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).     

Two-level structured self-adaptive surfaces with reversibly tunable properties

We report a route to fabricate two-level structured self-adaptive surfaces (SAS) of polymer materials. The first level of structure is built by a rough polymer film that consists of needlelike structures of micrometer size. The second level of structure is formed by the nanoscopic self-assembled domains of a demixed polymer brush irreversibly grafted onto the needles. By exposing the surface to solvents that are selective to one of the components of the brush, we reversibly tune the surface properties. The large-scale surface structure amplifies the response and enables us to control wettability, adhesion, and chemical composition of the surface over a wide range.     

Classical limit of the quantized hyperbolic toral automorphisms

The canonical quantization of any hyperbolic symplectomorphismA of the 2-torus yields a periodic unitary operator on aN-dimenional Hilbert space,N=1/h. We prove that this quantum system becomes ergodic and mixing at the classical limit (N,N prime) which can be interchanged with the time-average limit. The recovery of the stochastic behaviour out of a periodic one is based on the same mechanism under which the uniform distribution of the classical periodic orbits reproduces the Lebesgue measure: the Wigner functions of the eigenstates, supported on the classical periodic orbits, are indeed proved to become uniformly speread in phase space.     

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.     

Site-specific ligation of anthracene-1,8-dicarboxylates to an Mn12 core: a route to the controlled functionalisation of single-molecule magnets

A novel single-molecule magnet of the Mn12 family, [Mn12O12(O2CC6H5)8(L)4(H2O)4].8CH2Cl2, has been synthesised by site-specific ligand exchange using a tailor-made dicarboxylate (L2-), which leads to selective occupation of axial binding sites.