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The phrase "here arises the problem" is grammatically correct and can be used in written English.
It is a formal way of stating that a problem has emerged or become apparent in a particular situation. Example: "Upon analyzing the data, here arises the problem of a significant decrease in sales figures for the past quarter."
Exact(2)
Here arises the problem: how?
However, here arises the problem, for some nonshadow regions with low-intensity surface features may be identified as shadows, such as black cars or buildings.
Similar(58)
There then arises the problem of where.
This approach is more appropriate to cultural services, but here arises another problem, of how representative an expert is of the wider population's values.
Here arises a problem unique to humans.
The problem here arises from the large amount of information generated in the learning process, which hinders professors to meet each student's learning profile.
In this regard, the difference between the two groups studied here arises from the predilection of a problem signaled by a single notification for late detection.
"The lion's share of the problems here arise from cost issues," she added.
Here's where the problem arises: The trust referred to in the will only mentions Cooper, not his two younger sisters who were born after the will was signed.
And here is where the problem arose in 1996.
And here is where the problem arose.
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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