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...