Methods in Computational Molecular Physics: Proceedings of a NATO ASI Held in Bad Windsheim, Germany, July 22-August 2, 1991: v. 293 (NATO Science Series B: Physics) - Hardcover

Wilson, S.

Hardcover

ISBN 10: 0306442272 ISBN 13: 9780306442278

Publisher: Kluwer Academic / Plenum Publishers, 1992

Synopsis

This volume records the lectures given at a NATO Advanced Study Institute on Methods in Computational Molecular Physics held in Bad Windsheim, Germany, from 22nd July until 2nd. August, 1991. This NATO Advanced Study Institute sought to bridge the quite considerable gap which exist between the presentation of molecular electronic structure theory found in contemporary monographs such as, for example, McWeeny's Methods 0/ Molecular Quantum Mechanics (Academic Press, London, 1989) or Wilson's Electron correlation in moleeules (Clarendon Press, Oxford, 1984) and the realization of the sophisticated computational algorithms required for their practical application. It sought to underline the relation between the electronic structure problem and the study of nuc1ear motion. Software for performing molecular electronic structure calculations is now being applied in an increasingly wide range of fields in both the academic and the commercial sectors. Numerous applications are reported in areas as diverse as catalysis and interstellar chernistry, drug design and environmental studies, molecular biology and solid state physics. The range of applications continues to increase as scientists recognize the importance of molecular structure studies to their research activities. Recent years have seen a growing dependence of these applications on program packages, which are often not in the public domain and which may have a somewhat lirnited range of applicability dicta ted by the particular interests and prejudices of the program author.

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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

Synopsis

This Advanced Study Institute sought to bridge the gap between molecular electronic structure theory and the sophisticated computational algorithms required for practical application. Paper topics include: calculation of geometrical derivatives in molecular electronic structure theory; the many-body perturbation theory for vibrational-electronic mo

Edition details

• Publisher: Kluwer Academic / Plenum Publishers
• Publication date: 1992
• ISBN 10: 0306442272
• ISBN 13: 9780306442278
• Binding: Hardcover
• Language: English
• Number of pages: 574