On the Stokes system and on the biharmonic equation in the half‐space: an approach via weighted Sobolev spaces

In this paper, we investigate the Stokes system and the biharmonic equation in a half‐space of ?ⁿ. Our approach rests on the use of a family of weighted Sobolev spaces as a framework for describing the behaviour at infinity. A complete class of existence, uniqueness and regularity results for both the problems is proved. The proofs are mainly based on the principle of reflection. Copyright © 2002 John Wiley & Sons, Ltd.     

Role of iron in Na <Subscript>1.5</Subscript>Fe <Subscript>0.5</Subscript>Ti <Subscript>1.5</Subscript>(PO <Subscript>4</Subscript>) <Subscript>3</Subscript>/C as electrode material for Na-ion batteries studied by operando Mössbauer spectroscopy

The role of iron in Na _1.5Fe _0.5Ti _1.5(PO ₄)₃/C electrode material for Na batteries has been studied by ⁵⁷Fe Mössbauer spectroscopy in operando mode. The potential profile obtained in the galvanostatic regime shows three plateaus at different voltages due to different reaction mechanisms. Two of them, at 2.2 and 0.3 V vs Na ⁺/Na ⁰, have been associated to redox processes involving iron and titanium in Na _1.5Fe _0.5Ti _1.5(PO ₄)₃. The role of titanium was previously elucidated for NaTi ₂(PO ₄)₃ and the effect of the substitution of Fe for Ti was investigated with ⁵⁷Fe Mössbauer spectroscopy. We show that iron is an electrochemically active center at 2.2 V with the reversible Fe ³⁺/Fe ²⁺ transformation and then remains at the oxidation state Fe ²⁺ along the sodiation until the end of discharge at 0 V.     

The spectrum of a weighted Laplacian in the half‐space

J. Banasiak In this paper, we deal with spectral properties of a weighted Laplacian in the half‐space when a Dirichlet or a Neumann boundary condition is imposed. After proving that the spectrum is discrete under suitable assumptions, we give explicit formulae of eigenvalues and eigenfunctions in a specific case. In particular, the obtained eigenfunctions are rational or pseudo‐rational and have remarkable orthogonality properties. These results suggest the use of the discovered functions for approximating solutions of elliptic problems in the half‐space. Copyright © 2015 John Wiley & Sons, Ltd.     

Polyvinylpyrrolidone Behavior in Water/Ethanol Mixed Solvents: Comparison of Modeling Predictions with Experimental Results

The objective of this work is to study the behavior of a neutral polymer, polyvinylpyrrolidone (PVP), in a mixture of water and ethanol. A comparison of the experimental results with a theoretical model of effective solvent interaction with polymer (ESIP) was made. To do so, dynamic light scattering experiments were used to measure the hydrodynamic radius of PVP (M _w = 3.6 × 10⁵ g·mol^?1) as a function of the ethanol fraction, x _A, in the medium at 25 °C. We show that the polymer adopts an ideal chain–globule–coil conformation transition as the ethanol molar fraction varies. This transition is attributed to the change of the solvent quality which results from water and ethanol complex formation. On the other hand, the ternary PVP/water/ethanol system was described by the ESIP model. From the polymer–effective solvent interaction, the second virial coefficient of the polymer/effective solvent and the preferential adsorption parameter were calculated. The obtained results are in agreement with the reported experiments.     

Quantum-Chemical Study of the FeNCN Conversion-Reaction Mechanism in Lithium- and Sodium-Ion Batteries

We report a computational study on 3d transition-metal (Cr, Mn, Fe, and Co) carbodiimides in Li- and Na-ion batteries. The obtained cell voltages semi-quantitatively fit the experiments, highlighting the practicality of PBE+U as an approach for modeling the conversion-reaction mechanism of the FeNCN archetype with lithium and sodium. Also, the calculated voltage profiles agree satisfactorily with experiment both for full (Li-ion battery) and partial (Na-ion battery) discharge, even though experimental atomistic knowledge is missing up to now. Moreover, we rationalize the structural preference of intermediate ternaries and their characteristic lowering in the voltage profile using chemical-bonding and Mulliken-charge analysis. The formation of such ternary intermediates for the lithiation of FeNCN and the contribution of at least one ternary intermediate is also confirmed experimentally. This theoretical approach, aided by experimental findings, supports the atomistic exploration of electrode materials governed by conversion reactions.     

Efficient enantioselective synthesis of 3-aminochroman derivatives through ruthenium-Synphos catalyzed asymmetric hydrogenation

A highly enantioselective asymmetric hydrogenation of various trisubstituted enamides derived from chroman-3-ones promoted by cationic Ru-Synphos catalysts is reported. This atom-economical and clean method provides an efficient route to optically active 3-aminochroman derivatives, which are important pharmacophores found in numerous drug candidates, in high chemical yields and enantiomeric excesses up to 96%.     

A myristicin-rich essential oil from Daucus sahariensis growing in Algeria

The essential oils obtained by hydrodistillation from leaves and fruits of Daucus sahariensis Murb. were analyzed by GC/MS. The main constituents of the essential oil from the leaves were myristicin (34.3%), alpha-pinene (5.4%), cis-chrysanthenyl acetate (5.3%) and epi-alpha-bisabolol (4.8%), and those from the fruits myristicin (43.9%), alpha-pinene (13.1%), limonene (9.4%), and cis-chrysanthenyl acetate (7.4%). Myristicin, the main constituent of both essential oils, is generally absent in the oils from other Daucus species, permitting the hypothesis that this compound is a chemical marker of this Saharan species.     

Size-dependent magnetic properties of CoFe2O4 nanoparticles prepared in polyol

Highly crystalline CoFe(2)O(4) nanoparticles with different diameters ranging from 2.4 to 6.1 nm have been synthesized by forced hydrolysis in polyol. The size can be controlled through adjusting the nominal water/metal molar ratio. X-ray diffraction, transmission electron microscopy, x-ray absorption spectroscopy and (57)Fe M?ssbauer spectrometry were employed to investigate the structure and the microstructure of the particles produced. Magnetic measurements performed on these particles show that they are superparamagnetic with a size-dependent blocking temperature. At 5 K, high saturation magnetization (~85 emu g(-1)) approaching that of the bulk was found for the larger particles, whereas a very large coercivity (14.5 kOe) is observed for the 3.5 nm sized particles.     

Existence of two concomitant magnetic structures below T(Néel) for the natrochalcite, NaFe(II)2(H3O2)(MoO4)2

A comparative study of the magnetic properties and magnetic structures of the natrochalcite, NaFe(2)(D(3)O(2))(MoO(4))(2) (FeD) to those of the isostructural NaCo(2)(D(3)O(2))(MoO(4))(2) (CoD) and NaNi(2)(D(3)O(2))(MoO(4))(2) (NiD) is presented. The structural change is a shrinking of the unit cell in the order of the ionic radii of the transition metal, FeD > CoD > NiD. While NiD and CoD are canted-antiferromagnets with T(N) = 28 and 21 K, respectively, FeD is an anisotropic 2D-Ising antiferromagnet (T(N) = 17 K) with a spin-flop field of 14 kOe at 2 K and the presence of a hysteresis loop reaching only (1)/(4) of the saturation magnetization in 70 kOe. The critical field decreases almost linearly on warming to T(N). The neutron diffraction patterns of FeD below T(N) display numerous magnetic Bragg peaks which cannot be assigned to any one magnetic structure but fits well to two superposed sets, one with a temperature independent line width and has a propagation vector k(1) = (0, 0, 0) while for the other there is a clear dependence and k(2) = (0, 0, ?). In the k(1) = (0, 0, 0) magnetic structure the moments are parallel to each other within one chain and lie along the a-axis but are antiparallel to those in neighboring chains. In contrast CoD and NiD, for which k = (0, 0, 0), have their moments aligned along the b-axis and ac-plane, respectively. The second magnetic structure, k(2) = (0, 0, ?), is characterized by four sublattices, two per layer, where the moments are in the ab-plane and canted with a resultant along the a-axis which is compensated by those of the adjacent layers. For the k(2) = (0, 0, ?) structure, the scattering coherent length decreases, and the moments tend progressively toward the a-axis upon increasing temperature. The coexistence of two concomitant magnetic structures is unprecedented for compounds containing transition metal moment carriers.     

General asymmetric hydrogenation of 2-alkyl- and 2-aryl-substituted quinoxaline derivatives catalyzed by iridium-difluorphos: unusual halide effect and synthetic application

A general asymmetric hydrogenation of a wide range of 2-alkyl- and 2-aryl-substituted quinoxaline derivatives catalyzed by an iridium-difluorphos complex has been developed. Under mild reaction conditions, the corresponding biologically relevant 2-substituted-1,2,3,4-tetrahydroquinoxaline units were obtained in high yields and good to excellent enantioselectivities up to 95%. With a catalyst ratio of S/C = 1000 and on a gram scale, the catalytic activity of the Ir-difluorphos complex was maintained showing its potential value. Finally, we demonstrated the application of our process in the synthesis of compound (S)-9, which is an inhibitor of cholesteryl ester transfer protein (CETP).