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"This ability to edit and manage a campaign in real time as it happens has never existed globally before".
No such actionable hotline database has existed globally — but it doesn't need to be that way.
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We will prove that ( φ ^ 1, …, φ ^ k ) cannot exists globally, thus contradicting the global existence of (u1, ⋯, u k ).
Therefore, we get is a global supersolution of (1.1)–(1.3) and hence the solution to (1.1)–(1.3) exists globally by Proposition 2.4.
They established the existence of a critical length (a_) and proved that the solution exists globally if (0< a< a_), while the solution quenches if (a>a_).
Research on think tanks outside the Western world indicates that an even greater variety of organizations may exist globally.
It's a bold project, but one that seems to me strangely out of step with how Shakespeare already exists globally, in a jumble of languages, variations, refashionings, performance styles.
Opportunities exist globally in the neurosciences.
Hence, exists globally.
All solutions to (1.1)–(1.3) exist globally.
Therefore, the solution ((u,v)) of (1.1) exists globally.
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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