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.     

Application of accelerated heteronuclear single quantum coherence experiments to the rapid quantification of monosaccharides and disaccharides in dairy products

Monosaccharides and disaccharides are important dietary components, but if insufficiently metabolized by some population subgroups, they are also linked to disease patterns. Thus, the correct analytical identification, quantification, and labeling of these food components are crucial to inform and potentially protect consumers. Enzymatic assays and high-performance anion-exchange chromatography with pulsed amperometric detection are established methods for the quantification of monosaccharides and disaccharides that, however, require long measuring times (60–180 min). Accelerated methods for the identification and quantification of the nutritionally relevant monosaccharides and disaccharides d -glucose, d -galactose, d -fructose, sucrose, lactose, and maltose were therefore developed. To realize this goal, the NMR experiments HSQC (heteronuclear single quantum coherence) and acceleration by sharing adjacent polarization (ASAP)-HSQC were applied. Measurement times were reduced to 27 and 6 min, respectively, by optimizing the interscan delay and applying non-uniform sampling. The optimized methods were used to quantify d -glucose, d -galactose, d -fructose, sucrose, and lactose in various dairy products. Results of the HSQC and ASAP-HSQC methods are equivalent to the results of the reference methods in terms of both precision and accuracy, demonstrating that these methods can be used to correctly analyze nutritionally relevant monosaccharides and disaccharides in short times.