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By applying the Ritz minimization procedure to the energy expressions, a system of Mathieu Hill equations is formulated.
A system of discrete equations is obtained through application of the Ritz minimization procedure to the energy expressions.
This modified potential function is then used in the geometry minimization procedure to obtain the minimum energy pathway between the reactant and product structures.
For model selection, we propose a procedure grounded on the calculation of distances defined in a metric space and a minimization procedure to determine the optimal set of representative models.
In order to test empirically the properties of our estimation method we simulated the model with the optimal parameters obtained in Case 1, we used the simulation as a reference test sample, and we applied our minimization procedure to estimate one parameter at a time, fixing all the others to the optimal values.
The algorithm incorporated a minimization procedure to account for center.
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"That," the official continued, "is why the statute requires that there be minimization procedures to ensure that when communications of, or concerning, US persons are acquired in the course of lawful collection under Section 702, that information is minimized and is retained and disseminated only when appropriate.
A minimization procedure according to Pocock and Simon [ 20] and Borm et al. [ 21] was used to obtain optimal balance on the factors gender, study discipline and tutor, as they may influence learning behaviour and learning efficacy [ 19].
The proposed minimization procedure allowed to identify unknown parameters listed in Table 5 and the bending stiffness distributions shown in Fig. 17.
For almost all codes from R, the minimization procedure led to codes (O) that were better than the optimized version of the standard code (100% for the PRS, 98% for the Gilis matrix, see Figs. 4b, 5b).
To stop energy minimization of a ligand in its free state when it reaches at a local minimum conformation thus avoiding ligand folding we devised an NMA-monitored energy minimization (NEM) procedure to investigate whether the 100 ligands under study were in, near, or far from local minimum conformations.
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