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In order to solve the bivariate PBE an extended sectional grid technique is developed with improved computational efficiency.
This paper presents a study on the application of an extended sectional grid technique for the solution of the dynamic bivariate population balance equation (PBE) in batch particulate systems.
The performance of the extended sectional grid technique in terms of numerical accuracy and stability is assessed by a direct comparison of the calculated bivariate particle size distributions and/or distribution moments to available analytical solutions.
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Results extend cross-sectional findings and show reduced striatal engagement in adolescence compared to adulthood during preparation for action in an incentive context.
The purpose of this study was to extend cross-sectional observations and prospectively assess the variability of FC over time in SSc patients.
However, it was the process of overcoming the methodological challenges, which led to the conclusion that in this example percent low social class occupations was the most appropriate measure to use when extending cross-sectional analysis of standing balance and chair rise to life course investigation.
Since the main interest is determination of the moment capacity of beams, the procedure needs to be extended at cross-sectional level.
In an attempt to remedy this problem Chai and Bailey [ 21] extended the cross-sectional two-part model by suggesting a skew-normally distributed error in the regression equation for log-transformed positive values, and proposed a probit/log-skew normal mixture model for cross-sectional data.
These SHIP data extended a previous cross-sectional report of elevated A1C levels among participants with periodontitis (20) as well as an earlier publication from NHANES I reporting increased levels of baseline periodontal disease to predict incident diabetes during two decades of follow-up (4).
In this paper, we extend this modified sectional curvature from Lorentzian manifolds to semi-Riemannian manifolds under the name of 'bounded sectional curvature'.
Specifically, the method generally used in practice and based on a simple sectional analysis is extended to the case of steel-concrete composite beams in partial interaction.
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