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The phrase "under certain assumptions" is grammatically correct and can be used in written English to describe a situation or statement that is based on specific conditions or beliefs.
Example: "Under certain assumptions, the experiment yielded accurate results. However, these results may vary if the initial conditions are changed."
Exact(60)
The observer is globally asymptotically stable under certain assumptions.
A rigorous stability proof is provided under certain assumptions.
We show that under certain assumptions, this isosurface is optimal in the least squares sense.
The two models are theoretically equivalent under certain assumptions, hence are expected to yield similar results.
The protocol is proved to be optimal and energy efficient under certain assumptions.
We show that TS fuzzy modeling is equivalent to the ISSVR problem under certain assumptions.
The training algorithm is based on a Kalman filter, stable under certain assumptions.
Under certain assumptions, an explicit solution to the minimax problem is obtained.
We show that, under certain assumptions, the original update postulates are satisfied.
We show how to choose an access order such that, under certain assumptions, imposing that order incurs no performance penalty.
Under certain assumptions, the same fundamental equation relating torque to friction coefficient can be used for both machine elements.
More suggestions(15)
under certain situations
under specific assumptions
under certain conditions
under certain circumstances
under certain criteria
under certain hypotheses
under given assumptions
under some assumptions
under specified assumptions
under certain temperatures
under mild assumptions
under certain regimes
under certain guidances
under suitable assumptions
under traditional assumptions
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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