On a positive set theory with inequality

We introduce a quite natural Frege‐style set theory, which we call Strong‐Frege‐2 $(\mathsf {SF}_2)$, a sort of simplification of the theory considered in 13 (under the name Strong‐Frege‐3) and 1 (under the name F2). We give a model of a weaker variant of $\mathsf {SF}_2$, called $\mathsf {SF}_2\mathsf {AC}$, where atoms and coatoms are allowed. To construct the model we use an enumeration “almost without repetitions” of the Π¹₁ sets of natural numbers; such an enumeration can be obtained via a classical priority argument much in the style of 5 and 15 . © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Optical properties of a polyethylene dispersion with a luminescent silica prepared by surface grafting of a perylene derivative

A micrometric silica modified with perylene derivative (SiO₂–TES) has been prepared by hydrolysis–condensation reactions between silica and N,N’-bis-(3-triethoxysilylpropyl)-perylene-tetracarboxyldiimide (P-TES) and utilized as filler in LLDPE films together with a compatibilizer. Spectroscopic analyses on SiO₂–TES confirmed the grafting of P-TES on silica, while its amount was determined by thermogravimetric analysis. Solid state NMR provided information about the structure of silicon atoms involved in the condensation of SiO₂ and P-TES that resulted mainly in silicon atoms grafted with bi-dentate anchorages.UV–Vis and fluorescence analyses carried out on P-TES showed the ability of the dye to generate J-type aggregates in apolar solvents. The same analyses on SiO₂–TES revealed the presence of both isolated and aggregated dye molecules grafted on silica surface, while on polymeric dispersions of SiO₂–TES, they have shown only the presence of P-TES aggregates grafted to silica.Thanks to the direct correlation between optical properties (obtained both by UV–Vis and by fluorescence analyses) and the chemical environment of composites, the luminescent silica SiO₂–TES could be used to estimate the filler dispersion extent in different microcomposite polymer materials.     

Absorption and emission spectra of fluorescent silica nanoparticles from TD-DFT/MM/PCM calculations

A multi-scale computational protocol, which combines Quantum Mechanics and Molecular Mechanics (QM/MM) calculations with the polarisable continuum model (PCM), has been used to study the tetramethylrhodamine isothiocyanate (TRITC) fluorophore, embedded in three different environments, namely in water, on an amorphous silica surface and covalently encapsulated in a silica nanoparticle (C dot). Absorption and emission spectra have been simulated by using TD-B3LYP/PCM calculations, performed on the TRITC ground and excited state geometries, optimized at the QM/MM level. The results are in good agreement with experimental data confirming the caging effect played by the silica shell on the mobility of the TRITC molecule when covalently encapsulated in silica nanoparticles. This could result in a decrease of the nonradiative decay rate and thus an increase of the quantum yield of the molecule.     

Fluorescence spectra of organic dyes in solution: a time dependent multilevel approach

Classical all-atom molecular dynamics (MD) simulations and quantum mechanical (QM) time-dependent density functional theory (TD-DFT) calculations are employed to study the conformational and photophysical properties of the first emitter excited state of tetramethyl-rhodamine iso-thiocyanate fluorophore in aqueous solution. For this purpose, a specific and accurate force field has been parameterised from QM data to model the fluorophore's first bright excited state. During the MD simulations, the consequences of the π→π* electronic transition on the structure and microsolvation sphere of the dye has been analysed in some detail and compared to the ground state behaviour. Thereafter, fluorescence has been calculated at the TD-DFT level on configurations sampled from the simulated MD trajectories, allowing us to include time dependent solvent effects in the computed emission spectrum. The latter, when compared with the absorption spectrum, reproduces well the experimental Stokes shift, further validating the proposed multilevel computational procedure.     

Gas chromatographic quantitative analysis of methanol in wine: operative conditions, optimization and calibration model choice

The influence of the wine distillation process on methanol content has been determined by quantitative analysis using gas chromatographic flame ionization (GC-FID) detection. A comparative study between direct injection of diluted wine and injection of distilled wine was performed. The distillation process does not affect methanol quantification in wines in proportions higher than 10%. While quantification performed on distilled samples gives more reliable results, a screening method for wine injection after a 1:5 water dilution could be employed. The proposed technique was found to be a compromise between the time consuming distillation process and direct wine injection. In the studied calibration range, the stability of the volatile compounds in the reference solution is concentration-dependent. The stability is higher in the less concentrated reference solution. To shorten the operation time, a stronger temperature ramp and carrier flow rate was employed. With these conditions, helium consumption and column thermal stress were increased. However, detection limits, calibration limits, and analytical method performances are not affected substantially by changing from normal to forced GC conditions. Statistical data evaluation were made using both ordinary (OLS) and bivariate least squares (BLS) calibration models. Further confirmation was obtained that limit of detection (LOD) values, calculated according to the 3sigma approach, are lower than the respective Hubaux-Vos (H-V) calculation method. H-V LOD depends upon background noise, calibration parameters and the number of reference standard solutions employed in producing the calibration curve. These remarks are confirmed by both calibration models used.     

Recognizing Balanceable Matrices

A 0/±1 matrix is balanced if it does not contain a square submatrix with exactly two nonzero entries per row and per column in which the sum of all entries is 2 modulo 4. A 0/1 matrix is balanceable if its nonzero entries can be signed ±1 so that the resulting matrix is balanced. A signing algorithm due to Camion shows that the problems of recognizing balanced 0/±1 matrices and balanceable 0/1 matrices are equivalent. Conforti, Cornuéjols, Kapoor and Vušković gave an algorithm to test if a 0/±1 matrix is balanced. Truemper has characterized balanceable 0/1 matrices in terms of forbidden submatrices. In this paper we give an algorithm that explicitly finds one of these forbidden submatrices or shows that none exists. Received: October 2004     

Inclusive sum rules for isotopic spin

Inclusive sum rules for non-abelian symmetry generators and in particular for isospin are studied. A compact formalism is introduced which allows to exaract in a simple way all the consequences of invaraince properties.