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.     

Identification of vivianite,an unusual blue pigment,in a sixteenth century painting and its implications

Vivianite, a blue pigment employed in the past practically only in Northern and Central Europe, but with very limited use, was identified in an early sixteenth century painting, stylistically with Flemish features, from a church in Portugal. The identification of this iron phosphate mineral was made by SEM‐EDS based on the atomic ratio between phosphorus and iron in layers of blue paint (area analysis) and in particles of these same layers (spot analysis). This painting, about which there is no document to prove its authorship, becomes the first case, known in detail, of a sixteenth century painting containing vivianite. Moreover, this find and the presence of a chalk ground, also identified, strongly support the hypothesis of being a Flemish painting.     

Low concentration short time ozonation of rapeseed seeds reduces the stability of the oil and content of some antioxidant components

Ozonation is an innovative way to preserve high quality of seed during storage and it is an alternative to harmful organophosphorus agents. Disclosure of changes in the rapeseed oil under the influence of oxidative action of ozone on the seeds was the aim of the work and is presented for the first time. Two ozone concentrations and different length of ozonation were applied. The changes in tocopherols, phenolics, flavonoids contents, antiradical activity and oxidative stability were examined. The average vitamin E concentration was 33 mg per 100 g of oil before and 31.7 after ozonation of seeds. The average content of phenolic compounds was 14.3 mg of sinapic acid g⁻¹ and 16.9 after the ozone treatment. Changes in the flavonoids content and antioxidant activity were observed too. Ozonation caused a decrease in the vitamin E concentration which resulted also in reducing the quenching of free radicals and reduction of oil induction time.