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The phrase "after this delay" is correct and usable in written English.
It can be used to refer to a period of waiting or postponement that has just occurred before proceeding with an action or event.
Example: "After this delay, we can finally move forward with the project timeline."
Alternatives: "following this delay" or "subsequent to this delay".
Exact(8)
After this delay, a partition opened, leading to a flowerpot full of scented sand.
The catalysis required a certain contact duration between electrodes and live bacteria but after this delay, the metabolic activity of cells was no longer necessary.
After this delay, the OMR of the single fish was recorded for 70 seconds.
This implies that the benefit of the drug after this delay has not been evaluated.
After this delay, the fixation point was extinguished, instructing the monkey to make a saccade to the location of the target.
After this delay and again three months later, the participants performed an associative memory task on pairs of pictures with different relational distances (direct, inference of order 1 and order 2).
Similar(52)
These peaks only caused a few changes in the length of the tracks in regions 1 and 2. After this delayed reaction, which is consistent with the speed reduction and sinking of spheroids after a dark-light switch described above, the relative length of the bead tracks in all analyzed regions at the anterior pole changed with the same frequency as the fluctuations in the light intensity.
Extubation failure was defined as death or the need for reintubation within 72 h (1) after extubation; this delay was prolonged to 7 days (2) in case of noninvasive ventilation after extubation, which was systematic in older patients or those with cardiorespiratory disease, as per our weaning protocol.
While in the case of "Off-set 9, High-Visc" oil production started after 4 years, this delay decreased to only 3 months in the case of higher fracture permeability.
After tumors escape this delay they resume growth at rates similar to the other groups.
Overall, female TT took place on average 21 days after oviposition, and this delay was not significantly different between males and females (males: mean ± SD = 20.53±2.07 days, females: mean ± SD = 20.87±3.54 days; t-test: t = −0.315, df = 28, P = 0.755).
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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