The interaction of Cr(CO)3 on the (n, 0) nanotube side-walls: a density functional study through a cluster model approach

Density functional calculations have been performed to investigate the functionalization of single-wall carbon nanotubes (SWNTs) with the Cr(CO)₃ metal fragment, employing extended molecular models. A circumcoronene molecule (C₅₄H₁₈), made by the fusion of 19 hexagonal carbon rings, can be regarded as a fragment of a graphene sheet. To reproduce the curvature of the SWNT surface, suitable geometric constraints have been imposed on the C₅₄H₁₈ model, freezing the positions of the outer hydrogens along the directions of the nanotube C-C bonds. Geometry optimizations have then been performed under this constraint on the Cr(CO)₃-C₅₄H₁₈ complexes, pointing out the most favourable coordination sites on the hexagonal rings of the carbon atom surface and the electronic properties of the resulting system. The effect of the curvature on the metal coordination to nanotubes has been analysed by investigating the interaction of the Cr(CO)₃ metal complex with the C₅₄H₁₈ molecules, modelling (n, 0) nanotubes with different degrees of curvature, i.e. with various values of the chiral vector (n, 0).     

A High Resolution Scheme for the Numerical Simulation of Second Sound in Crystals

A high resolution essentially non-oscillatory (ENO) numerical scheme is applied to a new model of heat propagation in crystals for an accurate reconstruction of second sound waves. A splitting of the governing equations allows to approximate the differential terms and the forcing term by means of the ENO scheme and a Runge--Kutta third order scheme, respectively. Results obtained on data relative to a high purity crystal of NaF are in good agreement with the theoretical predictions.     

On the Admissibility of Some Linear and Projective Groups in Odd Characteristic

A bijective mapping defined on a finite group G is complete if the mapping defined by , , is bijective. In 1955 M. Hall and L. J. Paige conjectured that a finite group G has a complete mapping if and only if a Sylow 2-subgroup of G is non-cyclic or trivial. This conjecture is still open. In this paper we construct a complete mapping for the projective groups PSL and PGL(2,q),q odd. As a consequence, we prove that in odd characteristic the projective groups PGL(n,q GL , admit a complete mapping.