Abstract approach to non homogeneous Harnack inequality in doubling quasi metric spaces

We develop an abstract theory to obtain Harnack inequality for non homogeneous PDEs in the setting of quasi metric spaces. The main idea is to adapt the notion of double ball and critical density property given by Di Fazio, Guti\'errez, Lanconelli, taking into account the right hand side of the equation. Then we apply the abstract procedure to the case of subelliptic equations in non divergence form involving Grushin vector fields and to the case of X-elliptic operators in divergence form

Nonsmooth viscosity solutions of elementary symmetric functions of the complex Hessian

In this paper we prove the existence of nonsmooth viscosity solutions for Dirichlet problems involving elementary symmetric functions of the eigenvalues of the complex Hessian

Polysaccharide-based self-assembling nanohydrogels: An overview on 25-years research on pullulan

The aim of this overview is to review the evolution of the studies carried out, during more than 25 years, on nanohydrogels obtained by self-assembling of pullulan (PUL) using several hydrophobization strategies. After the first publications, mainly devoted to the preparation and characterization of PUL nanogels, a remarkable number of studies demonstrated how wide can be the field of applications within the main topic of biopharmaceutics. Numerous hydrophilic and lipophilic drugs were entrapped in the nanogel networks, consequently PUL nanogels have been proposed as delivery systems for single drugs and for combination therapies which allowed improvements of pharmacological activities and patient compliance. Furthermore, the large amount of water content allowed loading also proteins which could maintain their native structure and properties. Stimuli-sensitive and stealth PUL nanogel formulations allowed improving the performances of antitumor drugs. These nanohydrogels have also been studied for imaging techniques and for vaccines to be administered by injection and by mucosal application. The studies on PUL nanogels are still in progress and the perspectives for future researches are also addressed

The disappearance of cultural landscapes: the case of wooded-meadows in the Ligurian Apennines (NW Italy)

The \u201cwooded-meadows system\u201d is a multifunctional use of vegetation resources widespread in Europe since the Neolithic, and well documented in the Ligurian Apennines (NW Italy) between the Middle Ages and the first half of the 19th century. The management of wooded-meadows included: collection of fallen and dead branches in spring, later used for fuel; mowing and grazing in summer; collection of secondary products; making sheaves from branches in autumn, later used as cattle and sheep fodder; coppicing, pollarding and cutting of trees in winter. Three sites located in eastern Ligurian Apennines were studied by means of an interdisciplinary approach in order to better understand the impact and the consequences of this historical landuse practice on vegetation structure and composition. In particular, based on specific features of palynological diagrams, it was possible to conclude that (compared to the post-cultural phase) \u2013 when the wooded-meadows system was in use all the sites were characterized by: (1) lower pollen percentages of trees; (2) higher pollen percentages of shrubs and herbs; (3) higher percentages of anthropogenic pollen indicators; (4) higher values of palynological richness. This research also represents a contribution to issues of nature-conservation policy for the preservation of cultural landscapes

Dynamic Stresses of Lactic Acid Bacteria Associated to Fermentation Processes

Despite their negligible mass the microbial agents, starters and non starters, play a profound role in the characterization of the fermented foods in terms of chemical and sensorial properties. In fact, fermented foods may be defined as foods processed through the activity of microorganisms. Fermentation processes take a special place in the evolution of human cuisine, by altering the taste experience of food products, as well as extending the storage period. In particular, foods fermented with lactic acid bacteria (LAB) have constituted an important part of human diet and of fermentation processes (involving various foods, including milk, meat, vegetables and fruits) since ancient times. They have played an essential role in the preservation of agricultural resources and in the improvement of nutritional and organoleptic properties of human foods and animal feed. Moreover, these organisms nowadays are increasingly used as health promoting probiotics, enzyme and metabolite factories and vaccine delivery vehicles

Entropic long range order in a 3D spin glass model

We uncover a new kind of entropic long range order in finite dimensional spin glasses. We study the link-diluted version of the Edwards-Anderson spin glass model with bimodal couplings (J=+/-1) on a 3D lattice. By using exact reduction algorithms, we prove that there exists a region of the phase diagram (at zero temperature and link density low enough), where spins are long range correlated, even if the ground states energy stiffness is null. In other words, in this region twisting the boundary conditions cost no energy, but spins are long range correlated by means of pure entropic effects.Comment: 15 pages, 6 figures. v3: added a phase diagram for ferromagnetically biased coupling

Numerical determination of the exponents controlling the relationship between time, length and temperature in glass-forming liquids

There is a certain consensus that the very fast growth of the relaxation time $\tau$ occurring in glass-forming liquids on lowering the temperature must be due to the thermally activated rearrangement of correlated regions of growing size. Even though measuring the size of these regions has defied scientists for a while, there is indeed recent evidence of a growing correlation length $\xi$ in glass-formers. If we use Arrhenius law and make the mild assumption that the free-energy barrier to rearrangement scales as some power $\psi$ of the size of the correlated regions, we obtain a relationship between time and length, $T\log\tau \sim \xi^\psi$. According to both the Adam-Gibbs and the Random First Order theory the correlation length grows as $\xi \sim (T-T_k)^{-1/(d-\theta)}$, even though the two theories disagree on the value of $\theta$. Therefore, the super-Arrhenius growth of the relaxation time with the temperature is regulated by the two exponents $\psi$ and $\theta$ through the relationship $T\log\tau \sim (T-T_k)^{-\psi/(d-\theta)}$. Despite a few theoretical speculations, up to now there has been no experimental determination of these two exponents. Here we measure them numerically in a model glass-former, finding $\psi=1$ and $\theta=2$. Surprisingly, even though the values we found disagree with most previous theoretical suggestions, they give back the well-known VFT law for the relaxation time, $T\log\tau \sim (T-T_k)^{-1}$.Comment: 9 pages, 8 figure