1,3-Dipolar character of 2-vinyl quinazoline 3-oxides; first and second generation cycloaddition products

The reaction between the heteroaromatic N-oxides 1a, 1b and 1c with dimethyl acetylenedicarboxylate or methyl propiolate furnishes 1,3-benzodiazepines, the products of ring transformations of primarily formed cycloadducts. The structures of 8a and 10a have been confirmed by X-ray crystallographic analysis. The aldonitrone 1c also reacts with N-methylmaleimide and with phenyl vinyl sulfone to furnish the first examples of primary cycloaddition products from quinazoline 3-oxides.     

Existence and multiplicity of positive solutions for the p-Laplacian with nonlocal coefficient

We consider the Dirichlet problem with nonlocal coefficient given by in a bounded, smooth domain Ω⊂Rn (n?2), where Δp is the p-Laplacian, w is a weight function and the nonlinearity f(u) satisfies certain local bounds. In contrast with the hypotheses usually made, no asymptotic behavior is assumed on f. We assume that the nonlocal coefficient (q?1) is defined by a continuous and nondecreasing function satisfying a(t)>0 for t>0 and a(0)?0. A positive solution is obtained by applying the Schauder Fixed Point Theorem. The case a(t)=tγ/q (0<γ<p−1) will be considered as an example where asymptotic conditions on the nonlinearity provide the existence of a sequence of positive solutions for the problem with arbitrarily large sup norm.     

Application of Quasi-Monte Carlo Methods to Elliptic PDEs with Random Diffusion Coefficients: A Survey of Analysis and Implementation

This article provides a survey of recent research efforts on the application of quasi-Monte Carlo (QMC) methods to elliptic partial differential equations (PDEs) with random diffusion coefficients. It considers and contrasts the uniform case versus the lognormal case, single-level algorithms versus multi-level algorithms, first-order QMC rules versus higher-order QMC rules, and deterministic QMC methods versus randomized QMC methods. It gives a summary of the error analysis and proof techniques in a unified view, and provides a practical guide to the software for constructing and generating QMC points tailored to the PDE problems. The analysis for the uniform case can be generalized to cover a range of affine parametric operator equations.     

Determination of ultra trace levels of 1,2-dichloroethane in air by sample enrichment micromachined gas chromatography-differential mobility detection

A novel analytical procedure has been developed for the analysis of ultra trace levels of 1,2-dichloroethane (EDC) in air using sample enrichment in combination with micromachined gas chromatography (GC) and differential mobility detection (DMD). When compared to other contemporary GC techniques, such as GC-flame ionization detection, GC-electron capture detection, or GC-electrolytic conductivity detection, the employment of a DMD in combination with a preconcentrator provided better sensitivity and markedly improved selectivity. The increase in sensitivity reduces false-negative results, while the improvement in selectivity decreases the potential for false-positive results. Using the technique described, a complete analysis can be conducted in less than 10 min, with a detection limit of 0.7 ppb (v/v) of EDC and a short term precision of less than 6%. A correlation coefficient of 0.9988 was obtained over an EDC concentration range from 0.7 ppb to 36.4 ppb (v/v). The analytical system also has an on-board microTCD in series with the DMD, allowing both detector outputs to be monitored simultaneously. With the pre-concentration technique, the microTCD can detect EDC as low as 15 ppb (v/v) with a substantially enhanced linear dynamic range in addition to providing a confirmation means for the presence of EDC at the level cited.     

Fast RNA conjugations on solid phase by strain-promoted cycloadditions

Strain promoted cycloaddition is presented as a tool for RNA conjugation on the solid phase; RNA-cyclooctyne conjugates are prepared by cycloaddition to both azide (strain-promoted azide-alkyne cycloaddition, SPAAC) and nitrile oxide dipoles (strain-promoted nitrile oxide-alkyne cycloaddition, SPNOAC). The conjugation is compatible with 2'-OMe blocks and with 2'-O-TBDMS protection on the ribose moieties of the sugar. Nitrile oxide dipoles are found to be more reactive click partners than azides. The conjugation proceeds within 10 min in aqueous solvents, at room temperature without any metal catalyst and tolerates dipoles of varying steric bulk and electronic demands, including pyrenyl, coumarin and dabcyl derivatives.     

Cu(II)-promoted methanolysis of N,N-dipicolylacetamide. multistep activation by decoupling of > ̈̈N-C═O resonance via Cu(II)-N binding, delivery of the Cu(II):((-)OCH3) nucleophile, and metal ion assistance of the departure of the leaving group

The methanolysis of the Cu(II) complex of N-acetyl-N,N-bis(2-picolyl)amine (2) was investigated by a kinetic study as a function of pH in methanol at 25 °C and computationally by DFT calculations. The active species is the basic form of the complex (3(-)), or (1:Cu(II))((-)OCH(3))(HOCH(3))), and the rate constant for its solvolysis is k(max) = 1.5 × 10(-4) s(-1). The mechanism involves Cu(II) binding to the amide N lone pair, decoupling it from >N-C═O resonance, concomitant with Cu(II):((-)OCH(3)) delivery to the adjacent >N-C═O unit, followed by Cu(II)-assisted departure of the N,N-bis(2-picolyl)amide from a tetrahedral intermediate.     

The conformal boundary of Margulis space–times

In this Note, we show how to construct the conformal boundary of Margulis space–times $\text{R}{}^{\mathrm{1,2}}\text{/Γ}$ when Γ is an affine Schottky group. To cite this article: C. Frances, C. R. Acad. Sci. Paris, Ser. I 336 (2003).