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The phrase "assumed to be given" is correct and usable in written English.
It can be used in contexts where something is taken for granted or accepted as a fact without needing further proof or explanation.
Example: "In this analysis, we will consider certain variables as assumed to be given in order to simplify our calculations."
Alternatives: "taken as given" or "presumed to be provided".
Exact(60)
Lead times were assumed to be given constants and the net present value principle was applied.
The distributed source is assumed to be given in terms of piecewise space time Chebyshev polynomials.
Here, the characteristics of the network are assumed to be given and the focus has largely been on the controller.
The lift wind force is assumed to be given by a general fifth order polynomial in the effective flow incidence.
The relation between the angular range of α- and β-lines within the secondary shear zone is assumed to be given by the linear equation β = m0α.
Also the time-evolution of the socio-psychological position of members of the public was assumed to be given by a Langevin-type equation.
In particular, the force in a spring element is assumed to be given as a function of the displacement from the equilibrium position.
(ii) One BGA specimen configuration was used to obtain the mode I fracture energy, and the peak stress was assumed to be given by the yield stress.
This means that the noise source is implicitly assumed to be given by a coherent line source, which is not realistic in most cases.
The volume fractions of constituent materials composing the FG panels are assumed to be given by a simple power law distribution.
The wave function is assumed to be given in a finite difference or finite element representation with polynomial completeness to an arbitrary but fixed degree.
More suggestions(20)
assumed to be received
assumed to be delivered
assumed to be conceived
assumed to be devoted
assumed to be involved
assumed to be derived
assumed to be perceived
supposed to be given
assumed to be left
assumed to be removed
suggested to be given
assumed to be certain
assumed to be available
seemed to be given
assumed to be bounded
assumed to have given
assumed to be reworked
assumed to be biased
taken to be given
believed to be given
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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