Leon Chua is a foreign member of the Academia Europea and a recipient of eight USA patents and 12 docteur honoris causa. He has received numerous international awards, including the first IEEE Kirchhoff Award, the Neural Networks Pioneer Award, and the gTop 15 Cited Authorsh Award based on the ISI Citation Index in Engineering from 1991 to 2001.
When not immersed in science, he relaxes by searching for Wagner's leitmotifs, musing over Kandinsky's chaos, and contemplating Wittgenstein's inner thoughts.
Volume IV continues the author's odyssey on l-D cellular automata as chronicled in Volumes I, II and III, by uncovering a novel quasi-ergodicity phenomenon involving orbits meandering among omega-limit orbits of complex (group 5) and hyper (group 6) Bernoulli rules. This discovery is embellished with analytical formulas characterizing the fractal properties of characteristic functions, as well as explicit formulas for generating colorful and pedagogically revealing isomorphic basin tree diagrams. Many new results were derived and proved by uncovering subtle symmetries endowed by various subsets of the 256 Boolean cubes. For the first time, rigorous analyses were used to identify 67, out off 256 , local rules whose asymptotic behaviors consist of robust period-l orbits. The highlight of this continuing odyssey is the discovery of an isolated period-3240 Isle of Eden hidden among the dense omega-limit orbits of Wolfram's remarkable grandom number generatingh rule 30. This is the largest gem known to-date and readers are challenged to uncover even larger ones.
Contents:
Quasi-Ergodicity
Period-1 Rules
Readership:
Graduate students, researchers and academics interested in nonlinear dynamics, computer science and complexity theory.
400pp (approx.) Pub. date: Scheduled Winter 2010
ISBN: 978-981-4317-30-6
This is a book on many variable calculus. It is the second volume of a set of two. It includes proofs of all theorems presented, either in the text itself, or in an appendix. It also includes a sufficient introduction to linear algebra to allow the accurate presentation of many variable calculus.
The use of elementary linear algebra in presenting the topics of multi- variable calculus is more extensive than usual in this book. It makes many of these topics easier to understand and remember. The book will prepare readers for more advanced math courses and also for courses in physical science.
Supplementary materials are available upon request for all instructors who adopt this book as a course text. Please send your request to sales@wspc.com.
Matrices and Linear Transformations
Determinants
Spectral Theory
Vector Valued Functions
Vector Valued Functions of One Variable
Motion on a Space Curve
Some Curvilinear Coordinate Systems
Functions of Many Variables
The Derivative of a Function of Many Variables
Optimization
The Riemann Integral on ?n
The Integral in Other Coordinates
The Integral on Two Dimensional Surfaces in ?3
Calculus of Vector Fields
Stokes and Green's Theorems
Readership: Undergraduate students in mathematics; individuals who want to learn calculus.
450pp Pub. date: Oct 2010
ISBN: 978-981-4324-27-
ISBN: 978-981-4329-70-5(pbk)
This is a book on single variable calculus including most of the important applications of calculus. It also includes proofs of all theorems presented, either in the text itself, or in an appendix. It also contains an introduction to vectors and vector products which is developed further in Volume 2.
While the book does include all the proofs of the theorems, many of the applications are presented more simply and less formally than is often the case in similar titles.
Supplementary materials are available upon request for all instructors who adopt this book as a course text. Please send your request to sales@wspc.com.
This book is also available as a set with Volume 2: CALCULUS: Theory and Applications.
A Short Review of Precalculus
Functions
Derivatives
Some Important Special Functions
Properties of Derivatives
Applications of Derivatives
Antiderivatives
Applications of Antiderivatives
Other Differential Equations
The Integral
Infinite Series
Fundamentals
Vector Products
Readership: Undergraduate students in mathematics; individuals who want to learn calculus.
550pp Pub. date: Oct 2010
ISBN: 978-981-4324-26-7
ISBN: 978-981-4329-69-9(pbk)
The book provides a systemic treatment of time-dependent strong Markov processes with values in a Polish space. It describes its generators and the link with stochastic differential equations in infinite dimensions. In a unifying way, where the square gradient operator is employed, new results for backward stochastic differential equations and long-time behavior are discussed in depth. The book also establishes a link between propagators or evolution families with the Feller property and time-inhomogeneous Markov processes. This mathematical material finds its applications in several branches of the scientific world, among which are mathematical physics, hedging models in financial mathematics, and population models.
Introduction:
Introduction: Stochastic Differential Equations
Strong Markov Processes:
Strong Markov Processes on Polish Spaces
Strong Markov Processes: Proof on Main Results
Space-Time Operators and Miscellaneous Topics
Backward Stochastic Differential Equations:
Feynman?Kac Formulas, Backward Stochastic Differential Equations and Markov Processes
Viscosity Solutions, Backward Stochastic Differential Equations and Markov Processes
The Hamilton?Jacobi?Bellman Equation and the Stochastic Noether Theorem
Long Time Behavior:
On Non-Stationary Markov Processes and Dunford Projections
Coupling Methods and Sobolev Type Inequalities
Invariant Measure
Readership: Graduate students and researchers in mathematical physics, mathematics and statistics.
800pp (approx.) Pub. date: Nov 2010
ISBN: 978-981-4322-18-8
This monograph presents univariate and multivariate classical analyses of advanced inequalities. This treatise is a culmination of the author's last thirteen years of research work. The chapters are self-contained and several advanced courses can be taught out of this book. Extensive background and motivations are given in each chapter with a comprehensive list of references given at the end.
The topics covered are wide-ranging and diverse. Recent advances on Ostrowski type inequalities, Opial type inequalities, Poincare and Sobolev type inequalities, and Hardy?Opial type inequalities are examined. Works on ordinary and distributional Taylor formulae with estimates for their remainders and applications as well as Chebyshev?Gruss, Gruss and Comparison of Means inequalities are studied.
The results presented are mostly optimal, that is the inequalities are sharp and attained. Applications in many areas of pure and applied mathematics, such as mathematical analysis, probability, ordinary and partial differential equations, numerical analysis, information theory, etc., are explored in detail, as such this monograph is suitable for researchers and graduate students. It will be a useful teaching material at seminars as well as an invaluable reference source in all science libraries.
Readership: Graduate students and researchers in pure mathematics and applied mathematics.
450pp (approx.) Pub. date: Scheduled Winter 2010
ISBN: 978-981-4317-62-7
The book provides a comprehensive overview on the theory on analysis of singularities for partial differential equations (PDEs). It contains a summarization of the formation, development and main results on this topic. Some of the author's discoveries and original contributions are also included, such as the propagation of singularities of solutions to nonlinear equations, singularity index and formation of shocks.
Start of the Study on Analysis of Singularities
Analysis of Singularities for Linear PDEs
Analysis of Singularities for Nonlinear PDEs
Propagation of Singularities for Full Nonlinear Equations
Propagation of Strong Singularities
Formation of Shocks
Readership: Graduate students and researchers interested in analysis and differential equations.
300pp (approx.) Pub. date: Nov 2010
ISBN: 978-981-4304-83-2