Fractal Functions Fractal Surfaces and Wavelets

• Author : Peter R. Massopust
• Publisher : Academic Press
• Release Date : 2016-08-30
• ISBN : 012804408X

"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

• Author : Peter R. Massopust
• Publisher : Academic Press
• Release Date : 2016-09-02
• ISBN : 9780128044704

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

• Author : Christoph Bandt,Michael Barnsley,Robert Devaney,Kenneth J. Falconer,V. Kannan,Vinod Kumar P.B.
• Publisher : Springer
• Release Date : 2014-09-27
• ISBN : 9783319081052

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

• Author : N. M. Chuong,L. Nirenberg
• Publisher : World Scientific
• Release Date : 2004
• ISBN : 9789812702548

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

• Author : N M Chuong,L Nirenberg,W Tutschke
• Publisher : World Scientific
• Release Date : 2004-06-01
• ISBN : 9789814482110

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

• Author : E. Chandrasekhar,V. P. Dimri,V. M. Gadre
• Publisher : Taylor & Francis
• Release Date : 2013-11-20
• ISBN : 9781466553606

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

• Author : Santo Banerjee,D. Easwaramoorthy,A. Gowrisankar
• Publisher : Springer Nature
• Release Date : 2020-12-14
• ISBN : 9783030626723

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

• Author : Rogers Luke G,Ruiz Patricia Alonso,Teplyaev Alexander,Chen Joe Po-chou
• Publisher : World Scientific
• Release Date : 2020-02-26
• ISBN : 9789811215544

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

• Author : Peter Robert Massopust
• Publisher : Unknown
• Release Date : 2010
• ISBN : UCSD:31822037437092

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

• Author : Michael F. Barnsley,Dietmar Saupe,Edward R. Vrscay
• Publisher : Springer Science & Business Media
• Release Date : 2012-12-06
• ISBN : 9781468492446

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

• Author : Marat Akhmet,Mehmet Onur Fen,Ejaily Milad Alejaily
• Publisher : Springer Nature
• Release Date : 2020-01-01
• ISBN : 9783030358549

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

• Author : Wolfgang Dahmen,Andrew Kurdila,Peter Oswald
• Publisher : Elsevier
• Release Date : 1997-08-13
• ISBN : 0080537146

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

• Author : Santo Banerjee,A. Gowrisankar
• Publisher : CRC Press
• Release Date : 2022-07-07
• ISBN : 9781000625875

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

• Author : David R. Larson
• Publisher : American Mathematical Soc.
• Release Date : 2008
• ISBN : 9780821841440

This volume contains articles based on talks presented at the Special Session Frames and Operator Theory in Analysis and Signal Processing, held in San Antonio, Texas, in January of 2006. Recently, the field of frames has undergone tremendous advancement. Most of the work in this field is focused on the design and construction of more versatile frames and frames tailored towards specific applications, e.g., finite dimensional uniform frames for cellular communication. In addition, frames are now becoming a hot topic

• Author : Novak Miroslav M,Dewey T G
• Publisher : World Scientific
• Release Date : 1997-03-29
• ISBN : 9789814546065

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