Hypercomplex Iterations

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Hypercomplex Iterations

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Author : Yumei Dang
language : en
Publisher: World Scientific
Release Date : 2002

Hypercomplex Iterations written by Yumei Dang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

Includes an interactive tour of the space of hypercomplex Julia sets and an educational mini-documentary introducing fractals and hypercomplex geometry.

Hypercomplex Iterations Distance Estimation And Higher Dimensional Fractals With Cd Rom

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Author : Yumei Dang
language : en
Publisher: World Scientific
Release Date : 2002-08-06

Hypercomplex Iterations Distance Estimation And Higher Dimensional Fractals With Cd Rom written by Yumei Dang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-06 with Computers categories.

This book is based on the authors' research on rendering images of higher dimensional fractals by a distance estimation technique. It is self-contained, giving a careful treatment of both the known techniques and the authors' new methods. The distance estimation technique was originally applied to Julia sets and the Mandelbrot set in the complex plane. It was justified, through the work of Douady and Hubbard, by deep results in complex analysis. In this book the authors generalise the distance estimation to quaternionic and other higher dimensional fractals, including fractals derived from iteration in the Cayley numbers (octonionic fractals). The generalization is justified by new geometric arguments that circumvent the need for complex analysis. This puts on a firm footing the authors' present work and the second author's earlier work with John Hart and Dan Sandin. The results of this book will be of great interest to mathematicians and computer scientists interested in fractals and computer graphics.

The Self Evolving Cosmos

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Author : Steven M. Rosen
language : en
Publisher: World Scientific
Release Date : 2008

The Self Evolving Cosmos written by Steven M. Rosen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.

This unique book offers an original way of thinking about two of the most significant problems confronting modern theoretical physics: the unification of the forces of nature and the evolution of the universe. In bringing out the inadequacies of the prevailing approach to these questions, the author demonstrates the need for more than just a new theory. The meanings of space and time themselves must be radically rethought, which requires a whole new philosophical foundation. To this end, the book turns to the phenomenological writings of Maurice Merleau-Ponty and Martin Heidegger. Their insights into space and time bring the natural world to life in a manner well-suited to the dynamic phenomena of contemporary physics. In aligning continental thought with problems in physics and cosmology, the book makes use of topology . Phenomenological intuitions about space and time are systematically fleshed out via an unconventional and innovative approach to this qualitative branch of mathematics. The author''s pioneering work in topological phenomenology is applied to such topics as quantum gravity, cosmogony, symmetry, spin, vorticity, dimension theory, Kaluza-Klein and string theories, fermion-boson interrelatedness, hypernumbers, and the mind-matter interface. Sample Chapter(s). Chapter 1: Introduction Individuation and the Quest for Unity (77 KB). Contents: Introduction: Individuation and the Quest for Unity; The Obstacle to Unification in Modern Physics; The Phenomenological Challenge to the Classical Formula; Topological Phenomenology; The Dimensional Family of Topological Spinors; Basic Principles of Dimensional Transformation; Waves Carrying Waves: The Co-Evolution of Lifeworlds; The Forces of Nature; Cosmogony, Symmetry, and Phenomenological Intuition; The Self-Evolving Cosmos; The Psychophysics of Cosmogony. Readership: Philosophically-oriented readers drawn to current developments in physics and cosmology. For academics and scientists dealing with the foundations of physics, the philosophy of science in general, and or contemporary phenomenological thought.

Zero To Infinity The Foundations Of Physics

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Author : Peter Rowlands
language : en
Publisher: World Scientific
Release Date : 2007-10-17

Zero To Infinity The Foundations Of Physics written by Peter Rowlands and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-17 with Science categories.

Unique in its field, this book uses a methodology that is entirely new, creating the simplest and most abstract foundations for physics to date. The author proposes a fundamental description of process in a universal computational rewrite system, leading to an irreducible form of relativistic quantum mechanics from a single operator. This is not only simpler, and more fundamental, but also seemingly more powerful than any other quantum mechanics formalism available. The methodology finds immediate applications in particle physics, theoretical physics and theoretical computing. In addition, taking the rewrite structure more generally as a description of process, the book shows how it can be applied to large-scale structures beyond the realm of fundamental physics.

New Horizons For Second Order Cybernetics

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Author : Alexander Riegler
language : en
Publisher: World Scientific
Release Date : 2017-09-15

New Horizons For Second Order Cybernetics written by Alexander Riegler and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-15 with Computers categories.

In almost 60 articles this book reviews the current state of second-order cybernetics and investigates which new research methods second-order cybernetics can offer to tackle wicked problems in science and in society. The contributions explore its application to both scientific fields (such as mathematics, psychology and consciousness research) and non-scientific ones (such as design theory and theater science). The book uses a pluralistic, multifaceted approach to discuss these applications: Each main article is accompanied by several commentaries and author responses, which together allow the reader to discover further perspectives than in the original article alone. This procedure shows that second-order cybernetics is already on its way to becoming an idea shared by many researchers in a variety of disciplines.

Modern Differential Geometry Of Curves And Surfaces With Mathematica

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Author : Elsa Abbena
language : en
Publisher: CRC Press
Release Date : 2017-09-06

Modern Differential Geometry Of Curves And Surfaces With Mathematica written by Elsa Abbena and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-06 with Mathematics categories.

Presenting theory while using Mathematica in a complementary way, Modern Differential Geometry of Curves and Surfaces with Mathematica, the third edition of Alfred Gray’s famous textbook, covers how to define and compute standard geometric functions using Mathematica for constructing new curves and surfaces from existing ones. Since Gray’s death, authors Abbena and Salamon have stepped in to bring the book up to date. While maintaining Gray's intuitive approach, they reorganized the material to provide a clearer division between the text and the Mathematica code and added a Mathematica notebook as an appendix to each chapter. They also address important new topics, such as quaternions. The approach of this book is at times more computational than is usual for a book on the subject. For example, Brioshi’s formula for the Gaussian curvature in terms of the first fundamental form can be too complicated for use in hand calculations, but Mathematica handles it easily, either through computations or through graphing curvature. Another part of Mathematica that can be used effectively in differential geometry is its special function library, where nonstandard spaces of constant curvature can be defined in terms of elliptic functions and then plotted. Using the techniques described in this book, readers will understand concepts geometrically, plotting curves and surfaces on a monitor and then printing them. Containing more than 300 illustrations, the book demonstrates how to use Mathematica to plot many interesting curves and surfaces. Including as many topics of the classical differential geometry and surfaces as possible, it highlights important theorems with many examples. It includes 300 miniprograms for computing and plotting various geometric objects, alleviating the drudgery of computing things such as the curvature and torsion of a curve in space.

Introductory Lectures On Knot Theory

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Author : Louis H. Kauffman
language : en
Publisher: World Scientific
Release Date : 2012

Introductory Lectures On Knot Theory written by Louis H. Kauffman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book.

Mathematics Of Harmony As A New Interdisciplinary Direction And Golden Paradigm Of Modern Science Volume 1 The Golden Section Fibonacci Numbers Pascal Triangle And Platonic Solids

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Author : Alexey Stakhov
language : en
Publisher: World Scientific
Release Date : 2020-05-05

Mathematics Of Harmony As A New Interdisciplinary Direction And Golden Paradigm Of Modern Science Volume 1 The Golden Section Fibonacci Numbers Pascal Triangle And Platonic Solids written by Alexey Stakhov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-05 with Mathematics categories.

Volume I is the first part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.

Woods Hole Mathematics

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Author : Nils Tongring
language : en
Publisher: World Scientific
Release Date : 2004

Woods Hole Mathematics written by Nils Tongring and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

The central theme of this volume is the contemporary mathematics of geometry and physics, but the work also discusses the problem of the secondary structure of proteins, and an overview of arc complexes with proposed applications to macromolecular folding is given. OC Woods Hole has played such a vital role in both my mathematical and personal life that it is a great pleasure to see the mathematical tradition of the 1964 meeting resurrected forty years later and, as this volume shows, resurrected with new vigor and hopefully on a regular basis. I therefore consider it a signal honor to have been asked to introduce this volume with a few reminiscences of that meeting forty years ago.OCO Introduction by R Bott (Wolf Prize Winner, 2000)."

An Excursion In Diagrammatic Algebra

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Author : J. Scott Carter
language : en
Publisher: World Scientific
Release Date : 2012

An Excursion In Diagrammatic Algebra written by J. Scott Carter and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

1. A sphere -- 2. Surfaces, folds, and cusps -- 3. The inside and outside -- 4. Dimensions -- 5. Immersed surfaces -- 6. Movies -- 7. Movie moves -- 8. Taxonomic summary -- 9. How not to turn the sphere inside-out -- 10. A physical metaphor -- 11. Sarah's thesis -- 12. The eversion -- 13. The double point and fold surfaces