Sul teorema di unicità nella dinamica dei fluidi

Sunto Si dimostra, per le equazioni del moto dei fluidi, un teorema di unicità valido in domini illimitati, senza supporre condizioni di convergenza all’infinito per la velocità. Ad Antonio Signorini nel suo 70^mo compleanno.     

Single-particle resonances in a deformed relativistic potential

The positive-parity single-neutron levels in an axially-deformed relativistic quadrupole Woods-Saxon potential are analyzed. Neutron states are obtained as the solutions of the corresponding single-particle Dirac equation, using the coupled-channels method in the coordinate space. The evolution of the levels close to the continuum threshold and, in particular, the occurrence of singleneutron resonant states as the functions of the axial deformation parameter 0 β 0.5, are examined using the eigenphase representation. Calculations are performed for different values of the radius of the potential (R/r 0 ) 3 , corresponding to a variation of the mass number A.     

The Geometric Dual of a–Maximisation for Toric Sasaki–Einstein Manifolds

We show that the Reeb vector, and hence in particular the volume, of a Sasaki–Einstein metric on the base of a toric Calabi–Yau cone of complex dimension n may be computed by minimising a function Z on which depends only on the toric data that defines the singularity. In this way one can extract certain geometric information for a toric Sasaki–Einstein manifold without finding the metric explicitly. For complex dimension n = 3 the Reeb vector and the volume correspond to the R–symmetry and the a central charge of the AdS/CFT dual superconformal field theory, respectively. We therefore interpret this extremal problem as the geometric dual of a–maximisation. We illustrate our results with some examples, including the Y ^p,q singularities and the complex cone over the second del Pezzo surface.     

Kinetic and equilibrium studies on the polyazamacrocycle neotetren: metal-complex formation and DNA interaction

The macrocyclic polyamine 2,5,8,11,14-pentaaza[15]-[15](2,9)[1,10]phenanthrolinophane (neotetren) is studied in its ability to coordinate Cu(ii) even at very low pH values and to interact, as a metal complex, with DNA. The kinetics and equilibria for 1 : 1 and 2 : 1 metal-ligand complexes formation are studied by the stopped-flow method and UV spectrophotometry. Differently protonated complexes are formed, with rate constants much lower than that of water exchange at copper(II) and other Cu(II)/amine systems, this behaviour being ascribed to ring effects and intra-molecular hydrogen bonds. Concerning the DNA/copper(II)-neotetren complexes interaction, analysis of data suggests an intercalative mode of binding. The kinetic results for both DNA/CuL and DNA/Cu(2)L systems agree with the sequence D + S <-->D,S <-->DS where the metal complexes (D) react with the DNA sites (S) leading to fast formation of an externally bound form (D,S) which is converted into an intercalated complex (DS). A very slow process is also detected and ascribed to a conformational change in the polynucleotide secondary structure where the metal centre plays a crucial role. Chromatographic experiments demonstrate that both the investigated Cu(II)/L complexes are able to cleave DNA, but only in the presence of hydrogen peroxide.     

Clustering of financial time series

This paper addresses the topic of classifying financial time series in a fuzzy framework proposing two fuzzy clustering models both based on GARCH models. In general clustering of financial time series, due to their peculiar features, needs the definition of suitable distance measures. At this aim, the first fuzzy clustering model exploits the autoregressive representation of GARCH models and employs, in the framework of a partitioning around medoids algorithm, the classical autoregressive metric. The second fuzzy clustering model, also based on partitioning around medoids algorithm, uses the Caiado distance, a Mahalanobis-like distance, based on estimated GARCH parameters and covariances that takes into account the information about the volatility structure of time series. In order to illustrate the merits of the proposed fuzzy approaches an application to the problem of classifying 29 time series of Euro exchange rates against international currencies is presented and discussed, also comparing the fuzzy models with their crisp version.     

Molecularly Imprinted Polymers Combined with Electrochemical Sensors for Food Contaminants Analysis

Detection of relevant contaminants using screening approaches is a key issue to ensure food safety and respect for the regulatory limits established. Electrochemical sensors present several advantages such as rapidity; ease of use; possibility of on-site analysis and low cost. The lack of selectivity for electrochemical sensors working in complex samples as food may be overcome by coupling them with molecularly imprinted polymers (MIPs). MIPs are synthetic materials that mimic biological receptors and are produced by the polymerization of functional monomers in presence of a target analyte. This paper critically reviews and discusses the recent progress in MIP-based electrochemical sensors for food safety. A brief introduction on MIPs and electrochemical sensors is given; followed by a discussion of the recent achievements for various MIPs-based electrochemical sensors for food contaminants analysis. Both electropolymerization and chemical synthesis of MIP-based electrochemical sensing are discussed as well as the relevant applications of MIPs used in sample preparation and then coupled to electrochemical analysis. Future perspectives and challenges have been eventually given.     

Point interactions for 3D sub-Laplacians

In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point $q_0\in M$ exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on $C_0^{\infty }(M?\{q_0\})$ is essentially self-adjoint in $L^2(M)$. A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on $C_0^{\infty }(N?\{q_0\})$ is never essentially self-adjoint in $L^2(N)$, if $\dim ?N\le 3$. We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass.