On invariant Rings of Sylow subgroups of finite classical groups

In this thesis we study the invariant rings for the Sylow p-subgroups of the nite classical groups. We have successfully constructed presentations for the invariant rings for the Sylow p-subgroups of the unitary groups GU(3; Fq2) and GU(4; Fq2 ), the symplectic group Sp(4; Fq) and the orthogonal group O+(4; Fq) with q odd. In all cases, we obtained a minimal generating set which is also a SAGBI basis. Moreover, we computed the relations among the generators and showed that the invariant ring for these groups are a complete intersection. This shows that, even though the invariant rings of the Sylow p-subgroups of the general linear group are polynomial, the same is not true for Sylow p-subgroups of general classical groups. We also constructed the generators for the invariant elds for the Sylow p-subgroups of GU(n; Fq2 ), Sp(2n; Fq), O+(2n; Fq), O-(2n + 2; Fq) and O(2n + 1; Fq), for every n and q. This is an important step in order to obtain the generators and relations for the invariant rings of all these groups.

Dynamic headspace solid-phase microextraction combined with one-dimensional gas chromatography–mass spectrometry as a powerful tool to differentiate banana cultivars based on their volatile metabolite profile

In this study the effect of the cultivar on the volatile profile of five different banana varieties was evaluated and determined by dynamic headspace solid-phase microextraction (dHS-SPME) combined with one-dimensional gas chromatography–mass spectrometry (1D-GC–qMS). This approach allowed the definition of a volatile metabolite profile to each banana variety and can be used as pertinent criteria of differentiation. The investigated banana varieties (Dwarf Cavendish, Prata, Maçã, Ouro and Platano) have certified botanical origin and belong to the Musaceae family, the most common genomic group cultivated in Madeira Island (Portugal). The influence of dHS-SPME experimental factors, namely, fibre coating, extraction time and extraction temperature, on the equilibrium headspace analysis was investigated and optimised using univariate optimisation design. A total of 68 volatile organic metabolites (VOMs) were tentatively identified and used to profile the volatile composition in different banana cultivars, thus emphasising the sensitivity and applicability of SPME for establishment of the volatile metabolomic pattern of plant secondary metabolites. Ethyl esters were found to comprise the largest chemical class accounting 80.9%, 86.5%, 51.2%, 90.1% and 6.1% of total peak area for Dwarf Cavendish, Prata, Ouro, Maçã and Platano volatile fraction, respectively. Gas chromatographic peak areas were submitted to multivariate statistical analysis (principal component and stepwise linear discriminant analysis) in order to visualise clusters within samples and to detect the volatile metabolites able to differentiate banana cultivars. The application of the multivariate analysis on the VOMs data set resulted in predictive abilities of 90% as evaluated by the cross-validation procedure.