Frontiers Of Fractal Analysis
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Frontiers Of Fractal Analysis
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Author : Santo Banerjee
language : en
Publisher: CRC Press
Release Date : 2022
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 2022 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.
Fractal Frontiers Fractals In The Natural And Applied Sciences
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Author : Miroslav M Novak
language : en
Publisher: World Scientific
Release Date : 1997-03-29
Fractal Frontiers Fractals In The Natural And Applied Sciences written by Miroslav M Novak and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-03-29 with categories.
Historically, science has developed by reducing complex situations to simple ones, analyzing the components and synthesizing the original situation. While this 'reductionist' approach has been extremely successful, there are phenomena of such complexity that one cannot simplify them without eliminating the problem itself. Recently, attention has turned to such problems in a wide variety of fields. This is in part due to the development of fractal geometry. Fractal geometry provides the mathematical tools for handling complexity. The present volume is a collection of papers that deal with the application of fractals in both traditional scientific disciplines and in applied fields. This volume shows the advance of our understanding of complex phenomena across a spectrum of disciplines. While these diverse fields work on very different problems, fractals provide a unifying formalism for approaching these problems.
Fractal Analysis
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Author : Sid-Ali Ouadfeul
language : en
Publisher: BoD – Books on Demand
Release Date : 2019-04-03
Fractal Analysis written by Sid-Ali Ouadfeul and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-03 with Mathematics categories.
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.
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 Mathematics 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
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 : Fernando Brambila
language : en
Publisher: BoD – Books on Demand
Release Date : 2017-06-14
Fractal Analysis written by Fernando Brambila and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-14 with Mathematics categories.
Fractal analysis has entered a new era. The applications to different areas of knowledge have been surprising. Let us begin with the fractional calculus-fractal geometry relationship, which allows for modeling with extreme precision of phenomena such as diffusion in porous media with fractional partial differential equations in fractal objects. Where the order of the equation is the same as the fractal dimension, this allows us to make calculations with enormous precision in diffusion phenomena-particularly in the oil industry, for new spillage prevention. Main applications to industry, design of fractal antennas to receive all frequencies and that is used in all cell phones, spacecraft, radars, image processing, measure, porosity, turbulence, scattering theory. Benoit Mandelbrot, creator of fractal geometry, would have been surprised by the use of fractal analysis presented in this book: "Part I: Petroleum Industry and Numerical Analysis"; "Part II: Fractal Antennas, Spacecraft, Radars, Image Processing, and Measure"; and "Part III: Scattering Theory, Porosity, and Turbulence." It's impossible to picture today's research without fractal analysis.
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."
Musicality Of Human Brain Through Fractal Analytics
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Author : Dipak Ghosh
language : en
Publisher: Springer
Release Date : 2017-09-26
Musicality Of Human Brain Through Fractal Analytics written by Dipak Ghosh and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-26 with Technology & Engineering categories.
This book provides a comprehensive overview of how fractal analytics can lead to the extraction of interesting features from the complex electroencephalograph (EEG) signals generated by Hindustani classical music. It particularly focuses on how the brain responses to the emotional attributes of Hindustani classical music that have been long been a source of discussion for musicologists and psychologists. Using robust scientific techniques that are capable of looking into the most intricate dynamics of the complex EEG signals, it deciphers the human brain’s response to different ragas of Hindustani classical music, shedding new light on what happens inside the performer’s brain when they are mentally composing the imagery of a particular raga. It also explores the much- debated issue in the musical fraternity of whether there are any universal cues in music that make it identifiable for people throughout the world, and if so, what are the neural correlates associated with the universal cues? This book is of interest to researchers and scholars of music and the brain, nonlinear science, music cognition, music signal processing and music information retrieval. In addition, researchers in the field of nonlinear biomedical signal processing and music signal analysis benefit from this book.
Applied Analysis Optimization And Soft Computing
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Author : Tanmoy Som
language : en
Publisher: Springer Nature
Release Date : 2023-06-10
Applied Analysis Optimization And Soft Computing written by Tanmoy Som and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-10 with Mathematics categories.
This book contains select contributions presented at the International Conference on Nonlinear Applied Analysis and Optimization (ICNAAO-2021), held at the Department of Mathematics Sciences, Indian Institute of Technology (BHU) Varanasi, India, from 21–23 December 2021. The book discusses topics in the areas of nonlinear analysis, fixed point theory, dynamical systems, optimization, fractals, applications to differential/integral equations, signal and image processing, and soft computing, and exposes the young talents with the newer dimensions in these areas with their practical approaches and to tackle the real-life problems in engineering, medical and social sciences. Scientists from the U.S.A., Austria, France, Mexico, Romania, and India have contributed their research. All the submissions are peer reviewed by experts in their fields.
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.