The aim of this volume is to provide a synthetic account of past research, to give an up-to-date guide to current intertwined developments of control theory and nonsmooth analysis, and also to point to future research directions.
Contents:
Sensitivity of Control Systems with Measure-Valued Coefficients (Z Artstein)
Multiscale Singular Perturbation and Homogenization of Optimal Control Problems (M Bardi et al.)
Stability of Switched Systems (U Boscain)
Patchy Feedbacks for Stabilization and Optimal Control (F Ancona & A Bressan)
Regularity of Attainable Sets Under State Constraints (P Cannarsa et al.)
Regularity of Solutions in the Calculus of Variations (F Clarke)
Sampled-Data Redesign for Nonlinear Multi-Input Systems (L Grune & K Worthmann)
Stabilization for Nonholonomic Control Systems (L Rifford)
Proximal Characterization of Reachable Sets (V Rios & P Wolenski)
Strong Optimality of Singular Trajectories (G Stefani)
Stability Analysis of Sliding Mode Controllers (F Clarke & R Vinter)
Trajectories for Generalized Controls on the Heisenberg Group (P Mason)
Linear-Convex Control and Duality (R T Rockafellar & R Goebel)
Generalized Hopf Formulas (I Capuzzo Dolcetta)
High-Order Variations and Generalized Differentials (H Sussmann)
Readership: Researchers in control theory and applied mathematics.
300pp (approx.) Pub. date: Scheduled Summer 2008
ISBN 978-981-277-606-8
A Text for Mathematicians and Physicists
Operads provide a universal language to relate several disciplines in mathematics and physics. The focus of this book, which is the first of its kind, is the particularly striking relation between algebra, topology and string theory that is mediated by operads of graphs and surfaces in their role as a model of the correlation functions of quantum field theory. The text supplies all the necessary background material, including discussions of the relevant aspects of operads, cell models, moduli spaces, deformation quantization, graph Feynman rules and topological and conformal field theory in their open/closed versions. The central paradigm is Deligne's conjecture on the Hochschild cohomology and its generalizations to the cyclic, the A\ and the moduli space cases. Its solution is presented as a natural consequence of this operadic point of view of strings.
Starting at the basic definition and gradually proceeding to advanced topics at the forefront of research, the book provides the reader with a self-contained, uniform and natural approach to the subject which makes it a valuable resource for graduate students and researchers alike.
Contents:
Operads
Surfaces
Correlation functions
The Hochschild Complex
Deligne's Conjecture and Its Generalizations
Further Applications
Readership: Graduate students and researchers in mathematics and physics.
300pp (approx.) Pub. date: Scheduled Summer 2008
ISBN 978-981-277-596-2
This book presents a powerful way to study Einstein's special theory of relativity and its underlying hyperbolic geometry in which analogies with classical results form the right tool. It introduces the notion of vectors into analytic hyperbolic geometry, where they are called gyrovectors.
Newtonian velocity addition is the common vector addition, which is both commutative and associative. The resulting vector spaces, in turn, form the algebraic setting for the standard model of Euclidean geometry. In full analogy, Einsteinian velocity addition is a gyrovector addition, which is both gyrocommutative and gyroassociative. The resulting gyrovector spaces, in turn, form the algebraic setting for the Beltrami?Klein ball model of the hyperbolic geometry of Bolyai and Lobachevsky. Similarly, Mobius addition gives rise to gyrovector spaces that form the algebraic setting for the Poincare ball model of hyperbolic geometry.
In full analogy with classical results, the book presents a novel relativistic interpretation of stellar aberration in terms of relativistic gyrotrigonometry and gyrovector addition. Furthermore, the book presents, for the first time, the relativistic center of mass of an isolated system of noninteracting particles that coincided at some initial time t = 0.
The discovery of the relativistic center of mass in this book thus demonstrates once again the usefulness of the study of Einstein's special theory of relativity in terms of its underlying analytic hyperbolic geometry.
Contents:
Gyrogroups
Gyrocommutative Gyrogroups
Gyrogroup Extension
Gyrovectors and Cogyrovectors
Gyrovector Spaces
Rudiments of Differential Geometry
Gyrotrigonometry
Bloch Gyrovector of Quantum Information and Computation
Special Theory of Relativity: The Analytic Hyperbolic Geometric Viewpoint
Relativistic Gyrotrigonometry
Stellar and Particle Aberration
Readership: Undergraduates, graduate students, researchers and academics in geometry, algebra, mathematical physics, theoretical physics and astronomy.
630pp (approx.) Pub. date: Scheduled Spring 2008
ISBN 978-981-277-229-9
This is a comprehensive introduction to Landau?Lifshitz equations and Landau?Lifshitz?Maxwell
equations, beginning with the work by Yulin Zhou and Boling Guo in the
early 1980s and including most of the work done by this Chinese group led
by Zhou and Guo since. The book focuses on aspects such as the existence
of weak solutions in multi dimensions, existence and uniqueness of smooth
solutions in one dimension, relations with harmonic map heat flows, partial
regularity and long time behaviors.
The book is a valuable reference book for those who are interested in partial differential equations, geometric analysis and mathematical physics. It may also be used as an advanced textbook by graduate students in these fields.
Contents:
Physical Background of Landau?Lifshitz Equations and Landau?Lifshitz?Maxwell Equations
Existence of Weak Solutions to Landau?Lifshitz Equations and Landau?Lifshitz?Maxwell Equations in Multi-Dimensions
Existence and Uniqueness of Smooth Solutions for Landau?Lifshitz Equations with or without Gilbert Damping in One Dimension
Discovery of the Relations with Harmonic Map Heat Flows and Partial Regularity for Chen?Struwe Solutions on Two Dimensional Riemannian Manifolds
Partial Regularity for Weak Solutions to Landau?Lifshitz Equations and Landau?Lifshitz?Maxwell Equations in Higher Dimensions
Long Time Behaviors and Attractors
Readership: Mathematical physicists and researchers interested in Landau?Lifshitz equations.
400pp (approx.) Pub. date: Scheduled Summer 2008
ISBN 978-981-277-875-8