Analysis On Fractals
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Analysis On Fractals
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Author : Jun Kigami
language : en
Publisher: Cambridge University Press
Release Date : 2001-06-07
Analysis On Fractals written by Jun Kigami and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-07 with Mathematics categories.
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
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Author : Herb Kunze
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-18
Fractal Based Methods In Analysis written by Herb Kunze 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 2011-11-18 with Mathematics categories.
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 inOntario. The major focus of their research is on fractals and the applications of fractals.
Fractals In Probability And Analysis
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Author : Christopher J. Bishop
language : en
Publisher: Cambridge University Press
Release Date : 2017
Fractals In Probability And Analysis written by Christopher J. Bishop and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.
A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.
Differential Equations On Fractals
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Author : Robert S. Strichartz
language : en
Publisher: Princeton University Press
Release Date : 2006-08-20
Differential Equations On Fractals written by Robert S. Strichartz and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-20 with Mathematics categories.
Measure, energy, and metric -- Laplacian -- Spectrum of the laplacian -- Postcritically finite fractals -- Further topics.
Analysis And Probability
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Author : Palle E. T. Jorgensen
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-17
Analysis And Probability written by Palle E. T. Jorgensen 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 2007-10-17 with Mathematics categories.
If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is. —John von Neumann While this is a course in analysis, our approach departs from the beaten path in some ways. Firstly, we emphasize a variety of connections to themes from neighboring fields, such as wavelets, fractals and signals; topics typically not included in a gradu ate analysis course. This in turn entails excursions into domains with a probabilistic flavor. Yet the diverse parts of the book follow a common underlying thread, and to gether they constitute a good blend; each part in the mix naturally complements the other. In fact, there are now good reasons for taking a wider view of analysis, for ex ample the fact that several applied trends have come to interact in new and exciting ways with traditional mathematical analysis—as it was taught in graduate classes for generations. One consequence of these impulses from "outside" is that conventional boundaries between core disciplines in mathematics have become more blurred. Fortunately this branching out does not mean that students will need to start out with any different or additional prerequisites. In fact, the ideas involved in this book are intuitive, natural, many of them visual, and geometric. The required background is quite minimal and it does not go beyond what is typically required in most graduate programs.
Measure Topology And Fractal Geometry
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Author : Gerald A Edgar
language : en
Publisher: Springer
Release Date : 1990
Measure Topology And Fractal Geometry written by Gerald A Edgar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
This book provides the mathematics necessary for the study of fractal geometry. It includes background material on metric topology and measure theory and also covers topological and fractal dimension, including the Hausdorff dimension. Furthermore, the book contains a complete discussion of self-similarity as well as the more general "graph self-similarity."
The Fractal Geometry Of The Brain
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Author : Antonio Di Ieva
language : en
Publisher: Springer
Release Date : 2016-08-03
The Fractal Geometry Of The Brain written by Antonio Di Ieva and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-03 with Medical categories.
Reviews the most intriguing applications of fractal analysis in neuroscience with a focus on current and future potential, limits, advantages, and disadvantages. Will bring an understanding of fractals to clinicians and researchers also if they do not have a mathematical background, and will serve as a good tool for teaching the translational applications of computational models to students and scholars of different disciplines. This comprehensive collection is organized in four parts: (1) Basics of fractal analysis; (2) Applications of fractals to the basic neurosciences; (3) Applications of fractals to the clinical neurosciences; (4) Analysis software, modeling and methodology.
Fractal Analysis
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Author : Clifford Brown
language : en
Publisher: SAGE Publications
Release Date : 2010-04-14
Fractal Analysis written by Clifford Brown and has been published by SAGE Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-14 with Social Science categories.
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.
The Fractal Dimension Of Architecture
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Author : Michael J. Ostwald
language : en
Publisher: Birkhäuser
Release Date : 2016-09-01
The Fractal Dimension Of Architecture written by Michael J. Ostwald and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-01 with Mathematics categories.
Fractal analysis is a method for measuring, analysing and comparing the formal or geometric properties of complex objects. In this book it is used to investigate eighty-five buildings that have been designed by some of the twentieth-century’s most respected and celebrated architects. Including designs by Le Corbusier, Eileen Gray, Frank Lloyd Wright, Robert Venturi, Frank Gehry, Peter Eisenman, Richard Meier and Kazuyo Sejima amongst others, this book uses mathematics to analyse arguments and theories about some of the world’s most famous designs. Starting with 625 reconstructed architectural plans and elevations, and including more than 200 specially prepared views of famous buildings, this book presents the results of the largest mathematical study ever undertaken into architectural design and the largest single application of fractal analysis presented in any field. The data derived from this study is used to test three overarching hypotheses about social, stylistic and personal trends in design, along with five celebrated arguments about twentieth-century architecture. Through this process the book offers a unique mathematical insight into the history and theory of design.
Fractal Functions Dimensions And Signal Analysis
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Author : Santo Banerjee
language : en
Publisher: Springer Nature
Release Date : 2020-12-14
Fractal Functions Dimensions And Signal Analysis written by Santo Banerjee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-14 with Science categories.
This book introduces the fractal interpolation functions (FIFs) in approximation theory to the readers and the concerned researchers in advanced level. FIFs can be used to precisely reconstruct the naturally occurring functions when compared with the classical interpolants. The book focuses on the construction of fractals in metric space through various iterated function systems. It begins by providing the Mathematical background behind the fractal interpolation functions with its graphical representations and then introduces the fractional integral and fractional derivative on fractal functions in various scenarios. Further, the existence of the fractal interpolation function with the countable iterated function system is demonstrated by taking suitable monotone and bounded sequences. It also covers the dimension of fractal functions and investigates the relationship between the fractal dimension and the fractional order of fractal interpolation functions. Moreover, this book explores the idea of fractal interpolation in the reconstruction scheme of illustrative waveforms and discusses the problems of identification of the characterizing parameters. In the application section, this research compendium addresses the signal processing and its Mathematical methodologies. A wavelet-based denoising method for the recovery of electroencephalogram (EEG) signals contaminated by nonstationary noises is presented, and the author investigates the recognition of healthy, epileptic EEG and cardiac ECG signals using multifractal measures. This book is intended for professionals in the field of Mathematics, Physics and Computer Science, helping them broaden their understanding of fractal functions and dimensions, while also providing the illustrative experimental applications for researchers in biomedicine and neuroscience.