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.     

Modeling the 1,3-dipolar cycloaddition of nitrones to vinylboranes in competition with boration, cyclization, and oxidation reactions

Structures and energetics of reactants, reactant complexes, concerted transition structures, and products of the cycloaddition of the prototypical nitrone with vinylborane have been produced and discussed. Structure optimizations have been performed at the B3LYP/6-31G(d) and B3LYP/AUG-cc-pVDZ levels of approximation, and single-point calculations on the B3LYP geometries have been carried out at the MP4(SDTQ) level with the same basis sets. Kinetic contributions to standard enthalpies, entropies, and free enthalpies have been computed at the same levels of geometry optimizations. The effects of methyl and chloro substitution on the BH2 group and of methyl substitution on the vinyl moiety has been also explicitly considered. The most striking theoretical features of this cycloaddition are (i) the formation of reactant complexes where the nitrone oxygen is strictly bound up to the boron atom (B...O interactions), (ii) their persistence in the endo/exo transition structures, and (iii) energy profiles suggesting very high reaction rates, regiospecificity (5-borylisoxazolidines) and complete endo-stereoselectivity. The BH2 (BX2) substituent appears to induce a sort of intramolecular catalysis which is also largely selective in favor of the endo reaction path. Possible competitive reaction paths such as cyclization, organoboration, and oxidation have equally been investigated, on the same grounds, both with prototypical reagents and with dimethylvinylborane, dichlorovinylborane, 2-methyl-1-propenylborane, and 2-methyl-1-propenyldichloroborane. The transition structures for these reaction paths are significantly higher in energy than those of the corresponding 1,3-dipolar cycloadditions in the sequence oxidation > cyclization > boration > cycloaddition, whereas the resulting reaction products show the reversed sequence. Polar solvents appear to increase the competition of boration although maintaining its character of secondary reaction. As expected, the reaction rate of 1,3-dipolar cycloaddition is lowered by dimethyl substitution on the vinyl CH2 reacting center (i.e., for the reaction of 2-methyl-1-propenylborane and 2-methyl-1-propenyldichloroborane) whereas the reaction rate of boration is increased, the boration results being significantly competitive even in the gas phase. Experiments for the control of the above predictions are not yet available.     

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.