732 resultados para Transformations (Mathematics)


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Thesis (Ph.D.)--Cornell University, 1908.

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Given a compact 2 dimensional manifold M we classify all continuous flows phi without wandering points on M. This classification is performed by finding finitely many pairwise disjoint open phi-invariant subsets {U(1), U(2), ..., U(n)} of M such that U(i=1)(n) (U(i)) over bar = M and each U(i) is either a suspension of an interval exchange transformation, or a maximal open cylinder made up of closed trajectories of phi.

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An analytical set of field-induced coordinates is defined and is used to show that the vibrational degrees of freedom required to completely describe nuclear relaxation polarizabilities and hyperpolarizabilities is reduced from 3N-6 to a relatively small number. As this number does not depend upon the size of the molecule, the process provides computational advantages. A method is provided to separate anharmonic contributions from harmonic contributions as well as effective mechanical from electrical anharmonicity. The procedures are illustrated by Hartree-Fock calculations, indicating that anharmonicity can be very important

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An analytical set of field-induced coordinates is defined and is used to show that the vibrational degrees of freedom required to completely describe nuclear relaxation polarizabilities and hyperpolarizabilities is reduced from 3N-6 to a relatively small number. As this number does not depend upon the size of the molecule, the process provides computational advantages. A method is provided to separate anharmonic contributions from harmonic contributions as well as effective mechanical from electrical anharmonicity. The procedures are illustrated by Hartree-Fock calculations, indicating that anharmonicity can be very important

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Issued also as thesis (Ph. D.) University of California, 1916.

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"Supported in part by... NSF Grant GJ-217 and by BUILD."

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On cover: C00-1018-1152.

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"Separat-abdruck aus: Nova acta der Kaiserl. Leop.-Carol. deutschen Akademie der Naturforscher, Bd. 50. [1887]"

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Includes his Betrachtungen über die Kummer'sche Fläche und ihren Zusammenhang mit den hyperelliptischen Functionen p = 2. München : Akademische Buchdruckerei von F. Straub, 1878. 59 p.

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Mode of access: Internet.

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Mode of access: Internet.

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Available on demand as hard copy or computer file from Cornell University Library.

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Available on demand as hard copy or computer file from Cornell University Library.