Fractal Analysis

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Fractal Analysis

Clifford Brown,Larry Liebovitch
Fractal Analysis Book PDF

Author : Clifford Brown,Larry Liebovitch
Publisher : SAGE Publications
Page : 113 pages
File Size : 46,5 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.

Fractal Market Analysis

Edgar E. Peters
Fractal Market Analysis Book PDF

Author : Edgar E. Peters
Publisher : John Wiley & Sons
Page : 352 pages
File Size : 43,8 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.

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 : 55,6 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"--

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 : 44,8 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.

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 : 54,9 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.

Fractal Analysis of the Binding and Dissociation Kinetics for Different Analytes on Biosensor Surfaces

Ajit Sadana,Neeti Sadana
Fractal Analysis of the Binding and Dissociation Kinetics for Different Analytes on Biosensor Surfaces Book PDF

Author : Ajit Sadana,Neeti Sadana
Publisher : Elsevier
Page : 372 pages
File Size : 42,5 Mb
Release : 2007-12-20
Category : Science
ISBN : 0080555012

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Fractal Analysis of the Binding and Dissociation Kinetics for Different Analytes on Biosensor Surfaces by Ajit Sadana,Neeti Sadana Pdf

Biosensors are finding increasing applications in different areas. Over the last few years the areas where biosensors may be used effectively has increased dramatically. This book like the previous four books on analyte-receptor binding and dissociation kinetics by this author addresses the often neglected area. The kinetics of binding and dissociation in solution to appropriate receptors immobilized on biosensor surfaces occurs under diffusional limitations on structured surfaces. The receptors immobilized on the biosensor surface contribute to the degree of heterogeneity on the sensor chip surface. The fractal analysis examples presented throughout the book provide a convenient means to make quantitative the degree of heterogeneity present on the sensor surface, and relates it to the binding and dissociation rate coefficients. The fractal dimension is a quantitative measure of the degree of heterogeneity present on the biosensor surface. The book emphasizes medially-oriented examples. The detection of disease-related analytes is also emphasized. The intent being that if intractable and insidious diseases are detected earlier, they will be controlled better, eventually leading to a better prognosis. Chapter 3 is a new chapter that emphasizes enhancing the relevant biosensor performance parameters such as sensitivity, stability, selectivity, response time, etc. As usual, as done in previous books by this author, the last chapter provides an update of the economics involved in biosensors, and the difficulties encounters in starting-up a biosensor company. - Modelling of binding and dissociation kinetics of analyte-receptor reactions on biosensor surfaces: provides physical insights into these reactions occurring on biosensor surfaces. Very few researchers even attempt to analyze the kinetics of these types of reactions. - Fractal analysis used to model the binding and dissociation kinetics: original and unique approach. - Economic analysis provided in the last chapter: helps balance the book; besides providing much-needed information not available in the open literature. - Emphasis on improving biosensor performance parameters: helps make biosensors better. - Empahsis on medically-related analytes: helps in prognosis of diseases.

Frontiers of Fractal Analysis

Santo Banerjee,A. Gowrisankar
Frontiers of Fractal Analysis Book PDF

Author : Santo Banerjee,A. Gowrisankar
Publisher : CRC Press
Page : 182 pages
File Size : 49,7 Mb
Release : 2022-07-07
Category : Mathematics
ISBN : 9781000625875

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Frontiers of Fractal Analysis by Santo Banerjee,A. Gowrisankar Pdf

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 Analysis

Sid-Ali Ouadfeul
Fractal Analysis Book PDF

Author : Sid-Ali Ouadfeul
Publisher : BoD – Books on Demand
Page : 114 pages
File Size : 49,6 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.

Fractal Analysis and Chaos in Geosciences

Sid-Ali Ouadfeul
Fractal Analysis and Chaos in Geosciences Book PDF

Author : Sid-Ali Ouadfeul
Publisher : BoD – Books on Demand
Page : 186 pages
File Size : 48,5 Mb
Release : 2012-11-14
Category : Mathematics
ISBN : 9789535107293

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Fractal Analysis and Chaos in Geosciences by Sid-Ali Ouadfeul Pdf

The fractal analysis is becoming a very useful tool to process obtained data from chaotic systems in geosciences. It can be used to resolve many ambiguities in this domain. This book contains eight chapters showing the recent applications of the fractal/mutifractal analysis in geosciences. Two chapters are devoted to applications of the fractal analysis in climatology, two of them to data of cosmic and solar geomagnetic data from observatories. Four chapters of the book contain some applications of the (multi-) fractal analysis in exploration geophysics. I believe that the current book is an important source for researchers and students from universities.

Fractal Analysis: Basic Concepts And Applications

Carlo Cattani,Anouar Ben Mabrouk,Sabrine Arfaoui
Fractal Analysis Basic Concepts And Applications Book PDF

Author : Carlo Cattani,Anouar Ben Mabrouk,Sabrine Arfaoui
Publisher : World Scientific
Page : 244 pages
File Size : 43,6 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.

Mathematical Principle and Fractal Analysis of Mesoscale Eddy

Shu-Tang Liu,Yu-Pin Wang,Zhi-Min Bi,Yin Wang
Mathematical Principle and Fractal Analysis of Mesoscale Eddy Book PDF

Author : Shu-Tang Liu,Yu-Pin Wang,Zhi-Min Bi,Yin Wang
Publisher : Springer Nature
Page : 258 pages
File Size : 44,8 Mb
Release : 2021-06-29
Category : Technology & Engineering
ISBN : 9789811618390

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Mathematical Principle and Fractal Analysis of Mesoscale Eddy by Shu-Tang Liu,Yu-Pin Wang,Zhi-Min Bi,Yin Wang Pdf

This book focuses on universal nonlinear dynamics model of mesoscale eddies. The results of this book are not only the direct-type applications of pure mathematical limit cycle theory and fractal theory in practice but also the classic combination of nonlinear dynamic systems in mathematics and the physical oceanography. The universal model and experimental verification not only verify the relevant results that are obtained by Euler's form but also, more importantly, are consistent with observational numerical statistics. Due to the universality of the model, the consequences of the system are richer and more complete. The comprehensive and systematic mathematical modeling of mesoscale eddies is one of the major features of the book, which is particularly suited for readers who are interested to learn fractal analysis and prediction in physical oceanography. The book benefits researchers, engineers, and graduate students in the fields of mesoscale eddies, fractal, chaos, and other applications, etc.

A Fractal Analysis of Chemical Kinetics with Applications to Biological and Biosensor Interfaces

Ajit Sadana,Neeti Sadana,Richa Sadana
A Fractal Analysis of Chemical Kinetics with Applications to Biological and Biosensor Interfaces Book PDF

Author : Ajit Sadana,Neeti Sadana,Richa Sadana
Publisher : Elsevier
Page : 337 pages
File Size : 54,7 Mb
Release : 2018-07-31
Category : Technology & Engineering
ISBN : 9780444638823

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A Fractal Analysis of Chemical Kinetics with Applications to Biological and Biosensor Interfaces by Ajit Sadana,Neeti Sadana,Richa Sadana Pdf

A Fractal Analysis of Chemical Kinetics with Applications to Biological and Biosensor Interfaces analyzes the kinetics of binding and dissociation of different analytes by different biosensor techniques, demonstrating and then comparing each. Emphasis is placed on newer instrumentation techniques, such as SPRi (surface plasmon resonance imaging), and classical techniques, such as SPR (surface plasmon resonance), and finally, DNA biosensors and nanobiosensors. In addition, a final capstone chapter includes biosensor economics. These topics are all covered in one comprehensive book in a way that cannot be found elsewhere. Analyzes the kinetics of binding on biosensor surfaces Presents and compares different biosensor techniques Provides insights into the binding and dissociation mechanisms of analytes on biosensor surfaces Links the heterogeneity of biosensor surfaces to dissociation rate coefficients

Fractal Analysis in Machining

Prasanta Sahoo,Tapan Barman,J. Paulo Davim
Fractal Analysis in Machining Book PDF

Author : Prasanta Sahoo,Tapan Barman,J. Paulo Davim
Publisher : Springer Science & Business Media
Page : 86 pages
File Size : 48,9 Mb
Release : 2011-08-21
Category : Technology & Engineering
ISBN : 9783642179228

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Fractal Analysis in Machining by Prasanta Sahoo,Tapan Barman,J. Paulo Davim Pdf

The concept of fractals is often considered to describe surface roughness. Fractals retain all the structural information and are characterized by a single descriptor, the fractal dimension, D. Fractal dimension is an intrinsic property of the surface and independent of the filter processing of measuring instrument as well as the sampling length scale. This book cover fractal analysis of surface roughness in different machining processes such as Computer Numeric Control (CNC) end milling, CNC turning, electrical discharge machining and cylindrical grinding. The content here presented adds a significant contribution to the existing literature, with interest to both industrial and academic public.

Fractal Analysis of Breast Masses in Mammograms

Thanh Cabral,Rangaraj Rangayyan
Fractal Analysis of Breast Masses in Mammograms Book PDF

Author : Thanh Cabral,Rangaraj Rangayyan
Publisher : Springer Nature
Page : 104 pages
File Size : 52,7 Mb
Release : 2022-06-01
Category : Technology & Engineering
ISBN : 9783031016547

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Fractal Analysis of Breast Masses in Mammograms by Thanh Cabral,Rangaraj Rangayyan Pdf

Fractal analysis is useful in digital image processing for the characterization of shape roughness and gray-scale texture or complexity. Breast masses present shape and gray-scale characteristics in mammograms that vary between benign masses and malignant tumors. This book demonstrates the use of fractal analysis to classify breast masses as benign masses or malignant tumors based on the irregularity exhibited in their contours and the gray-scale variability exhibited in their mammographic images. A few different approaches are described to estimate the fractal dimension (FD) of the contour of a mass, including the ruler method, box-counting method, and the power spectral analysis (PSA) method. Procedures are also described for the estimation of the FD of the gray-scale image of a mass using the blanket method and the PSA method. To facilitate comparative analysis of FD as a feature for pattern classification of breast masses, several other shape features and texture measures are described in the book. The shape features described include compactness, spiculation index, fractional concavity, and Fourier factor. The texture measures described are statistical measures derived from the gray-level cooccurrence matrix of the given image. Texture measures reveal properties about the spatial distribution of the gray levels in the given image; therefore, the performance of texture measures may be dependent on the resolution of the image. For this reason, an analysis of the effect of spatial resolution or pixel size on texture measures in the classification of breast masses is presented in the book. The results demonstrated in the book indicate that fractal analysis is more suitable for characterization of the shape than the gray-level variations of breast masses, with area under the receiver operating characteristics of up to 0.93 with a dataset of 111 mammographic images of masses. The methods and results presented in the book are useful for computer-aided diagnosis of breast cancer. Table of Contents: Computer-Aided Diagnosis of Breast Cancer / Detection and Analysis of\newline Breast Masses / Datasets of Images of Breast Masses / Methods for Fractal Analysis / Pattern Classification / Results of Classification of Breast Masses / Concluding Remarks

Harmonic Analysis And Fractal Analysis Over Local Fields And Applications

Su Weiyi
Harmonic Analysis And Fractal Analysis Over Local Fields And Applications Book PDF

Author : Su Weiyi
Publisher : World Scientific
Page : 332 pages
File Size : 51,6 Mb
Release : 2017-08-17
Category : Mathematics
ISBN : 9789813200524

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Harmonic Analysis And Fractal Analysis Over Local Fields And Applications by Su Weiyi Pdf

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.