Crystallographic space groups and algorithms.
Item
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Title
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Crystallographic space groups and algorithms.
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Identifier
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AAI9000683
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identifier
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9000683
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Creator
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Cook, Michael.
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Contributor
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Adviser: Louis Auslander
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Date
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1989
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics
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Abstract
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A mathematical derivation of the 230 crystallographic space groups is presented, based on their solvability. This approach only works in three dimensions, but the deeper insight provided is useful in structuring the computation of crystallographic Fourier transforms.;Next, attention is focussed on primitive space groups from the triclinic, monoclinic, and orthorhombic classes. Algorithms are given for passing from the space group to a program which computes the Fourier transform on data exhibiting the symmetry of that group. In addition, the program (1) Uses only non-redundant data, that is, data on an asymmetric unit. (2) Reduces to one-dimensional symmetrized transforms on that set.;Thus the computation of the Fourier transform is completely reduced to an asymmetric unit, while retaining the use of one-dimensional FFT's.;An abstract data type, "biased" fundamental domains, is developed for representing convenient asymmetric units for primitive triclinic, monoclinic, and orthorhombic space groups. In terms of this data type two basic algorithms are developed: (1) Computing asymmetric units. (2) Mapping between asymmetric units.;The process of going from a given space group to a program has been embodied in a program generator for this class of groups (written in Fortran), which is thoroughly discussed, and included, together with sample output.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
