When is a Cleft Extension H-Azumaya?

We show which H ^op -cleft extensions of k for a dual quasi-triangular Hopf algebra (H, r) are H-Azumaya. The result is given in terms of bijectivity of a map defined in terms of the universal r-form r and the 2-cocycle σ, generalizing a well-known result for the commutative and co-commutative case. We illustrate the Theorem with an explicit computation for the Hopf algebras of type E(n).Presented by A. Verschoren     

Turing vegetation patterns in a generalized hyperbolic Klausmeier model

The formation of Turing vegetation patterns in flat arid environments is investigated in the framework of a generalized version of the hyperbolic Klausmeier model. The extensions here considered involve, on the one hand, the strength of the rate at which rainfall water enters into the soil and, on the other hand, the functional dependence of the inertial times on vegetation biomass and soil water. The study aims at elucidating how the inclusion of these generalized quantities affects the onset of bifurcation of supercritical Turing patterns as well as the transient dynamics observed from an uniformly vegetated state towards a patterned state. To achieve these goals, linear and multiple-scales weakly nonlinear stability analysis are addressed, this latter being inspected in both large and small spatial domains. Analytical results are then corroborated by numerical simulations, which also serve to describe more deeply the spatio-temporal evolution of the emerging patterns as well as to characterize the different timescales involved in vegetation dynamics.     

Laplace equations,Lefschetz properties and line arrangements

In this note we extend the main result in [6] on artinian ideals failing Lefschetz properties, varieties satisfying Laplace equations and existence of suitable singular hypersurfaces. Moreover we characterize the minimal generation of ideals generated by powers of linear forms by the configuration of their dual points in the projective plane and we use this result to improve some propositions on line arrangements and Strong Lefschetz Property at range 2 in [6]. The starting point was an example in [3]. Finally we show the equivalence among failing SLP, Laplace equations and some unexpected curves introduced in [3].     

Minimizing nonsmooth DC functions via successive DC piecewise-affine approximations

We introduce a proximal bundle method for the numerical minimization of a nonsmooth difference-of-convex (DC) function. Exploiting some classic ideas coming from cutting-plane approaches for the convex case, we iteratively build two separate piecewise-affine approximations of the component functions, grouping the corresponding information in two separate bundles. In the bundle of the first component, only information related to points close to the current iterate are maintained, while the second bundle only refers to a global model of the corresponding component function. We combine the two convex piecewise-affine approximations, and generate a DC piecewise-affine model, which can also be seen as the pointwise maximum of several concave piecewise-affine functions. Such a nonconvex model is locally approximated by means of an auxiliary quadratic program, whose solution is used to certify approximate criticality or to generate a descent search-direction, along with a predicted reduction, that is next explored in a line-search setting. To improve the approximation properties at points that are far from the current iterate a supplementary quadratic program is also introduced to generate an alternative more promising search-direction. We discuss the main convergence issues of the line-search based proximal bundle method, and provide computational results on a set of academic benchmark test problems.     

Positive solutions for some non-autonomous Schrödinger-Poisson systems

In this paper we study the Schrödinger-Poisson system

(SP)     

Wave features of a hyperbolic prey–predator model

A hyperbolic predator–prey model is proposed within the context of extended thermodynamics. The nature of the steady state solutions for the uniform and non‐uniform perturbations are analyzed. The existence of smooth traveling wave‐like solutions, related to the invasion of the predator population into a prey‐only state is discussed. Validation of the model in point is also accomplished by searching for numerical solutions of the system, which also points out limit cycles in the populations. Copyright © 2010 John Wiley & Sons, Ltd.     

Electrosprayed Shrimp and Mushroom Nanochitins on Cellulose Tissue for Skin Contact Application

Cosmetics has recently focused on biobased skin-compatible materials. Materials from natural sources can be used to produce more sustainable skin contact products with enhanced bioactivity. Surface functionalization using natural-based nano/microparticles is thus a subject of study, aimed at better understanding the skin compatibility of many biopolymers also deriving from biowaste. This research investigated electrospray as a method for surface modification of cellulose tissues with chitin nanofibrils (CNs) using two different sources—namely, vegetable (i.e., from fungi), and animal (from crustaceans)—and different solvent systems to obtain a biobased and skin-compatible product. The surface of cellulose tissues was uniformly decorated with electrosprayed CNs. Biological analysis revealed that all treated samples were suitable for skin applications since human dermal keratinocytes (i.e., HaCaT cells) successfully adhered to the processed tissues and were viable after being in contact with released substances in culture media. These results indicate that the use of solvents did not affect the final cytocompatibility due to their effective evaporation during the electrospray process. Such treatments did not also affect the characteristics of cellulose; in addition, they showed promising anti-inflammatory and indirect antimicrobial activity toward dermal keratinocytes in vitro. Specifically, cellulosic substrates decorated with nanochitins from shrimp showed strong immunomodulatory activity by first upregulating then downregulating the pro-inflammatory cytokines, whereas nanochitins from mushrooms displayed an overall anti-inflammatory activity via a slight decrement of the pro-inflammatory cytokines and increment of the anti-inflammatory marker. Electrospray could represent a green method for surface modification of sustainable and biofunctional skincare products.     

Mott-insulator States of ultracold atoms in optical resonators

We study the low temperature physics of an ultracold atomic gas in the potential formed inside a pumped optical resonator. Here, the height of the cavity potential, and hence the quantum state of the gas, depends not only on the pump parameters, but also on the atomic density through a dynamical ac-Stark shift of the cavity resonance. We derive the Bose-Hubbard model in one dimension and use the strong coupling expansion to determine the parameter regime in which the system is in the Mott-insulator state. We predict the existence of overlapping, competing Mott-insulator states, and bistable behavior in the vicinity of the shifted cavity resonance, controlled by the pump parameters. Outside these parameter regions, the state of the system is in most cases superfluid.     

Antimicrobial Effect and Cytotoxic Evaluation of Mg-Doped Hydroxyapatite Functionalized with Au-Nano Rods

Hydroxyapatite (HA) is the main inorganic mineral that constitutes bone matrix and represents the most used biomaterial for bone regeneration. Over the years, it has been demonstrated that HA exhibits good biocompatibility, osteoconductivity, and osteoinductivity both in vitro and in vivo, and can be prepared by synthetic and natural sources via easy fabrication strategies. However, its low antibacterial property and its fragile nature restricts its usage for bone graft applications. In this study we functionalized a MgHA scaffold with gold nanorods (AuNRs) and evaluated its antibacterial effect against S. aureus and E. coli in both suspension and adhesion and its cytotoxicity over time (1 to 24 days). Results show that the AuNRs nano-functionalization improves the antibacterial activity with 100% bacterial reduction after 24 h. The toxicity study, however, indicates a 4.38-fold cell number decrease at 24 days. Although further optimization on nano-functionalization process are needed for cytotoxicity, these data indicated that Au-NRs nano-functionalization is a very promising method for improving the antibacterial properties of HA.