Global analytic regularity for non-linear second order operators on the torus

Assuming a subelliptic a-priori estimate we prove global analytic regularity for non-linear second order operators on a product of tori, using the method of majorant series.

     

On the three-dimensional Wigner-Poisson problem with inflow boundary conditions

We study the Wigner-Poisson problem in a bounded spatial domain, with non-homogeneous and time-dependent “inflow” boundary conditions. This system is a quantum model of charge transport in a semiconductor device coupled with reservoirs, in presence of a self-consistent potential and of an external one. We state a local-in-time well-posedness result for the problem. The main difficulty is proving in the three-dimensional case that the non-linear potential term is a Lipschitz perturbation of the “affine” streaming operator, in an appropriately weighted L²-space.     

Synthesis of polyarylacetylenes by γ‐ray‐induced polymerization of terminal alkynes. Nanostructures of ortho‐substituted derivatives

Terminal aryl alkynes RC₆H₄C?CH with substituents of different electronic properties and ring position (R = H, 4‐CF₃, 4‐OMe, 2‐CF₃, 2‐OMe, 2‐Me) were exposed to γ‐radiation (50–400 kGy) in organic solvents (hexane, 1,4‐dioxane, ethylacetate, methanol, tetrahydrofuran), at room temperature. The effects arising from substituent, solvent, dilution, and radiation dose allowed to define the conditions suitable for polymerization, which was favored in methanol at increasing dilution of the alkyne. Ortho‐substitution represented the key structural element in the substrate, and the derived polyarylacetylenes were characterized in detail, including gel permeation chromatography, thermal analysis, infrared, NMR, UV–vis, fluorescence, and scanning electron microscope spectroscopy. The results are consistent with the formation of irregular polymers mainly composed of trans‐transoid chains. Controlled aggregation of the polymers by means of an osmosis‐based procedure in solvent/non‐solvent mixtures allowed the formation of nanostructured materials, in particular of hollow nanospheres from THF/water. The methodology sets the basis for the development of γ‐rays‐induced polymerization of alkynes, in a transition metal catalyst‐free environment. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Vitamin C: an experimental and theoretical study on the gas‐phase structure and ion energetics of protonated ascorbic acid

In order to investigate the gas‐phase mechanisms of the acid catalyzed degradation of ascorbic acid (AA) to furan, we undertook a mass spectrometric (ESI/TQ/MS) and theoretical investigation at the B3LYP/6‐31 + G(d,p) level of theory. The gaseous reactant species, the protonated AA, [C₆H₈O₆]H⁺, were generated by electrospray ionization of a 10^?3 M H₂O/CH₃OH (1 : 1) AA solution. In order to structurally characterize the gaseous [C₆H₈O₆]H⁺ ionic reactants, we estimated the proton affinity and the gas‐phase basicity of AA by the extended Cooks's kinetic method and by computational methods at the B3LYP/6‐31 + G(d,p) level of theory. As expected, computational results identify the carbonyl oxygen atom (O2) of AA as the preferred protonation site. From the experimental proton affinity of 875.0 ± 12 kJ mol^?1 and protonation entropy ΔS_p 108.9 ± 2 J mol^?1 K^?1, a gas‐phase basicity value of AA of 842.5 ± 12 kJ mol^?1 at 298 K was obtained, which is in agreement with the value issuing from quantum mechanical computations. Copyright © 2016 John Wiley & Sons, Ltd.     

On the Alexander-Hirschowitz theorem

The Alexander-Hirschowitz theorem says that a general collection of k double points in imposes independent conditions on homogeneous polynomials of degree d with a well-known list of exceptions. Alexander and Hirschowitz completed its proof in 1995, solving a long standing classical problem, connected with the Waring problem for polynomials. We expose a self-contained proof based mainly on the previous works by Terracini, Hirschowitz, Alexander and Chandler, with a few simplifications. We claim originality only in the case d=3, where our proof is shorter. We end with an account of the history of the work on this problem.     

An Integration by Parts Formula in Sobolev Spaces

We prove the following formula

Palladium(II) Complexes with the 4,5-Bis(diphenylphosphino)acenaphthene Ligand and Their Reactivity with Ethylene

The last two decades have witnessed the development of homogeneous catalysts for ethylene homo- and co-polymerization reactions based on late transition metals. When Pd(II) is the metal of choice, the best ligand-metal combination deals with either bidentate nitrogen-donor molecules or phosphinobenzene sulfonate derivatives. In this contribution we have investigated the coordination chemistry to Pd(II) of a bidentate phosphorus ligand, namely 4,5-bis(diphenylphosphino)acenaphthene ( 1 ). Starting from the neutral complex, [Pd( 1 )(CH₃)Cl], we obtained the cationic derivatives [Pd( 1 )(CH₃)(L)][SbF₆], with L being either CH₃CN or 3,5-lutidine. Using in situ NMR spectroscopy we investigated the reaction of [Pd( 1 )(CH₃)(NCCH₃)][SbF₆] with ethylene, at room temperature, and ambient ethylene pressure. We discovered that [Pd( 1 )(CH₃)(NCCH₃)][SbF₆] acts as a catalyst for butenes and hexenes synthesis with the relevant Pd-ethyl intermediate as the catalyst resting state. At the same time the color of the solution turned from pale yellow to light red due to the formation of the dinuclear species [Pd(μ-η²−C₆H₅)PPh)−PPh₂]₂[SbF₆]₂. Both the neutral Pd(II) complex, activated in situ by NaSbF₆, and the monocationic acetonitrile derivative were tested in the ethylene homopolymerization reaction at high pressure, leading to low molecular weight, branched, polyethylene.