Recent results on graphs with convex quadratic stability number

The main results about graphs with convex quadratic stability number (that is, graphs for which the stability number can be determined by convex quadratic programming) are surveyed including the most recently obtained. Furthermore, a few algorithmic techniques for the recognition of this type of graphs in particular families are presented

Reconhecimento de grafos com número de estabilidade quadrático convexo

São apresentados os principais e mais recentes resultados sobre grafos com número de estabilidade quadrático convexo (que são grafos cujo número de estabilidade pode ser determinado através de técnicas de programação quadrática convexa) e descritas algumas estratégias algorítmicas para o reconhecimento de grafos deste tipo em famílias particulares

Kinetic energy of protons in ice Ih and water: a path integral study

The kinetic energy of H and O nuclei has been studied by path integral molecular dynamics simulations of ice Ih and water at ambient pressure. The simulations were performed by using the q-TIP4P/F model, a point charge empirical potential that includes molecular flexibility and anharmonicity in the OH stretch of the water molecule. Ice Ih was studied in a temperature range between 210-290 K, and water between 230-320 K. Simulations of an isolated water molecule were performed in the range 210-320 K to estimate the contribution of the intramolecular vibrational modes to the kinetic energy. Our results for the proton kinetic energy, K_H, in water and ice Ih show both agreement and discrepancies with different published data based on deep inelastic neutron scattering experiments. Agreement is found for water at the experimental melting point and in the range 290-300 K. Discrepancies arise because data derived from the scattering experiments predict in water two maxima of K_H around 270 K and 277 K, and that K_H is lower in ice than in water at 269 K. As a check of the validity of the employed water potential, we show that our simulations are consistent with other experimental thermodynamic properties related to K_H, as the temperature dependence of the liquid density, the heat capacity of water and ice at constant pressure, and the isotopic shift in the melting temperature of ice upon isotopic substitution of either H or O atoms. Moreover, the temperature dependence of K_H predicted by the q-TIP4P/F model for ice Ih is found to be in good agreement to results of path integral simulations using ab initio density functional theory.Comment: 11 pages, 6 figures, 2 table

The Distance to the M31 Globular Cluster System

The distance to the centroid of the M31 globular cluster system is determined by fitting theoretical isochrones to the observed red-giant branches of fourteen globular clusters in M31. The mean true distance modulus of the M31 globular clusters is found to be 24.47 +/- 0.07 mag. This is consistent with distance modulii for M31 that have been obtained using other distance indicators.Comment: 11 pages, 2 postscript figures, uses aaspp4.sty, to be published in the May 1998 Astronomical Journa