Making simple proofs simpler

An open partition \pi{} [Cod09a, Cod09b] of a tree T is a partition of the vertices of T with the property that, for each block B of \pi, the upset of B is a union of blocks of \pi. This paper deals with the number, NP(n), of open partitions of the tree, V_n, made of two chains with n points each, that share the root

Pre-MS depletion, accretion and primordial 7Li

We reconsider the role of pre-main sequence (pre-MS) Li depletion on the basis of new observational and theoretical evidence: i) new observations of Halpha emissions in young clusters show that mass accretion could be continuing till the first stages of the MS, ii) theoretical implications from helioseismology suggest large overshooting values below the bottom of the convective envelopes. We argue here that a significant pre-MS 7Li destruction, caused by efficient overshoot mixing, could be followed by a matter accretion after 7Li depletion has ceased on MS thus restoring Li almost to the pristine value. As a test case we show that a halo dwarf of 0.85 Msun with an extended overshooting envelope starting with an initial abundance of A(Li) = 2.74 would burn Li completely, but an accretion rate of the type 1e-8xe^{-t/3e6} Msun yr$^{-1}$ would restore Li to end with an A(Li) = 2.31. A self-regulating process is required to produce similar final values in a range of different stellar masses to explain the PopII Spite plateau. However, this framework could explain why open cluster stars have lower Li abundances than the pre-solar nebula, the absence of Li in the most metal poor dwarfs and a number of other features which lack of a satisfactory explanation.Comment: To be published in Memorie della Societ\`a Astronomica Italiana Supplementi Vol. 22, Proceedings of Lithium in the cosmos, Iocco F., Bonifacio P., Vangioni E., ed

Evolution of planetary nebulae II. Population effects on the bright cut-off of the PNLF

We investigate the bright cut-off of the [OIII]l5007 planetary nebula luminosity function (PNLF), that has been suggested as a powerful extragalactic distance indicator. Theoretical PNLFs are constructed via Monte-Carlo simulations of populations of PNe, whose individual properties are described with the aid of recent PN synthetic models (Marigo et al. 2001), coupled to a detailed photoionisation code (CLOUDY). The basic dependences of the cut-off magnitude M* are then discussed. We find that: (i) In galaxies with recent or ongoing star formation, the modelled PNLF present M* values between -4 and -5, very close to the observationally-calibrated value for the LMC. (ii) In these galaxies, the PNLF cut-off is produced by PNe with progenitor masses of about 2.5 Msun, while less massive stars give origin to fainter PNe. As a consequence M* is expected to depend strongly on the age of the last burst of star formation, dimming by as much as 5 mag as we go from young to 10-Gyr old populations. (iii) Rather than on the initial metallicity of a stellar population, M* depends on the actual [O/H] of the observed PNe, a quantity that may differ significantly from the initial value (due to dredge-up episodes), especially in young and intermediate-age PN populations. (iv) Also the transition time from the end of AGB to the PN phase, and the nuclear-burning properties (i.e. H- or He-burning) of the central stars introduce non-negligible effects on M*. The strongest indication derived from the present calculations is a serious difficulty to explain the age-invariance of the cut-off brightness over an extended interval, say from 1 to 13 Gyr, that observations of PNLFs in galaxies of late-to-early type seem to suggest.Comment: 22 pages, to appear in Astronomy & Astrophysic

MASSCLEAN - MASSive CLuster Evolution and ANalysis Package - Description, Tests, and Results

MASSCLEAN is a new, sophisticated and robust stellar cluster image and photometry simulation package. This package is able to create color-magnitude diagrams and standard FITS images in any of the traditional optical and near-infrared bands based on cluster characteristics input by the user, including but not limited to distance, age, mass, radius and extinction. At the limit of very distant, unresolved clusters, we have checked the integrated colors created in MASSCLEAN against those from other simple stellar population (SSP) models with consistent results. Because the algorithm populates the cluster with a discrete number of tenable stars, it can be used as part of a Monte Carlo Method to derive the probabilistic range of characteristics (integrated colors, for example) consistent with a given cluster mass and age. We present the first ever mass dependent integrated colors as a function of age, derived from over 100,000 Monte Carlo runs, which can be used to improve the current age determination methods for stellar clusters.Comment: 4 pages, 5 figures, Proceedings International Astronomical Union Symposium No. 266, Star Clusters - Basic Galactic Building Blocks throughout Time and Space, Editors: Richard de Grijs & Jacques R. D. Lepin

Evolution of Planetary Nebulae I. An improved synthetic model

We present a new synthetic model to follow the evolution of a planetary nebula (PN) and its central star, starting from the onset of AGB phase up to the white dwarf cooling sequence. The model suitably combines various analytical prescriptions to account for different (but inter-related) aspects of planetary nebulae, such as: the dynamical evolution of the primary shell and surrounding ejecta, the photoionisation of H and He by the central star, the nebular emission of a few relevant optical lines (e.g. Hbeta; HeII4686; [OIII]5007). Predictions of the synthetic model are tested by comparison with both findings of hydrodynamical calculations, and observations of Galactic PNe. The sensitiveness of the results to the models parameters (e.g. transition time, mass of the central star, H-/He-burning tracks, etc.) is also discussed. We briefly illustrate the systematic differences that are expected in the luminosities and lifetimes of PNe with either H- or He-burning central stars, which result in different ``detection probabilities'' across the H-R diagram, in both Hbeta and [OIII]5007 lines. Adopting reasonable values of the model parameters, we are able to reproduce, in a satisfactory way, many general properties of PNe, like the ionised mass--nebular radius relationship, the trends of a few main nebular line ratios, and the observed ranges of nebular shell thicknesses, electron densities, and expansion velocities. The models naturally predict also the possible transitions from optically-thick to optically-thin configurations (and vice versa). In this context, the origin of the Zanstra discrepancy is also analysed. (abridged)Comment: 28 pages, 23 postscript figures, to appear in A&

Chemico-toxicological studies on psychotropic drugs

Sve veća i nekontrolirana upotreba psihofarmaka ogleda se u povećanoj kazuistici otrovanja tim sredstvima. Da omogući sistematski postupak pri toksikološkoj analizi, autor predlaže farmakološku klasifikaciju psihofarmaka kojih podskupine dijeli dalje prema kemijskoj strukturi. Na kraju daje pregled kromatografskih metoda za identifikaciju psihotropnih lijekova i predlaže da se prihvate i unificiraju one koje daju najviše korisnih podataka.An ever g-rowing and often uncontrolled use of ·psychotropic drugs is reflected in the increased incidence of poisonings due to these substances. To enable a systematic approach to toxicological analysis, the author suggests a pharmacological basis for the classification of psychotropic drugs. A further division into subgroups is made according to chemical structures. At the end a review is given of chromatographic methods for the identification of psychotropic drugs, and those that have proved to provide most satisfactory results are recommended as the methods of choice

Dynamic fracture: an example of convergence towards a discontinuous quasi-static solution

International audienceConsidering a one-dimensional problem of debonding of a thin film in the context of Griffith's theory, we show that the dynamical solution converges, when the speed of loading goes down to 0, to a quasistatic solution including an unstable phase of propagation. In particular, the jump of the debonding induced by this instability is governed by a principle of conservation of the total quasistatic energy, the kinetic energy being negligible

Modelling of intermediate-age stellar populations: III Effects of dust-shells around AGB stars

In this paper,we present single stellar population models of intermediate age stellar populations where dust-enshrouded AGB stars are introduced. The formation of carbon stars is also accounted for, and is taken to be a function of both initial mass and metallicity. The effect of the dusty envelopes around AGB stars on the optical/near-infrared spectral energy distribution were introduced using semi-emipirical models where the mass-loss and the photospheric chemistry determine the spectral properties of a star along the AGB sequence. The spectral dichotomy between O-rich stars and C-rich stars is taken into account in the modelling. We have investigated the AGB sequence morphology in he near-infrared CMD as a function of time and metallicity. We show that this diaggram is characterized by three morphological features, occupied by optically bright O-rich stars, optically bright C-rich stars, and dust-enshrouded O-rich and C-rich stars respectively. Our models are able to reproduce the distribution of the three AGB subtype stellar populations in colour-colour diagrams. Effects of dusty envelopes on the luminosity function are also investigated (Abriged).Comment: 11 pages, 9 figures, accepted for publication in A&