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They are introduced, where appropriate, only to simplify the final formulae.
The final formulae are well-adapted to numerical calculations of "output" spectra by electronic means.
The final formulae for the overall properties show explicitly the dependence on (i) the properties of the phases, (ii) the radius of the cylindrical fiber and (iii) the lattice sums associated with the square array.
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Finally, by substituting all these results into the definition (4.1), we obtain the final formula for the higher-order correlation of the network.
A video that will be uploaded Sept. 9 to Wheaties's Web site will announce the final formula.
The final formulas contain only Bézier points and matrix of degree elevation.
The final formula of money multiplier is derived respectively as the rational response of the bank to the corresponding regulation.
It is the final Formula 1 race of the year and the BBC awards for the 2014 season have been handed out.
The properties of the final formula were evaluated, including viscosity, temperature stability, anti-H2S performance, gel sealing pressure, gel strength gel breaking performance, etc.
The final formula used in treatment group was a combination of the record in the "Zhang Medicinee" and the formula frequency used in clinical trials.
The final formula is expressed as follows: QA 4 = 1 N blk ∑ i = 1 M - 7 ∑ j = 1 N - 7 E w u - v ⋅ MaskEff, (16).
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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