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The phrase "a problem is encountered" is correct and usable in written English.
It can be used in contexts where you want to describe a situation in which an issue arises or is faced.
Example: "During the experiment, a problem is encountered that requires immediate attention from the research team."
Alternatives: "an issue arises" or "a challenge is faced."
Exact(4)
Cleanup of excessive warnings when a problem is encountered.
Such a problem is encountered when laser-Doppler velocity measurements are carried out in acoustics.
A problem is encountered at the outset, however, for terms such as beautiful and ugly seem too vague in their application and too subjective in their meaning to divide the world successfully into those things that do, and those that do not, exemplify them.
This is consistent with a relatively low per-base probability (∼6 × 10−4) that a problem is encountered during gap filling over the range of gap sizes observed.
Similar(56)
If a problem was encountered that was considered to affect the results of testing, the femoral head was discarded.
When a clustering problem is encountered, the researcher must be aware that choosing an incorrect clustering method and distance measure may significantly affect the results of the analysis.
A similar problem is encountered in the participant-based experiment because the number of participants was not high enough to represent expressive scenarios.
However, a methodological problem is encountered in deriving the industrial structure matrix in terms of its invariance to the two linkages, as described in the following section in detail.
Residents who perform the job, decide in favor of C-section as soon as even a small problem is encountered due to their lack of experience.
In this paper, the modified polynomial expansion method is developed to solve problems of identifying the time dependent heat source, in which an inverse problem is encountered.
When a dependency loop or other revision problem is encountered, a Real Human has to apply a considerable amount of systems expertise to resolve the problem.
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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