On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density

We are concerned with the long time behaviour of solutions to the fractional porous medium equation with a variable spatial density. We prove that if the density decays slowly at infinity, then the solution approaches the Barenblatt-type solution of a proper singular fractional problem. If, on the contrary, the density decays rapidly at infinity, we show that the minimal solution multiplied by a suitable power of the time variable converges to the minimal solution of a certain fractional sublinear elliptic equation.Comment: To appear in DCDS-

On the stability of solutions of semilinear elliptic equations with Robin boundary conditions on Riemannian manifolds

We investigate existence and nonexistence of stationary stable nonconstant solutions, i.e. patterns, of semilinear parabolic problems in bounded domains of Riemannian manifolds satisfying Robin boundary conditions. These problems arise in several models in applications, in particular in Mathematical Biology. We point out the role both of the nonlinearity and of geometric objects such as the Ricci curvature of the manifold, the second fundamental form of the boundary of the domain and its mean curvature. Special attention is devoted to surfaces of revolution and to spherically symmetric manifolds, where we prove refined results

New Insights into Bile Acids Related Signaling Pathways in the Onset of Colorectal Cancer

Colorectal cancer (CRC) ranks as the second among the causes of tumor death worldwide, with an estimation of 1.9 million new cases in 2020 and more than 900,000 deaths. This rate might increase by 60% over the next 10 years. These data are unacceptable considering that CRC could be successfully treated if diagnosed in the early stages. A high-fat diet promotes the hepatic synthesis of bile acids (BAs) increasing their delivery to the colonic lumen and numerous scientific reports correlate BAs, especially secondary BAs, with CRC incidence. We reviewed the physicochemical and biological characteristics of BAs, focusing on the major pathways involved in CRC risk and progression. We specifically pointed out the role of BAs as signaling molecules and the tangled relationships among their nuclear and membrane receptors with the big bang of molecular and cellular events that trigger CRC occurrence

3-O-Benzhydryl-2,5-dide­oxy-2,5-imino-2-C-methyl-l-lyxono-1,4-lactone

The title bicyclic lactone, C19H19NO3, is an inter­mediate in the synthesis of chiral α-methyl­prolines and branched C-methyl pyrrolidines; the absolute configuration was determined by the use of d-erythronolactone as the starting material. It exhibits no unusual crystal packing features, and each mol­ecule acts as a donor and acceptor for one C—H⋯O hydrogen bond

Decapod crustaceans associated with an artificial reef (Adriatic Sea)

The aim of this study is to increase the knowledge on the distribution of decapod crustaceans associated with an artificial reef positioned on sandy-mud bottoms in the central Adriatic Sea. The reef is constituted of concrete modules assembled in pyramids and concrete poles. Hard and soft bottom samples were collected from 2001, just after reef construction, to 2005 (4 surveys per year). Regarding the soft seabed, three sites close to a pyramid, three inside the reef area at a distance of 10-15 m from the structures, and three 200 m outside the reef (control sites) were randomly sampled during each survey. At the same time, three pyramids (vertical and horizontal walls) and three poles were also investigated. After taxonomical analysis, decapod crustaceans were analysed using abundance and species richness. Sites and years were compared using a balanced, fixed effect, 2-way ANOVA and PERMANOVA. In addition, SIMPER analysis was performed to identify those species typifying each community inhabiting both the soft bottom and the artificial substrates. The results showed that the artificial reef induced an increase in both abundance and diversity of the decapods of the natural habitat. In fact, man-made substrates may offer new available space for biological colonization and allow the settlement of new species usually living on hard bottoms, thus increasing the complexity of the original benthic communities