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So, pending an unforeseen satisfactory analysis of "a exists," this proposition will have to be analysed as a complex of propositions not involving a.
A is said to be a sectorial operator of type ((M,theta,q,mu)) if there exists (muinmathbb{R}), (00) such that the q-resolvent of A exists outside the sector (mu+S_{theta}={mu+lambda^{q}:lambdainmathbb{C},|operatorname{Arg} -lambda ^{q} -lambda}) and (|R(lambda^{q},A)|
Similar(58)
"The possibility of a recall exists," Alfredo Avella, president of the electoral council, told reporters today.
Consequently, the possibility of a trade exists.
Part of a diary exists from that period.
If a culture of kindness exists, a troll will have a harder time spewing rage.
If a state of affairs obtains, then an obtaining state of affairs exists, a fact exists.
Only fragments of a government exist.
No wonder stories of a jinx exist.
(Neither man would say how much of a gap existed).
A continuation of what exists – not a true category break.
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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