Computing Fekete and Lebesgue points: Simplex, square, disk

We have computed point sets with maximal absolute value of the Vandermonde determinant (Fekete points) or minimal Lebesgue constant (Lebesgue points) on three basic bidimensional compact sets: the simplex, the square, and the disk. Using routines of the Matlab Optimization Toolbox, we have obtained some of the best bivariate interpolation sets known so far.     

Methylcarbonate and bicarbonate phosphonium salts as catalysts for the nitroaldol (Henry) reaction

Phosphonium ionic liquids exchanged with bicarbonate and methylcarbonate anions (CILs) exhibit catalytic performances comparable to those of sterically hindered (non nucleophilic) organosuperbases such as DBU. At 25-50 °C, under solventless conditions, CILs efficiently catalyze the Henry addition of different aldehydes and ketones to nitroalkanes: not only they allow the selective formation of nitroaldols but they unlock a novel high-yielding access to dinitromethyl derivatives of ketones.     

Adaptive Bivariate Chebyshev Approximation

We propose an adaptive algorithm which extends Chebyshev series approximation to bivariate functions, on domains which are smooth transformations of a square. The method is tested on functions with different degrees of regularity and on domains with various geometries. We show also an application to the fast evaluation of linear and nonlinear bivariate integral transforms.     

Product Gauss cubature over polygons based on Green’s integration formula

We have implemented in Matlab a Gauss-like cubature formula over convex, nonconvex or even multiply connected polygons. The formula is exact for polynomials of degree at most 2n-1 using N∼mn ² nodes, m being the number of sides that are not orthogonal to a given line, and not lying on it. It does not need any preprocessing like triangulation of the domain, but relies directly on univariate Gauss–Legendre quadrature via Green’s integral formula. Several numerical tests are presented. AMS subject classification (2000)  65F20     

Detection of follicular transport of lidocaine and metabolism in adipose tissue in pig ear skin by DESI mass spectrometry imaging

Desorption electrospray ionization (DESI) mass spectrometry imaging is demonstrated as a detection technique for penetration experiments of drugs in skin. Lidocaine ointment was used as the model compound in ex vivo experiments with whole pig ears as the skin model. Follicular transport of lidocaine into the deeper skin layers is demonstrated for the first time. Furthermore, metabolism of lidocaine to 3-OH-lidocaine was observed in subcutaneous tissue as well as in lobules of white adipose tissue surrounding the hair follicles. These results suggest that it is advantageous to use full thickness skin, including subcutaneous tissue, for skin metabolism studies.

Ionic Liquids Made with Dimethyl Carbonate: Solvents as well as Boosted Basic Catalysts for the Michael Reaction

This article describes 1) a methodology for the green synthesis of a class of methylammonium and methylphosphonium ionic liquids (ILs), 2) how to tune their acid–base properties by anion exchange, 3) complete neat‐phase NMR spectroscopic characterisation of these materials and 4) their application as active organocatalysts for base‐promoted carbon–carbon bond‐forming reactions. Methylation of tertiary amines or phosphines with dimethyl carbonate leads to the formation of the halogen‐free methyl‐onium methyl carbonate salts, and these can be easily anion‐exchanged to yield a range of derivatives with different melting points, solubility, acid–base properties, stability and viscosity. Treatment with water, in particular, yields bicarbonate‐exchanged liquid onium salts. These proved strongly basic, enough to efficiently catalyse the Michael reaction; experiments suggest that in these systems the bicarbonate basicity is boosted by two orders of magnitude with respect to inorganic bicarbonate salts. These basic ionic liquids used in catalytic amounts are better even than traditional strong organic bases. The present work also introduces neat NMR spectroscopy of the ionic liquids as a probe for solute–solvent interactions as well as a tool for characterisation. Our studies show that high catalytic efficacy of functional ionic liquids can be achieved by integrating their green synthesis, along with a fine‐tuning of their structure. Demonstrating that ionic liquid solvents can be made by a truly green procedure, and that their properties and reactivity can be tailored to the point of bridging the gap between their use as solvents and as catalysts.     

A fast Nyström-Broyden solver by Chebyshev compression

When a Nyström-Broyden method is used to solve numerically Urysohn integral equations, the main problem is to evaluate the action of the integral operator at a low cost. Here we suitably approximate the relevant discrete integral operator of dimensionn by itsm-degree truncated Chebyshev series expansion (withm?n), reducing the complexity from the basic ${\mathcal{O}}(n^2 )$ to ${\mathcal{O}}(mn)$ . A technique to evaluate cheaply suchm is presented. Several linear and nonlinear examples are considered.     

Reaction of functionalized anilines with dimethyl carbonate over NaY faujasite. 3. chemoselectivity toward mono-N-methylation

In the presence of NaY faujasite, dimethyl carbonate (MeOCO(2)Me, DMC) is a highly chemoselective methylating agent of functionalized anilines such as aminophenols (1), aminobenzyl alcohols (2), aminobenzoic acids (3), and aminobenzamides (4). The reaction proceeds with the exclusive formation of N-methylanilines without any concurrent O-methylation or N-/O-methoxy carbonylation side processes. Particularly, only mono-N-methyl derivatives [XC(6)H(4)NHMe, X = o-, m-, and p-OH; o- and p-CH(2)OH; o- and p-CO(2)H; o- and p-CONH(2)] are obtained with selectivity up to 99% and isolated yields of 74-99%. DMC, which usually promotes methylations only at T > 120 degrees C, is activated by the zeolite catalyst and it reacts with compounds 1, 2, and 4, at 90 degrees C. Aminobenzoic acids (3) require a higher reaction temperature (> or =130 degrees C).     

Nucleophilic displacements in supercritical carbon dioxide under phase-transfer catalysis conditions. 2. Effect of pressure and kinetics

The nucleophilic displacement on n-octylmesylate (n-C(8)H(17)OSO(2)CH(3), 1) with four different anions (I(-), Br(-), N(3)(-), and SCN(-)) is investigated under liquid-supercritical phase-transfer catalysis (LSc-PTC) conditions, i.e. in a biphase system of supercritical carbon dioxide (scCO(2)) and water, in the presence of both silica supported and conventional onium salts. The CO(2) pressure greatly affects the concentration of 1 in the sc-phase and plays a major role on its conversion. For example, at 50 degrees C and with a supported PT-catalyst, the conversion of 1 into n-octyl iodide drops by a factor of 5 as the CO(2) pressure is increased from 80 to 150 bar, while in the same pressure range, the solubility of n-octylmesylate in scCO(2) shows a 6-fold increase, indicating that the reagent is desorbed from the catalyst. Under LSc-PTC conditions, pseudo-first-order kinetic rate constants, evaluated for the investigated reactions, show that the performance of scCO(2) as a PTC solvent and the relative nucleophilicity order of the anions (N(3)(-) > I(-) > or = Br(-) > SCN(-)) are comparable to those of toluene and n-heptane. The behavior of conventional phosphonium salts in the scCO(2)/H(2)O biphase system suggests that the reaction may take place either within small droplets of PT-catalyst containing water or in a separate third liquid phase of the PT-catalyst itself.     

Mono-N-methylation of primary amines with alkyl methyl carbonates over Y faujasites. 2. Kinetics and selectivity

In the presence of a Na-exchanged Y faujasite, the reaction of primary aromatic amines 1 with 2-(2-methoxyethoxy)methylethyl carbonate [MeO(CH(2))(2)O(CH(2))(2)OCO(2)Me, 2a] yields the corresponding mono-N-methyl derivatives ArNHMe with selectivity up to 95%, at substantially quantitative conversions. At 130 degrees C, the reaction can be run under diffusion-free conditions and is strongly affected by the solvent polarity: for instance, in going from xylene (epsilon(r) = 2.40) to triglyme (epsilon(r) = 7.62) as the solvent, the pseudo-first-order rate constant for the aniline (1a) disappearance shows a 5-fold decrease. In DMF (epsilon(r) = 38.25), the same reaction does not occur at all. Competitive adsorption of the solvent and the substrate onto the catalytic sites accounts for this result. The behavior of alkyl-substituted anilines ZC(6)H(4)NH(2) [Z = p-Me, p-Et, p-Pr, p-(n-Bu) (1b-e); Z = 3,5-di-tert-butyl- and 2,4,6-tri-tert-butylanilines (1f,g)] and p-alkoxyanilines p-ZC(6)H(4)NH(2) [Z = OMe, OEt, OPr, O-n-Bu (1b'-e')] clearly indicates a steric effect of ring substituents: as diffusion of the amine into the catalytic pores is hindered, the reaction hardly proceeds and the mono-N-methyl selectivity (S(M/D)) drops as well. Moreover, the strength of adsorption of the amine onto the catalyst influences the rate and the selectivity as well: the reaction of p-anisidine and p-toluidine-despite the higher nucleophilicity of these compounds-is slower and even less selective with respect to aniline. From a mechanistic viewpoint, the intermediacy of carbamates ArN(Me)CO(2)R [R = MeO(CH(2))(2)O(CH(2))(2)] is suggested. At 90 degrees C, the reaction of benzylamine (7)-a model for aliphatic amines-with dimethyl carbonate shows that the reaction outcome can be improved by tuning the amphoteric properties of the catalyst: in going from CsY to the more acidic LiY zeolite, methylation is not only more selective (S(M/D) ratio increases from 77% to 84%) but even much faster (CsY, conversion of 36% after 22 h; LiY, conversion of 43% after 7 h).