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The phrase "a quite simple manner" is correct and usable in written English.
It can be used to describe a way of doing something that is easy or straightforward.
Example: "The instructions were presented in a quite simple manner, making it easy for everyone to follow along."
Alternatives: "a very simple way" or "an easy manner".
Exact(2)
By a proper selection of this cost function, we can design and implement algorithms in a quite simple manner, regardless of the availability of process and measurement noise densities.
As a promising tool for ultrafast material analyses, we propose to utilize the X-ray pulse which may be generated in a quite simple manner using subpicosecond electron linacs.
Similar(57)
It works in a quite simple fashion.
We came up with a quite simple idea, really.
Growth investing is also a quite simple concept.
Hydra shows a quite simple morphology presenting an advantage for modeling attempts.
THz pulse-imaging is a quite simple methodology and a pump and probe beam are used.
I have usually begun a play in quite a simple manner; found a couple of characters in a particular context, thrown them together and listened to what they said, keeping my nose to the ground.
The proposed algorithm establishes global stability results in quite a simple manner as it does not require formulation of error dynamics.
Rather, his words provided biographical information about Manolete in a clear, simple manner.
This conjecture characterises high-dimensional spheres in a very simple manner.
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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