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  • 1
    Electronic Resource
    Electronic Resource
    RELIGIOUS ENCOUNTER AND THE JAMAA (1967)
    Oxford, UK : Blackwell Publishing Ltd
    Heythrop journal 8 (1967), S. 0 
    Details
    ISSN: 1468-2265
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Philosophy , Theology and Religious Studies
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1468-2265.1967.tb00734.x
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  • 2
    Electronic Resource
    Electronic Resource
    On spectral properties of Harper-like models (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1197-1214 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study spectral properties of Harper-like models by algebraic and combinatorial methods and derive sufficient conditions for the existence of spectral gaps with qualitative estimates. For this class the Chambers relation holds and we obtain an analytic expression for the representation dependent part. Models corresponding to the rectangular and triangular lattice are studied. In the second case we show that one class of spectral gaps is open for magnetic fields with "rational magnetic flux per unit cell." A quantitative estimate for the gap widths is given for the anisotropic case and for "irrational magnetic flux" fulfilling some Liouville condition the spectrum is a Cantor set. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532795
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  • 3
    Electronic Resource
    Electronic Resource
    Arithmetic properties of spectra produced by Farey hierarchies of approximants (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1317-1333 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We discuss the consequences of the hierarchical nature of series of approximants of aperiodic crystals on their diffraction patterns and spectra of elementary excitations. We show how a linear form defined on Z3 can be used to order Bragg reflections in diffraction patterns according to their amplitudes, and gaps in spectra of elementary excitations according to their widths, for all the structures in the hierarchy. Bragg peaks amplitudes and gap widths are projective functions on P(Z3), recursively defined on 2D Farey sets (generalization of Farey series). © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532804
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  • 4
    Electronic Resource
    Electronic Resource
    Symmetry of incommensurate crystal phases. I. Commensurate basic structures (1980)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 399-408 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The superspace-group approach [Janner & Janssen (1977), Phys. Rev. B, 15, 643-658] is used to solve the symmetry problem of incommensurate crystal phases in the case of displacive- and occupation-wave modulation. Generalization is given to cover magnetic modulation as well. The symmetry conditions imposed by the superspace group on the crystal structure are derived and applied to the following incommensurate crystals, whose structures have been discussed in the literature independently from the present point of view: K2SeO4, 2H-TaSe2, NaNO2 and Cr. The superspace groups describing the symmetry of these compounds are indicated and the structural implications of the corresponding symmetry elements discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739480000885
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  • 5
    Electronic Resource
    Electronic Resource
    Symmetry of incommensurate crystal phases. II. Incommensurate basic structure (1980)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 408-415 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In this second part [part I: Acta Cryst. (1980), A36, 399-408] the superspace-group approach is formulated for a class of crystals (called composite crystals) which involve a basic structure composed of subsystems, each one having three-dimensional space-group symmetry, but being mutually incommensurate. By taking into account the interaction among these subsystems, or other second-order effects, one is led to the actual structure, which very often is modulated, and in any case incommensurate. Neither the basic structure nor the actual one has a three-dimensional space-group symmetry but both allow a superspace-group characterization of their symmetry properties. The aim of the present paper is to show how these concepts apply in practice. Accordingly, two composite crystals, extensively studied in the literature, are considered from the present point of view: the organic compound (TTF)7I5 - x, i.e. C42H28S28.I5 - x, and the polymercury cation compound Hg3 - δAsF6. The regularities found in these two compounds are interpreted and fit naturally with the corresponding superspace-symmetry groups.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739480000897
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  • 6
    Electronic Resource
    Electronic Resource
    The superspace groups for incommensurate crystal structures with a one-dimensional modulation (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 625-636 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A complete list of (3 + 1)-dimensional superspace groups is presented. These groups describe the symmetry of incommensurate crystal structures with a one-dimensional modulation. A short discussion is given of applications. Extinction rules and Bravais types are tabulated in order to facilitate the determination of the superspace-group symmetry.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739481001447
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  • 7
    Electronic Resource
    Electronic Resource
    Point group symmetry applications: methods and tables by P. H. Butler (1983)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 39 (1983), S. 271-271 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767383000628
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  • 8
    Electronic Resource
    Electronic Resource
    A note on the superspace groups for one-dimensionally modulated structures (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 528-530 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A computer generation of all the non-equivalent superspace groups for one-dimensionally modulated structures has been performed. Comparison of this result with the previous list by de Wolff, Janssen & Janner [Acta Cryst. (1981), A37, 625-636] shows that three superspace groups in this list are equivalent to others and that six groups had been overlooked. The new list contains 775 (3 + 1)-dimensional superspace groups. Some ambiguous points in the notation of the superspace groups and the selection of the wave vector are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385001167
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  • 9
    Electronic Resource
    Electronic Resource
    Wyckoff positions used for the classification of Bravais classes of modulated crystals (1983)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 39 (1983), S. 667-670 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Wyckoff positions of centrosymmetric symmorphic space groups, if properly interpreted, can be used to derive the Bravais classes of modulated crystals. This program is worked out here for the incommensurate case and assuming that the modulation wave vectors are symmetry related, i.e. are (integral combinations of) vectors of one star. The corresponding classes are called elementary Bravais classes (EBC's). It is shown that for three-dimensional crystals the maximal internal dimension for these EBC's is nine. It is explained in what sense this approach leads to a complete list.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S010876738300135X
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  • 10
    Electronic Resource
    Electronic Resource
    The symmetry of quasiperiodic systems. Erratum (1991)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 47 (1991), S. 605-605 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Fig. 1 of the paper by Janssen [Acta Cryst. (1991). 47, 243–245] was not reproduced clearly. A revised figure is given here.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767391006499
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