Improved Sobolev embeddings,profile decomposition,and concentration-compactness for fractional Sobolev spaces

We obtain an improved Sobolev inequality in \(\dot{H}^s\) spaces involving Morrey norms. This refinement yields a direct proof of the existence of optimizers and the compactness up to symmetry of optimizing sequences for the usual Sobolev embedding. More generally, it allows to derive an alternative, more transparent proof of the profile decomposition in \(\dot{H}^s\) obtained in Gérard (ESAIM Control Optim Calc Var 3:213–233, 1998) using the abstract approach of dislocation spaces developed in Tintarev and Fieseler (Concentration compactness. Functional-analytic grounds and applications. Imperial College Press, London, 2007). We also analyze directly the local defect of compactness of the Sobolev embedding in terms of measures in the spirit of Lions (Rev Mat Iberoamericana 1:145–201, 1985, Rev Mat Iberoamericana 1:45–121, 1985). As a model application, we study the asymptotic limit of a family of subcritical problems, obtaining concentration results for the corresponding optimizers which are well known when \(s\) is an integer (Rey in Manuscr Math 65:19–37, 1989, Han in Ann Inst Henri Poincaré Anal Non Linéaire 8:159–174, 1991, Chou and Geng in Differ Integral Equ 13:921–940, 2000).     

Precise Tuning of Surface Composition and Electron‐Transfer Properties of Graphene Oxide Films through Electroreduction

Graphene materials are generally prepared from the exfoliation of graphite oxide (GO) to graphene oxide, followed by subsequent chemical or thermal reduction. These methods, although efficient in removing most of the oxygen functionalities from the GO material, lack control over the extent of the reduction process. We demonstrate here an electrochemical reduction procedure that not only allows for precise control of the reduction process to obtain a graphene material with a well‐defined C/O ratio in the range of 3 to 10, but also one that is able to tune the electrocatalytic properties of the reduced material. A method that is able to precisely control the amount and density of the oxygen functionalities on the graphene material as well as its electrochemical behaviour is very important for several applications such as electronics, bio‐composites and electrochemical devices.     

A Simple Synthesis of (R)(S)(E)-3,7-Dimethyl-2-octene-1,8-dioc Acid,a Copulation Release Pheromone Component of the Azuki Bean Weevil

(R)(S)(E)-3,7-dimethyl-2-octene-1,8-dioic acid, (R)(S)(E)-1, also named callosobruchusic acid, has been synthetized in five steps using a simple reaction sequence based on the zirconium-catalyzed methylalumination of commercially available 4-pentyn-1-ol, 2a, or its O-tert-butyldimethylsilyl ether, 2b.     

Hydroalumination of silylacetylenes: a novel and highly stereoselective synthesis of (E)-telluro(silyl)ketene acetals and their applications in Sonogashira cross-coupling reactions

The hydroalumination of silylacetylenes with DIBAL-H followed by the addition of n-butyllithium generated in situ the (Z)-β-vinylorganosilane alanates intermediates, which were trapped with butyltellurenyl bromide (C₄H₉TeBr), furnishing exclusively the (E)-1-butyltelluro-1-tri(organyl)silyl-2-organyl-1-alkenes in 45-70% yields. These telluro(silyl)ketene acetals were utilized as substrates in Sonogashira cross-coupling Pd-catalyzed reactions, furnishing the (Z)-1,4-diorganyl-2-tri(organyl)silyl-1-buten-3-ynes with total control of regio- and stereochemistry in 62-80% yield.     

Chemically-modified graphenes for oxidation of DNA bases: analytical parameters

We studied the electroanalytical performances of chemically-modified graphenes (CMGs) containing different defect densities and amounts of oxygen-containing groups, namely graphite oxide (GPO), graphene oxide (GO), thermally reduced graphene oxide (TR-GO) and electrochemically reduced graphene oxide (ER-GO) by comparing the sensitivity, selectivity, linearity and repeatability towards the oxidation of DNA bases. We have observed that for differential pulse voltammetric (DPV) detection of adenine and cytosine, all CMGs showed enhanced sensitivity to oxidation, while for guanine and thymine, ER-GO and TR-GO exhibited much improved sensitivity over bare glassy carbon (GC) as well as over GPO and GO. There is also significant selectivity enhancement when using GPO for adenine and TR-GO for thymine. Our results have uncovered that the differences in surface functionalities, structure and defects of various CMGs largely influence their electrochemical behaviour in detecting the oxidation of DNA bases. The findings in this report will provide a useful guide for the future development of label-free electrochemical devices for DNA analysis.     

Fragment-based and classical quantitative structure–activity relationships for a series of hydrazides as antituberculosis agents

Worldwide, tuberculosis (TB) is the leading cause of death among curable infectious diseases. Multidrug-resistant Mycobacterium tuberculosis is an emerging problem of great importance to public health, and there is an urgent need for new anti-TB drugs. In the present work, classical 2D quantitative structure-activity relationships (QSAR) and hologram QSAR (HQSAR) studies were performed on a training set of 91 isoniazid derivatives. Significant statistical models (classical QSAR, q (2) = 0.68 and r (2) = 0.72; HQSAR, q (2) = 0.63 and r (2) = 0.86) were obtained, indicating their consistency for untested compounds. The models were then used to evaluate an external test set containing 24 compounds which were not included in the training set, and the predicted values were in good agreement with the experimental results (HQSAR, [Formula: see text] ; classical QSAR, [Formula: see text]).     

PANI–WO3·2H2O Nanocomposite: Phase Interaction and Evaluation of Electronic Properties by Combined Experimental Techniques and Ab-Initio Calculation

The development of conjugated polymer-based nanocomposites by adding metallic particles into the polymerization medium allows the proposition of novel materials presenting improved electrical and optical properties. Polyaniline Emeraldine-salt form (ES–PANI) has been extensively studied due to its controllable electrical conductivity and oxidation states. On the other hand, tungsten oxide (WO₃) and its di-hydrated phases, such as WO₃·2H₂O, have been reported as important materials in photocatalysis and sensors. Herein, the WO₃·2H₂O phase was directly obtained during the in-situ polymerization of aniline hydrochloride from metallic tungsten (W), allowing the formation of hybrid nanocomposites based on its full oxidation into WO₃·2H₂O. The developed ES–PANI–WO₃·2H₂O nanocomposites were successfully characterized using experimental techniques combined with Density Functional Theory (DFT). The formation of WO₃·2H₂O was clearly verified after two hours of synthesis (PW₂ nanocomposite), allowing the confirmation of purely physical interaction between matrix and reinforcement. As a result, increased electrical conductivity was verified in the PW₂ nanocomposite: the DFT calculations revealed a charge transfer from the p-orbitals of the polymeric phase to the d-orbitals of the oxide phase, resulting in higher conductivity when compared to the pure ES–PANI.     

A Cross-Shaped Monomer as Building Block for Molecular Textiles

The exploration of new materials is timeless. Especially 2D-materials have gotten much interest in the last decades. This work proposes a new route towards a fascinating class of 2D materials: molecular textiles. The suggested bottom-up approach focuses on the 2D self-assembly of a cross-shaped monomer at the water/air interface. A 3D cross-shaped motive was designed, synthesized, and characterized, which exhibits the required structural features, i. e., static and dynamic control. Analysis of the cross-shaped motive by ¹H-NMR spectroscopy, X-ray structure, and chiral stationary phase HPLC proved the rigidity and stability of the system, and thus also its potential for the here suggested new strategy towards molecular textiles. Three variants of a Schiff-base precursor pair functionalized monomer were synthesized and characterized by ¹H-NMR spectroscopy, ¹³C-NMR spectroscopy, and mass spectrometry. Finally, the network formation of the monomer is shown to be triggered by deprotonation of its ammonium salt, corroborated with FT-IR analysis.     

η3‐Benzyl‐Nickel‐Diimine Complex: Synthesis and Catalytic Properties in Ethylene Polymerization

The oxidative addition of benzyl chloride to Ni(cod)₂ in the presence of 1,4‐bis(2,6‐diisopropylphenyl)acenaphthenediimine followed by chloride abstraction affords [(η³‐CH₂C₆H₅)Ni(α‐diimine)][PF₆] (α‐diimine = 1,4‐bis(2,6‐diisopropylphenyl)acenaphthenediimine) in 70% yield. The complex is active in ethylene polymerization in the presence of methylaluminoxane and under mild reaction conditions. The polyethylenes obtained are highly branched, have very low densities, do not show T_m or measurable crystallinity and have molecular weights ranging from 80 × 10³ to 290 × 10³ g · mol⁻¹.