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Discover Ludwig"there exist some" is a grammatically correct and usable phrase in written English.
You can use it to introduce a list or group of things, for example: "There exist some common misconceptions about immigrants in the United States."
Exact(60)
If not, then there exist some λ ∈ ( 0, 1 ] and u ∈ ∂ Ω such that (3.10) holds.
Suppose this false, then there exist some and some such that while and for all unless.
By the separation theorem of convex sets, there exist some, such that (3.6).
If is not true, then there exist some and such that (221).
However there exist some difficulties.
There exist some drawbacks with local regions.
There exist some different results from the previous linear solutions.
For the geometrical nonlinear deformation, there exist some errors.
In fact, there exist some equivalent properties between them.
Since, there exist some points, such that (3.24).
There exist some important differences between conditions (2.2) and (2.5).
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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