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Fractal Analysis Applications And Updates
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Book Synopsis Fractal Analysis by : Fernando Brambila
Download or read book Fractal Analysis written by Fernando Brambila and published by BoD – Books on Demand. This book was released on 2017-06-14 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fractal Analysis by : Clifford Brown
Download or read book Fractal Analysis written by Clifford Brown and published by SAGE Publications. This book was released on 2010-04-14 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fractal-Based Methods in Analysis by : Herb Kunze
Download or read book Fractal-Based Methods in Analysis written by Herb Kunze and published by Springer Science & Business Media. This book was released on 2011-11-18 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fractal Analysis - Applications and Updates by : Sid-Ali Ouadfeul
Download or read book Fractal Analysis - Applications and Updates written by Sid-Ali Ouadfeul and published by BoD – Books on Demand. This book was released on 2024-04-24 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes ten chapters that discuss applications and updates in fractal analysis across the full spectrum of sciences, including mathematical concepts, cities, material physics, medicine, climate, and image processing. It is a valuable source of knowledge for researchers and students working on fractal analysis and its applications.
Book Synopsis Frontiers of Fractal Analysis by : Santo Banerjee
Download or read book Frontiers of Fractal Analysis written by Santo Banerjee and published by CRC Press. This book was released on 2024-10-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fractal Analysis by : Fernando Brambila
Download or read book Fractal Analysis written by Fernando Brambila and published by BoD – Books on Demand. This book was released on 2017-07-26 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal analysis has entered a new era. The applications to different areas of knowledge have been surprising. Benoit Mandelbrot, creator of fractal geometry, would have been surprised by the use of fractal analysis presented in this book. Here we present the use of fractal geometry, in particular, fractal analysis in two sciences: health sciences and social sciences and humanities. Part 1 is Health Science. In it, we present the latest advances in cardiovascular signs, kidney images to determine cancer growth, EEG signals, magnetoencephalography signals, and photosensitive epilepsy. We show how it is possible to produce ultrasonic lenses or even sound focusing. In Part 2, we present the use of fractal analysis in social sciences and humanities. It includes anthropology, hierarchical scaling, human settlements, language, fractal dimension of different cultures, cultural traits, and Mesoamerican complexity. And in Part 3, we present a few useful tools for fractal analysis, such as graphs and correlation, self-affine and self-similar graphs, and correlation function. It is impossible to picture today's research without fractal geometry.
Book Synopsis Fractal Market Analysis by : Edgar E. Peters
Download or read book Fractal Market Analysis written by Edgar E. Peters and published by John Wiley & Sons. This book was released on 1994-02-08 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Fractals written by Dinesh Kumar and published by CRC Press. This book was released on 2017-02-03 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an insight into the advantages and limitations of the use of fractals in biomedical data. It begins with a brief introduction to the concept of fractals and other associated measures and describes applications for biomedical signals and images. Properties of biological data in relations to fractals and entropy, and the association with health and ageing are also covered. The book provides a detailed description of new techniques on physiological signals and images based on the fractal and chaos theory. The aim of this book is to serve as a comprehensive guide for researchers and readers interested in biomedical signal and image processing and feature extraction for disease risk analyses and rehabilitation applications. While it provides the mathematical rigor for those readers interested in such details, it also describes the topic intuitively such that it is suitable for audience who are interested in applying the methods to healthcare and clinical applications. The book is the outcome of years of research by the authors and is comprehensive and includes other reported outcomes.
Book Synopsis Fractal Geometries Theory and Applications by : Alain Le Mehaute
Download or read book Fractal Geometries Theory and Applications written by Alain Le Mehaute and published by CRC Press. This book was released on 1991-11-11 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal geometry, based on recursive mathematical schemas, provides a means for modeling a great number of natural phenomena. For this reason, it is of increasing interest to physicists, chemists, biologists, and geographers, among others. A major quality of fractality is that it not only unifies phenomena previously thought to be anomalous or disparate in a single theoretical framework, but it also promotes a return to graphical treatment, which had been almost completely banished from scientific thought in favor of analysis. This book casts a new, lively light on scientific territories still not fully explored. It is designed for research workers, engineers, and experimentalists faced with problems of measure and action in heterogenous materials and environments. Several color plates illustrate the implications and consequences of this theory for most of the questions raised by the taking into consideration of time in a fractal space.
Book Synopsis Fractal Dimension for Fractal Structures by : Manuel Fernández-Martínez
Download or read book Fractal Dimension for Fractal Structures written by Manuel Fernández-Martínez and published by Springer. This book was released on 2019-04-23 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a generalised approach to fractal dimension theory from the standpoint of asymmetric topology by employing the concept of a fractal structure. The fractal dimension is the main invariant of a fractal set, and provides useful information regarding the irregularities it presents when examined at a suitable level of detail. New theoretical models for calculating the fractal dimension of any subset with respect to a fractal structure are posed to generalise both the Hausdorff and box-counting dimensions. Some specific results for self-similar sets are also proved. Unlike classical fractal dimensions, these new models can be used with empirical applications of fractal dimension including non-Euclidean contexts. In addition, the book applies these fractal dimensions to explore long-memory in financial markets. In particular, novel results linking both fractal dimension and the Hurst exponent are provided. As such, the book provides a number of algorithms for properly calculating the self-similarity exponent of a wide range of processes, including (fractional) Brownian motion and Lévy stable processes. The algorithms also make it possible to analyse long-memory in real stocks and international indexes. This book is addressed to those researchers interested in fractal geometry, self-similarity patterns, and computational applications involving fractal dimension and Hurst exponent.
Book Synopsis The Fractal Geometry of the Brain by : Antonio Di Ieva
Download or read book The Fractal Geometry of the Brain written by Antonio Di Ieva and published by Springer. This book was released on 2016-08-03 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Harmonic Analysis And Fractal Analysis Over Local Fields And Applications by : Weiyi Su
Download or read book Harmonic Analysis And Fractal Analysis Over Local Fields And Applications written by Weiyi Su and published by World Scientific. This book was released on 2017-08-17 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Measure, Topology, and Fractal Geometry by : Gerald A. Edgar
Download or read book Measure, Topology, and Fractal Geometry written by Gerald A. Edgar and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Fractal Analysis for Natural Hazards by : Giuseppe Cello
Download or read book Fractal Analysis for Natural Hazards written by Giuseppe Cello and published by Geological Society of London. This book was released on 2006 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Fractal Dimension of Architecture by : Michael J. Ostwald
Download or read book The Fractal Dimension of Architecture written by Michael J. Ostwald and published by Birkhäuser. This book was released on 2016-09-01 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fractals: A Very Short Introduction by : Kenneth Falconer
Download or read book Fractals: A Very Short Introduction written by Kenneth Falconer and published by OUP Oxford. This book was released on 2013-09-26 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fractals in Biology and Medicine by : Gabriele A. Losa
Download or read book Fractals in Biology and Medicine written by Gabriele A. Losa and published by Springer Science & Business Media. This book was released on 1994 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: In March 2000 leading scientists gathered at the Centro Seminariale Monte Verità, Ascona, Switzerland, for the Third International Symposium on "Fractals 2000 in Biology and Medicine". This interdisciplinary conference provided stimulating contributions from the very topical field Fractals in Biology and Medicine. This volume highlights the growing power and efficacy of the fractal geometry in understanding how to analyze living phenomena and complex shapes.
