Analytic, Algebraic and Geometric Aspects of Differential Equations: Będlewo, Poland, September 2015, Filipuk Galina, Haraoka Yoshishige, Michalik Slawomir
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 Рейтинг: Цена: 22359.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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: Han Fei Et Al Название: Geometric Analysis Around Scalar Curvatures ISBN: 9813100540 ISBN-13(EAN): 9789813100541 Издательство: World Scientific Publishing Цена: 13939.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This volume contains three expanded lecture notes from the program Scalar Curvature in Manifold Topology and Conformal Geometry that was held at the Institute for Mathematical Sciences from 1 November to 31 December 2014. The first chapter surveys the recent developments on the fourth-order equations with negative exponent from geometric points of view such as positive mass theorem and uniqueness results. The next chapter deals with the recent important progress on several conjectures such as the existence of non-flat smooth hyper-surfaces and Serrin's over-determined problem. And the final chapter induces a new technique to handle the equation with critical index and the sign change coefficient as well as the negative index term. These topics will be of interest to those studying conformal geometry and geometric partial differential equations.
Автор: P.H. Kersten; I.S. Krasil`shchik Название: Geometric and Algebraic Structures in Differential Equations ISBN: 9401065659 ISBN-13(EAN): 9789401065658 Издательство: Springer Рейтинг: Цена: 11173.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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.
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 Рейтинг: Цена: 32142.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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.
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.
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: Xiaoping Xu Название: Algebraic Approaches to Partial Differential Equations ISBN: 3642368735 ISBN-13(EAN): 9783642368738 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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 Рейтинг: Цена: 27878.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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.
Описание: 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 Painlev -Yosida theorem, which relates Painlev 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.
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: Stephen Campbell; Achim Ilchmann; Volker Mehrmann; Название: Applications of Differential-Algebraic Equations: Examples and Benchmarks ISBN: 3030037177 ISBN-13(EAN): 9783030037178 Издательство: Springer Рейтинг: Цена: 11179.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This volume encompasses prototypical, innovative and emerging examples and benchmarks of Differential-Algebraic Equations (DAEs) and their applications, such as electrical networks, chemical reactors, multibody systems, and multiphysics models, to name but a few. Each article begins with an exposition of modelling, explaining whether the model is prototypical and for which applications it is used. This is followed by a mathematical analysis, and if appropriate, a discussion of the numerical aspects including simulation. Additionally, benchmark examples are included throughout the text.Mathematicians, engineers, and other scientists, working in both academia and industry either on differential-algebraic equations and systems or on problems where the tools and insight provided by differential-algebraic equations could be useful, would find this book resourceful.
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