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"while there exists" is a correct and usable phrase in written English.
It is typically used to describe a situation that is ongoing, or that is expected to be ongoing for a certain amount of time. For example: "While there exists a need for increased access to quality healthcare, our organization strives to provide resources and support to our members."
Exact(46)
While there exists, happily, no "cynicism commission" to prevent columnists from indulging in merriment over what they regard to be folly, it would be folly no less to dismiss the idea that taxpayer-financed art should be accountable to taxpayers.
While there exists a colonial tradition of relegating the non-west to the past of the west – and some suggest leaving it to rot in hopelessness – the trendier option involves incorporating Afghans into modernity by teaching them to live in a globalised present.
While there exists channel measurement of broadband communication system including WCDMA [20] and LTE [21].
While there exists limited data on enforcement, it appears unvigorous (National Highway Traffic Safety Administration 2004; Borglund et al. 1999).
While there exists a rich literature on estimation consensus, detection consensus problems only recently started to receive attention.
While there exists a broad range of models, methods and tools for the development of goods, the development of services has hardly become a topic of scientific literature.
Similar(14)
The specific power output is found to be a decreasing function of the internal irreversibility parameter and isobaric temperature ratio while there exist the optimal values of the state point temperatures at which the specific power output attains its maximum value for a typical set of operating parameters.
All these worked separately and while there existed opportunities to strengthen synergies, these opportunities were not explored.
While there exist in the literature some algorithms to reconstruct sbTSTC phylogenetic networks from biological sequences, no distance metric was known on this class that is both mathematically consistent and computationally efficient.
While there exist brilliant academics who are dedicated to higher education, they seem to be in the minority.
"The most undesirable effect of the inter-Korean summit is that the nation is now seized by a euphoria as if the threat of a war has disappeared and unification is already achieved, while there exist no real changes," said Lee Hoi Chang, head of the conservative Grand National Party.
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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