Enforcing Local Non-Zero Constraints in PDEs and Applications to Hybrid Imaging Problems

We study the boundary control of solutions of the Helmholtz and Maxwell equations to enforce local non-zero constraints. These constraints may represent the local absence of nodal or critical points, or that certain functionals depending on the solutions of the PDE do not vanish locally inside the domain. Suitable boundary conditions are classically determined by using complex geometric optics solutions. This work focuses on an alternative approach to this issue based on the use of multiple frequencies. Simple boundary conditions and a finite number of frequencies are explicitly constructed independently of the coefficients of the PDE so that the corresponding solutions satisfy the required constraints. This theory finds applications in several hybrid imaging modalities: some examples are discussed.     

Coordination properties of the multifunctional S,N,S zwitterionic ligand EtNHC(S)Ph2PNPPh2C(S)NEt

The reaction of trialkylphoshanes and amino-phosphanes with isothiocyanates yields adducts containing the zwitterionic thioamidyl-phosphonium P⁺C(S)N^? functional group. Ligands containing this group were not previously studied, probably due to their instability towards dissociation, in the presence of metal species able to coordinate the P atom. The ligand EtNHC(S)Ph₂PNPPh₂C(S)NEt (HEtSNS) was obtained by reaction of Ph₂PNHPPh₂ with ethylisothiocyanate and proved to be very versatile: it can be protonated giving cation H₂EtSNS⁺ and deprotonated forming the dianion–cation EtSNS^?. HEtSNS and its derivatives behave as ligands showing five possible coordination fashions, S,N,S tridentate and S,S-bidentate (with a bite-angle varying from 180° to 90°), S-monodentate, S,S bridging and N,N,N interaction. Here we describe the coordination chemistry of HEtSNS, in particular towards Rh, Cu, Ag and Au, and some properties of its complexes which are still the only examples containing the P⁺C(S)N^? zwitterionic group.     

Well-defined transition metal complexes with phosphorus and nitrogen ligands for 1,3-dienes polymerization

This article provides an overview on recent progress in the polymerization of 1,3-dienes catalyzed by transition metal complexes with phosphorus and nitrogen ligands. Polymers having different microstructures (cis-1,4; 1,2; mixed cis-1,4/1,2) and tacticity (iso- or syndiotactic) were obtained from various 1,3-dienes (1,3-butadiene, isoprene, 1,3-pentadienes, 1,3-hexadienes) depending on the catalyst used, clearly suggesting that the catalyst structure (i.e. metal nature, type of ligand) strongly affects the polymerization chemo- and stereoselectivity. However, as indicated by the results obtained in the polymerization of substituted butadienes, a fundamental role in determining the selectivity is also played by the type of monomer: polymers with different structure, some of them completely new, were obtained from different monomers with the same catalyst. All these observations permitted to confirm, and in some cases to improve, the knowledge on the diene polymerization mechanism.     

Strategies for improving the water solubility of new antitumour nitronaphthylbutadiene derivatives

Different nitronaphthylbutadienes have been previously proved to have antitumour activity. The main drawback of these derivatives is their low water solubility. With the aim of facilitating the administration of these new drugs we have synthesized the hexyl (2Z,4E)-2-methylsulfanyl-5-(1-naphthyl)-4-nitro-2,4-pentadienoate analogue (1-Naph-NHCB) which is demonstrated to be easily included into cyclodextrins and/or entrapped into liposomes. Its antitumour activity was revealed to be almost comparable with that of the previously studied methyl analogue ester (1-Naph-NMCB). On the other hand, in vitro studies with different cancer cell lines showed that the cytotoxic activity of both 1-Naph-NMCB and 1-Naph-NHCB were fully preserved and in some cases also enhanced when entrapped into liposomal carriers.     

Expanding stereochemical and skeletal diversity using petasis reactions and 1,3-dipolar cycloadditions

A short and modular synthetic pathway using intramolecular 1,3-dipolar cycloaddition reactions and yielding functionalized isoxazoles, isoxazolines, and isoxazolidines is described. The change in shape of previous compounds and those in this study is quantified and compared using principal moment-of-inertia shape analysis.     

fMRI study of motor cortex activity modulation in early Parkinson's disease

Parkinson's disease is a neurological disorder associated with the disfunction of dopaminergic pathways of the basal ganglia, mainly resulting in a progressive alteration in the execution of voluntary movements. We present a functional magnetic resonance imaging (fMRI) study on cortical activations during simple motor task performance, in six early–stage hemiparkinsonian patients and seven healthy volunteers. We acquired data in three sessions, during which subjects performed the task with right or left hand, or bimanually. We observed consistent bilateral activations in cingulate cortex and dorsolateral prefrontal cortex of Parkinsonian subjects during the execution of the task with the affected hand. In addition, patients showed both larger and stronger activations in motor cortex of the affected hemisphere with respect to the healthy hemisphere. Compared with the control group, patients showed a hyperactivation of the dorsolateral prefrontal cortex of the affected hemisphere. We concluded that a presymptomatic reorganization of the motor system is likely to occur in Parkinson's disease at earlier stages than previously hypothesized. Moreover, our results support fMRI as a sensitive technique for revealing the initial involvement of motor cortex areas at the debut of this degenerative disorder.     

Time-like minimal submanifolds as singular limits of nonlinear wave equations

We consider the sharp interface limit ?→0⁺ of the semilinear wave equation in R¹⁺ⁿ, where takes values in R^k, k=1,2, and W is a double-well potential if k=1 and vanishes on the unit circle and is positive elsewhere if k=2. For fixed ?>0 we find some special solutions, constructed around minimal surfaces in Rⁿ. In the general case, under some additional assumptions, we show that the solutions converge to a Radon measure supported on a time-like k-codimensional minimal submanifold of the Minkowski space-time. This result holds also after the appearance of singularities, and enforces the observation made by J. Neu that this semilinear equation can be regarded as an approximation of the Born-Infeld equation.     

Preparation and Flame Retardancy Properties of Novel PA12 and PE/Layered Titanoniobates Nanocomposites

Summary: We report herein a study performed on a layered titanoniobate KTiNbO₅ modified by octadecylamine to evaluate the fire retardancy properties of this novel hybrid nanofiller dispersed in PA12 and LLDPE, by polymer melt intercalation. The nanocomposites have been characterized using Electron Microscopy techniques to evaluate the degree of exfoliation and the morphologies. Thermogravimetric analyses and cone calorimeter tests have been carried out to assess the fire retardant performances.     

Hypergraph decomposition and secret sharing

A secret sharing scheme is a protocol by which a dealer distributes a secret among a set of participants in such a way that only qualified sets of them can reconstruct the value of the secret whereas any non-qualified subset of participants obtain no information at all about the value of the secret. Secret sharing schemes have always played a very important role for cryptographic applications and in the construction of higher level cryptographic primitives and protocols.In this paper we investigate the construction of efficient secret sharing schemes by using a technique called hypergraph decomposition, extending in a non-trivial way the previously studied graph decomposition techniques. A major advantage of hypergraph decomposition is that it applies to any access structure, rather than only structures representable as graphs. As a consequence, the application of this technique allows us to obtain secret sharing schemes for several classes of access structures (such as hyperpaths, hypercycles, hyperstars and acyclic hypergraphs) with improved efficiency over previous results. Specifically, for these access structures, we present secret sharing schemes that achieve optimal information rate. Moreover, with respect to the average information rate, our schemes improve on previously known ones.In the course of the formulation of the hypergraph decomposition technique, we also obtain an elementary characterization of the ideal access structures among the hyperstars, which is of independent interest.