A proximal method with logarithmic barrier for nonlinear complementarity problems

We study the proximal method with the regularized logarithmic barrier, originally stated by Attouch and Teboulle for positively constrained optimization problems, in the more general context of nonlinear complementarity problems with monotone operators. We consider two sequences generated by the method. We prove that one of them, called the ergodic sequence, is globally convergent to the solution set of the problem, assuming just monotonicity of the operator and existence of solutions; for convergence of the other one, called the proximal sequence, we demand some stronger property, like paramonotonicity of the operator or the so called “cut property” of the problem.     

Compactness and existence results in weighted Sobolev spaces of radial functions. Part II: existence

We apply the compactness results obtained in the first part of this work, to prove existence and multiplicity results for finite energy solutions to the nonlinear elliptic equation

$$-\triangle u + V \left(\left|x\right|\right) u = g \left(\left|x\right|, u\right) \quad {\rm in} \Omega \subseteq \mathbb{R}^{N},\,N \geq 3,$$

where \({\Omega}\) is a radial domain (bounded or unbounded) and u satisfies u =  0 on \({\partial\Omega}\) if \({\Omega \neq\mathbb{R}^{N}}\) and \({u \rightarrow 0}\) as \({\left|x\right| \rightarrow \infty}\) if \({\Omega}\) is unbounded. The potential V may be vanishing or unbounded at zero or at infinity and the nonlinearity g may be superlinear or sublinear. If g is sublinear, the case with a forcing term \({g\left(\left|\cdot\right|, 0\right) \neq 0}\) is also considered. Our results allow to deal with V and g exhibiting behaviours at zero or at infinity which are new in the literature and, when \({\Omega = \mathbb{R}^{N}}\), do not need to be compatible with each other.

     

W*-rigidity for the von Neumann algebras of products of hyperbolic groups

We show that if \({\Gamma = \Gamma_1\times\dotsb\times \Gamma_n}\) is a product of \({{\rm n} \geq 2}\) non-elementary ICC hyperbolic groups then any discrete group \({\Lambda}\) which is \({W^*}\)-equivalent to \({\Gamma}\) decomposes as a direct product of n ICC groups and does not decompose as a direct product of k ICC groups when \({{\rm n} \not= {\rm k}}\). This gives a group-level strengthening of Ozawa and Popa’s unique prime decomposition theorem by removing all assumptions on the group \({\Lambda}\). This result in combination with Margulis’ normal subgroup theorem allows us to give examples of lattices in the same Lie group which do not generate stably equivalent II₁ factors.     

Kinetics of channel formation in bilayer lipid membranes (BLMs) and tethered BLMs: monazomycin and melittin

The kinetics of channel formation by the polyene-like antibiotic monazomycin, both in a bilayer lipid membrane (BLM) and in a tethered BLM (tBLM), and by the peptide melittin in a tBLM, is investigated. Stepping the applied potential from a value at which channels are not formed to one at which they are formed yields current vs time curves that are sigmoidal on a BLM, while they show a maximum on a tBLM; in the latter case, sigmoidal curves are obtained by plotting the charge against time. These curves are interpreted on the basis of a general kinetic model, which accounts for the potential-dependent penetration of adsorbed monomeric molecules into the lipid bilayer, followed by their aggregation with channel formation by a mechanism of nucleation and growth. In the case of monazomycin, which is present in the solution in the form of relatively hydrophilic clusters and is adsorbed as such on top of the lipid bilayer, penetration into the bilayer following a potential jump is assumed to be preceded by a potential-independent disaggregation of the adsorbed clusters into adsorbed monomers.     

Catalytic Oxidation of CO on a Curved Pt(111) Surface: Simultaneous Ignition at All Facets through a Transient CO-O Complex**

The catalytic oxidation of CO on transition metals, such as Pt, is commonly viewed as a sharp transition from the CO-inhibited surface to the active metal, covered with O. However, we find that minor amounts of O are present in the CO-poisoned layer that explain why, surprisingly, CO desorbs at stepped and flat Pt crystal planes at once, regardless of the reaction conditions. Using near-ambient pressure X-ray photoemission and a curved Pt(111) crystal we probe the chemical composition at surfaces with variable step density during the CO oxidation reaction. Analysis of C and O core levels across the curved crystal reveals that, right before light-off, subsurface O builds up within (111) terraces. This is key to trigger the simultaneous ignition of the catalytic reaction at different Pt surfaces: a CO-Pt-O complex is formed that equals the CO chemisorption energy at terraces and steps, leading to the abrupt desorption of poisoning CO from all crystal facets at the same temperature.     

Palladium-catalyzed stereoconvergent formylation of (E/Z)-β-bromo-β-fluorostyrenes: straightforward access to (Z)-α-fluorocinnamic aldehydes and (Z)-β-fluorocinnamic alcohols

We report here the stereoconvergent formylation of (E/Z)-β-bromo-β-fluorostyrene mixtures with carbon monoxide and sodium formate catalyzed by palladium. Optimization of reaction conditions leads to the corresponding pure (Z)-α-fluorocinnamaldehydes in good yields. The reaction was extended to styrenes bearing electro-attracting or electro-donating groups. The obtained α-fluoroaldehydes were smoothly reduced to the corresponding (Z)-β-fluorocinnamic alcohol by NaBH(4). The reaction could be performed on functionalized substrates as demonstrated by the access to the glucoside of β-fluoroconiferyl alcohol, (Z)-β-fluoroconiferin, a strong inhibitor of lignin polymerization.     

Photochemistry of acetylacetone isolated in parahydrogen matrices upon 266 nm irradiation

The photochemistry of the chelated enol form of acetylacetone (AcAc) was investigated by UV excitation of the S(2) state at 266 nm in parahydrogen matrices, complemented by experiments in neon and normal hydrogen matrices. Infrared (IR) spectroscopy, combined with theoretical calculations, was used to identify the photoproducts. Isomerization towards various non-chelated forms (no intramolecular H-bond) of AcAc is the dominant channel whereas fragmentation is very minor. The isomerization kinetics is monitored by IR spectroscopy. Among the seven non-chelated conformers of AcAc, only three are formed in parahydrogen matrices, whereas four are observed in normal hydrogen matrices. This difference suggests that an active tunnelling process between conformers occurs in parahydrogen but is quenched in normal hydrogen where guest-host interactions are stronger. Fragmentation and isomerization of excited AcAc are discussed in the light of these new data. The role of the intermediate triplet state in the S(2)→ S(0) relaxation is confirmed, as the importance of phonons in the condensed phase.     

Valorization of Artichoke Industrial By-Products Using Green Extraction Technologies: Formulation of Hydrogels in Combination with Paulownia Extracts

The integral valorization of artichoke bracts generated during industrial canning of artichoke was assessed. The extraction of bioactive compounds was addressed with pressurized hot water under subcritical conditions. The performance of this stage on the extraction of phenolics with antioxidant properties and the saccharidic fraction using conventional and microwave heating was compared. The microwave assisted process was more efficient than the conventional one regarding extraction yields of total solubles, and glucose and fructose oligomers and phenolics, because lower operational temperatures and shorter times were needed. Degradation of fructose oligomers was observed at temperatures higher than 160 °C, whereas the maximal phenolic content occurred at 220 °C. Both the extracts and the residual solids, obtained at conditions leading to maximum phenolics yields, were evaluated for the production of starch-based hydrogels, supplemented with Paulownia leaves’ aqueous extracts.