Analysis On Fractals

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Analysis on Fractals

Jun Kigami
Analysis on Fractals Book PDF

Author : Jun Kigami
Publisher : Cambridge University Press
Page : 238 pages
File Size : 44,9 Mb
Release : 2001-06-07
Category : Mathematics
ISBN : 9780521793216

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Analysis on Fractals by Jun Kigami Pdf

This book covers analysis on fractals, a developing area of mathematics which focuses on the dynamical aspects of fractals, such as heat diffusion on fractals and the vibration of a material with fractal structure. The book provides a self-contained introduction to the subject, starting from the basic geometry of self-similar sets and going on to discuss recent results, including the properties of eigenvalues and eigenfunctions of the Laplacians, and the asymptotical behaviors of heat kernels on self-similar sets. Requiring only a basic knowledge of advanced analysis, general topology and measure theory, this book will be of value to graduate students and researchers in analysis and probability theory. It will also be useful as a supplementary text for graduate courses covering fractals.

Fractal-Based Methods in Analysis

Herb Kunze,Davide La Torre,Franklin Mendivil,Edward R. Vrscay
Fractal Based Methods in Analysis Book PDF

Author : Herb Kunze,Davide La Torre,Franklin Mendivil,Edward R. Vrscay
Publisher : Springer Science & Business Media
Page : 417 pages
File Size : 55,9 Mb
Release : 2011-11-18
Category : Mathematics
ISBN : 9781461418917

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Fractal-Based Methods in Analysis by Herb Kunze,Davide La Torre,Franklin Mendivil,Edward R. Vrscay Pdf

The idea of modeling the behaviour of phenomena at multiple scales has become a useful tool in both pure and applied mathematics. Fractal-based techniques lie at the heart of this area, as fractals are inherently multiscale objects; they very often describe nonlinear phenomena better than traditional mathematical models. In many cases they have been used for solving inverse problems arising in models described by systems of differential equations and dynamical systems. "Fractal-Based Methods in Analysis" draws together, for the first time in book form, methods and results from almost twenty years of research in this topic, including new viewpoints and results in many of the chapters. For each topic the theoretical framework is carefully explained using examples and applications. The second chapter on basic iterated function systems theory is designed to be used as the basis for a course and includes many exercises. This chapter, along with the three background appendices on topological and metric spaces, measure theory, and basic results from set-valued analysis, make the book suitable for self-study or as a source book for a graduate course. The other chapters illustrate many extensions and applications of fractal-based methods to different areas. This book is intended for graduate students and researchers in applied mathematics, engineering and social sciences. Herb Kunze is a professor of mathematics at the University of Guelph in Ontario. Davide La Torre is an associate professor of mathematics in the Department of Economics, Management and Quantitative Methods of the University of Milan. Franklin Mendivil is a professor of mathematics at Acadia University in Nova Scotia. Edward Vrscay is a professor in the department of Applied Mathematics at the University of Waterloo in Ontario. The major focus of their research is on fractals and the applications of fractals.

Fractals in Probability and Analysis

Christopher J. Bishop,Yuval Peres
Fractals in Probability and Analysis Book PDF

Author : Christopher J. Bishop,Yuval Peres
Publisher : Cambridge University Press
Page : 415 pages
File Size : 41,5 Mb
Release : 2017
Category : Mathematics
ISBN : 9781107134119

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Fractals in Probability and Analysis by Christopher J. Bishop,Yuval Peres Pdf

A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.

Measure, Topology, and Fractal Geometry

Gerald A. Edgar
Measure Topology and Fractal Geometry Book PDF

Author : Gerald A. Edgar
Publisher : Springer Science & Business Media
Page : 231 pages
File Size : 48,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475741346

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Measure, Topology, and Fractal Geometry by Gerald A. Edgar Pdf

From the reviews: "In the world of mathematics, the 1980's might well be described as the "decade of the fractal". Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. However, the book also contains many good illustrations of fractals (including 16 color plates), together with Logo programs which were used to generate them. ... Here then, at last, is an answer to the question on the lips of so many: 'What exactly is a fractal?' I do not expect many of this book's readers to achieve a mature understanding of this answer to the question, but anyone interested in finding out about the mathematics of fractal geometry could not choose a better place to start looking." #Mathematics Teaching#1

Fractal Market Analysis

Edgar E. Peters
Fractal Market Analysis Book PDF

Author : Edgar E. Peters
Publisher : John Wiley & Sons
Page : 352 pages
File Size : 52,5 Mb
Release : 1994-02-08
Category : Business & Economics
ISBN : 0471585246

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Fractal Market Analysis by Edgar E. Peters Pdf

A leading pioneer in the field offers practical applications of this innovative science. Peters describes complex concepts in an easy-to-follow manner for the non-mathematician. He uses fractals, rescaled range analysis and nonlinear dynamical models to explain behavior and understand price movements. These are specific tools employed by chaos scientists to map and measure physical and now, economic phenomena.

Fractal Analysis for Natural Hazards

Giuseppe Cello,Bruce D. Malamud
Fractal Analysis for Natural Hazards Book PDF

Author : Giuseppe Cello,Bruce D. Malamud
Publisher : Geological Society of London
Page : 190 pages
File Size : 41,8 Mb
Release : 2006
Category : Mathematics
ISBN : 1862392013

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Fractal Analysis for Natural Hazards by Giuseppe Cello,Bruce D. Malamud Pdf

In the Earth Sciences, the concept of fractals and scale invariance is well-recognized in many natural objects. However, the use of fractals for spatial and temporal analyses of natural hazards has been less used (and accepted) in the Earth Sciences. This book brings together twelve contributions that emphasize the role of fractal analyses in natural hazard research, including landslides, wildfires, floods, catastrophic rock fractures and earthquakes. A wide variety of spatial and temporal fractal-related approaches and techniques are applied to 'natural' data, experimental data, and computer simulations. These approaches include probabilistic hazard analysis, cellular-automata models, spatial analyses, temporal variability, prediction, and self-organizing behaviour. The main aims of this volume are to present current research on fractal analyses as applied to natural hazards, and to stimulate the curiosity of advanced Earth Science students and researchers in the use of fractals analyses for the better understanding of natural hazards.

Analysis and Probability

Palle E. T. Jorgensen
Analysis and Probability Book PDF

Author : Palle E. T. Jorgensen
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 44,6 Mb
Release : 2007-10-17
Category : Mathematics
ISBN : 9780387330822

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Analysis and Probability by Palle E. T. Jorgensen Pdf

Combines analysis and tools from probability, harmonic analysis, operator theory, and engineering (signal/image processing) Interdisciplinary focus with hands-on approach, generous motivation and new pedagogical techniques Numerous exercises reinforce fundamental concepts and hone computational skills Separate sections explain engineering terms to mathematicians and operator theory to engineers Fills a gap in the literature

Fractal Analysis

Clifford Brown,Larry Liebovitch
Fractal Analysis Book PDF

Author : Clifford Brown,Larry Liebovitch
Publisher : SAGE Publications
Page : 113 pages
File Size : 43,9 Mb
Release : 2010-04-14
Category : Social Science
ISBN : 9781483343129

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Fractal Analysis by Clifford Brown,Larry Liebovitch Pdf

A specialized presentation of fractal analysis oriented to the social sciences This primer uses straightforward language to give the reader step-by-step instructions for identifying and analyzing fractal patterns and the social process that create them. By making fractals accessible to the social science students, this book has a significant impact on the understanding of human behavior. This is the only book designed to introduce fractal analysis to a general social science audience.

Frontiers of Fractal Analysis

Santo Banerjee,Arulprakash Gowrisankar
Frontiers of Fractal Analysis Book PDF

Author : Santo Banerjee,Arulprakash Gowrisankar
Publisher : Unknown
Page : 128 pages
File Size : 42,8 Mb
Release : 2022
Category : Fractal analysis
ISBN : 1032138734

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Frontiers of Fractal Analysis by Santo Banerjee,Arulprakash Gowrisankar Pdf

"The best accomplishment in human research is feasibly they understand the natural phenomena can be exhibited by mathematical models. The history of describing natural objects using geometry is as old as the advent of science itself. Traditionally lines, squares, rectangles, circles, spheres, etc. have been the basis of our intuitive understanding of the geometry. However, nature is not restricted to such Euclidean objects which are only characterized typically by integer dimensions. Hence, the conventional geometric approach cannot meet the requirements of solving or analysing nonlinear problems which are related with natural phenomena, therefore, the fractal theory has been born, which aims to understand complexity and provide an innovative way to recognize irregularity and complex systems"--

Differential Equations on Fractals

Robert S. Strichartz
Differential Equations on Fractals Book PDF

Author : Robert S. Strichartz
Publisher : Princeton University Press
Page : 196 pages
File Size : 46,7 Mb
Release : 2006-08-20
Category : Mathematics
ISBN : 069112731X

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Differential Equations on Fractals by Robert S. Strichartz Pdf

Measure, energy, and metric -- Laplacian -- Spectrum of the laplacian -- Postcritically finite fractals -- Further topics.

Fractals and Hyperspaces

Keith R. Wicks
Fractals and Hyperspaces Book PDF

Author : Keith R. Wicks
Publisher : Springer
Page : 175 pages
File Size : 55,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540466109

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Fractals and Hyperspaces by Keith R. Wicks Pdf

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.

A Tale of Two Fractals

A.A. Kirillov
A Tale of Two Fractals Book PDF

Author : A.A. Kirillov
Publisher : Springer Science & Business Media
Page : 148 pages
File Size : 55,9 Mb
Release : 2013-04-23
Category : Mathematics
ISBN : 9780817683825

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A Tale of Two Fractals by A.A. Kirillov Pdf

Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals is intended to help bridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The work is designed to give young, non-specialist mathematicians a solid foundation in the theory of fractals, and, in the process, to equip them with exposure to a variety of geometric, analytical, and algebraic tools with applications across other areas.

Fractals in Music

Charles B. Madden
Fractals in Music Book PDF

Author : Charles B. Madden
Publisher : High Art Press
Page : 228 pages
File Size : 53,8 Mb
Release : 1999
Category : Mathematics
ISBN : 0967172756

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Fractals in Music by Charles B. Madden Pdf

Fractals in Music is intended for advanced students of music theory, whether individuals, composers, students, or teachers. It is intelligible to anyone having some knowledge of algebra and trigonometry. The many illustrations clarify such concepts as self-similarity and transforms. Book jacket.

Fractals: A Very Short Introduction

Kenneth Falconer
Fractals A Very Short Introduction Book PDF

Author : Kenneth Falconer
Publisher : OUP Oxford
Page : 144 pages
File Size : 54,8 Mb
Release : 2013-09-26
Category : Mathematics
ISBN : 9780191663444

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Fractals: A Very Short Introduction by Kenneth Falconer Pdf

Many are familiar with the beauty and ubiquity of fractal forms within nature. Unlike the study of smooth forms such as spheres, fractal geometry describes more familiar shapes and patterns, such as the complex contours of coastlines, the outlines of clouds, and the branching of trees. In this Very Short Introduction, Kenneth Falconer looks at the roots of the 'fractal revolution' that occurred in mathematics in the 20th century, presents the 'new geometry' of fractals, explains the basic concepts, and explores the wide range of applications in science, and in aspects of economics. This is essential introductory reading for students of mathematics and science, and those interested in popular science and mathematics. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Fractal Analysis

Sid-Ali Ouadfeul
Fractal Analysis Book PDF

Author : Sid-Ali Ouadfeul
Publisher : BoD – Books on Demand
Page : 114 pages
File Size : 50,7 Mb
Release : 2019-04-03
Category : Mathematics
ISBN : 9781789854336

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Fractal Analysis by Sid-Ali Ouadfeul Pdf

The aim of this book is to show some applications of fractal analysis in the fields of sciences. The first chapter introduces the readers to the book, while the second chapter shows the methods and challenges of fractal analysis of time-series data sets. The third chapter demonstrates fractal geometry as an attractive choice for miniaturized planar microwave filter design. The fourth chapter presents fractal antennas for wearable applications. The objective of the fifth chapter is to show some Parrondian games in discrete dynamic systems, while the last chapter reveals fractal structures of carbon nanotube system arrays.