Fractal Functions, Dimensions and Signal Analysis, Banerjee Santo, Easwaramoorthy D., Gowrisankar A.

Автор: Rogers Luke G, Ruiz Patricia Alonso, Teplyaev Alexander, Chen Joe Po-chou
Название: Analysis, Probability And Mathematical Physics On Fractals
ISBN: 9811215529 ISBN-13(EAN): 9789811215520
Издательство: World Scientific Publishing
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Цена: 153120.00 T
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Описание: In the 50 years since Mandelbrot identified the fractality of coastlines, mathematicians and physicists have developed a rich and beautiful theory describing the interplay between analytic, geometric and probabilistic aspects of the mathematics of fractals. Using classical and abstract analytic tools developed by Cantor, Hausdorff, and Sierpinski, they have sought to address fundamental questions: How can we measure the size of a fractal set? How do waves and heat travel on irregular structures? How are analysis, geometry and stochastic processes related in the absence of Euclidean smooth structure? What new physical phenomena arise in the fractal-like settings that are ubiquitous in nature?This book introduces background and recent progress on these problems, from both established leaders in the field and early career researchers. The book gives a broad introduction to several foundational techniques in fractal mathematics, while also introducing some specific new and significant results of interest to experts, such as that waves have infinite propagation speed on fractals. It contains sufficient introductory material that it can be read by new researchers or researchers from other areas who want to learn about fractal methods and results.

Автор: Shier John
Название: Fractalize That! : A Visual Essay On Statistical Geometry
ISBN: 9813275162 ISBN-13(EAN): 9789813275164
Издательство: World Scientific Publishing
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Цена: 73920.00 T
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Описание: Fractalize That! A Visual Essay on Statistical Geometry brings a new class of geometric fractals to a wider audience of mathematicians and scientists. It describes a recently discovered random fractal space-filling algorithm. Connections with tessellations and known fractals such as Sierpinski are developed. And, the mathematical development is illustrated by a large number of colorful images that will charm the readers.The algorithm claims to be universal in scope, in that it can fill any spatial region with smaller and smaller fill regions of any shape. The filling is complete in the limit of an infinite number of fill regions. This book presents a descriptive development of the subject using the traditional shapes of geometry such as discs, squares, and triangles. It contains a detailed mathematical treatment of all that is currently known about the algorithm, as well as a chapter on software implementation of the algorithm.The mathematician will find a wealth of interesting conjectures supported by numerical computation. Physicists are offered a model looking for an application. The patterns generated are often quite interesting as abstract art. Readers can also create these computer-generated art with the advice and examples provided.

Автор: Lapidus Michel L., Frankenhuijsen Machiel van
Название: Fractal Geometry, Complex Dimensions and Zeta Functions / Geometry and Spectra of Fractal Strings
ISBN: 0387332855 ISBN-13(EAN): 9780387332857
Издательство: Springer
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Цена: 49330.00 T
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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: Hoverstadt
Название: The Fractal Organisation - Creating Sustainable Organisations with the Viable System Model
ISBN: 0470060565 ISBN-13(EAN): 9780470060568
Издательство: Wiley
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Цена: 33790.00 T
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Описание: Stafford Beer was ` one of the most remarkable figures which British operational research has produced...he founded two major and pioneering OR groups; wrote some of the best books about the subject; and was a world leader in the development of systems ideas ` (extract from obituary- OR newsletter).

Автор: Stitchx, Warrington Tracy
Название: Fractal Cross Stitch Collection Volume 5
ISBN: 1500288810 ISBN-13(EAN): 9781500288815
Издательство: Неизвестно
Цена: 19490.00 T
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Автор: Michael Frame, Nial Neger
Название: Kitchen Science Fractals: A Lab Manual For Fractal Geometry
ISBN: 9811218455 ISBN-13(EAN): 9789811218453
Издательство: World Scientific Publishing
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Цена: 132000.00 T
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Описание: This book provides a collection of 43 simple computer and physical laboratory experiments, including some for an artist's studio and some for a kitchen, that illustrate the concepts of fractal geometry. In addition to standard topics — iterated function systems (IFS), fractal dimension computation, the Mandelbrot set — we explore data analysis by driven IFS, construction of four-dimensional fractals, basic multifractals, synchronization of chaotic processes, fractal finger paints, cooking fractals, videofeedback, and fractal networks of resistors and oscillators.

Автор: Michael Frame, Nial Neger
Название: Kitchen Science Fractals: A Lab Manual For Fractal Geometry
ISBN: 9811218927 ISBN-13(EAN): 9789811218927
Издательство: World Scientific Publishing
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Цена: 47520.00 T
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Описание: This book provides a collection of 43 simple computer and physical laboratory experiments, including some for an artist's studio and some for a kitchen, that illustrate the concepts of fractal geometry. In addition to standard topics — iterated function systems (IFS), fractal dimension computation, the Mandelbrot set — we explore data analysis by driven IFS, construction of four-dimensional fractals, basic multifractals, synchronization of chaotic processes, fractal finger paints, cooking fractals, videofeedback, and fractal networks of resistors and oscillators.

Автор: Michel L. Lapidus; Machiel van Frankenhuijsen
Название: Fractal Geometry, Complex Dimensions and Zeta Functions
ISBN: 1489988386 ISBN-13(EAN): 9781489988386
Издательство: Springer
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Цена: 83850.00 T
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Описание: In its Second Edition, this in-depth study of the vibrations of fractal strings interlinks number theory, spectral geometry and fractal geometry. Includes a geometric reformulation of the Riemann hypothesis and a new final chapter on recent topics and results.

Автор: Rosenberg
Название: A Survey of Fractal Dimensions of Networks
ISBN: 3319900463 ISBN-13(EAN): 9783319900469
Издательство: Springer
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Цена: 46570.00 T
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Автор: Rosenberg Eric
Название: Fractal Dimensions of Networks
ISBN: 3030431681 ISBN-13(EAN): 9783030431686
Издательство: Springer
Цена: 60550.00 T
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Описание: Fractal Dimensions of Networks ties the theory and methods for computing fractal dimensions of networks to the "classic" theory of dimensions of geometric objects.The goal of the book is to provide a unified treatment of fractal dimensions of sets and networks.

Автор: Michel L. Lapidus; Goran Radunovi?; Darko ?ubrini?
Название: Fractal Zeta Functions and Fractal Drums
ISBN: 3319447041 ISBN-13(EAN): 9783319447049
Издательство: Springer
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Цена: 121110.00 T
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Описание: This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums.

Автор: Massopust, Peter R.
Название: Fractal Functions, Fractal Surfaces, and Wavelets
ISBN: 012804408X ISBN-13(EAN): 9780128044087
Издательство: Elsevier Science
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Цена: 83080.00 T
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Описание: Fractal Functions, Fractal Surfaces, and Wavelets, Second Edition, is the first systematic exposition of the theory of local iterated function systems, local fractal functions and fractal surfaces, and their connections to wavelets and wavelet sets. The book is based on Massopust’s work on and contributions to the theory of fractal interpolation, and the author uses a number of tools—including analysis, topology, algebra, and probability theory—to introduce readers to this exciting subject. . Though much of the material presented in this book is relatively current (developed in the past decades by the author and his colleagues) and fairly specialized, an informative background is provided for those entering the field. With its coherent and comprehensive presentation of the theory of univariate and multivariate fractal interpolation, this book will appeal to mathematicians as well as to applied scientists in the fields of physics, engineering, biomathematics, and computer science. In this second edition, Massopust includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, further develops the connections to wavelets and wavelet sets, and deepens and extends the pedagogical content.