Ronald J Stern

Nonlinear Analysis, Differential Equations and Control - NATO Science Series C Ronald J Stern 1999 edition

Marc Notes: Published in cooperation with NATO Scientific Affairs Division.; Proceedings of the NATO Advanced Study Institute and Seminaire de Mathematiques Superieures on Nonlinear Analysis, Differential Equations, and Control, Montreal, Canada, July 27-August 7, 1998--T.p. verso.; Includes bibliographical references and index. Table of Contents: Preface. Participants. Contributors. Viscosity solutions and analysis in LINFINITY; E. N. Barron. Multifunctional and functional analytic techniques in nonsmooth analysis; J. M. Borwein, Q. J. Zhu. Relaxed optimal control problems and applications to shape optimization; G. Buttazzo. Invariance, monotonicity, and applications; F. H. Clarke, et al. On the stabilization of some nonlinear control systems: results, tools, and applications; J.-M. Coron. Smooth variational principles and non-smooth analysis in Banach spaces; R. Deville. Controlled Markov processes and mathematical finance; W. H. Fleming. Variational methods in local and global non-smooth analysis; A. Ioffe. BSDEs, weak convergence and homogenization of semilinear PDEs; E. Pardoux. Stability and stabilization: discontinuities and the effect of disturbances; E. D. Sontag. Index."Publisher Marketing: This text summarizes the latest developments, both applied and theoretical, in nonlinear and nonsmooth mathematics. The topics range from the highly theoretical, such as infinitesimal nonsmooth calculus, to the very applied (e.g. stabilization techniques in control systems, stochastic control, nonlinear feedback design, nonsmooth optimization). The contributions, all of which are written by renowned practitioners in the area, are self contained."

Contributor Bio:  Stern, Ronald J Stern-Concordia University, Montreal, CanadaContributor Bio:  North Atlantic Treaty Organization Dedication. Preface. Acknowledgments. Clifford Geometric Algebras in Multilinear Algebra and Non-Euclidean Geometries.- Geometric algebra Projective Geometries; Affine and other geometries; Affine Geometry of pseudo-euclidean space; Conformal Geometry and the Horosphere; References. Content-Based Information Retrieval by Group Theoretical Methods.- Introduction; Motivating Examples; General Concept; Fault Tolerance.- Applications, Prototypes, and Test Results; Related Work and Future Research; References.- Four Problems in Radar.-Introduction; Radar Fundamentals; Radar Waveforms; Signal Processing; Space-Time Adaptive Processing; Four Problems in Radar; Conclusions. Introduction to Generalized Classical and Quantum Signal and System Theories on Groups and Hypergroups.-Generalized classical signal/system theory on hypergroups; Generalized quantum signal/system theory on hypergroups; Conclusion; References. Lie Groups and Lie Algebras in Robotics.- Introduction -- Rigid Body Motions; Lie Groups; Finite Screw Motions; Mechanical Joints; Invisible Motion and Gripping; Forward Kinematics; Lie Algebra; The Adjoint Representation; The Exponential Map Derivatives of Exponentials; Jacobians; Concluding Remarks; References. Quantum/Classical Interface: a Geometric Approach from the Classical Side.- Introduction Paravector Space as Spacetime; Eigenspinors; Spin; Dirac Equation; Bell's Theorem; Qubits and Entanglement; Conclusions; References. PONS, Reed-Muller Codes, and Group Algebras.- Introduction; Analytic Theory of One-Dimensional PONS (Welti); Shapiro Sequences, Reed-Muller Codes, and Functional Equations; Group Algebras; Reformulation of Classical PONS; Group Algebra of Classical PONS; GroupAlgebra Convolution; Splitting Sequences; Historical Appendix on PONS; References. Clifford Algebras as a Unified Language.- Introduction; Clifford algebras as models of physical spaces; Clifford Algebras as Models of Perceptual Multicolor Spaces; Hypercomplex-Valued invariants of nD multicolor images; Conclusions; Acknowledgments; References. Recent Progress and Applications in Group FFTs.-Introduction; Finite group FFTs; FFTs for compact groups; Noncompact groups; References. Group Filters and Image Processing.- Introduction: Classical Digital Signal Processing; Abelian Group DSP; Nonabelian Groups; Examples; Group Transforms; Group Filters; Line-like Images; Acknowledgments; References. A Geometric Algebra Approach to Some Problems of Robot Vision.- Introduction; Local Analysis of Multi-dimensional Signals; Knowledge Based Neural Computing; Acknowledgments; References. Group Theory in Radar and Signal Processing.- Introduction; How a Radar Works; Representations; Representations and Radar; Ambiguity Functions; The Wide Band Case; References. Geometry of Paravector Space with Applications to Relativistic Physics.- Clifford Algebras in Physics; Paravector Space as Spacetime; Interpretation; Eigenspinors; Maxwell's Equation; Conclusions; References. A Unified Approach to Fourier-Clifford-Prometheus Transforms- Introduction; New construction of classical and multiparametric Prometheus transforms; PONS associated with Abelian groups; Fast Fourier-Prometheus Transforms; Conclusions; Acknowledgments; References. Fast Color Wavelet Transforms.- Introduction; Color images; Color Wavelet-Haar-Prometheus transforms; Edge detection and compression of color images; Conclusion; Acknowledgments; References. Selected Problems; Various Authors.- Transformations of Euclidean Space and Clifford Geometric; Algebra; References; On the Distribution of Kloosterman Sums on Polynomials over Quaternions; References; Harmonic Sliding Analysis Problems; References; Spectral Analysis under Conditions of Uncertainty; A Canonical Basis for Maximal Tori of the Reductive Centrizer of a Nilpotent Element; References; 6 The Quantum Chaos Conjecture References; Four Problems in Radar; Topic Index; Author Index