Fractals In Probability And Analysis
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Author | : Christopher J. Bishop |
Publisher | : Cambridge University Press |
Total Pages | : 415 |
Release | : 2017 |
Genre | : Mathematics |
ISBN | : 1107134110 |
Download Fractals in Probability and Analysis Book in PDF, Epub and Kindle
A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.
Author | : Patricia Alonso Ruiz |
Publisher | : World Scientific |
Total Pages | : 594 |
Release | : 2020-02-26 |
Genre | : Mathematics |
ISBN | : 9811215545 |
Download Analysis, Probability And Mathematical Physics On Fractals Book in PDF, Epub and Kindle
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.
Author | : Palle E. T. Jorgensen |
Publisher | : Springer Science & Business Media |
Total Pages | : 320 |
Release | : 2007-10-17 |
Genre | : Mathematics |
ISBN | : 0387330828 |
Download Analysis and Probability Book in PDF, Epub and Kindle
Combines analysis and tools from probability, harmonic analysis, operator theory, and engineering (signal/image processing) Interdisciplinary focus with hands-on approach, generous motivation and new pedagogical techniques Numerous exercises reinforce fundamental concepts and hone computational skills Separate sections explain engineering terms to mathematicians and operator theory to engineers Fills a gap in the literature
Author | : Jun Kigami |
Publisher | : Cambridge University Press |
Total Pages | : 238 |
Release | : 2001-06-07 |
Genre | : Mathematics |
ISBN | : 0521793211 |
Download Analysis on Fractals Book in PDF, Epub and Kindle
This book covers analysis on fractals, a developing area of mathematics which focuses on the dynamical aspects of fractals, such as heat diffusion on fractals and the vibration of a material with fractal structure. The book provides a self-contained introduction to the subject, starting from the basic geometry of self-similar sets and going on to discuss recent results, including the properties of eigenvalues and eigenfunctions of the Laplacians, and the asymptotical behaviors of heat kernels on self-similar sets. Requiring only a basic knowledge of advanced analysis, general topology and measure theory, this book will be of value to graduate students and researchers in analysis and probability theory. It will also be useful as a supplementary text for graduate courses covering fractals.
Author | : Herb Kunze |
Publisher | : Springer Science & Business Media |
Total Pages | : 417 |
Release | : 2011-11-18 |
Genre | : Mathematics |
ISBN | : 1461418917 |
Download Fractal-Based Methods in Analysis Book in PDF, Epub and Kindle
The idea of modeling the behaviour of phenomena at multiple scales has become a useful tool in both pure and applied mathematics. Fractal-based techniques lie at the heart of this area, as fractals are inherently multiscale objects; they very often describe nonlinear phenomena better than traditional mathematical models. In many cases they have been used for solving inverse problems arising in models described by systems of differential equations and dynamical systems. "Fractal-Based Methods in Analysis" draws together, for the first time in book form, methods and results from almost twenty years of research in this topic, including new viewpoints and results in many of the chapters. For each topic the theoretical framework is carefully explained using examples and applications. The second chapter on basic iterated function systems theory is designed to be used as the basis for a course and includes many exercises. This chapter, along with the three background appendices on topological and metric spaces, measure theory, and basic results from set-valued analysis, make the book suitable for self-study or as a source book for a graduate course. The other chapters illustrate many extensions and applications of fractal-based methods to different areas. This book is intended for graduate students and researchers in applied mathematics, engineering and social sciences. Herb Kunze is a professor of mathematics at the University of Guelph in Ontario. Davide La Torre is an associate professor of mathematics in the Department of Economics, Management and Quantitative Methods of the University of Milan. Franklin Mendivil is a professor of mathematics at Acadia University in Nova Scotia. Edward Vrscay is a professor in the department of Applied Mathematics at the University of Waterloo in Ontario. The major focus of their research is on fractals and the applications of fractals.
Author | : K. J. Falconer |
Publisher | : Cambridge University Press |
Total Pages | : 184 |
Release | : 1985 |
Genre | : Mathematics |
ISBN | : 9780521337052 |
Download The Geometry of Fractal Sets Book in PDF, Epub and Kindle
A mathematical study of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Considers questions of local density, the existence of tangents of such sets as well as the dimensional properties of their projections in various directions.
Author | : De-Jun Feng |
Publisher | : Springer |
Total Pages | : 360 |
Release | : 2014-08-01 |
Genre | : Mathematics |
ISBN | : 3662439204 |
Download Geometry and Analysis of Fractals Book in PDF, Epub and Kindle
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.
Author | : Michel Laurent Lapidus |
Publisher | : American Mathematical Soc. |
Total Pages | : 592 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 0821836382 |
Download Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot Book in PDF, Epub and Kindle
This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers--including two articles by Mandelbrot--provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry. In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications. This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.
Author | : Robert S. Strichartz |
Publisher | : Princeton University Press |
Total Pages | : 186 |
Release | : 2018-06-05 |
Genre | : Mathematics |
ISBN | : 0691186839 |
Download Differential Equations on Fractals Book in PDF, Epub and Kindle
Differential Equations on Fractals opens the door to understanding the recently developed area of analysis on fractals, focusing on the construction of a Laplacian on the Sierpinski gasket and related fractals. Written in a lively and informal style, with lots of intriguing exercises on all levels of difficulty, the book is accessible to advanced undergraduates, graduate students, and mathematicians who seek an understanding of analysis on fractals. Robert Strichartz takes the reader to the frontiers of research, starting with carefully motivated examples and constructions. One of the great accomplishments of geometric analysis in the nineteenth and twentieth centuries was the development of the theory of Laplacians on smooth manifolds. But what happens when the underlying space is rough? Fractals provide models of rough spaces that nevertheless have a strong structure, specifically self-similarity. Exploiting this structure, researchers in probability theory in the 1980s were able to prove the existence of Brownian motion, and therefore of a Laplacian, on certain fractals. An explicit analytic construction was provided in 1989 by Jun Kigami. Differential Equations on Fractals explains Kigami's construction, shows why it is natural and important, and unfolds many of the interesting consequences that have recently been discovered. This book can be used as a self-study guide for students interested in fractal analysis, or as a textbook for a special topics course.
Author | : Dietrich Stoyan |
Publisher | : |
Total Pages | : 456 |
Release | : 1994-10-20 |
Genre | : Mathematics |
ISBN | : |
Download Fractals, Random Shapes and Point Fields Book in PDF, Epub and Kindle
There has been an increasing interest in the statistical analysis of geometric objects and structures in many branches of science and engineering in recent years. The aim of this book is to present these statistical methods for practical use by non-mathematicians by outlining the mathematical ideas rather than concentrating on detailed proofs. The clarity of exposition ensures that the book will be a valuable resource for researchers and practitioners in many scientific disciplines who wish to use these methods in their work. In particular, the book is suited to materials scientists, geologists, environmental scientists, and biologists.