POLYNOMIAL IDENTITIES OF FINITE DIMENSIONAL SIMPLE ALGEBRAS

Let F be an algebraically closed field and let A and B be arbitrary finite dimensional simple algebras over F. We prove that A and B are isomorphic if and only if they satisfy the same identities.

Bias correction in a multivariate normal regression model with general parameterization

This paper derives the second-order biases Of maximum likelihood estimates from a multivariate normal model where the mean vector and the covariance matrix have parameters in common. We show that the second order bias can always be obtained by means of ordinary weighted least-squares regressions. We conduct simulation studies which indicate that the bias correction scheme yields nearly unbiased estimators. (C) 2009 Elsevier B.V. All rights reserved.

Multivariate Analysis for the Classification Differentiation of Brazilian Sugarcane Spirits by Analysis of Organic and Inorganic Compounds

Brazilian sugarcane spirits were analyzed to elucidate similarities and dissimilarities by principal component analysis. Nine aldehydes, six alcohols, and six metal cations were identified and quantified. Isobutanol (LD 202.9 mu gL-1), butiraldehyde (0.08-0.5 mu gL-1), ethanol (39-47% v/v), and copper (371-6068 mu gL-1) showed marked similarities, but the concentration levels of n-butanol (1.6-7.3 mu gL-1), sec-butanol (LD 89 mu gL-1), formaldehyde (0.1-0.74 mu gL-1), valeraldehyde (0.04-0.31 mu gL-1), iron (8.6-139.1 mu gL-1), and magnesium (LD 1149 mu gL-1) exhibited differences from samples.