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The models were proven reliable through comparisons to intravenous data.
MVDA based models were proven useful and should be routinely implemented for bioprocesses.
The PRO and MEC models were proven to be valid.
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Various models were proved to perform very well.
The mathematical models for calculating kinetics values were established, and the models were proved to be valid for predicting lignocellulosic biomass pyrolysis behavior.
Homogeneous models cannot capture this rock failure mechanism while heterogeneous models are proven capable of capturing it.
The value and accuracy of this model were proven shortly thereafter.
First, the existing models are proved wrong by the facts.
Finally, good predictive ability of the suggested models was proved with five additional verification experiments.
Theoretical convergence of our continuous and discrete models is proved and our methods are tested in numerical experiments.
In the next step, accuracy and validity of these mathematical models are proved both statistically and experimentally.
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