Graphs and Digraphs: A graph G = (V,E) is a structure that represents a discrete set V objects, called vertices or nodes, and a set of pairwise relations E between these objects, called edges. Edges may be directed from one vertex to another or may be undirected. The term “graph” means an undirected graph, and directed graphs are often called digraphs (see Fig. 1). Graphs and digraphs provide a...

Ab initio calculations at HF/6-31G* level of theory for geometry optimization and MP2/6-31G*//HF/6-31G* for a single point total energy calculation are reported for the importantenergy-minimum conformations and transition-state geometries of 1, 3-diazacyclohepta-1, 2-diene (2) and 1, 3-diazacycloocta-1, 2-diene (3). The C2 symmetric twist-chair (2-TC)conformation of 2 is calculated to be 7.4 kJ...

Bessel beams are widely used in optical metrology mainly because of their large Rayleigh range (focal length). Radial/azimuthal polarization of such beams is of interest in the fields of material processing, plasma absorption or communication. In this paper an experimental set-up is presented, which generates a Bessel-type vector beam with a spatial polarization, oscillating along the optical a...