Lattice-ordered Abelian groups and Schauder bases of unimodular fans

Baker-Beynon duality theory yields a concrete representation of any finitely generated projective Abelian lattice-ordered group in terms of piecewise linear homogeneous functions with integer coefficients, defined over the support of a fan . A unimodular fan over determines a Schauder basis of : its elements are the minimal positive free generators of the pointwise ordered group of -linear support functions. Conversely, a Schauder basis of determines a unimodular fan over : its maximal cones are the domains of linearity of the elements of . The main purpose of this paper is to give various representation-free characterisations of Schauder bases. The latter, jointly with the De Concini-Procesi starring technique, will be used to give novel characterisations of finitely generated projective Abelian lattice ordered groups. For instance, is finitely generated projective iff it can be presented by a purely lattice-theoretical word.

     

Intramolecular vibrational force fields for linear carbon chains through an adaptative linear scaling scheme

In this work, the vibrational force fields of hydrogen-capped oligoynes of increasing chain lengths are investigated by means of density functional theory calculations. It is shown that the interaction force constants between CC stretching coordinates decrease slowly with the distance between the two bonds considered. The consequence for the frequency dispersion of longitudinal optical (LO) phonons of an infinite polyyne chain is discussed and related to the observed behavior of the spectra of finite-size molecules. Effects of the exchange-correlation functional and of the basis set on the vibrational force constants are also investigated and the need for a scaling procedure is pointed out. Accordingly, new force fields which allow predictions in very good quantitative agreement with the available experimental data for oligoynes have been obtained, providing a sound assignment of alpha and beta lines.     

Pahs and trace elements in PM(2.5) at the Venice Lagoon

The results of an experimental analysis carried out to investigate PM(2.5) concentration levels and the content of polycyclic aromatic hydrocarbons, as well as inorganic trace elements in the atmospheric particles are presented. Measurements were taken with a micrometeorological station equipped with an optical PM(2.5) detector, and simultaneously, particles were collected on filters for subsequent chemical analyses. The average value of daily PM(2.5) concentration is 21.5 ug/m3 and real-time measurements indicate that the average concentration during the day (8 am to 8 pm) is about 25% lower than the nocturnal average. Short-time averages of PM2.5 decrease when the wind speed increases as consequence of the more efficient mixing. Meteorological measurements indicate the presence of a local daily (breeze) circulation with wind blowing from the Alps or the Adriatic Sea and, during this circulation, larger concentrations were observed, with wind coming from the Alps. Days of high PM(2.5) concentration with dominant anthropic or with prevalent crustal contributions were identified. Regarding trace metals, their average concentrations are comparable to those found in others urban areas, except for Cd (3 ng m(-3)), probably due to the presence of glass-works in Murano. The highest concentrations are observed for K (99 ng m(-3)) and Na (73 ng m(-3)), which are the main constituents of marine spray, while the lowest concentrations are observed for elements such as Cs and Co (respectively 0.01 and 0.02 ng m(-3)). Also the concentrations of PAH are comparable with those of other industrial areas, as their sum ranges from 0.16 ng m(-3) to 3.73 ng m(-3), but if considered as B(a)P toxicity equivalent, they are largely lower (0.036 +/- 0.026 ng m(-3)). From the analyses of discriminating ratios, it has been found that the main origin of PAH in PM(2.5) samples may be petrogenic, probably related to the presence of refinery and petrochemical plants on the mainland, although the contribution of combustion processes cannot be excluded.     

Derivatized humic acids modified gold electrode: electrochemical characterization and analytical applications

The preparation and application of a humic acids modified gold electrode (HA-CME) have been described. Derivatization of HAs as β-thioesters caused their partial fragmentation and, thus, a consequent separation by size exclusion chromatography (SEC) was necessary.The CME prepared with functionalized HAs having an average MW of 52000 demonstrated to be effective for trace As(III) determination (LOQ = 0.3 μg L⁻¹). This CME has been characterized both by electrochemical techniques and atomic force microscopy (AFM). The HA-CME provided reliable measurements in natural waters at different salinity with no need of desalting the sample. Total inorganic arsenic could be determined after reduction of As(V) with SO₂. Under these conditions, organic arsenic species were not mineralized and did not interfere.     

Structure, conformation, stereodynamics, dimer formation, and absolute configuration of axially chiral atropisomers of hindered biphenyl carbinols

NMR spectra of biphenyl derivatives bearing a single CR2OH substituent in the ortho position indicate that they exist as sp (more stable) and ap (less stable) conformers, due to the restricted rotation about the Ar-CR2OH bond. When R = Et (compound 2) the corresponding rotation barrier was determined (7.5 kcal mol-1) by line shape simulation of the low-temperature NMR spectra. Introduction of the prochiral i-Pr group in the position 3' of a biphenyl with the CMe2OH substituent in the position 2 (4) allowed the determination of the enantiomerization barrier (due to the Ar-Ar bond rotation) for the stereolabile axially chiral atropisomers (13.95 kcal mol(-1)). DFT computations of these barriers were all in agreement with the experiments. Biphenyls bearing two CR2OH groups in the 2,2' positions were found to exist as configurationally stable atropisomers: when R = Me (7) they were separated by enantioselective HPLC and the absolute configuration assigned on the basis of the corresponding CD spectra. In solution, compounds 6 (R = H) and 7 (R = Me) were found to originate a dimer, due to H-bond interactions between two enantiomers. In the case of 7, the free energy of activation (9.5 kcal mol-1) for the exchange of the monomer with the dimer could be measured, for the first time, by dynamic NMR. The conformational preferences, predicted by computations for the biphenyls with two CR2OH substituents in the 2,2' positions, were confirmed by X-ray diffraction in the case of R = H (6), R = Me (7), and R = i-Pr (9).     

Conformation and stereodynamics of symmetrically ortho-disubstituted aryl carbinols and aryl ethers

By making use of low-temperature dynamic NMR spectroscopy, the rotation barriers about the sp3-sp2 bond have been determined in a number of hindered benzyl alcohols symmetrically substituted in the ortho positions, the substituents being F, Cl, Br, and Me. The free energies of activation covered the range 4.6-10.1 kcal mol-1. Ab initio computations matched satisfactorily the trend of these values and predicted the conformation adopted by these compounds. In one case, this result could be also confirmed by the X-ray diffraction structure. In the case of the corresponding methyl ethers two barriers could be measured, corresponding to the passage across two distinguishable transition states: the higher barriers covered the range 5.0-8.1 kcal mol-1 and the lower ones the range 4.7-6.2 kcal mol-1.     

Crotylation versus propargylation: two routes for the synthesis of the C13-C18 fragment of the antibiotic branimycin

The C13-C18 fragment 3 of the novel antibiotic branimycin was prepared along two highly stereocontrolled routes. The first one uses a standard Roush crotylation protocol, whereas the second one proceeds via an allenyl silane propargylation with unexpected stereochemical consequences, which are discussed in detail.