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This textbook is intended to supplement the classical theory of uni- and multivariate splines and their approximation and interpolation properties with those of fractals, fractal functions, and fractal surfaces. This synthesis will complement currently required courses dealing with these topics and expose the prospective reader to some new and deep relationships. In addition to providing a classical introduction to the main issues involving approximation and interpolation with uni- and multivariate splines, cardinal and exponential splines, and their connection to wavelets and multiscale analysis, which comprises the first half of the book, the second half will describe fractals, fractal functions and fractal surfaces, and their properties. This also includes the new burgeoning theory of superfractals and superfractal functions. The theory of splines is well-established but the relationship to fractal functions is novel. Throughout the book, connections between these two apparently different areas will be exposed and presented. In this way, more options are given to the prospective reader who will encounter complex approximation and interpolation problems in real-world modeling. Numerous examples, figures, and exercises accompany the material.
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$62.03 |
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 (4.5 / 5.0) UNDERSTANDING NONLINEAR DYNAMICS is based on an undergraduate course taught for many years to students in the biological sciences. The text provides a clear and accessible development of many concepts from contemporary dynamics, including stability and multistability, cellular automata and excitable media, fractals, cycles, and chaos. A chapter on time-series analysis builds on this foundation to provide an introduction to techniques for extracting information about dynamics from data. The text will be useful for courses offered in the life sciences or other applied science programs, or as a supplement to emphasize the application of subjects presented in mathematics or physics courses. Extensive examples are derived from the experimental literature, and numerous exercise sets can be used in teaching basic mathematical concepts and their applications. Concrete applications of the mathematics are illustrated in such areas as biochemistry, neurophysiology, cardiology, and ecology. The text also provides an entry point for researchers not familiar with mathematics but interested in applications of nonlinear dynamics to the life sciences.
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$34.00 |
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 (5.0 / 5.0) The only integrative approach to chaos and random fractal theory
Chaos and random fractal theory are two of the most important theories developed for data analysis. Until now, there has been no single book that encompasses all of the basic concepts necessary for researchers to fully understand the ever-expanding literature and apply novel methods to effectively solve their signal processing problems. Multiscale Analysis of Complex Time Series fills this pressing need by presenting chaos and random fractal theory in a unified manner. <p> Adopting a data-driven approach, the book covers: Additionally, the book illustrates almost every concept presented through applications and a dedicated Web site is available with source codes written in various languages, including Java, Fortran, C, and MATLAB, together with some simulated and experimental data. The only modern treatment of signal processing with chaos and random fractals unified, this is an essential book for researchers and graduate students in electrical engineering, computer science, bioengineering, and many other fields.
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$61.05 |
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 (3.5 / 5.0) Fractal geometry is the geometry of the natural world. It mirrors the uneven but real shapes of nature, the world as we actually experience it. Introducing Fractal Geometry traces the development of this revolutionary new discipline.
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$107.22 |
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 (4.0 / 5.0) Colene and her multi-dimensional allies must help fulfill a prophecy in Nona's male-dominated universe. But first, Nona herself must cross dimensions to a world more unpredictable than any she has encountered--a world called Earth.
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$3.18 |
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(5.0 / 5.0) Historically, the language and concepts within clinical theory have been steeped in linear assumptions and reductionist thinking. Because the essence of psychotherapy involves change, <EM>Psyche’s Veil suggests that clinical practice is inherently a nonlinear affair. In this book Terry Marks-Tarlow provides therapists with new language, models and metaphors to narrow the divide between theory and practice, while bridging the gap between psychology and the sciences. By applying contemporary perspectives of chaos theory, complexity theory and fractal geometry to clinical practice, the author discards traditional conceptions of health based on ideals of regularity, set points and normative statistics in favour of models that emphasize unique moments, variability, and irregularity. Psyche’s Veil further explores philosophical and spiritual implications of contemporary science for psychotherapy. Written at the interface between artistic, scientific and spiritual aspects of therapy, <EM>Psyche’s Veil is a case-based book that aspires to a paradigm shift in how practitioners conceptualize critical ingredients for internal healing. Novel treatment of sophisticated psychoanalytical issues and tie-ins to interpersonal neurobiology make this book appeal to both the specialist practitioner, as well as the generalist reader.<P><P>. <P>
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$35.53 |
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Establishing a new genre of musical analysis, this book goes beyond the usual analysis of chord symbols and period forms to examine such topics as: Fibonacci number and golden mean proportions, Statistics for distinguishing among styles, Self-similarity in form. This second edition includes many new illustrations and concepts, including: Orbit drawings of attractors, Correlation coefficients, Melodic dimensions. It is intended for readers with little mathematical background and requires only algrebra and trigonometry.
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$50.00 |
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(4.0 / 5.0) Published in cooperation with the National Council of Teachers of Mathematics, this text is based on lectures given to various communities of teachers and students. Written especially for teachers and intended for classroom use at high school and college levels, the book also can be used for independent study.
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$24.99 |
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(4.5 / 5.0) Concepts, methods and techniques of statistical physics in the study of correlated, as well as uncorrelated, phenomena are being applied ever increasingly in the natural sciences, biology and economics in an attempt to understand and model the large variability and risks of phenomena. This is the first textbook written by a well-known expert that provides a modern up-to-date introduction for workers outside statistical physics. The emphasis of the book is on a clear understanding of concepts and methods, while it also provides the tools that can be of immediate use in applications. Although this book evolved out of a course for graduate students, it will be of great interest to researchers and engineers, as well as to post-docs in geophysics and meteorology.
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$55.14 |
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(3.5 / 5.0) The study of nonlinear dynamical systems has advanced tremendously in the last 20 years, making a big impact on science and technology. This book provides all the techniques and methods used in nonlinear dynamics. The concepts and underlying mathematics are discussed in detail.
The numerical and symbolic methods are implemented in C++, SymbolicC++ and Java. Object-oriented techniques are also applied. The book contains more than 150 ready-to-run programs. The text has also been designed for a one-year course at both the junior and senior levels in nonlinear dynamics. The topics discussed in the book are part of e-learning and distance learning courses conducted by the International School for Scientific Computing, University of Johannesburg. Contents: Nonlinear and Chaotic Maps; Time Series Analysis; Autonomous Systems in the Plane; Nonlinear Hamilton Systems; Nonlinear Dissipative Systems; Nonlinear Driven Systems; Controlling of Chaos; Synchronization of Chaos; Fractals; Cellular Automata; Solving Differential Equations; Neural Networks; Genetic Algorithms; Gene Expression Programming; Optimization; Discrete Wavelets; Discrete Hidden Markov Processes; Fuzzy Sets and Fuzzy Logic.
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$48.99 |