Abstract: Based on the statistical principle, it is proved that the cutoff moment problem of the molecular weight distribution (MWD) has a unique solution in the polymerization reaction object, that is, moments of the distribution function correspond to the distribution function, and all moments of the MWD can be deduced from the finite lower order moments. The number of independent lower order moments is equal to the independent parameters of the distribution function, which provides the theoretical basis for the distributed function of finite order moment control. The correctness of above conclusion is testified by simulation results.

Key words: Molecular weight distribution, moment, polymerization, Hausdorff moment problem 

摘要： 基于统计学原理证明了在聚合反应对象中分子量分布函数(Molecular Weight Distribution, MWD)的截断矩问题具有唯一解，即分布函数的矩与分布函数一一对应，且由有限低阶矩可推导MWD的所有矩值，独立低阶矩的个数与分布函数独立参数相等。这一结论为基于有限阶矩控制分布函数提供了理论基础，仿真实验证明了上述结论的正确性。

关键词: 分子量分布函数, 矩, 聚合反应, Hausdorff矩问题