Boundedness of extremal solutions in dimension 4

In this paper we establish the boundedness of the extremal solution u^∗$u^{\ast }$ in dimension N=4$N=4$ of the semilinear elliptic equation −Δu=λf(u)$-\Delta u=\lambda f\left(u\right)$, in a general smooth bounded domain Ω⊂R^N$\Omega \subset {\mathbb{R}}^N$, with Dirichlet data u_|∂Ω=0$u{|}_{\partial \Omega }=0$, where f$f$ is a C¹$C^1$ positive, nondecreasing and convex function in [0,∞)$[0,\infty )$ such that f(s)/s→∞$f\left(s\right)/s\to \infty$ as s→∞$s\to \infty$.     

Regioselective synthesis of pyrrolin-3-ones and 2,3,4,5-tetrahydro[1,3]-oxazines from N-vinylic amidines

Achiral and optically active N-vinylic amidines are obtained by simple addition of amidines to acetylenic esters. Thermal intramolecular cyclization of these substrates containing a carboxylate group in position 3 gives pyrrolin-3-ones. The enaminone character of these compounds towards propargyl bromide, diethyl azodicarboxylate, diethyl acetylenedicarboxylate, ethyl propiolate and phenyl isocyanate is studied and functionalized pyrrolin-3-one derivatives are obtained. The reaction of the pyrrolinones prepared with diethyl ketomalonate leads to new 1,3-oxazine derivatives.     

Surface Characterisation of Cerium-Doped Silica Coatings Obtained by Sol-Gel

The chemical composition of cerium-doped silica coatings prepared via sol-gel were studied using X-ray photoelectron spectroscopy (XPS) in conjunction with Ar⁺-ion sputtering, Rutherford back-scattering spectroscopy (RBS) and photoluminescence (PL) spectroscopy. XPS results showed that cerium was incorporated in the silica network as Ce(III). The absence of PL emissions from Ce(III) was explained by a clustering of the ions producing a quenching of the luminescence. XPS combined with Ar⁺ and RBS showed that the distribution of Ce is not uniform across the coating, showing a maximum concentration in an inner layer of the coating.     

New layered double hydroxides containing intercalated manganese oxide species: synthesis and characterization

Manganese oxide species (MnO(x)) have been intercalated within the gallery spaces of Mg-Al layered double hydroxides (LDHs). Synthesis of these materials was achieved by ion-exchange of the LDH-nitrate precursor with permanganate anion followed by reduction with organic reagents, such as glucose, ethanol, and ascorbic acid. Elemental analysis, X-ray diffraction, FT-IR spectroscopy, Raman spectroscopy, HR-TEM, and N(2) sorption analyses have been used to characterize these materials. TEM micrographs of LDH-MnO(x) materials revealed platelike morphology, characteristic of hydrotalcite-like compounds. Chemical analysis results showed that permanganate anions exchanged with nitrate anions. FT-IR and Raman spectroscopy confirmed the reduction of the permanganate anions after treatment with the organic reagents. The XRD diffraction patterns of LDH-MnO(x) revealed that the layer structure is maintained after all synthetic steps. The observed basal spacings of intercalates varied depending on the reducing agent; the largest expansion was 9.93A, corresponding to the use of ascorbic acid. The specific surface areas were also affected according to the organic reagent used, indicating that the structural modifications in the interlayer domain observed by X-ray diffraction also influence the microtextural properties.     

Classification and pattern recognition of acyclic octenes based on mass spectra

Two SIMCA models were developed for the classification of acyclic octene isomers, which only form a fraction of a very complex product mixture obtained, for example, from the transformation of 1-butene. The effects of spectral transformation, namely autocorrelation and logarithmic intensity ratios transforms, and (square-root) scaling of the octane isomers mass-spectral data were investigated. Both the spectral-features preprocessing methods and scaling were found to be vital for an adequate development and improvement of the classification models. The best SIMCA models were successfully applied on gas-chromatography-mass spectroscopy (GC-MS) analysis collected from the dimerization of 1-butene over heterogeneous catalysts in the liquid phase.     

Colorimetric determination of persulfate with alcian blue

Alcian blue buffered at pH 2.5 is oxidized by persulfate. The plot of optical density at 615 mμ vs. concentration of persulfate (within the range of 10 to 80 μg) is linear. The assay is not affected by bromate and iodate.     

A representation of recursively enumerable sets through Horn formulas in higher recursion theory

We prove the existence of graphs with empty intersection of their longest paths or cycles as subgraphs of lattices on the torus and the Möbius strip.     

Probability of ionization of sputtered particles as a function of their energy: Part I: Negative Si ions

In this study we have investigated how the probability of ionization of sputtered Si atoms to form negative ions depends on the energy of the atoms. We have determined the ionization probability from experimental SIMS energy distributions using a special experimental technique, which included de-convolution of the energy distribution with an instrumental transmission function, found by separate measurements.We found that the ionization probability increases as a power law ∼E^0.677 for particles sputtered with energies of 0-10 eV, then becomes a constant value (within the limits of experimental error) for particles sputtered with energies of 30-100 eV. The energy distributions of Si⁻ ions, measured under argon and cesium ion sputtering, confirmed this radical difference between the yields from low and high-energy ions.To explain these results we have considered ionization mechanisms that are different for the low energy atoms (<10 eV) and for the atoms emitted with higher energy (>30 eV).     

Critical distance for secondary ion formation: Experimental SIMS measurements

We have performed direct experimental measurements of the critical distance for the secondary ion formation process. To this end, we compared the experimentally measured energy distribution of secondary Si⁻ ions with the theoretical energy distribution (Sigmund-Thompson relation) of secondary Si atoms. Our model states that the maxima positions of these two energy distributions differ by the Coulomb interaction potential between the outgoing ion (Si⁻ in our case) and a charge with the opposite polarity formed at the surface after electron transition between the outgoing Si atom and the surface. Quite a reasonable value was obtained for the critical distance, but with a large scatter in experimental data. The conclusion has been made that the experimental technique should be improved to get more precise values of the critical distance, which is of high importance for practical purposes.