Gaussian Self-Affinity and Fractals: Globality, The Earth, 1/f Noise, and R/S

Autor Benoit Mandelbrot F.J. Damerau, M. Frame, K. McCamy, J.W. Van Ness, J.R. Wallis

en Limba Engleză Hardback – 13 dec 2001

This third volume of the Selected Works focusses on a detailed study of fraction Brownian motions. The fractal themes of "self-affinity" and "globality" are presented, while extensive introductory material, written especially for this book, precedes the papers and presents a number of striking new observations and conjectures. The mathematical tools so discussed will be valuable to diverse scientific communities.

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Specificații

ISBN-13: 9780387989938
ISBN-10: 0387989935
Pagini: 654
Ilustrații: X, 654 p.
Dimensiuni: 155 x 235 x 37 mm
Greutate: 1.1 kg
Ediția:2002
Editura: Springer
Colecția Springer
Locul publicării:New York, NY, United States

Public țintă

Research

Descriere

Benoit Mandelbrot¿s pioneering research in fractal geometry has affected many areas of mathematics, physics, finance and other disciplines. The papers reprinted in this third volume of his Selected Works center on a detailed study of fractional Brownian functions, best known as the mathematical tools behind the celebrated fractal landscapes. Extensive introductory material preceding the reprints incorporates striking new observations and conjectures. This book explores the fractal themes of ¿self-affinity¿ and ¿globality.¿ The ubiquity of ¿wild¿ temporal and spatial variability led Mandelbrot, in the early 1960¿s, to conclude that those phenomena lie beyond the usual statistical techniques and represent a new state of indeterminism. New mathematical tools are needed, and this book contributes to their development.

Cuprins

Advances in Old But Open Topics * Broad Continuing Issues * Introductions from the 1960s * Fractional Brownian Motions * Fractional Brownian Surfaces * Self-Affine Cartoons in Grids; Their Multiple Fractal Dimensions * R/S Analysis and Its Uses

Recenzii

From the reviews of the first edition:
"Written in Mandelbrot’s unique, thought-provoking style, these papers and commentaries contain a wealth of ideas which will appeal to mathematicians, statisticians, scientists and economists alike. It is a book both for dipping into and for detailed study, making readily accessible seminal papers which contain ideas that are as relevant now as when first published." (K. Falconer, Proceedings of the Edinburgh Mathematical Society, Vol. 48, 2005)
"This book contains the author’s works in areas ranging from statistics, mathematics, physics, hydrology to economics and finance … as well as more than 200 pages of new material written especially for this volume. … To summarize, Volume H of Mandelbrot’s Selecta is a major contribution to the understanding of wild self-affine variability and randomness. I believe that … it will have a great impact on future research in mathematics, statistics, physics and other applied areas." (Yimin Xiao, Zentralblatt MATH, Vol. 1007, 2003)
"This book is a complete and encyclopaedic synthesis of problems and themes in self-affinity, fractals, multifractal geometry and globality. … a very exhaustive and complete bibliography on the different connected subjects (with more than 500 references) may be very useful for researchers or users." (Michèle Mastrangelo-Dehen, Mathematical Reviews, Issue 2003 a)
"This volume is volume H of a program of publications of selected works (old and new) of Benoit B. Mandelbrot. … The most valuable feature of the book is to bring together highly important papers … for this reason this book should be in the library of any scientist interested in the origin of the concepts of self-affinity and fractals and their numerous applications in science." (Christian Michaux, Simon Stevin Bulletin, 2003)

Caracteristici

3rd volume in the series of Mandelbrot's Selecta
Extensive introductory material
Striking new observations and conjectures
Valuable mathematical tool for diverse scientific communities

Papetărie, jocuri, reviste