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A careful proof of this property has been made in [6].
And even the most careful proof reader can miss the absence of a negative sign in text he or she has written and read many times, so inadvertent mistakes in published papers are an unfortunate feature of the scientific literature.
The authors thank Prof. Dr. Michael F.G. Schmidt, Freie Universität Berlin, Germany for kindly providing the IPEC-J2 celineine, and Yangzhou University, China for kindly providing E. coli strains 8813 (F18ac ETEC) for this study as well as visiting Scholar Dr. Miro Ferreri from Germany for his careful proof reading of our manuscript.
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A few trial runs, some careful proofing and numerous small adjustments later (a tiny piece of newsprint stuck onto the packing can make all the difference), the finished job emerges: crisp, tangibly different, immensely satisfying.
We thank Mary-Ann Schneider for careful proof-reading of the manuscript.
We thank Joshua Stevens-Stein for his careful proof-reading.
Following careful proof-reading (ISPOR stage 9) by all sites, this produced agreement on the final CDIS with staff and service user versions in five languages.
This work has been generally well supported by government, academic institutions and businesses and many people make their living in medical research governed by careful statistical proof.
But the truth is, many of them are more careful about proofing their work than traditional publishers seem to be.
One must be careful in mathematical proofs as to what are the premises.
This follows by a careful inspection of the proof of [16, Proposition B.15, Theorem B.16].
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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