Exact(3)
If and, can be chosen arbitrarily subject to (10) and (12).
The optimal, when these two conditions are met, is given by (15) (ii) If and, can be chosen arbitrarily subject to (10) and (12).
The value of α is selected arbitrarily, subject to the condition that it be sufficiently smaller than unity; this probability is as a surrogate for the velocity of sand particles.
Similar(57)
"If a manual recount gives effect to partially punched ballots, or counts ambiguous ballots based on the canvassing boards' subjective interpretation of voters' intent, it arbitrarily subjects voters in other counties to unequal treatment," the suit maintains.
"If a manual recount gives effect to partially punched ballots, or counts ambiguous ballots based on the canvassing boards' subjective interpretation of voters' intent, it arbitrarily subjects voters in other counties to unequal treatment in violation of the 14th Amendment," reads the "complaint for declaratory and injunctive relief" that is the basis for Monday's scheduled hearing.
These children are often allowed to roam the streets unchecked, but then arbitrarily subjected to harsh punishments.
Immigrants at the facility are also routinely and arbitrarily subjected to solitary confinement and receive sub-minimum wages of $1-$1-$4day for a full day of work.
Resultant E. coli colonies were picked arbitrarily and subjected to single-pass sequencing from the 5′ end of the cDNA insert.
Three stroke subjects were arbitrarily selected from normal subjects, patients with acute stroke, and patients with stroke sequela, respectively.
A postdoc we'll call Maura Lee Upright had a PI who "outwardly expressed support for 'true' results but would often arbitrarily dismiss some subject's data [and] never published negative results".
Due to the lack of precise quantitative evidence on the relative empowerment potential of these factors (8), the questions were, arbitrarily, weighted equally, subject to future adaptation.
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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