Uniform bounds on growth in o-minimal structures

We prove that a function definable with parameters in an o-minimal structure is bounded away from infinity as its argument goes to infinity by a function definable without parameters, and that this new function can be chosen independently of the parameters in the original function. This generalizes a result in a paper of Friedman and Miller. Moreover, this remains true if the argument is taken to approach any element of the structure (or plus/minus infinity), and the function has limit any element of the structure (or plus/minus infinity).Comment: 3 pages. To appear in Mathematical Logic Quarterl

Studies on the Biosynthesis of γ–Decalactone in Sporobolomyces odorus

Incubation of racemic ethyl [2,2-2H2]-(E)-3,4-epoxydecanoate and the corresponding acid with intact cells of Sporobolomyces odorus led to the formation of deuterium labeled γ-decalaetone. The detection of labeled 2-decen-4-olide and 4-oxodecanoic acid made it possi­ble to propose the biogenetic sequence leading to γ-decalactone. The determination of the en­ antiomeric ratio of the lactone revealed an unspecific metabolism of the precursor. In contrast to the (E)-isomer, after administration of ethyl [5,6-2H2]-(Z)-3,4-epoxydeeanoate no transfor­mation could be detected. These results indicate that (E)-3,4-epoxydecanoic acid, formed from (E)-3-decenoyl-CoA , an intermediate of the β-oxidation of linoleic acid, is the genuine precur­sor in the biosynthesis of γ-decalactone

Elementary properties of minimal and maximal points in Zariski spectra

AbstractWe investigate connections between arithmetic properties of rings and topological properties of their prime spectrum. Any property that the prime spectrum of a ring may or may not have, defines the class of rings whose prime spectrum has the given property. We ask whether a class of rings defined in this way is axiomatizable in the model theoretic sense. Answers are provided for a variety of different properties of prime spectra, e.g., normality or complete normality, Hausdorffness of the space of maximal points, compactness of the space of minimal points

On ordinary differentially large fields

We provide a characterisation of differentially large fields in arbitrary characteristic and a single derivation in the spirit of Blum axioms for differentially closed fields. In the case of characteristic zero, we use these axioms to characterise differential largeness in terms of being existentially closed in the differential algebraic Laurent series ring, and we prove that any large field of infinite transcendence can be equipped with a differentially large structure. As an application, we show that there is no real closed and differential field that has a prime model extension in closed ordered differential fields, unless it is itself a closed ordered differential field.Comment: 14 page

Relationships between volatile compounds and sensory characteristics in virgin olive oil by analytical and chemometric approaches

BACKGROUND: The volatile fraction of virgin olive oil is characterised by low molecular weight compounds that vaporise at room temperature. In order to obtain an aroma profile similar to natural olfactory perception, the composition of the volatile compounds was determined by applying dynamic headspace gas chromatography, performed at room temperature, with a cryogenic trap directly connected to a gas chromatograph\u2013mass spectrometer system. Samples were also evaluated according to European Union and International Olive Council official methods for sensory evaluation. In this paper, the composition of the volatile fraction of 25 extra virgin olive oils fromdifferent regions of Italywas analysed and some preliminary considerations on relationships between chemical composition of volatile fraction and sensory characteristics are reported. RESULTS: Forty-two compounds were identified bymeans of the particular analytical technique used. All the analysed samples, classified as extra virgin by the panel test, never present peaks whose magnitude is important enough in defected oils. The study was focused on the evaluation of volatile compounds responsible for the positive impact on olive odour properties (\u2018green\u2013fruity\u2019 and \u2018sweet\u2019) and olfactory perception. CONCLUSION: Chemometric evaluation of data, obtained through headspace analysis and the panel test evaluation, showed a correlation between chemical compounds and sensory properties. On the basis of the results, the positive attributes of virgin olive oil are divided into two separated groups: sweet types or green types. Sixteen volatile compounds with known positive impact on odour properties were extracted and identified. In particular, eight compounds seem correlated with sweet properties whereas the green sensation appears to be correlated with eight other different substances. The content of the compounds at six carbon atoms proves to be very important in defining positive attributes of extra virgin olive oils and sensory evaluation