analytic Aspects of Integrable Systems and Painleve Equations

Algebraic and Analytic Aspects of Integrable Systems and Painleve Equations

This volume contains the proceedings of the AMS Special Session on Algebraic and Analytic Aspects of Integrable Systems and Painlevé Equations, held on January 18, 2014, at the Joint Mathematics Meetings in Baltimore, MD. The theory of integrable systems has been at the forefront of some of the most important developments in mathematical physics in the last 50 years. The techniques to study such systems have solid foundations in algebraic geometry, differential geometry, and group representation theory. Many important special solutions of continuous and discrete integrable systems can be written in terms of special functions such as hypergeometric and basic hypergeometric functions. The analytic tools developed to study integrable systems have numerous applications in random matrix theory, statistical mechanics and quantum gravity. One of the most exciting recent developments has been the emergence of good and interesting discrete and quantum analogues of classical integrable differential equations, such as the Painlevé equations and soliton equations. Many algebraic and analytic ideas developed in the continuous case generalize in a beautifully natural manner to discrete integrable systems. The editors have sought to bring together a collection of expository and research articles that represent a good cross section of ideas and methods in these active areas of research within integrable systems and their applications.

Symmetries Integrable Systems and Representations

J. Syst. Sci. Complex. 23, 153–176 (2010) Yamada, Y.: Padé method to Painlevé equations. Funkc. Ekvacioj 52, 83–92 (2009) Yamada, Y.: A Lax formalism for the elliptic difference Painlevé equation. SIGMA 5, 042 (2009). 15 p.

Symmetries  Integrable Systems and Representations

Symmetries Integrable Systems and Representations

This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.

Algebraic Methods and Q special Functions

Indeed, generically—for a general solution to a system of Fuchsian linear differential equations, we have max { H(PD ... It is these classes of rational solutions to Painlevé equations that provide exact cases of Padé approximations in ...

Algebraic Methods and Q special Functions

Algebraic Methods and Q special Functions

There has been revived interest in recent years in the study of special functions. Many of the latest advances in the field were inspired by the works of R. A. Askey and colleagues on basic hypergeometric series and I. G. Macdonald on orthogonal polynomials related to root systems. Significant progress was made by the use of algebraic techniques involving quantum groups, Hecke algebras, and combinatorial methods. The CRM organized a workshop for key researchers in the field to present an overview of current trends. This volume consists of the contributions to that workshop. The topics include basic hypergeometric functions, algebraic and representation-theoretic methods, combinatorics of symmetric functions, root systems, and the connections with integrable systems.

Partition Functions and Automorphic Forms

Phys. system 44, 1396–1414 by Padé method. ... M. Noumi, S. Tsujimoto, Y. Yamada, Padé interpolation problem for elliptic Painlevé equation, in Symmetries, Integrable Systems and Representations, ed. by K. Iohara, et al.

Partition Functions and Automorphic Forms

Partition Functions and Automorphic Forms

This book offers an introduction to the research in several recently discovered and actively developing mathematical and mathematical physics areas. It focuses on: 1) Feynman integrals and modular functions, 2) hyperbolic and Lorentzian Kac-Moody algebras, related automorphic forms and applications to quantum gravity, 3) superconformal indices and elliptic hypergeometric integrals, related instanton partition functions, 4) moonshine, its arithmetic aspects, Jacobi forms, elliptic genus, and string theory, and 5) theory and applications of the elliptic Painleve equation, and aspects of Painleve equations in quantum field theories. All the topics covered are related to various partition functions emerging in different supersymmetric and ordinary quantum field theories in curved space-times of different (d=2,3,...,6) dimensions. Presenting multidisciplinary methods (localization, Borcherds products, theory of special functions, Cremona maps, etc) for treating a range of partition functions, the book is intended for graduate students and young postdocs interested in the interaction between quantum field theory and mathematics related to automorphic forms, representation theory, number theory and geometry, and mirror symmetry.

Regional Conference on Science Technology and Social Sciences RCSTSS 2016

4 Conclusion In this work, we employed the Daftardar–Gejji and Jafari method for solving the Painlevé equation II. The numerical results by DJM are in good agreement with those obtained by OHAM, HPM, ACE, CSM and VIM-Pade method.

Regional Conference on Science  Technology and Social Sciences  RCSTSS 2016

Regional Conference on Science Technology and Social Sciences RCSTSS 2016

This book gathers selected theoretical and applied science papers presented at the 2016 Regional Conference of Sciences, Technology and Social Sciences (RCSTSS 2016), organized biannually by the Universiti Teknologi MARA Pahang, Malaysia. Addressing a broad range of topics, including architecture, computer science, engineering, environmental and management, furniture, forestry, health and medicine, material science, mathematics, plantation and agrotechnology, sports science and statistics, the book serves as an essential platform for disseminating research findings, and inspires positive innovations in the region’s development. The carefully reviewed papers in this volume present work by researchers of local, regional and global prominence. Taken together, they offer a valuable reference guide and point of departure for all academics and students who want to pursue further research in their respective fields.

Handbook of Ordinary Differential Equations

3.5 3.6 3.7 3.8 Method 3.4.1 of Expansion in Powers of the Independent Variable 3.4.2 Padé Approximants Movable Singularities of Solutions of Ordinary Differential Equations. Painlevé Equations 3.5.1 Preliminary Remarks.

Handbook of Ordinary Differential Equations

Handbook of Ordinary Differential Equations

The Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, is an exceptional and complete reference for scientists and engineers as it contains over 7,000 ordinary differential equations with solutions. This book contains more equations and methods used in the field than any other book currently available. Included in the handbook are exact, asymptotic, approximate analytical, numerical symbolic and qualitative methods that are used for solving and analyzing linear and nonlinear equations. The authors also present formulas for effective construction of solutions and many different equations arising in various applications like heat transfer, elasticity, hydrodynamics and more. This extensive handbook is the perfect resource for engineers and scientists searching for an exhaustive reservoir of information on ordinary differential equations.

Discrete Systems and Integrability

... difference equations, 27 linear difference equations, 370–383 characteristic equation, 372 factorization method, ... 124 Padé approximants Orthogonal polynomials, 124 Padé table discrete-time Toda lattice, 122 Painlevé method, ...

Discrete Systems and Integrability

Discrete Systems and Integrability

A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts.

Princeton Companion to Applied Mathematics

See ordinary differential equations (ODEs) Ohm's law, 477, 663–65; cardiac diffusion tensor and, 625; modified for ion ... 300 Padé–Laplace method, 255 PageRank algorithm, 4, 48,276,364, 755–57 Painlevé equations, 163–65, 180, 185, 235; ...

Princeton Companion to Applied Mathematics

Princeton Companion to Applied Mathematics

This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index

Encyclopaedia of Mathematics

... Fra Luce see: Fra Luce Pacioli Padé, H. see: Padé approximation Page, A. see: Page theorem Painlevé, P. see: Boundary properties of analytic functions; Cluster set, Painlevé equation, Painlevé problem; Parameter-introduction method; ...

Encyclopaedia of Mathematics

Encyclopaedia of Mathematics

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

More Books:

How to Have an Enemy
Language: en
Pages: 250
Authors: Melissa Florer-Bixler
Categories: Religion
Type: BOOK - Published: 2021-06-20 - Publisher: MennoMedia, Inc.

Does Jesus’ call to love our enemies mean that we should remain silent in the face of injustice? Jesus called us to love our enemies. But to befriend an enemy, we first have to acknowledge their existence, understand who they are, and recognize the ways they are acting in opposition
Civilization and Its Enemies
Language: en
Pages: 256
Authors: Lee Harris
Categories: Philosophy
Type: BOOK - Published: 2004-03-11 - Publisher: Simon and Schuster

Forgetfulness occurs when those who have been long inured to civilized order can no longer remember a time in which they had to wonder whether their crops would grow to maturity without being stolen or their children sold into slavery by a victorious foe....They forget that in time of danger,
To Take An Enemy's Heart Chapter 37
Language: en
Pages: 28
Authors: yusa
Categories: Comics & Graphic Novels
Type: BOOK - Published: 2019-04-12 - Publisher: NETCOMICS

Completed series: Kindle edition: 64-chapter set; paperback: 9-volume set.Kassan is believed to be the sole survivor of the Azkun clan, after Master Igen, a ruthless ruler, slaughters his family.Master Igen brings the young boy as a slave into his home, exploiting, beating and starving him.The only one who cares about
Having the Mind of Christ
Language: en
Pages: 192
Authors: Matt Tebbe, Ben Sternke
Categories: Religion
Type: BOOK - Published: 2022-07-26 - Publisher: InterVarsity Press

Despite our deep desire to live in the freedom that Christ offers, we are acutely aware of the gap between a transformed life and our reality. While behavioral changes can bear good results, true transformation requires a change in paradigm. Pastors Matt Tebbe and Ben Sternke share eight axioms that
Enemies and How to Love Them
Language: en
Pages: 142
Authors: Gerard Vanderhaar
Categories: Religion
Type: BOOK - Published: 2013-09-01 - Publisher: Wipf and Stock Publishers

This compassionate book describes the making of enemies in our personal, social, and national lives. It goes on to outline a nonviolent approach to resolving enmity wherever it arises. It taps the rich resources of Jesus' two-thousand-year-old formula, "Love your enemies," with the help of our contemporary understanding of Gandhian