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On the basis of numerical optimization, the optimum conditions for synthesis were: reaction time 6 h, reaction temperature 65 °C, using dried tetrahydrofuran as solvent and sodium methoxide as the base.
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We emphasize the combination of numerical optimization and geometric knowledge.
One interest of numerical optimization is whether the global solution can be obtained by the algorithm applied.
However, maximum-likelihood solutions for these models generally require application of numerical optimization algorithms, which are computationally demanding, and thus infeasible for GWA studies using a single processor.
Such formulations of Einstein's field equations are the basis of numerical relativity.
On the basis of model graphs and numerical optimization, the validation was done in a laboratory batch fermenter with cellulase, pectinase, temperature and time of nine cellulase filter paper unit/gram cellulose (FPU/g-cellulose), 72 international units/gram pectin (IU/g-pectin), 37 °C and 15 h, respectively.
The combination of advanced numerical optimization techniques with reduced order based models enables the possibility of efficiently solve dynamic optimization problems related to complex distributed biological systems.
Thus the observers gain depend on a time and is defined on the basis of the numerical solving of optimization problem with differential linear matrix inequalities or the numerical solving of corresponding matrix comparison system.
It was also suggested that the application of a novel numerical optimization method for analyzing H LF-NMR data [ 6, 7] provides better resolved relaxation time distributions and more accurate solutions compared with those shown by existing numerical tools.
We used the HyPhy package [26] to perform a joint numerical optimization of branch lengths for each of the N alignments and the rates in the Q matrix.
Numerical optimization of functions was done using the Powell local optimizer using a maximum of five restarts, exit tolerance of 10−8 and a maximum of 10 function evaluations.
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