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On color groups of Bravais colorings of planar modules with quasicrystallographic symmetries Enrico Paolo C. Bugarin*, I, Ma. Louise Antonette N. De Las PeñasI, Imogene F. EvidenteII, Rene P. FelixII and Dirk FrettloehIII I Mathematics Department, Ateneo de Manila University, Loyola Heights, Quezon City, Philippines II Institute of Mathematics, University of the Philippines, Diliman, Quezon City, Philippines III Faculty of Mathematics, University of Bielefeld, 33501 Bielefeld, Germany Received June 15, 2008; accepted July 27, 2008 Color groups / Lattices

Enumerating and identifying semiperfect colorings of symmetrical patterns Rene P. Felix and Manuel Joseph C. Loquias*; 1 Institute of Mathematics, University of the Philippines, Diliman, C. P. Garcia Avenue, 1101 Diliman, Quezon City, Philippines Received March 3, 2008; accepted July 22, 2008 Semiperfect colorings / Equivalent colorings / Color symmetry / Color groups Abstract. If G is the symmetry group of an uncolored pattern then a coloring of the pattern is semiperfect if the associated color group H is a subgroup of G of index 2. We give results on how to

Colorings of single-wall carbon nanotubes Mark L. LoyolaI, Ma. Louise Antonette N. De Las Peñas*, I and Antonio M. Basilio, S. J.II I Mathematics Department, Ateneo de Manila University, Loyola Heights, 1108 Quezon City, Philippines II Chemistry Department, Ateneo de Manila University, Loyola Heights, 1108 Quezon City, Philippines Received February 28, 2012; accepted July 2, 2012 Published online: August 20, 2012 Single-wall carbon nanotubes / Symmetry groups / Color symmetry / Color groups / Structural analogues of carbon nanotubes Abstract. In this work, we

Zeitschrift für Kristallographie, Bd. 115, S. 231—234 (1961) Farbgruppen Von b. L. van der waerden und J. J. burckharüt Mathematisches Institut der Universität Zürich Mit 1 Abbildung im Text (Eingegangen am 15. Januar 1961) Abstract The notions Colour-Symmetry Group and Colour Group are defined. A simple method is given, by which all possible colour groups corresponding to a given symmetry group can be found. Auszug Die Begriffe Farbsymmetriegruppe mid Farbgruppe werden definiert. Es wird eine einfache Methode angegeben, die es gestattet, zu einer gegebenen

polycolor symmetry is derived from elementary considerations. It is shown that each color group is characterized by a symmetry group 67, and a subgroup H which determines a homomorphism from 67 to a group P of color permutations. Various ways in which the properties of H can affect the color groups are discussed. The 32 crystallographic point groups are classified in a new way which facilitates the determination of subgroups and hence of color groups. Several treatments of color symmetry that have appeared in the literature are discussed. They seem to differ in their

Zeitschrift für Kristallographie 208, 199-206 (1993) © by R. Oldenbourg Verlag, München 1993 - 0044-2968/93 $ 3.00 + 0.00 Laue and Patterson symmetry in the complex case A. J. C. Wilson International Tables for Crystallography St. John's College, Cambridge CB2 1TP, England Dedicated to Professor E. F. Bertaut on the occasion ofhis eightieth birthday Received: January 13, 1993; revised April 19, 1993 Laue symmetry (generalized) j Patterson symmetry / Dispersion ('anomalous scattering') / Colour groups / Arithmetic crystal classes / International Tables for

Colorings of lattices based on subgroup orbits Ma. Lailani B. Walo* and René P. Felix Institute of Mathematics, University of the Philippines, Diliman., C.P. Garcia Ave, Diliman, Quezon City, 1101, Philippines Received March 1, 2011; accepted July 5, 2011 Lattice / Orbits / Normalizer / Color group Abstract. In this paper, orbit colorings of a lattice L were considered, extending the idea of obtaining lattice color- ings based on cosets of a sublattice. Given a subgroup S of finite index in the symmetry group G of the lattice L, if TðSÞ is the subgroup of

Abstract

The aim of research was to analyse winter wheat of different grain colour and to compare newly bred coloured genotypes from our breeding in grain yield and technological and nutritional quality. The set of seven purple, five blue and four yellow wheats of different origin, including seven newly bred genotypes from Vígľaš-Pstruša, was evaluated in the field experiments established by randomised complete block design in two replications in Piešťany, in the vegetations 2012/13 and 2013/14. In seven wheat varieties differing in grain colours (selected after two of each colour plus control red variety Ilona) anthocyanin composition was evaluated by HPLC analysis. Significant differences were between growing years and among colour groups in most analysed traits. Blue grain newly bred K 3575 699/3 showed the highest anthocyanin content (by 33.5% higher compared to blue grain registered variety Scorpion). However, blue grain genotypes showed negative agronomic traits combined with low number and grain weight per spike and high plant height. In new purple variety PS Karkulka, declared grain yield and its quality were confirmed and the highest mineral content (Fe, Zn, Cu, Mn) was found in selected set. Purple grain newly bred PS 5711 had lower anthocyanin content (by 17.7%), but in quality it was comparable to PS Karkulka. Varieties with yellow endosperm showed the highest number and weight of grains per spike, however it was significantly lower to Ilona. The breeding goal of coloured winter wheat is still to improve the grain yield as well as additional agronomics traits.

Zeitschrif t fü r Kr i s t a l log raph ie 208, 1 9 9 - 2 0 6 (1993) < by R. O l d e n b o u r g Verlag, M ü n c h e n 1993 - 0044-2968/93 $ 3.00 + 0.00 Laue and Patterson symmetry in the complex case A. J. C. Wilson International Tables for Crystallography St. John's College, Cambridge CB2 1TP, England Dedicated to Professor E. F. Bertaut ort the occasion of his eightieth birthday Received: January 13, 1993; revised April 19, 1993 Laue symmetry (generalized) / Patterson symmetry / Dispersion ('anomalous scattering') / Colour groups / Arithmetic crystal

polycolor symmetry is derived from elementary considerations. I t is shown tha t each color group is characterized by a symmetry group β , and a subgroup Η which determines a homomorphism from β to a group Γ of color permutations. Various ways in which the properties of Η can affect the color groups are discussed. The 32 crystallographic point groups are classified in a new way which facilitates the determination of subgroups and hence of color groups. Several t reatments of color symmetry t h a t have appeared in the literature are discussed. They seem to differ