Color symmetry and group theory

The Molecular Symmetry Group Theory for Trimethylamine-BH3 Addend(BH3 Free of Rotation)

Theory of color symmetry for periodic and quasiperiodic crystals

The author presents a theory of color symmetry applicable to the description and classification of periodic as well as quasiperiodic colored crystals. This theory is an extension to multicomponent fields of the Fourier-space approach of Rokhsar, Wright, and Mermin. It is based on the notion of indistinguishability and a generalization of the traditional concepts of color point group and color s...

Full Non-Rigid Group Theory and Symmetry of Melamine

The non-rigid molecule group (NRG) theory in which the dynamic symmetry operations are defined as physical operations is a new field in chemistry. Smeyers, in a series of papers, applied this notion to determine the character table of restricted NRG of some molecules. For example, Smeyers and Villa computed the r-NRG of the triple equivalent methyl rotation in pyramidal trimethylamine with inve...

Color Symmetry, Semigroups, Fractals

We discuss within one common context topics of color symmetry, using semigroups for generalization of symmetry, fractals, and some naturally occurring interrelations thereof. This free essay is emotionally inspired by the impressive scientific work of Prof. Douglas Jay Klein and his numerous collaborators, who contributed into diverse fields of chemistry, physics, and mathematics. (doi: 10.5562...

The Symmetry of Intersection Numbers in Group Theory

For suitable subgroups of a finitely generated group, we define the intersection number of one subgroup with another subgroup and show that this number is symmetric. We also give an interpretation of this number. If one considers two simple closed curves L and S on a closed orientable surface F , one can define their intersection number to be the least number of intersection points obtainable b...