A new class of estimators of a “scale” second order parameter

For a large class of heavy-tailed distribution functions F in the domain of attraction for maxima of an Extreme Value distribution with tail index γ>0, the function A(t), controlling the speed of convergence of maximum values, linearly normalized, towards a non-degenerate limiting random variable, may be parameterized as , ρ < 0, β∈ℝ, where β and ρ are second order parameters. The estimation of ρ, the “shape” second order parameter has been extensively addressed in the literature, but practically nothing has been done related to the estimation of the “scale” second order parameter β. In this paper, and motivated by the importance of a reliable β-estimation in recent reduced bias tail index estimators, we shall deal with such a topic. Under a semi-parametric framework, we introduce a class of β-estimators and study their consistency. We deal with the conditions enabling us to get the asymptotic normality of the members of this class, and we illustrate the behaviour of the estimators, through Monte Carlo simulation techniques. Research partially supported by FCT / POCTI and POCI / FEDER.     

Semiclassical structure of chaotic resonance eigenfunctions

We study the resonance (or Gamow) eigenstates of open chaotic systems in the semiclassical limit, distinguishing between left and right eigenstates of the nonunitary quantum propagator and also between short-lived and long-lived states. The long-lived left (right) eigenstates are shown to concentrate as variant Planck's over 2pi-->0 on the forward (backward) trapped set of the classical dynamics. The limit of a sequence of eigenstates [psi(variant Planck's over)] 2pi-->0 is found to exhibit a remarkably rich structure in phase space that depends on the corresponding limiting decay rate. These results are illustrated for the open baker's map, for which the probability density in position space is observed to have self-similarity properties.     

Effect of salt identity on the phase diagram for a globular protein in aqueous electrolyte solution

Monte Carlo simulations are used to establish the potential of mean force between two globular proteins in an aqueous electrolyte solution. This potential includes nonelectrostatic contributions arising from dispersion forces first, between the globular proteins, and second, between ions in solution and between each ion and the globular protein. These latter contributions are missing from standard models. The potential of mean force, obtained from simulation, is fitted to an analytic equation. Using our analytic potential of mean force and Barker-Henderson perturbation theory, we obtain phase diagrams for lysozyme solutions that include stable and metastable fluid-fluid and solid-fluid phases when the electrolyte is 0.2 M NaSCN or NaI or NaCl. The nature of the electrolyte has a significant effect on the phase diagram.     

Oxygen clamps in gold nanowires

We investigate how the insertion of an oxygen atom in an atomically thin gold nanowire can affect its rupture. We find, using ab initio total energy density functional theory calculations, that O atoms when inserted in gold nanowires form not only stable but also very strong bonds, in such a way that they can extract atoms from a stable tip, serving in this way as a clamp that could be used to pull a string of gold atoms.     

Chromotropic acid-functionalized polyurethane foam: A new sorbent for on-line preconcentration and determination of cobalt and nickel in lettuce samples

A chromotropic acid-functionalized polyurethane foam has been developed for use in an on-line preconcentration system for cobalt and nickel determination. The packing material was prepared by covalent coupling of chromotropic acid with the polyurethane foam through an azo group. Co and Ni ions were sorbed in the mini-column, from which they could be eluted directly to the nebulizer-burner system of a flame atomic absorption spectrometer. Elution of cobalt and nickel from the mini-column can be accomplished with 0.50 and 0.75 M HCl solutions, respectively. The enrichment factors obtained were 22 (Co) and 27 (Ni), for 60 s preconcentration time, and 57 (Co) and 59 (Ni), if a preconcentration time of 180 s was used. Under the optimum conditions, the proposed procedure allowed the determination of metals with detection limits of 0.43 (cobalt) and 0.52 microg/L (nickel), respectively, on using preconcentration periods of 180 s. The accuracy of the developed procedure was evaluated by analysis of the certified reference materials NIST 1515 Apple Leaves and NIST 1570a Spinach Leaves. The method was applied to the analysis of lettuce samples. The contents of cobalt in the samples analyzed varied from 0.75 to 0.98 microg/g. Nickel was not detected in the lettuce samples.     

Four-Boson Systems Close to a Universal Regime

Universal properties of weakly-bound four-boson systems near the scaling limit are discussed by considering recent results obtained from the solution of Faddeev-Yakubovsky (FY) equations, which confirm a previous conjecture on a four-body scale dependence. In the present contribution, within a discussion on our numerical results obtained for the binding energies of two consecutive tetramer states, we are analyzing the relative relevance of the two possible configurations of the four-body system.     

Scales, Universality and Finite-Range Correction in Three-body Systems

The scale invariance manifested by the weakly-bound Efimov states implies that all the Efimov spectrum can be merged in a single scaling function. By considering this scaling function, the ratio between two consecutive energy levels, ${E_3^{\rm (N+1)}}$ and ${E_3^{\rm (N)}}$ , can be obtained from a two-body low-energy observable (usually the scattering length a), given in units of the three-body energy level N. The zero-ranged scaling function is improved by incorporating finite range corrections in first order of r ₀/a (r ₀ is the potential effective range). The critical condition for three-identical bosons in s-wave, when the excited ${E_3^{\rm (N+1)}}$ state disappears in the 2 + 1 threshold, is given by ${\sqrt{E_2/E_3^{\rm (N)}} \approx 0.38+0.12 ({r_0}/{a})}$ .