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Fractal Functions Fractal Surfaces And Wavelets

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Fractal Functions Fractal Surfaces and Wavelets

Fractal Functions  Fractal Surfaces  and Wavelets Book
Author : Peter R. Massopust
Publisher : Academic Press
Release : 2016-09-02
ISBN : 0128044705
Language : En, Es, Fr & De

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Book Description :

Fractal Functions, Fractal Surfaces, and Wavelets, Second Edition, is the first systematic exposition of the theory of local iterated function systems, local fractal functions and fractal surfaces, and their connections to wavelets and wavelet sets. The book is based on Massopust’s work on and contributions to the theory of fractal interpolation, and the author uses a number of tools—including analysis, topology, algebra, and probability theory—to introduce readers to this exciting subject. Though much of the material presented in this book is relatively current (developed in the past decades by the author and his colleagues) and fairly specialized, an informative background is provided for those entering the field. With its coherent and comprehensive presentation of the theory of univariate and multivariate fractal interpolation, this book will appeal to mathematicians as well as to applied scientists in the fields of physics, engineering, biomathematics, and computer science. In this second edition, Massopust includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, further develops the connections to wavelets and wavelet sets, and deepens and extends the pedagogical content. Offers a comprehensive presentation of fractal functions and fractal surfaces Includes latest developments in fractal interpolation Connects fractal geometry with wavelet theory Includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, and further develops the connections to wavelets and wavelet sets Deepens and extends the pedagogical content

Interpolation and Approximation with Splines and Fractals

Interpolation and Approximation with Splines and Fractals Book
Author : Peter Robert Massopust
Publisher : Oxford University Press, USA
Release : 2010
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

This unique textbook emphasizes the communalities between splines and fractals in interpolation and approximation theory, with particular emphasis on fractal functions and fractal surfaces. It presents the classical theory of splines and their properties, and also gives an introduction to the burgeoning new theory of superfractals and superfractal functions.

Fractals Wavelets and their Applications

Fractals  Wavelets  and their Applications Book
Author : Christoph Bandt,Michael Barnsley,Robert Devaney,Kenneth J. Falconer,V. Kannan,Vinod Kumar P.B.
Publisher : Springer
Release : 2014-09-27
ISBN : 3319081055
Language : En, Es, Fr & De

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Book Description :

Fractals and wavelets are emerging areas of mathematics with many common factors which can be used to develop new technologies. This volume contains the selected contributions from the lectures and plenary and invited talks given at the International Workshop and Conference on Fractals and Wavelets held at Rajagiri School of Engineering and Technology, India from November 9-12, 2013. Written by experts, the contributions hope to inspire and motivate researchers working in this area. They provide more insight into the areas of fractals, self similarity, iterated function systems, wavelets and the applications of both fractals and wavelets. This volume will be useful for the beginners as well as experts in the fields of fractals and wavelets.

Fractal Functions Dimensions and Signal Analysis

Fractal Functions  Dimensions and Signal Analysis Book
Author : Santo Banerjee,D. Easwaramoorthy,A. Gowrisankar
Publisher : Springer Nature
Release : 2020-12-14
ISBN : 3030626725
Language : En, Es, Fr & De

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Book Description :

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.

Abstract and Applied Analysis

Abstract and Applied Analysis Book
Author : N. M. Chuong,L. Nirenberg
Publisher : World Scientific
Release : 2004
ISBN : 9812702547
Language : En, Es, Fr & De

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Book Description :

This volume takes up various topics in Mathematical Analysis including boundary and initial value problems for Partial Differential Equations and Functional Analytic methods. Topics include linear elliptic systems for composite material OCo the coefficients may jump from domain to domain; Stochastic Analysis OCo many applied problems involve evolution equations with random terms, leading to the use of stochastic analysis. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences. Contents: Deterministic Analysis: Differentiation of Hypergeometric Functions with Respect to Parameters (Yu A Brychkov & K O Geddes); On the Lagrange Problem About the Strongest Columns (Yu V Egorov); Wavelet Based Fast Solution of Boundary Integral Equations (H Harbrecht & R Schneider); Semi-Classical Methods in GinzburgOCoLandau Theory (B Helffer); Stability of Equilibriums in One-Dimensional Motion of Compressible Viscous Gas Forced by Self-Gravity (Y Iwata & Y Yamamoto); Estimates for Elliptic Systems for Composite Material (L Nirenberg); On Asymptotics for the Mabuchi Energy Functional (D H Phong & J Sturm); Regularity of Solutions of the Initial Boundary Value Problem for Linearized Equations of Ideal Magneto-Hydrodynamics (M Yamamoto); Stochastic Analysis: Impulsive Stochastic Evolution Inclusions with Multi-Valued Diffusion (N U Ahmed); Some of Future Directions of White Noise Analysis (T Hida); Constructing Random Probability Distributions (T P Hill & D E R Sitton); Multiparameter Additive Processes of Mixture Type (K Inoue); The Random Integral Representation Hypothesis Revisited: New Classes of S-Selfdecomposable Laws (Z J Jurek); Semigroups and Processes with Parameter in a Cone (J Pedersen & K-I Sato); and other papers. Readership: Researchers and academics in the fields of analysis and differential equations, approximation theory, probability and statistics."

Abstract and Applied Analysis

Abstract and Applied Analysis Book
Author : N M Chuong,L Nirenberg,W Tutschke
Publisher : World Scientific
Release : 2004-06-01
ISBN : 9814482110
Language : En, Es, Fr & De

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Book Description :

This volume takes up various topics in Mathematical Analysis including boundary and initial value problems for Partial Differential Equations and Functional Analytic methods. Topics include linear elliptic systems for composite material — the coefficients may jump from domain to domain; Stochastic Analysis — many applied problems involve evolution equations with random terms, leading to the use of stochastic analysis. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) • CC Proceedings — Engineering & Physical Sciences Contents:Deterministic Analysis:Differentiation of Hypergeometric Functions with Respect to Parameters (Yu A Brychkov & K O Geddes)On the Lagrange Problem About the Strongest Columns (Yu V Egorov)Wavelet Based Fast Solution of Boundary Integral Equations (H Harbrecht & R Schneider)Semi-Classical Methods in Ginzburg–Landau Theory (B Helffer)Stability of Equilibriums in One-Dimensional Motion of Compressible Viscous Gas Forced by Self-Gravity (Y Iwata & Y Yamamoto)Estimates for Elliptic Systems for Composite Material (L Nirenberg)On Asymptotics for the Mabuchi Energy Functional (D H Phong & J Sturm)Regularity of Solutions of the Initial Boundary Value Problem for Linearized Equations of Ideal Magneto-Hydrodynamics (M Yamamoto)Stochastic Analysis:Impulsive Stochastic Evolution Inclusions with Multi-Valued Diffusion (N U Ahmed)Some of Future Directions of White Noise Analysis (T Hida)Constructing Random Probability Distributions (T P Hill & D E R Sitton)Multiparameter Additive Processes of Mixture Type (K Inoue)The Random Integral Representation Hypothesis Revisited: New Classes of S-Selfdecomposable Laws (Z J Jurek)Semigroups and Processes with Parameter in a Cone (J Pedersen & K-I Sato)and other papers Readership: Researchers and academics in the fields of analysis and differential equations, approximation theory, probability and statistics. Keywords:Almost Complex Manifolds;Noncommutative Geometry;Lagrange Problem;Boundary Value Problem

Wavelets and Fractals in Earth System Sciences

Wavelets and Fractals in Earth System Sciences Book
Author : E. Chandrasekhar,V. P. Dimri,V. M. Gadre
Publisher : Taylor & Francis
Release : 2013-11-20
ISBN : 146655360X
Language : En, Es, Fr & De

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Book Description :

The subject of wavelet analysis and fractal analysis is fast developing and has drawn a great deal of attention in varied disciplines of science and engineering. Over the past couple of decades, wavelets, multiresolution, and multifractal analyses have been formalized into a thorough mathematical framework and have found a variety of applications w

Analysis Probability And Mathematical Physics On Fractals

Analysis  Probability And Mathematical Physics On Fractals Book
Author : Rogers Luke G,Ruiz Patricia Alonso,Teplyaev Alexander,Chen Joe Po-chou
Publisher : World Scientific
Release : 2020-02-26
ISBN : 9811215545
Language : En, Es, Fr & De

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Book Description :

In the 50 years since Mandelbrot identified the fractality of coastlines, mathematicians and physicists have developed a rich and beautiful theory describing the interplay between analytic, geometric and probabilistic aspects of the mathematics of fractals. Using classical and abstract analytic tools developed by Cantor, Hausdorff, and Sierpinski, they have sought to address fundamental questions: How can we measure the size of a fractal set? How do waves and heat travel on irregular structures? How are analysis, geometry and stochastic processes related in the absence of Euclidean smooth structure? What new physical phenomena arise in the fractal-like settings that are ubiquitous in nature?This book introduces background and recent progress on these problems, from both established leaders in the field and early career researchers. The book gives a broad introduction to several foundational techniques in fractal mathematics, while also introducing some specific new and significant results of interest to experts, such as that waves have infinite propagation speed on fractals. It contains sufficient introductory material that it can be read by new researchers or researchers from other areas who want to learn about fractal methods and results.

Dynamics with Chaos and Fractals

Dynamics with Chaos and Fractals Book
Author : Marat Akhmet,Mehmet Onur Fen,Ejaily Milad Alejaily
Publisher : Springer Nature
Release : 2020-01-01
ISBN : 3030358542
Language : En, Es, Fr & De

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Book Description :

The book is concerned with the concepts of chaos and fractals, which are within the scopes of dynamical systems, geometry, measure theory, topology, and numerical analysis during the last several decades. It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. This is the first time in the literature that the description of chaos is initiated from a single motion. Chaos is now placed on the line of oscillations, and therefore, it is a subject of study in the framework of the theories of dynamical systems and differential equations, as in this book. The techniques introduced in the book make it possible to develop continuous and discrete dynamics which admit fractals as points of trajectories as well as orbits themselves. To provide strong arguments for the genericity of chaos in the real and abstract universe, the concept of abstract similarity is suggested.

Fractals in Multimedia

Fractals in Multimedia Book
Author : Michael F. Barnsley,Dietmar Saupe,Edward R. Vrscay
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1468492446
Language : En, Es, Fr & De

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Book Description :

This IMA Volume in Mathematics and its Applications FRACTALS IN MULTIMEDIA is a result of a very successful three-day minisymposium on the same title. The event was an integral part of the IMA annual program on Mathemat ics in Multimedia, 2000-2001. We would like to thank Michael F. Barnsley (Department of Mathematics and Statistics, University of Melbourne), Di etmar Saupe (Institut fUr Informatik, UniversiUit Leipzig), and Edward R. Vrscay (Department of Applied Mathematics, University of Waterloo) for their excellent work as organizers of the meeting and for editing the proceedings. We take this opportunity to thank the National Science Foundation for their support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume grew out of a meeting on Fractals in Multimedia held at the IMA in January 2001. The meeting was an exciting and intense one, focused on fractal image compression, analysis, and synthesis, iterated function systems and fractals in education. The central concerns of the meeting were to establish within these areas where we are now and to develop a vision for the future.

Fractal Frontiers Fractals In The Natural And Applied Sciences

Fractal Frontiers  Fractals In The Natural And Applied Sciences Book
Author : Novak Miroslav M,Dewey T G
Publisher : World Scientific
Release : 1997-03-29
ISBN : 9814546062
Language : En, Es, Fr & De

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Book Description :

This popular science book shows that chemists do have a sense of humor, and this book is a celebration of the quirky side of scientific nomenclature. Here, some molecules are shown that have unusual, rude, ridiculous or downright silly names. Written in an easy-to-read style, anyone — not just scientists — can appreciate the content. Each molecule is illustrated with a photograph and/or image that relates directly or indirectly to its name and molecular structure. Thus, the book is not only entertaining, but also educational./a

Multiscale Wavelet Methods for Partial Differential Equations

Multiscale Wavelet Methods for Partial Differential Equations Book
Author : Wolfgang Dahmen,Andrew Kurdila,Peter Oswald
Publisher : Elsevier
Release : 1997-08-13
ISBN : 9780080537146
Language : En, Es, Fr & De

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Book Description :

This latest volume in the Wavelets Analysis and Its Applications Series provides significant and up-to-date insights into recent developments in the field of wavelet constructions in connection with partial differential equations. Specialists in numerical applications and engineers in a variety of fields will find Multiscale Wavelet for Partial Differential Equations to be a valuable resource. Covers important areas of computational mechanics such as elasticity and computational fluid dynamics Includes a clear study of turbulence modeling Contains recent research on multiresolution analyses with operator-adapted wavelet discretizations Presents well-documented numerical experiments connected with the development of algorithms, useful in specific applications

Fractals in Engineering

Fractals in Engineering Book
Author : Jacques Lévy-Véhel,Evelyne Lutton
Publisher : Springer Science & Business Media
Release : 2005-12-06
ISBN : 1846280486
Language : En, Es, Fr & De

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Book Description :

The application of fractals in the engineering sciences is evolving swiftly and the editors have turned to Springer for the third time to bring you the latest research emerging from the rapid growth in techniques available for the employment of the ideas of fractals and complexity to a variety of disciplines in and associated with the engineering field. The strong potential of this research can be seen in real industrial situations with recent progress being made in areas such as chemical engineering, internet traffic, physics and finance. Image processing continues to be a major field of application for fractal analysis and is well-represented here. It is important to note that the applications models are presented with a firm basis in theoretical argument, the qualitative observation of fractal phenomena no longer being sufficient. Consisting of papers written by a world-wide pool of experts, the multidisciplinary approach of this third volume will be of particular interest to industrial researchers and practitioners as well as to academics from many backgrounds. Fractals in Engineering: New Trends in Theory and Applications continues the publication of engineering-related research in fractal techniques begun in Fractals in Engineering and Fractals: Theory and Applications in Engineering (Springer London 1997 and 1999).

Mathematical Theorems

Mathematical Theorems Book
Author : Lyudmila Alexeyeva
Publisher : BoD – Books on Demand
Release : 2020-12-09
ISBN : 1838800719
Language : En, Es, Fr & De

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Book Description :

Download Mathematical Theorems book written by Lyudmila Alexeyeva, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Emergent Nature

Emergent Nature Book
Author : Miroslav M Novak
Publisher : World Scientific
Release : 2002-02-04
ISBN : 9814488879
Language : En, Es, Fr & De

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Book Description :

This book, based on presentations made at the international conference Fractals 2002, is of interest to everyone in the general field of nonlinear dynamics. The abundance of papers from numerous disciplines makes it exciting reading and provides a unifying thread through the topics, such as ray tracing, structure of peptides, modeling fractal surfaces, cancer growth, macaque monkey cortical neurons, occurrence of earthquakes, and patterns of the World Wide Web. Contents: Modeling Cerebellar Dynamics (M G Velarde et al.)Two and Three Dimensional Computer Simulation of Cancer Growth (S Flores Ascencio et al.)Structural and Dynamic Complexity of an Elastin-Related Peptide (A Bonelli et al.)Cumulative Effective Hölder Exponent Based Indicator for Real-Time Fetal Heartbeat Analysis During Labour (Z R Struzik & W J van Wijngaarden)Fractal Features in the Nonstationarity of Physiological Time Series (P Ch Ivanov et al.)Fractal Analysis of Aggregates of Non-Uniformly Sized Particles: An Application to Macaque Monkey Cortical Pyramidal Neurons (B I Henry et al.)Dynamics of Solar Magnetic Field from Synoptic Charts (N G Makarenko & L M Karimova)Side-Branching in the Nonlinear Zone: A Self-Similar Region in Dendritic Crystal Growth (R González-Cinca)and other papers Readership: Researchers in nonlinear science. Keywords:

Fractal Analysis

Fractal Analysis Book
Author : Fernando Brambila
Publisher : BoD – Books on Demand
Release : 2017-07-26
ISBN : 953513213X
Language : En, Es, Fr & De

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Book Description :

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.

Computer Applications in the Mineral Industries

Computer Applications in the Mineral Industries Book
Author : Heping Xie
Publisher : CRC Press
Release : 2020-12-17
ISBN : 1000107949
Language : En, Es, Fr & De

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Book Description :

This text covers the use of computer applications in the mineral industries, encompassing topics such as the use of computer visualization in mining systems and aspects such as ventilation and safety.

Chaos and Fractals

Chaos and Fractals Book
Author : C.A. Pickover
Publisher : Elsevier
Release : 1998-08-03
ISBN : 9780080528861
Language : En, Es, Fr & De

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Book Description :

These days computer-generated fractal patterns are everywhere, from squiggly designs on computer art posters to illustrations in the most serious of physics journals. Interest continues to grow among scientists and, rather surprisingly, artists and designers. This book provides visual demonstrations of complicated and beautiful structures that can arise in systems, based on simple rules. It also presents papers on seemingly paradoxical combinations of randomness and structure in systems of mathematical, physical, biological, electrical, chemical, and artistic interest. Topics include: iteration, cellular automata, bifurcation maps, fractals, dynamical systems, patterns of nature created through simple rules, and aesthetic graphics drawn from the universe of mathematics and art. Chaos and Fractals is divided into six parts: Geometry and Nature; Attractors; Cellular Automata, Gaskets, and Koch Curves; Mandelbrot, Julia and Other Complex Maps; Iterated Function Systems; and Computer Art. Additionally, information on the latest practical applications of fractals and on the use of fractals in commercial products such as the antennas and reaction vessels is presented. In short, fractals are increasingly finding application in practical products where computer graphics and simulations are integral to the design process. Each of the six sections has an introduction by the editor including the latest research, references, and updates in the field. This book is enhanced with numerous color illustrations, a comprehensive index, and the many computer program examples encourage reader involvement.

Discrete Wavelet Transforms

Discrete Wavelet Transforms Book
Author : Hannu Olkkonen
Publisher : BoD – Books on Demand
Release : 2011-09-12
ISBN : 9533076542
Language : En, Es, Fr & De

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Book Description :

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms - Biomedical Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book reviews the recent progress in DWT algorithms for biomedical applications. The book covers a wide range of architectures (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in implementations of the DWT algorithms in biomedical signal analysis. Applications include compression and filtering of biomedical signals, DWT based selection of salient EEG frequency band, shift invariant DWTs for multiscale analysis and DWT assisted heart sound analysis. Part II addresses speech analysis, modeling and understanding of speech and speaker recognition. Part III focuses biosensor applications such as calibration of enzymatic sensors, multiscale analysis of wireless capsule endoscopy recordings, DWT assisted electronic nose analysis and optical fibre sensor analyses. Finally, Part IV describes DWT algorithms for tools in identification and diagnostics: identification based on hand geometry, identification of species groupings, object detection and tracking, DWT signatures and diagnostics for assessment of ICU agitation-sedation controllers and DWT based diagnostics of power transformers.The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications.

Thinking in Patterns

Thinking in Patterns Book
Author : Miroslav Michal Novak
Publisher : World Scientific
Release : 2004
ISBN : 9812388222
Language : En, Es, Fr & De

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Book Description :

Fractal geometry, together with the broader fields of nonlinear dynamics and complexity, represented a large segment of modern science at the end of the 20th century. Penetration of the resulting new paradigms into practically all academic disciplines has confirmed the fundamental assertion of universal formalism common to a wide range of human endeavors.This book contains an extended article by B B Mandelbrot, reviewing his contribution to fractal geometry and outlining some unsolved problems, with illustrations especially of finance and physics. It covers a range of multidisciplinary topics ? from the biology of aging, through the self-similar shape of plants, image decompression and solar magnetic fields, to sound reflection in the street. The book is a treasure trove for innovative researchers working in fields related to fractal geometry.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings? (ISTP? / ISI Proceedings)? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)? CC Proceedings ? Engineering & Physical Sciences