A family of algebraically closed fields containing the polynomials in several variables

We introduce a family of fields of series with support in strongly convex rational cones. All these fields contain the polynomials in several variables. We prove that they are algebraically closed with a construction that is analogous to the Newton polygon for algebraic curves. As a corollary we show the existence of fractional power solutions with support in cones for systems of equation

Addition-deletion results for the minimal degree of a Jacobian syzygy of a union of two curves

Let $C:f=0$ be a reduced curve in the complex projective plane. The minimal degree $mdr(f)$ of a Jacobian syzygy for $f$, which is the same as the minimal degree of a derivation killing $f$, is an important invariant of the curve $C$, for instance it can be used to determined whether $C$ is free or nearly free. In this note we study the relations of this invariant $mdr(f)$ with a decomposition of $C$ as a union of two curves $C_1$ and $C_2$, without common irreducible components. When all the singularities that occur are quasihomogeneous, a result by Schenck, Terao and Yoshinaga yields finer information on this invariant in this setting. Using this, we give some geometrical criteria, the first ones of this type in the existing literature as far as we know, for a line to be a jumping line for the rank 2 vector bundle of logarithmic vector fields along a reduced curve $C$.Comment: v4. Proposition 5.5 modified, one reference updated, the rest unchange

LEFSCHETZ PROPERTIES OF JACOBIAN ALGEBRAS AND JACOBIAN MODULES

Let V :f=0 be a hypersurface of degreed≥3 in the complex projective space P^n,n≥3,having only isolated singularities.Let M(f) be the associatedJ Jacobian algebra and H:ℓ=0 be a hyperplane in P^n avoiding the singularities of V, but such that V∩H is singular.We related the Lefschetz type properties of the linear maps ℓ:M(f)_k→M(f)_k+1induced by the multiplication by linearf orm ℓ to the singularities of the hyperplane section V∩H.Similar results are obtained for the Jacobian module N(f)

Objective Knowledge Mediates the Relationship between the Use of Social Media and COVID-19-Related False Memories

The exposure to relevant social and/or historical events can increase the generation of false memories (FMs). The Coronavirus Disease 2019 (COVID-19) pandemic is a calamity challenging health, political, and journalistic bodies, with media generating confusion that has facilitated the spread of fake news. In this respect, our study aims at investigating the relationships between memories (true memories, TMs vs. FMs) for COVID-19-related news and different individual variables (i.e., use of traditional and social media, COVID-19 perceived and objective knowledge, fear of the disease, depression and anxiety symptoms, reasoning skills, and coping mechanisms). One hundred and seventy-one university students (131 females) were surveyed. Overall, our results suggested that depression and anxiety symptoms, reasoning skills, and coping mechanisms did not affect the formation of FMs. Conversely, the fear of loved ones contracting the infection was found to be negatively associated with FMs. This finding might be due to an empathy/prosociality-based positive bias boosting memory abilities, also explained by the young age of participants. Furthermore, objective knowledge (i) predicted an increase in TMs and decrease in FMs and (ii) significantly mediated the relationships between the use of social media and development of both TMs and FMs. In particular, higher levels of objective knowledge strengthened the formation of TMs and decreased the development of FMs following use of social media. These results may lead to reconsidering the idea of social media as the main source of fake news. This claim is further supported by either the lack of substantial differences between the use of traditional and social media among participants reporting FMs or the positive association between use of social media and levels of objective knowledge. The knowledge about the topic rather than the type of source would make a difference in the process of memory formation

Fatty acids as biomarkers of the production season of caciocavallo palermitano cheese

This experiment aims to evaluate the potential of fatty acids (FA) of Caciocavallo Palermitano cheese as biomarkers of production season and pasture-based diet. A total of 48 cheeses were made in the four seasons with milk from two farms that raised cows of Cinisara breed. The animals were fed on pasture with supplementation of wheat bran and wheat straw in the barn, and in summer also with Opuntia ficus-indica cladodes. The chemical composition and FA profile of cheese were influenced by the season and not by the farm. In particular, cheeses produced in spring were characterized by higher protein and lower fat, and showed higher contents in trans-vaccenic acid, α-linolenic acid, rumenic acid, n-3 polyunsaturated FA (PUFA), and total PUFA. In winter, the lower availability of grazing forage, requiring a higher level of feeding integration, was responsible for an increase of saturated FA (SFA). The multivariate analysis distinguished clearly the cheeses made in winter and spring, while those produced in autumn and summer showed some overlapping points. Further investigations should be carried out to evaluate the effects of type and level of feeding integration on the presence of FA more suitable to be used as biomarkers of period and diet

Dianthus borbonicus (Caryophyllaceae), a new species from Sicily

Dianthus borbonicus a new species occurring in North-Western Sicily is described and illustrated. It is a rare chasmophyte belonging to the D. sylvestris group, which is exclusive of a rupestrian stand near Rocca Busambra (Ficuzza). Its macro- and micromorphological features (seed testa sculptures, and leaf anatomy), ecology, conservation status and a comparison with the related species are provided too

The Rationale for the Intra-Articular Administration of Clodronate in Osteoarthritis

Background: Several pharmacological therapeutic approaches have been proposed to manage osteoarthritis (OA), including intra-articular (IA) injections. Although the discovery of clodronate, a bisphosphonate, dates back to the 1960s and the effects of its IA administration have been investigated for decades in animal models, mechanisms of action of this drug are not quite clear, particularly in OA. This scoping review is an overview of the biological as well as the clinical role of clodronic acid in OA. Method: A scoping review based on the PRISMA-ScR (Preferred Reporting Items for Systematic Reviews and Meta-Analyses Extension for Scoping Reviews) model was performed to characterize the mechanisms of action of IA clodronate in OA and to evaluate its efficacy from a clinical point of view. Results: Several effects of clodronate have been observed in animal models of OA, including depletion of synovial lining cells that results in reduced production of chemokines (IL-1, TNF- α), growth factors (TGF-β, BMP 2/4), and metalloproteases (MMP 2/3/9); prevention of cartilage damage, synovial hyperplasia, and proteoglycans loss; reduction in joint inflammation, joint swelling, and osteophyte formation. From a clinical perspective, patients with knee OA treated with IA clodronate experienced improvements in pain and joint mobility. Conclusion: Clodronate appears to have different mechanisms of action interfering with the pathogenic processes contributing to OA development and progression. This intervention demonstrated positive effects for patients affected by knee OA