Fractals And Hyperspaces

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Fractals And Hyperspaces

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Author : Keith R. Wicks
language : en
Publisher: Springer
Release Date : 2006-11-14

Fractals And Hyperspaces written by Keith R. Wicks and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Addressed to all readers with an interest in fractals, hyperspaces, fixed-point theory, tilings and nonstandard analysis, this book presents its subject in an original and accessible way complete with many figures. The first part of the book develops certain hyperspace theory concerning the Hausdorff metric and the Vietoris topology, as a foundation for what follows on self-similarity and fractality. A major feature is that nonstandard analysis is used to obtain new proofs of some known results much more slickly than before. The theory of J.E. Hutchinson's invariant sets (sets composed of smaller images of themselves) is developed, with a study of when such a set is tiled by its images and a classification of many invariant sets as either regular or residual. The last and most original part of the book introduces the notion of a "view" as part of a framework for studying the structure of sets within a given space. This leads to new, elegant concepts (defined purely topologically) of self-similarity and fractality: in particular, the author shows that many invariant sets are "visually fractal", i.e. have infinite detail in a certain sense. These ideas have considerable scope for further development, and a list of problems and lines of research is included.

Weighted Approximation With Varying Weight

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Author : Vilmos Totik
language : en
Publisher: Springer
Release Date : 1994-02-28

Weighted Approximation With Varying Weight written by Vilmos Totik and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-02-28 with Mathematics categories.

A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.

Fractals And Chaos

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Author : Paul S. Addison
language : en
Publisher: CRC Press
Release Date : 1997-01-01

Fractals And Chaos written by Paul S. Addison and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Science categories.

Fractals and Chaos: An Illustrated Course provides you with a practical, elementary introduction to fractal geometry and chaotic dynamics-subjects that have attracted immense interest throughout the scientific and engineering disciplines. The book may be used in part or as a whole to form an introductory course in either or both subject areas. A prominent feature of the book is the use of many illustrations to convey the concepts required for comprehension of the subject. In addition, plenty of problems are provided to test understanding. Advanced mathematics is avoided in order to provide a concise treatment and speed the reader through the subject areas. The book can be used as a text for undergraduate courses or for self-study.

Fractal Functions Fractal Surfaces And Wavelets

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Author : Peter R. Massopust
language : en
Publisher: Academic Press
Release Date : 2016-09-02

Fractal Functions Fractal Surfaces And Wavelets written by Peter R. Massopust and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-02 with Mathematics categories.

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. - Offers a comprehensive presentation of fractal functions and fractal surfaces - Includes latest developments in fractal interpolation - Connects fractal geometry with wavelet theory - Includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, and further develops the connections to wavelets and wavelet sets - Deepens and extends the pedagogical content

A Concise Introduction To Hypercomplex Fractals

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Author : Andrzej Katunin
language : en
Publisher: CRC Press
Release Date : 2017-10-05

A Concise Introduction To Hypercomplex Fractals written by Andrzej Katunin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-05 with Computers categories.

This book presents concisely the full story on complex and hypercomplex fractals, starting from the very first steps in complex dynamics and resulting complex fractal sets, through the generalizations of Julia and Mandelbrot sets on a complex plane and the Holy Grail of the fractal geometry – a 3D Mandelbrot set, and ending with hypercomplex, multicomplex and multihypercomplex fractal sets which are still under consideration of scientists. I tried to write this book in a possibly simple way in order to make it understandable to most people whose math knowledge covers the fundamentals of complex numbers only. Moreover, the book is full of illustrations of generated fractals and stories concerned with great mathematicians, number spaces and related fractals. In the most cases only information required for proper understanding of a nature of a given vector space or a construction of a given fractal set is provided, nevertheless a more advanced reader may treat this book as a fundamental compendium on hypercomplex fractals with references to purely scientific issues like dynamics and stability of hypercomplex systems.

Fractals Everywhere

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Author : Michael F. Barnsley
language : en
Publisher: Courier Corporation
Release Date : 2013-10-03

Fractals Everywhere written by Michael F. Barnsley and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-03 with Mathematics categories.

Up-to-date text focuses on how fractal geometry can be used to model real objects in the physical world, with an emphasis on fractal applications. Includes solutions, hints, and a bonus CD.

Atomicity Through Fractal Measure Theory

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Author : Alina Gavriluţ
language : en
Publisher: Springer Nature
Release Date : 2019-11-02

Atomicity Through Fractal Measure Theory written by Alina Gavriluţ and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-02 with Mathematics categories.

This book presents an exhaustive study of atomicity from a mathematics perspective in the framework of multi-valued non-additive measure theory. Applications to quantum physics and, more generally, to the fractal theory of the motion, are highlighted. The study details the atomicity problem through key concepts, such as the atom/pseudoatom, atomic/nonatomic measures, and different types of non-additive set-valued multifunctions. Additionally, applications of these concepts are brought to light in the study of the dynamics of complex systems. The first chapter prepares the basics for the next chapters. In the last chapter, applications of atomicity in quantum physics are developed and new concepts, such as the fractal atom are introduced. The mathematical perspective is presented first and the discussion moves on to connect measure theory and quantum physics through quantum measure theory. New avenues of research, such as fractal/multifractal measure theory with potential applications in life sciences, are opened.

Fractal Geometry

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Author : Kenneth Falconer
language : en
Publisher: John Wiley & Sons
Release Date : 2007-12-10

Fractal Geometry written by Kenneth Falconer and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-10 with Mathematics categories.

Since its original publication in 1990, Kenneth Falconer's Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. It introduces the general mathematical theory and applications of fractals in a way that is accessible to students from a wide range of disciplines. This new edition has been extensively revised and updated. It features much new material, many additional exercises, notes and references, and an extended bibliography that reflects the development of the subject since the first edition. * Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals. * Each topic is carefully explained and illustrated by examples and figures. * Includes all necessary mathematical background material. * Includes notes and references to enable the reader to pursue individual topics. * Features a wide selection of exercises, enabling the reader to develop their understanding of the theory. * Supported by a Web site featuring solutions to exercises, and additional material for students and lecturers. Fractal Geometry: Mathematical Foundations and Applications is aimed at undergraduate and graduate students studying courses in fractal geometry. The book also provides an excellent source of reference for researchers who encounter fractals in mathematics, physics, engineering, and the applied sciences. Also by Kenneth Falconer and available from Wiley: Techniques in Fractal Geometry ISBN 0-471-95724-0 Please click here to download solutions to exercises found within this title: http://www.wileyeurope.com/fractal

The Blocking Technique Weighted Mean Operators And Hardy S Inequality

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Author : Karl-Goswin Grosse-Erdmann
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-01-19

The Blocking Technique Weighted Mean Operators And Hardy S Inequality written by Karl-Goswin Grosse-Erdmann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-19 with Mathematics categories.

This book presents the first comprehensive treatment of the blocking technique which consists in transforming norms in section form into norms in block form, and vice versa. Such norms appear throughout analysis. The blocking technique is a powerful, yet elementary, tool whose usefulnes is demonstrated in the book. In particular, it is shown to lead to the solution of three recent problems of Bennett concerning the inequalities of Hardy and Copson. The book is addressed to researchers and graduate students. An interesting feature is that it contains a dictionary of transformations between section and block norms and will thus be useful to researchers as a reference text. The book requires no knowledge beyond an introductory course in functional analysis.

Projective Modules And Complete Intersections

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Author : Satya Mandal
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-10-10

Projective Modules And Complete Intersections written by Satya Mandal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-10-10 with Mathematics categories.

In these notes on "Projective Modules and Complete Intersections" an account on the recent developments in research on this subject is presented. The author's preference for the technique of Patching isotopic isomorphisms due to Quillen, formalized by Plumsted, over the techniques of elementary matrices is evident here. The treatment of Basic Element theory here incorporates Plumstead's idea of the "generalized dimension functions". These notes are highly selfcontained and should be accessible to any graduate student in commutative algebra or algebraic geometry. They include fully self-contained presentations of the theorems of Ferrand-Szpiro, Cowsik-Nori and the techniques of Lindel.