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True Density (true + density)
Selected AbstractsThermal expansion of organic crystals and precision of calculated crystal density: A survey of Cambridge Crystal DatabaseJOURNAL OF PHARMACEUTICAL SCIENCES, Issue 5 2007Changquan Calvin Sun Abstract True density is a physical property of both fundamental and practical importance to the study of pharmaceutical powders. True density may be calculated from crystal structure. However, precision of such calculated density is not well understood. Furthermore, thermal expansion properties of organic crystals have rarely been characterized. A survey of Cambridge Crystal Database is conducted to assess (1) precision of calculated crystal density from crystal structure; (2) thermal expansion properties of organic crystals. It is shown that calculated crystal density exhibits, on average, a relative standard deviation (RSD) of ,0.4%. It is found that crystal density generally increases linearly with decreasing temperature provided no phase change occurs. Slope of the line, termed thermal density gradient, of organic crystals ranges between 0.04 and 1.74 mg,cm,3,K,1 with an average of ,0.2 mg,cm,3,K,1. It is shown that majority polymorph pairs exhibit significantly different thermal expansion behavior and their density,temperature lines can cross. This likely contributes to the less than perfect prediction of relative stability of polymorphs at ambient temperature using the density rule. © 2007 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 96: 1043,1052, 2007 [source] A novel method for deriving true density of pharmaceutical solids including hydrates and water-containing powdersJOURNAL OF PHARMACEUTICAL SCIENCES, Issue 3 2004Changquan (Calvin) Sun Abstract True density is commonly measured using helium pycnometry. However, most water-containing powders, for example, hydrates, amorphous drugs and excipients, and most tablet formulations, release water when exposed to a dry helium atmosphere. Because released water brings significant errors to the measured true density and drying alters the nature of water-containing solids, the helium pycnometry is not suitable for those substances. To overcome this problem, a novel method has been developed to accurately calculate powder true density from compaction data. No drying treatment of powder samples is required. Consequently, the true density thus obtained is relevant to tableting characterization studies because no alteration to the solid is induced by drying. This method involves nonlinear regression of compaction pressure-tablet density data based on a modified Heckel equation. When true density values of water-free powders derived by this novel method were plotted against values measured using pycnometry, a regression line with slope close to unity and intercept close to zero was obtained. Thus, the validity of this method was supported. Using this new method, it was further demonstrated that helium pycnometry always overestimates true densities of water containing powders, for example, hydrates, microcrystalline cellulose (MCC), and tablet formulations. The calculated true densities of powders were the same for different particle shapes and sizes of each material. This further suggests that true density values calculated using this novel method are characteristic of given materials and independent of particulate properties. © 2004 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 93:646,653, 2004 [source] Comparing density forecast models,JOURNAL OF FORECASTING, Issue 3 2007Yong Bao Abstract In this paper we discuss how to compare various (possibly misspecified) density forecast models using the Kullback,Leibler information criterion (KLIC) of a candidate density forecast model with respect to the true density. The KLIC differential between a pair of competing models is the (predictive) log-likelihood ratio (LR) between the two models. Even though the true density is unknown, using the LR statistic amounts to comparing models with the KLIC as a loss function and thus enables us to assess which density forecast model can approximate the true density more closely. We also discuss how this KLIC is related to the KLIC based on the probability integral transform (PIT) in the framework of Diebold et al. (1998). While they are asymptotically equivalent, the PIT-based KLIC is best suited for evaluating the adequacy of each density forecast model and the original KLIC is best suited for comparing competing models. In an empirical study with the S&P500 and NASDAQ daily return series, we find strong evidence for rejecting the normal-GARCH benchmark model, in favor of the models that can capture skewness in the conditional distribution and asymmetry and long memory in the conditional variance.,,Copyright © 2007 John Wiley & Sons, Ltd. [source] A novel method for deriving true density of pharmaceutical solids including hydrates and water-containing powdersJOURNAL OF PHARMACEUTICAL SCIENCES, Issue 3 2004Changquan (Calvin) Sun Abstract True density is commonly measured using helium pycnometry. However, most water-containing powders, for example, hydrates, amorphous drugs and excipients, and most tablet formulations, release water when exposed to a dry helium atmosphere. Because released water brings significant errors to the measured true density and drying alters the nature of water-containing solids, the helium pycnometry is not suitable for those substances. To overcome this problem, a novel method has been developed to accurately calculate powder true density from compaction data. No drying treatment of powder samples is required. Consequently, the true density thus obtained is relevant to tableting characterization studies because no alteration to the solid is induced by drying. This method involves nonlinear regression of compaction pressure-tablet density data based on a modified Heckel equation. When true density values of water-free powders derived by this novel method were plotted against values measured using pycnometry, a regression line with slope close to unity and intercept close to zero was obtained. Thus, the validity of this method was supported. Using this new method, it was further demonstrated that helium pycnometry always overestimates true densities of water containing powders, for example, hydrates, microcrystalline cellulose (MCC), and tablet formulations. The calculated true densities of powders were the same for different particle shapes and sizes of each material. This further suggests that true density values calculated using this novel method are characteristic of given materials and independent of particulate properties. © 2004 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 93:646,653, 2004 [source] Solution of the crystallographic phase problem by iterated projectionsACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2003Veit Elser An algorithm for determining crystal structures from diffraction data is described which does not rely on the usual reciprocal-space formulations of atomicity. The new algorithm implements atomicity constraints in real space, as well as intensity constraints in reciprocal space, by projections that restore each constraint with the minimal modification of the scattering density. To recover the true density, the two projections are combined into a single operation, the difference map, which is iterated until the magnitude of the density modification becomes acceptably small. The resulting density, when acted upon by a single additional operation, is by construction a density that satisfies both intensity and atomicity constraints. Numerical experiments have yielded solutions for atomic resolution X-ray data sets with over 400 non-hydrogen atoms, as well as for neutron data, where positivity of the density cannot be invoked. [source] | ||||||||||