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In addition, the non-linear ordinary differential equation is solved using the homotopy perturbation method (HPM) and one another expressions for the non-linear frequency parameters and non-linear to linear frequency ratio are obtained.
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You will get another expression for f up to a constant that depends on x.
Thus (3.2) gives another expression for the Donald relative entropy.
Thus (3.1) gives us another expression for the Donald relative entropy.
Chit-chat is another expression for small talk: conversation topics which aren't important but are part of everyday social communication, like talking about the weather.
On the other hand, recalling the power-series expansion of the function e x, we have another expression for the Estrada index of G as follows: E E ( G ) = ∑ k = 0 ∞ M k ( G ) k !
Another expression for the probability of detection over Nakagmai fading channels can easily be derived by rewriting the right-hand side of (21) as: Q u γ, λ ′ = 1 - ∑ n ≥ 0 exp - γ / 2 γ 2 n γ ∗ ( u + n, λ ′ / 2 ) n !
"Being on the same page" is another expression for which there is as yet no known vaccine, along with "at the end of the day". "At the end of the day" is "spot on"(yet another popular one) since it introduces a visual and temporal element into the monotony of cliché.
Consequently, the assumption introduces another expression for the heating of the remaining 95% of water from 155 °C to 158 °C.
"Perhaps the 'study of budgeting' is just another expression for the 'study of politics' The opportunities for comparison are ample, the outcomes are specific and quantifiable" (Wildavsky 1974, p 3).
And this, they claim (again pace Williams), is because tropes are essentially of some object, because they are ways the objects are (for another expression of this view, see Heil 2003: 126f).
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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