  Two varieties of the universal stellar initial mass function (IMF) viz., the
Kroupa and the Chabrier IMF, have emerged over the last decade to explain the
observed distribution of stellar masses. The possibility of the universal
nature of the stellar IMF leads us to the interesting prospect of a universal
mode of star-formation. It is well-known that turbulent fragmentation of gas in
the interstellar medium produces a lognormal distribution of density which is
further reflected by the mass-function for clumps at low and intermediate
masses. Stars condense out of unstable clumps through a complex interplay
between a number of dynamic processes which must be accounted for when tracing
the origin of the stellar IMF. In the present work, applying the theory of
gravitational fragmentation we first derive the mass function (MF) for clumps.
Then a core mass function (CMF) is derived by allowing the clumps to fragment,
having subjected each one to a random choice of gas temperature. Finally, the
stellar IMF is derived by applying a random core-to-star conversion efficiency,
$\epsilon$, in the range of 5%-15% to each CMF. We obtain a power-law IMF that
has exponents within the error-bars on the Kropua IMF. This derived IMF is
preceded by a similar core mass function which suggests, gravoturbulent
fragmentation plays a key role in assembling necessary conditions that relate
the two mass-functions. In this sense the star-formation process, at least at
low redshifts where gas cooling is efficient, is likely to be universal. We
argue that the observed knee in the CMF and the stellar IMF may alternatively
be interpreted in terms of the characteristic temperature at which gas in
potential star-forming clouds is likely to be found. Our results also show that
turbulence in star-forming clouds is probably driven on large spatial scales
with a power-spectrum steeper than Kolmogorov-type.
