Measuring Bismuth Oxide Particle Size and Morphology in Film-Coated Tablets

The assessment of active pharmaceutical ingredient (API) particle size and morphology is of great importance for the pharmaceutical industry since it is expected to significantly affect physicochemical properties. However, very few methods are published for the determination of API morphology and particle size of film-coated (FC) tablets. In the current study we provide a methodology for the measurement of API particle size and morphology which could be applied in several final products. Bismuth Oxide 120 mg FC Tabs were used for our method development, which contain bismuth oxide (as tripotassium dicitratobismuthate (bismuth subcitrate)) as the active substance. The sample preparation consists of partial excipient dissolution in different solvents. Following this procedure, the API particles were successfully extracted from the granules. Particle size and morphology identification in Bismuth Oxide 120 mg FC Tabs was conducted using micro-Raman mapping spectroscopy and ImageJ software. The proposed methodology was repeated for the raw API material and against a reference listed drug (RLD) for comparative purposes. The API particle size was found to have decreased compared to the raw API, while the API morphology was also affected from the formulation manufacturing process. Comparison with the RLD product also revealed differences, mainly in the API particle size and secondarily in the crystal morphology.     

A q-Analogue of the Stirling Formula and a Continuous Limiting Behaviour of the q-Binomial Distribution—Numerical Calculations

In this article, we derive an asymptotic formula for the q-factorial number of order n using the saddle point method. This formula is a q-analogue, for 0?<?q?<?1, of the usual Stirling formula for the factorial number of order n. Also, this formula is used to provide a continuous limiting behaviour of the q-Binomial distribution in the sense of pointwise convergence. Specifically, the q-Binomial distribution converges to a continuous Stieltjes–Wigert distribution. Furthermore, we present some numerical calculations, using the computer program MAPLE, indicating a quite strong convergence.