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Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.<P>Key Features: <P>- The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings<P>- Complex dimensions of a fractal string, defined as the poles of an associated zeta function, are studied in detail, then used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra<P>- Explicit formulas are extended to apply to the geometric, spectral, and dynamic zeta functions associated with a fractal - Examples of such formulas include Prime Orbit Theorem with error term for self-similar flows, and a tube formula - The method of diophantine approximation is used to study self-similar strings and flows<P>- Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functions<P>Throughout new results are examined. The final chapter gives a new definition of fractality as the presence of nonreal complex dimensions with positive real parts.<P>The significant studies and problems illuminated in this work may be used in a classroom setting at the graduate level. Fractal Geometry, Complex Dimensions and Zeta Functions will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics. 
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$19.22 |
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This book combines prose memoirs supplying context with poems supplying the rhythm and pulse of real lives. Nothing is prettied up, nothing beautiful is toned down, and nothing spiritual is denied. If you think beat poetry is anything else, you haven't read this book. Ferlinghetti says this book is "beater than the Beats." What are you waiting for?
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$15.00 |
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 (5.0 / 5.0) In recent years there has been an explosive growth in the study of physical, biological, and economic systems that can be profitably studies using densities. Because of the general inaccessibility of the mathematical literature to the nonspecialist, little diffusion of the applicable mathematics into the study of these "chaotic" systems has taken place. This book will help bridge that gap. To show how densities arise in simple deterministic systems, the authors give a unified treatment of a variety of mathematical system generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial-differential equations. Examples have been drawn from many fields to illustrate the utility of the concepts and techniques presented, and the ideas in this book should thus prove useful in the study of a number of applied sciences. The authors assume that the reader has a knowledge of advanced calculus and differential equations. Basic concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and stochastic integrals and differential equations are introduced as needed. Physicists, chemists, and biomathematicians studying chaotic behavior will find this book of value. It will also be a useful reference or text for mathematicians and graduate students working in ergodic theory and dynamical systems.
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$101.18 |
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Painter Perry Hall uses a set of experimental techniques that draw upon the organizing principles found in nature. In his Decalcomania paintings, he uses pressure to shape complex networks of interlocking lines and ridges of paint into organic compositions that evoke the notion of 'growing' a painting. In his Livepaintings (time-based paintings), he stimulates paint with temperature changes, vibration, turbulence, and various substances, transforming paint flows into compositions he captures onto video. In the Sound Drawings, sound waves are channeled into a vessel containing oil or acrylics: Hall paints by changing the qualities of the sound, in effect, 'playing' the paint like a musical instrument. His innovative paintings are a fascinating and beautiful collaboration with "material intelligence" and a meditation on the dynamics found in nature. Over 190 full-color reproductions. For more information and images of Hall's paintings: http://www.lovebrain.net/paintings
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$31.58 |
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 (4.5 / 5.0) Benoit Mandelbrot discovered what is now called the M-Set in the early seventies and coined the term fractal to describe the geometry behind it. The power and the beauty of fractals were only capable of being seen with the advent of computers, which become psychedelic windows on the infinite when using simple fractal equations. In 1992 Nigel Lesmoir-Gordon made the TV documentary, The Colors of Infinity about the Mandelbrot Set and fractals, which has since been seen right round the world. Nigel s enthusiasm brought together a dream team of contributors for the film who all now contribute to the book tracking how fractals have developed since the film was made. Sir Arthur C Clarke presented the film and in the book gives a lucidly simple account of the mathematics of the M-Set. Benoit Mandelbrot, the Belgian mathematician explains how it began. Professor Michael Barnsley, the computer graphics researcher who developed fractal image compression technology, explains the applications of the breakthroughs. Professor Ian Stewart, author of Does God Play Dice? adds his insights into the beautifully simple equation that gives birth to fractals. Two of the most interesting applications of fractal geometry, reflected by the two new contributors to the book, are to the Internet and to the Stock Market. Dr Gary Flake, Chief Technology Officer at Overture, the leading provider of commercial search on the Internet and just taken over by Yahoo for 1.6 billion dollars, discusses the profoundly fractal nature of the Web in his article: The Self-ish Web. Robert Prechter Jr is President of Elliott Wave International, Inc. and founder of the Socionomics Institute. His latest title is Socionomics: The Science of History and Social Prediction (2003). He writes about how fractals can help us understand the oscillations of stock markets. In the back of the book is a DVD of the original documentary with soundtrack by David Gilmour of Pink Floyd PLUS a 30-minute fractal animation to the music of members of Quintessence.
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$89.00 |
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(5.0 / 5.0) Fractals are the visual depictions of mathematical equations, the same equations, in fact, that describe natural phenomena such as coastlines, plant shapes and weather patterns. A computer program assigns a color to each point in the image based on the answers to a chosen equation, which then results in abstract fractal shapes. Dozens of variables are manipulated in order to create these fascinating images. Equations representing the images accompany each picture. The Fractal Cosmos 2010 wall calendar features the organic designs of Alice Kelley, who says, Fractals are an intuitive glimpse into the infinite order that comprises the natural world, as well as being proof that math is beautiful.
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$13.99 |
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(5.0 / 5.0) The main theme of this book is the "path integral technique" and its applications to constructive methods of quantum physics. The central topic is probabilistic foundations of the Feynman-Kac formula. Starting with main examples of Gaussian processes (the Brownian motion, the oscillatory process, and the Brownian bridge), the author presents four different proofs of the Feynman-Kac formula. Also included is a simple exposition of stochastic Itô calculus and its applications, in particular to the Hamiltonian of a particle in a magnetic field (the Feynman-Kac-Itô formula).
Among other topics discussed are the probabilistic approach to the bound of the number of ground states of correlation inequalities (the Birman-Schwinger principle, Lieb's formula, etc.), the calculation of asymptotics for functional integrals of Laplace type (the theory of Donsker-Varadhan) and applications, scattering theory, the theory of crushed ice, and the Wiener sausage. <P>Written with great care and containing many highly illuminating examples, this classic book is highly recommended to anyone interested in applications of functional integration to quantum physics. It can also serve as a textbook for a course in functional integration.
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$29.99 |
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(5.0 / 5.0) Fractals are shapes in which an identical motif repeats itself on an ever diminishing scale. A coastline, for instance, is a fractal, with each bay or headland having its own smaller bays and headlands--as is a tree with a trunk that separates into two smaller side branches, which in their turn separate into side branches that are smaller still. No longer mathematical curiosities, fractals are now a vital subject of mathematical study, practical application, and popular interest. For readers interested in graphic design, computers, and science and mathematics in general, Hans Lauwerier provides an accessible introduction to fractals that makes only modest use of mathematical techniques. Lauwerier calls this volume a "book to work with." Readers with access to microcomputers can design new figures, as well as re-create famous examples. They can start with the final chapter, try out one of the programs described there (preferably in a compiled version such as TURBO BASIC), and consult the earlier chapters for whatever is needed to understand the fractals produced in this way. The first chapter, which builds on the relationship of binary number systems to the "tree fractal" described above, is the best place to start if one has no computer. There will be much to enjoy on the way, including the beautiful color illustrations.
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$8.73 |
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 (4.0 / 5.0) Fractal Functions, Fractal Surfaces, and Wavelets is the first systematic exposition of the theory of fractal surfaces, a natural outgrowth of fractal sets and fractal functions. It is also the first treatment to bring these general considerations to bear on the burgeoning field of wavelets. The text is based on Massopusts work on and contributions to the theory of fractal functions, and the author uses a number of tools--including analysis, topology, algebra, and probability theory--to introduce readers to this new subject. Though much of the material presented in this book is relatively current (developed in the past decade by the author and his colleagues) and fairly specialized, an informative background is provided for those <br><br><br>* First systematic treatment of fractal surfaces
* Links fractals and wavelets * Provides background for those entering the field * Contains color insert
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$77.95 |
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This book is for the student to gain a basic understanding o fpattern grading. While the basic concepts of grading are simple, there are intircacies of grading which take professional expertise and many years of epxerience to learn. In this book, the student will learn the essentials of grading patterns.
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$45.00 |