Analytic, Algebraic and Geometric Aspects of Differential Equations: Będlewo, Poland, September 2015, Filipuk Galina, Haraoka Yoshishige, Michalik Slawomir

Автор: Douglas N. Arnold
Название: Finite Element Exterior Calculus
ISBN: 1611975530 ISBN-13(EAN): 9781611975536
Издательство: Mare Nostrum (Eurospan)
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Цена: 48910.00 T
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Описание: Computational methods to approximate the solution of differential equations play a crucial role in science, engineering, mathematics, and technology. The key processes that govern the physical world—wave propagation, thermodynamics, fluid flow, solid deformation, electricity and magnetism, quantum mechanics, general relativity, and many more—are described by differential equations. We depend on numerical methods for the ability to simulate, explore, predict, and control systems involving these processes. The finite element exterior calculus, or FEEC, is a powerful new theoretical approach to the design and understanding of numerical methods to solve partial differential equations (PDEs). The methods derived with FEEC preserve crucial geometric and topological structures underlying the equations and are among the most successful examples of structure-preserving methods in numerical PDEs. This volume aims to help numerical analysts master the fundamentals of FEEC, including the geometrical and functional analysis preliminaries, quickly and in one place. It is also accessible to mathematicians and students of mathematics from areas other than numerical analysis who are interested in understanding how techniques from geometry and topology play a role in numerical PDEs.

Автор: Peter Benner; Matthias Bollh?fer; Daniel Kressner;
Название: Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory
ISBN: 3319384317 ISBN-13(EAN): 9783319384313
Издательство: Springer
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Цена: 88500.00 T
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Описание: This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory.

Автор: Galina Filipuk; Yoshishige Haraoka; S?awomir Micha
Название: Analytic, Algebraic and Geometric Aspects of Differential Equations
ISBN: 3319528416 ISBN-13(EAN): 9783319528410
Издательство: Springer
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Цена: 149060.00 T
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Описание: Preface.- An introduction to Dunkl theory and its analytic aspects.- Holonomic Systems.- Sub-Riemannian geometry and hypoelliptic operators.- Asymptotic analysis and summability of formal power series.- WKB analysis and Stokes geometry of differential equations.- Transcendental Meromorphic Solutions of P34and Small Targets.- Towards the convergence of generalized power series solutions of algebraic ODEs.- Connection problem for regular holonomic systems in several variables.- On k-summability of formal solutions for certain higher order partial differential operators with polynomial coefficients.- On Stokes phenomena for the alternate discrete PI equation.- Flat structures and algebraic solutions toPainlevй VI equation.- Relation of Semi-classical orthogonal polynomials to General Schlesinger systems via Twistor theory.- Some notes on the multi-level Gevrey solutions of singularly perturbed linear partial differential equations.- Reducibility of hypergeometric equations.- Parametric Borel summability of partial differential equations of irregular singular type.

Автор: P.H. Kersten; I.S. Krasil`shchik
Название: Geometric and Algebraic Structures in Differential Equations
ISBN: 9401065659 ISBN-13(EAN): 9789401065658
Издательство: Springer
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Цена: 74490.00 T
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Описание: The geometrical theory of nonlinear differential equations originates from classical works by S. Lie and A. Backlund. It obtained a new impulse in the sixties when the complete integrability of the Korteweg-de Vries equation was found and it became clear that some basic and quite general geometrical and algebraic structures govern this property of integrability.
Nowadays the geometrical and algebraic approach to partial differential equations constitutes a special branch of modern mathematics.
In 1993, a workshop on algebra and geometry of differential equations took place at the University of Twente (The Netherlands), where the state-of-the-art of the main problems was fixed. This book contains a collection of invited lectures presented at this workshop. The material presented is of interest to those who work in pure and applied mathematics and especially in mathematical physics.

Автор: P.A. Clarkson
Название: Applications of Analytic and Geometric Methods to Nonlinear Differential Equations
ISBN: 0792324579 ISBN-13(EAN): 9780792324577
Издательство: Springer
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Цена: 363360.00 T
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Описание: Contains articles on the reduction of the self-dual Yang-Mills (SDYM) equations to soliton equations and the relationship between the IST and twistor methods. This book also contains articles on perturbed soliton equations.

Автор: Michael Hitrik; Dmitry Tamarkin; Boris Tsygan; Ste
Название: Algebraic and Analytic Microlocal Analysis
ISBN: 3030015866 ISBN-13(EAN): 9783030015862
Издательство: Springer
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Цена: 214280.00 T
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Описание: This book presents contributions from two workshops in algebraic and analytic microlocal analysis that took place in 2012 and 2013 at Northwestern University. Featured papers expand on mini-courses and talks ranging from foundational material to advanced research-level papers, and new applications in symplectic geometry, mathematical physics, partial differential equations, and complex analysis are discussed in detail. Topics include Procesi bundles and symplectic reflection algebras, microlocal condition for non-displaceability, polarized complex manifolds, nodal sets of Laplace eigenfunctions, geodesics in the space of K?hler metrics, and partial Bergman kernels. This volume is a valuable resource for graduate students and researchers in mathematics interested in understanding microlocal analysis and learning about recent research in the area.

Автор: P.A. Clarkson
Название: Applications of Analytic and Geometric Methods to Nonlinear Differential Equations
ISBN: 9401049246 ISBN-13(EAN): 9789401049245
Издательство: Springer
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Цена: 363360.00 T
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Описание: In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years. (1) The inverse scattering transform (IST), using complex function theory, which has been employed to solve many physically significant equations, the soliton' equations. (2) Twistor theory, using differential geometry, which has been used to solve the self-dual Yang--Mills (SDYM) equations, a four-dimensional system having important applications in mathematical physics. Both soliton and the SDYM equations have rich algebraic structures which have been extensively studied.
Recently, it has been conjectured that, in some sense, all soliton equations arise as special cases of the SDYM equations; subsequently many have been discovered as either exact or asymptotic reductions of the SDYM equations. Consequently what seems to be emerging is that a natural, physically significant system such as the SDYM equations provides the basis for a unifying framework underlying this class of integrable systems, i.e. soliton' systems. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods.
The majority of nonlinear evolution equations are nonintegrable, and so asymptotic, numerical perturbation and reduction techniques are often used to study such equations. This book also contains articles on perturbed soliton equations. Painlev analysis of partial differential equations, studies of the Painlev equations and symmetry reductions of nonlinear partial differential equations.


(ABSTRACT)
In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years; the inverse scattering transform (IST), for soliton' equations and twistor theory, for the self-dual Yang--Mills (SDYM) equations. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. Additionally, it contains articles on perturbed soliton equations, Painlev analysis of partial differential equations, studies of the Painlev equations and symmetry reductions of nonlinear partial differential equations.

Автор: Galina Filipuk, Alberto Lastra, Slawomir Michalik, Yoshitsugu Takei, Henryk Zoladek
Название: Complex Differential and Difference Equations: Proceedings of the School and Conference held at Bedlewo, Poland, September 2-15, 2018
ISBN: 3110609525 ISBN-13(EAN): 9783110609523
Издательство: Walter de Gruyter
Цена: 161100.00 T
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Описание: With a balanced combination of longer survey articles and shorter, peer-reviewed research-level presentations on the topic of differential and difference equations on the complex domain, this edited volume presents an up-to-date overview of areas such as WKB analysis, summability, resurgence, formal solutions, integrability, and several algebraic aspects of differential and difference equations.

Автор: Hitoshi Konno, Hidetaka Sakai, Junichi Shiraishi, Takao Suzuki, Yasuhiko Yamada
Название: Representation Theory, Special Functions and Painvleve Equations - RIMS 2015
ISBN: 4864970505 ISBN-13(EAN): 9784864970501
Издательство: Mare Nostrum (Eurospan)
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Цена: 97020.00 T
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Описание: Contains 15 papers covering a variety of topics in the research fields where Masatoshi Noumi has made significant contributions over the years - representation theory, special functions, Painleve equations, among others.

Автор: Anton Dzhamay, Kenichi Maruno, Christopher M. Ormerod
Название: Algebraic and Analytic Aspects of Integrable Systems and Painleve Equations
ISBN: 1470416549 ISBN-13(EAN): 9781470416546
Издательство: Mare Nostrum (Eurospan)
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Цена: 104410.00 T
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Описание: Contains the proceedings of the AMS Special Session on Algebraic and Analytic Aspects of Integrable Systems and Painleve Equations, held January 2014. This collection of expository and research articles represent a good cross section of ideas and methods in these active areas of research within integrable systems and their applications.

Автор: Xiaoping Xu
Название: Algebraic Approaches to Partial Differential Equations
ISBN: 3642368735 ISBN-13(EAN): 9783642368738
Издательство: Springer
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Цена: 93160.00 T
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Описание: This book presents various algebraic techniques for solving partial differential equations to yield exact solutions, techniques developed by the author in recent years and with emphasis on physical equations.

Автор: Andrei Agrachev, Davide Barilari, Ugo Boscain
Название: A Comprehensive Introduction to Sub-Riemannian Geometry
ISBN: 110847635X ISBN-13(EAN): 9781108476355
Издательство: Cambridge Academ
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Цена: 185850.00 T
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Описание: This comprehensive introduction to sub-Riemannian geometry proceeds from classical topics to cutting-edge theory and applications. The only prerequisites are calculus, linear algebra and differential equations. It can be used for graduate courses in Riemannian or sub-Riemannian geometry, or as a reference for researchers in several disciplines.