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The mapping defined by.
Nevertheless, a mapping defined by.
and, is the mapping defined by (2.8).
Consider the mapping defined by (3.7).
We consider the mapping : defined by (320).
Let be the mapping defined by.
The mapping, defined by, is continuous in.
Consider a mapping defined by (3.5).
Let be a mapping defined by.
For each, the mapping defined by (2.1).
Consider the mapping defined by, for all.
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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