Convergence of generalized gradients

For the graphs of Clarke's generalized gradients we prove that $$lim sup_{n \to + \infty } gph \partial f_n \subset gph \partial f in (E, strong) \times (E^* , weak).$$ provided that the sequencef _n of locally Lipschitz functions on a Banach spaceE with separable dual is strongly epi-convergent tof, equi-lower semidifferentiable and locally equibounded. This result extends [21] to the infinite-dimensional setting, and finds applications to the continuous behavior of the multiplier rule and of the generalized gradients of integral functionals under data perturbations.     

Role of surface integrals in the Hamiltonian formulation of general relativity

It is shown that if the phase space of general relativity is defined so as to contain the trajectories representing solutions of the equations of motion then, for asymptotically flat spaces, the Hamiltonian does not vanish but its value is given rather by a nonzero surface integral. If the deformations of the surface on which the state is defined are restricted so that the surface moves asymptotically parallel to itself in the time direction, then the surface integral gives directly the energy of the system, prior to fixing the coordinates or solving the constraints. Under more general conditions (when asymptotic Poincaré transformations are allowed) the surface integrals giving the total momentum and angular momentum also contribute to the Hamiltonian. These quantities are also identified without reference to a particular fixation of the coordinates. When coordinate conditions are imposed the associated reduced Hamiltonian is unambiguously obtained by introducing the solutions of the constraints into the surface integral giving the numerical value of the unreduced Hamiltonian. In the present treatment there are therefore no divergences that cease to be divergences after coordinate conditions are imposed. The procedure of reduction of the Hamiltonian is explicity carried out for two cases: (a) Maximal slicing, (b) ADM coordinate conditions.A Hamiltonian formalism which is manifestly covariant under Poincaré transformations at infinity is presented. In such a formalism the ten independent variables describing the asymptotic location of the surface are introduced, together with corresponding conjugate momenta, as new canonical variables in the same footing with the g_ij, π^ij. In this context one may fix the coordinates in the “interior” but still leave open the possibility of making asymptotic Poincaré transformations. In that case all ten generators of the Poincaré group are obtained by inserting the solution of the constraints into corresponding surface integrals.     

The MAST-edge centred lumped scheme for the flow simulation in variably saturated heterogeneous porous media

A novel methodology is proposed for the solution of the flow equation in a variably saturated heterogeneous porous medium. The computational domain is descretized using triangular meshes and the governing PDEs are discretized using a lumped in the edge centres numerical technique. The dependent unknown variable of the problem is the piezometric head. A fractional time step methodology is applied for the solution of the original system, solving consecutively a prediction and a correction problem. A scalar potential of the flow field exists and in the prediction step a MArching in Space and Time (MAST) formulation is applied for the sequential solution of the Ordinary Differential Equation of the cells, ordered according to their potential value computed at the beginning of the time step. In the correction step, the solution of a large linear system with order equal to the number of edges is required. A semi-analytical procedure is also proposed for the solution of the prediction step. The computational performance, the order of convergence and the mass balance error have been estimated in several tests and compared with the results of other literature models.     

Structure and Properties of Electrochemically Synthesized Silver Nanoparticles in Aqueous Solution by High-Resolution Techniques

The aim of this work was to deeply investigate the structure and properties of electrochemically synthesized silver nanoparticles (AgNPs) through high-resolution techniques such as transmission electron microscopy (TEM), scanning electron microscopy (SEM), Zeta Potential measurements, and matrix-assisted laser desorption/ionization time of flight mass spectrometry (MALDI-TOF-MS). Strong brightness, tendency to generate nanoclusters containing an odd number of atoms, and absence of the free silver ions in solution were observed. The research also highlighted that the chemical and physical properties of the AgNPs seemed to be related to their peculiar oxidative state as suggested by X-ray photoelectron spectroscopy (XPS) and X-ray powder diffraction (XRPD) analyses. Finally, the MTT assay tested the low cytotoxicity of the investigated AgNPs.     

Cell protection from Ca2+-overloading by bioactive molecules extracted from olive pomace

We are reporting in the present study that molecules extracted from olive pomace prevent cell death induced by Ca²⁺-overloading in different cell types. Exposure of cells to these molecules counteracts the Ca²⁺-induced cell damages by reducing the activation of the Ca²⁺-dependent protease calpain, acting possibly through the modification of the permeability to Ca²⁺ of the plasma membrane. The purification step by RP-HPLC suggests that effective compound(s), differing from the main biophenols known to be present in the olive pomace extract, could be responsible for this effect. Our observations suggest that bioactive molecules present in the olive pomace could be potential candidates for therapeutic applications in pathologies characterised by alterations of intracellular Ca²⁺ homeostasis.     

Mutual induced coordination in halogen-bonded anionic assemblies with (6,3) cation-templated topologies

We describe the use of halogen bonding for the deliberate construction of cation-templated anionic (6,3) networks thanks to a strategy based on the mutual induced fitting of the valences of the building blocks.     

Photochemistry of dicyanopyridines

The photochemistry of a variety of dicyanopyridines (2,3-, 2,4-, 2,5-, 2,6-, 3,4- and 3,5-dicyanopyridine) in solution at room temperature was investigated. Pulsed UV (308 nm) laser irradiation in deoxygenated acetonitrile yields the triplet state with lifetimes between 4 and 10 μs and absorption bands in the 400 and 320 nm regions. In the presence of added HCl an air-insensitive transient (τ ≈ 10–12 μs, λ_max ≈ 360–380 nm) was observed, suggesting the formation of a protonated excited state.

Irradiation in the presence of amines resulted in the production of the pyridyl radical anion (τ ≈ 40–80 μs, air sensitive, λ_max ≈ 360–380 nm) formed by electron transfer from the amine to the pyridine triplet excited state. Stern-Volmer analysis gave electron transfer rate constants in the range (1–8) × 10⁻⁸ M⁻¹ s⁻¹.

In methanol solvent, irradiation yielded an air-insensitive transient assigned as the neutral pyridyl radical (τ ≈ 30–200 μs, λ_max ≈ 370–385 nm). The formation of these transients is discussed in the context of previous photochemical electron spin resonance and product studies.     

New Class of Chiral Diphosphine Ligands for Highly Efficient Transition Metal-Catalyzed Stereoselective Reactions: The Bis(diphenylphosphino) Five-membered Biheteroaryls

The synthesis and application of three examples of a new class of chiral (C(2)) atropisomeric diphosphines characterized by two interconnected five-membered heteroaromatic rings, with hindered rotation around the interanular bond, are described. Optically pure (+)- and (-)-2,2'-bis(diphenylphosphino)-4,4',6,6'-tetramethyl-3,3'-bibenzo[b]thiophene (tetraMe-bitianp) (1a) and the parent unsubstituted system (+)- and (-)-bitianp (1b) were synthesized. They were found to be optically stable at 100 degrees C and were successfully employed as ligands in the Ru(II)-catalyzed hydrogenation of alpha- and beta-oxo esters to the corresponding alpha- and beta-hydroxy esters and in the hydrogenation of olefinic substrates. The optical and chemical yields were comparable with those reported for the same Ru(II)-binap-catalyzed reactions carried out under the same experimental conditions. The 2,2'-bis(diphenylphosphino)-3,3'-bibenzo[b]furan (1c), the oxygenated analogue of bitianp, was found to be configurationally unstable at room temperature. Complete structural X-ray elucidation of the Pd complexes of 1a-c is reported. The advantages of these biheteroaromatic ligands over the classical biaryl systems are discussed.