Computational Noncommutative Algebra and Applications [electronic resource] /

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; Group Algebra 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.

Bibliographic Details

Main Authors:	Byrnes, Jim. editor., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Dordrecht : Springer Netherlands, 2004
Subjects:	Mathematics., Algebra., Algebraic geometry., Algebraic Geometry.,
Online Access:	http://dx.doi.org/10.1007/1-4020-2307-3
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