Sulle equazioni di una curva monomiale proiettiva

Riassunto Si dà una costruzione di un insieme minimale di generatori omogenei per l'ideale di una curva monomiale proiettiva e una limitazione per il grado delle equazioni che la definiscono.

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Summary A construction of a minimal system of homogeneous generators for the ideal of a monomial projective curve and a degree bound for its defining equations are given.

     

Low-lying electronic states of Ben clusters (n = 7, 10, 13) and of the Be7H system

Self-consistent-field (SCF) calculations have been performed by means of a pseudopotential (PP) technique on medium-size Be_n clusters (n = 7, 10, 13). Correlation effects have been taken into account through multireference double-excitation configuration-interaction (MRD CI) procedure. Particular attention has been paid to the existence of Be clusters with many nearly degenerated states of singlet and triplet spin multiplicity. The SCF ordering of these states is frequently reversed in CI. Planar and non-planar Be clusters show comparable high stabilities caused by a strong sp hybridization. Two sections of the potential energy surface for the interaction of a H atom with the Be₇(7,0) cluster have been determined. Two regions of low energy found in this energy surface: one inside and the second outside the cluster border, are separated by an energy barrier. The CI results, indicating the directly overhead position as the absolute minimum of the surface, are in qualitative agreement with previous SCF studies on similar systems. The modifications of the cluster geometry (shrinkage or relaxation) caused by the interaction with the H atom in the directly overhead position are found to be very small.     

Computational study on the interaction of water with 2- and 3-hydroxypyridine and the corresponding pyridones

SCF –MO –LCAO ab-initio computations were carried out for the four tautomers 2-pyridone, 2-hydroxypyridine, 3-pyridone, and 3-hydroxypyridine interacting with a water molecule placed at different positions and orientations around each of them. The computed interaction energies were fitted by an analytical potential consisting of a 6–12 Lennard-Jones term plus a Coulombic one. The root-mean-square deviation of the fit is 2.5 kJ/mol. We report isoenergy contour maps for some important cross sections and obtain a qualitative trend of the solvation entropy, in agreement with available experimental data. The obtained potentials were used for Monte Carlo simulation of four clusters consisting of a tautomer molecule as solute and 50 water molecules, at 300 K. The problem of the transferability of fitting constants is also examined.     

A note on heuristics for the traveling salesman problem

We introduce subclasses of the traveling salesman problem (TSP) and analyze the behaviour of heuristics on them. We derive bounds for the performance of the algorithms.     

The vilsmeier-haack formylation of 1,2,3-trimethylindole

The title reaction yields mainly a side-chain monosubstituted formyl derivative, namely 2-(1,3-dimethylindolyl)acetaldehyde.     

Study of the reaction of bis- and tris-pyrylium and -thiopyrylium cations with methoxide ion. Electronic effects of the heterocyclic rings as substituents

The bis- and tris-pyrylium and thiopyrylium cations 1-4 were prepared in gram scale by heterocyclization of the corresponding bis- and tris-1,5-pentanediones 6 and 8. Their reaction with CD3ONa in CD3OD was studied by 1H NMR at -40 degrees C and at +25 degrees C. At low temperature, kinetically controlled mixtures of 2H and/or 4H adducts were detected, whereas at room temperature the mixtures equilibrated to yield, in all of the cases, the more stable 2H adducts exclusively. A spectrophotometric study of the reactions with sodium methoxide in methanol was carried out at 25.0 degrees C with the aim of determining the stepwise equilibrium constants for the addition of MeO- at the alpha position of the heteroaromatic rings. The obtained equilibrium constants allowed the evaluation of the electronic effects of chalcogenopyrylium and 2H-chalcogenopyran subunits as substituents. Despite the different sensitivity to electronic effects, pyrylium and thiopyrylium rings have a similar electron-withdrawing effect with a sigma(+)p approximately 0.8 and a sigma(+)m approximately 0.5. Apart from the expected importance of the inductive effect due to the positive charge, the difference between these two values remarks the importance of the resonance contribution. In contrast both the neutral 2H-pyranyl and thiopyranyl rings have a negligible effect as substituents, independently of the position, para or meta, they occupy.     

Dynamical Aspects of TEM-1 β-Lactamase Probed by Molecular Dynamics

The dynamical aspects of the fully hydrated TEM-1 β-lactamase have been determined by a 5 ns Molecular Dynamics simulation. Starting from the crystallographic coordinates, the protein shows a relaxation in water with an overall root mean square deviation from the crystal structure increasing up to 0.17 nm, within the first nanosecond. Then a plateau is reached and the molecule fluctuates around an equilibrium conformation. The results obtained in the first nanosecond are in agreement with those of a previous simulation (Diaz et al., J. Am. Chem. Soc., (2003) 125, 672–684). The successive equilibrium conformation in solution shows an increased mobility characterized by the following aspects. A flap-like translational motion anchores the Ω-loop to the body of the enzyme. A relevant part of the backbone dynamics implies a rotational motion of one domain relative to the other. The water molecules in the active site can exchange with different residence times. The H-bonding networks formed by the catalytic residues are frequently interrupted by water molecules that could favour proton transfer reactions. An additional simulation, where the aspartyl dyad D214–D233 was considered fully deprotonated, shows that the active site is destabilized.     

Nature of the chemical bond between metal atoms and oxide surfaces: new evidences from spin density studies of K atoms on alkaline earth oxides

We have studied the interaction of K atoms with the surface of polycrystalline alkaline-earth metal oxides (MgO, CaO, SrO) by means of CW- and Pulsed-EPR, UV-Vis-NIR spectroscopies and DFT cluster model calculations. The K adsorption site is proposed to be an anionic reverse corner formed at the intersection of two steps, where K binds by more than 1 eV, resulting in thermally stable species up to about 400 K. The bonding has small covalent and large polarization contributions, and the K atom remains neutral, with one unpaired electron in the valence shell. The interaction results in strong modifications of the K electronic wave function which are directly reflected by the hyperfine coupling constant, (K)a(iso). This is found to be a very efficient "probe" to measure the degree of metal-oxide interaction which directly depends on the substrate basicity. These results provide an original and general model of the early stages of the metal-support interaction in the case of ionic oxides.     

Aggregation tendency and reactivity toward AgX of cationic half-sandwich ruthenium(II) complexes bearing neutral N,O-ligands

The aggregation tendency of complexes [Ru(eta6-cymene)(N,O)Cl]X [N,O = 2-benzoylpyridine (2-bzpy), 1, and 2-acetylpyridine (2-acpy), 2, X- = BPh4- or PF6-] has been studied by means of PGSE NMR experiments. It was found that complexes with PF6- as counterion are mainly present in CD2Cl2 as ion pairs at low concentration, as a mixture of ion triples and free anions at medium concentration and as ion quadruples at elevated concentration. 19F, 1H-HOESY NMR experiments revealed that in ion triples and ion quadruples two cationic Ru-units pair up. Consistently, in the solid-state structure of 1PF6, determined through X-ray single-crystal investigation, two cationic Ru-units are held together by an intermolecular pi-pi stacking interaction between the pyridyl rings. Complexes having BPh4- as counterion are only present in solution as even aggregates, namely ion pairs at low concentration and ion quadruples at elevated concentration. In such a case a counteranion bridges two cationic Ru-units as observed in the solid-state structure of 1BPh4. The reactivity of complexes 1-2 toward AgX salts has been investigated in different solvents. Bicationic [Ru(eta6-cymene)(N,O)(MeCN)]X2 (N,O = 2-bzpy, 3, and 2-acpy, 4) and [Ru(MeCN)4(N,O)]X2 (N,O = 2-bzpy, 5, and 2-acpy, 6) complexes were obtained by the reaction of 1 and 2 with AgX in the presence of three equivalents of acetonitrile or in acetonitrile, respectively. The reaction of 1 with AgPF6 in acetone afforded complex [Ru(eta6-cymene)(N,O,O)]PF6 (7, where N,O,O = 4-alcoxide-4-phenyl-4-(pyridin-2-yl)butan-2-one) from the C-C coupling of a deprotonated methyl group of the coordinated acetone and the C=O moiety of 2-bzpy ligand.