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The Geometry Of Fractal Sets

Author : K. J. Falconer
ISBN : 0521337054
Genre : Mathematics
File Size : 63.91 MB
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This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of such sets are studied, as well as the dimensional properties of their projections in various directions. In the case of sets of integral dimension the dramatic differences between regular 'curve-like' sets and irregular 'dust like' sets are exhibited. The theory is related by duality to Kayeka sets (sets of zero area containing lines in every direction). The final chapter includes diverse examples of sets to which the general theory is applicable: discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, convexity and so on. There is an emphasis on the basic tools of the subject such as the Vitali covering lemma, net measures and Fourier transform methods.
Category: Mathematics

Fractal Geometry And Applications Analysis Number Theory And Dynamical Systems

Author : Benoit B. Mandelbrot
ISBN : 9780821836378
Genre : Ergodic theory
File Size : 35.60 MB
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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.
Category: Ergodic theory

Fractal Geometry And Stochastics Iii

Author : Christoph Bandt
ISBN : 9783034878913
Genre : Mathematics
File Size : 40.2 MB
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This up-to-date monograph, providing an up-to-date overview of the field of Hepatitis Prevention and Treatment, includes contributions from internationally recognized experts on viral hepatitis, and covers the current state of knowledge and practice regarding the molecular biology, immunology, biochemistry, pharmacology and clinical aspects of chronic HBV and HCV infection. The book provides the latest information, with sufficient background and discussion of the literature to benefit the newcomer to the field.
Category: Mathematics

Fractals In Probability And Analysis

Author : Christopher J. Bishop
ISBN : 9781107134119
Genre : Mathematics
File Size : 61.64 MB
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This is a mathematically rigorous introduction to fractals which emphasizes examples and fundamental ideas. Building up from basic techniques of geometric measure theory and probability, central topics such as Hausdorff dimension, self-similar sets and Brownian motion are introduced, as are more specialized topics, including Kakeya sets, capacity, percolation on trees and the traveling salesman theorem. The broad range of techniques presented enables key ideas to be highlighted, without the distraction of excessive technicalities. The authors incorporate some novel proofs which are simpler than those available elsewhere. Where possible, chapters are designed to be read independently so the book can be used to teach a variety of courses, with the clear structure offering students an accessible route into the topic.
Category: Mathematics

Graph Directed Markov Systems

Author : R. Daniel Mauldin
ISBN : 0521825385
Genre : Mathematics
File Size : 39.50 MB
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Monograph on Graph Directed Markov Systems with backgound and research level material.
Category: Mathematics

Analysis On Fractals

Author : Jun Kigami
ISBN : 0521793211
Genre : Mathematics
File Size : 50.37 MB
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Self-contained introduction to analysis on fractals, a developing area of mathematics, for graduates and researchers.
Category: Mathematics

Taehan Suhakhoe Hoebo

Author :
ISBN : UOM:39015068671299
Genre : Mathematics
File Size : 22.15 MB
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Category: Mathematics