Sheaves, local homeomorphisms and local sets as Hilbert locale modules

We give a thorough account of the various equivalent notions for \sheaf" on a locale, namely the separated and complete presheaves, the local home- omorphisms, and the local sets, and to provide a new approach based on quantale modules whereby we see that sheaves can be identi¯ed with certain Hilbert modules in the sense of Paseka. This formulation provides us with an interesting category that has immediate meaningful relations to those of sheaves, local homeomorphisms and local sets. The concept of B-set (local set over the locale B) present in [3] is seen as a simetric idempotent matrix with entries on B, and a map of B-sets as de¯ned in [8] is shown to be also a matrix satisfying some conditions. This gives us useful tools that permit the algebraic manipulation of B-sets. The main result is to show that the existing notions of \sheaf" on a locale B are also equivalent to a new concept what we call a Hilbert module with an Hilbert base. These modules are the projective modules since they are the image of a free module by a idempotent automorphism On the ¯rst chapter, we recall some well known results about partially ordered sets and lattices. On chapter two we introduce the category of Sup-lattices, and the cate- gory of locales, Loc. We describe the adjunction between this category and the category Top of topological spaces whose restriction to spacial locales give us a duality between this category and the category of sober spaces. We ¯nish this chapter with the de¯nitions of module over a quantale and Hilbert Module. Chapter three concerns with various equivalent notions namely: sheaves of sets, local homeomorphisms and local sets (projection matrices with entries on a locale). We ¯nish giving a direct algebraic proof that each local set is isomorphic to a complete local set, whose rows correspond to the singletons. On chapter four we de¯ne B-locale, study open maps and local homeo- morphims. The main new result is on the ¯fth chapter where we de¯ne the Hilbert modules and Hilbert modules with an Hilbert and show this latter concept is equivalent to the previous notions of sheaf over a locale.

Analytical characterization of the aroma of Tinta Negra Mole red wine: Identification of the main odorants compounds

A method for the simultaneous determination of major and minor volatiles composition in different types (dry, medium dry, sweet and medium sweet) of a young Tinta Negra Mole (TNM) monovarietal red wine from 2003 harvest has been validated. Wine samples preparation includes a dichloromethane liquid–liquid extraction followed by concentration under a nitrogen atmosphere. The extracted fraction was analysed by gas chromatography–mass spectrometry and give quantitative information for more than 86 analytes whose concentration range from few μg l−1 to 259.1 mg l−1. The method enables high recovery of volatile compounds in wine good linearity with (r2) values higher than 0.980 and good sensitivity. The limits of detection range from 0.003 to 0.534 mg l−1 and limits of quantification from 0.009 to 1.170 mg l−1. The method allows satisfactory determination of more than 80 compounds in the TNM red wines. These wines are characterized by a high content of higher alcohols, ethyl esters, fatty acids and lactones. The levels of sulphur compounds in Tinta Negra Mole medium sweet wines are very low, but they have the highest concentration of carbonyl compounds. Quantitative analysis of the main odorants followed by the determination of aroma index allow us elucidate the aroma of these varieties. On the basis of their odour description and odour threshold, the most powerful odorants of Tinta Negra Mole wines were tentatively established.

A sensitive microextraction by packed sorbent-based methodology combined with ultra-high pressure liquid chromatography as a powerful technique for analysis of biologically active flavonols in wines

A new approach based on microextraction by packed sorbent (MEPS) and reversed-phase high-throughput ultra high pressure liquid chromatography (UHPLC) method that uses a gradient elution and diode array detection to quantitate three biologically active flavonols in wines, myricetin, quercetin, and kaempferol, is described. In addition to performing routine experiments to establish the validity of the assay to internationally accepted criteria (selectivity, linearity, sensitivity, precision, accuracy), experiments are included to assess the effect of the important experimental parameters such as the type of sorbent material (C2, C8, C18, SIL, and C8/SCX), number of extraction cycles (extract-discard), elution volume, sample volume, and ethanol content, on the MEPS performance. The optimal conditions of MEPS extraction were obtained using C8 sorbent and small sample volumes (250 μL) in five extraction cycle and in a short time period (about 5 min for the entire sample preparation step). Under optimized conditions, excellent linearity View the MathML source(Rvalues2>0.9963), limits of detection of 0.006 μg mL−1 (quercetin) to 0.013 μg mL−1 (myricetin) and precision within 0.5–3.1% were observed for the target flavonols. The average recoveries of myricetin, quercetin and kaempferol for real samples were 83.0–97.7% with relative standard deviation (RSD, %) lower than 1.6%. The results obtained showed that the most abundant flavonol in the analyzed samples was myricetin (5.8 ± 3.7 μg mL−1). Quercetin (0.97 ± 0.41 μg mL−1) and kaempferol (0.66 ± 0.24 μg mL−1) were found in a lower concentration. The optimized MEPSC8 method was compared with a reverse-phase solid-phase extraction (SPE) procedure using as sorbent a macroporous copolymer made from a balanced ratio of two monomers, the lipophilic divinylbenzene and the hydrophilic N-vinylpyrrolidone (Oasis HLB) were used as reference. MEPSC8 approach offers an attractive alternative for analysis of flavonols in wines, providing a number of advantages including highest extraction efficiency (from 85.9 ± 0.9% to 92.1 ± 0.5%) in the shortest extraction time with low solvent consumption, fast sample throughput, more environmentally friendly and easy to perform.

A fast method using a new hydrophilic–lipophilic balanced sorbent in combination with ultra-high performance liquid chromatography for quantification of significant bioactive metabolites in wines

This manuscript describes the development and validation of an ultra-fast, efficient, and high throughput analytical method based on ultra-high performance liquid chromatography (UHPLC) equipped with a photodiode array (PDA) detection system, for the simultaneous analysis of fifteen bioactive metabolites: gallic acid, protocatechuic acid, (−)-catechin, gentisic acid, (−)-epicatechin, syringic acid, p-coumaric acid, ferulic acid, m-coumaric acid, rutin, trans-resveratrol, myricetin, quercetin, cinnamic acid and kaempferol, in wines. A 50-mm column packed with 1.7-μm particles operating at elevated pressure (UHPLC strategy) was selected to attain ultra-fast analysis and highly efficient separations. In order to reduce the complexity of wine extract and improve the recovery efficiency, a reverse-phase solid-phase extraction (SPE) procedure using as sorbent a new macroporous copolymer made from a balanced ratio of two monomers, the lipophilic divinylbenzene and the hydrophilic N-vinylpyrrolidone (Oasis™ HLB), was performed prior to UHPLC–PDA analysis. The calibration curves of bioactive metabolites showed good linearity within the established range. Limits of detection (LOD) and quantification (LOQ) ranged from 0.006 μg mL−1 to 0.58 μg mL−1, and from 0.019 μg mL−1 to 1.94 μg mL−1, for gallic and gentisic acids, respectively. The average recoveries ± SD for the three levels of concentration tested (n = 9) in red and white wines were, respectively, 89 ± 3% and 90 ± 2%. The repeatability expressed as relative standard deviation (RSD) was below 10% for all the metabolites assayed. The validated method was then applied to red and white wines from different geographical origins (Azores, Canary and Madeira Islands). The most abundant component in the analysed red wines was (−)-epicatechin followed by (−)-catechin and rutin, whereas in white wines syringic and p-coumaric acids were found the major phenolic metabolites. The method was completely validated, providing a sensitive analysis for bioactive phenolic metabolites detection and showing satisfactory data for all the parameters tested. Moreover, was revealed as an ultra-fast approach allowing the separation of the fifteen bioactive metabolites investigated with high resolution power within 5 min.

Determination of lipophilic and hydrophilic antioxidants in Solanum Lycopersicum L. tomato from Gordal variety by LL-USAE combined with UHPLC-PDA/FLR

Tomato (Lycopersicon esculentum L.) is one of the main constituents of the Mediterranean diet. Its consumption has been proposed to reduce the risk of cardiovascular diseases and certain types of cancer. It is therefore one of the most popular and extensively consumed vegetable crop worldwide. To gain insights on the potential of Lycopersicon esculentum L. as bioactive food, two analytical methodologies were developed to determine the levels of the lipophilic -tocopherol, α-tocopherol, β-carotene, lycopene; and hydrophilic antioxidants ascorbic acid. The quantification of total carotenoids (β-carotene and lycopene) was assessed through a liquid–liquid ultrasound assisted extraction (LL-USAE) in combination with ultraviolet-visible spectroscopy (UV-Vis), according to method of mean, for total carotenoids (λmáx = 450 nm. The ultra-high performance liquid chromatographic using both photodiode array and fluorescence detection (UHPLC-PDA/FLR), allows the identification and quantification of the target lipophilic and hydrophilic antioxidants. This methodology UHPLC-PDA/FLR is fast, simple and revealed a high sensitivity for the compounds under study. The limits of detection (LODs) and quantification (LOQs) obtained were much lower (about 10 times) than the reported in literature. The method LL-USAE/UV-Vis was validated and applied to different tomato foodstuffs. The results reveal a small increase of carotenoids content during maturation, reaching the maximum level when ripe. These results complement those obtained by the ORAC and TBARS assays that show an increase of antioxidant capacity during maturation. The LODs ans LOQs obtained were also about 10 times lower than reported in literature. The carotenoid content was also evaluated by LL-USAE/UV-Vis in different tomatoes varieties. Regional variety present the high carotenoid level, followed by campari and gordal, and at last grape. This methodology was also applied to different processed food samples containing tomatoes derivatives. Highest carotenoids content were obtained in concentrated tomato foodstuffs.