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: 32600.00 T 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.
Автор: Levitan; I.S. Sargsjan Название: Sturm—Liouville and Dirac Operators ISBN: 0792309928 ISBN-13(EAN): 9780792309925 Издательство: Springer Рейтинг: Цена: 102480.00 T 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.
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: 62380.00 T 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).
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