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Acta Crystallographica Section A, 1969
It is shown that the real one-dimensional irreducible representations of a crystallographic point group induce the magnetic symmetry groups associated with the point group and also give the number of independent non-vanishing constants required to describe any magnetic property for the induced magnetic symmetry groups.
T. S. G. Krishna Murty +1 more
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It is shown that the real one-dimensional irreducible representations of a crystallographic point group induce the magnetic symmetry groups associated with the point group and also give the number of independent non-vanishing constants required to describe any magnetic property for the induced magnetic symmetry groups.
T. S. G. Krishna Murty +1 more
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1978
The idea of a group is one of the great unifying ideas of mathematics. It arises in the study of symmetries, both of mathematical and of scientific objects. Very surprisingly, the examination of these symmetries leads to deep insights which are not available by direct inspection: while the notion of a group is very easy to explain, the applications of ...
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The idea of a group is one of the great unifying ideas of mathematics. It arises in the study of symmetries, both of mathematical and of scientific objects. Very surprisingly, the examination of these symmetries leads to deep insights which are not available by direct inspection: while the notion of a group is very easy to explain, the applications of ...
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1978
Let us now consider more formally the question of groups and symmetries. Mathematically a group is defined by a set of axioms, and for the sake of completeness these axioms are stated here.
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Let us now consider more formally the question of groups and symmetries. Mathematically a group is defined by a set of axioms, and for the sake of completeness these axioms are stated here.
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1988
Those discrete groups which play the central role in solid-state physics are the point groups and their extensions (double, colour groups), the translation groups, and the combination of both (the space groups). These groups and the meaning of their elements are discussed in the following sections.
Wolfgang Ludwig, Claus Falter
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Those discrete groups which play the central role in solid-state physics are the point groups and their extensions (double, colour groups), the translation groups, and the combination of both (the space groups). These groups and the meaning of their elements are discussed in the following sections.
Wolfgang Ludwig, Claus Falter
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2009
Up to this point, structures of mostly finite objects have been discussed. Thus, point groups were applicable to their symmetries. A simplified classification of various symmetries was presented in Chapter 2 (cf., Figure 2-31 and Table 2-2). Point-group symmetries are characterized by the lack of periodicity in any direction.
Magdolna Hargittai, István Hargittai
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Up to this point, structures of mostly finite objects have been discussed. Thus, point groups were applicable to their symmetries. A simplified classification of various symmetries was presented in Chapter 2 (cf., Figure 2-31 and Table 2-2). Point-group symmetries are characterized by the lack of periodicity in any direction.
Magdolna Hargittai, István Hargittai
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1974
A mathematical fact of very great significance for relativity theory is the existence of the familiar homomorphism* between the group SL(2,C) of complex unimodular (2 × 2) matrices and the Lorentz group 0(1,3). This homomorphism $$SL\left( {2,C} \right) \to 0\left( {1,3} \right)$$ (1.1) is a local isomorphism and maps SL(2,C) onto the ...
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A mathematical fact of very great significance for relativity theory is the existence of the familiar homomorphism* between the group SL(2,C) of complex unimodular (2 × 2) matrices and the Lorentz group 0(1,3). This homomorphism $$SL\left( {2,C} \right) \to 0\left( {1,3} \right)$$ (1.1) is a local isomorphism and maps SL(2,C) onto the ...
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1982
Thus far the treatment of symmetry has been restricted to the proper rotational and reflection symmetries of space lattices. The discussion of the symmetry of crystalline solids does not end with the presentation of the 14 Bravais lattice types because the symmetry of a solid is the symmetry of its three-dimensionally periodic particle density, and ...
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Thus far the treatment of symmetry has been restricted to the proper rotational and reflection symmetries of space lattices. The discussion of the symmetry of crystalline solids does not end with the presentation of the 14 Bravais lattice types because the symmetry of a solid is the symmetry of its three-dimensionally periodic particle density, and ...
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Material symmetry group and constitutive equations of micropolar anisotropic elastic solids
, 2016V. Eremeyev, W. Pietraszkiewicz
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A rotation symmetry group detection technique for the characterization of Islamic Rosette Patterns
Pattern Recognition Letters, 2015Aziza El Ouaazizi +2 more
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