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.     

Selectivity of purine alkylation by a quinone methide. Kinetic or thermodynamic control?

The alkylation reaction of 9-methyladenine and 9-methylguanine (as prototype substrates of deoxy-adenosine and -guanosine), by the parent o-quinone methide (o-QM), has been investigated in the gas phase and in aqueous solution, using density functional theory at the B3LYP/6-311+G(d,p) level. The effect of the medium on the reactivity, and on the stability of the resulting adducts, has been investigated by using the C-PCM solvation model to assess which adduct arises from the kinetically favorable path, or from an equilibrating process. The calculations indicate that the most nucleophilic site of the methyl-substituted nucleobases in the gas phase is the guanine oxygen atom (O(6)) (DeltaG()(gas) = 5.6 kcal mol(-)(1)), followed by the adenine N1 (DeltaG)(gas) = 10.3 kcal mol(-)(1)), while other centers exhibit a substantially lower nucleophilicity. The bulk effect of water as a solvent is the dramatic reduction of the nucleophilicity of both 9-methyladenine N1 (DeltaG)(solv) = 14.5 kcal mol(-)(1)) and 9-methylguanine O(6) (DeltaG)(solv) = 17.0 kcal mol(-)(1)). As a result there is a reversal of the nucleophilicity order of the purine bases. While O(6) and N7 nucleophilic centers of 9-methylguanine compete almost on the same footing, the reactivity gap between N1 and N7 of 9-methyladenine in solution is highly reduced. Regarding product stability, calculations predict that only two of the adducts of o-QM with 9-methyladenine, those at NH(2) and N1 positions, are lower in energy than reactants, both in the gas phase and in water. However, the adduct at N1 can easily dissociate in water. The adducts arising from the covalent modification of 9-methylguanine are largely more stable than reactants in the gas phase, but their stability is markedly reduced in water. In particular, the oxygen alkylation adduct becomes slightly unstable in water (DeltaG(solv) = +1.4 kcal mol(-)(1)), and the N7 alkylation product remains only moderately more stable than free reactants (DeltaG(solv) = -2.8 kcal mol(-)(1)). Our data show that site alkylations at the adenine N1 and the guanine O(6) and N7 in water are the result of kinetically controlled processes and that the selective modification of the exo-amino groups of guanine N2 and adenine N6 are generated by thermodynamic equilibrations. The ability of o-QM to form several metastable adducts with purine nucleobases (at guanine N7 and O(2), and adenine N1) in water suggests that the above adducts may act as o-QM carriers.