Описание: The definition of "photonics" has been broadened in recent years to include nonlinear and quantum optics, today usually based on laser light. This book covers the fundamental properties of photon and light beams, both experimentally and theoretically. It covers the essentials of linear interactions and most of the nonlinear interactions between light and matter in both the transparent and absorbing cases. It also provides a basic knowledge of modern lasers, as well as the principles of nonlinear optical spectroscopy. It is self-consistent and enriched by a large number of calculated illustrations, examples, and descriptive tables. Graduate students in physics and electrical engineering, as well as other sciences, will find this book a thorough introduction to the field, while for lecturers and scientists it offers a rich source of useful information and a ready-to-hand reference. About 4000 references open access to original literature.The second edition is completely revised and enlarged.
Описание: This three-week summer program considered the symmetries preserving various natural geometric structures. The articles in the first part are expository but all contain significant new material. All articles were thoroughly refereed and the range of interrelated work ensures that this will be an extremely useful collection.
Автор: Boris Kruglikov; Valentin Lychagin; Eldar Straume Название: Differential Equations - Geometry, Symmetries and Integrability ISBN: 3642269338 ISBN-13(EAN): 9783642269332 Издательство: Springer Рейтинг: Цена: 23058.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book contains papers presented at the Abel Symposium 2008, which focused on the modern theory of differential equations and their applications in geometry, mechanics, and mathematical physics. It presents a modern approach to this classical subject.
Описание: This is a detailed exposition of algebraic and geometrical aspects related to the theory of symmetries and recursion operators for nonlinear partial differential equations (PDE), both in classical and in super, or graded, versions.
Автор: A.M. Vinogradov Название: Symmetries of Partial Differential Equations ISBN: 9401073708 ISBN-13(EAN): 9789401073707 Издательство: Springer Рейтинг: Цена: 41787.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Higher symmetries, conservation laws, partial differential equations, infinitely prolonged equations, generating functions. More exactly, we will focus our attention on the main conceptual points as well as on the problem of how to find all higher symmetries and conservation laws for a given system of partial differential equations.
Автор: Boris Kruglikov; Valentin Lychagin; Eldar Straume Название: Differential Equations - Geometry, Symmetries and Integrability ISBN: 3642008720 ISBN-13(EAN): 9783642008726 Издательство: Springer Рейтинг: Цена: 23058.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The Abel Symposium 2008 focused on the modern theory of differential equations and their applications in geometry, mechanics, and mathematical physics. This title consists of original contributions and overview lectures of the participants of the Symposium. It includes papers that present the modern approach to this classical subject.
Автор: W.I. Fushchich; A.G. Nikitin Название: Symmetries of Maxwell`s Equations ISBN: 9401081662 ISBN-13(EAN): 9789401081665 Издательство: Springer Рейтинг: Цена: 14365.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the fina\ question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu\ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Автор: Decio Levi; Rapha?l Rebelo; Pavel Winternitz Название: Symmetries and Integrability of Difference Equations ISBN: 3319566652 ISBN-13(EAN): 9783319566658 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations.
Автор: A.M. Vinogradov Название: Symmetries of Partial Differential Equations ISBN: 0792305949 ISBN-13(EAN): 9780792305941 Издательство: Springer Рейтинг: Цена: 41787.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: W.I. Fushchich; A.G. Nikitin Название: Symmetries of Maxwell`s Equations ISBN: 9027723206 ISBN-13(EAN): 9789027723208 Издательство: Springer Рейтинг: Цена: 16979.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the fina\ question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu\ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Symmetries and Semi-invariants in the Analysis of Nonlinear Systems details the analysis of continuous- and discrete-time dynamical systems described by differential and difference equations respectively. Differential geometry provides the essential tools for the analysis, tools such as first-integrals or orbital symmetries, together with normal forms of vector fields and of maps. The use of such tools allows the solution of some important problems, studied in detail in the text, which include linearization by state immersion and the computation of nonlinear superposition formulae for nonlinear systems described by solvable Lie algebras.
The theory is developed for general nonlinear systems and, in view of their importance for modeling physical systems, specialized for the class of Hamiltonian systems. By using the strong geometric structure of Hamiltonian systems, the results proposed are stated in a quite different, less complex and more easily comprehensible manner. Throughout the text the results are illustrated by many examples, some of them being physically motivated systems, so that the reader can appreciate how much insight is gained by means of these techniques. Various control systems applications of the techniques are characterized including:
- computation of the flow of nonlinear systems;
- computation of semi-invariants;
- computation of Lyapunov functions for stability analysis.
Symmetries and Semi-invariants in the Analysis of Nonlinear Systems will be of interest to researchers and graduate students studying control theory, particularly with respect to nonlinear systems. All the necessary background and mathematical derivations are related in detail but in a simple writing style that makes the book accessible in depth to readers having a standard knowledge of real analysis, linear algebra and systems theory.
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