Non-existence of extremals for the Adimurthi–Druet inequality

The Adimurthi–Druet [1] inequality is an improvement of the standard Moser–Trudinger inequality by adding a $L^2$-type perturbation, quantified by $\alpha \in [0,{\lambda }_1)$, where ${\lambda }_1$ is the first Dirichlet eigenvalue of Δ on a smooth bounded domain. It is known [3], [10], [14], [19] that this inequality admits extremal functions, when the perturbation parameter α is small. By contrast, we prove here that the Adimurthi–Druet inequality does not admit any extremal, when the perturbation parameter α approaches ${\lambda }_1$. Our result is based on sharp expansions of the Dirichlet energy for blowing sequences of solutions of the corresponding Euler–Lagrange equation, which take into account the fact that the problem becomes singular as $\alpha \to {\lambda }_1$.     

Screening of Three Transition Metal‐Mediated Reactions Compatible with DNA‐Encoded Chemical Libraries

The construction of DNA‐encoded chemical libraries (DECLs) crucially relies on the availability of chemical reactions, which are DNA‐compatible and which exhibit high conversion rates for a large number of diverse substrates. In this work, we present our optimization and validation procedures for three copper and palladium‐catalyzed reactions (Suzuki cross‐coupling, Sonogashira cross‐coupling, and copper(I)‐catalyzed alkyne‐azide cycloaddition (CuAAC)), which have been successfully used by our group for the construction of large encoded libraries.     

Determination of boron and hydrogen in materials for multicrystalline solar cell production with prompt gamma activation analysis

Journal of Radioanalytical and Nuclear Chemistry - For the optimization of the manufacturing process of multicrystalline silicon (mc-Si) for solar cells in order to reduce energy consumption and...     

Azulenesulfonium Salts: Accessible,Stable, and Versatile Reagents for Cross‐Coupling

Azulenesulfonium salts may be readily prepared from the corresponding azulenes by an S_EAr reaction. These azulene sulfonium salts are bench‐stable species that may be employed as pseudohalides for cross‐coupling. Specifically, their application in Suzuki–Miyaura reactions has been demonstrated with a diverse selection of coupling partners. These azulenesulfonium salts possess significant advantages in comparison with the corresponding azulenyl halides, which are known to be unstable and difficult to prepare in pure form.     

The assay of pterostilbene in spiked matrices by liquid chromatography tandem mass spectrometry and isotope dilution method

Pterostilbene (trans‐3,5‐dimethoxy‐4‐hydroxystilbene) is an active component found in several plant species, exhibiting important pharmacological properties. A new and reliable method of assaying this phyto compound in various matrices is presented; the assay is based on (1) the selectivity of liquid chromatography (LC) hyphenated with electrospray ionisation (ESI), (2) the specificity of a two‐step mass spectrometric analysis (MS/MS) and (3) the accuracy of the isotope dilution method. The labelled analogue may be conveniently synthesised in a few steps. The sensitivity of the method is confirmed by the very low limit of detection (LOD) and limit of quantitation (LOQ) values achieved in the assay of pterostilbene in two distinct fortified matrices, and is further supported by the observed accuracy values. Copyright © 2010 John Wiley & Sons, Ltd.