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"Preliminary facts show that the decision was wrong.
ScienceNOW reported preliminary facts and figures yesterday.
We first recall some preliminary facts.
This section is devoted to some preliminary facts.
Section 2 contains preliminary facts we need in the paper.
In the second part, we give preliminary facts and definition.
In this section, we introduce notations, definitions and preliminary facts.
In Section 2, we recall some definitions and preliminary facts.
In this section we collect preliminary facts for future reference.
In Section 2, we introduce notations, definitions, and preliminary facts.
In this section, we introduce notations, definitions and preliminary facts which are used throughout this article.
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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