Fractals And Hyperspaces

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Fractals and Hyperspaces

Author : Keith R. Wicks
Publisher : Springer
ISBN 13 : 354046610X
Total Pages : 175 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Fractals and Hyperspaces by : Keith R. Wicks

Download or read book Fractals and Hyperspaces written by Keith R. Wicks and published by Springer. This book was released on 2006-11-14 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Clifford Wavelets, Singular Integrals, and Hardy Spaces

Author : Marius Mitrea
Publisher : Springer
ISBN 13 : 9783540578840
Total Pages : 136 pages
Book Rating : 4.5/5 (788 download)

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Book Synopsis Clifford Wavelets, Singular Integrals, and Hardy Spaces by : Marius Mitrea

Download or read book Clifford Wavelets, Singular Integrals, and Hardy Spaces written by Marius Mitrea and published by Springer. This book was released on 1994-04-28 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses the extensions of basic Fourier Analysis techniques to the Clifford algebra framework. Topics covered: construction of Clifford-valued wavelets, Calderon-Zygmund theory for Clifford valued singular integral operators on Lipschitz hyper-surfaces, Hardy spaces of Clifford monogenic functions on Lipschitz domains. Results are applied to potential theory and elliptic boundary value problems on non-smooth domains. The book is self-contained to a large extent and well-suited for graduate students and researchers in the areas of wavelet theory, Harmonic and Clifford Analysis. It will also interest the specialists concerned with the applications of the Clifford algebra machinery to Mathematical Physics.

A Concise Introduction to Hypercomplex Fractals

Author : Andrzej Katunin
Publisher : CRC Press
ISBN 13 : 135180121X
Total Pages : 103 pages
Book Rating : 4.3/5 (518 download)

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Book Synopsis A Concise Introduction to Hypercomplex Fractals by : Andrzej Katunin

Download or read book A Concise Introduction to Hypercomplex Fractals written by Andrzej Katunin and published by CRC Press. This book was released on 2017-10-05 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 and Universal Spaces in Dimension Theory

Author : Stephen Lipscomb
Publisher : Springer Science & Business Media
ISBN 13 : 0387854940
Total Pages : 259 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis Fractals and Universal Spaces in Dimension Theory by : Stephen Lipscomb

Download or read book Fractals and Universal Spaces in Dimension Theory written by Stephen Lipscomb and published by Springer Science & Business Media. This book was released on 2008-10-28 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historically, for metric spaces the quest for universal spaces in dimension theory spanned approximately a century of mathematical research. The history breaks naturally into two periods - the classical (separable metric) and the modern (not-necessarily separable metric). The classical theory is now well documented in several books. This monograph is the first book to unify the modern theory from 1960-2007. Like the classical theory, the modern theory fundamentally involves the unit interval. Unique features include: * The use of graphics to illustrate the fractal view of these spaces; * Lucid coverage of a range of topics including point-set topology and mapping theory, fractal geometry, and algebraic topology; * A final chapter contains surveys and provides historical context for related research that includes other imbedding theorems, graph theory, and closed imbeddings; * Each chapter contains a comment section that provides historical context with references that serve as a bridge to the literature. This monograph will be useful to topologists, to mathematicians working in fractal geometry, and to historians of mathematics. Being the first monograph to focus on the connection between generalized fractals and universal spaces in dimension theory, it will be a natural text for graduate seminars or self-study - the interested reader will find many relevant open problems which will create further research into these topics.

Fractals and Chaos

Author : Paul S. Addison
Publisher : CRC Press
ISBN 13 : 9780849384431
Total Pages : 276 pages
Book Rating : 4.3/5 (844 download)

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Book Synopsis Fractals and Chaos by : Paul S. Addison

Download or read book Fractals and Chaos written by Paul S. Addison and published by CRC Press. This book was released on 1997-01-01 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Peter R. Massopust
Publisher : Academic Press
ISBN 13 : 0128044705
Total Pages : 428 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Fractal Functions, Fractal Surfaces, and Wavelets by : Peter R. Massopust

Download or read book Fractal Functions, Fractal Surfaces, and Wavelets written by Peter R. Massopust and published by Academic Press. This book was released on 2016-09-02 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Classical Diophantine Equations

Author : Vladimir G. Sprindzuk
Publisher : Springer
ISBN 13 : 3540480838
Total Pages : 244 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Classical Diophantine Equations by : Vladimir G. Sprindzuk

Download or read book Classical Diophantine Equations written by Vladimir G. Sprindzuk and published by Springer. This book was released on 2006-11-15 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, now that the book appears in English, close studyand emulation. In particular those emphases allow him to devote the eighth chapter to an analysis of the interrelationship of the class number of algebraic number fields involved and the bounds on the heights of thesolutions of the diophantine equations. Those ideas warrant further development. The final chapter deals with effective aspects of the Hilbert Irreducibility Theorem, harkening back to earlier work of the author. There is no other congenial entry point to the ideas of the last two chapters in the literature.

Mathematical Research Today and Tomorrow

Author : Carlos Casacuberta
Publisher : Springer Science & Business Media
ISBN 13 : 9783540560111
Total Pages : 132 pages
Book Rating : 4.5/5 (61 download)

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Book Synopsis Mathematical Research Today and Tomorrow by : Carlos Casacuberta

Download or read book Mathematical Research Today and Tomorrow written by Carlos Casacuberta and published by Springer Science & Business Media. This book was released on 1992-12-14 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Symposium on the Current State and Prospects of Mathematics was held in Barcelona from June 13 to June 18, 1991. Seven invited Fields medalists gavetalks on the development of their respective research fields. The contents of all lectures were collected in the volume, together witha transcription of a round table discussion held during the Symposium. All papers are expository. Some parts include precise technical statements of recent results, but the greater part consists of narrative text addressed to a very broad mathematical public. CONTENTS: R. Thom: Leaving Mathematics for Philosophy.- S. Novikov: Role of Integrable Models in the Development of Mathematics.- S.-T. Yau: The Current State and Prospects of Geometry and Nonlinear Differential Equations.- A. Connes: Noncommutative Geometry.- S. Smale: Theory of Computation.- V. Jones: Knots in Mathematics and Physics.- G. Faltings: Recent Progress in Diophantine Geometry.

Similarity Problems and Completely Bounded Maps

Author : Gilles Pisier
Publisher : Springer
ISBN 13 : 3662215373
Total Pages : 170 pages
Book Rating : 4.6/5 (622 download)

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Book Synopsis Similarity Problems and Completely Bounded Maps by : Gilles Pisier

Download or read book Similarity Problems and Completely Bounded Maps written by Gilles Pisier and published by Springer. This book was released on 2013-11-11 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes revolve around three similarity problems, appearing in three dif ferent contexts, but all dealing with the space B(H) of all bounded operators on a complex Hilbert space H. The first one deals with group representations, the second one with C* -algebras and the third one with the disc algebra. We describe them in detail in the introduction which follows. This volume is devoted to the background necessary to understand these three open problems, to the solutions that are known in some special cases and to numerous related concepts, results, counterexamples or extensions which their investigation has generated. For instance, we are naturally lead to study various Banach spaces formed by the matrix coefficients of group representations. Furthermore, we discuss the closely connected Schur multipliers and Grothendieck's striking characterization of those which act boundedly on B(H). While the three problems seem different, it is possible to place them in a common framework using the key concept of "complete boundedness", which we present in detail. In some sense, completely bounded maps can also be viewed as spaces of "coefficients" of C*-algebraic representations, if we allow "B(H) valued coefficients", this is the content of the fundamental factorization property of these maps, which plays a central role in this volume. Using this notion, the three problems can all be formulated as asking whether "boundedness" implies "complete boundedness" for linear maps satisfying cer tain additional algebraic identities.

Existence Families, Functional Calculi and Evolution Equations

Author : Ralph DeLaubenfels
Publisher : Springer
ISBN 13 : 3540483225
Total Pages : 254 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Existence Families, Functional Calculi and Evolution Equations by : Ralph DeLaubenfels

Download or read book Existence Families, Functional Calculi and Evolution Equations written by Ralph DeLaubenfels and published by Springer. This book was released on 2006-11-15 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an operator-theoretic approach to ill-posed evolution equations. It presents the basic theory, and the more surprising examples, of generalizations of strongly continuous semigroups known as 'existent families' and 'regularized semigroups'. These families of operators may be used either to produce all initial data for which a solution in the original space exists, or to construct a maximal subspace on which the problem is well-posed. Regularized semigroups are also used to construct functional, or operational, calculi for unbounded operators. The book takes an intuitive and constructive approach by emphasizing the interaction between functional calculus constructions and evolution equations. One thinks of a semigroup generated by A as etA and thinks of a regularized semigroup generated by A as etA g(A), producing solutions of the abstract Cauchy problem for initial data in the image of g(A). Material that is scattered throughout numerous papers is brought together and presented in a fresh, organized way, together with a great deal of new material.

Theory and Formal Methods 1993

Author : Geoffrey Burn
Publisher : Springer Science & Business Media
ISBN 13 : 1447135032
Total Pages : 333 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Theory and Formal Methods 1993 by : Geoffrey Burn

Download or read book Theory and Formal Methods 1993 written by Geoffrey Burn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the fIrst workshop held by the Theory and Formal Methods Section ofthe Imperial College Department of Computing. It contains papers from almost every member of the Section, from our long-term academic visitors, and from those who have recently left us. The papers fall into four broad areas: • semantics • concurrency • logic • specification with some papers spanning a number of disciplines. The subject material varies from work on mathematical foundations to practical applications of this theory, expressing the Section's commitment to both the foundations of computer science, and the application of theory to real computing problems. In preparing the workshop and these proceedings, care was taken to ensure that there were papers overviewing a field, as well as ones whose primary aim was to present new scientifIc results. This had a dual purpose: to bring our Section members up to speed in some of the areas being worked on by the Section; and to provide the reader of the proceedings not only with a good introduction to many of the specifIc areas being investigated by the Section, but also with details of some of our latest results. All the papers presented at the workshop were revised following comments made by the workshop participants, and all were subsequently reviewed by at least two people before producing the fInal versions contained in this volume.

Developments in Theoretical Computer Science

Author : J. Dassow
Publisher : CRC Press
ISBN 13 : 9782881249617
Total Pages : 290 pages
Book Rating : 4.2/5 (496 download)

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Book Synopsis Developments in Theoretical Computer Science by : J. Dassow

Download or read book Developments in Theoretical Computer Science written by J. Dassow and published by CRC Press. This book was released on 1994-10-07 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

Author : Bernold Fiedler
Publisher : Springer Science & Business Media
ISBN 13 : 3642565891
Total Pages : 816 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems by : Bernold Fiedler

Download or read book Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems written by Bernold Fiedler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.

Fractal Dimension for Fractal Structures

Author : Manuel Fernández-Martínez
Publisher : Springer
ISBN 13 : 3030166457
Total Pages : 217 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Fractal Dimension for Fractal Structures by : Manuel Fernández-Martínez

Download or read book Fractal Dimension for Fractal Structures written by Manuel Fernández-Martínez and published by Springer. This book was released on 2019-04-23 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a generalised approach to fractal dimension theory from the standpoint of asymmetric topology by employing the concept of a fractal structure. The fractal dimension is the main invariant of a fractal set, and provides useful information regarding the irregularities it presents when examined at a suitable level of detail. New theoretical models for calculating the fractal dimension of any subset with respect to a fractal structure are posed to generalise both the Hausdorff and box-counting dimensions. Some specific results for self-similar sets are also proved. Unlike classical fractal dimensions, these new models can be used with empirical applications of fractal dimension including non-Euclidean contexts. In addition, the book applies these fractal dimensions to explore long-memory in financial markets. In particular, novel results linking both fractal dimension and the Hurst exponent are provided. As such, the book provides a number of algorithms for properly calculating the self-similarity exponent of a wide range of processes, including (fractional) Brownian motion and Lévy stable processes. The algorithms also make it possible to analyse long-memory in real stocks and international indexes. This book is addressed to those researchers interested in fractal geometry, self-similarity patterns, and computational applications involving fractal dimension and Hurst exponent.

Projective Modules and Complete Intersections

Author : Satya Mandal
Publisher : Springer Science & Business Media
ISBN 13 : 9783540635642
Total Pages : 132 pages
Book Rating : 4.6/5 (356 download)

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Book Synopsis Projective Modules and Complete Intersections by : Satya Mandal

Download or read book Projective Modules and Complete Intersections written by Satya Mandal and published by Springer Science & Business Media. This book was released on 1997-10-10 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Blocking Technique, Weighted Mean Operators and Hardy's Inequality

Author : Karl-Goswin Grosse-Erdmann
Publisher : Springer Science & Business Media
ISBN 13 : 9783540639022
Total Pages : 132 pages
Book Rating : 4.6/5 (39 download)

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Book Synopsis The Blocking Technique, Weighted Mean Operators and Hardy's Inequality by : Karl-Goswin Grosse-Erdmann

Download or read book The Blocking Technique, Weighted Mean Operators and Hardy's Inequality written by Karl-Goswin Grosse-Erdmann and published by Springer Science & Business Media. This book was released on 1998-01-19 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Continuous Exponential Martingales and BMO

Author : Norihiko Kazamaki
Publisher : Springer
ISBN 13 : 3540484213
Total Pages : 102 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Continuous Exponential Martingales and BMO by : Norihiko Kazamaki

Download or read book Continuous Exponential Martingales and BMO written by Norihiko Kazamaki and published by Springer. This book was released on 2006-11-15 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: In three chapters on Exponential Martingales, BMO-martingales, and Exponential of BMO, this book explains in detail the beautiful properties of continuous exponential martingales that play an essential role in various questions concerning the absolute continuity of probability laws of stochastic processes. The second and principal aim is to provide a full report on the exciting results on BMO in the theory of exponential martingales. The reader is assumed to be familiar with the general theory of continuous martingales.