Collapsing manifolds with boundary

This paper studies manifolds-with-boundary collapsing in the Gromov– Hausdorff topology. The main aim is an understanding of the relationship of the topology and geometry of a limiting sequence of manifolds-with-boundary to that of a limit space, which is presumed to be without geodesic terminals. The first group of results provide a fiber bundle structure to the manifolds-with-boundary. One of the main theorems establishes a disc bundle structure for any manifold-with-boundary having two-sided bounds on sectional curvature and second fundamental form, and a lower bound on intrinsic injectivity radius, which is sufficiently close in the Gromov–Hausdorff topology to a closed manifold. Another result is a rough version of Toponogov’s Splitting Theorem. The second group of results identify Gromov–Hausdorff limits of certain sequences of manifolds with non-convex boundaries as Alexandrov spaces of curvature bounded below.     

High‐performance liquid chromatography/mass spectrometric and proton nuclear magnetic resonance spectroscopic studies of the transacylation and hydrolysis of the acyl glucuronides of a series of phenylacetic acids in buffer and human plasma

The use of high‐performance liquid chromatography/mass spectrometry (HPLC/MS) and proton nuclear magnetic resonance (¹H NMR) spectroscopy for the kinetic analysis of acyl glucuronide (AG) isomerisation and hydrolysis of the 1‐β‐O‐acyl glucuronides (1‐β‐O‐AG) of phenylacetic acid, (R)‐ and (S)‐α‐methylphenylacetic acid and α,α‐dimethylphenylacetic acid is described and compared. Each AG was incubated in both aqueous buffer, at pH 7.4, and control human plasma at 37°C. Aliquots of these incubations, taken throughout the reaction time‐course, were analysed by HPLC/MS and ¹H NMR spectroscopy. In buffer, transacylation reactions predominated, with relatively little hydrolysis to the free aglycone observed. In human plasma incubations the calculated rates of reaction were much faster than for buffer and, in contrast to the observations in buffer, hydrolysis to the free aglycone was a significant contributor to the overall reaction. A diagnostic analytical methodology based on differential mass spectrometric fragmentation of 1‐β‐O‐AGs compared to the 2‐, 3‐ and 4‐positional isomers, which enables selective determination of the former, was confirmed and applied. These findings show that HPLC/MS offers a viable alternative to the more commonly used NMR spectroscopic approach for the determination of the transacylation and hydrolysis reactions of these AGs, with the major advantage of having the capability to do so in a complex biological matrix such as plasma. Copyright © 2010 John Wiley & Sons, Ltd.     

Green synthesis of para-Menthane-3,8-diol from Eucalyptus citriodora: Application for repellent products

A simple and efficient method was developed for the synthesis of para-Menthane-3,8-diol (PMD), a well-known repellent active against mosquitoes, from Eucalyptus citriodora essential oil by a treatment of citric acid in a biphasic medium (H₂O/essential oil). The E. citriodora contains as main component (+)-citronellal (74% in the present case), which cyclises (Prins reaction) to form cis/trans PMD isomers. As an example, an emulsion containing an aqueous solution of 7% citric acid and E. citriodora oil at 50°, conducted after 15 h stirring to 82% conversion of (+)-citronellal with a selectivity of 80% with the remaining presence of monoterpenes and sesquiterpenes in the medium. Investigations of lasting protection on human volunteers are carried out using a cage test bioassay protocol and Aedes aegypti mosquitoes. At 20% in ⁱPrOH, the new reaction mixture showed a complete protection of 303 min compared to 22 min with the pure essential oil. The modified oil was compared with N,N-diethyl-m-methylbenzamide (DEET), the most popular active used in repellent formulations. Thermogravimetric analyses (TGA) of E. citriodora, the modified oil, PMD, DEET, and (+)-citronellal were performed and showed a slow evaporation rate for PMD and DEET as well as for the modified oil, which may explain their long lasting protection action.     

Lewis acid-mediated addition of silylated methylenecyclopropane to aldehydes—synthesis of tetrahydrofuran derivatives

Lewis acid-mediated intermolecular addition of silylated methylenecyclopropane to aldehydes provides a novel route to tetrahydrofuran derivatives.     

Cycle-free partial orders and chordal comparability graphs

This paper studies a number of problems on cycle-free partial orders and chordal comparability graphs. The dimension of a cycle-free partial order is shown to be at most 4. A linear time algorithm is presented for determining whether a chordal directed graph is transitive, which yields an O(n ²) algorithm for recognizing chordal comparability graphs. An algorithm is presented for determining whether the transitive closure of a digraph is a cycle-free partial order in O(n+m _t)time, where m _tis the number of edges in the transitive closure.