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Exact(2)
In view of estimate (17), the above expression can be bounded by.
Using the inequality ( 1 + u ) ≤ e − l / d e ω ( u ) / d from (14), the right-hand side of the above expression can be bounded by (32).
Similar(58)
The values of can be bounded according to the expression on the right-hand side, holding with equality for a uniform PDP.
The number of frames for expansion can be bounded.
"Music expression can be measured quantitatively".
Its most concentrated expression can be found in pop music.
For the terrorists free expression can be grounds for execution.
Sotomayor's mode of expression can be inelegant.
These expressions can be used to estimate the upper-bound for the stress that is frozen into the outermost layer of the plastic pipe (since this layer is quenched first, shortly after extrusion).
At each amplitude two analytic expressions can be constructed which constitute upper and lower bounds to the exact value of the frequency.
From an analogous argument in the proof of Corollary 3.2 in [11], we can show that this expression is bounded from below by a positive constant which is independent of η > 0 and x ∈ Ω. Therefore (HJ3) is satisfied.
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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