Spectral and Scattering Theory for Ordinary Differential Equations: Vol. I: Sturm-Liouville Equations, Bennewitz Christer, Brown Malcolm, Weikard Rudi
Автор: Oksendal Название: Stochastic Differential Equations ISBN: 3540047581 ISBN-13(EAN): 9783540047582 Издательство: Springer Рейтинг: Цена: 8223.00 р. Наличие на складе: Есть (1 шт.) Описание: Gives an introduction to the basic theory of stochastic calculus and its applications. This book offers examples in order to motivate and illustrate the theory and show its importance for many applications in for example economics, biology and physics.
Автор: Masjed-Jamei Mohammad Название: Special Functions and Generalized Sturm-Liouville Problems ISBN: 3030328198 ISBN-13(EAN): 9783030328191 Издательство: Springer Рейтинг: Цена: 7685.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book discusses theoretical and applied aspects of Sturm-Liouville theory and its generalization. It introduces and classifies generalized Sturm-Liouville problems in three different spaces: continuous, discrete, and q-discrete spaces, focusing on special functions that are solutions of a regular or singular Sturm-Liouville problem. Further, it describes the conditions under which the usual Sturm-Liouville problems with symmetric solutions can be extended to a larger class, particularly highlighting the solutions of generalized problems that result in new orthogonal sequences of continuous or discrete functions.
Sturm-Liouville theory is central to problems in many areas, such as engineering, mathematics, physics, and biology. This accessibly written book on the topic is a valuable resource for a broad interdisciplinary readership, from novices to experts.
Автор: Levitan; I.S. Sargsjan Название: Sturm—Liouville and Dirac Operators ISBN: 0792309928 ISBN-13(EAN): 9780792309925 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 'Et moi, ...- si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point allC: .' human. race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com- puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'ttre of this series.
Автор: Vladimir Kozlov; Vladimir Maz`ya Название: Theory of a Higher-Order Sturm-Liouville Equation ISBN: 3540630651 ISBN-13(EAN): 9783540630654 Издательство: Springer Рейтинг: Цена: 4890.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The aim of this book is to develop a detailed theory of a generalized Sturm-Liouville equation, which includes conditions of solvability, classes of uniqueness, positivity properties of solutions, and Green`s functions, asymptotic properties of solutions at infinity.
Описание: Introduction.- Preliminaries on Sturm-Liouville equations.- Finite interval.- Half-line.- Quantum scattering problem on the half-line.- Scattering problem on the line.- Inverse scattering transform method.- Main transmutation operators.- Series representations.- Series representations for the Jost solution.- Sturm-Liouville problems on finite intervals.- Spectral problems on infinite intervals.- The inverse problem on a finite interval.- Solving the inverse problem on a half-line.- Inverse quantum scattering on the half-line.- Inverse scattering on the line.
This unique book's subject is meanders (connected, oriented, non-self-intersecting planar curves intersecting the horizontal line transversely) in the context of dynamical systems. By interpreting the transverse intersection points as vertices and the arches arising from these curves as directed edges, meanders are introduced from the graphtheoretical perspective. Supplementing the rigorous results, mathematical methods, constructions, and examples of meanders with a large number of insightful figures, issues such as connectivity and the number of connected components of meanders are studied in detail with the aid of collapse and multiple collapse, forks, and chambers. Moreover, the author introduces a large class of Morse meanders by utilizing the right and left one-shift maps, and presents connections to Sturm global attractors, seaweed and Frobenius Lie algebras, and the classical Yang-Baxter equation.
Contents
Seaweed Meanders
Meanders
Morse Meanders and Sturm Global Attractors
Right and Left One-Shifts
Connection Graphs of Type I, II, III and IV
Meanders and the Temperley-Lieb Algebra
Representations of Seaweed Lie Algebras
CYBE and Seaweed Meanders
Автор: William T. Reid; J. Burns; T. Herdman; C. Ahlbrand Название: Sturmian Theory for Ordinary Differential Equations ISBN: 0387905421 ISBN-13(EAN): 9780387905426 Издательство: Springer Рейтинг: Цена: 9357.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A major portion of the study of the qualitative nature of solutions of differential equations may be traced to the famous 1836 paper of Sturm 1), (here, as elsewhere throughout this manuscript, numbers in square brackets refer to the bibliography at the end of this volume), dealing with oscilla- tion and comparison theorems for linear homogeneous second order ordinary differential equations. The associated work of Liouville introduced a type of boundary problem known as a "Sturm-Liouville problem," involving, in particular, an introduction to the study of the asymptotic behavior of solu- tions of linear second order differential equations by the use of integral equations. In the quarter century following the 1891 Gottingen dissertation 1) of Maxime Bacher (1867-1918), he was instru- mental in the elaboration and extension of the oscillation, separation, and comparison theorems of Sturm, both in his many papers on the subject and his lectures at the Sorbonne in 1913-1914, which were subsequently published as his famous Leaons sur Zes methodes de Sturm 7).
Описание: Suitable for students in the fields of mathematics, science, and engineering, this title provides a theoretical approach to dynamical systems and chaos. It helps them to analyze the types of differential equations that arise in their area of study.
Описание: Incorporates the fourth version of the software package Mathematica (4.x). This title includes a section of Mathematica projects in each chapter, a chapter on Green`s functions, a chapter on boundary value problems, and material on inverse operators, Legendre functions, and Bessel functions.
Описание: This volume contains lectures and invited papers from the Focus Program on 'Nonlinear Dispersive Partial Differential Equations and Inverse Scattering' held at the Fields Institute from July 31-August 18, 2017. The conference brought together researchers in completely integrable systems and PDE with the goal of advancing the understanding of qualitative and long-time behavior in dispersive nonlinear equations. The program included Percy Deift’s Coxeter lectures, which appear in this volume together with tutorial lectures given during the first week of the focus program. The research papers collected here include new results on the focusing ?nonlinear Schr?dinger (NLS) equation, the massive Thirring model, and the Benjamin-Bona-Mahoney equation as dispersive PDE in one space dimension, as well as the Kadomtsev-Petviashvili II equation, the Zakharov-Kuznetsov equation, and the Gross-Pitaevskii equation as dispersive PDE in two space dimensions.The Focus Program coincided with the fiftieth anniversary of the discovery by Gardner, Greene, Kruskal and Miura that the Korteweg-de Vries (KdV) equation could be integrated by exploiting a remarkable connection between KdV and the spectral theory of Schrodinger's equation in one space dimension. This led to the discovery of a number of completely integrable models of dispersive wave propagation, including the cubic NLS equation, and the derivative NLS equation in one space dimension and the Davey-Stewartson, Kadomtsev-Petviashvili and Novikov-Veselov equations in two space dimensions. These models have been extensively studied and, in some cases, the inverse scattering theory has been put on rigorous footing. It has been used as a powerful analytical tool to study global well-posedness and elucidate asymptotic behavior of the solutions, including dispersion, soliton resolution, and semiclassical limits.
Автор: Ahmad Shair Название: Textbook on Ordinary Differential Equations ISBN: 3319164074 ISBN-13(EAN): 9783319164076 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics. A complete Solutions Manual, containing solutions to all the exercises published in the book, is available.
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