  The origin of the stellar initial mass function (IMF) is a fundamental issue
in the theory of star formation. It is generally fit with a composite power
law. Some clues on the progenitors can be found in dense starless cores that
have a core mass function (CMF) with a similar shape. In the low-mass end,
these mass functions increase with mass, albeit the sample may be somewhat
incomplete; in the high-mass end, the mass functions decrease with mass. There
is an offset in the turn-over mass between the two mass distributions. The
stellar mass for the IMF peak is lower than the corresponding core mass for the
CMF peak in the Pipe Nebula by about a factor of three. Smaller offsets are
found between the IMF and the CMFs in other nebulae. We suggest that the offset
is likely induced during a starburst episode of global star formation which is
triggered by the formation of a few O/B stars in the multi-phase media, which
naturally emerged through the onset of thermal instability in the cloud-core
formation process. We consider the scenario that the ignition of a few massive
stars photoionizes the warm medium between the cores, increases the external
pressure, reduces their Bonnor?Ebert mass, and triggers the collapse of some
previously stable cores. We quantitatively reproduce the IMF in the low-mass
end with the assumption of additional rotational fragmentation.
