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The phrase "actually established by the" is correct and usable in written English.
It can be used when discussing the origins or foundations of something, often to clarify or emphasize the legitimacy of that establishment.
Example: "The regulations were actually established by the governing body to ensure compliance and safety."
Alternatives: "truly created by the" or "genuinely set up by the".
Exact(2)
However, this was not actually established by the authors.
In general, the connection between candidates, i.e. unions of disjoint intervals and the combinatorics of structures is actually established by the algorithm itself via backtracking: at the end of the DP-algorithm a structure is being generated that realizes the previously computed energy as mfe-structure.
Similar(58)
This relation between and or and is actually established by using the change-of-basis matrix W1/2 defined by Eq. (10).
#2: "The need actually will probably be established by the clinical fraternity....All you have to do after that is convince the people on down the chain, from the hospital clinical researchers right down to the guy in the street who says 'It's a good idea to have one of these.
However, this topological structure is sufficiently explained by the planarity of the graphs, and in fact the topological patterns established by the transportation links actually serve to reduce the amount of small-world structure.
Knowing to which extent the rights of hospitalized children established by the charters are actually respected is of paramount importance for planning measures aimed at guaranteeing the rights of sick children and their psycho-physical wellbeing in the hospital.
The administration ended up using the Clean Air Act, legislation signed in 1970 by Richard Nixon that actually established the EPA.
On the ohther hand, amici claim this language somehow erases such distinctions by deeming Exchanges to have been "established by the State" no matter who actually established them.
However, Weyble says, guidelines that were well established by the 1990s showed that the swirl was actually caused by a condition caused flashover, which occurs when built-up heat from an enclosed fire causes the spontaneous ignition of combustibles.
Now it turns out that some framework of universal entitlement, established by the principles of justice, solidarity and humanity, would actually be quite helpful.
Evaluate your options based on how well they actually address the issue and how well they fit into any internal procedures already established by the company.
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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