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"under this description" is correct and usable in written English.
You can use it to refer to a description that is being provided or alluded to in the context. For example: "She described the house as having an elegant appearance; under this description, I could imagine the large windows, gleaming hardwood floors, and beautiful furniture."
Exact(8)
And it was under this description that it won its second prize of 1984, the Pegasus Prize for Maori Literature.
All those who fell under this description would automatically become members.
Most explanations in disciplines like biology, psychology and economics fall under this description, as do a number of straightforwardly physical explanations.
Under this description, rational theology belonged to scientia indeed, it was the "queen of sciences"—because its premises were the highest and most certain.
Under this description, the PBL process models are semi-structured, since there is no schema to constrain the depth and degree of the processes.
Under this description, a sharp visual experience would correspond to a posterior density function that is tightly focused around the actual location of the edge, while a blurry experience would correspond to one in which the density function if more broadly distributed.
Similar(52)
They describe the behavior of the system under ideal condition, though this description may not always be verifiable in true or real markets.
This description falls under the heading of "Collective Person" (Gesamtperson).
Nothing known about the case suggests that this description will stand up under examination.
We will expand on this below under the description of Mokken scaling.
This was grouped under the description of "asocial" and coded as a Negative Stereotype.
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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