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The phrase "achieved for a set" is not correct and lacks clarity in written English.
It may be intended to convey a specific accomplishment related to a defined group or collection, but it requires additional context to be meaningful.
Example: "The results achieved for a set of experiments were impressive, demonstrating significant improvements."
Alternatives: "attained for a group" or "accomplished for a collection".
Exact(1)
According to the theory given above, the requirement for a direct observation number of, say, 100 collisions for the first block is achieved for a set of about 1 × 1011 InChIKeys which would require 3 terabytes just to store the keys.
Similar(59)
Here Dr. Sager showed that for a set of discharge letters a recall of 92.5% and a precision of 98.6% could be achieved for a limited set of pre-selected data using the parser produced by the Linguistic String Project at New York University [ 1- 3].
The process model obtained by the empirical relation can predict how much strength can be achieved for a given set of the process parameters, thus providing prior knowledge of part strength before actually making a SL part.
Structural code-coverage criteria are metrics to analyze and quantify the control-flow coverage that is achieved for a given set of test data.
Good to moderate interrater reliability was achieved for a final set of three timing codes: Before the Workshop (kappa = 0.77); During the Workshop (kappa = 0.69); and After the Workshop (kappa = 0.45).
Therefore, comprehensiveness can be achieved for a limited set of features, in a specific landscape, and at a limited spatial resolution – not for all features, everywhere, and at high resolution.
Energy balance must be achieved for an illumination set. .
Energy balance must be achieved for an illumination set.
Reconstruction of ancestral sequences can in principle be achieved for any set of homologous sequences, including for example viral polymerase sequences.
Due to the scarcity of the data, the optimal prediction (76%, 41 out of 54 true) is achieved for a rather large set of threshold values.
Better results may be achieved for a lidar measurement set-up which is adapted specifically for investigating coherence.
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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