470pp (approx.) Pub. date: Feb 2012
ISBN: 978-981-4368-89-6
ISBN: 978-981-4368-90-2(pbk)
This is a twenty-first century book designed to meet the challenges of understanding and solving interdisciplinary problems. The book creatively incorporates gcutting-edgeh research ideas and techniques at the undergraduate level. The book also is a unique research resource undergraduate/graduate students and interdisciplinary researchers. It emphasizes and exhibits the importance of conceptual understandings and its symbiotic relationship in the problem solving process.
The book is proactive in preparing for the modeling of dynamic processes in various disciplines. It introduces a gbreak-down-the problemh type of approach in a way that creates gfunh and gexcitementh. The book presents many learning tools like gstep-by-step procedures (critical thinking)h, the concept of gmathh being a language, applied examples from diverse fields, frequent recaps, flowcharts and exercises. Uniquely, this book introduces an innovative and unified method of solving nonlinear scalar differential equations. This is called the gEnergy/Lyapunov Function Methodh. This is accomplished by adequately covering the standard methods with creativity beyond the entry level differential equations course.
Problem Solving Process
Algebra of Matrices
Determinants
Matrix Calculus
Mathematical Modeling
Integrable Differential Equations
Linear Homogeneous Equations
Linear Non homogeneous Equations
Energy Function Method
Reduced Linear Differential Equations
Variable Separable, Homogeneous, Bernoulli, and Essentially Time-Invariant Differential Equations
Linear Homogeneous Systems
Procedure of Finding Fundamental Matrix Solution
General Linear Homogeneous Systems
Linear Non homogeneous Systems
Companion system
The Laplace Transform
Applications of Laplace Transform
Fundamental Conceptual Algorithms and Analysis
Method of Variation of Parameters
Generalized Method of Variation of Parameters
Differential Inequalities and Comparison Method
Hybrid Method: Energy/Lyapunov and Comparison Methods
Linear Hybrid Systems
Linear Hereditary Systems
Qualitative Properties of Solution Process
Linear Stochastic Systems
Several applied Examples and Illustrations from the Biological, Chemical, Medical, Engineering, Physical and Social Sciences
Readership: Undergraduates, advanced undergraduates, postgraduates, member of the public with an interest in science and technology.
388pp (approx.) Pub. date: Feb 2012
ISBN: 978-981-4383-45-5
This volume consists of research papers and expository survey articles presented by the invited speakers of the conference on gHarmony of Grobner Bases and the Modern Industrial Societyh. Topics include computational commutative algebra, algebraic statistics, algorithms of D-modules and combinatorics. This volume also provides current trends on Grobner bases and will stimulate further development of many research areas surrounding Grobner bases.
Polyhedral Approach to Statistical Learning Graphical Models
Implementation of a Primary Decomposition Package
Computing Tropical Resultants
Running Markov Chain Without Markov Basis
Incomplete A-Hypergeometric Systems
Degree Bounds for a Minimal Markov Basis for the Three-State Toric Homogeneous Markov Chain Model
Readership: Graduates and researchers in the field of Grobner bases.
200pp (approx.) Pub. date: Mar 2012
ISBN: 978-981-4390-37-8
This book tries to point out the mathematical importance of the Partial Differential Equations of First Order (PDEFO) in Physics and Applied Sciences. The intention is to provide mathematicians with a wide view of the applications of this branch in physics, and to give physicists and applied scientists a powerful tool for solving some problems appearing in Classical Mechanics, Quantum Mechanics, Optics, and General Relativity. This book is intended for senior or first year graduate students in mathematics, physics, or engineering curricula.
This book is unique in the sense that it covers the applications of PDEFO in several branches of applied mathematics, and fills the theoretical gap between the formal mathematical presentation of the theory and the pure applied tool to physical problems that are contained in other books.
Improvements made in this second edition include corrected typographical errors; rewritten text to improve the flow and enrich the material; added exercises in all chapters; new applications in Chapters 1, 2, and 5 and expanded examples.
Geometric Concepts and Generalities
Partial Differential Equations of First Order
Physical Applications I
Nonlinear Partial Differential Equations of First Order
Physical Applications II
Characteristic Surfaces of Linear Partial Differential Equation of Second Order
Readership: Mathematicians, physicists, applied scientists, senior or first year graduate students in mathematics, physics or engineering.
352pp Pub. date: Mar 2012
ISBN: 978-981-4390-51-4
Leon Chua is a foreign member of the Academia Europea and a recipient of eight USA patents and 13 docteur honoris causa. He has received numerous international awards, including the first IEEE Kirchhoff Award, the Neural Networks Pioneer Award, the Guggenheim Fellow Award, and the gTop 15 Cited Authorsh Award based on the ISI Citation Index in Engineering from 1991 to 2001.
This penultimate volume contains numerous original, elegant, and surprising results in 1-dimensional cellular automata. Perhaps the most exciting, if not shocking, new result is the discovery that only 82 local rules, out of 256, suffice to predict the time evolution of any of the remaining 174 local rules from an arbitrary initial bit-string configuration. This is contrary to the well-known folklore that 256 local rules are necessary, leading to the new concept of quasi-global equivalence.
Another surprising result is the introduction of a simple, yet explicit, infinite bit string called the super string S, which contains all random bit strings of finite length as sub-strings. As an illustration of the mathematical subtlety of this amazing discrete testing signal, the super string S is used to prove mathematically, in a trivial and transparent way, that rule 170 is as chaotic as a coin toss.
Yet another unexpected new result, among many others, is the derivation of an explicit basin tree generation formula which provides an analytical relationship between the basin trees of globally-equivalent local rules. This formula allows the symbolic, rather than numerical, generation of the time evolution of any local rule corresponding to any initial bit-string configuration, from one of the 88 globally-equivalent local rules.
But perhaps the most provocative idea is the proposal for adopting rule
137, over its three globally-equivalent siblings, including the heretofore
more well-known rule 110, as the prototypical universal Turing machine.
Period-2 Rules:
Recap of Period-2 Rules
Basin Tree Diagrams
Robust Ö-Limit Orbits of Local Rules Belonging to Group 2
Quasi Global-Equivalence
Super String S and Super Decimal xS
Concluding Remarks
Period-3, Period-6, and Permutive Rules:
List of the 88 Minimal Equivalence Rules
Basin Tree Diagrams, Omega-Limit Orbits and Time-Ñ Characteristic Function of Rules from Group 3
Robust Ö-Limit Orbits of Rules from Group 3
Permutive Rules
Concluding Remarks
Readership: Graduate students, researchers and academics interested in nonlinear dynamics, computer science and complexity theory.
300pp (approx.) Pub. date: Scheduled Spring 2013
ISBN: 978-981-4374-70-5
Complex Analytic Geometry is one of the most important fields of Mathematics. It has a long history that culminated in the Cauchy integral formula in the 19th century. The theory was vastly developed and closely related to many other fields of Mathematics as well as the Sciences, where numerous applications have been found.
This book starts off with the basic material, introducing characteristic classes mainly via the Chern?Weil theory, explaining the idea of localization of characteristic classes and presenting the aforementioned invariants and relations in a unified way from this perspective. Its exposition is carried out in a self-containing manner. Recent developments are also discussed.
The profound consequences of this subject will make the book useful for mathematical students on fields as diverse as Algebraic Geometry, Differential Geometry, Topology, Complex Dynamical Systems and Mathematical Physics.
Analytic Functions of Several Complex Variables
Complex Manifolds and Analytic Varieties
Local Theory with Relevant Commutative Algebra
Vector Bundles and Grassmann Manifolds
Vector Fields and Differential Forms
Cech?de Rham and Cech?Dolbeault Cohomologies
Chern and Atiyah Classes via Chern?Weil Theory
Localization of Characteristic Classes and Associated Residues
Grothendieck Residues
Various Important Analytic Invariants as Residues of Chern Classes
Coherent Sheaves
Hirzebruch and Grothendieck Riemann?Roch Theorems
Analytic Intersection Theory on Singular Varieties
Characteristic Classes of Singular Varieties
448pp (approx.) Pub. date: Apr 2012
ISBN: 978-981-4383-57-8
This volume is a collection of solicited and refereed articles from distinguished researchers across the field of stochastic analysis and its application to finance. The articles represent new directions and newest developments in this exciting and fast growing area. The covered topics range from Markov processes, backward stochastic differential equations, stochastic partial differential equations, stochastic control, potential theory, functional inequalities, optimal stopping, portfolio selection, to risk measure and risk theory.
It will be a very useful book for young researchers who want to learn about the research directions in the area, as well as experienced researchers who want to know about the latest developments in the area of stochastic analysis and mathematical finance.
Web Markov Skeleton Processes
Generalised Burgers Equations
Backward Stochastic Differential Equations (BSDEs) Driven by Fractional Brownian Motion
Measure Solutions of BSDEs with Generator of Quadratic Growth
Parameter Estimates of Drift Brownian Motion
Spectral Bounds on Feymann?Kac Semigroups
Stochastic Analysis on Lie Group
Potential Theory of Subordinate Brownian Motion
Stochastic Control of Stochastic Partial Differential Equations with Delay
and other papers
Readership: Graduates and researchers in stochatic analysis and mathematical finance.
World Scientific Series on Nonlinear Science, Series A
400pp (approx.) Pub. date: Scheduled Summer 2012
ISBN: 978-981-4368-82-7
Although the dynamic behavior of piecewise-smooth systems is still far from being understood completely, some significant results in this field have been achieved in the last twenty years. The investigation of these systems is important not only because they represent adequate models for many applications ranging from mechanical and electrical engineering up to financial markets, but also due to the importance of the phenomena observed in other types of dynamical systems as well. It is natural, therefore, to begin the analysis with the most simple subclass of piecewise-smooth systems (namely one-dimensional maps) for which many phenomena can be investigated much more easily than for higher-dimensional systems. In this book, we consider both continuous and discontinuous one-dimensional piecewise-linear maps and summarize the results related to bifurcation structures in regular and robust chaotic domains. The map replacement technique based on symbolic dynamics allows us to offer significantly more analytical proofs than what is usually possible.
Introduction: Continuous and Discontinuous Piecewise-Smooth and Especially Piecewise-Linear Models (An Overview). Bifurcations in Piecewise Smooth Systems
General Concepts: Border Collision and Crisis Bifurcations, Map Replacement Technique
Continuous Piecewise-Linear Maps: Bifurcation Structures in Regular and Chaotic Domains
Discontinuous Piecewise-Linear Maps: Period Adding and Bandcount Adding Bifurcation Structures
Discontinuous Piecewise-Linear Maps: Period Increment and Bandcount Increment Bifurcation Structures
Multi-Dimensional Parameter Spaces and Their Organizing Centers
Readership: Researchers and graduate students working in the field of piecewise-smooth systems.