The Galactic IMF: origin in the combined mass distribution functions of
  dust grains and gas clouds
  We present here a theoretical model to account for the stellar IMF as a
result of the composite behaviour of the gas and dust distribution functions.
Each of these has previously been modelled and the models tested against
observations. The model presented here implies a relation between the
characteristic size of the dust grains and the characteristic final mass of the
stars formed within the clouds containing the grains, folded with the relation
between the mass of a gas cloud and the characteristic mass of the stars formed
within it. The physical effects of dust grain size are due to equilibrium
relations between the efficiency of grains in cooling the clouds, which is a
falling function of grain size, and the efficiency of grains in catalyzing the
production of molecular hydrogen, which is a rising function of grain size. We
show that folding in the effects of grain distribution can yield a reasonable
quantitative account of the IMF, while gas cloud mass function alone cannot do
so.
