Sulla ergodicità delle funzioni di una variabile aleatoria

Riassunto Dato uno spazio di probabilità (Ω.F,m) ed una trasformazioneT di Ω in Ω, si studiano alcune proprietà ergodiche della trasformazione indotta da una variabile aleatoria sul suo codominio. Si dà una condizione necessaria perchè sia ancora ergodica ogni funzione di una variabile aleatoria ergodica assegnata. Si stabilisce una condizione sufficiente per la ergodicità di una variabile aleatoria.

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Résumé Etant donné un espace de probabilité (Ω,F,m) et une applicationT mesurable de Ω dans Ω, on étudie certaines propriétés ergodiques de la application induite par une variable aléatorie sur son image. On donne une condition nécessaire pour que la fonction composée d’une variable aléatoire ergodique soit encore une variable aléatorie ergodique. On établit une condition suffisante pour l’ergodicité d’une variable aléatoire quelconque.

     

The anomalous effective action in three-dimensional gauge theories

Summary We analyse the effective action for gauge fields in odd dimensions, obtained by integrating out the fermions in the Feynman path integral. In particular, we discuss the generation of a Chern-Simons term by massless fermions minimally coupled to an Abelian gauge field. We review two methods of revealing the presence of a Chern-Simons term in the effective action: first, as the consequence of a nontrivial holonomy of the fermionic ground state, then as the result of the generation of an anomalous imaginary part of the effective action. We derive the most general form of the anomalous effective action at the lowest nontrivial order of a derivative expansion in time. We discuss the implications of our analysis for the theory of the fractional quantum Hall effect as well as for the quantization of anomalous theories. To speed up publication, the authors have agreed not to receive proofs which have been supervised by the Scientific Committee.     

Solute-Solvent Interactions in the Nematic and Smectic A Phases of 4 4-di-n-Heptylazoxybenzene Studied by Deuteron NMR

The orientational order parameters have been measured by deuteron N.M.R. of both solute (at low dilution) and solvent in various binary mixtures involving the liquid crystal 4,4'-di-n-heptylazoxybenzene (HAB). The solutes studied were azoxybenzene-d₁₀ and n-heptylbenzene-d₇ which are fragments of HAB, azobenzene-d₁₀ because of its similarity to azoxybenzene, and anthracene-d₁₀ because of its known structure and symmetric shape. The major and biaxial order parameters of the solutes are analysed in terms of a molecular field model for the potential of mean torque for biaxial particles. The behaviour of the solute order parameters on approaching and entering the smectic A phase is interpreted in terms of a temperature and phase dependent partitioning of the solute between aromatic and aliphatic regions of the solvent.     

Development of an analytical method for monitoring worker populations exposed to platinum-group elements

The increasing industrial use of platinum-group elements (PGEs), namely Ir, Pd, Pt and Rh, and related allergies such as rhinitis, conjunctivitis, asthma, urticaria and contact dermatitis, have led to a growing need to monitor selected populations of exposed workers. In this study, the levels of PGEs were measured in indoor airborne particulate matter and in biological samples taken from employees of a plant where car catalytic converters are produced and precious metals are recovered from spent carbon catalysts. The development of an analytical procedure based on quadrupole inductively coupled plasma mass spectrometry (Q-ICP-MS) for the analysis of PGEs in airborne particulate matter and on sector field inductively coupled plasma mass spectrometry (SF-ICP-MS) for the analysis of PGEs in blood, serum, urine and hair is described. For airborne particulate matter deposited on filters, the limits of detection (LoDs) were found to be 0.006 ng m⁻³, 0.020 ng m⁻³, 0.018 ng m⁻³ and 0.006 ng m⁻³ for Ir, Pd, Pt and Rh, respectively. Repeatability of measurements ranged from 1.8 to 8.5%, while recovery was in the range from 92 to 102%. For biological samples LoDs in blood, serum, urine and hair ranged from (in ng l⁻¹) 0.2–0.6 for Ir, 5–10 for Pd, 1–3 for Pt and 2–3 for Rh. For all biological materials, the repeatability varied from 1.1 to 12% for the four elements. Recovery data for the determination of PGEs in biological matrices were found to range from 84.0 to 107.8%. The method was applied to the determination of either total or respirable airborne PGEs collected from five different work areas in the plant. The difference between areas with high and low exposure correlates closely with metal levels in hair, blood and urine. The correlation coefficients between Pt in airborne particulate matter and Pt in biological materials was 0.994, 0.991 and 0.970 for blood, hair and urine, respectively.     

Standardized methods for measuring radionuclides in drinking water

Summary In 2002 the Italian Standardisation Organisation (UNI) - Nuclear Energy Commission (UNICEN) - appointed a working group with the main task of writing a set of standards on drinking water measurements. To date two standards have been designed, namely, for total alpha- and beta-activity, and ²²²Rn. Further procedures are under development for measuring ²²⁶Ra and U isotopes, and gamma-emitting radionuclides in water. The paper gives an overview of these standards, both developed and under study, with special attention to the validation of the methods.     

Determination of Mg, Ti and Cl in Ziegler-Natta catalysts by WDXRF

A method for determination of Mg, Ti and Cl in Ziegler-Natta (ZN) catalysts by wavelength dispersive X-ray fluorescence (WDXRF) spectrometry was developed. For comparative reasons, Ti was determined by spectrophotometry, Mg by complexometry and Cl by argentometric titration. Direct pressing was shown to be unsuitable for sample preparation due to catalyst decomposition. For Ti and Mg measurements, catalyst samples were calcinated at 1000 °C and pressed at 275 MPa. Their determination by the fundamental parameters based on the Ti Ka line measurement was shown to be equivalent to those results obtained by univariate calibration or by the classical methods. Cl was determined by aqueous extraction, followed by deposition on a support. Chloride loss was observed. Fixation of Cl as AgCl on polytetrafluoroethylene (FHLC) millipore membrane afforded the best results. Nevertheless, measurements by WDXRF were shown to be inferior to those obtained by argentometric titration.     

Reaction of Phenanthrene‐9,10‐dione with Phenanthrene‐9,10‐diol: Synthesis and Characterization of the First ortho‐Quinhydrone Derivative

Treatment of phenanthrene‐9,10‐dione (PQ) with phenanthrene‐9,10‐diol (PQH₂), as prepared by catalytic hydrogenation of PQ, in toluene solution or in the solid state afforded crystalline ‘9,10‐phenanthrenequinhydrone’ (PQH), the first example of an ortho‐quinhydrone. PQH was characterized by analytical and spectroscopic methods, including X‐ray and CP/MAS ¹³C‐NMR analyses. The crystal structure of PQH showed pairs of planar molecules linked by H‐bonds and organized in columns parallel to the crystallographic axis a. The solid‐state structure of PQH was compared with those of the parent compounds, PQ and PQH₂, the latter being reported for the first time. PQH was found to be stable in the solid state only, the components PQ and PQH₂ being formed upon dissolution in media of even low polarity such as toluene.     

Continuity of the Visibility Function in the Boundary

The visibility function of a compact set SE ^d assigns to each xS the Lebesgue outer measure of its star in S. This function was introduced by G. Beer in 1972. In 1991, A. Forte Cunto characterized the points of discontinuity of the visibility function in the boundary of a planar Jordan domain. In a recent paper, the present authors extended this characterization to compact subsets of E ^d with certain topological restrictions. These restrictions are removed here and it is proved that the visibility function of a compact subset of E ^d is continuous at a point if and only if the set of restricted visibility of this point has null Lebesgue outer measure. Mathematics Subject Classifications (2000): Primary: 52A35, Secondary: 52A10. Key words: starshaped set, Beer's visibility function, point of restricted visibility.     

Two Sides to One Story—Aroma Chemical and Sensory Signature of Lugana and Verdicchio Wines

Lugana and Verdicchio are two Italian white wines with a Protected Designation of Origin (PDO) label. These two wine types are produced in different regions using the same grape variety. The aim of this work is to investigate the existence of volatile chemical markers that could help to elucidate differences between Lugana and Verdicchio wines both at chemical and sensory levels. Thirteen commercial wine samples were analyzed by Gas Chromatography-Mass Spectrometry (GC-MS), and 76 volatile compounds were identified and quantified. Verdicchio and Lugana had been differentiated on the basis of 19 free and glycosidically bound compounds belonging to the chemical classes of terpenes, benzenoids, higher alcohols, C₆ alcohols and norisoprenoids. Samples were assessed by means of a sorting task sensory analysis, resulting in two clusters formed. These results suggested the existence of 2 product types with specific sensory spaces that can be related, to a good extend, to Verdicchio and Lugana wines. Cluster 1 was composed of six wines, 4 of which were Lugana, while Cluster 2 was formed of 7 wines, 5 of which were Verdicchio. The first cluster was described as “fruity”, and “fresh/minty”, while the second as “fermentative” and “spicy”. An attempt was made to relate analytical and sensory data, the results showed that damascenone and the sum of 3 of esters the ethyl hexanoate, ethyl octanoate and isoamyl acetate, was characterizing Cluster 1. These results highlighted the primary importance of geographical origin to the volatile composition and perceived aroma of Lugana and Verdicchio wines.