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The phrase "due reflection" is correct and usable in written English
It can be used when discussing the act of thinking carefully or considering something thoughtfully before making a decision. Example: "After due reflection, I have decided to accept the job offer."
Exact(16)
After due reflection, the firm decided that it could use another four lathes, at that.
Smallweed replies after due reflection: I guess you could say that, yes.
"Actually," admitted the 22-year-old from Oldham, after due reflection, "he seemed to have been out there a while by the time we turned up.
After due reflection I decided that it would be preferable, at least initially, to take a high-paying job in journalism and sacrifice a small proportion of the masterpieces to expediency".
But the observation was unnecessary to the decision, and in that sense extrajudicial, and, though made by one who seldom used words without due reflection, ought not to outweigh the important considerations referred to which lead to a different conclusion.
Naturally, when we've been talking about a subject as full of implications as the subject of our family conference that evening, every question must be weighed respectfully and with due reflection.
Similar(44)
P ref for the smaller fibers is mainly due to reflection at the tips, whereas reflection from the base and backplane is included with values for the larger fibers.
The primary loss mechanisms are expected to be Fresnel reflections (R), mode coupling, radiation, and loss due to reflection towards the source.
Simovski and co calculate that an ordinary anti-reflection coating about 7percentnt of the light is lost due to reflection while 46percentnt is lost to transmission.
But the onset due to reflection from the first surface is maintained in the time profile and hence the time delayed reflections appear as background noise in our reconstruction.
The white areas are due to reflection off the metal lines of the TFT.
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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