Asymptotic spherical symmetry of the free boundary in degenerate diffusion equations

Summary A general class of nonlinear degenerate parabolic equations in many space dimensions is considered and two main results concerning the free boundary are proved: (i) the «eventual» Lipschitz continuity in the space variable, (ii) the asymptotic spherical symmetry in a stronger sense than the «almost radiality» proved by Aronson & Caffarelli [2] for the porous medium equation. The proofs make use of geometric ideas based on the comparison principle and the method of moving planes.     

A convenient preparation of 3-isopropyl-1-methylcyclopentylmethanol and 1-isopropyl-3-methylcyclopentylmethanol via Favorskii rearrangement

The Favorskii rearrangement of suitable α-chloro derivatives of commercially available (+)- and (−)-carvone, and (−)-menthone served efficiently to prepare the title compounds featuring delicious fruity, floral olfactory notes.     

Counterfeit drugs: analytical techniques for their identification

In recent years, the number of counterfeit drugs has increased dramatically, including not only “lifestyle” products but also vital medicines. Besides the threat to public health, the financial and reputational damage to pharmaceutical companies is substantial. The lack of robust information on the prevalence of fake drugs is an obstacle in the fight against drug counterfeiting. It is generally accepted that approximately 10% of drugs worldwide could be counterfeit, but it is also well known that this number covers very different situations depending on the country, the places where the drugs are purchased, and the definition of what constitutes a counterfeit drug. The chemical analysis of drugs suspected to be fake is a crucial step as counterfeiters are becoming increasingly sophisticated, rendering visual inspection insufficient to distinguish the genuine products from the counterfeit ones. This article critically reviews the recent analytical methods employed to control the quality of drug formulations, using as an example artemisinin derivatives, medicines particularly targeted by counterfeiters. Indeed, a broad panel of techniques have been reported for their analysis, ranging from simple and cheap in-field ones (colorimetry and thin-layer chromatography) to more advanced laboratory methods (mass spectrometry, nuclear magnetic resonance, and vibrational spectroscopies) through chromatographic methods, which remain the most widely used. The conclusion section of the article highlights the questions to be posed before selecting the most appropriate analytical approach.     

Zinc oxide nanostructured layers for gas sensing applications

Various kinds of zinc oxide (ZnO) nanostructures, such as columns, pencils, hexagonal pyramids, hexagonal hierarchical structures, as well as smooth and rough films, were grown by pulsed laser deposition using KrF and ArF excimer lasers, without use of any catalyst. ZnO films were deposited at substrate temperatures from 500 to 700°C and oxygen background pressures of 1, 5, 50, and 100 Pa. Quite different morphologies of the deposited films were observed using scanning electron microscopy when different laser wavelengths (248 or 193 nm) were used to ablate the bulk ZnO target. Photoluminescence studies were performed at different temperatures (down to 7 K). The gas sensing properties of the different nanostructures were tested against low concentrations of NO₂. The variation in the photoluminescence emission of the films when exposed to NO₂ was used as transduction mechanism to reveal the presence of the gas. The nanostructured films with higher surface-to-volume ratio and higher total surface available for gas adsorption presented higher responses, detecting NO₂ concentrations down to 3 ppm at room temperature.     

Unitary equivalence of automorphisms of separable C*-algebras

We prove that the automorphisms of any separable C*-algebra that does not have continuous trace are not classifiable by countable structures up to unitary equivalence. This implies a dichotomy for the Borel complexity of the relation of unitary equivalence of automorphisms of a separable unital C*-algebra: Such relation is either smooth or not even classifiable by countable structures.     

Pulsed laser ablation deposition of thin films on large substrates

We have designed and built an ultra-high vacuum chamber which allows thin film deposition on large area (up to 100 mm diameter) flat substrates and on three-dimensional substrates (e.g. 100 mm long, 50 mm diameter cylinders) by the pulsed laser deposition and reactive pulsed laser deposition techniques. Heating of substrates during and after film deposition is possible using either resistive heaters or a lamp array. Metal (Cu) and metal nitride (TiN) and carbide (TiC) films were deposited on Si wafers (60 and 100 mm diameter), three-dimensional steel substrates (steel cylinders and screws), Teflon plates, and paper sheets.     

Geodetic VLBI data analysis using VLBI3 software

Summary VLBI (Very Long Baseline Interferometry) geodetic data have been analysed. Baseline, lengths of several thousands kilometers and their time rates have been estimated from a subset of data, spanning three years, of the IRIS project and using VLBI3 software. A weighted-least-squares estimation has been carried out with thea priori standard deviations of the data modified to account for systematic biases due to mismodelling of the clocks and atmosphere. Comparisons with independent analysis show an agreement to the cm level or better both in baseline lengths and rates.     

Photoelectron-beam generation up to short threshold

We report on the behaviour of electron beams extracted from metal cathodes illuminated by a powerful XeCl-laser beam. The target materials used were Zn, Y and Ge. During the electron extraction a plasma was created on the target surface. At high laser energies and high accelerating voltages the plasma introduces an impedance into the cathode-anode region. Owing to the plasma formation short-circuits occur in the accelerating region thus limiting the maximum output current. Under our experimental conditions, a laser energy of 27 mJ and 3 mm of distance cathode-anode, a maximum output corrent density of about 4.9 A/cm² was obtained with the Zn cathode. The yttrium target may provide a higher current density but so far it could not be demonstrated due to plasma formation which short-circuits the anode-cathode region. The experimental results obtained with Ge targets are interesting for obtaining short electron pulses.     

Wavelength-dispersive spectral analysis and quantification of monazites by electron-probe microanalysis

The problem of determining the chemical composition of monazite grains through electron probe microanalysis is studied, by using a scanning electron microscope with a wavelength dispersive spectrometer. A careful qualitative analysis is performed with the purpose of determining all the elements present in the samples, the lines to be used in the quantifications trying to minimize interferences, the angular positions and the acquisition times for the measurement of peak and background intensities and the crystals to be used. Particular emphasis is devoted to the analysis of Th, U and Pb, which are used to determine the age of the rock by means of the U-Th-Pb method, commonly used in geochronology. Quantitative determinations of the chemical composition of monazite grains are performed, optimizing the experimental conditions on the basis of the qualitative analysis. The determinations were made under two different criteria of quantification of oxygen, and the dissimilar results obtained are discussed.