Hausdorff Calculus: Applications to Fractal Systems, Yingjie Liang, Wen Chen, Wei Cai
Автор: Mattila Название: Fourier Analysis and Hausdorff Dimension ISBN: 1107107350 ISBN-13(EAN): 9781107107359 Издательство: Cambridge Academ Рейтинг: Цена: 11563.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: During the past two decades there has been active interplay between geometric measure theory and Fourier analysis. This book for graduate students and researchers describes part of that development, concentrating on the relationship between the Fourier transform and Hausdorff dimension. It covers classical results as well as cutting-edge research.
Автор: West Bruce, Bologna Mauro, Grigolini Paolo Название: Physics of Fractal Operators ISBN: 0387955542 ISBN-13(EAN): 9780387955544 Издательство: Springer Рейтинг: Цена: 13060.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This text describes the statistcal behavior of complex systems and shows how the fractional calculus can be used to model the behavior. The book gives general strategies for understanding wave propagation through random media, the nonlinear response of complex materials, and the fluctuations of heat transport in heterogeneous materials.
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: Bl. Sendov; Gerald Beer Название: Hausdorff Approximations ISBN: 9401067872 ISBN-13(EAN): 9789401067874 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 a1Ie.' 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'etre of this series.
Автор: Bl. Sendov; Gerald Beer Название: Hausdorff Approximations ISBN: 0792309014 ISBN-13(EAN): 9780792309017 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 a1Ie.' 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'etre of this series.
Автор: Felix Hausdorff; S.D. Chatterji; R. Remmert; W. Sc Название: Felix Hausdorff-Gesammelte Werke ISBN: 3540417605 ISBN-13(EAN): 9783540417606 Издательство: Springer Рейтинг: Цена: 11101.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
This book is a monograph on harmonic analysis and fractal analysis over local fields. It can also be used as lecture notes/textbook or as recommended reading for courses on modern harmonic and fractal analysis. It is as reliable as Fourier Analysis on Local Fields published in 1975 which is regarded as the first monograph in this research field.
The book is self-contained, with wide scope and deep knowledge, taking modern mathematics (such as modern algebra, point set topology, functional analysis, distribution theory, and so on) as bases. Specially, fractal analysis is studied in the viewpoint of local fields, and fractal calculus is established by pseudo-differential operators over local fields. A frame of fractal PDE is constructed based on fractal calculus instead of classical calculus. On the other hand, the author does his best to make those difficult concepts accessible to readers, illustrate clear comparison between harmonic analysis on Euclidean spaces and that on local fields, and at the same time provide motivations underlying the new concepts and techniques. Overall, it is a high quality, up to date and valuable book for interested readers.
Автор: Robert G. Niemeyer, Erin P.J. Pearse, John A. Rock, Tony Samuel Название: Horizons of Fractal Geometry and Complex Dimensions ISBN: 1470435810 ISBN-13(EAN): 9781470435813 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 16302.00 р. Наличие на складе: Нет в наличии.
Описание: This volume contains the proceedings of the 2016 Summer School on Fractal Geometry and Complex Dimensions, in celebration of Michel L. Lapidus's 60th birthday, held from June 21-29, 2016, at California Polytechnic State University, San Luis Obispo, California. The theme of the contributions is fractals and dynamics and content is split into four parts, centered around the following themes: Dimension gaps and the mass transfer principle, fractal strings and complex dimensions, Laplacians on fractal domains and SDEs with fractal noise, and aperiodic order (Delone sets and tilings).
Автор: Gerald A. Edgar Название: Integral, Probability, and Fractal Measures ISBN: 1441931120 ISBN-13(EAN): 9781441931122 Издательство: Springer Рейтинг: Цена: 10335.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book may be considered a continuation of my Springer-Verlag text Mea- sure, Topology, and Fractal Geometry. It presupposes some elementary knowl- edge of fractal geometry and the mathematics behind fractal geometry. Such knowledge might be obtained by study of Measure, Topology, and Fractal Ge- ometry or by study of one of the other mathematically oriented texts (such as 13] or 87]). I hope this book will be appropriate to mathematics students at the beginning graduate level in the U.S. Most references are numbered and may be found at the end of the book; but Measure, Topology, and Fractal Geometry is referred to as MTFG]. One of the reviews of MTFG] says that it "sacrific es] breadth of coverage 1 for systematic development" -although I did not have it so clearly formulated as that in my mind at the time I was writing the book, I think that remark is exactly on target. That sacrifice has been made in this volume as well. In many cases, I do not include the most general or most complete form of a result. Sometimes I have only an example of an important development. The goal was to omit most material that is too tedious or that requires too much background.
Автор: Christoph Bandt; Umberto Mosco; Martina Z?hle Название: Fractal Geometry and Stochastics III ISBN: 3034896123 ISBN-13(EAN): 9783034896122 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Fractal geometry is used to model complicated natural and technical phenomena in various disciplines like physics, biology, finance, and medicine. Since most convincing models contain an element of randomness, stochastics enters the area in a natural way. This book documents the establishment of fractal geometry as a substantial mathematical theory. As in the previous volumes, which appeared in 1998 and 2000, leading experts known for clear exposition were selected as authors. They survey their field of expertise, emphasizing recent developments and open problems. Main topics include multifractal measures, dynamical systems, stochastic processes and random fractals, harmonic analysis on fractals.
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