“…Pedagogical benefits can be found in the large number of Maple programs, some of which are analogous to C++ programs, including those for splines and fractals. To avoid tedious typing, readers will be able to download many of the programs from the Birkhauser web site. …”
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“…All kinds of singular interactions described by potentials supported on small sets (like the Dirac δ-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. …”
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“…Along the way, he offers intimate biographical sketches of celebrated and neglected thinkers, from the physicist Emmy Noether to the computing pioneer Alan Turing and the discoverer of fractals, Benoit Mandelbrot. Holt offers a painless and playful introduction to many of our most beautiful but least understood ideas, from Einsteinian relativity to string theory, and also invites us to consider why the greatest logician of the twentieth century believed the U.S. …”
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“…Methods discussed in the book are subsequently used to solved problems arising in many fields of science, technology, and engineering, including epidemiology, chaos, solitons, fractals, diffusion, groundwater, and fluid mechanics. …”
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“…We discover bacterial calcium fluctuations are temporal-fractals resulting from a property known as self-organized criticality (SOC). …”
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“…New concepts, such as artificial neural networks, fuzzy logic, evolutionary algorithms, chaos and fractals, cellular automata, etc., are being more commonly used to analyse ecosystem databases and to make predictions for river management purposes. …”
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“…Here, because the spatial distribution of mineral deposits has been postulated to be fractals (i.e., the patterns of these features are self-similar across a range of spatial scales), we show for the first time that micro-geochemical anomalies (as proxies of micro-scale patterns of ore minerals), from few discrete parts of the Sossego iron-oxide copper-gold (IOCG) deposit in the Carajás Mineral Province (CMP) of Brazil, exhibit trends of macro-scale faults that are known to have controlled IOCG mineralization in the CMP. …”
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“…In order to allow polymer melts and solutions to be discussed, a short chapter acquaints readers with scaling concepts by discussing random walks and fractals. Part II of the lecture series is essentially devoted to the presentation of the dynamics of simple and complex liquids in terms of the generalized hydrodynamics concept, such as that introduced by Mori and Zwanzig. …”
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“…In particular, let us mention the emergence of some "new" concepts (such as fractals, scaling laws, finite size effects, and so on) in this field. …”
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“…This textbook takes the reader on a tour of the most important landmarks of theoretical physics: classical, quantum, and statistical mechanics, relativity, electrodynamics, as well as the most modern and exciting of all: elementary particles and the physics of fractals. The second edition has been supplemented with a new chapter devoted to concise though complete presentation of dynamical systems, bifurcations and chaos theory. …”
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“…Others explore the beauty of fractals, or examine endless possibilities of applications to problems of physics, chemistry, biology and other sciences. …”
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“…What if it were possible to use that same framework to generalize the complex numbers or fractals to any dimension, to play with geometry on a computer, as well as to make calculations in robotics, ray-tracing and brain science? …”
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