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It can hold this case in reserve as a means to seek additional assets once it sees how the criminal prosecution unfolds.
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We showed in Section 2 that axiom (A3) does not hold for (integrals based on) SFAPs, so by Remark 2.11, the mean value theorem does not hold in this case.
Theorem 1 will hold in this case.
The same observations with the top 100 cases also hold in this case.
But a carefully designed counterexample shows that the opposite does not hold in this case.
However, the nucleation and growth mechanism may hold in this case.
Obviously, the area law will drastically fail to hold for this case.
In fact, Corollary 2.1 does not hold for this case (see Sung [18]).
It is clear that condition (2.7) does not hold in this case.
end{aligned} (3.41) It is obvious that (3.28) and (3.29) still hold for this case.
Consequently, α ∗>0 must hold in this case, which completes the proof of Lemma 1.1.
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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