  Linear analysis of the formation of protostellar cores in planar magnetic
interstellar clouds yields information about length scales involved in star
formation. Combining these length scales with various distributions of other
environmental variables, (i.e., column density and mass-to-flux ratio) and
applying Monte Carlo methods allow us to produce synthetic core mass functions
(CMFs) for different environmental conditions. Our analysis shows that the
shape of the CMF is directly dependent on the physical conditions of the cloud.
Specifically, magnetic fields act to broaden the mass function and develop a
high-mass tail while ambipolar diffusion will truncate this high-mass tail. In
addition, we analyze the effect of small number statistics on the shape and
high-mass slope of the synthetic CMFs. We find that observed core mass
functions are severely statistically limited, which has a profound effect on
the derived slope for the high-mass tail.
