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The phrase "correspondingly in" is grammatically correct and can be used in written English.
It is used to emphasize a certain comparison between two or more things. For example, "The temperature outside dropped correspondingly in the house" implies that the temperature outside and the temperature inside the house decreased simultaneously.
Exact(59)
Correspondingly, in these books Simenon tends not to give us the violence straight on.
Correspondingly, in nontribal societies, cultic functions belong to the office of the king.
Correspondingly, in ways beautifully enhanced by the staging and production design, all the world -- or at least most of Cyprus -- becomes Iago's stage.
Their earnings rose correspondingly in the decade, by nearly 16percentto to $20,790, though that still left them making far less than men.
Correspondingly, in the numerically evaluated results, we used β = 1.
Drivers who used both SQC FCWs performed correspondingly in their car-following behaviors.
The fitting results are presented correspondingly in Tables 2 and 3.
Correspondingly, in Fig. 4(a), the distribution exhibits an appearance of point cloud.
Correspondingly, in Fig. 9, the running times are depicted as a function of N P.
Correspondingly, in these environments, customer co-creation in NPD requires multi-issue negotiation with issue trade-offs.
Similar(1)
The second and third, the out- correspondingly in-degree of the gene in the TRN.
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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