PubMed · 5216220
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U Kuno. 1965. A model for serial verbal learning.. https://doi.org/10.1007/bf02289496
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The acceptance of a tablet batch is based both on the content uniformity test and on the assay. It is shown that these two characteristics are not independent, and the acceptance criteria for them are not even consistent. For content uniformity range three methods of calculation are compared: the present European Pharmacopoeia method, a tolerance range method with improved k tolerance factor and a one-way random effects analysis of variance model. To resolve the inconsistency several options are discussed: applying the holistic content uniformity range alone; using content uniformity standard deviation and assay mean simultaneously or applying a criterion based on Taguchi's quadratic loss function.
Many contemporary problems in science involve making predictions based on partial observation of extremely complicated spatially extended systems with many degrees of freedom and with physical instabilities on both large and small scale. Various new ensemble filtering strategies have been developed recently for these applications, and new mathematical issues arise. Because ensembles are extremely expensive to generate, one such issue is whether it is possible under appropriate circumstances to take long time steps in an explicit difference scheme and violate the classical Courant-Friedrichs-Lewy (CFL)-stability condition yet obtain stable accurate filtering by using the observations. These issues are explored here both through elementary mathematical theory, which provides simple guidelines, and the detailed study of a prototype model. The prototype model involves an unstable finite difference scheme for a convection-diffusion equation, and it is demonstrated below that appropriate observations can result in stable accurate filtering of this strongly unstable spatially extended system.