A Fullerene with pentagons, hexagons, and heptagons is considered. The number of carbons is 458. It contains 8 heptagonal rings, 21 pentagons, and 212 hexagons. Keywords-component; fullerene; heptagon; pentagon adjacency penalty rule; fullerene with many carbons

We present an investigation of the structural and electronic properties of an ordered grain boundary (GB) formed by separated pentagon-heptagon pairs in single-layer graphene/SiO2 using scanning tunneling microscopy/spectroscopy (STM/STS), coupled with density functional theory (DFT) calculations. It is observed that the pentagon-heptagon pairs, i.e., (1,0) dislocations, form a periodic quasi-o...

An Ansatz is proposed for the heptagon relation, that is, an algebraic imitation of five-dimensional Pachner move 4–3. The formula in question realized terms matrices acting a direct sum one-dimensional linear spaces corresponding to 4-faces.

Defect states in nitrogen-containing float-zone silicon are investigated both n- and p-type materials using deep-level transient spectroscopy (DLTS) minority-carrier (MCTS). This enables a mapping of the defect landscape entire electronic bandgap an investigation whether properties defects depend on semiconductor type. Two defects, E1/E2 pair E4/E6 pair, investigated, no evidence is found for to

A molecular-dynamics simulation has been carried out for amorphous selenium. The simulation used 64 atoms in a constant volume simple cubic cell. The pair correlation function, g…r†, and structure factor, S…Q†, were computed and compared with experimental and previous theoretical studies. The average coordination number is exactly 2. Only one defect, an intimate valence alternation pair type de...

From the pentagon onwards, the area of the regular convex polygon with n sides and unit diameter is greater for each odd number n than for the next even number n + 1. Moreover, from the heptagon onwards, the difference in areas decreases when n increases. Similar properties hold for the perimeter. A new proof of a result of Reinhardt follows.

We construct a smooth family of Hamiltonian systems, together with a family of group symmetries and momentum maps, for the dynamics of point vortices on surfaces parametrized by the curvature of the surface. Equivariant bifurcations in this family are characterized, whence the stability of the Thomson heptagon is deduced without recourse to the Birkhoff normal form, which has hitherto been a ne...