Sulla formula risolutiva di un particolare problema della magneto-idrodinamica

ANNALI DELL'UNIVERSITA' DI FERRARA - Si presenta sotto una forma adatta all’interpretazione fisica la formula risolutiva di un problema trattato in un lavoro precedente e riguardante...     

Definition of a nucleophilicity scale

This work deals with exploring some empirical scales of nucleophilicity. We have started evaluating the experimental indices of nucleophilicity proposed by Legon and Millen on the basis of the measure of the force constants derived from vibrational frequencies using a probe dipole H-X (X = F,CN). The correlation among some theoretical parameters with this experimental scale has been evaluated. The theoretical parameters have been chosen as the minimum of the electrostatic potential V(min), the binding energy (BE) between the nucleophile and the H-X dipole, and the electrostatic potential measured at the position of the hydrogen atom V(H) when the complex nucleophile and dipole H-X is in the equilibrium geometry. All of them present good correlations with the experimental nucleophilicity scale. In addition, the BEs of the nucleophiles with two other Lewis acids (one hard, BF(3), and the other soft, BH(3)) have been evaluated. The results suggest that the Legon and Millen nucleophilicity scale and the electrostatic potential derived scales can describe in good approximation the reactivity order of the nucleophiles only when the interactions with a probe electrophile is of the hard-hard type. For a covalent interaction that is orbital controlled, a new nucleophilicity index using information of the frontier orbitals of both, the nucleophile and the electrophile has been proposed.     

EDXRF and multivariate statistical analysis of fragments from Marajoara ceramics

In this work, 102 fragments of Marajoara ceramics, belonging to the National Museum collection (Rio de Janeiro, Brazil), were analyzed using energy dispersive X‐ray fluorescence (EDXRF) and principal component analysis (PCA) in order to identify possible groups of samples that present similar behaviors or different characteristics. This information will give an important aid to a more accurate classification of these artifacts. The EDXRF measurements were carried out with a portable system developed in the Nuclear Instrumentation Laboratory consisting of an Oxford TF3005 X‐ray tube, with W anode, and an Si‐PIN XR‐100CR detector from Amptek, working at 25 kV and 100 µA, acquisition time of 600 s and a beam collimation of 2 mm. PCA applied to the X‐ray fluorescence results revealed a clear cluster separation to the samples. Copyright © 2009 John Wiley & Sons, Ltd.     

Singular rational curves with points of nearly-maximal weight

In this article we study rational curves with a unique unibranch genus-g singularity, which is of κ-hyperelliptic type in the sense of [27]; we focus on the cases $\kappa =0$ and $\kappa =1$, in which the semigroup associated to the singularity is of (sub)maximal weight. We obtain a partial classification of these curves according to the linear series they support, the scrolls on which they lie, and their gonality.     

Choreographies in the <Emphasis Type="Italic">n</Emphasis>-vortex Problem

We consider the equations of motion of n vortices of equal circulation in the plane, in a disk and on a sphere. The vortices form a polygonal equilibrium in a rotating frame of reference. We use numerical continuation in a boundary value setting to determine the Lyapunov families of periodic orbits that arise from the polygonal relative equilibrium. When the frequency of a Lyapunov orbit and the frequency of the rotating frame have a rational relationship, the orbit is also periodic in the inertial frame. A dense set of Lyapunov orbits, with frequencies satisfying a Diophantine equation, corresponds to choreographies of n vortices. We include numerical results for all cases, for various values of n, and we provide key details on the computational approach.     

Enhancement of two-photon absorption cross-section and singlet-oxygen generation in porphyrins upon beta-functionalization with donor-acceptor substituents

The microwave-enhanced synthesis, comparative singlet oxygen sensitization efficiency, and nonlinear optical characterization of a new beta-functionalized porphyrin and its copper complex are described. We show that the introduction of a donor-acceptor push-pull conjugated fragment in the beta position strongly perturbs the porphyrin electronic structure leading to a remarkable one- and two-photon NIR absorption enhancement.     

Iteration-complexity of first-order penalty methods for convex programming

This paper considers a special but broad class of convex programming problems whose feasible region is a simple compact convex set intersected with the inverse image of a closed convex cone under an affine transformation. It studies the computational complexity of quadratic penalty based methods for solving the above class of problems. An iteration of these methods, which is simply an iteration of Nesterov’s optimal method (or one of its variants) for approximately solving a smooth penalization subproblem, consists of one or two projections onto the simple convex set. Iteration-complexity bounds expressed in terms of the latter type of iterations are derived for two quadratic penalty based variants, namely: one which applies the quadratic penalty method directly to the original problem and another one which applies the latter method to a perturbation of the original problem obtained by adding a small quadratic term to its objective function.     

Characterizing unusual metal substrates for gap‐mode tip‐enhanced Raman spectroscopy

In this article, the electromagnetic (EM) field in gap‐mode tip‐enhanced Raman spectroscopy (TERS) is investigated theoretically and experimentally for a range of commonly used and unusual metal and nonmetal substrates. By approaching a metal tip to a substrate, both form a coupled system that confines the EM field created at the tip apex. The influence of the substrate onto the EM field enhancement is observed in a top‐illumination gap‐mode TERS setup for different metal substrates. These include Au, the most commonly used substrate, and also a wide range of rarely or previously unused TERS substrates (Cu, Ag, Al, Pd, Pt, Ni, Ti, Mo, W, stainless steel, Al₂O₃, SiO₂). Self‐assembled monolayers of thiols and brilliant cresyl blue thin film samples are investigated experimentally on nine metal substrates, all showing considerable TERS enhancement. With finite difference time domain and finite element simulations used, the article provides a good estimate of the EM field enhancement for a wide range of substrates for users to estimate how well a substrate of choice will perform in a gap‐mode TERS experiment. The reduction in EM field strength |E²| compared with Au is less than an order of magnitude for many metals (Calculations: Cu 92%, Ag 81%, Ni 53%). This article experimentally shows that a wide variety of conductive substrates can be used, when one is willing to trade a fraction of the EM field enhancement. TERS was seen on all metal substrates including stainless steel, yet quantification was not always possible. These qualitative results were complemented with intensities from calculations. The wider variety of substrates will increase the applicability of TERS and evolve it one step further towards use in standard analytics. Copyright © 2012 John Wiley & Sons, Ltd.