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The phrase "under this notion" is grammatically correct and commonly used in written English.
It is typically used to introduce a concept or idea that is being discussed or analyzed in a sentence. Example: Under the notion of "survival of the fittest," it is argued that competition among individuals drives evolution.
Exact(7)
Under this notion, American troops would also seize the oil fields around Basra, in southeastern Iraq, and sell the oil to finance the Iraqi opposition in the south and the Kurds in the north, one senior official said.
Under this notion, systems are classified into consolidated, quasi-consolidated, neutrally consolidated, unconsolidated, quasi-unconsolidated and mixed types.
Under this notion, Ostrom developed eight design principles to which self-governing institutional arrangements adhere, while the role of the state is minimal.
Under this notion, it is interesting to note that the apoptosis-inducing activity of LJK-11 appeared to be selective comparing to its universal anti-mitosis activity.
Under this notion, the same circular string can be seen as n different linear strings, which would all be considered equivalent.
Under this notion, the modular approach filtered the differentially expressed molecules, as derived from classic statistical tests, to a smaller more reliable set and more importantly contextualized them into neighborhoods.
Similar(53)
"It's a feel-good message, but under that is this notion of normality, which is deeply repressive and exclusive," said Luke Timothy Johnson, a professor of New Testament at Emory University and a former priest who has written critical articles about theology of the body.
Today's meeting (you can track it via the Twitter hashtag #gnh) reflects a global build-up of this notion under other names, as an array of nations and agencies develop systems for measuring well-being that go well beyond what can be measured in dollars.
Formally, the robustness of the system is defined as: (4) where ϕ is the specification of the functionality in temporal logic and T p is the trace representing the behavior of the system under perturbation p. This notion of robustness corresponds to a mean functionality, that is, describes on average how the system behaves under perturbations.
Hence both substance and accident are included under this analogous notion of being and this single object of the intellect (PB 2.135 36; Wippel, 1981, 19 24).
In Syria, Libya and Afghanistan this notion is under threat as warlords and insurgents vie for local power, ignoring our state boundaries.
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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