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"based on only the" is a grammatically correct phrase and can be used in written English.
It is typically used to introduce a condition or limitation in a statement or argument. Here is an example: "His decision was based on only the information provided by the witness, so it may not be entirely accurate."
Exact(60)
We compared two methods for predicting muscle activities and postures, based on only the distribution of keyboard/mouse/idle tasks (task-based predictions) or on a comprehensive set of 104 task, questionnaire, workstation, and anthropometric parameters (expanded model predictions).
The current results are based on only the first third of the full telescope survey.
Grain boundary energy depends on all five parameters although simplified descriptions based on only the angle is sometimes sufficient.
The analysis and design of engineering systems based on only the first law is not adequate [1].
The investigators' report, based on only the district's side of the story, claims that we were "irresponsible" for saying the superintendent "overreacted" by calling the police.
For production in China, the factor is based on only the relative CED and GHG-footprint of Chinese electricity (over time).
Smart clustering using discrete optimization algorithms leads to a design load reduction of up to 13% compared to designs based on only the highest loaded turbine position.
Admission control based on only the bottleneck tier is not efficient as different sessions impose different resource consumptions at the different tiers.
To avoid the design complexity and computational load, both the observers are designed based on only the component mole balance equation around the reflux drum.
The review summarizes the need of evolutionary SI method that automates the model structure selection and its parameter evaluation based on only the system data.
The frequency-response-function (FRF) curvature method encompasses the first three referred steps being based on only the measured data without the need for any modal identification.
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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