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Suppose that and one of the following two conditions is valid: for ; for and is bijective.
Suppose that one of the following three conditions is valid: (i) for and ; (ii) for and is bijective; (iii)(ii) holds and.
Step 3: Test if either of the terminal conditions is valid: 1) the modified forecasting error (x_{t,1} = p_{t}^{F,1} - p_{t},{kern 1pt} quad t in DB^) meets the required precision; 2) the modification order has reached the scheduled number.
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All presented equations and conditions are valid for tankers.
In the Wilhelminenstollen, controllable hydraulic boundary conditions are valid.
We suppose that such conditions are valid: (i).
Assume that and the following conditions are valid: (224).
Furthermore, it enabled us to deduce if the results recorded from other conditions were valid.
Proof: The hypotheses imposed on f, c and d imply that the following conditions are valid.
The consistency of these specifications can be guaranteed by proving that some automatically generated verification conditions are valid.
The p-value for diff-in-Hansen test suggests that additional moment conditions are valid for the system GMM model.
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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