Showing papers on "Symmetry (geometry) published in 1983"
443 citations
TL;DR: In this paper, the space-group frequency for approximately 30 000 organic compounds in the NBS Crystal Data Identification File has been calculated for each of the 230 space groups and it is shown that it is not uncommon for the metric symmetry to exceed the reported crystal symmetry.
Abstract: The space-group frequency for approximately 30 000 organic compounds in the NBS Crystal Data Identification File has been calculated for each of the 230 space groups. 75% of the compounds have been reported in only five space groups: P21/c (36.0%), P{\bar 1} (13.7%), P212121 (11.6%), P21 (6.7%) and C2/c (6.6%). In contrast, there are 29 space groups with only one entry and 35 space groups with none at all. Although the space-group frequencies should be fairly representative of their distribution in nature, certain frequencies are over- or under-estimated. An analysis of the metric symmetry for about 30 000 lattices using a matrix technique has revealed that it is not uncommon for the metric symmetry to exceed the reported crystal symmetry. In many of these cases, the structures have been described in space groups of unnecessarily low symmetry. By explicitly checking for the highest possible metric symmetry during the space-group-determination procedure, errors of this type can be prevented.
108 citations
01 Jan 1983
TL;DR: In this article, two new approaches to derive 3D surface orientation information (shape) from two-dimensional image cues are presented. The two approaches are the method of affine-transformable patterns and the shape-from-texture paradigm.
Abstract: In this paper we demonstrate two new approaches to deriving three-dimensional surface orientation information (“shape‘) from two-dimensional image cues. The two approaches are the method of affine-transformable patterns and the shape-from-texture paradigm. They are introduced by a specific application common to both: the concept of skewed symmetry. Skewed symmetry is shown to constrain the relationship of observed distortions in a known object regularity to a small subset of possible underlying surface orientations. Besides this constraint, valuable in its own right, the two methods are shown to generate other surface constraints as well. Some applications are presented of skewed symmetry to line drawing analysis, to the use of gravity in shape understanding, and to global shape recovery.
87 citations
Book•
01 Jan 1983
77 citations
TL;DR: Approximate locations of axes of symmetry of a 2-dimensional region are detected on the basis of its border because of the way the border is treated in a hierarchical manner where a lower level means a greater number of sides.
66 citations
55 citations
TL;DR: In this article, the authors used X-ray diffraction intensity data collected from a small spherical synthetic single crystal and used for a structure parameter refinement assuming F$\overline{4}$3m symmetry.
Abstract: The crystal structure of magnesium aluminate is conventionally described within a symmetry corresponding to the centrosymmetrical space group Fd3m but this has created difficulties for the interpretation of many of its physical properties. Therefore, extensive X-ray diffraction intensity data have been collected from a small spherical synthetic single crystal and used for a structure parameter refinement assuming F$\overline{4}$3m symmetry as proposed by Grimes (Phil. Mag. 26, 1217-1226 (1972)), and also for refinement according to conventional symmetry. The F$\overline{4}$3m assumption yields the first direct measurement of the suspected deviations from the centrosymmetrical structure, and is found to provide a significantly superior fit to the experimental data, especially at high angles and with reflexions having structure factors less than 10.0. The weak reflexions include nine that are forbidden under Fd3m symmetry and it is shown that there is satisfactory agreement between observed and calculated structure factors in these cases.
49 citations
TL;DR: In this article, two classes of invariant tests are proposed for testing a probability distribution on a compact Riemannian manifold for symmetry under the action of a given group of isometries.
Abstract: For testing a probability distribution on a compact Riemannian manifold for symmetry under the action of a given group of isometries, two classes of invariant tests are proposed and some properties noted. These tests are based on Sobolev norms and generalize Gine's Sobolev tests of uniformity. For general compact manifolds randomization tests analogous to Wellner's tests for the two-sample case are suggested. For the circle, distribution-free tests of symmetry based on uniform scores are provided.
37 citations
TL;DR: In this paper, a strong symmetry for the Harry-Dym equation is found, which is hereditary and can be used to generate infinitely many Lie-Backlund symmetries.
Abstract: A recursion operator (strong symmetry) for the Harry-Dym equation is found. It is also hereditary, and can be used to generate infinitely many Lie-B\"acklund symmetries.
TL;DR: In this paper, the group theoretical aspects of infinitesimal regular Riemann-Hilbert transforms are discussed with an eye to the comparison with the hidden symmetry transformations proposed by us before.
Abstract: We obtain explicit expressions for infinitesimal regular Riemann-Hilbert (RH) transforms. Using them, the group theoretical aspects of infinitesimal RH transforms are discussed with an eye to the comparison with the hidden symmetry transformations proposed by us before. We find that the RH transforms have very rich group structure; e.g. in the 2-d principal chiral models, their group contains two Kac-Moody algebras as subalgebras. But not all of them are nontrivial hidden symmetries of the theory.
TL;DR: In this article, K-cyclic frequency domain symmetry conditions for N-dimensional sampled signals are introduced and a theorem is given that specifies the interrelationships between the sample values.
Abstract: In this paper, K-cyclic frequency domain symmetry conditions for N-dimensional sampled signals are introduced. It is shown that these frequency domain symmetry conditions result in certain interrelationships between the sample values. A theorem is given that specifies these interrelationships. Several interesting properties of K-cyclic symmetries are discussed. Also, a systematic approach is given for finding the parameters of several commonly encountered symmetry conditions. Certain implications to multidimensional digital filtering are discussed, including L p optimality and the reduction in computation for design and implementation.
TL;DR: In this article, the non-vanishing three-index photon of d = 11 supergravity parallelizes the seven-sphere, and its residual bosonic symmetry is found to be an SO(7) subgroup of the original SO(8).
TL;DR: In this article, a generalization of Hirshfeld's approach to the case of variable lattice constants is suggested, where the symmetry of the multidimensional parameter space is defined by the direct product of the molecular point group and a normalizer NA(F) of the space group F.
Abstract: In calculating the lattice-energy hypersurface by the systematic variation of the molecular rigid-body parameters and the lattice constants, the ranges to be scanned depend on the molecular symmetry and on the space group. A generalization of Hirshfeld's approach [Hirshfeld (1968). Acta Cryst. A24, 301-311] applicable to the case of variable lattice constants is suggested. The symmetry of the multidimensional parameter space is defined by the direct product of the molecular point group and a normalizer NA(F) of the space group F. The normalizer NA (F) is a group of affine transformations of the crystal axes that leave invariant the coordinates of equivalent positions. An asymmetric unit of the parameter space is obtained through keeping the lattice constants within such ranges that satisfy the Niggli reduced-cell conditions.
TL;DR: The extended D = 4 euclidean superconformal algebra SL(2, N ; H) in quaternionic as well as complex notation was given in this article.
TL;DR: In this paper, a method called group overlap method for constructing the symmetry orbitals and for calculating the group overlap integrals is proposed, which is used for the qualitative and quantitative MO study of structural polyhedrons.
Abstract: The MO theory of structural polyhedrons is one of the basic subjects closely related to the bonding theory of complex compounds and clusters. A series of valuable papers on this subject have been contributed by Hoffman, Wade, King, and Lauher et al. A method called “group overlap method” for constructing the symmetry orbitals and for calculating the group overlap integrals is proposed. It is hoped that the group overlap method may be used for the qualitative and quantitative MO study of structural polyhedrons.
TL;DR: In this article, the effect of symmetry of parts on the time taken to handle parts during manual assembly is studied, and it is experimentally shown that part symmetry can be classified into four categories; in each category, the parts require significantly different orientation times.
Dissertation•
01 Jan 1983
TL;DR: Thesis (Ph.D.) as discussed by the authors, Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1984, Boston, MA, USA, U.S.
Abstract: Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1984.
TL;DR: In this article, the symmetry of groups of order 144 is discussed and a procedure is outlined in which correspondence between distinctive combinatorial objects is established by inducing permutations of m elements from available permutations for n elements.
Abstract: Structures XY⋅3XY⋅2XY3 of symmetry C2v (of which propane is an example) are examined and the rearrangement due to the internal rotation of the end groups XY3 studied. The isomerization graph is constructed, various forms of which are displayed and the symmetry of which has been determined. The order of the group is 72. There are nine prime (irreducible) representations (4A + E + 4G) with the following partitioning of the elements into classes: 1, 42, 62, 9, 122, 18. When the mechanism for rearrangement is generalized to include enantiomers, a duplex graph is produced with the order of the group 144 which is isomorphic to the group S2(S3,S2) (generalized wreath product of the symmetric group S2 and S3). The corresponding graph has been constructed and displayed in one of more symmetrical forms. Isomorphism of groups of order 144 is discussed and a procedure is outlined in which correspondence between distinctive combinatorial objects is established by inducing permutations of m elements from available permutations of n elements. The scheme is based on selection of suitable graph invariants in one system and their labeling as m objects which form the basis for representation of the symmetry for the other system.
Patent•
08 Dec 1983
TL;DR: In this article, a clamp fitting for pipes is described, where the transverse plane of symmetry of the staple is offset by a distance oriented in the same direction as the one from the bottom of the forks towards their lateral opening.
Abstract: The present invention relates to a clamp fitting for pipes, wherein the transverse plane (P 1 ) of symmetry of the strap is offset, with respect to the transverse plane (P 2 ) of symmetry of the staple, by a distance (d) oriented in the same direction as the one from the bottom of the forks towards their lateral opening.
TL;DR: In this article, the authors illustrate the physical significance of such symmetries by giving a concrete realisation of an invariance under rotation in two dimensions for a tetragonal system, which may be exhibited conveniently using a (two-dimensional) perspex model on an overhead projector.
Abstract: Certain Jahn-Teller systems, in which the frequencies and couplings of participating modes are suitably constrained, possess a hidden symmetry corresponding to invariance under a rotation in two, three, four or five dimensions. The authors illustrate the physical significance of such symmetries by giving a concrete realisation of an invariance under rotation in two dimensions for a tetragonal system. This may be exhibited conveniently using a (two-dimensional) perspex model on an overhead projector. The model also affords a simple illustration of the use of spatial and time-reversal symmetries in generating selection rules on the ion-vibration coupling.
01 Jan 1983
TL;DR: The theory of color symmetry has been studied extensively in the last few decades as discussed by the authors, with a focus on color symmetry as a way of illustrating concepts in elementary group theory, such as subgroup, coset, normality, conjugacy, and so forth.
Abstract: Color symmetry-the symmetrical distribution of colors in regular patterns-is as old as ornamental art itself. Beautiful examples from many cultures can be found in the colored plates of Owen Jones' classic Grammar of Ornament [12] and, in our time, in the tessellations of M. C. Escher. Also striking are the patterns of "identity and difference" [2] that are found in nature, for example in the arrangements in crystals of different atoms, or of magnetic spins [8]. Colors are often used in structure models to represent such nongeometric characteristics. In this article, we give an introduction to the mathematical theory of color symmetry that has been developed in recent years. This theory complements and extends the usual characterization of the symmetry of an object by describing the ways of coloring it that are consistent with its symmetry. In addition to being of interest in its own right and for its applications, color symmetry provides a simple way of illustrating concepts in elementary group theory, such as subgroup, coset, normality, conjugacy, and so forth; we hope it will turn out to be a useful topic in introductory algebra courses. More advanced students will find that the theory of permutation groups provides a unified framework for examining various aspects of color symmetry; reformulating in more abstract terms the theory outlined here is an instructive exercise. As an example of the problem of coloring an object symmetrically, suppose we wish to color each face of an octahedron with one of two colors, say, black and white. Intuitively we expect that in a symmetrical distribution of colors, four faces should be black and four white. There are many
TL;DR: In this article, a class of aromatic molecules with fused benzene rings is considered and the group-theoretical problem of symmetry in terms of ΓKek χKek is solved; explicit formulas are given for the symmetry groupsD3h andC2v.
Abstract: A class of aromatic molecules with fused benzene rings is considered. It is characterized by one, two or three straight chains of benzene rings meeting at one ring. The group-theoretical problem of symmetry in terms of ΓKek χKek is solved; explicit formulas are given for the symmetry groupsD3h andC2v.
TL;DR: In this paper, a general method for generating complete sets of states for l(
Abstract: General methods of generating complete sets of states for l(
TL;DR: In this paper, Symmetry of Form and Emblematic Design in El conde Partinuples is discussed. But it is not discussed in the context of the present paper.
Abstract: (1983). Symmetry of Form and Emblematic Design in El conde Partinuples. Kentucky Romance Quarterly: Vol. 30, No. 1, pp. 61-76.