Fractal Functions Fractal Surfaces And Wavelets

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Fractal Functions, Fractal Surfaces, and Wavelets

Author : Peter R. Massopust
Publisher : Academic Press
ISBN 13 : 0128044705
Total Pages : 428 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Fractal Functions, Fractal Surfaces, and Wavelets by : Peter R. Massopust

Download or read book Fractal Functions, Fractal Surfaces, and Wavelets written by Peter R. Massopust and published by Academic Press. This book was released on 2016-09-02 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Fractals, Wavelets, and their Applications

Author : Christoph Bandt
Publisher : Springer
ISBN 13 : 3319081055
Total Pages : 499 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Fractals, Wavelets, and their Applications by : Christoph Bandt

Download or read book Fractals, Wavelets, and their Applications written by Christoph Bandt and published by Springer. This book was released on 2014-09-27 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Wavelets and Fractals in Earth System Sciences

Author : E. Chandrasekhar
Publisher : Taylor & Francis
ISBN 13 : 1466553596
Total Pages : 308 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Wavelets and Fractals in Earth System Sciences by : E. Chandrasekhar

Download or read book Wavelets and Fractals in Earth System Sciences written by E. Chandrasekhar and published by Taylor & Francis. This book was released on 2013-11-20 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 with significant impact in several branches of earth system sciences. Wavelets and Fractals in Earth System Sciences highlights the role of advanced data processing techniques in present-day research in various fields of earth system sciences. The book consists of ten chapters, providing a well-balanced blend of information about the role of wavelets, fractals, and multifractal analyses with the latest examples of their application in various research fields. By combining basics with advanced material, this book introduces concepts as needed and serves as an excellent introductory material and also as an advanced reference text for students and researchers.

Fractal Functions, Dimensions and Signal Analysis

Author : Santo Banerjee
Publisher : Springer Nature
ISBN 13 : 3030626725
Total Pages : 132 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Fractal Functions, Dimensions and Signal Analysis by : Santo Banerjee

Download or read book Fractal Functions, Dimensions and Signal Analysis written by Santo Banerjee and published by Springer Nature. This book was released on 2020-12-14 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Interpolation and Approximation with Splines and Fractals

Author : Peter Robert Massopust
Publisher :
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Interpolation and Approximation with Splines and Fractals by : Peter Robert Massopust

Download or read book Interpolation and Approximation with Splines and Fractals written by Peter Robert Massopust and published by . This book was released on 2010 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is intended to supplement the classical theory of uni- and multivariate splines and their approximation and interpolation properties with those of fractals, fractal functions, and fractal surfaces. This synthesis will complement currently required courses dealing with these topics and expose the prospective reader to some new and deep relationships. In addition to providing a classical introduction to the main issues involving approximation and interpolation with uni- and multivariate splines, cardinal and exponential splines, and their connection to wavelets and multiscale analysis, which comprises the first half of the book, the second half will describe fractals, fractal functions and fractal surfaces, and their properties. This also includes the new burgeoning theory of superfractals and superfractal functions. The theory of splines is well-established but the relationship to fractal functions is novel. Throughout the book, connections between these two apparently different areas will be exposed and presented. In this way, more options are given to the prospective reader who will encounter complex approximation and interpolation problems in real-world modeling. Numerous examples, figures, and exercises accompany the material.

Shape in Picture

Author : Ying-Lie O
Publisher : Springer Science & Business Media
ISBN 13 : 366203039X
Total Pages : 685 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Shape in Picture by : Ying-Lie O

Download or read book Shape in Picture written by Ying-Lie O and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fields of image analysis, computer vision, and artificial intelligence all make use of descriptions of shape in grey-level images. Most existing algorithms for the automatic recognition and classification of particular shapes have been devel oped for specific purposes, with the result that these methods are often restricted in their application. The use of advanced and theoretically well-founded math ematical methods should lead to the construction of robust shape descriptors having more general application. Shape description can be regarded as a meeting point of vision research, mathematics, computing science, and the application fields of image analy sis, computer vision, and artificial intelligence. The NATO Advanced Research Workshop "Shape in Picture" was organised with a twofold objective: first, it should provide all participants with an overview of relevant developments in these different disciplines; second, it should stimulate researchers to exchange original results and ideas across the boundaries of these disciplines. This book comprises a widely drawn selection of papers presented at the workshop, and many contributions have been revised to reflect further progress in the field. The focus of this collection is on mathematical approaches to the construction of shape descriptions from grey-level images. The book is divided into five parts, each devoted to a different discipline. Each part contains papers that have tutorial sections; these are intended to assist the reader in becoming acquainted with the variety of approaches to the problem.

CRC Concise Encyclopedia of Mathematics

Author : Eric W. Weisstein
Publisher : CRC Press
ISBN 13 : 1420035223
Total Pages : 3253 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis CRC Concise Encyclopedia of Mathematics by : Eric W. Weisstein

Download or read book CRC Concise Encyclopedia of Mathematics written by Eric W. Weisstein and published by CRC Press. This book was released on 2002-12-12 with total page 3253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d

Thinking in Patterns

Author : Miroslav Michal Novak
Publisher : World Scientific
ISBN 13 : 9812388222
Total Pages : 336 pages
Book Rating : 4.8/5 (123 download)

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Book Synopsis Thinking in Patterns by : Miroslav Michal Novak

Download or read book Thinking in Patterns written by Miroslav Michal Novak and published by World Scientific. This book was released on 2004 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

New Perspectives on Nonlinear Dynamics and Complexity

Author : Dimitri Volchenkov
Publisher : Springer Nature
ISBN 13 : 303097328X
Total Pages : 198 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis New Perspectives on Nonlinear Dynamics and Complexity by : Dimitri Volchenkov

Download or read book New Perspectives on Nonlinear Dynamics and Complexity written by Dimitri Volchenkov and published by Springer Nature. This book was released on 2022-07-29 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents select, recent developments in nonlinear and complex systems reported at the 1st Online Conference on Nonlinear Dynamics and Complexity, held on November 23-25, 2020. It provides an exchange recent developments, discoveries, and progresses in Nonlinear Dynamics and Complexity. The collection presents fundamental and frontier theories and techniques for modern science and technology, stimulates more research interest for exploration of nonlinear science and complexity; and passes along new knowledge and insight to the next generation of engineers and technologists in a range of fields.

Chaos and Fractals

Author : C.A. Pickover
Publisher : Elsevier
ISBN 13 : 0080528864
Total Pages : 469 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Chaos and Fractals by : C.A. Pickover

Download or read book Chaos and Fractals written by C.A. Pickover and published by Elsevier. This book was released on 1998-08-03 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Emergent Nature: Patterns, Growth And Scaling In The Sciences

Author : Miroslav M Novak
Publisher : World Scientific
ISBN 13 : 9814488879
Total Pages : 458 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Emergent Nature: Patterns, Growth And Scaling In The Sciences by : Miroslav M Novak

Download or read book Emergent Nature: Patterns, Growth And Scaling In The Sciences written by Miroslav M Novak and published by World Scientific. This book was released on 2002-02-04 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Iterated Function Systems for Real-Time Image Synthesis

Author : Slawomir Nikiel
Publisher : Springer Science & Business Media
ISBN 13 : 1846286867
Total Pages : 153 pages
Book Rating : 4.8/5 (462 download)

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Book Synopsis Iterated Function Systems for Real-Time Image Synthesis by : Slawomir Nikiel

Download or read book Iterated Function Systems for Real-Time Image Synthesis written by Slawomir Nikiel and published by Springer Science & Business Media. This book was released on 2007-05-28 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive explanation of iterated function systems and how to use them in generation of complex objects. Discussion covers the most popular fractal models applied in the field of image synthesis; surveys iterated function system models; explores algorithms for creating and manipulating fractal objects, and techniques for implementing the algorithms, and more. The book includes both descriptive text and pseudo-code samples for the convenience of graphics application programmers.

13th Chaotic Modeling and Simulation International Conference

Author : Christos H. Skiadas
Publisher : Springer Nature
ISBN 13 : 3030707954
Total Pages : 1080 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis 13th Chaotic Modeling and Simulation International Conference by : Christos H. Skiadas

Download or read book 13th Chaotic Modeling and Simulation International Conference written by Christos H. Skiadas and published by Springer Nature. This book was released on 2021-12-14 with total page 1080 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gathering the proceedings of the 13th CHAOS2020 International Conference, this book highlights recent developments in nonlinear, dynamical and complex systems. The conference was intended to provide an essential forum for Scientists and Engineers to exchange ideas, methods, and techniques in the field of Nonlinear Dynamics, Chaos, Fractals and their applications in General Science and the Engineering Sciences. The respective chapters address key methods, empirical data and computer techniques, as well as major theoretical advances in the applied nonlinear field. Beyond showcasing the state of the art, the book will help academic and industrial researchers alike apply chaotic theory in their studies.

Applied Analysis, Optimization and Soft Computing

Author : Tanmoy Som
Publisher : Springer Nature
ISBN 13 : 9819905974
Total Pages : 425 pages
Book Rating : 4.8/5 (199 download)

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Book Synopsis Applied Analysis, Optimization and Soft Computing by : Tanmoy Som

Download or read book Applied Analysis, Optimization and Soft Computing written by Tanmoy Som and published by Springer Nature. This book was released on 2023-06-10 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Integral, Probability, and Fractal Measures

Author : Gerald A. Edgar
Publisher : Springer Science & Business Media
ISBN 13 : 1475729588
Total Pages : 292 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Integral, Probability, and Fractal Measures by : Gerald A. Edgar

Download or read book Integral, Probability, and Fractal Measures written by Gerald A. Edgar and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing the mathematical background required for the study of fractal topics, this book deals with integration in the modern sense, together with mathematical probability. The emphasis is on the particular results that aid the discussion of fractals, and follows Edgars Measure, Topology, and Fractal Geometry. With exercises throughout, this is and ideal text for beginning graduate students both in the classroom and for self-study.

Frontiers of Fractal Analysis

Author : Santo Banerjee
Publisher : CRC Press
ISBN 13 : 1000625877
Total Pages : 183 pages
Book Rating : 4.0/5 (6 download)

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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 2022-07-07 with total page 183 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.

Discrete Wavelet Transforms

Author : Hannu Olkkonen
Publisher : BoD – Books on Demand
ISBN 13 : 9533076542
Total Pages : 382 pages
Book Rating : 4.5/5 (33 download)

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Book Synopsis Discrete Wavelet Transforms by : Hannu Olkkonen

Download or read book Discrete Wavelet Transforms written by Hannu Olkkonen and published by BoD – Books on Demand. This book was released on 2011-09-12 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.