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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.
Yesterday's final formula one grand prix of the 2009 season in Abu Dhabi attracted 4.8 million viewers and a 37% share, between 12.05pm and 3.15pm on BBC1.
After being with us the entire century so far, one of the most popular of champions, and a sublimely talented one too, will – alongside Felipe Massa – drive his final Formula One race on Sunday.
"There is still no final formula, either in terms of the hierarchy or about the names or the specific responsibilities," said Mr. Rajoub, who insisted that no decisions would be made under American or Israeli pressure.
In his final Formula One race, Michael Schumacher, running sixth, sportingly moved over and ceded his position to Vettel, to give him a small extra boost in his championship points quest.
The final formulas contain only Bézier points and matrix of degree elevation.
"I don't think we should ever look for a final formula," he says.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com