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The phrase "under different principles" is correct and usable in written English.
It can be used when discussing various foundational ideas or rules that govern a situation or concept.
Example: "The two theories operate under different principles, leading to distinct conclusions about the nature of reality."
Alternatives: "based on different foundations" or "according to varying principles".
Exact(1)
Participating laboratories operated under different principles, varying from exploratory research to good clinical laboratory practice (GCLP) and good laboratory practice (GLP).
Similar(58)
Ding et al. [11] studied a multiple source-destination pairs communication system under four different relaying strategies, i.e., based on different principles, the harvested energy from multiple sources is allocated among the different destinations by the relay node.
But our hall is based on different principles".
Rimington, though, argues the competition has different principles.
How did these very different principles work out in practice?
Remember that each person has different principles.
for many people, works on a different principle.
Microsoft, understandably, says a different principle is at stake.
Here, we develop a population genetic model to investigate the effect of recombination between mean- and variance-modifiers of phenotype on the geometric mean principle under different environmental regimes and fitness landscapes.
To investigate variation of microbial community structures in bones exposed to different environments and under different taphonomic conditions, a Principle Component Analysis (PCA) was performed using PC-ORD (MjM Software Design, Gleneden Beach, OR).
Therefore, it is of interest to investigate the relationship between the two, for different drugs and under different conditions, to discover what general principles exist.
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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