منابع مشابه
Hexagonal projected symmetries.
In the study of pattern formation in symmetric physical systems, a three-dimensional structure in thin domains is often modelled as a two-dimensional one. This paper is concerned with functions in {\bb R}^{3} that are invariant under the action of a crystallographic group and the symmetries of their projections into a function defined on a plane. A list is obtained of the crystallographic group...
متن کاملSymmetries in Hexagonal Quasigroups
When it doesn’t cause confusion, we can omit the sign “·”, e.g. instead of (a · b) · (c · d) we may write ab · cd. In this article, Q will always be a hexagonal quasigroup. The basic example of hexagonal quasigroup is formed by the points of Euclidean plane, with the operation · such that the points a, b and a · b form a positively oriented regular triangle. This structure was used for all the ...
متن کاملSymmetries of Projected Wallpaper Patterns
In this paper we study periodic functions of one and two variables that are invariant under a subgroup of the Euclidean group. Starting with a function defined on the plane we obtain a function of one variable by two methods: we project the values of the function on a strip into its edge, by integrating along the width; and we restrict the function to a line. If the functions had been obtained ...
متن کاملSymmetries of Hexagonal Molecular Graphs on the Torus
Symmetric properties of some molecular graphs on the torus are studied. In particular we determine which cubic cyclic Haar graphs are 1-regular, which is equivalent to saying that their line graphs are 1 2-arc-transitive. Although these symmetries make all vertices and all edges indistinguishable , they imply intrinsic chirality of the corresponding molecular graph.
متن کاملTechnical report: Two observations on probability distribution symmetries for randomly-projected data
In this technical report, we will make two observations concerning symmetries of the probability distribution resulting from projection of a piece of p-dimensional data onto a random m-dimensional subspace of $\mathbb{R}^p$, where m<p. In particular, we shall observe that such distributions are unchanged by reflection across the original data vector and by rotation about the original data vector
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ژورنال
عنوان ژورنال: Acta Crystallographica Section A Foundations and Advances
سال: 2015
ISSN: 2053-2733
DOI: 10.1107/s2053273315012905