On-line arbitrarily vertex decomposable trees

A tree T is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to the order of T there is a sequence of vertex-disjoint subtrees of T whose orders are given by τ. An on-line version of the problem of characterizing arbitrarily vertex decomposable trees is completely solved here.     

On the Neighbour-Distinguishing Index of a Graph

A proper edge colouring of a graph G is neighbour-distinguishing provided that it distinguishes adjacent vertices by sets of colours of their incident edges. It is proved that for any planar bipartite graph G with Δ(G)≥12 there is a neighbour-distinguishing edge colouring of G using at most Δ(G)+1 colours. Colourings distinguishing pairs of vertices that satisfy other requirements are also considered.     

New pi-extended water-soluble squaraines as singlet oxygen generators

[graph: see text] Condensation of squaric acid with a number of differently substituted 2-pyrrolyl derivatives afforded three new classes of squaraines. Their sharp and intense absorption bands in the biological window (700-900 nm), inherent singlet oxygen generation capabilities, together with proper functionalization allowing good water solubility make them suitable candidates as new non-porphyrinic singlet oxygen photosensitizers for photodynamic therapy (PDT).     

Interaction between zigzag single-wall carbon nanotubes and polymers: a density-functional study

Density-functional all-electrons calculations within local-density approximation show that the two isoelectronic polymers poly(para-phenylene) and poly(para-borazylene) weakly interact with zigzag single-walled carbon nanotubes. The analysis of the electronic properties of the joint systems, both with the polymer inside and outside the nanotubes, reveals a physisorption process with small changes in band structures and densities of states with respect to the constituents. We evaluate the potential barrier arising between polymers and nanotubes. Finally, we remark a generic selectivity of poly(para-phenylene) with respect to the electronic behavior of nanotubes, leading to a change in the density of states of metallic tubules.     

Direct minimization of the energy functional in LCAO-MO density matrix formalism I. Closed and open shell systems

A direct method of minimization of the energy expression for closed and open shell systems in LCAO-MO density matrix formalism is presented. The method makes use of a unitary transformation acting directly on the density matrices. Expressions of the gradient and second energy derivatives are worked out. Some preliminary calculations to test the rate of minimization using a variable metric method have been made on H₂S and SO molecules and have given satisfactory results.[/p]