Flat 3-webs of degree one on the projective plane

The aim of this work is to study global $3$-webs with vanishing curvature. We wish to investigate degree $3$ foliations for which their dual web is flat. The main ingredient is the Legendre transform, which is an avatar of classical projective duality in the realm of differential equations. We find a characterization of degree $3$ foliations whose Legendre transform are webs with zero curvature.Comment: 14 page

On the density of second order differential equations without algebraic solutions on P2

We prove that a generic second order diferential equation in the projective plane has no algebraic solutions when the bidegree is big enough. We also prove an analogous result for webs on P2

Sensory profile, shelf life, and dynamics of bioactive compounds during cold storage of 17 edible flowers

In this study, 17 edible flowers (Allium ursinum L., Borago officinalis L., Calendula officinalis L., Centaurea cyanus L., Cichorium intybus L., Dianthus carthusianorum L., Lavandula angustifolia Mill., Leucanthemum vulgare (Vaill.) Lam., Paeonia officinalis L., Primula veris L., Robinia pseudoacacia L., Rosa canina L., Rosa pendulina L., Salvia pratensis L., Sambucus nigra L., Taraxacum officinale Weber, and Tropaeolum majus L.) were investigated to assess their sensory profile at harvest and their shelf life and bioactive compounds dynamics during cold storage. The emerging market of edible flowers lacks this information; thus, the characteristics and requirements of different flower species were provided. In detail, a quantitative descriptive analysis was performed by trained panelists at flower harvest, evaluating 10 sensory descriptors (intensity of sweet, sour, bitter, salt, smell, specific flower aroma, and herbaceous aroma; spiciness, chewiness, and astringency). Flower visual quality, biologically active compounds content (total polyphenols and anthocyanins), and antioxidant activity (FRAP, DPPH, and ABTS assays) were evaluated both at harvest and during storage at 4 °C for 14 days to assess their shelf life. Generally, species had a wide range of peculiar sensory and phytochemical characteristics at harvest, as well as shelf life and bioactive compounds dynamics during postharvest. A strong aroma was indicated for A. ursinum, D. carthusianorum, L. angustifolia, and L. vulgare, while B. officinalis and C. officinalis had very low values for all aroma and taste descriptors, resulting in poor sensory profiles. At harvest, P. officinalis, R. canina, and R. pendulina exhibited the highest values of polyphenols (884–1271 mg of gallic acid equivalents per 100 g) and antioxidant activity (204–274 mmol Fe2+/kg for FRAP, 132–232 and 43–58 µmol of Trolox equivalent per g for DPPH and ABTS). The species with the longest shelf life in terms of acceptable visual quality was R. pendulina (14 days), followed by R. canina (10 days). All the other species lasted seven days, except for C. intybus and T. officinale that did not reach day 3. During cold storage, the content of bioactive compounds differed, as total phenolics followed a different trend according to the species and anthocyanins remained almost unaltered for 14 days. Considering antioxidant activity, ABTS values were the least variable, varying in only four species (A. ursinum, D. carthusianorum, L. angustifolia, and P. officinalis), while both DPPH and FRAP values varied in eight species. Taken together, the knowledge of sensory profiles, phytochemical characteristics and shelf life can provide information to select suitable species for the emerging edible flower market

Mechanisms of Moral Disengagement in the Transition from Cybergossip to Cyberaggression: A Longitudinal Study

The internet is an area where young people establish relationships and develop socially, emotionally and morally, but it also gives rise to certain forms of online behaviour, such as cybergossip, which are associated with cyberaggression and other risky behaviour. The aims of this study were to verify whether a longitudinal association exists between cybergossip and cyberaggression, and to discover which mechanisms of moral disengagement may mediate this relationship. The final sample consisted of 1392 students (50% girls; Mage = 13.47; SD = 0.77), who were surveyed in a three-wave longitudinal study at six-month intervals. The results obtained confirmed a direct, positive relationship between cybergossip, subsequent cyberaggression and the mediation exerted by cognitive restructuring in this transition. We discuss the importance of recognizing and detecting the fine distinction between online gossip and cyberaggression with the intention of doing harm, and focus on the justifications used by young people to normalize online bullying. To sum up, there is a clear need to encourage ethical, responsible behaviour in online interactions in order to achieve well-balanced, more sustainable relationships in classrooms