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The first involves the murder of a colleague at Edenvale College in Toronto -- a murder that, as in traditional detective stories, is duly solved by Smiricky, the clues leading logically to a tidy if complex solution.
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The interaction between frictional forces of sliding system in two horizontal directions is duly considered and coupled differential equations of motion of the system are solved in the incremental form using step-by-step method with iterations.
"Solve any problem" is his motto, and he duly sets to work on the glitches in Michel's existence.
Duly, Nigel was encouraged to shove on a frock and do a bit of circumspect "tidying", which didn't solve much, but we got to have a gawp.
Duly noted.
He duly fell short.
He duly obliged.
He was duly dissuaded.
All right — duly warned?
Evans duly converted.
Jonathan Trott and Ian Bell duly performed it.
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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