On the spin- 1/2 Aharonov–Bohm problem in conical space: Bound states,scattering and helicity nonconservation

In this work the bound state and scattering problems for a spin- 1/2 particle undergone to an Aharonov–Bohm potential in a conical space in the nonrelativistic limit are considered. The presence of a δ$\delta$-function singularity, which comes from the Zeeman spin interaction with the magnetic flux tube, is addressed by the self-adjoint extension method. One of the advantages of the present approach is the determination of the self-adjoint extension parameter in terms of physics of the problem. Expressions for the energy bound states, phase-shift and S$S$ matrix are determined in terms of the self-adjoint extension parameter, which is explicitly determined in terms of the parameters of the problem. The relation between the bound state and zero modes and the failure of helicity conservation in the scattering problem and its relation with the gyromagnetic ratio g$g$ are discussed. Also, as an application, we consider the spin- 1/2 Aharonov–Bohm problem in conical space plus a two-dimensional isotropic harmonic oscillator.     

Correlation of Electron Beams and Hard X‐ray Emissions in ISTTOK Tokamak

The paper reports on experimental studies of electron beams in the ISTTOK tokamak, those were performed by means of an improved four‐channel detector. The Cherenkov‐type detector measuring head was equipped with four radiators made of two types of alumina‐nitrate (AlN) poly‐crystals: machinable and translucent ones, both of 10 mm in diameter and 2.5 mm in thickness. The movable support that enabled the whole detectors to be placed inside the tokamak vacuum chamber, at chosen positions along the ISTTOK minor radius. Since the electron energy distribution is one of the most important characteristics of tokamak plasmas, the main aim of the study was to perform estimations of an energy spectrum of the recorded electrons. For this purpose the radiators were coated with molybdenum (Mo) layers of different thickness. The technique based on the use of Cherenkov‐type detectors enabled the detection of fast electrons (of energy above 66 keV) and determination of their spatial and temporal characteristics in the ISTTOK experiment. Measurements of hard X‐rays (HXR), which were emitted during ISTTOK discharges, have also been performed. Particular attention was paid to the correlation measurements of HXR pulses with run‐away electron beams. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sample Preparation for the Determination of Metals in Food Samples Using Spectroanalytical Methods—A Review

Abstract

The present article gives an overview of recent publications and modern techniques of sample preparation for food analysis employing atomic and inorganic mass spectrometric techniques, such as flame atomic absorption spectrometry, chemical vapor generation atomic absorption and atomic fluorescence spectrometry, graphite furnace atomic absorption spectrometry, inductively coupled plasma optical emission spectrometry, and inductively coupled plasma mass spectrometry. Among the most frequently applied sample preparation techniques for food analysis are dry ashing, usually with the addition of an ashing aid, and acid digestion, preferably with the assistance of microwave energy. Slurry preparation, particularly with the assistance of ultrasound, is increasingly used to reduce acid consumption and sample preparation time. Direct analysis of solid samples is gaining importance in the field of food analysis as it offers the highest sensitivity, avoids the use of acids and other aggressive reagents, makes possible the analysis of micro‐samples, and can be applied for fast screening analysis, e.g., of fresh meat.     

Theory of the liquid-vapour interface of a binary mixture of Lennard-Jones fluids

We present results of calculations of the equilibrium surface tension and density profiles for the liquid-vapour interface of a binary mixture of Lennard-Jones 12-6 fluids. The calculations are based on a density-functional theory for the Helmholtz free energy of the inhomogeneous mixture. This is a ‘microscopic’ generalization of the van der Waals-Cahn-Hilliard theory for the interface of a binary mixture.

Our calculations cover the full range of liquid-vapour coexistence and the whole range of concentration. We find a correlation between the excess surface tension of the mixture and the surface segregation (adsorption) of the species with the lower surface tension. The ways in which segregation and excess surface tension depend on the Lennard-Jones parameters of the pure components are briefly discussed. Our results for the excess surface tension of mixtures of Ar and N₂ and Ar and CH₄ are compared with experiment; the agreement is reasonable.     

Mathematics in chemistry: indeterminate forms and their meaning

The mathematical language and its tools are complementary to the formalism in chemistry, in particular at an advanced level. It is thus crucial, for its understanding, that students acquire a solid knowledge in Calculus and that they know how to apply it. The frequent occurrence of indeterminate forms in multiple areas, particularly in Physical Chemistry, justifies the need to properly understand the limiting process in such cases. This article emphasizes the importance of the L’Hôpital's rule as a practical tool, although often neglected, to obtain the more common indeterminate limits, through the use of some specific examples as the radioactive decay, spectrophotometric error, Planck's radiation law, second-order kinetics, or consecutive reactions.     

An Inexact Steepest Descent Method for Multicriteria Optimization on Riemannian Manifolds

In this paper, we present an inexact version of the steepest descent method with Armijo’s rule for multicriteria optimization in the Riemannian context given in Bento et al. (J. Optim. Theory Appl., 154: 88–107, 2012). Under mild assumptions on the multicriteria function, we prove that each accumulation point (if any) satisfies first-order necessary conditions for Pareto optimality. Moreover, assuming that the multicriteria function is quasi-convex and the Riemannian manifold has nonnegative curvature, we show full convergence of any sequence generated by the method to a Pareto critical point.     

ℤ2-Codimensions of the Grassmann Algebra

Let E be the infinite-dimensional Grassmann algebra over a field F of characteristic zero, and consider L the F-vector space spanned by all generators of E. Let ? _l be any fixed automorphism of E of order 2 such that L is an homogeneous subspace.

Our goal is to finish the computation of the sequences of ? _l -codimensions, by finding its exact value for the unique open case, that is, when the subspace of L corresponding to the eigenvalue 1 is finite-dimensional. As a consequence we get the ?-codimensions for a large amount of arbitrary automorphisms ? of E of order 2.