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Discover Ludwig"there exits" is a correct usage of the English language.
You can use it to refer to a location, situation, or circumstance that is existing or present. For example, "There exits a strong sense of community in this small town."
Exact(60)
(5 For, there exits, such that (2.7).
Since, then there exits a constant such that a.e.
If is bounded below, then there exits such that (2.13).
If φ is bounded below, then there exits z ∈ X such that.
If such that do not vanish for any, then there exits such that (2.20).
For,, then there exits a constant independent of and such that (4.6).
Recently, in [3], Cuesta proved that if is sectorial operator for some,, and, then there exits such that.
Topological analysis of electron density reveals that there exits intramolecular hydrogen bonds in Py-based copolymers, which is in favor of improvement of the coplanar conformation for them.
Hence { δ n } is a non-increasing sequence which is bounded below ( 0 ≤ δ n ), then there exits some δ ≥ 0 such that lim n → ∞ δ n = δ.
(ii) Assume that there exits such that.
Assume that there exits such that.
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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