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Nevanlinna Theory and Complex Differential Equations

2011-06-01 Mathematics
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Release : 2011-06-01
Genre : Mathematics
Kind : eBook
Book Rating : 146/5 ( reviews)

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Book Synopsis Nevanlinna Theory and Complex Differential Equations by : Ilpo Laine

Download or read book Nevanlinna Theory and Complex Differential Equations written by Ilpo Laine. This book was released on 2011-06-01. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Nevanlinna Theory, Normal Families, and Algebraic Differential Equations

2017-07-24 Mathematics
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Release : 2017-07-24
Genre : Mathematics
Kind : eBook
Book Rating : 007/5 ( reviews)

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Book Synopsis Nevanlinna Theory, Normal Families, and Algebraic Differential Equations by : Norbert Steinmetz

Download or read book Nevanlinna Theory, Normal Families, and Algebraic Differential Equations written by Norbert Steinmetz. This book was released on 2017-07-24. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a modern introduction to Nevanlinna theory and its intricate relation to the theory of normal families, algebraic functions, asymptotic series, and algebraic differential equations. Following a comprehensive treatment of Nevanlinna’s theory of value distribution, the author presents advances made since Hayman’s work on the value distribution of differential polynomials and illustrates how value- and pair-sharing problems are linked to algebraic curves and Briot–Bouquet differential equations. In addition to discussing classical applications of Nevanlinna theory, the book outlines state-of-the-art research, such as the effect of the Yosida and Zalcman–Pang method of re-scaling to algebraic differential equations, and presents the Painlevé–Yosida theorem, which relates Painlevé transcendents and solutions to selected 2D Hamiltonian systems to certain Yosida classes of meromorphic functions. Aimed at graduate students interested in recent developments in the field and researchers working on related problems, Nevanlinna Theory, Normal Families, and Algebraic Differential Equations will also be of interest to complex analysts looking for an introduction to various topics in the subject area. With examples, exercises and proofs seamlessly intertwined with the body of the text, this book is particularly suitable for the more advanced reader.

On Complex Differential Equations in the Unit Disc

2000 Differential equations
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Release : 2000
Genre : Differential equations
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis On Complex Differential Equations in the Unit Disc by : Janne Heittokangas

Download or read book On Complex Differential Equations in the Unit Disc written by Janne Heittokangas. This book was released on 2000. Available in PDF, EPUB and Kindle. Book excerpt:

Painlevé Differential Equations in the Complex Plane

2008-08-22 Mathematics
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Release : 2008-08-22
Genre : Mathematics
Kind : eBook
Book Rating : 096/5 ( reviews)

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Book Synopsis Painlevé Differential Equations in the Complex Plane by : Valerii I. Gromak

Download or read book Painlevé Differential Equations in the Complex Plane written by Valerii I. Gromak. This book was released on 2008-08-22. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first comprehensive treatment of Painlevé differential equations in the complex plane. Starting with a rigorous presentation for the meromorphic nature of their solutions, the Nevanlinna theory will be applied to offer a detailed exposition of growth aspects and value distribution of Painlevé transcendents. The subsequent main part of the book is devoted to topics of classical background such as representations and expansions of solutions, solutions of special type like rational and special transcendental solutions, Bäcklund transformations and higher order analogues, treated separately for each of these six equations. The final chapter offers a short overview of applications of Painlevé equations, including an introduction to their discrete counterparts. Due to the present important role of Painlevé equations in physical applications, this monograph should be of interest to researchers in both mathematics and physics and to graduate students interested in mathematical physics and the theory of differential equations.

Complex Delay-Differential Equations

2021-06-08 Mathematics
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Release : 2021-06-08
Genre : Mathematics
Kind : eBook
Book Rating : 402/5 ( reviews)

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Book Synopsis Complex Delay-Differential Equations by : Kai Liu

Download or read book Complex Delay-Differential Equations written by Kai Liu. This book was released on 2021-06-08. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

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