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Cantor’s ternary function is generalized to arbitrary base-change functions in non-integer bases. They turn out to have radically different continuity, differentiability and monotonicity properties, depending on the particular bases involved in their definition.

Spiramycin, a widely used veterinary macrolide antibiotic, was found at traceable levels (nanograms per litre range) in Po River water (N-Italy). The aqueous environmental fate of this antibiotic compound was studied through drug decomposition, the identification of the main and secondary transformation products (TPs), assessment of mineralisation and the investigation of drug TPs toxicity. Initially, laboratory experiments were performed, with the aim of stimulating the antibacterial transformation processes followed in aquatic systems. The TPs were identified through the employment of the liquid chromatography (LC)-mass spectrometry technique. Under illumination, spiramycin degraded rapidly and transformed into numerous organic (intermediate) compounds, of which 11 could be identified, formed through five initial transformation routes. These laboratory simulation experiments were verified in situ to check the mechanism previously supposed. Po River water was sampled and analysed (by LC-high-resolution mass spectrometry) at eight sampling points. Among the previously identified TPs, five of them were also found in the river water. Three of them seem to be formed through a direct photolysis process, while the other two are formed through indirect photolysis processes mediated by natural photo sensitisers. The transformation occurring in the aquatic system involved hydroxylation, demethylation and the detachment of forosamine or mycarose sugars. Toxicity assays using Vibrio fischeri proved that even if spiramycin did not exhibit toxicity, its transformation proceeded through the formation of toxic products.

We will deal with the following problem: Let M be an n × n matrix with real entries. Under which conditions the family of inequalities:{\bf x}\in {\open {R}}^n; {\bf x} \ge {\bf 0};{\bf M}\cdot{\bf x}\ge {\bf 0}has non–trivial solutions? We will prove that a sufficient condition is given bym_{i,j}+m_{j,i}\ge0\quad(1\le i,j\le n);from this result we will derive an elementary proof of the existence theorem for Variational Inequalities in the framework of Monotone Operators.

Completing a series of works begun by Wiener [34], Paley and Wiener [28] and Ingham [9], a far-reaching generalization of Parseval"s identity was obtained by Beurling [4] for nonharmonic Fourier series whose exponents satisfy a uniform gap condition. Later this gap condition was weakened by Ullrich [33], Castro and Zuazua [5], Jaffard, Tucsnak and Zuazua [11] and then in [2] in some particular cases. In this paper we prove a general theorem which contains all previous results. Furthermore, applying a different method, we prove a variant of this theorem for nonharmonic Fourier series with vector coefficients. This result, partly motivated by control-theoretical applications, extends several earlier results obtained in [15] and [2]. Finally, applying these results we obtain an optimal simultaneous observability theorem concerning a system of vibrating strings.

Reversed-phase high performance liquid chromatography with diode array detection was used to analyze phenolic compounds contained in bark extracts of two different poplar clones known to have different resistance toDiscosporium populeum infection. Statistical treatments both monovariate and multivariate were applied to the results in order to identify regularities useful to discriminate the polar resistance and to check the importance of seasonal and cultivation site related factors. For the two clones examined phenolic compounds showed great discrimination ability not influenced by either sample collection period or cultivation site.

Capillary SFC with supercritical CO2 as mobile phase and flame ionization detection was adopted to separate and determine triacylglycerols in vegetable and fish oils. The effect on separation of many experimental variables has been checked along with the selectivity of several stationary phases of different polarity. A standard mixture of 13 triacylglycerols was used to optimize the procedure and their retention times were used as reference to identify peaks in real samples. In spite of the fact that many peaks remained unidentified, the chromatograms obtained were useful as fingerprint analyses of the real samples examined.

The RP-HPLC technique has been applied to the analysis of the flavonoid content of leaf extracts from various genotypes ofPopulus nigra andPopulus deltoides and from several of their hybrids. Two elution procedures different either as regards gradient program or the type of organic modifier used were checked to optimize the reliability of the results obtained. Before making any identification, the chromatographic profiles proved so typical of each species as to allow of their use as fingerprints in this type of taxonomic problem. Individual identifications were carried out by spiking real samples with known amounts of standard substances. The presence of flavonoid compounds previously identified was confirmed and a few new identifications were proposed.

A reversed-phase HPLC method for resolution of phenoic compounds is presented. A new derivatization reaction has been developed employing diazotized 4-amino-benzonitrile, which reacts also with parasubstituted phenols. The products of the reaction can be extracted in n-butanol, allowing preconcentration and clean-up steps; the extracts are very stable and show strong absorption in the visible, where many interferences are avoided. The possibility of resolution of complex mixtures is discussed with reference to the use of reversed-phase columns using octadecyl- and phenyl bonded silica.

The kinetics and mechanism of oxidation of a series of alcohols, namely cyclohexanol, cyclopentanol, pentan-2-ol and benzyl alcohol, by silver(II) perchlorate in perchloric acid solution. have been investigated by the stopped-flow technique. These oxidations proceed through two parallel pathways involving Ag2+ and AgOH+ species. In the case of benzyl alcohol, the hydroxo species, which has been found to be almost universally reactive toward different organic substrates, is inactive; this behaviour has been interpreted in terms of interaction of the oxidant with the aromatic moiety in the alcohol. The reactivities are discussed in terms of substrate reaction sites with reference to electronic availability and reaction products.

A new method of studying unconfined flow through porous media has been illustrated. This method is based on the use of variational inequalities which allows us to obtain uniqueness and existence theormes.

Un problema di frontiera libera (moto di un fluido attraverso una diga in terra non omogenea) e ricondotto allo studio di una disequazione variazionale. Si danno condizioni sul coefficiente di permeabilita sufficienti ad assicurare che la parte bagnata della diga e un sottografico.

Gradient elution RP-HPLC has been applied to the separation of the constituents of synthetic tanning agents. Information obtained from the chromatographic results was used to assess the possibility of optimizing the conditions of synthesis, to find out the number of species formed and to make a start at correlating the composition of the tanning agents and their properties.

A general chromatographic model has been set up starting from a set of equations based on the concept of the velocity of a solute along the column. The composition of the mobile phase is taken into account solely as a numerical factor entering into suitable equations and totally independent of the chemical-properties of the constituents. A few isocratic experimental runs are necessary as input data, and subsequently a small amount of computational effort is sufficient to make predictions of retention times under gradient elution conditions for solutes of whatever chemical structure. The prediction errors are dependent on the steepness of the linear gradient chosen but are, in any case, acceptably low.

FeIII reacts with mercaptocarboxylic acids (HORSH), such as 2-mercaptoethanoic acid, 2-mercaptopropanoic acid, 2-mercapto-1,4-butanedioic acid and penicillamine (2-amino3-methyl-3-mercaptobutanoic acid) to give, in perchloric acid medium, 1∶1 complexes, Fe3++HORSH⇄Fe(OSR)++ 2H+. These complexes then undergo redox decomposition to give a disulphide dimer: 2Fe(OSR)++2H+⇄2Fe2++ HOR-S- S- ROH. The present study reports equilibrium data on the stability of the intermediate complexes, and kinetic data for the fast complex formation, as well as for the slower redox decomposition.

We study the approximation of linear parabolic problems by means of Galerkin approximation in space and θ-method in time. The error is evaluated in norms of typeHtδ (H1x) ⋂Htδ+1/2 (Lx2) for |δ|≤1/2. We prove error estimates which are optimal with respect to the regularity assumptions on the right-hand side of the equation.

The chromatographic behaviour of Cu(II), Fe(II), Ni(II) and Co(II) complexes with 4-(2-pyridylazo)resorcinol was studied. The experimental results were very sensitive even to less obvious operational parameters like the kind of the cation (sodium or ammonium) of the phosphate salt used as buffer. The puzzling pattern of the data obtained was interpreted in terms of the equations formulated by Horvath's ‘olvophobic” theory which correlates the capacity factors of the solutes with the surface tension of the mobile phase. A satisfactory rationalization of the data was obtained together with qualitative information on the stoichiometry and charge state of metal complexes. Useful suggestions about the direction to address the experimental work in order to obtain the best results was also obtained.

Si studia l'equivalenza tra una nozione diuniforme stabilita e la nozione diA-stabilita per alcuni schemi di discretizzazione di problemi di evoluzione.

Si stabiliscono condizioni atte ad assicurare la validita della (*) dell’introduzione; e si applica la (*) ad alcune questioni connesse alla trattazione dei problemi ai limiti per le equazioni differenziali alle derivate parziali.

Si studia un’equazione differenziale astratta con dominio variabile. I risultati si applicano in particolare al problema misto, di tipo Cauchymisto, per l’equazione del calore (cfr. le successive (1.1), (1.2), (1.3), (1.4)) relativamente al quale,senza alcuna ipotesi di regolarita sull’ insieme portante il dato di Dirichlet, si da un teorema di esistenza e unicita, in classi funzionali molto ampie per la soluzione e per i dati.

Si studia la regolarita (del tipo diGevrey) per le soluzioni delle equazioni differenziali astratte del tipo (*) e (**) dell'introduzione.

Elliptic free boundary problems in the theory of fluid flow through porous media are studied by a new method, which reduces the problems to variational inequalities: existence and uniqueness theorems are proved.

Si studia il problema di Cauchy per equazioni differenziali lineari astratte in spazi di Hilbert, in una impostazione che permette di trattare contemporaneamente sia le equazioni differenziali astratte usuali, sia quelle con argomenti ritardati, sia le equazioni integro-differenziali.

Si dimostra esistenza e unicita della soluzione di un problema di frontiera libera che traduce il moto di filtrazione di liquidi attraverso mezzi porosi.