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.

---

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.