Recent Developments In Fractals And Related Fields

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Recent Developments in Fractals and Related Fields

Author : Julien Barral
Publisher : Birkhäuser
ISBN 13 : 3319578057
Total Pages : 312 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Recent Developments in Fractals and Related Fields by : Julien Barral

Download or read book Recent Developments in Fractals and Related Fields written by Julien Barral and published by Birkhäuser. This book was released on 2017-08-23 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals, including both original research contributions, as well as surveys from many of the leading experts on modern fractal theory and applications. It is an outgrowth of the Conference of Fractals and Related Fields III, that was held on September 19-25, 2015 in île de Porquerolles, France. Chapters cover fields related to fractals such as harmonic analysis, multifractal analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, wavelets, potential theory, partial differential equations, fractal tilings, combinatorics, and signal and image processing. The book is aimed at pure and applied mathematicians in these areas, as well as other researchers interested in discovering the fractal domain.

Recent Developments in Fractals and Related Fields

Author : Julien Barral
Publisher :
ISBN 13 : 9780817648893
Total Pages : 444 pages
Book Rating : 4.6/5 (488 download)

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Book Synopsis Recent Developments in Fractals and Related Fields by : Julien Barral

Download or read book Recent Developments in Fractals and Related Fields written by Julien Barral and published by . This book was released on 2010-08-01 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Further Developments in Fractals and Related Fields

Author : Julien Barral
Publisher : Springer Science & Business Media
ISBN 13 : 081768400X
Total Pages : 296 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Further Developments in Fractals and Related Fields by : Julien Barral

Download or read book Further Developments in Fractals and Related Fields written by Julien Barral and published by Springer Science & Business Media. This book was released on 2013-02-20 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, following in the tradition of a similar 2010 publication by the same editors, is an outgrowth of an international conference, “Fractals and Related Fields II,” held in June 2011. The book provides readers with an overview of developments in the mathematical fields related to fractals, including original research contributions as well as surveys from many of the leading experts on modern fractal theory and applications. The chapters cover fields related to fractals such as: *geometric measure theory *ergodic theory *dynamical systems *harmonic and functional analysis *number theory *probability theory Further Developments in Fractals and Related Fields is aimed at pure and applied mathematicians working in the above-mentioned areas as well as other researchers interested in discovering the fractal domain. Throughout the volume, readers will find interesting and motivating results as well as new avenues for further research.

Recent Developments in Fractals and Related Fields

Author : Julien Barral
Publisher : Birkhäuser
ISBN 13 : 9780817648879
Total Pages : 419 pages
Book Rating : 4.6/5 (488 download)

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Book Synopsis Recent Developments in Fractals and Related Fields by : Julien Barral

Download or read book Recent Developments in Fractals and Related Fields written by Julien Barral and published by Birkhäuser. This book was released on 2010-08-12 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the engineering, mathematical, and scienti?c communities with s- ni?cant developments in harmonic analysis, ranging from abstract harmonic analysis to basic applications. The title of the series re?ects the importance of applications and numerical implementation, but richness and relevance of applications and implementation depend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the int- leaving of theory and applications and their creative symbiotic evolution is axiomatic. Harmonic analysis is a wellspring of ideas and applicability that has ?o- ished, developed, and deepened over time within many disciplines and by means of creative cross-fertilizationwith diverse areas. The intricate and f- damental relationship between harmonic analysis and ?elds such as signal processing, partial di?erential equations (PDEs), and image processing is - ?ected in our state-of-the-art ANHA series. Our vision of modern harmonic analysis includes mathematical areas such as wavelet theory, Banach algebras, classical Fourier analysis, time-frequency analysis, and fractal geometry, as well as the diverse topics that impinge on them.

Further Developments in Fractals and Related Fields

Author : Julien Barral
Publisher : Birkhäuser
ISBN 13 : 9780817684013
Total Pages : 288 pages
Book Rating : 4.6/5 (84 download)

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Book Synopsis Further Developments in Fractals and Related Fields by : Julien Barral

Download or read book Further Developments in Fractals and Related Fields written by Julien Barral and published by Birkhäuser. This book was released on 2013-02-20 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, following in the tradition of a similar 2010 publication by the same editors, is an outgrowth of an international conference, “Fractals and Related Fields II,” held in June 2011. The book provides readers with an overview of developments in the mathematical fields related to fractals, including original research contributions as well as surveys from many of the leading experts on modern fractal theory and applications. The chapters cover fields related to fractals such as: *geometric measure theory *ergodic theory *dynamical systems *harmonic and functional analysis *number theory *probability theory Further Developments in Fractals and Related Fields is aimed at pure and applied mathematicians working in the above-mentioned areas as well as other researchers interested in discovering the fractal domain. Throughout the volume, readers will find interesting and motivating results as well as new avenues for further research.

Frontiers of Fractal Analysis

Author : Santo Banerjee
Publisher : CRC Press
ISBN 13 : 1000625877
Total Pages : 182 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 182 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.

Multifractional Stochastic Fields: Wavelet Strategies In Multifractional Frameworks

$Download Multifractional Stochastic Fields: Wavelet Strategies In Multifractional Frameworks PDF Online Free$

Author : Ayache Antoine
Publisher : World Scientific
ISBN 13 : 9814525677
Total Pages : 236 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Multifractional Stochastic Fields: Wavelet Strategies In Multifractional Frameworks by : Ayache Antoine

Download or read book Multifractional Stochastic Fields: Wavelet Strategies In Multifractional Frameworks written by Ayache Antoine and published by World Scientific. This book was released on 2018-09-24 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional Brownian Motion (FBM) is a very classical continuous self-similar Gaussian field with stationary increments. In 1940, some works of Kolmogorov on turbulence led him to introduce this quite natural extension of Brownian Motion, which, in contrast with the latter, has correlated increments. However, the denomination FBM is due to a very famous article by Mandelbrot and Van Ness, published in 1968. Not only in it, but also in several of his following works, Mandelbrot emphasized the importance of FBM as a model in several applied areas, and thus he made it to be known by a wide community. Therefore, FBM has been studied by many authors, and used in a lot of applications.In spite of the fact that FBM is a very useful model, it does not always fit to real data. This is the reason why, for at least two decades, there has been an increasing interest in the construction of new classes of random models extending it, which offer more flexibility. A paradigmatic example of them is the class of Multifractional Fields. Multifractional means that fractal properties of models, typically, roughness of paths and self-similarity of probability distributions, are locally allowed to change from place to place.In order to sharply determine path behavior of Multifractional Fields, a wavelet strategy, which can be considered to be new in the probabilistic framework, has been developed since the end of the 90's. It is somehow inspired by some rather non-standard methods, related to the fine study of Brownian Motion roughness, through its representation in the Faber-Schauder system. The main goal of the book is to present the motivations behind this wavelet strategy, and to explain how it can be applied to some classical examples of Multifractional Fields. The book also discusses some topics concerning them which are not directly related to the wavelet strategy.

Frontiers of Fractal Analysis

Author : Santo Banerjee
Publisher :
ISBN 13 : 9781032138732
Total Pages : pages
Book Rating : 4.1/5 (387 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 . This book was released on 2022 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "The best accomplishment in human research is feasibly they understand the natural phenomena can be exhibited by mathematical models. The history of describing natural objects using geometry is as old as the advent of science itself. Traditionally lines, squares, rectangles, circles, spheres, etc. have been the basis of our intuitive understanding of the 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"--

Recent Advances in Mathematics and Technology

Author : Serge Dos Santos
Publisher : Springer Nature
ISBN 13 : 3030352021
Total Pages : 190 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Recent Advances in Mathematics and Technology by : Serge Dos Santos

Download or read book Recent Advances in Mathematics and Technology written by Serge Dos Santos and published by Springer Nature. This book was released on 2020-02-21 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters in this volume are based on talks given at the inaugural Technology, Engineering and Mathematics Conference (TEM18), held from March 26 to 27, 2018 in Kenitra, Morocco. Advances in mathematical modeling, optimization, numerical analysis, signal processing, and computer science are presented by leading experts in these fields. There is a particular emphasis on stochastic analysis, machine learning algorithms, and deep learning models, which are highly relevant to the state-of-the-art in augmented, virtual, and mixed realities. Topics include: Harmonic analysis Big data analytics and applications Biomathematics Computer engineering and applications Economics and financial engineering Medical imaging and non-destructive testing This volume is ideal for engineers and researchers working in technological fields that need to be modeled and simulated using the tools of modern mathematics.

Recent Developments in Fractal Geometry and Dynamical Systems

Author : Sangita Jha
Publisher : American Mathematical Society
ISBN 13 : 1470472163
Total Pages : 270 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Recent Developments in Fractal Geometry and Dynamical Systems by : Sangita Jha

Download or read book Recent Developments in Fractal Geometry and Dynamical Systems written by Sangita Jha and published by American Mathematical Society. This book was released on 2024-04-18 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the virtual AMS Special Session on Fractal Geometry and Dynamical Systems, held from May 14–15, 2022. The content covers a wide range of topics. It includes nonautonomous dynamics of complex polynomials, theory and applications of polymorphisms, topological and geometric problems related to dynamical systems, and also covers fractal dimensions, including the Hausdorff dimension of fractal interpolation functions. Furthermore, the book contains a discussion of self-similar measures as well as the theory of IFS measures associated with Bratteli diagrams. This book is suitable for graduate students interested in fractal theory, researchers interested in fractal geometry and dynamical systems, and anyone interested in the application of fractals in science and engineering. This book also offers a valuable resource for researchers working on applications of fractals in different fields.

Fractals in Engineering

Author : Jacques Lévy-Véhel
Publisher : Springer Science & Business Media
ISBN 13 : 1846280486
Total Pages : 290 pages
Book Rating : 4.8/5 (462 download)

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Book Synopsis Fractals in Engineering by : Jacques Lévy-Véhel

Download or read book Fractals in Engineering written by Jacques Lévy-Véhel and published by Springer Science & Business Media. This book was released on 2005-12-06 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

New Trends in Applied Harmonic Analysis

Author : Akram Aldroubi
Publisher : Birkhäuser
ISBN 13 : 3319278738
Total Pages : 334 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis New Trends in Applied Harmonic Analysis by : Akram Aldroubi

Download or read book New Trends in Applied Harmonic Analysis written by Akram Aldroubi and published by Birkhäuser. This book was released on 2016-04-21 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a selection of written notes corresponding to courses taught at the CIMPA School: "New Trends in Applied Harmonic Analysis: Sparse Representations, Compressed Sensing and Multifractal Analysis". New interactions between harmonic analysis and signal and image processing have seen striking development in the last 10 years, and several technological deadlocks have been solved through the resolution of deep theoretical problems in harmonic analysis. New Trends in Applied Harmonic Analysis focuses on two particularly active areas that are representative of such advances: multifractal analysis, and sparse representation and compressed sensing. The contributions are written by leaders in these areas, and cover both theoretical aspects and applications. This work should prove useful not only to PhD students and postdocs in mathematics and signal and image processing, but also to researchers working in related topics.

Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II

Author : David Carfi
Publisher : American Mathematical Soc.
ISBN 13 : 0821891480
Total Pages : 372 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II by : David Carfi

Download or read book Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II written by David Carfi and published by American Mathematical Soc.. This book was released on 2013-10-24 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoît Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry and various aspects of dynamical systems in applied mathematics and the applications to other sciences. Also included are articles discussing a variety of connections between these subjects and various areas of physics, engineering, computer science, technology, economics and finance, as well as of mathematics (including probability theory in relation with statistical physics and heat kernel estimates, geometric measure theory, partial differential equations in relation with condensed matter physics, global analysis on non-smooth spaces, the theory of billiards, harmonic analysis and spectral geometry). The companion volume (Contemporary Mathematics, Volume 600) focuses on the more mathematical aspects of fractal geometry and dynamical systems.

Fractal Geometry and Stochastics V

Author : Christoph Bandt
Publisher : Birkhäuser
ISBN 13 : 3319186604
Total Pages : 340 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Fractal Geometry and Stochastics V by : Christoph Bandt

Download or read book Fractal Geometry and Stochastics V written by Christoph Bandt and published by Birkhäuser. This book was released on 2015-07-08 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects significant contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five topical sections: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. Each part starts with a state-of-the-art survey followed by papers covering a specific aspect of the topic. The authors are leading world experts and present their topics comprehensibly and attractively. Both newcomers and specialists in the field will benefit from this book.

Geometry and Analysis of Fractals

Author : De-Jun Feng
Publisher : Springer
ISBN 13 : 3662439204
Total Pages : 360 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Geometry and Analysis of Fractals by : De-Jun Feng

Download or read book Geometry and Analysis of Fractals written by De-Jun Feng and published by Springer. This book was released on 2014-08-01 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong. The volume offers insights into a number of exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematical physics.

Analysis, Applications, and Computations

Author : Uwe Kähler
Publisher : Springer Nature
ISBN 13 : 3031363752
Total Pages : 696 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Analysis, Applications, and Computations by : Uwe Kähler

Download or read book Analysis, Applications, and Computations written by Uwe Kähler and published by Springer Nature. This book was released on 2023-12-01 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the contributions of the participants of the 13th International ISAAC Congress 2021, held in Ghent, Belgium. The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on current research in mathematical analysis and its various interdisciplinary applications.

Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science

Author : Isaac Pesenson
Publisher : Birkhäuser
ISBN 13 : 3319555561
Total Pages : 510 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science by : Isaac Pesenson

Download or read book Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science written by Isaac Pesenson and published by Birkhäuser. This book was released on 2017-08-09 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as: The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems. Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets. Applications of harmonic analysis to data science and statistics Boundary-value problems for PDE's including the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.