Scaled discrete derivatives of singularly perturbed elliptic problems

Numerical approximations to the solution of a singularly perturbed elliptic convection–diffusion problem in two space dimensions are generated using a monotone finite difference operator on a tensor product of piecewise‐uniform Shishkin meshes. The bilinear interpolants of these numerical approximations are parameter‐uniformly convergent to the solution of the continuous problem, in the pointwise maximum norm. In this article, discrete approximations to the first derivatives of the solution are shown to be globally first‐order (up to logarithmic factors) uniformly convergent, when the errors are scaled within the analytical layers of the continuous problem. Numerical results are presented to illustrate the theoretical error bounds established in an appropriated weighted C¹–norm. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 225–252, 2015     

Chemistry of O‐ and H‐Containing Species on the (001) Surface of Anatase TiO2: A DFT Study

The chemistry of oxygen, hydrogen, water, and other species containing both oxygen and hydrogen atoms on the anatase TiO₂ (001) surface is investigated by DFT. The adsorption energy of atoms and radicals depends appreciably on the position and mode of adsorption, and on the coverage. Molecular hydrogen and oxygen interact weakly with the clean surface. However, H₂O dissociates spontaneously to give two nonidentical hydroxyl groups, and this provides a model for hydroxylation of TiO₂ surfaces by water. The mobility of the hydroxyl groups created by water splitting is initially impeded by a diffusion barrier close to 1 eV. The O₂ adsorption energy increases significantly in the presence of H atoms. Hydroperoxy (OOH) formation is feasible if at least two H atoms are present in the direct vicinity of O₂. In the adsorbed OOH, the O? O bond is considerably lengthened and thus weakened.     

Synthesis and Characterisation of Diruthenium Paddlewheel Compounds Bearing 2,6-Di(p-tolyl)benzoate Ligands

The mixed carboxylate diruthenium complexes trans-[Ru ₂ ^II,III (O₂CCH₃)₂(O₂CAr)₂Cl] (I) and trans-[Ru ₂ ^II,II (O₂CCH₃)₂(O₂CAr)₂] (II) (O₂CAr = 2,6-di(p-tolyl)benzoate) have been synthesised along with [Ru ₂ ^II,III (O₂CAr)₄Cl] (III) and the homoleptic complex [Ru ₂ ^II,II (O₂CAr)₄] (IV). The structures trans-[Ru₂(O₂CCH₃)₂(O₂CAr)₂Cl(thf)]·(thf) and [Ru₂(O₂CAr)₄Cl(η ¹-CH₂Cl₂)] were determined by X-ray crystallography, and display the expected paddlewheel arrangement of the carboxylate ligands around the diruthenium core. The structure of III is a rare example of a structurally characterised dichloromethane complex, highlighting the Lewis acidic nature of the diruthenium axial position. The bulky ^?O₂CAr ligand protects the axial positions from intermolecular interactions in the absence of strong nucleophiles for III and IV, and the effect this has on the electronic structure of the diruthenium core in these complexes was investigated by cyclic voltammetry, electronic absorption spectroscopy and magnetic susceptibility studies.     

Antimony(III)-D, L-tartrates exhibit proton-assisted enantioselective binding in solution and in the gas phase

The negative ion mode ESI mass spectral analysis of antimony(III)-D- and -L-tartrate (“tartar emetic”), in association with leucine enantiomeric isotopomers, revealed remarkable proton-assisted enantioselective molecular recognition phenomena. The current study infers that recognition of amino acids by antimony(III)-D,L-tartrate complexes requires that the chiral selector associate a proton to become enantioselective. The dianionic selector itself failed to show enantiomeric discrimination capacity. This observation was shown to be consistent both in solution-phase targeting full scan and gas-phase targeting collision threshold dissociation (CTD) experiments. Importantly, this disparity in enantioselective binding capacity between the dianionic and the protonated monoanionic representatives of antimony(III)-D- and-L-tartrates could only be clearly revealed by ESI-MS and tandem mass spectrometry experiments as described herein. This finding urges a more in-depth study of mechanisms associated with exhibited enantiomeric resolving capacity of antimony tartrates in HPLC and CE applications, as well as in former ESI-MS association studies.     

Comparison of membrane assisted solvent extraction,stir bar sorptive extraction,and solid phase microextraction in analysis of tetramine in food

Three environmentally friendly extraction techniques, membrane assisted solvent extraction (MASE), stir bar sorptive extraction (SBSE), and headspace solid phase microextraction (HS‐SPME), were compared for the direct analysis of the highly toxic rodenticide tetramine in food. The optimized MASE method was applied to seven foods fortified with tetramine and compared to previously reported SBSE and HS‐SPME results. Parameters such as the standard addition linearity (MASE (0.964–0.999), SBSE (0.966–0.999), HS‐SPME (0.955–0.999)), recovery (MASE (12–86%), SBSE (36–130%), HS‐SPME (50–200%)), reproducibility (MASE (3.0–30%), SBSE (4.4–9.6%), HS‐SPME (1–12%)), and LOD (MASE (1.6–6.4 ng/g), SBSE (0.2–2.1 ng/g), HS‐SPME (0.9–4.3 ng/g)) were compared.     

Convergent approaches for the synthesis of the antitumoral peptide, Kahalalide F. Study of orthogonal protecting groups

Kahalalide compounds are peptides that are isolated from a Hawaiian herbivorous marine species of mollusc, Elysia rufescens, and its diet, the green alga Bryopsis sp. Kahalalide F and its synthetic analogues are the most promising compounds of the Kahalalide family because they show antitumoral activity. Linear solid-phase syntheses of Kahalalide F have been reported. Here we describe several new improved synthetic routes based on convergent approaches with distinct orthogonal protection schemes for the preparation of Kahaladide analogues. These strategies allow a better control and characterization of the intermediates because more reactions are performed in solution.     

Influence of the Operative Conditions on the Characteristics of Poly(D,L-lactide-co-glycolide) Synthesized in Supercritical Carbon Dioxide

Summary: The co-polymerizations of D,L -lactide and glycolide in supercritical carbon dioxide (scCO₂) using zinc (II) ethylhexanoate (ZnOct₂) as catalyst and methanol as initiator have been investigated. The influence of stirring rate (N), temperature (T), and mass carbon dioxide (m_CO2) on molecular weight distribution (MWD); co-polymer composition; and conversion has been studied by means an experimental factorial design. The stirring rate has the greatest influence on conversion. Due to the heterogeneous nature of the process the mass transfer enhancement, that the grater turbulence produces, favors greatly the incorporation of monomers into the polymer phase. An important decrease of molecular weight is observed independently of reaction conditions for high conversion values because some thermal degradation or rearrangement reactions are taking place. The influence of the initiator, methanol, on the molecular weight has been also studied. Methanol acts as an effective chain transfer agent initiating more growing chains than expected, what also contributes to get low molecular weights.     

Straightforward synthesis of indolizidine alkaloid 167B

The synthetic access to indolizidines, substituted in C-5 position, was reported with good diastereoselectivity. The strategy developed was based on a key step of Michael addition associated with a Clauson-Kaas condensation.     

Fourier multipliers on weighted -spaces

In his 1986 paper in the Rev. Mat. Iberoamericana, A. Carbery proved that a singular integral operator is of weak type on if its lacunary pieces satisfy a certain regularity condition. In this paper we prove that Carbery's result is sharp in a certain sense. We also obtain a weighted analogue of Carbery's result. Some applications of our results are also given.