Isolated singularities of some semilinear elliptic equations

Let Ω be an open subset of $\text{R}{}^{\mathrm{<mi\; mathvariant="italic"\; is="true">N</mi>}}$, N ? 3, containing 0. We consider the solutions of ?Δu(x) + g(u(x)) = f(x) in Ω-{0}, where g is nondecreasing and f is bounded and we study the possible singularities at 0: when u(x) = o(|x|^{1 ? N}) we prove that u is isotropic near 0 and show that either it is a C¹ function in Ω (removable singularity) or |x|^{N ? 2}u(x) → c, c ≠ 0 (weak singularity) or |x|^{N ? 2} |u(x) |→ + ∞ (strong singularity). We also characterize the g's for which solutions with a weak singularity exist and improve a previous removability result of H. Brézis and L. Véron (Arch. Rational Mech. Anal.23 (1979), 153–166).     

Oxidative dearomatization of phenols and anilines via lambda(3)- and lambda(5)-iodane-mediated phenylation and oxygenation

Treatment of 2-methylphenols with chloro(diphenyl)-lambda(3)-iodane led to their regioselective dearomatizing 2-phenylation into cyclohexa-2,4-dienone derivatives via a proposed ligand coupling reaction. In the same vein of investigation, treatment of 2-methylanilines with the lambda(5)-iodane 2-iodoxybenzoic acid IBX reagent led to their regioselective dearomatization into previously undescribed ortho-quinol imines.     

Emulsified microemulsions and oil-containing liquid crystalline phases

Self-assembled nanostructures, such as inverted type mesophases of the cubic or hexagonal geometry or reverse microemulsion phases, can be dispersed using a polymeric stabilizer, such as the PEO-PPO-PEO triblock copolymer Pluronic F127. The particles, which are described in the present study, are based on monolinolein (MLO)-water mixtures. When adding tetradecane (TC) to the MLO-water-F127 system at constant temperature, the internal nanostructure of the kinetically stabilized particles transforms from a Pn3m (cubosomes) to a H2 (hexosomes) and to a water-in-oil (W/O, L2) microemulsion phase (emulsified microemulsion (EME)). To our knowledge, this is the first time that the formation of stable emulsified microemulsion (EME) systems has been described and proven to exist even at room temperature. The same structural transitions can also be induced by increasing temperature at constant tetradecane content. The internal nanostructure of the emulsified particles is probed using small-angle X-ray scattering (SAXS) and cryogenic transmission electron microscopy (cryo-TEM). At each investigated composition and temperature, the internal structure of the dispersions is observed to be identical to the corresponding structure of the nondispersed, fully hydrated bulk phase. This is clear evidence for the fact that the self-assembled inner particle nanostructure is preserved during the dispersion procedure. In addition, the internal structure of the particles is in thermodynamic equilibrium with the surrounding water phase. The internal structure of the dispersed, kinetically stabilized particles is a "real" and stable self-assembled nanostructure. To emphasize this fact, we denoted this new family of colloidal particles (cubosomes, hexosomes, and EMEs) as "ISASOMES" (internally self-assembled particles or "somes").     

Near-IR luminescence of monolayer-protected metal clusters

Visible-near-IR luminescence spectra of gold MPCs that are similar, irrespective of the number of core atoms (all <2 nm diameter) and different monolayers, are reported. The luminescence can be quantitatively invoked by introducing polar ligands into nonpolar MPC monolayers and by galvanic exchange of metal atoms on the MPC core surface with different metals. The observed emissions are believed to result from surface-localized states that depend on both the core metal of the nanoparticle and the ligands attached to the metal surface.     

Halogénures Alcalins: Un Modèle Incluant une Délocalisation à Courte Distance Application à la Stabilité Relative des Divers Arrangements Cristallins

The introduction of symmetry-adapted hybrid atomic orbitals on the metallic atoms allows us to divide the crystal into elementary cells which contain 8 valence electrons each. These cells are described by linear combinations of the halogen valence shell s and p orbitals and the hybrid orbitals of the nearest metallic atoms which point to the halogen. The electronic delocalization of the halogen ions is very weak (?0.02) for: LiF, NaF, KF, LiCl, NaCI, and KCI. The cell energy in the crystal is obtained by using a first-order perturbative treatment. In agreement with experiment, the f.c.c. type is found more stable than the b.c.c. or the blende type.     

Relaxometric study of copper [15]metallacrown-5 gadolinium complexes derived from alpha-aminohydroxamic acids

Proton nuclear magnetic relaxation dispersion (NMRD) profiles were recorded between 0.24 mT and 1.4 T for lanthanum(III)- and gadolinium(III)-containing [15]metallacrown-5 complexes derived from alpha-aminohydroxamic acids and with copper(II) as the ring metal. The influence of the different R-groups on the proton relaxivity was investigated, and a linear relationship between the relaxivity and the molecular mass of the metallacrown complex was found. The selectivity of the metallacrown complexes was tested by transmetalation experiments with zinc(II) ions. The crystal structure of the copper [15]metallacrown-5 gadolinium complex with glycine hydroximate ligands is reported.     

Effect of actin concentration on the structure of actin-containing liposomes

Liposomes encapsulating monomeric actin (G-actin) were produced via extrusion through 400 and 600 nm pore diameter polycarbonate membranes in low ionic strength buffer (G-buffer). After actin-containing liposomes were subjected to high ionic strength polymerization buffer (F-buffer), morphological changes in the structure of actin-containing liposomes were studied using asymmetric flow field-flow fractionation (AFFF) coupled with multiangle static light scattering (MASLS). The general shape of these liposomes was initially determined by fitting three form factors, which describe the angular distribution of scattered light from a spherical thin shell, thin disk, and thin rod, to the experimentally measured light scattering spectra to regress the dimensions of the liposomes corresponding to the proposed geometry. Light scattering spectra that yielded a best fit to the thin disk model were analyzed further and fit to the ellipsoidal of revolution form factor to regress both the major and minor axis dimensions. The results of this analysis showed that actin-containing liposomes extruded through 400 and 600 nm pore diameter membranes in F-buffer, at a low actin concentration (0.1 mg/mL), assumed a spherical shape, which is also the case for plain liposomes (no actin present) in G-buffer and F-buffer. When the actin concentration was increased to 1 mg/mL, the polymerizing actin filaments stretched the initially spherical liposome into a disklike shape. However, when the actin concentration was further increased to 5 mg/mL, the liposomes reverted back to a spherical shape.     

IR and theoretical studies of monocarbonyl Ni complexes formed by adsorption of CO at low pressure on silica-supported Ni(II) ions

This work reports on the reactivity of coordination vacancies of Ni(II) ions grafted onto the tridentate silica support (Ni(II)(3c) ions) with respect to CO used as a probe molecule. The adsorption of CO at 77 K in the 0.3 to 3.5 Pa CO pressure range is studied by FTIR on two samples differing in the dispersion of nickel. Quantum chemical calculations by the DFT method are performed to investigate, using a cluster approach, the binding of Ni to silica and, after CO adsorption, the geometry of the resulting carbonyl Ni complexes. Silica is modeled by using clusters composed of three types of monodentate ligands, SiO(-), SiOSi and/or SiOH, found on the surface of silica. This work is devoted to the monocarbonyl complexes. Whatever the sample, only one type of monocarbonyl is formed from Ni(II)(3c) ions. It is shown that the charge of the silica cluster is the major parameter influencing the CO IR frequency whereas the nature and the size of the silica cluster do not affect the CO bond length, confirming that local electrostatic interactions predominate. Only the 1- charged silica cluster Si(5)O(3)(-), composed of SiO(-), 2SiOSi fragments, respectively, reproduces the Ni[bond]O distances derived from EXAFS for the Ni(II)(3c) grafted site and gives CO frequencies in good agreement with the experimental values. It is shown that CO is stabilized by a magnetic transition from the (3)Ni(2+) triplet to the (1)Ni(2+) singlet state occurring upon adsorption.