中文摘要：

云核质量函数（CMF）是分子云中致密云核的一个基本观测性质,被用来研究恒星的初始质量函数（IMF）的成因。CMF可以用积分和微分两种形式来表达。样本较小时,积分形式的CMF拟合出的结果能够清晰地反映出云核的数目;样本较大时,微分形式的CMF可以合并数据明确地表述CMF。一般来说,CMF有幂律和正态对数两种函数形式。在湍流存在的情况下,正态对数函数可以更好地拟合CMF;幂律形式的CMF谱指数在一定范围内波动,其大小与天区和样本有关。Salpeter提出恒星的初始质量函数（IMF）是一个幂律函数,很多研究认为CMF与IMF是相似的。而近期的一些研究工作认为CMF与IMF是不相同的,这主要有三方面的原因：（1）用一个具体的幂律函数去拟合一个任意的积分函数是不可靠的;（2）只有当M Mmax（或者Mmax-→∞）时,积分形式的CMF可以近似地认为是幂律形式的;（3）采用Monte Carlo方法拟合CMF能够增加拟合结果的可信度。

英文摘要：

Star formation is a fundamental field in astrophysics, within which the core mass function（CMF） of molecular clouds is a hot topic. Different models of molecular core evolution predicted different CMFs. Comparing CMF with stellar initial mass function（IMF） would help reveal the origin of stellar mass and the conversion rate between cloud cores and stars.In this review, we describe two expressions of CMFs, namely, differential CMF and cumulative CMF. When the sample size is small, cumulative CMF can clearly reflect the number of cloud cores. When the sample size is big, differential CMF is a straightforward representation based on binning the data. We research and read most of the highly cited papers published before 2013 that are related with CMF. Based on these studies, we found that two function forms of CMF, namely, power law CMF and log-normal CMF, are widely used. Fitting a log-normal function to CMF produces a better result for cores under the influence of turbulence. The CMF power law index fluctuates in a fixed interval and varys from region to region. The stellar IMF is generally thought to follow a power law function.Many research work indicate that CMF resembles IMF. However, some recent researches conclude that CMF tends to be different from IMF. The conclusion is based on that（1）fitting a power-law directly to an arbitrary cumulative function is unreliable,（2） cumulative CMF can be approximated by a power-law only at M Mmax（or Mmax-→ ∞）,（3） with fitting CMF Monte Carlo approach gets a flatter index than β.