deletions | additions       diff --git a/For_each_of_the_equal__.tex b/For_each_of_the_equal__.tex  index fcf5150..4b94cce 100644  --- a/For_each_of_the_equal__.tex  +++ b/For_each_of_the_equal__.tex 
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\begin{equation}   \frac{dN}{dM} = M^{\beta} \exp\left(-\frac{M}{M_c}\right),  \end{equation}  which is a power-law mass distribution with an exponential truncation. The cutoff (truncation) mass in the distribution is $M_c$ and the index of the distribution is $\beta$. We consider a pure power-law distribution, letting $M_c\to\infty$ and we also consider a Schechter function, constraining $\beta=-2$ and optimizing for $M_{c}$. The pure power-law function has been traditionally considered in previous on molecular cloud mass distributions \citep{Solomon_1987,Rosolowsky_2005a}. The \citet{Schechter_1976} form of the mass distribution is expected for the gravitational fragmentation of a gas distribution below a characteristic mass (e.g., the Jeans mass).  In all cases, we limit the fits to clouds with masses $M>3\times 10^{5}~M_{\odot}$ as determined by the minimum mass of clouds admitted by our cataloging procedure. The {\sc powerlaw} package optimizes the fits to the data using the procedure described in \citet{Clauset_2009}, which uses a maximum likelihood framework and a Kolmogorov-Smirnoff test to assess goodness-of-fit. Of note, the method provides likelihoods for favoring one functional representation over another. In Figure \ref{fig:massfits}, we show the fits of the pure