The exact distribution of extremes of a non-gaussian process

The exact distribution of extremes of a non-gaussian stationary discrete process is obtained and their crossing intervals are studied in terms of the autocorrelation coefficients for any level of crossing. This process is an important model for some physical magnitudes.     

Absence of Cooper-type bound states in three- and few-electron systems

It is shown that the appearance of a fixed-point singularity in the kernel of the two-electron Cooper problem is responsible for the formation of the Cooper pair for an arbitrarily weak attractive interaction between two electrons. This singularity is absent in the problem of three and few superconducting electrons at zero temperature on the full Fermi sea. Consequently, such three- and few-electron systems on the full Fermi sea do not form Cooper-type bound states for an arbitrarily weak attractive pair interaction. Received: 9 February 1998 / Revised and Accepted: 13 May 1998     

On removable singularities of locally solvable differential operators

We study removable sets of solutions of locally solvable partial differential operators with smooth coefficients and characterize them in terms of capacity in the sense of Harvey and Polking. For operators of order one we are able to give a geometric characterization of removable sets in terms of orbits in the sense of Sussmann. Oblatum 2-IX-1995 & 14-V-1996     

Optimization of the separation of flavonoids using solvent-modified micellar electrokinetic chromatography

In this work the separation of eighteen flavonoids was attempted using reduced-flow micellar elektrokinetic chromatography (RF-MEKC) electrolytes modified by selected solvents with differing properties: methanol (MeOH), acetonitrile (ACN) and tetrahydrofuran (THF). Structural aspects such as unsaturation of the C ring, number and position of OH groups, methylation and glycosylation as well as solvent effects and their impact on the electrophoretic behavior of flavonoids were addressed. By evaluating the electropherograms obtained from mixture-designed electrolytes and searching for changes in the critical pairs, a favorable separation condition was achieved using 20 mmol/L phosphate buffer at pH 2.5 containing 50 mmol/L sodium dodecyl sulfate (SDS), 15% ACN and 5% THF (one critical pair) in less than 12 min with 1.5% coefficient of variation (CV) for retention factor and 3% CV for peak area (n = 5). The applicability of the proposed separation condition was demonstrated by the inspection of flavonoids in herbal extracts of Neem.     

Proton radioactivity: The case for <Superscript>53m</Superscript>Co proton-emitter isomer

The partial proton emission half-life for ^53mCo unstable isomer is re-examined in the framework of a semiempirical model based on tunneling through a Coulomb-plus-centrifugal-plus-overlapping potential barrier within the spherical nucleus approximation. It is shown that the known measured half-life value of 17s is compatible with a large prolate shape for ^53mCo proton emitter and a high angular momentum ℓ = 11 assigned to the proton transition to the ground state of ⁵²Fe .     

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.