Fractal Analysis Basic Concepts And Applications

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Fractal Analysis Basic Concepts And Applications

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Author : Carlo Cattani
language : en
Publisher: World Scientific
Release Date : 2022-02-24

Fractal Analysis Basic Concepts And Applications written by Carlo Cattani and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-24 with Mathematics categories.

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.

Fractal Analysis

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Author : Carlo Cattani
language : en
Publisher: Advances in Mathematics for Ap
Release Date : 2022

Fractal Analysis written by Carlo Cattani and has been published by Advances in Mathematics for Ap this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Mathematics categories.

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.

Frontiers Of Fractal Analysis

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Author : Santo Banerjee
language : en
Publisher: CRC Press
Release Date : 2024-10-08

Frontiers Of Fractal Analysis written by Santo Banerjee and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-08 with Mathematics categories.

The history of describing natural objects using geometry is as old as the advent of science itself, in which traditional shapes are the basis of our intuitive understanding of 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. Although the concepts of fractal geometry have found wide applications in many forefront areas of science, engineering and societal issues, they also have interesting implications of a more practical nature for the older classical areas of science. Since its discovery, there has been a surge of research activities in using this powerful concept in almost every branch of scientific disciplines to gain deep insights into many unresolved problems. This book includes eight chapters which focus on gathering cutting-edge research and proposing application of fractals features in both traditional scientific disciplines and in applied fields.

Harmonic Analysis And Fractal Analysis Over Local Fields And Applications

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Author : Weiyi Su
language : en
Publisher: World Scientific
Release Date : 2017-08-17

Harmonic Analysis And Fractal Analysis Over Local Fields And Applications written by Weiyi Su and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-17 with Mathematics categories.

This book is a monograph on harmonic analysis and fractal analysis over local fields. It can also be used as lecture notes/textbook or as recommended reading for courses on modern harmonic and fractal analysis. It is as reliable as Fourier Analysis on Local Fields published in 1975 which is regarded as the first monograph in this research field.The book is self-contained, with wide scope and deep knowledge, taking modern mathematics (such as modern algebra, point set topology, functional analysis, distribution theory, and so on) as bases. Specially, fractal analysis is studied in the viewpoint of local fields, and fractal calculus is established by pseudo-differential operators over local fields. A frame of fractal PDE is constructed based on fractal calculus instead of classical calculus. On the other hand, the author does his best to make those difficult concepts accessible to readers, illustrate clear comparison between harmonic analysis on Euclidean spaces and that on local fields, and at the same time provide motivations underlying the new concepts and techniques. Overall, it is a high quality, up to date and valuable book for interested readers.

Fractals In Science

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Author : Armin Bunde
language : en
Publisher: Springer
Release Date : 2013-12-21

Fractals In Science written by Armin Bunde and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-21 with Science categories.

Applying fractal geometry to science is bringing about a breakthrough in our understanding of complex systems in nature that show self-similar or self-affine features. Self-similar and self-affine processes appear everywhere in nature, in galaxies and landscapes, in earthquakes and geological cracks, in aggregates and colloids, in rough surfaces and interfaces, in glassy materials and polymers, in proteins as well as in other large molecules. Fractal structures appear also in the human body; well known examples include the lung and the vascular system. Furthermore, fractal geometry is an important tool in the analysis of phenomena as diverse as rhythms in music melodies and in the human heart beat and DNA sequences. Since the pioneering work of B.B. Mandelbrot, this interdisciplinary field has expanded very rapidly. The scientific community applying fractal concepts is very broad and ranges from astronomers, geoscientists, physicists, chemists and engineers to biologists and those engaging in medical research.

Fractal Market Analysis

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Author : Edgar E. Peters
language : en
Publisher: John Wiley & Sons
Release Date : 1994-02-08

Fractal Market Analysis written by Edgar E. Peters 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 1994-02-08 with Business & Economics categories.

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

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Author : Clifford Brown
language : en
Publisher: SAGE
Release Date : 2010-04-14

Fractal Analysis written by Clifford Brown and has been published by SAGE 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. Key Features Detailed examples help readers learn and understand the analytical methods presented. Matlab codes for programs allow users to implement, on their own, some of the techniques described in the text. Visit http://www.ccs.fau.edu/~liebovitch/larry.html for more details. Clear and logical explanations of fractals and their analysis enable the instructor to easily teach and the student to easily learn the material. This is the only book designed to introduce fractal analysis to a general social science audience. Learn more about “The Little Green Book” - QASS Series! Click Here

Wavelet Analysis

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Author : Sabrine Arfaoui
language : en
Publisher:
Release Date : 2023-05-21

Wavelet Analysis written by Sabrine Arfaoui and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-21 with categories.

This book provides a basic and self-contained introduction to the ideas underpinning wavelet theory and its diverse applications. This book is suitable for master's or PhD students, senior researchers, or scientists working in industrial settings, where wavelets are used to model real world phenomena.

The Structural Stabilization Of Polymers Fractal Models

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Author : Kozlov
language : en
Publisher: CRC Press
Release Date : 2006-07-01

The Structural Stabilization Of Polymers Fractal Models written by Kozlov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-01 with Science categories.

This monograph deals with the structural aspects of transport processes of gases, physical ageing and thermo-oxidative degradation of polymers in detail. Fractal analysis, cluster models of the polymer structurea ‘s amorphous state as well as irreversible aggregation models are used as main structural models. It is shown that the polymer structure

Fractal Geometry In Human Geography And Planning

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Author : Cécile Tannier
language : en
Publisher: John Wiley & Sons
Release Date : 2024-08-27

Fractal Geometry In Human Geography And Planning written by Cécile Tannier 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 2024-08-27 with Social Science categories.

The aim of this book is to provide an overview of the concepts and methods used in fractal analysis and modeling in order to study the spatial distribution of human settlements. The main concepts and mathematical tools are reviewed, and emphasis is placed on the practical benefits of their application and the pitfalls to be avoided when using them. The first part of the book is devoted to the basic concepts and geometric reference figures required for fractal analysis in human geography. In the second part, the principles of four major families of analysis methods are explained in detail: fractal analyses of point sequences, fractal methods for morphological delineation of urban agglomerations, multifractal analyses and cross scale signatures. The third part of the book is devoted to applications of fractal geometry in urban and regional planning.