Описание: This self-contained book is devoted to the study of the acoustic wave equations and the Maxwell system, the two most common waves equations that are encountered in physics or in engineering. It presents a detailed analysis of their mathematical and physical properties. In particular, the author focuses on the study of the harmonic exterior problems, building a mathematical framework which provides the existence and uniqueness of the solutions. Acoustic and electromagnetic waves underlie a vast range of modern technology from sonar, radio, and television to microwave heating and electromagnetic compatibility analysis. Mathematical modeling of these waves has undergone considerable growth in recent years, and this timely book, written by a leading international researcher, presents the research in a careful and complete way.
Описание: The first edition of this book is a collection of a series of lectures given by Professor Victor Kac at the TIFR, Mumbai, India in December 1985 and January 1986. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations.The first is the canonical commutation relations of the infinite dimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra gℓ∞ of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary highest weight representations of the current (= affine Kac-Moody) algebras. These Lie algebras appear in the lectures in connection to the Sugawara construction, which is the main tool in the study of the fourth incarnation of the main idea, the theory of the highest weight representations of the Virasoro algebra. In particular, the book provides a complete proof of the Kac determinant formula, the key result in representation theory of the Virasoro algebra.The second edition of this book incorporates, as its first part, the largely unchanged text of the first edition, while its second part is the collection of lectures on vertex algebras, delivered by Professor Kac at the TIFR in January 2003. The basic idea of these lectures was to demonstrate how the key notions of the theory of vertex algebras -- such as quantum fields, their normal ordered product and lambda-bracket, energy-momentum field and conformal weight, untwisted and twisted representations -- simplify and clarify the constructions of the first edition of the book.This book should be very useful for both mathematicians and physicists. To mathematicians, it illustrates the interaction of the key ideas of the representation theory of infinite dimensional Lie algebras and of the theory of vertex algebras; and to physicists, these theories are turning into an important component of such domains of theoretical physics as soliton theory, conformal field theory, the theory of two-dimensional statistical models, and string theory.
Описание: The first edition of this book is a collection of a series of lectures given by Professor Victor Kac at the TIFR, Mumbai, India in December 1985 and January 1986. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations.The first is the canonical commutation relations of the infinite dimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra gℓ∞ of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary highest weight representations of the current (= affine Kac-Moody) algebras. These Lie algebras appear in the lectures in connection to the Sugawara construction, which is the main tool in the study of the fourth incarnation of the main idea, the theory of the highest weight representations of the Virasoro algebra. In particular, the book provides a complete proof of the Kac determinant formula, the key result in representation theory of the Virasoro algebra.The second edition of this book incorporates, as its first part, the largely unchanged text of the first edition, while its second part is the collection of lectures on vertex algebras, delivered by Professor Kac at the TIFR in January 2003. The basic idea of these lectures was to demonstrate how the key notions of the theory of vertex algebras -- such as quantum fields, their normal ordered product and lambda-bracket, energy-momentum field and conformal weight, untwisted and twisted representations -- simplify and clarify the constructions of the first edition of the book.This book should be very useful for both mathematicians and physicists. To mathematicians, it illustrates the interaction of the key ideas of the representation theory of infinite dimensional Lie algebras and of the theory of vertex algebras; and to physicists, these theories are turning into an important component of such domains of theoretical physics as soliton theory, conformal field theory, the theory of two-dimensional statistical models, and string theory.
Автор: S.-V. Stratila; D.-V. Voiculescu Название: Representations of AF-Algebras and of the Group U. (infinite) ISBN: 3540074031 ISBN-13(EAN): 9783540074038 Издательство: Springer Рейтинг: Цена: 3487.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: F. L. Williams Название: Tensor Products of Principal Series Representations ISBN: 3540065679 ISBN-13(EAN): 9783540065678 Издательство: Springer Рейтинг: Цена: 3492.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Torben T. Nielsen Название: Bose Algebras: The Complex and Real Wave Representations ISBN: 3540540415 ISBN-13(EAN): 9783540540410 Издательство: Springer Рейтинг: Цена: 3487.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The mathematics of Bose-Fock spaces is built on the notion of a commutative algebra. This book is suitable for mathematicians interested in analysis in infinitely many dimensions or in the mathematics of quantum fields and to theoretical physicists who can profit from the use of an effective and rigorous Bose formalism.
Автор: Verschaffel Название: Use of Representations in Reasoning and Problem Solving ISBN: 0415556732 ISBN-13(EAN): 9780415556736 Издательство: Taylor&Francis Рейтинг: Цена: 24499.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Use of Representations in Reasoning and Problem Solving brings together contributions from leading international researchers in from educational psychology, cognitive science and related fields, to document the role which representations play in our understanding, learning and communication.
Автор: Shimon Whiteson Название: Adaptive Representations for Reinforcement Learning ISBN: 3642422314 ISBN-13(EAN): 9783642422317 Издательство: Springer Рейтинг: Цена: 15672.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Presenting the main results of new algorithms for reinforcement learning, this book also introduces a novel method for devising input representations as well as presenting a way to find a minimal set of features sufficient to describe the agent`s current state.
Автор: Kaleem Siddiqi; Stephen Pizer Название: Medial Representations ISBN: 1402086571 ISBN-13(EAN): 9781402086571 Издательство: Springer Рейтинг: Цена: 12157.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Offering a consolidated account on medial representations, this book will serve the science and engineering communities using medial models and will provide learning material for students entering this field.
Автор: Kaleem Siddiqi; Stephen Pizer Название: Medial Representations ISBN: 9048179467 ISBN-13(EAN): 9789048179466 Издательство: Springer Рейтинг: Цена: 12157.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Offering a consolidated account on medial representations, this book will serve the science and engineering communities using medial models and will provide learning material for students entering this field.
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