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The phrase "improvement achieved" is correct and usable in written English.
You might use this phrase to indicate that progress has been made in a certain area, such as in the example sentence: "We are pleased to report that significant improvement has been achieved in reducing our environmental impact."
Exact(60)
How was this improvement achieved?
An obvious but potentially overlooked method is productivity improvement, achieved through process enhancements, for instance, or technical innovations.
The improvement achieved with the catalyst is established by comparison with a blank (reaction without catalyst).
To calculate the improvement achieved in organising care for patients without appointments after introducing corrective measures.
Small-signal analysis carried proves the improvement achieved by proposed architecture.
In this article, classification made on the parametric improvement achieved by adopting CLDs.
Results show the significance of performance improvement achieved by vanilla LSTM.
Thus, the improvement achieved in the protection of crops is outstanding.
Results exhibit outstanding performance improvement achieved by the proposed protocol for all metrics.
The directivity improvement associated with the third director is moderate (~33%) compared to the improvement achieved by the second director (~54%).
Extensive experimental results illustrate the performance improvement achieved by this strategy over the traditional one for a variety of situations.
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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