Existence of maximizers for Sobolev–Strichartz inequalities

We prove the existence of maximizers of Sobolev–Strichartz estimates for a general class of propagators, involving relevant examples, as for instance the wave, Dirac and the hyperbolic Schrödinger flows.     

Solution-Based,Anion-Doping of Li4Ti5O12 Nanoflowers for Lithium-Ion Battery Applications

Solution-based, anionic doping represents a convenient strategy with which to improve upon the conductivity of candidate anode materials such as Li₄Ti₅O₁₂ (LTO). As such, novel synthetic hydrothermally-inspired protocols have primarily been devised herein, aimed at the large-scale production of unique halogen-doped, micron-scale, three-dimensional, hierarchical LTO flower-like motifs. Although fluorine (F) doping has been explored, the use of chlorine (Cl) dopants is the primary focus here. Several experimental variables, such as dopant amount, lithium hydroxide concentration, and titanium butoxide purity, were probed and perfected. Furthermore, the Cl doping process did not damage the intrinsic LTO morphology. The analysis, based on interpreting a compilation of SEM, XRD, XPS, and TEM-EDS results, was used to determine an optimized dopant concentration of Cl. Electrochemical tests demonstrated an increased capacity via cycling of 12 % for a Cl-doped sample as compared with pristine LTO. Moreover, the Cl-doped LTO sample described in this study exhibited the highest discharge capacity yet reported at an observed rate of 2C for this material at 143mAh g⁻¹. Overall, these data suggest that the Cl dopant likely enhances not only the ion transport capabilities, but also the overall electrical conductivity of our as-prepared structures. To help explain these favorable findings, theoretical DFT calculations were used to postulate that the electronic conductivity and Li diffusion were likely improved by the presence of increased Ti³⁺ ion concentration coupled with widening of the Li migration channel.     

Gas chromatography–triple-quadrupole mass spectrometry for analysis of selected polyhalogenated pollutants in plants. Comparison of extraction methods

Different extraction methods, followed by gas chromatography coupled to triple quadrupole mass spectrometry, were evaluated for simultaneous extraction of seven polychlorinated biphenyls (PCBs) and six polybrominated diphenyl ethers (PBDEs) from common weeds. Pressurized liquid extraction (PLE) with in-cell clean-up, ultrasound-assisted extraction (UAE) with in-column clean-up, and UAE with dispersive solid-phase extraction (dSPE) clean-up were evaluated and compared. In-cell clean-up with 4 g Florisil and 0.5 g graphitized carbon black (GCB) and two extraction cycles of 10 min with n-hexane–ethyl acetate 80:20 (v/v) at 60 °C were used for the PLE procedure. UAE with in-column clean-up was conducted under conditions similar to those reported for the PLE method whereas in UAE with dSPE clean-up purification of the extract was performed after extraction using primary and secondary amine sorbent (PSA) and GCB. Recovery from 82 to 104 % was obtained for all the compounds by PLE whereas, in general, lower extraction efficiency was obtained by UAE with in-column clean-up (especially for BDE-17 and BDE-183, for which recovery was 70 and 41 %, respectively) and by UAE with dSPE clean-up, for which the main drawback is that BDE-183 cannot be extracted. Finally, PLE was used for analysis of PCBs and PBDEs in different plants (Lolium rigidum, Lactuca serriola, Malva sylvestris, and Verbascum thapsus) collected from residential and/or rural areas of Madrid (Spain). Several of the analyzed compounds were detected at low levels in these plants, but only PCB-153 could be quantified.

A paradigm shift in rate determining step from single electron transfer between phenylsulfinylacetic acids and iron(III) polypyridyl complexes to nucleophilic attack of water to the produced sulfoxide radical cation: a non‐linear Hammett

Mechanism of oxidative decarboxylation of phenylsulfinylacetic acids (PSAAs) by iron(III) polypyridyl complexes in aqueous acetonitrile medium has been investigated spectrophotometrically. An initial intermediate formation between PSAA and [Fe(NN)₃]³⁺ is confirmed from the observed Michaelis–Menten kinetics and fractional order dependence on PSAA. Significant rate retardation with concentration of [Fe(NN)₃]³⁺ is rationalized on the basis of coordination of a water molecule at the carbon atom adjacent to the ring nitrogen of the metal polypyridyl complexes by nucleophilic attack at higher concentrations. Electron‐withdrawing and electron‐releasing substituents in PSAA facilitate the reaction and Hammett correlation gives an upward ‘V’ shaped curve. The apparent upward curvature is rationalized based on the change in the rate determining step from electron transfer to nucleophilic attack, by changing the substituents from electron‐releasing to electron‐withdrawing groups. Electron‐releasing substituents in PSAA accelerate the electron transfer from PSAA to the complex and also stabilize the intermediate through resonance interaction leading to negative reaction constants (ρ). Conversely, electron‐withdrawing groups, while retarding the electron transfer exert an accelerating effect on the nucleophilic attack of H₂O which leading to low magnitude of ρ⁺ compared to high ρ^? values of electron‐releasing groups. Marcus theory is applied, and a fair agreement is seen with the experimental values. Copyright © 2016 John Wiley & Sons, Ltd.     

Maximum entropy principle and coherent harmonic generation using a single-pass free-electron laser

Single-pass free-electron lasers constitute an example of systems with long-range interactions. The light-particle interplay leading to the power growth and successive relaxation towards a quasi-stationary state is governed by the Vlasov equation. A maximum entropy principle inspired to Lynden-Bell's theory of “violent relaxation" for the Vlasov equation can be invoked to analytically characterize the behaviour of the saturated system. In particular, we here concentrate on the case of coherent harmonic generation obtained from an externally seeded free-electron laser and provide a simple strategy to predict the laser intensity as well as the final electron-beam energy distribution.     

Molecular Recognition of Nucleotides in Water by Scorpiand‐Type Receptors Based on Nucleobase Discrimination

The detection of nucleotides is of crucial importance because they are the basic building blocks of nucleic acids. Scorpiand‐based polyamine receptors functionalized with pyridine or anthracene units are able to form stable complexes with nucleotides in water, based on coulombic, π–π stacking, and hydrogen‐bonding interactions. This behavior has been rationalized by means of an exploration with NMR spectroscopy and DFT calculations. Binding constants were determined by potentiometry. Fluorescence spectroscopy studies have revealed the potential of these receptors as sensors to effectively and selectively distinguish guanosine‐5′‐triphosphate (GTP) from adenosine‐5′‐triphosphate (ATP).     

Enhanced photocatalytic activity of zeolite-encapsulated TiO2 clusters by complexation with organic additives and N-doping.

In the literature it was found that titanium oxide clusters of a few metal atoms encapsulated inside the micropores of zeolite Y exhibit large blue shifts in the Ti-O ligand-to-metal charge-transfer band as compared to non-encapsulated bulk titanium dioxide particles. This blue shift of the Ti-O absorption band is believed to have a negative effect on the photocatalytic activity of zeolite-encapsulated TiO2. We report here on circumventing this problem and increasing visible-light absorption by means of a red shift of the absorption band caused by addition of some organic molecular modifiers containing acidic OH groups that can strongly bind with titanol groups TiOH. In the studied series of zeolite-encapsulated TiO2 samples, the red shift of the optical spectrum follows the order: catechol > 4-aminobenzoic acid > benzoic acid. Also N-doping of zeolite-encapsulated TiO2 clusters by thermal treatment with urea leads to a red shift of the TiO2 absorption band that depends on the annealing and hydration conditions. By comparison to the degradation of phenol in aqueous solution, we have demonstrated that these changes in the absorption spectrum on addition of the organic modifier are also reflected in the photocatalytic activity of the samples; a greater increase in photocatalytic activity (about 30%) was observed for the additive catechol.