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Computer Mathematics
This volume covers some of the most recent and significant advances in computer mathematics, including algebraic, symbolic, numeric and geometric computation, automated mathematical reasoning, mathematical software and computer-aided geometric design. Researchers, engineers, academics and graduate students interested in doing mathematics using computers will find this volume good reading and a valuable reference. Contents: Solution of a Linear Differential Equations in the Form of Power Series and Its Application (T Kitamoto); On the Specification for Solvers of Polynomial Systems (D Lazard); OMEI: An Open Mathematical Engine Interface (W Liao et al.); Polynomial Solutions of Algebraic Diffe...
Computer Mathematics
This volume contains selected papers presented at the Fourth Asian Symposium on Computer Mathematics. There are 39 peer-reviewed contributions together with full papers and extended abstracts by the four invited speakers, G.H. Gonnet, D. Lazard, W. McCune and W.-T. Wu, and these cover some of the most significant advances in computer mathematics, including algebraic, symbolic, numeric and geometric computation, automated mathematical reasoning, mathematical software, and computer-aided geometric design.
Chaotic Maps
This book consists of lecture notes for a semester-long introductory graduate course on dynamical systems and chaos taught by the authors at Texas A&M University and Zhongshan University, China. There are ten chapters in the main body of the book, covering an elementary theory of chaotic maps in finite-dimensional spaces. The topics include one-dimensional dynamical systems (interval maps), bifurcations, general topological, symbolic dynamical systems, fractals and a class of infinite-dimensional dynamical systems which are induced by interval maps, plus rapid fluctuations of chaotic maps as a new viewpoint developed by the authors in recent years. Two appendices are also provided in order t...
Chaos In Nature (Second Edition)
This book is devoted to the history of chaos theory, from celestial mechanics (three-body problem) to electronics and meteorology. Many illustrative examples of chaotic behaviors exist in various contexts found in nature (chemistry, astrophysics, biomedicine). This book includes the most popular systems from chaos theory (Lorenz, Rössler, van der Pol, Duffing, logistic map, Lozi map, Hénon map etc.) and introduces many other systems, some of them very rarely discussed in textbooks as well as in scientific papers. The contents are formulated with an original approach as compared to other books on chaos theory.
Encounters with Chaos and Fractals, Second Edition
Now with an extensive introduction to fractal geometry Revised and updated, Encounters with Chaos and Fractals, Second Edition provides an accessible introduction to chaotic dynamics and fractal geometry for readers with a calculus background. It incorporates important mathematical concepts associated with these areas and backs up the definitions and results with motivation, examples, and applications. Laying the groundwork for later chapters, the text begins with examples of mathematical behavior exhibited by chaotic systems, first in one dimension and then in two and three dimensions. Focusing on fractal geometry, the author goes on to introduce famous infinitely complicated fractals. He analyzes them and explains how to obtain computer renditions of them. The book concludes with the famous Julia sets and the Mandelbrot set. With more than enough material for a one-semester course, this book gives readers an appreciation of the beauty and diversity of applications of chaotic dynamics and fractal geometry. It shows how these subjects continue to grow within mathematics and in many other disciplines.
Lectures on Fractal Geometry and Dynamical Systems
Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These two areas interact with each other and with the theory of chaos in a fundamental way: many dynamical systems (even some very simple ones) produce fractal sets, which are in turn a source of irregular 'chaotic' motions in the system. This book is an introduction to these two fields, with an emphasis on the relationship between them. The first half of the book introduces some of the key ideas in fractal geometry and dimension theory - Cantor sets, Hausdorff dimension, box dimension - using dynamical notions ...
Collisions, Rings, and Other Newtonian $N$-Body Problems
The fourth chapter analyzes collisions, while the last chapter discusses the likelihood of collisions and other events."--Jacket.
Developing Capacity for Innovation in Complex Systems
Based on a theoretical analysis and supported by both explorative qualitative and quantitative research, this book examines the many reasons why an initiative becomes an innovation and why some organizations are better at innovation than others. Developing Capacity for Innovation in Complex Systems offers insights into the history of the idea of innovation, as well as knowledge around different discourses on innovation. The purpose of this book is to help organisations further their aspirations and work with innovation. It is based on three premises: (1) that capacity can be developed, (2) that it is worthwhile trying to do so, and (3) there are however no guarantees for success. Providing a...
Social Networks in the History of Innovation and Invention
This book integrates history of science and technology with modern social network theory. Using examples from the history of machines, as well as case studies from wireless, radio and chaos theory, the author challenges the genius model of invention. Network analysis concepts are presented to demonstrate the societal nature of invention in areas such as steam power, internal combustion engines, early aviation, air conditioning and more. Using modern measures of network theory, the author demonstrates that the social networks of invention from the 19th and early 20th centuries have similar characteristics to modern 21st C networks such as the World Wide Web. The book provides evidence that exponential growth in technical innovation is linked to the growth of historical innovation networks.
Complex Adaptive Leadership
Complex Adaptive Leadership argues leadership should not be something only exercised by nominated leaders. It is a complex dynamic process involving all those engaged in a particular enterprise. The theoretical background to this lies in complexity science and chaos theory - spoken and written about in the context of leadership for the last 20 years, but still little understood. We all seem intuitively to know leadership 'isn't what it used to be' but we still cling to old assumptions which look anachronistic in changing and challenging times. Organisations and their contexts are increasingly paradoxical and uncertain. A broader approach to leadership is needed. Nick Obolensky has practised ...
