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The phrase "are only dependent on" is correct and usable in written English.
It can be used when discussing a situation or condition that relies solely on specific factors or elements.
Example: "The success of the project is only dependent on the team's collaboration and communication."
Alternatives: "are solely reliant on" or "depend exclusively on".
Exact(25)
The coefficients are only dependent on the non-integer orders.
The obtained results are only dependent on the Lipschitz-like constant matrices without regard to the nonlinear forms.
References [20, 32] investigated the passivity of NNs with time-varying delay, in which the input and output variables are only dependent on the time.
In this paper, P1‒P3 are only dependent on the geometric parameter of the hinge, and thus they are named as fundamental integrations.
Furthermore, the widths of these plateaus are mainly determined by the lattice structure and inter-stack coupling, and the heights are only dependent on the lattice structure.
It can be observed in (11) that the concerned interferences are only dependent on the sampling value of the ECIR, yet they do not relate to the value of ECIR at any other time.
Similar(35)
The demand is only dependent on the initial facing assignment and does not change between replenishments, when one of several facings are empty.
where C is only dependent on and, not dependent on.
where, the positive constant is only dependent on and, and is a sufficiently large positive number.
It is only dependent on the initial amount of drug that was incorporated.
which is only dependent on the solution of the problem in (16) and illustrated in Figure5.
More suggestions(1)
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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