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Showing papers on "Symmetry (geometry) published in 1991"


Journal ArticleDOI
TL;DR: In this paper, a dichotomy method for indexing powder diffraction patterns for low-symmetry lattices is studied in terms of an optimization of bound relations used in the comparison of observed data with the calculated patterns generated at each level of the analysis.
Abstract: The dichotomy method for indexing powder diffraction patterns for low-symmetry lattices is studied in terms of an optimization of bound relations used in the comparison of observed data with the calculated patterns generated at each level of the analysis. A rigorous mathematical treatment is presented for monoclinic and triclinic cases. A new program, DICVOL91, has been written, working from the cubic end of the symmetry sequence to triclinic lattices. The search of unit cells is exhaustive within input parameter limits, although a few restrictions for the hkl indices of the first two diffraction lines have been introduced in the study of triclinic symmetry. The efficiency of the method has been checked by means of a large number of accurate powder data, with a very high success rate. Calculation times appeared to be quite reasonable for the majority of examples, down to monoclinic symmetry, but were less predictable for triclinic cases. Applications to all symmetries, including cases with a dominant zone, are discussed.

1,459 citations


Journal ArticleDOI
TL;DR: The Limits of Symmetry: A Game Theory Approach to Symmetric and Asymmetric Public Relations as discussed by the authors is a game theoretic approach to public relations with respect to symmetry.
Abstract: (1991). The Limits of Symmetry: A Game Theory Approach to Symmetric and Asymmetric Public Relations. Public Relations Research Annual: Vol. 3, No. 1-4, pp. 115-131.

183 citations


Journal ArticleDOI
Andreas Kuehnle1
TL;DR: Symmetry is an effective feature for locating vehicle rears and three symmetry criteria are presented: contour symmetry, gray level symmetry and horizontal line symmetry.

178 citations




Journal ArticleDOI
TL;DR: In this article, the authors derived some general properties for intergrowth structures, using the superspace-group theory as developed by Janner and Janssen [Acta Crystallogr. A36, 408 (1980)].
Abstract: Composite crystals are crystals that consist of two or more subsystems, in first approximation each one having its own three-dimensional periodicity. The symmetry of these subsystems is then characterized by an ordinary space group. Due to their mutual interaction the true structure consists of a collection of incommensurately modulated subsystems. In this paper we derive some general properties for intergrowth structures, using the superspace-group theory as developed by Janner and Janssen [Acta Crystallogr. A36, 408 (1980)]. In particular, the pseudoinverse is defined of the matrices relating the subsystem periodicities to the translation vectors in superspace. This pseudoinverse is then used to reformulate the relations between the structure and symmetry in three-dimensional space and in (3+d)-dimensional superspace. As an extension of the theory, subsystem superspace groups are defined, that characterize the symmetry of the individual, incommen- surately modulated subsystems. The relation between a unified description of the symmetry and an independent description of the subsystems is analyzed in detail, both on the level of the basic structure (translational symmetric subsystems) and on the level of the modulated structure (incommensurately modulated subsystems). The concepts are illustrated by the analysis of the diffraction symmetry of the intergrowth compound ${\mathrm{Hg}}_{3\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$${\mathrm{AsF}}_{6}$.

61 citations


Journal ArticleDOI
01 Jan 1991-Nature
TL;DR: In this paper, it was shown that within the point group of the polyhedron the symmetries spanned by the sets of vertices, faces and edges are also related.
Abstract: POLYHEDRAL cages and clusters are widespread in chemistry. Examples of fully triangulated polyhedra (deltahedra) are the skeletons of closo-boranes BnH2−n, many heteroboranes and transition-metal carbonyls1. Three-connected cages occur for carbon2,3 and in zeolites1. The numbers v, f and e of vertices, faces and edges of a convex polyhedron are related by Euler's theorem4,5 v+f=e + 2. Here we show that within the point group of the polyhedron the symmetries spanned by the sets of vertices, faces and edges are also related. We prove a general theorem relating these symmetries for convex polyhedra, and give further relations specific to deltahedra and 3-connected polyhedra. The latter extensions of Euler's theorem to point-group characters allow us to generate complete sets of internal vibrational coordinates from bond stretches for deltahedra, and to classify, from symmetry properties alone, the bonding or antibonding nature of molecular orbitals of 3-connected cages.

51 citations


Journal ArticleDOI
TL;DR: Observers judged whether 2 successive computer-displayed rotations of a cube were the same or different as the axes of the successive rotations departed from the canonical axis of the environment.
Abstract: Observers judged whether 2 successive computer-displayed rotations of a cube were the same or different. With respect to the observers, each rotation was about a vertical axis (Y), a horizontal (line-of-sight) axis (Z), an axis tilted just 10 degrees from vertical or horizontal, or a maximally oblique axis. Independently, with respect to the cube, each rotation was about a symmetry axis through opposite faces (F) or through opposite corners (C), an axis tilted 10 degrees from one of these symmetry axes, or an axis of extreme nonsymmetry. Speed and accuracy of comparison decreased as the axes of the successive rotations departed from the canonical axes of the environment (Z, or especially, Y), or even more sharply, from the symmetry axes of the cube (C, or especially, F). The internalized principles that guide the perceptual representation of rigid motions evidently are ones of kinematic geometry more than of physics. Language: en

51 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that all the symmetries possible for the elastic tensors can be reduced to the twelve symmets already used in the description of the crystal classes.
Abstract: It is shown that all symmetries possible for the elastic tensors can be reduced to the twelve symmetries already used in the description of the crystal classes. Each symmetry can be characterized by a group of rotations generated by no more than two rotations. The use of a canonical basis related to such rotations considerably simplifies the component forms of the elasticity tensor. This result applies to non-symmetric tensors; for symmetric tensors, the number of independent symmetries reduces from twelve to ten. After the present work was submitted, the following paper came to our attention: 14. S.C. Cowin and M.M. Mehrabadi, On the identification of material symmetry for anisotropic elastic materials. Q. Jl. Mech. appl. Math.40 (1987) 451–476. This paper contains an independent analysis of the partial ordering ≺ among the crystallographic elastic symmetries. However, it does not deal with the problem of the completeness of these symmetries.

51 citations


Journal ArticleDOI
TL;DR: In this article, a simple and general scheme to exploit any discrete point group symmetry in two-electron integral transformations is introduced, which has been implemented together with integral pre-screening techniques in direct 2E integral transformations and is extended to subsequent MO integral processing steps like MP2 or solution of the coupled-perturbed Hartree-Fock equations (CPHF).
Abstract: A simple and general scheme to exploit any discrete point group symmetry in two-electron integral transformations is introduced. It has been implemented together with integral pre-screening techniques in direct two-electron integral transformations. Its application has also been extended to subsequent MO integral processing steps like MP2 or solution of the coupled-perturbed Hartree-Fock equations (CPHF). Timings for representative applications are presented.

39 citations



Journal ArticleDOI
TL;DR: In this paper, the hidden symmetry associated with this non-standard BGR is shown to be the q-deformed Lie superalgebra Uq (gl(1|1)) and the result shows that the BGR solution is indeed the Q-deformable BGR.
Abstract: The formulae of the Faddeev-Reshetikhin-Takhtajan (FRT) method in supersymmetric case are presented transparently and consistently. With the help of these formulae, the simplest “non-standard” solution of braid group representation (BGR) is re-examined. The result shows that the hidden symmetry associated with this “non-standard” BGR is indeed the q-deformed Lie superalgebra Uq (gl(1|1)).

Journal ArticleDOI
TL;DR: The superspace representation of BRST transformations as translations in the direction of an extra anti-commuting coordinate is reviewed in this paper and the quantum Yang-Mills action is shown to possess an infinitely reducible pre-gauge symmetry, which must be gauge fixed.

Journal ArticleDOI
TL;DR: The procedure consists of computing the axes of ‘microsymmetry’ for pairs of microsegments based on the mean square error criterion, mapping the axes into two-dimensional parameter space, and detecting the peaks in the parameter space to obtain the global axes of symmetry.

Journal ArticleDOI
TL;DR: Parameter-dependent systems of nonlinear equations with symmetry are treated by a combination of symbolic and numerical computations, and it is here that symmetrical normal forms, symmetry reduced systems, and block diagonal Jacobians are computed.
Abstract: Parameter-dependent systems of nonlinear equations with symmetry are treated by a combination of symbolic and numerical computations. In the symbolic part of the algorithm the complete analysis of the symmetry occurs, and it is here that symmetrical normal forms, symmetry reduced systems, and block diagonal Jacobians are computed. Given a particular problem, the symbolic algorithm can create and compute through the list of possible bifurcations thereby forming a so-called tree of decisions correlated to the different types of symmetry breaking bifurcation points. The remaining part of the algorithm deals with the numerical pathfollowing based on the implicit reparameterization as suggested and worked out by Deutlhard, Fiedler, and Kunkel. The symmetry breaking bifurcation points are computed using recently developed augmented systems incorporating the use of symmetry.

Journal ArticleDOI
TL;DR: In this article, the displacement of the representative point for a chiral object away from the nearest point representing an achiral object in a multi-dimensional configuration space is quantified, and the most chiral triangle in terms of this measure corresponds to one that is infinitely flat.
Abstract: Chiral objects, viewed as distorted derivatives of achiral ones, may be represented by points in a configuration space that is spanned by a set of symmetry coordinates derived for the symmetry group of the achiral object of highest symmetry. We propose a measure (d) that quantifies the displacement of the representative point for a chiral object away from thenearest point representing an achiral object in such a multi-dimensional configuration space. If the symmetry coordinates are chosen so as to yield a similarity invariant measure, then the valuesd; obtained for a series ofi chiral objects can serve as a basis for comparing the degrees of chirality of these objects. The chirality of triangles inE 2 is studied by this method, and it is shown that the most chiral triangle in terms of this measure corresponds to one that is infinitely flat, and that may be approached but is never attained. This result is compared to others obtained previously for the same system by the use of different measures of chirality.

01 May 1991
TL;DR: In this article, a geometric representation in terms of characteristic invariants for an important family of subgroups of the proper Euclidean group is defined, called a $TR$ group, which is a semidirect product of a translation group and a rotation group.
Abstract: In this dissertation group theory, being the standard mathematical tool for describing symmetry, is used to characterize the symmetries of bodies and features, especially the symmetries relevant to contact between bodies Such a characterization reveals the necessity of intersecting subgroups of the proper Euclidean group ${\cal E}\sp{+}$ The central theoretical results of this dissertation are to establish this necessity mathematically and to provide a compact representation for the subgroups of ${\cal E}\sp{+}$ that leads an efficient group intersection algorithm I define a geometric representation in terms of characteristic invariants for an important family of subgroups of ${\cal E}\sp{+}$ Each member of this family is called a $TR$ group since it is a semidirect product of a translation group $T$ and a rotation group $R$ I prove that there is a one-to-one correspondence between $TR$ groups and their characteristic invariants I also prove that the intersection of $TR$ groups is closed and can be efficiently calculated from their characteristic invariants A practical issue addressed in this dissertation is the linkage between mechanical design and robotic task-level planning The formal treatment of $TR$ symmetry groups has been embedded into the implementation of an assembly planning system ${\cal KA}$3, which takes as input the geometric boundary models of assembly components provided by an off-the-shelf geometric solid modeller PADL2, and a set of instructions in the form of 'body A fits body B' ${\cal KA}$3 finds a set of detailed robotic assembly task specifications in three steps: Step one: ${\cal KA}$3 finds mating features from the boundary models of assembly components using a salient feature library and the symmetry group intersection algorithm Step two: ${\cal KA}$3 applies techniques used in constraint satisfaction problems (CSP) to satisfy kinematic and spatial constraints for each candidate assembly configuration Step three: ${\cal KA}$3 generates a partially ordered sequence of contact states for assembly components through an analysis of disassembly via translational motion The interaction between algebra and geometry within a group theoretic framework and the interaction between CSP techniques and heuristic search strategies provide us with a unified computational treatment of reasoning about how parts with multiple contacting features fit together

Journal ArticleDOI
TL;DR: In this article, the authors define a uniformity on a frame using entourages and introduce two new symmetry conditions for a quasi-uniform space, open-set symmetry and small-set symmetric.
Abstract: The purpose of this paper is to define a uniformity on a frame using entourages. A definition of uniformities in terms of covers has been given byA. Pultr ([8], [10]). We introduce two new symmetry conditions for a quasi-uniform space, open-set symmetry and small-set symmetry. We prove that a quasi-uniformityU is a uniformity if and only if it is both open-set symmetric and small-set symmetric. The category of (covering) uniform frames is isomorphic with the category of entourage uniform frames.


Journal ArticleDOI
TL;DR: A high symmetry class of tensors with an orthogonal basis of decomposable symmetrized tensors is presented, and this is a counter-example of the claim presented in [1].
Abstract: We present a high symmetry class of tensors with an orthogonal basis of decomposable symmetrized tensors, and this is a counter-example of the claim presented in [1].

Journal ArticleDOI
TL;DR: In this article, the symmetry groups of quasiperiodic systems are discussed in a formalism that uses space groups with dimension larger than three and three main types are distinguished: modulated crystal phases, incommensurate composite structures and quasicrystals.
Abstract: A discussion is given of the symmetry groups of quasiperiodic systems. This is done in a formalism that uses space groups with dimension larger than three. Three main types are distinguished: modulated crystal phases, incommensurate composite structures and quasicrystals. For these the differences and similarities are discussed and the canonical embedding in higher-dimensional space is given, which requires some generalizations of earlier definitions. The equivalence relation between space groups for quasiperiodic systems is different from that for ordinary space groups, because of the presence of a distinct physical space. Apart from higher-dimensional space groups, some quasiperiodic systems have self-similarity properties. Examples are given and the relationship with space-group symmetry is discussed.


Book ChapterDOI
01 Jan 1991
TL;DR: In this article, a classification of ODE symmetries was carried out by S. Lie at the end of the last century, summarizing Lie's work (only a small part of it is preserved in text books).
Abstract: I I n t r o d u c t i o n . How can we make such a classification? One has to choose a group G acting on the set of ODE (ordinary differential equations). The stabilizer G~ of the equation 6 = 0 is its symmetry group. The equations of the orbit G.£ have "same symmetry": their stabilizers are conjugated to G~. More generally, the union of the orbits with stabilizers conjugated to Ge form the stratum of ODE with symmetry G~ (up to a conjugation). Such a classification of ODE symmetries was implicitly carried by S. Lie at the end of the last century. The number of strata is infinite; but we shall explain how they can be obtained, summarizing Lie's work (only a small part of it is preserved in text books) and adding some recent contributions. In the X I X ~h century, analytic transformations:


Journal ArticleDOI
Sergio Ferrara1
TL;DR: In this paper, the authors review some aspects of the geometry of the moduli space of superstring vacua with (2, 2) superconformal symmetry, its connection with the deformation theory of holomorphic three forms and its relation to space-time supersymmetry.
Abstract: We review some aspects of the geometry of the moduli space of superstring vacua with (2, 2) superconformal symmetry, its connection with the deformation theory of holomorphic three forms and its relation to space-time supersymmetry.

Book
01 Jan 1991
TL;DR: Symmetry Elements and Symmetry Operations - Groups and their Basic Properties - Matrices - Representations of Groups - Reducible and Irreducible Representations - Some Important REDUCible Representation- Adapted Linear Combinations - Group Theory and Vibrational Spectroscopy - Some Further Aspects of Vibrations - Symmetric and Bonding - Electronic Spectrograms and Electronic Spectro-Chemical Reactions - Answers to Exercises - Bibliography - Appendix - Index as discussed by the authors
Abstract: Symmetry Elements and Symmetry Operations - Groups and their Basic Properties - Matrices - Representations of Groups - Reducible and Irreducible Representations - Some Important Reducible Representations - Symmetry Adapted Linear Combinations - Group Theory and Vibrational Spectroscopy - Some Further Aspects of Vibrational Spectroscopy - Symmetry and Bonding - Electronic Spectroscopy - Orbital Symmetry and Chemical Reactions - Answers to Exercises - Bibliography - Appendix - Index

Book ChapterDOI
21 Mar 1991
TL;DR: The algorithm presented is an extension of Weinberg's algorithm for determining isomorphisms of planar triply connected graphs and can be utilized for various purposes in artificial intelligence, robotics, assembly planning and machine vision.
Abstract: In this paper we present a simple and efficient algorithm for determining the rotational symmetries of polyhedral objects in O(m2) time using O(m) space where m represents the number of edges of the object. Our algorithm is an extension of Weinberg's algorithm for determining isomorphisms of planar triply connected graphs. The symmetry information detected by our algorithm can be utilized for various purposes in artificial intelligence, robotics, assembly planning and machine vision. In particular, an application of symmetry analysis to object recognition will be described in some detail.

Journal ArticleDOI
TL;DR: In this article, it was shown that every function of three variables is uniquely expressible as the sum of a symmetric function, a skew-symmetric function and a cyclic symmetric functions, where Pn is the number of partitions of the integer n.
Abstract: The attempt to generalize this fact to functions of n variables led Alfred Young to develop his theory of symmetrizers, now subsumed in the theory of representations of the symmetric group. According to this theory, a function of n variables is uniquely expressible as the sum of Pn functions, each one belonging to a different symmetry class, where Pn is the number of partitions of the integer n. Unfortunately, a simple intuitive description of such symmetry classes has never been given except for n = 2. It is known that for functions of three variables, there is only one other symmetry class besides the two obvious symmetry classes of symmetric functions and of skew-symmetric functions. We give this third symmetry class a very simple characterization, one that seems to have been overlooked. We show that it consists of all cyclic-symmetric functions. We prove that every function of three variables is uniquely expressible as the sum of a symmetric function, a skew-symmetric function and a cyclic-symmetric function. To make this note self-contained, we have added a short derivation of some known formulas. We believe that the underlying idea of this note will extend to functions of n variables. We hope the present note will at least entice the reader to further study of the vast theory of symmetry classes.


Journal ArticleDOI
TL;DR: In this paper, a Shilnikov-type analysis for heteroclinic orbits of a symmetric system is presented, which differs from the usual case in that it involves a symmetry and there is more than one connecting orbit at the critical parameter value.