Symmetry, Volume 3, Issue 1

The 1,4-conjugate addition of nucleophiles to α,β-unsaturated carbonyl compounds represents one fundamental bond-forming reaction in organic synthesis. The development of effective organocatalysts for the enantioselective conjugate addition of malona...

Much is already known about single mirror symmetry, but multiple mirror symmetry is still understood poorly. In particular, perceptually, multiple symmetry does not seem to behave as suggested by the number of symmetry axes alone. Here, theoretical i...

We show that in long-time the heat semi-group on a path group associated to a Bilaplacian on the group tends to the Haar distribution on a path group.

Although symmetry may be important for understanding the selection of form in art over the historical period, this preference may have originally stemmed from certain basic perceptual mechanism that initially arose during prehistory. The first signs...

Among the symmetries in physics, the rotation symmetry is most familiar to us. It is known that the spherical harmonics serve useful purposes when the world is rotated. Squeeze transformations are also becoming more prominent in physics, particularly...

In this paper, we analyze a few interrelated concepts about graphs, such as their degree, entropy, or their symmetry/asymmetry levels. These concepts prove useful in the study of different types of Systems, and particularly, in the analysis of Comple...