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end{aligned} Now we apply the mean value theorem and the Taylor formula.
Most TRT analysis methods apply the mean of the inlet and outlet temperatures of the circulating fluid along the entire borehole length.
To solve the optimization problem, the authors apply the mean value cross-decomposition method, which results in an implementation-friendly solution.
To conclude the proof, it remains to take into account (4.7) and apply the Mean Value Theorem: φ ( 1 ) − φ ( 0 ) = φ ′ for some ε ∈ ( 0, 1 ).
We apply the mean market output in order to account for scale effects which may not be adequately captured by variability between farms in the mean market income or land area.
For the purpose of the first aim (dimensionality in symptom load in relation to help-seeking), we apply the mean-score of the scale as a continuous variable (each sum-score value labelled with percentiles in the total population).
Equal Pay Day is calculated by applying the mean gender pay gap to the calendar year.
Applying the mean value theorem for integral and simplifying as before, we obtain (44).
Recent research [9, 31] applies the mean field principle while using the Naming Game model for their experiments.
Subtracting Equation (3.8) from Equation (3.10) and then applying the mean value theorem on f, we obtain.
Note that here we have applied the mean value theorem with ξ valued between 0 and δ.
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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