A remark on intersection of convex sets

Let X be a real Banach space. Let be a family of closed, convex subsets of X. We show that either the intersection ?_γ∈Γ(G_γ)^? of the ?-neighborhood of the sets G_γ is bounded for each ?>0, or it is unbounded for each ?>0. From this we derive a fixed point theorem for suitable maps that move some points along a bounded direction in Hilbert spaces.     

Ettore Majorana’s Course on Theoretical Physics: A Recent Discovery

We analyze in some detail the course that Ettore Majorana gave on theoretical physics at the University of Naples between January and March 1938, just prior to his mysterious disappearance. We discuss, in particular, the recently discovered Moreno Lecture Notes, in which all of Majorana’s lectures are recorded, six of which are not present in those that are preserved in the Domus Galilaeana in Pisa, Italy. Antonino Drago is a retired professor of history of physics at the University of Naples “Federico II.” Salvatore Esposito is a researcher on theoretical physics and history of physics at the University of Naples “Federico II.”     

Nickel nanostructured materials from liquid phase photodeposition

Liquid Phase Photo-Deposition (LPPD) technique has been used to obtain both colloidal particles and thin films of metallic and chloride nickel from solutions of only precursor Ni(acac)₂ (acac=2,4-pentandionato). Metallic nickel was obtained from ethanol solutions by direct nickel(II) photoreduction at 254 nm and by acetone sensitised reaction at 300 nm. In this latter process the rate was higher than in the first one. NiCl₂ was formed from CCl₄ solution by a solvent-initiated reaction. TEM analysis, performed on colloidal particles of nickel, showed that their dimensions are in the range 2–4 nm. The films did not present carbon contamination and were characterized by AFM, XPS and GIXRD. Metallic films consisted of particles of 20–40 nm that are the result of the aggregation of smaller crystallites (4–5 nm). Larger agglomerations (around 200 nm) have been observed for NiCl₂ films.     

Deposition and properties of high-carbon iron films

Thin high-carbon iron films were deposited by pulsed laser deposition onto grids for transmission electron microscopy using pre-combined carbon/iron targets with equal area ratio. The deposited films of about 20 nm in thickness were directly characterized by transmission electron microscopy. The films showed a variety of phases, surprisingly also including the NaCl-type FeC phase, which was theoretically predicted in the literature. For comparison, thin high-carbon stainless-steel films were deposited onto oxidized Si wafers with different carbon ratios in the targets (10, 20, 40 and 50 at.%). These films were characterized by means of Mössbauer Spectroscopy, the magneto-optical Kerr-effect, grazing incidence X-ray diffraction and Rutherford backscattering spectrometry. With these methods clearly defined multilayer-structures were observed which could lead to interesting magneto-resistance phenomena if the thickness of the multilayers can be controlled by the processing parameters.     

The Effect of Platinum on Diffusion Kinetics in β‐NiAl: Implications for Thermal Barrier Coating Lifetimes

Platinum is added to thermal barrier coatings (TBCs) as it is observed empirically to extend their lifetime, but the mechanism by which Pt acts is unknown. Since Pt has been proposed to alter diffusivities in NiAl, a key component of TBCs, we use first‐principles quantum mechanics calculations to investigate atomic level diffusion mechanisms. Here, we examine the effect of Pt on five previously proposed mechanisms for Ni diffusion in NiAl: next‐nearest‐neighbor jumps, the triple defect mechanism, and three variants of the six jump cycle. We predict that Pt increases the rate of Ni diffusion by stabilizing point defects and defect clusters that are diffusion intermediates. Previously, we predicted the triple defect mechanism to be a dominant Ni diffusion mechanism; it simultaneously results in long‐range Al diffusion in the opposite direction. Since Pt increases the rate of Ni diffusion, it also increases Al diffusion in NiAl, which may be key to extending the coating lifetime.     

Sequence and phosphorylation level determination of two donkey β‐caseins by mass spectrometry

Two coeluting components, with experimentally measured M_r values of 25529 and 24606 Da, were identified by reversed‐phase high‐performance liquid chromatography (RP‐HPLC) and mass spectrometric analysis in the dephosphorylated casein fraction of a milk sample collected from an individual donkey belonging to the Ragusano breed of the east of Sicily. By coupling enzymatic digestions, matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry (MALDI‐TOF MS) and RP‐HPLC/nano‐electrospray ionization tandem mass spectrometry (nESI‐MS/MS) analysis, the two proteins were identified as donkey β‐CNs and their sequences characterized completely, using the two known β‐CNs from mare as references. The two donkey β‐CNs, showing a mass difference of 923 Da, differ by the presence of the domain E²⁷SITHINK³⁴ in the full‐length component (M_r 25529 Da). In comparison with the mare's β‐CNs used as reference, they present nine amino acid substitutions: L→S³⁷, R→H⁵², S→N⁸¹, P→V⁸⁴, L→V⁹¹, R→Q²⁰³, P→L/I²⁰⁶, L→F²¹⁰ and A→P²¹⁹. Together, these substitutions account for the increase of 18 Da in the M_r of the donkey β‐CNs with respect to the counterparts from the mare. The molecular mass determination by ESI‐MS for the phosphorylated proteins showed that the full‐length component was composed of highly multi‐phosphorylated isoforms with five to seven phosphate groups. By analogy with the homologous mare's β‐CNs, the full‐length (226 amino acids) β‐CN was termed variant A, whereas the shorter (218 amino acids) β‐CN was termed variant A^Δ5. Copyright © 2009 John Wiley & Sons, Ltd.