The aim of this talk is to review the methodology required to translate the observed luminosity function of a stellar sample into the mass function of the stars constituting the sample. Emphasis is given to the stellar models which necessarily underlie this operation, as the mass function is proportional to the derivative of the mass{luminosity relation, and this latter quantity can not be deri...

Evidence supporting the hypothesis of an invariant stellar Initial Mass Function is strong and varied. The intra-cluster medium in rich clusters of galaxies is one of the few contrary locations where recent interpretations of the chemical abundances have favoured an IMF that is biased towards massive stars, compared to the ‘normal’ IMF. This interpretation hinges upon the neglect of Type Ia sup...

It is studied to what extent the characteristics of multi-IMF (intermediate-mass fragments) events can be derived from the properties of the observed single-IMF transverse-energy spectra. It is found that the spectra of total transverse IMF energy (Et) in multi-IMF events are well represented by “synthetic” spectra obtained by a multiple folding of the single-IMF transverse energy spectrum. Fur...

The stellar initial mass function (IMF) in star clusters is reviewed. Uncertainties in the observations are emphasized. We suggest there is a distinct possibility that cluster IMFs vary systematically with density or pressure. Dense clusters could have additional formation processes for massive stars that are not present in low density regions, making the slope of the upper mass IMF somewhat sh...

We investigate the metal enrichment of elliptical galaxies in the framework of hierarchical models of galaxy formation. The semi-analytical model we use in this Letter, which has been used to study the metal enrichment of the intracluster medium (ICM) by Nagashima et al., includes the effects of flows of gas and metals both into and out of galaxies and the processes of metal enrichment due to b...

We determine the mass functions (MFs) and dynamical parameters of 15 nearby open clusters (OCs) using unprecedented data set Gaia Early Data Release 3. select members each cluster by combining photometric (colour magnitude) astrometric (parallax proper motions) stars, minimizing contamination from Galactic field interlopers. By comparing observed distribution stars along main sequence with best...

This paper presents a pitch estimation method of noisy speech signal using empirical mode decomposition (EMD). The normalized autocorrelation function (NACF) of the noisy speech signal is decomposed into a finite set of band-limited signals termed as intrinsic mode functions (IMFs) using EMD. The periodicity of one IMF is supposed to be equal to the accurate pitch period. A conventional autocor...

In this study, inverse nodal problem is solved for the p-Laplacian operator with two potential functions. We present some asymptotic formulas which have been proved in [17,18] for the eigenvalues, nodal points and nodal lengths, provided that a potential function is unknown. Then, using the nodal points we reconstruct the potential function and its derivatives. We also introduce a solution of i...

We study the initial mass function (IMF) of NGC 3603, one of the most massive galactic star-forming regions, to answer a fundamental question in current astrophysics is the IMF universal, or does it vary? Using our very deep high angular resolution images obtained with the NAOS-CONICA adaptive optics system at the VLT/ESO, we have successfully revealed the low-mass stellar population in the clu...