The Pearson product-moment correlation coefficient is being used to evaluate the similarity of the high-performance liquid chromatographic fingerprints of traditional Chinese medicine (TCM) in China. It is confirmed that a large range of peak areas produced the wrong results. A new algorithm concerning weighted Pearson product-moment correlation coefficient is proposed in this article. The results for both real cases and simulated data sets show that the weighted Pearson product-moment correlation coefficients allow relatively larger differences for large values, smaller differences for small values, and more reliable results than the unweighted Pearson product-moment correlation coefficients. Weight selection depends on the specific scientific problem.
Regarding sugar and salt crystallization with large single crystals, the
agglomerate thermodynamics and geometric morphologies, not the dynamics,
dominate the particle size distribution (PSD). To consider this issue, a
PSD design model is proposed for limited large crystal agglomeration. In
this model, the agglomeration thermodynamic criticality is determined by
estimating the adhesion and dispersion forces between single crystals.
The geometric agglomerate morphologies are described by corresponding
single crystal units stacking with porosity. By seed well-controlled of
population, the key parameters of PSD (D01, D50 and D99) are precisely
designed. For erythritol, the model design accuracies are 92%-99% in
the 1.2 L and 10 L crystallizers, indicating that it can design PSD at
various crystallization scales. Concerning the general research
attention to microcrystal agglomeration kinetics (mostly active
pharmaceutical ingredients), this model effectively guides the sugar and
salt PSD design with limited large crystal agglomeration.
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