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(The latter should thus be upper case "I", but older German uses upper case "J" for upper case "I").
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The results should thus be treated cautiously.
Thus, is upper semicontinuous with nonempty convex compact values.
Therefore, y ∈ Uz and thus U is upper semi-continuous.
Thus is an upper bound of, whence.
Thus is an upper bound of.
Thus, the BER is upper bounded by P1 + P3.
Thus, the per-flow throughput is upper bounded by.
Thus, are lower and upper solutions of (3.14), respectively.
They should thus represent an upper bound of the effect in reality.
This idea is corroborated by the experiences of patient F1, who had been told by her clinician that her superior (upper) vision was affected, and thus was confident she should avoid potential hazards within this location.
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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