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Fractal Functions, Fractal Surfaces, and Wavelets

Fractal Functions, Fractal Surfaces, and Wavelets
  • Author : Peter R. Massopust
  • Publisher :Unknown
  • Release Date :2016-09-02
  • Total pages :426
  • ISBN : 9780128044704
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Summary : 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

Wavelets, Fractals, and Fourier Transforms

Wavelets, Fractals, and Fourier Transforms
  • Author : M.. Farge,James Gerald Hunt,M. Farge,Julian C. R. Hunt,J. C. Vassilicos,John Christos Vassilicos,Institute of Mathematics and Its Applications,Department of Applied Mathematics and Theoretical Physics J C R Hunt,Institute of mathematics and its applications (GB).,Société de mathématiques appliquées et industrielles
  • Publisher :Unknown
  • Release Date :1993
  • Total pages :403
  • ISBN : UOM:39015029896126
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Summary : Recently there have been many developments and new applications of mathematical techniques for describing complex algebraic functions and analysing empirical continuous data derived from many different types of signal, for example turbulent flowa, oil well logs, electrical signals from the eyeetc. Probably the most important and rapidly developing of these techniques involve Fourier methods, fractals and wavelets. This international conference on these developments provides a useful introduction to the mathematics of wavelets, fractals, and Fourier Transforms, and to their manyapplications. Readers will appreciate that the different methods of analysis expose very different aspects of complex signals and surfaces and that the most suitable method often depends on the application under consideration.

Fractals, Wavelets, and their Applications

Fractals, Wavelets, and their Applications
  • Author : Christoph Bandt,Michael Barnsley,Robert Devaney,Kenneth J. Falconer,V. Kannan,Vinod Kumar P.B.
  • Publisher :Unknown
  • Release Date :2014-09-27
  • Total pages :508
  • ISBN : 9783319081052
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Summary : 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.

Interpolation and Approximation with Splines and Fractals

Interpolation and Approximation with Splines and Fractals
  • Author : Peter Robert Massopust
  • Publisher :Unknown
  • Release Date :2010
  • Total pages :319
  • ISBN : UCSD:31822037437092
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Summary : 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.

Wavelets and Fractals in Earth System Sciences

Wavelets and Fractals in Earth System Sciences
  • Author : E. Chandrasekhar,V. P. Dimri,V. M. Gadre
  • Publisher :Unknown
  • Release Date :2013-11-20
  • Total pages :306
  • ISBN : 9781466553606
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Summary : 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

Abstract and Applied Analysis

Abstract and Applied Analysis
  • Author : N. M. Chuong,L. Nirenberg
  • Publisher :Unknown
  • Release Date :2004
  • Total pages :567
  • ISBN : 9789812702548
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Summary : 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."

Boletín de la Sociedad Matemática Mexicana

Boletín de la Sociedad Matemática Mexicana
  • Author : Sociedad Matemática Mexicana
  • Publisher :Unknown
  • Release Date :1998
  • Total pages :229
  • ISBN : UOM:39015050438475
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Summary :

Scattering, Natural Surfaces, and Fractals

Scattering, Natural Surfaces, and Fractals
  • Author : Giorgio Franceschetti,Daniele Riccio
  • Publisher :Unknown
  • Release Date :2006-12-08
  • Total pages :304
  • ISBN : 9780080469010
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Summary : Scattering, Natural Surfaces, and Fractals provides a comprehensive overview of electromagnetic scattering from natural surfaces, ranging from the classical to the more recent (fractal) approach. As remote sensing applications become increasingly important, this text provides readers with a solid background in interpretation, classification and thematization of microwave images. The “scattering problem is discussed in detail with emphasis on its application to electromagnetic wave propagation, remote sensing, radar detection, and electromagnetic diagnostics. Natural surface and fractals complete this treatise focusing on how the fractal model represents our natural environment and other planets in our solar system, most recently as used to research the planet Venus and Titan, one of the moons of Saturn. An example of how scattering, fractals, and natural surfaces are of great importance is the following: Natural oil slicks in the ocean have been found to be fractal while man-made ones (generated by illegal washing of oil carrying ships) are not. Processing of an ocean image from space may detect the latter by means of a fractal analysis. An elegant and clear treatment of a rigorous topic with informative prose and realistic illustrations of scattering Provides readers with a solid background in interpretation, classification, and thematization of microwave images The only book available on fractal models and their application to scattering

Advances in Imaging and Electron Physics

Advances in Imaging and Electron Physics
  • Author : Peter W. Hawkes
  • Publisher :Unknown
  • Release Date :2002-11-04
  • Total pages :400
  • ISBN : 0080490050
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Summary : Advances in Imaging and Electron Physics merges two long-running serials--Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. The series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science and digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains.

Wavelets

Wavelets
  • Author : M.V. Altaisky
  • Publisher :Unknown
  • Release Date :2005-02
  • Total pages :154
  • ISBN : 8173715033
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Summary :

Fractal Analysis

Fractal Analysis
  • Author : Fernando Brambila
  • Publisher :Unknown
  • Release Date :2017-06-14
  • Total pages :294
  • ISBN : 9789535131915
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Summary : 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.

Proceedings

Proceedings
  • Author : Wayne A. Davis,Kellogg S. Booth,Alain Fournier
  • Publisher :Unknown
  • Release Date :1998
  • Total pages :246
  • ISBN : UOM:39015040327358
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Summary :

Fractals in Engineering

Fractals in Engineering
  • Author : Jacques Levy Vehel,Evelyne Lutton,Claude Tricot
  • Publisher :Unknown
  • Release Date :2012-12-06
  • Total pages :402
  • ISBN : 9781447109952
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Summary : Fractal analysis research is expanding into a variety of engineering domains. The strong potential of this work is now beginning to be seen in important applications in real industrial situations. Recent research progress has already led to new developments in domains such as signal processing and chemical engineering, and the major advances in fractal theory that underlie such developments are detailed here. New domains of applications are also presented, among them environmental science and rough surface analysis. Sections include multifractal analysis, iterated function systems, random processes, network traffic analysis, fractals and waves, image compression, and applications in physics. Fractals in Engineering emphasizes the connection between fractal analysis research and applications to industry. It is an important volume that illustrates the scientific and industrial value of this exciting field.

Proceedings

Proceedings
  • Author : IEEE Computer Society
  • Publisher :Unknown
  • Release Date :2002
  • Total pages :801
  • ISBN : STANFORD:36105111628330
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Summary : This text contains information on computer engineering as presented at the 6th International Conference on w/CD-ROM Information Visualisation (IV 2002).

A Wavelet Tour of Signal Processing

A Wavelet Tour of Signal Processing
  • Author : Stephane Mallat
  • Publisher :Unknown
  • Release Date :1999-09-14
  • Total pages :620
  • ISBN : 0080520839
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Summary : This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and École Polytechnique in Paris. Provides a broad perspective on the principles and applications of transient signal processing with wavelets Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurements Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet Content is accessible on several level of complexity, depending on the individual reader's needs New to the Second Edition Optical flow calculation and video compression algorithms Image models with bounded variation functions Bayes and Minimax theories for signal estimation 200 pages rewritten and most illustrations redrawn More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics

Demonstratio mathematica

Demonstratio mathematica
  • Author : Anonim
  • Publisher :Unknown
  • Release Date :2000
  • Total pages :229
  • ISBN : UCSC:32106015087866
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Proceedings

Proceedings
  • Author : Anonim
  • Publisher :Unknown
  • Release Date :1992
  • Total pages :229
  • ISBN : UOM:39015032608039
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Analele Universității București

Analele Universității București
  • Author : Anonim
  • Publisher :Unknown
  • Release Date :2002
  • Total pages :229
  • ISBN : STANFORD:36105123834785
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Summary :

Introduction to Wavelets and Wavelet Transforms

Introduction to Wavelets and Wavelet Transforms
  • Author : Sidny Burrus,C. S. Burrus,Ramesh A. Gopinath,Haitao Guo,JAN E AUTOR ODEGARD,IVAN W AUTOR SELESNICK
  • Publisher :Unknown
  • Release Date :1998
  • Total pages :268
  • ISBN : STANFORD:36105019319495
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Summary : Advanced undergraduate and beginning graduate students, faculty, researchers and practitioners in signal processing, telecommunications, and computer science, and applied mathematics. It assumes a background of Fourier series and transforms and of linear algebra and matrix methods. This primer presents a well balanced blend of the mathematical theory underlying wavelet techniques and a discussion that gives insight into why wavelets are successful in signal analysis, compression, dection, numerical analysis, and a wide variety of other theoretical and practical applications. It fills a gap in the existing wavelet literature with its unified view of expansions of signals into bases and frames, as well as the use of filter banks as descriptions and algorithms.

Advances in Heat and Mass Transfer in Biotechnology

Advances in Heat and Mass Transfer in Biotechnology
  • Author : Anonim
  • Publisher :Unknown
  • Release Date :2000
  • Total pages :229
  • ISBN : UOM:39015047794600
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Summary :

Mathematical Reviews

Mathematical Reviews
  • Author : Anonim
  • Publisher :Unknown
  • Release Date :2005-06
  • Total pages :229
  • ISBN : UOM:39015062317246
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Summary :