Symmetry, Volume 6, Issue 3

Chlorophylls are a fundamental class of tetrapyrroles and function as the central reaction center, accessory and photoprotective pigments in photosynthesis. Their unique individual photochemical properties are a consequence of the tetrapyrrole macroc...

We propose an entropic argument as partial explanation of the observed scarcity of twinned structures in crystalline samples of synthetic organic polymeric materials. Polymeric molecules possess a much larger number of conformational degrees of freed...

The paper deals with the recognition of symmetric three-dimensional (3D) bodies that can be rotated and translated. We provide a complete list of all existing combinations of rotation and reflection symmetries in 3D. We define 3D complex moments b...

The last fifteen years have seen the identification of some of the mechanisms involved in anterior neural plate specification, patterning, and morphogenesis, which constitute the first stages in the formation of the forebrain. These studies have prov...

Controlled mirror symmetry breaking arising from chemical and physical origin is currently one of the hottest issues in the field of supramolecular chirality. The dynamic twisting abilities of solvent molecules are often ignored and unknown, although...

The crystal structure development of jojoba-like esters incorporating either 1-decenoic acid and/or 1-decenol, namely octadec-9-enyl dec-9-enoate (JLE-28₁), and its isomer dec-9-enyl oleate (JLE-28₂) was investigated to reveal the effect of symmetry...

Variable-temperature NMR spectroscopy is probably the most convenient and sensitive technique to monitor changes in molecular structure in solution. Rearrangements that are rapid on the NMR time-scale exhibit simplified spectra, whereby non-equivalen...

Symmetry operations of layers periodic in two dimensions restrict the geometry the lattice according to the five two-dimensional Bravais types of lattices. In order-disorder (OD) structures, the operations relating equivalent layers generally leave i...

Extensions of real numbers in more than two dimensions, in particular quaternions and octonions, are finding applications in physics due to the fact that they naturally capture symmetries of physical systems. However, in the conventional mathematical...

Gestalt Algebra gives a formal structure suitable for describing complex patterns in the image plain. This can be useful for recognizing hidden structure in images. The work at hand refers to the laws of perceptual psychology. A manifold called the G...

Autosolvation is an important factor in stabilizing the architecture of medium complicated molecules. It is a kind of “supramolecular force” acting in intramolecular manner, consisting of orbital-orbital interactions between polar groups, separated b...

Assur graphs are a tool originally developed by mechanical engineers to decompose mechanisms for simpler analysis and synthesis. Recent work has connected these graphs to strongly directed graphs and decompositions of the pinned rigidity matrix. Many...

The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group Sp(2). It is shown that this oscillator system contains the essential fea...