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end{aligned} This implies that the required estimate holds.
The required estimate then follows by combining the resulting inequalities.
By definition (mathrm{Ker} rho _V = _nmathrm{Br}(K _V), so we obtain the required estimate.
Plugging in our bound on ∥z∥, we obtain the required estimate.
Now, a suitable application of part (ii) of Theorem 2.3 to (3.6) yields the required estimate in (3.3).
end{aligned}We will obtain the required estimate if we take (t=1/(a^{-1/2}+1)).
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To justify those profits, Enron had to leap through some hoops related to fair market values of those rights, which required estimating future profits.
We also required estimated 2001 payouts no greater than 70%.
The results showed that the number of inputs required estimating outputs varied with sex difference.
This required estimating 3 extra variables: 1 variance each for the 2 random coefficients plus a covariance term.
In order to estimate standard errors of the log hazards for each treatment, we required estimates of the uncertainty associated with four treatment contrasts.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com