  Supersonic turbulence fragments the interstellar medium into dense sheets,
filaments, cores and large low density voids. The turbulence is driven on large
scales, probably predominantly by supernovae. The scaling properties of
supersonic turbulence are well described by a new analytical theory. The
distribution of proto-stellar core masses depends primarily on the power
spectrum of the turbulent flow, and on the jump conditions for near isothermal
shocks in a magnetized gas. For the predicted velocity power spectrum index
beta=1.74, consistent with results of numerical experiments of supersonic
turbulence as well as with Larson's velocity-size relation, one obtains by
scaling arguments a power law mass distribution of dense cores with a slope
equal to 3/(4-beta) = 1.33, consistent with the slope of the Salpeter stellar
initial mass function (IMF). Results from numerical simulations confirm this
scaling. Both the analytical model for the stellar IMF and its numerical
estimate show that turbulent fragmentation can also explain the origin of brown
dwarfs.
