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We study the last application in more detail by applying the derived results to Gaussian fields representing irregular sea surfaces.
By applying the derived heat transfer model to the performed ethene hydrogenation experiments, the reactor temperature can be predicted satisfactorily in the whole range of performed experiments.
The validity of the proposed strategy is confirmed by applying the derived models to the parts of the experimental results that were not included in the analyses.
The optimal free-boundary shapes are determined by applying the derived shape gradient function to the H1 gradient method for shells, which is a parameter-free shape optimization method proposed by one of the authors.
Computational experiences indicate that by applying the derived upper bound for the number of hubs the proposed heuristic is capable of obtaining optimal solutions for all small-scaled problems very efficiently.
By applying the derived prognostic index, it can be seen that those in RPA class 2 with a score of 9 or greater (i.e. leptomeningeal disease, five ECM sites or three ECM sites and PD in brain on imaging) have a median survival of only 21 days and are unlikely to benefit from WBRT.
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Numerical examples of simply supported cross-ply beams subjected to transverse sinusoidal loads are analytically solved by directly applying the derived formulas.
We generated pronunciation variants by successively applying the derived rewrite rules to the canonical representations in the baseline lexicon.
By applying the newly derived solution, a homogenization analysis of a composite reinforced by polygon-shaped fibers is performed.
The interval containing a population parameter is established by calculating that statistic from values measured on a random sample taken from the population and by applying the knowledge (derived from probability theory) of the fidelity with which the properties of a sample represent those of the entire population.
The full-dataset classifier has an unknown accuracy which is estimated by applying the classifier derived on the training set to the test set.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com