On flows of H 3/2-vector fields on the circle

In this paper we study the regularity of flow maps of H ^3/2-vector fields on the circle in terms of fractional Sobolev spaces. This problem is motivated by the understanding of the geometry of Bers’s universal Teichmüller space.     

Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations

We investigate quantitative properties of nonnegative solutions \(u(x)\ge 0\) to the semilinear diffusion equation \(\mathcal {L}u= f(u)\), posed in a bounded domain \(\Omega \subset \mathbb {R}^N\) with appropriate homogeneous Dirichlet or outer boundary conditions. The operator \(\mathcal {L}\) may belong to a quite general class of linear operators that include the standard Laplacian, the two most common definitions of the fractional Laplacian \((-\Delta )^s\) (\(0<s<1\)) in a bounded domain with zero Dirichlet conditions, and a number of other nonlocal versions. The nonlinearity f is increasing and looks like a power function \(f(u)\sim u^p\), with \(p\le 1\). The aim of this paper is to show sharp quantitative boundary estimates based on a new iteration process. We also prove that, in the interior, solutions are Hölder continuous and even classical (when the operator allows for it). In addition, we get Hölder continuity up to the boundary. Particularly interesting is the behaviour of solution when the number \(\frac{2s}{1-p}\) goes below the exponent \(\gamma \in (0,1]\) corresponding to the Hölder regularity of the first eigenfunction \(\mathcal {L}\Phi _1=\lambda _1 \Phi _1\). Indeed a change of boundary regularity happens in the different regimes \(\frac{2s}{1-p} \gtreqqless \gamma \), and in particular a logarithmic correction appears in the “critical” case \(\frac{2s}{1-p} = \gamma \). For instance, in the case of the spectral fractional Laplacian, this surprising boundary behaviour appears in the range \(0<s\le (1-p)/2\).     

Spectral theory for commutative algebras of differential operators on Lie groups

The joint spectral theory of a system of pairwise commuting self-adjoint left-invariant differential operators L₁,…,Ln on a connected Lie group G is studied, under the hypothesis that the algebra generated by them contains a “weighted subcoercive operator” of ter Elst and Robinson (1998) [52]. The joint spectrum of L₁,…,Ln in every unitary representation of G is characterized as the set of the eigenvalues corresponding to a particular class of (generalized) joint eigenfunctions of positive type of L₁,…,Ln. Connections with the theory of Gelfand pairs are established in the case L₁,…,Ln generate the algebra of K-invariant left-invariant differential operators on G for some compact subgroup K of Aut(G).     

Deligne��s representation theory in complex rank and objects of integral type

Working with Pierre Deligne??s category of representations of the ??symmetric group S _t with t a complex number?? we give negative answers to certain questions on ${\otimes}$ -categories raised by Bruno Kahn and Charles A. Weibel.     

Boosts in an Arbitrary Direction and Maximal Causal Velocities in a Deformed Minkowski Space

We discuss boosts in a deformed Minkowski space, i.e., a four-dimensional spacetime with metric coefficients depending on nonmetric coordinates (in particular on the energy). The general form of a boost in an arbitrary direction is derived in the case of space anisotropy. Two maximal trivector velocities are mathematically possible, an isotropic and an anisotropic one. However, only the anisotropic velocity has physical meaning, being invariant indeed under deformed boosts.     

Laboratory simulation of inertial and frictional effects on barotropic rotating flows over and past obstacles: Comparison with simple numerical and analytical models

Summary This paper presents the results of laboratory experiments designed to simulate some basic process of large-scale flows interacting with obstacles, also in order to better understand details of subsynoptic disturbances that are created in the lee of large topographic features. For this event, the experimental facilities of the Istituto di Cosmogeofisica of Consiglio Nazionale delle Ricerche (CNR) were exploited, consisting in a hydraulic channel mounted on a rotating platform, along whose longitudinal axis a hemispherical obstacle was towed at various speeds. Because of the conversion of potential vorticity, the experimental results showed, as expected, the existence of a region of anticyclonic circulation, located above the obstacle; however, also an asymmetric pattern of positive vorticity located downwind of the obstacle did appear, which cannot be interpreted in terms of simple quasi-geostrophic inviscid dynamics. This behaviour is not surprising, if one considers that the real flow near the obstacle could hardly ever match the conditions of inviscid quasi-geostrophy (Ro≪1,E∼0), but was similar to that characterising the zone close to the surface of the obstacle, where inertial and viscous effects are not negligible. Finally, in order to investigate the importance of these effects on the interaction processes, simple numerical and analytical models were applied, by which the consistency of some laboratory simulations, chosen among the most significant ones, could be compared.     

Synthese stereoselective DU (±)-β-santalol

We describe here a new convergent and stereoselective synthesis of (±)-β-santalol. This synthesis involves in the last step an original deprotective method of methoxyethoxymethyl ether using pyridinium tosylate.     

Environmental exposure assessment framework for nanoparticles in solid waste

Information related to the potential environmental exposure of engineered nanomaterials (ENMs) in the solid waste management phase is extremely scarce. In this paper, we define nanowaste as separately collected or collectable waste materials which are or contain ENMs, and we present a five-step framework for the systematic assessment of ENM exposure during nanowaste management. The framework includes deriving EOL nanoproducts and evaluating the physicochemical properties of the nanostructure, matrix properties and nanowaste treatment processes as well as transformation processes and environment releases, eventually leading to a final assessment of potential ENM exposure. The proposed framework was applied to three selected nanoproducts: nanosilver polyester textile, nanoTiO₂ sunscreen lotion and carbon nanotube tennis racquets. We found that the potential global environmental exposure of ENMs associated with these three products was an estimated 0.5–143 Mg/year, which can also be characterised qualitatively as medium, medium, low, respectively. Specific challenges remain and should be subject to further research: (1) analytical techniques for the characterisation of nanowaste and its transformation during waste treatment processes, (2) mechanisms for the release of ENMs, (3) the quantification of nanowaste amounts at the regional scale, (4) a definition of acceptable limit values for exposure to ENMs from nanowaste and (5) the reporting of nanowaste generation data.     

Complexes of tetracyclines with divalent metal cations investigated by stationary and femtosecond-pulsed techniques

Spectroscopic techniques both in steady-state (in absorption and emission) and pulsed (absorption of excited states with femtosecond resolution) conditions were used to study the complexation process between six molecules belonging to the tetracycline family and Mg(2+); in the case of TC the study was extended to the metal ions Ca(2+) and Cu(2+). The study was carried out in aqueous solution at various pH values, where one acid-base form of the substrate prevails over the others. The processing of experimental results, performed by means of Singular Value Decomposition and Global Analysis methods, allowed us to evaluate the extent of interaction through the association constants, to identify the number of equilibria present in solution and the stoichiometry (1:1 or 1:2) of the tetracycline:metal ion complex, and to define the spectral and photophysical properties of the latter (in terms of fluorescence quantum yields, lifetimes and rate constants). In fact, the (allowed) radiative decay process is a minor root for the lowest excited state of the complexes which mainly decay to the ground state by internal conversion. Details of the complexation sites are proposed for the various protonated forms of tetracyclines, and for the various cations in the case of TC. In particular, the molecular structure seems to affect significantly the dynamics of interaction when the upper peripheral region of tetracycline is rich in additional hydroxyl groups. Moreover, the state of protonation of the substrate produces changes in the order of the complexation sites, whose affinity for the cation increases significantly when they are negatively charged owing to the loss of protons. Magnesium and calcium (hard cations) give similar interactions, at least in acid solution, while copper(ii) (borderline cation) binds more efficiently on different sites, thus forming complexes with different properties.