Computational noncommutative algebra and applications

Dedication. Preface. Acknowledgments. Clifford Geometric Algebras in Multilinear Algebra and Non-Euclidean Geometries Garret Sobczyk.- 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 Michael Clausen, Frank Kurth.- Introduction Motivating Examples General Concept Fault Tolerance.- Applications, Prototypes, and Test Results Related Work and Future Research References.- Four Problems in Radar Michael C. Wicks and Braham Himed.- 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 Valeriy Labunets.-Generalized classical signal/system theory on hypergroups Generalized quantum signal/system theory on hypergroups Conclusion References. Lie Groups and Lie Algebras in Robotics J.M. Selig.- 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 William E. Baylis.- Introduction Paravector Space as Spacetime Eigenspinors Spin Dirac Equation Bell's Theorem Qubits and Entanglement Conclusions References. PONS, Reed-Muller Codes, and Group Algebras Myoung An et al.- 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 Valeriy Labunets.- 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 Daniel N. Rockmore.- Introduction Finite group FFTs FFTs for compact groups Noncompact groups References. Group Filters and Image Processing Richard Tolimieri and Myoung An.- 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 Gerald Sommer.- Introduction Local Analysis of Multi-dimensional Signals Knowledge Based Neural Computing Acknowledgments References. Group Theory in Radar and Signal Processing William Moran, Jonathan H. Manton.- 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 William E. Baylis.- Clifford Algebras in Physics Paravector Space as Spacetime Interpretation Eigenspinors Maxwell's Equation Conclusions References. A Unified Approach to Fourier-Clifford-Prometheus Transforms Ekaterima L.-Rundbla et al.- 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 Ekaterina L.-Rundblad et al.- 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