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.     

On the Logic of Common Belief

We investigate an axiomatization of the notion of common belief (knowledge) that makes use of no rules of inference (apart from Modus Ponens and Necessitation) and highlight the property of the set of accessibility relations that characterizes each axiom. Mathematics Subject Classification: 03B45, 68T25.