Random Lie-point symmetries of stochastic differential equations

We study the invariance of stochastic differential equations under random diffeomorphisms, and establish the determining equations for random Lie-point symmetries of stochastic differential equations, both in Ito and in Stratonovich form. We also discuss relations with previous results in the literature.Comment: In new version (November 2017) we have added an important ERRATUM. Due to a trivial mistake in a formula, several examples should be revised; more relevant, the qualitatove results of Section VIII turn out to be wrong, as discussed in the erratum. See also arXiv:1711.0199

Principi di spontaneizzazione di Diospyros kaki (Ebenaceae) in Sicilia

A spontaneous group of plants of Diospyros kaki is reported in a rural area near Menfi, in the province of Agrigento. This is the first record of naturalization of this Asian species – after long time cultivated in various countries of the Mediterranean Basin - observed in Italy

Influence of Compliant Joints in Four-Legged Robots

Legged animals are capable of rapid movements, are efficient from the energy point of view, and are able to adapt their gaits to environmental conditions. Motions like walking, trotting, galloping, and jumping, are difficult to evaluate and replicate due to their being consequences of complex interactions of different systems (such as the musculoskeletal system and the central and peripheral nervous systems, including also the influence of the environment). In this paper, we analyzed the behavior of a four-legged robot constituted by one active DOF in each leg (using commercial servomotors) and one passive DOF in each knee and in the spine (using springs). Our objective was to increase the motion performances of the robot by varying the stiffness of the springs. The results obtained from the simulation underline how the stiffness of the spine influences the performance of the robot by increasing the speed and reducing the energy required by the servomotors

Quasi-Monotonicity Formulas for Classical Obstacle Problems with Sobolev Coefficients and Applications

We establish Weiss’ and Monneau’s type quasi-monotonicity formulas for quadratic energies having matrix of coefficients in a Sobolev space with summability exponent larger than the space dimension and provide an application to the corresponding free boundary analysis for the related classical obstacle problems

A new species of Smyrnium (Apiaceae) related to S. perfoliatum

On the basis of plant collections recently carried out in Sicily as well as the study of the herbarium material kept in PAL and PAL-Gr, a new species of Smyrnium (Apiaceae) is described here. This new taxon, named Smyrnium dimartinoi, is related to S. perfoliatum and is presently known from Sicily, Crete and realistically elsewhere in the Mediterranean. In such range it occurs in open woods and clearings of the Mediterranean-temperate and submontane belt