This volume includes the best papers presented at the CHAOS 2008 International Conference on Chaotic Modeling, Simulation and Applications. It provides a valuable collection of new ideas, methods, and techniques in the field of nonlinear dynamics, chaos, fractals and their applications in general science and in engineering sciences.
It touches on many fields such as chaos, dynamical systems, nonlinear systems, fractals and chaotic attractors. It also covers mechanics, hydrofluid dynamics, chaos in meteorology and cosmology, Hamiltonian and quantum chaos, chaos in biology and genetics, chaotic control, and chaos in economy and markets, and chaotic simulations; thus, containing cutting-edge interdisciplinary research with high-interest applications.
These contributions present new solutions by analyzing the relevant data and through the use of recent advances in different fields, especially in chaotic simulation methods and techniques.
Chaos and Dynamical Systems
Nonlinear Systems
Fractals
Chaotic Attractors
Mechanics
Hydrofluid Dynamics
Chaotic Advection
Chaos in Meteorology and Cosmology
Bifurcation
Hamiltonian and Quantum Chaos
Plasma Physics
Chaos in Biology and Genetics
Chaos in Medicine and Physiology
Chaotic Control
Time Series Analysis and Forecasting Chaotic Systems
Chaos in Economy and Markets
Traffic Flow
Chaotic Simulations
Readership: Mathematicians, physicists, economists, general scientists and engineers.
436pp Pub. date: May 2009
ISBN: 978-981-4271-33-2
This book highlights various topics on measure theory and vividly demonstrates that the different questions of this theory are closely connected with the central measure extension problem. Several important aspects of the measure extension problem are considered separately: set-theoretical, topological and algebraic. Also, various combinations (e.g., algebraic-topological) of these aspects are discussed by stressing their specific features. Several new methods are presented for solving the above mentioned problem in concrete situations. In particular, the following new results are obtained: the measure extension problem is completely solved for invariant or quasi-invariant measures on solvable uncountable groups; non-separable extensions of invariant measures are constructed by using their ergodic components; absolutely non-measurable additive functionals are constructed for certain classes of measures; the structure of algebraic sums of measure zero sets is investigated.
The material presented in this book is essentially self-contained and is oriented towards a wide audience of mathematicians (including postgraduate students). New results and facts given in the book are based on (or closely connected with) traditional topics of set theory, measure theory and general topology such as: infinite combinatorics, Martin's Axiom and the Continuum Hypothesis, Luzin and Sierpinski sets, universal measure zero sets, theorems on the existence of measurable selectors, regularity properties of Borel measures on metric spaces, and so on. Essential information on these topics is also included in the text (primarily, in the form of Appendixes or Exercises), which enables potential readers to understand the proofs and follow the constructions in full details. This not only allows the book to be used as a monograph but also as a course of lectures for students whose interests lie in set theory, real analysis, measure theory and general topology.
The Problem of Extending Partial Functions
Some Aspects of the Measure Extension Problem
Invariant Measures
Quasi-Invariant Measures
Measurability Properties of Real-Valued Functions
Some Properties of Step-Functions Connected with Extensions of Measures
Almost Measurable Real-Valued Functions
Several Facts From General Topology
Weakly Metrically Transitive Measures
Non-Measurable Subgroups of Uncountable Solvable Groups
Algebraic Sums of Measure Zero Sets
The Absolute Non-Measurability of Minkowski's Sum of Certain Universal Measure Zero Sets
Absolutely Non-Measurable Additive Sierpinski?Zygmund Functions
Relatively Measurable Sierpinski?Zygmund Functions
A Non-Separable Extension of the Lebesgue Measure without New Null-Sets
Metrical Transitivity and Non-Separable Extensions of Invariant Measures
Non-Separable Left Invariant Measures on Uncountable Solvable Groups
Universally Measurable Additive Functionals
Some Subsets of the Euclidean Plane
Restrictions of Functions
Appendices:
Some Set-Theoretical Facts and Constructions
Measurable Selectors
Borel Measures on Metric Spaces
Continuous Nowhere Approximately Differentiable Functions
Some Facts About Commutative Groups
Elements of Descriptive Set Theory
Readership: This book is written for a wide audience of mathematicians, including academics and postgraduate students. The book is self-contained and can be used as a textbook for set theory, real analysis, measure theory and general topology.
420pp Pub. date: May 2009
ISBN: 978-90-78677-20-8
Professor Kuang-Chao Chou (also known as Guang-Zhao Zhou) is the former President of Chinese Academy of Sciences. He has been elected as the Academician of Chinese Academy of Sciences, Foreign Associate of the US National Academy of Sciences, Fellow of the Third World Academy of Science, Foreign Member of Soviet (Russian) Academy of Sciences, Czechoslovak Academy of Sciences, Bulgarian Academy of Sciences, Romania Academy of Sciences, Mongolian Academy of Sciences, the European Academy of Arts, Sciences and Humanities, Membre fondateur Academie Francophone d'Ingenieurs.
He also served as the director of Institute of Theoretical Physics at the Chinese Academy of Sciences, the Dean of the Science School of Tsinghua University, the Chairman of the China Association for Sciences and Technology, the President of Pacific Science Association, Vice President of Third World Academy of Sciences.
hZhou is a first rate physicist: broad, powerful and very quick in grasping new ideas. His style of doing physics reminds me of that of Landau, Salam, and of Teller.h
C N Yang
hHis published papers have won uniformly high praises by the international scientific community and his articles are always written with depth and elegance.h
T D Lee
This volume presents a collection of selected papers written by Prof Chou. The papers are organized into four parts according to the subject of research areas and the language of publishing journals. Part I (in English) and Part III (in Chinese) are papers on field theories, particle physics and nuclear physics, Part II (in English) and Part IV (in Chinese) are papers on statistical physics and condensed matter physics. From the published papers, it illustrates and is clearly evident how Prof Chou was constantly at the frontiers of theoretical physics in various periods and carried out creative research works experimenting with initial ideas and motivations, as well as how he has driven and worked in different key research directions of theoretical physics, all for which he has made significant contributions to various interesting research areas and interdisciplinary fields.
Particle Physics
Field Theory
Nuclear Physics
Condensed Matter Physics
Statistical Physics
Partial Conservation of Axial Current
Nonlinear Sigma Models in Symmetric Coset and Curved Spaces
U(1) Anomaly
Chiral Dynamical Theory
Topological Origin of Yang-Mills Gauge Anomalies
Phenomenology of Weak Interaction
Closed Time Path Green's Function
Spontaneous Symmetry Breaking and Time Reversal Invariance in the Nonequilibrium System
CP Violation
Origin of Mass
Neutrino Physics
Super-Symmetric Theory
Low Energy Phenomena of Grand Unification Theory
Readership: Physicists, graduate students and researchers interested in physics.
1136pp Pub. date: May 2009
ISBN: 978-981-4280-37-2
Volume III continues the author's quest for developing a pedagogical, self-contained, yet rigorous analytical theory of 1-D cellular automata via a nonlinear dynamics perspective. Using carefully conceived and illuminating color graphics, the global dynamical behaviors of the 50 (out of 256) local rules that have not yet been covered in Volumes I and II are exposed via their stunningly revealing basin tree diagrams. The Bernoulli ĐŃ-shift dynamics discovered in Volume II is generalized to hold for all 50 (or 18 globally equivalent) local rules via complex and hyper Bernoulli wave dynamics. Explicit global state transition formulas derived for rules 60, 90, 105, and 150 reveal a new scale-free phenomenon. The most surprising new result unveiled in this volume is the gIsle of Edenh found hidden in most (almost 90%) of the 256 local rules. Readers are challenged to hunt for long-period, isolated Isles of Eden. These are rare gems waiting to be discovered.
Readership: Graduate students, researchers and academics interested in nonlinear dynamics, computer science and complexity theory.
350pp Pub. date: Jun 2009
ISBN: 978-981-283-793-6
This book contains the contributions by the participants in the nine of a series of workshops. Throughout the series of workshops, the contributors are consistently aiming at higher achievements of studies of the current topics in complex analysis, differential geometry and mathematical physics and further in any intermediate areas, with expectation of discovery of new research directions. Concerning the present one, it is worthwhile to mention that, in addition to the new developments of the traditional trends, many attractive and pioneering works were presented and their results were contributed to the present volume. The contents of this volume therefore will provide not only significant and useful information for researchers in complex analysis, differential geometry and mathematical physics (including their related areas), but also interesting mathematics for non-specialists and a broad audience. The present volume contains new developments and trends in the studies on constructions of holomorphic Cliffordian functions; the swelling constructions of minimal surfaces with higher genus in flat tori; the spectral properties of soliton equations on symmetric spaces; new types of shallow water waves described by Camassa?Holm type equations, the properties of pseudo-hermitian boson and fermion coherent states; fractals and chaos on orthorhombic lattices, and even an ambitious proposal of a graph model for Kaehler manifolds with Kaehler magnetic fields.
A Discrete Model for Kaehler Magnetic Fields on a Complex Hyperbolic Space
A Characterization of Clifford Minimal Hypersurfaces of a Sphere in Terms of Their Geodesics
Hyperbolic Gauss Maps and Parallel Surfaces in Hyperbolic Three-Space
Generalizations of Conjugate Connections
Heisenberg Relations in the General Case
A Short Note on the Double-Complex Laplace Operator
Monogenic, Hypermonogenic and Holomorphic
Cliffordian Functions ? A Survey
On Multicomponent Evolution Equations on Symmetric Spaces with Constant Boundary Conditions
Relativistic Strain and Electromagnetic Photon-Like Objects
Cyclic Hyper-Scalar Systems
Poisson Structures of Equations Associated with Groups of Diffeomorphisms
On the Lax Pair for Two and Three Wave Interaction System
New Integrable Equations of MKdV Type
Persistence of Solutions for Some Integrable Shallow Water Equations
Mathematical Outlook of Fractals and Chaos Related to Simple Orthorhombic Ising?Onsager?Zhang Lattices
Readership: Graduate students and researchers in analysis, differential geometry and mathematical physics including their intermediate fields.
300pp Pub. date: Jul 2009
ISBN: 978-981-4277-71-6