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Let us first assume for simplicity that ( Π, g ) is strictly quadratic and bi-quadratic.
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That suggests that things could be tighter than first assumed for Grab if it isn't able to fully capitalize on the Uber acquisition.
For the convenience of presenting the main optical losses, we first assume that for glass κ2 = 0.
Here, we first assume that and for each have been estimated imperfectly; that is, and, where and are the estimation errors of and ( represents the estimation error of ), respectively.
To calculate the consequences of altered CMRO2 by hypercapnia, we first assume different values for ΔCMRO2 during hypercapnia and calculate the corresponding calibration constant A (see equation above) from exemplary published BOLD/CBF data during hypercapnia.
First assume that and are positive for all for some.
end{aligned}For the following, we first assume (fin widehat{B}^1_sigma ) for some (sigma >0).
For the following, let us first assume that the psychometric function for volume perception estimated in G. soricina has the same parameters (threshold = 0.75, lapse rate = 0.05, slope = 1.6, average values from Table 2 in Toelch and Winter 2007) in G. commissarisi.
To check for (15), first assume that (15) is also inactive at x*, which infers M*N*W b − K 1 < 0.
Our main theorem can now be formulated as follows: (7) First, assume that Equation (6) holds for ζ=0, and thus.
More precisely, one first assumes that for each w ∈ R q fixed, the frozen fast SDE, d v t = F ( v t, w ) d t + Σ ( v t, w ) ⋅ d B ( t ), admits a unique invariant measure, denoted ρ w ( d v ).
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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