continuous dynamical systems and mappings
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1: 32.16 Physical Applications
§32.16 Physical Applications
…2: About Color Map
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Continuous Phase Mapping
►For the continuous phase mapping, we map the phase continuously onto the hue, as both are periodic. … ► …3: Bibliography
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Conformal Invariants, Inequalities, and Quasiconformal Maps.
John Wiley & Sons Inc., New York.
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The Riemann Hypothesis and the Hamiltonian of a Quantum Mechanical System.
In Number Theory and Dynamical Systems (York, 1987), M. M. Dodson and J. A. G. Vickers (Eds.),
London Math. Soc. Lecture Note Ser., Vol. 134, pp. 153–172.
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Continuous Hahn polynomials.
J. Phys. A 18 (16), pp. L1017–L1019.
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Spinning Tops: A Course on Integrable Systems.
Cambridge Studies in Advanced Mathematics, Vol. 51, Cambridge University Press, Cambridge.
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Center for Algorithms and Interactive Scientific Software.
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4: 18.39 Applications in the Physical Sciences
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Introduction and One-Dimensional (1D) Systems
… ►As in classical dynamics this sum is the total energy of the one particle system. … ►1D Quantum Systems with Analytically Known Stationary States
… ►§18.39(v) Other Applications
►For applications of Legendre polynomials in fluid dynamics to study the flow around the outside of a puff of hot gas rising through the air, see Paterson (1983). …5: 1.5 Calculus of Two or More Variables
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§1.5(i) Partial Derivatives
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… ►Polar Coordinates
… ►Again the mapping is one-to-one except perhaps for a set of points of volume zero. …6: 23.20 Mathematical Applications
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§23.20(i) Conformal Mappings
… ►The interior of is mapped one-to-one onto the lower half-plane. … ►For examples of conformal mappings of the function , see Abramowitz and Stegun (1964, pp. 642–648, 654–655, and 659–60). ►For conformal mappings via modular functions see Apostol (1990, §2.7). …7: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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►When is absolutely continuous, i.
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§1.18(vi) Continuous Spectra and Eigenfunction Expansions: Simple Cases
… ►and completeness relation … ► … ►§1.18(vii) Continuous Spectra: More General Cases
…8: 1.9 Calculus of a Complex Variable
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Continuity
… ► … ►§1.9(iv) Conformal Mapping
… ►We then say that the mapping is conformal (angle-preserving) at . … ► …9: 20.12 Mathematical Applications
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►For an application of a generalization in affine root systems see Macdonald (1972).
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►The space of complex tori (that is, the set of complex numbers in which two of these numbers and are regarded as equivalent if there exist integers such that ) is mapped into the projective space via the identification .
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