Описание: This book presents applications of hypercomplex analysis to boundary value and initial-boundary value problems from various areas of mathematical physics. Given that quaternion and Clifford analysis offer natural and intelligent ways to enter into higher dimensions, it starts with quaternion and Clifford versions of complex function theory including series expansions with Appell polynomials, as well as Taylor and Laurent series. Several necessary function spaces are introduced, and an operator calculus based on modifications of the Dirac, Cauchy-Fueter, and Teodorescu operators and different decompositions of quaternion Hilbert spaces are proved. Finally, hypercomplex Fourier transforms are studied in detail. All this is then applied to first-order partial differential equations such as the Maxwell equations, the Carleman-Bers-Vekua system, the Schr?dinger equation, and the Beltrami equation. The higher-order equations start with Riccati-type equations. Further topics include spatial fluid flow problems, image and multi-channel processing, image diffusion, linear scale invariant filtering, and others. One of the highlights is the derivation of the three-dimensional Kolosov-Mushkelishvili formulas in linear elasticity. Throughout the book the authors endeavor to present historical references and important personalities. The book is intended for a wide audience in the mathematical and engineering sciences and is accessible to readers with a basic grasp of real, complex, and functional analysis.
Описание: Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. This book offers an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. It can be used as an introductory text to the theory underpinning fitted mesh methods.
Описание: Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.Key Features: - The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings- Complex dimensions of a fractal string, defined as the poles of an associated zeta function, are studied in detail, then used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra- Explicit formulas are extended to apply to the geometric, spectral, and dynamic zeta functions associated with a fractal- Examples of such formulas include Prime Orbit Theorem with error term for self-similar flows, and a tube formula- The method of diophantine approximation is used to study self-similar strings and flows- Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functionsThroughout new results are examined. The final chapter gives a new definition of fractality as the presence of nonreal complex dimensions with positive real parts.The significant studies and problems illuminated in this work may be used in a classroom setting at the graduate level. Fractal Geometry, Complex Dimensions and Zeta Functions will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics.
Автор: Hale Jack K., Magalhaes Luis T., Oliva Waldyr Название: Dynamics in Infinite Dimensions ISBN: 0387954635 ISBN-13(EAN): 9780387954639 Издательство: Springer Рейтинг: Цена: 9357.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book presents an introduction to the geometric theory of infinite dimensional dynamical systems. Many of the fundamental results are presented for asymptotically smooth dynamical systems that have applications to functional differential equations as well as classes of dissipative partial differential equations. However, as in the earlier edition, the major emphasis is on retarded functional differential equations. This updated version also contains much material on neutral functional differential equations. The results in the earlier edition on Morse-Smale systems for maps are extended to a class of semiflows, which include retarded functional differential equations and parabolic partial differential equations.
Автор: Bracci Название: Geometric Function Theory in Higher Dimension ISBN: 3319731254 ISBN-13(EAN): 9783319731254 Издательство: Springer Рейтинг: Цена: 10760.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The book collects the most relevant outcomes from the INdAM Workshop "Geometric Function Theory in Higher Dimension" held in Cortona on September 5-9, 2016. In particular, it offers a selection of original contributions on Loewner theory in one and higher dimensions, semigroups theory, iteration theory and related topics.
Автор: Vladimir N. Dubinin; Nikolai G. Kruzhilin Название: Condenser Capacities and Symmetrization in Geometric Function Theory ISBN: 3034808429 ISBN-13(EAN): 9783034808422 Издательство: Springer Рейтинг: Цена: 13275.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: After an introduction to the theory of condenser capacities in the plane, the monotonicity of the capacity under various special transformations (polarization, Gonchar transformation, averaging transformations and others) is established, followed by various types of symmetrization which are one of the main objects of the book.
Автор: Shi-Hai Dong Название: Wave Equations in Higher Dimensions ISBN: 940178230X ISBN-13(EAN): 9789401782302 Издательство: Springer Рейтинг: Цена: 15672.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This volume describes quantum wave equations in higher dimensions at an advanced level, placing all current mathematical and physical concepts and techniques at the reader`s disposal. Readers will learn about quantum wave equations in higher dimensions and their broad range of applications.
Автор: Saunders MacLane Название: Mathematics Form and Function ISBN: 1461293405 ISBN-13(EAN): 9781461293408 Издательство: Springer Рейтинг: Цена: 14533.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book records my efforts over the past four years to capture in words a description of the form and function of Mathematics, as a background for the Philosophy of Mathematics. My efforts have been encouraged by lec- tures that I have given at Heidelberg under the auspices of the Alexander von Humboldt Stiftung, at the University of Chicago, and at the University of Minnesota, the latter under the auspices of the Institute for Mathematics and Its Applications. Jean Benabou has carefully read the entire manuscript and has offered incisive comments.
George Glauberman, Car- los Kenig, Christopher Mulvey, R. Narasimhan, and Dieter Puppe have provided similar comments on chosen chapters. Fred Linton has pointed out places requiring a more exact choice of wording.
Many conversations with George Mackey have given me important insights on the nature of Mathematics. I have had similar help from Alfred Aeppli, John Gray, Jay Goldman, Peter Johnstone, Bill Lawvere, and Roger Lyndon. Over the years, I have profited from discussions of general issues with my colleagues Felix Browder and Melvin Rothenberg.
Ideas from Tammo Tom Dieck, Albrecht Dold, Richard Lashof, and Ib Madsen have assisted in my study of geometry. Jerry Bona and B. L.
Foster have helped with my examina- tion of mechanics. My observations about logic have been subject to con- structive scrutiny by Gert Miiller, Marian Boykan Pour-El, Ted Slaman, R. Voreadou, Volker Weispfennig, and Hugh Woodin.
Описание: This book deals with the numerical analysis and efficient numerical treatment of high-dimensional integrals using sparse grids and other dimension-wise integration techniques with applications to finance and insurance.
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