The Initial Mass Function as given by the fragmentation
  The dichotomy between a universal mass function (IMF) and a variable IMF which depends on local physical parameters characterises observational and theoretical stellar astronomy. In this contribution the available distributions of probability are briefly reviewed. The physical nature of two of them, gamma variate and lognormal, is then explained once the framework of the fragmentation is introduced. Interpolating techniques are then applied to the sample of the first 10 pc and to the open cluster NGC6649: in both cases lognormal distribution produces the best fit. The three power law function has also been investigated and visual comparison with an artificially generated sample of 100000 stars suggests that the variations in the spectral index are simply due to the small number of stars available in the observational sample. In order to derive the sample of masses, a new formula that allows us to express the mass as a function of the absolute magnitude and (B-V) for MAIN V, GIANTS III and SUPERGIANTS I is derived. 
Lorenzo Zaninetti