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More precisely, let us introduce the following.
To state our result precisely, let us give our setting.
More precisely, let us first recall some related notations.
To state this more precisely, let us introduce the notion of a contraction.
More precisely, let us recall the notions of Hadamard well-posedness and generalized Hadamard well-posedness.
More precisely, let us start with the next double inequality (2.1).
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More precisely, it will let us detect low frequency alleles, which might have been or will be selected for a clonal expansion in the evolution of that population.
Before we state the core idea of UMP alphabet, let us precisely define catastrophic parameters and state a couple of important lemmas based on them.
An old puzzle is puzzling precisely because our intuitions let us down on this point: Imagine a chessboard with $1 on the first square, $2 on the second, then $4, $8, $16 and so on.
But BP won't be allowed to move on until we know precisely how shamefully the company let us all down.
The famous "Lubitsch touch" is the way he puts his finger on things off-screen that he can't show on-screen, and Hawks's comedies, with their scintillating and borderline-smutty symbols of unexpressed desires and deeds, let us know precisely what he wasn't allowed to tell us.
Write better and faster with AI suggestions while staying true to your unique style.
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