A note about the structure ofπ 2 SiHSiH

Summary It has been computed the potential-energy curve ofπ ² SiH, as a function of the silicon hydrogen bond distance, by means ofab initio HFR-MO-LCAD-SCF-CI method. It has been investigated, in particular, the influence of different basis sets on the computed structural and vibrational properties of above-quoted molecule. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Noncommutative Geometry of the Moyal Plane: Translation Isometries, Connes’ Distance on Coherent States, Pythagoras Equality

We study the metric aspect of the Moyal plane from Connes’ noncommutative geometry point of view. First, we compute Connes’ spectral distance associated with the natural isometric action of ${\mathbb{R}^2}$ R 2 on the algebra of the Moyal plane ${\mathcal{A}}$ A . We show that the distance between any state of ${\mathcal{A}}$ A and any of its translated states is precisely the amplitude of the translation. As a consequence, we obtain the spectral distance between coherent states of the quantum harmonic oscillator as the Euclidean distance on the plane. We investigate the classical limit, showing that the set of coherent states equipped with Connes’ spectral distance tends towards the Euclidean plane as the parameter of deformation goes to zero. The extension of these results to the action of the symplectic group is also discussed, with particular emphasis on the orbits of coherent states under rotations. Second, we compute the spectral distance in the double Moyal plane, intended as the product of (the minimal unitization of) ${\mathcal{A}}$ A by ${\mathbb{C}^2}$ C 2 . We show that on the set of states obtained by translation of an arbitrary state of ${\mathcal{A}}$ A , this distance is given by the Pythagoras theorem. On the way, we prove some Pythagoras inequalities for the product of arbitrary unital and non-degenerate spectral triples. Applied to the Doplicher- Fredenhagen-Roberts model of quantum spacetime [DFR], these two theorems show that Connes’ spectral distance and the DFR quantum length coincide on the set of states of optimal localization.     

Nuclear magnetic resonance in contemporary art: the case of “Moon Surface” by Turcato

Nuclear Magnetic Resonance (NMR) methodologies were applied to characterize the constitutive materials and the state of degradation of a contemporary painting. The investigation was mandatory to plan a suitable restoration. Noninvasive, portable NMR allowed the detection of degraded regions of the painting based on the measurement of longitudinal relaxation time. A few samples were investigated by high resolution solid state NMR and NMR in solution, which allowed us to identify the polyurethane constituting the artefact, to investigate the microstructure in detail, and to assess that the degradation process mostly affected the ethylene units used to cap the polypropylene oxide polymeric chain. As a matter of fact, a shortening of longitudinal relaxation time was accompanied by a degradation of ethylene units. The degradation of the inorganic loading was investigated by ²⁷Al MAS, which evidenced the absence of penta-coordinated aluminum in degraded samples.     

On balanced Hermitian structures on Lie groups

We present several methods for the construction of balanced Hermitian structures on Lie groups. In our methods a partial differential equation is involved so that the resulting structures are in general non homogeneous. In particular, we prove that for 3-step nilpotent Lie groups G of dimension 6, any left-invariant complex structure on G admits a balanced Hermitian metric. Starting from normal almost contact structures, we construct balanced metrics on 6-dimensional manifolds, generalizing warped products. Finally, explicit balanced Hermitian structures are also given on solvable Lie groups defined as semidirect products ${\mathbb{R}^k \ltimes \mathbb{R}^{2n-k}}$ .     

Molecular-cluster studies of defects in silicon lattices

Summary Ab initio HF-SCF-LCAO calculations have been performed on Si _n H _2n+n (n=1 to 5) by means of four different basis sets. Total energies, first ionization potentials, minimum-energy geometries and torsional barriers of rotation around the Si−Si bond have been computed in order to test the accuracy of the basis sets used.

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Riassunto Sono stati eseguiti calcoliab initio HF-LCAO-SCF su composti della famiglia dei silani lineari (Si _n H _2n+2 ,n=1, ..., 5) mediate quatro differenti insiemi di funzioni di base. Sono state calcolate energie totali, primi potenziali di ionizzazione, geometrie al minimo di energia e barriere torsionali attorno al legame Si−Si per poter verificare l'accuratezza degl'insiemi di funzioni di base usati.

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Резюме Сначала проводятся вычисления HF-SCF-LCAO в семействе соединений Si _n H _2n+1 (n от 1 до 5), используя четыре различных базисных системы. С целью проверки точнсти использованных базисных систем систем бычислены полные знергии, первые потенциалы ионизации, геометрии с минимльной энергией и барьеры врашения вокруг связи Si−Si.