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The phrase "are assumed here" is correct and usable in written English.
It can be used when stating that certain conditions or facts are taken for granted in the context of a discussion or argument.
Example: "In this analysis, several factors are assumed here to be constant, allowing us to focus on the primary variables."
Alternatives: "are taken as given" or "are considered to be true".
Exact(19)
The material properties of FG plates are assumed here to vary through thickness of plate in a continuous manner.
The material properties of FG plates are assumed here to be varying through thickness of plate in a continuous manner.
Two carriers are assumed here, which are allowed to play three different strategies: point-to-point (PP), hub-and-spoke (HS) or multi-hub.
In contrast with single-phase wall-bounded flow theory, shear-driven annular liquid films are assumed here to behave as fluid-bounded flows, mostly interacting with the shearing gas-entrained droplets core flow.
Without loss of generality, vanishing initial conditions are assumed here.
For simplicity, reciprocal channel conditions are assumed here as well.
Similar(41)
(We are assuming here that the man in question isn't in an arm lock or lip lock with a woman next to him).
That won't be assumed here.
It was assumed here that efficient anti-scale chemicals would be available.
The second strategy is assumed here, as it allows free horizontal motion and accurate landing.
A baffle is assumed here to have the shape of a thin annular circular plate.
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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