On uniqueness of fractional powers of multi-valued linear operators and the incomplete Cauchy problem

We obtain uniqueness of additive families {A _t } _t>0 of fractional powers of a multi-valued sectorial linear operator A ?? A ₁ in a Banach space, satisfying a certain kind of continuity with respect to the exponent and a spectral property, from uniqueness of the solutions of the second-order incomplete Cauchy problem associated with A. We show the close relationship between the multiplicativity and the uniqueness of fractional powers.     

Calculation of the electronic properties of neutral and ionized divalent-metal clusters

The electronic properties of neutral and ionized divalent-metal clusters have been studied using a microscopic theory, which takes into account the interplay between van der Waals (vdW) and covalent bonding in the neutral clusters, and the competition between hole delocalization and polarization energy in the ionized clusters. By calculating the ground-state energies of neutral and ionized Hg _n clusters, we determine the size dependence of the bond character and the ionization potentialI _p (n). For neutral Hg _n clusters we obtain a transition from van der Waals to covalent behaviour at the critical sizen _c ～10–20 atoms. Results forI _p (Hg _n ) withn≤20 are in good agreement with experiments, and suggest that small Hg _n ⁺ clusters can be viewed as consisting of a positive trimer core Hg ₃ ⁺ surrounded byn?3 polarized neutral atoms.     

The quantitative electrochemical generation of bromine in acetic acid

The quantitative electrochemical generation of bromine at a platinum electrode in acetic acid is described. Coulometric methods for the determination of hydroquinone and 2-methylhydroquinone are reported. The best results are obtained with 0.7–1.1 M potassium acetate solutions as supporting electrolyte, and biamperometric end-point detection. The effects of water and acetic anhydride on the accuracy of titrations are discussed. Determination of the formal redox potential of the Br₂/Br^- system in a 0.9 M potassium acetate solution in acetic acid showed that bromide is oxidized directly to bromine at a platinum electrode with 100% current efficiency.     

Functional-integral study of spin fluctuations in small Fe clusters

Finite temperature magnetic properties of small Fe_N clusters (N ≤6) are determined in the framework of a spin-fluctuation itinerant-electron theory based on a functional integral formulation of the canonical partition function and derived statistical averages. The free energy associated to each configuration of the exchange fields throughout the cluster are calculated by using Haydock-Heine-Kellys recursion method. The statistical averages of physical interest are obtained by performing parallel-tempering Monte Carlo simulations. Representative results are discussed for the average magnetization per atom as a function of temperature. The interplay between local environment and magnetization curves is analyzed by considering the low-temperature limit of the local spin-fluctuations energies ΔF_l(ξ) at different atoms l. The electronic calculations are contrasted with the predictions of simple of phenomenological Heisenberg-like models.     

New strategy for the asymmetric synthesis of phenyl ketone cyanohydrins: quaternization of cyanohydrins derived from 2-p-tolylsulfinyl benzaldehyde

[reaction: see text] Optically pure functionalized cyanohydrins derived from 1-[2-(p-tolylsulfinyl)phenyl] ethanone can be obtained by the reaction of 2-p-tolylsulfinyl benzaldehyde derived cyanohydrins with bases and further treatment with suitable electrophiles. High yields and excellent stereoselectivities (up to de >98%) were obtained for these remote 1,4-asymmetric induction processes controlled by a sulfinyl chiral inductor.     

Numerical limit analysis bounds for ductile porous media with oblate voids

The paper is devoted to a numerical limit analysis of a hollow spheroidal model with a von Mises solid matrix. To this purpose, existing kinematic and static 3D-FEM codes for the case of spherical cavities have been modified and improved to account for the model of a spheroidal cavity confocal with the external spheroidal boundary. The optimized conic programming formulations and the resulting codes appear to be very efficient. This framework is then applied to the derivation of numerical upper and lower anisotropic bounds in the case of an oblate void. The numerical results obtained from a series of tests are presented and allow to assess the accuracy of closed-form expressions of the macroscopic criteria proposed by [Gologanu et al., 1994] and [Gologanu et al., 1997] for porous media with oblate voids.