Fractured Fractals And Broken Dreams

Author : Guy David
Publisher : Unknown
Page : 0 pages
File Size : 45,8 Mb
Release : 1997
Category : Fractals
ISBN : 1383020124

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Fractured Fractals and Broken Dreams by Guy David Pdf

Author : Guy David,Stephen Semmes
Publisher : Oxford University Press
Page : 226 pages
File Size : 55,9 Mb
Release : 1997
Category : Mathematics
ISBN : 0198501668

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Fractured Fractals and Broken Dreams by Guy David,Stephen Semmes Pdf

This book proposes new notions of coherent geometric structure. Fractal patterns have emerged in many contexts, but what exactly is a "pattern" and what is not? How can one make precise the structures lying within objects and the relationships between them? The foundations laid herein provide a fresh approach to a familiar field. From this emerges a wide range of open problems, large and small, and a variety of examples with diverse connections to other parts of mathematics. One of the main features of the present text is that the basic framework is completely new. This makes it easier for people to get into the field. There are many open problems, with plenty of opportunities that are likely to be close at hand, particularly as concerns the exploration of examples. On the other hand the general framework is quite broad and provides the possibility for future discoveries of some magnitude. Fractual geometries can arise in many different ways mathematically, but there is not so much general language for making comparisons. This book provides some tools for doing this, and a place where researchers in different areas can find common ground and basic information.

Author : Michael Frame,Amelia Urry
Publisher : Yale University Press
Page : 536 pages
File Size : 52,9 Mb
Release : 2016-01-01
Category : Mathematics
ISBN : 9780300197877

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Fractal Worlds by Michael Frame,Amelia Urry Pdf

In this essential primer, mathematician Michael Frame, a close collaborator with Benoit Mandelbrot, the founder of fractal geometry, and poet Amelia Urry explore the amazing world of fractals as they appear in nature, art, medicine, and technology

Author : Kenneth Falconer
Publisher : John Wiley & Sons
Page : 404 pages
File Size : 48,7 Mb
Release : 2014-02-03
Category : Mathematics
ISBN : 9781119942399

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Fractal Geometry by Kenneth Falconer Pdf

The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. The book introduces and develops the general theory and applications of fractals in a way that is accessible to students and researchers from a wide range of disciplines. Fractal Geometry: Mathematical Foundations and Applications is an excellent course book for undergraduate and graduate students studying fractal geometry, with suggestions for material appropriate for a first course indicated. The book also provides an invaluable foundation and reference for researchers who encounter fractals not only in mathematics but also in other areas across physics, engineering and the applied sciences. Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals Carefully explains each topic using illustrative examples and diagrams Includes the necessary mathematical background material, along with notes and references to enable the reader to pursue individual topics Features a wide range of exercises, enabling readers to consolidate their understanding Supported by a website with solutions to exercises and additional material www.wileyeurope.com/fractal Leads onto the more advanced sequel Techniques in Fractal Geometry (also by Kenneth Falconer and available from Wiley)

Author : Carlo Cattani,Anouar Ben Mabrouk,Sabrine Arfaoui
Publisher : World Scientific
Page : 244 pages
File Size : 42,6 Mb
Release : 2022-02-24
Category : Mathematics
ISBN : 9789811239458

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Fractal Analysis: Basic Concepts And Applications by Carlo Cattani,Anouar Ben Mabrouk,Sabrine Arfaoui Pdf

The aim of this book is to provide a basic and self-contained introduction to the ideas underpinning fractal analysis. The book illustrates some important applications issued from real data sets, real physical and natural phenomena as well as real applications in different fields, and consequently, presents to the readers the opportunity to implement fractal analysis in their specialties according to the step-by-step guide found in the book.Besides advanced undergraduate students, graduate students and senior researchers, this book may also serve scientists and research workers from industrial settings, where fractals and multifractals are required for modeling real-world phenomena and data, such as finance, medicine, engineering, transport, images, signals, among others.For the theorists, rigorous mathematical developments are established with necessary prerequisites that make the book self-containing. For the practitioner often interested in model building and analysis, we provide the cornerstone ideas.

Author : Michel L. Lapidus,Goran Radunović,Darko Žubrinić
Publisher : Springer
Page : 685 pages
File Size : 54,9 Mb
Release : 2017-06-07
Category : Mathematics
ISBN : 9783319447063

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Fractal Zeta Functions and Fractal Drums by Michel L. Lapidus,Goran Radunović,Darko Žubrinić Pdf

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. It provides a significant extension of the existing theory of zeta functions for fractal strings to fractal sets and arbitrary bounded sets in Euclidean spaces of any dimension. Two new classes of fractal zeta functions are introduced, namely, the distance and tube zeta functions of bounded sets, and their key properties are investigated. The theory is developed step-by-step at a slow pace, and every step is well motivated by numerous examples, historical remarks and comments, relating the objects under investigation to other concepts. Special emphasis is placed on the study of complex dimensions of bounded sets and their connections with the notions of Minkowski content and Minkowski measurability, as well as on fractal tube formulas. It is shown for the first time that essential singularities of fractal zeta functions can naturally emerge for various classes of fractal sets and have a significant geometric effect. The theory developed in this book leads naturally to a new definition of fractality, expressed in terms of the existence of underlying geometric oscillations or, equivalently, in terms of the existence of nonreal complex dimensions. The connections to previous extensive work of the first author and his collaborators on geometric zeta functions of fractal strings are clearly explained. Many concepts are discussed for the first time, making the book a rich source of new thoughts and ideas to be developed further. The book contains a large number of open problems and describes many possible directions for further research. The beginning chapters may be used as a part of a course on fractal geometry. The primary readership is aimed at graduate students and researchers working in Fractal Geometry and other related fields, such as Complex Analysis, Dynamical Systems, Geometric Measure Theory, Harmonic Analysis, Mathematical Physics, Analytic Number Theory and the Spectral Theory of Elliptic Differential Operators. The book should be accessible to nonexperts and newcomers to the field.

Author : David Carfi,Michel Laurent Lapidus,Erin P. J. Pearse,Machiel Van Frankenhuysen
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 53,7 Mb
Release : 2013-10-22
Category : Mathematics
ISBN : 9780821891476

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Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics: Fractals in pure mathematics by David Carfi,Michel Laurent Lapidus,Erin P. J. Pearse,Machiel Van Frankenhuysen Pdf

This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoit Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry (and some aspects of dynamical systems) in pure mathematics. Also included are articles discussing a variety of connections of fractal geometry with other fields of mathematics, including probability theory, number theory, geometric measure theory, partial differential equations, global analysis on non-smooth spaces, harmonic analysis and spectral geometry. The companion volume (Contemporary Mathematics, Volume 601) focuses on applications of fractal geometry and dynamical systems to other sciences, including physics, engineering, computer science, economics, and finance.

Author : Stephen Semmes
Publisher : Oxford University Press
Page : 180 pages
File Size : 49,6 Mb
Release : 2001
Category : Mathematics
ISBN : 0198508069

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Some Novel Types of Fractal Geometry by Stephen Semmes Pdf

This book deals with fractal geometries that have features similar to ones of ordinary Euclidean spaces, while at the same time being quite different from Euclidean spaces.. A basic example of this feature considered is the presence of Sobolev or Poincaré inequalities, concerning the relationship between the average behavior of a function and the average behavior of its small-scale oscillations. Remarkable results in the last few years through Bourdon-Pajot and Laakso have shown that there is much more in the way of geometries like this than have been realized, only examples related to nilpotent Lie groups and Carnot metrics were known previously. On the other had, 'typical' fractals that might be seen in pictures do not have these same kinds of features. This text examines these topics in detail and will interest graduate students as well as researchers in mathematics and various aspects of geometry and analysis.

Author : Paolo Ciatti
Publisher : World Scientific
Page : 460 pages
File Size : 52,9 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812811059

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Topics in Mathematical Analysis by Paolo Ciatti Pdf

"This volume consists of a series of lecture notes on mathematical analysis. The contributors have been selected on the basis of both their outstanding scientific level and their clarity of exposition. Thus, the present collection is particularly suited to young researchers and graduate students. Through this volume, the editors intend to provide the reader with material otherwise difficult to find and written in a manner which is also accessible to nonexperts."--BOOK JACKET.

Author : Anonim
Publisher : ScholarlyEditions
Page : 1182 pages
File Size : 54,5 Mb
Release : 2013-05-01
Category : Mathematics
ISBN : 9781490109541

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Issues in General and Specialized Mathematics Research: 2013 Edition by Anonim Pdf

Issues in General and Specialized Mathematics Research: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about General Mathematics. The editors have built Issues in General and Specialized Mathematics Research: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General Mathematics in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General and Specialized Mathematics Research: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Author : Siegfried Graf,Harald Luschgy
Publisher : Springer
Page : 238 pages
File Size : 41,7 Mb
Release : 2007-05-06
Category : Mathematics
ISBN : 9783540455776

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Foundations of Quantization for Probability Distributions by Siegfried Graf,Harald Luschgy Pdf

Due to the rapidly increasing need for methods of data compression, quantization has become a flourishing field in signal and image processing and information theory. The same techniques are also used in statistics (cluster analysis), pattern recognition, and operations research (optimal location of service centers). The book gives the first mathematically rigorous account of the fundamental theory underlying these applications. The emphasis is on the asymptotics of quantization errors for absolutely continuous and special classes of singular probabilities (surface measures, self-similar measures) presenting some new results for the first time. Written for researchers and graduate students in probability theory the monograph is of potential interest to all people working in the disciplines mentioned above.

Author : Marcel Berger
Publisher : Springer Science & Business Media
Page : 840 pages
File Size : 50,6 Mb
Release : 2010-07-23
Category : Mathematics
ISBN : 9783540709978

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Geometry Revealed by Marcel Berger Pdf

Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces, convex sets, etc., crucial ideas and above all abstract concepts needed for attaining the results are elucidated. These are conceptual notions, each built "above" the preceding and permitting an increase in abstraction, represented metaphorically by Jacob's ladder with its rungs: the 'ladder' in the Old Testament, that angels ascended and descended... In all this, the aim of the book is to demonstrate to readers the unceasingly renewed spirit of geometry and that even so-called "elementary" geometry is very much alive and at the very heart of the work of numerous contemporary mathematicians. It is also shown that there are innumerable paths yet to be explored and concepts to be created. The book is visually rich and inviting, so that readers may open it at random places and find much pleasure throughout according their own intuitions and inclinations. Marcel Berger is t he author of numerous successful books on geometry, this book once again is addressed to all students and teachers of mathematics with an affinity for geometry.

Author : John M. Mackay,Jeremy T. Tyson
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 44,7 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821852293

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Conformal Dimension by John M. Mackay,Jeremy T. Tyson Pdf

Conformal dimension measures the extent to which the Hausdorff dimension of a metric space can be lowered by quasisymmetric deformations. Introduced by Pansu in 1989, this concept has proved extremely fruitful in a diverse range of areas, including geometric function theory, conformal dynamics, and geometric group theory. This survey leads the reader from the definitions and basic theory through to active research applications in geometric function theory, Gromov hyperbolic geometry, and the dynamics of rational maps, amongst other areas. It reviews the theory of dimension in metric spaces and of deformations of metric spaces. It summarizes the basic tools for estimating conformal dimension and illustrates their application to concrete problems of independent interest. Numerous examples and proofs are provided. Working from basic definitions through to current research areas, this book can be used as a guide for graduate students interested in this field, or as a helpful survey for experts. Background needed for a potential reader of the book consists of a working knowledge of real and complex analysis on the level of first- and second-year graduate courses.

Author : Guy David,Stephen Semmes
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 55,7 Mb
Release : 2000
Category : Fourier analysis
ISBN : 9780821820483

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Uniform Rectifiability and Quasiminimizing Sets of Arbitrary Codimension by Guy David,Stephen Semmes Pdf

This book is intended for graduate students and research mathematicians interested in calculus of variations and optimal control; optimization.

Author : Alessandra Carbone,Stephen Semmes
Publisher : Oxford Mathematical Monographs
Page : 524 pages
File Size : 54,7 Mb
Release : 2000
Category : Computers
ISBN : 0198507291

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A Graphic Apology for Symmetry and Implicitness by Alessandra Carbone,Stephen Semmes Pdf

This book brings into focus the contrast between explicit and implicit algorithmic descriptions of objects and presents a new geometric language for the study of combinatorial and logical problems in complexity theory. These themes are considered in a variety of settings, sometimes crossing traditional boundaries. Special emphasis is given to moderate complexity - exponential or polynomial - but objects with multi-exponential complexity also fit in. Among the items under consideration are graphs, formal proofs, languages, automata, groups, circuits, some connections with geometry of metric spaces, and complexity classes (P, NP, co-NP).