Formalization of Ring Theory in PVS

This paper presents a PVS development of relevant results of the theory of rings. The PVS theory includes complete proofs of the three classical isomorphism theorems for rings, and characterizations of principal, prime and maximal ideals. Algebraic concepts and properties are specified and formalized as generally as possible allowing in this manner their application to other algebraic structures. The development provides the required elements to formalize important algebraic theorems. In particular, the paper presents the formalization of the general algebraic-theoretical version of the Chinese remainder theorem (CRT) for the theory of rings, as given in abstract algebra textbooks, proved as a consequence of the first isomorphism theorem. Also, the PVS theory includes a formalization of the number-theoretical version of CRT for the structure of integers, which is the version of CRT found in formalizations. CRT for integers is obtained as a consequence of the general version of CRT for the theory of rings.

     

The influence of sonication time on the biogenic amines formation as a critical point in uncured dry-fermented beef manufacturing

In this study, the influence of sonication time on the biogenic amines formation as a critical point in uncured dry-fermented beef manufacturing was studied. Samples of musculus semimembranosus were sonicated at different times (5 and 10 min) using ultrasound cold bath (4 °C) in acid whey (US 40 kHz and acoustic power 480 W). The effect of sonication on biogenic amine (BA) formation was investigated during 93 days of ripening period. Other parameters (pH value, water activity, microbial counts) that might provide further information on the product under study were also determined. The use of ultrasound during beef marinating in acid whey has a positive effect on retarding histamine (HIS), cadaverine (CAD), tyramine (TYR) and putrescine (PUT) formation. Moreover, the sonication treatment did not inhibit the growth of lactic acid bacteria (LAB) in dry-fermented beef during the whole ripening period. The pathogen bacteria (Staphylococcus aureus, Clostridium sp., Listeria monocytogenes) were not detected in all samples neither after 31 nor after 93 days of ripening period.     

Bioinformatic characterization of the extracellular lipases from Kluyveromyces marxianus

Lipases are hydrolytic enzymes that break the ester bonds of triglycerides, generating free fatty acids and glycerol. Extracellular lipase activity has been reported for the nonconventional yeast Kluyveromyces marxianus, grown in olive oil as a substrate, and the presence of at least eight putative lipases has been detected in its genome. However, to date, there is no experimental evidence on the physiological role of the putative lipases nor their structural and catalytic properties. In this study, a bioinformatic analysis of the genes of the putative lipases from K. marxianus L-2029 was performed, particularly identifying and characterizing the extracellular expected enzymes, due to their biotechnological relevance. The amino acid sequence of 10 putative lipases, obtained by in silico translation, ranged between 389 and 773 amino acids. Two of the analysed putative proteins showed a signal peptide, 25 and 33 amino acids long for KmYJR107Wp and KmLIP3p, and a molecular weight of 44.53 and 58.23 kDa, respectively. The amino acid alignment of KmLIP3p and KmYJR107Wp with the crystallized lipases from a patatin and the YlLip2 lipase from Yarrowia lipolytica, respectively, revealed the presence of the hydrolase characteristic motifs. From the 3D models of putative extracellular K. marxianus L-2029 lipases, the conserved pentapeptide of each was determined, being GTSMG for KmLIP3p and GHSLG for KmYJR107Wp; besides, the genes of these two enzymes (LIP3 and YJR107W) are apparently regulated by oleate response elements. The phylogenetic analysis of all K. marxianus lipases revealed evolutionary affinities with lipases from abH15.03, abH23.01, and abH23.02 families.