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The phrase "considered problem" is correct and usable in written English.
You can use it to describe a situation that is widely accepted as a problem and is being given serious attention. For example, "Climate change has become a considered problem that requires immediate action."
Exact(59)
Those meeting three or four criteria are generally considered problem gamblers at risk of developing more serious gambling addictions.
The considered problem is NP-hard.
The considered problem is illustrated with a calculation example.
Figure 1 shows the geometry of the considered problem.
Now, let us introduce our main considered problem.
To our best knowledge, no paper has considered problem (1.1).
So, by this corollary, the considered problem has solutions.
The CRB for the considered problem has also been derived.
The considered problem can be reformulated as follows.
We prove that the considered problem has the Volterra property.
Section 3 proposes the optimal solution to the considered problem.
Related(17)
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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