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The structure of a star is uniquely determined by its mass and chemical composition.
Moreover, by the axiom of extensionality, this set X is uniquely determined by ϕ(x).
Eudoxus said, in effect, that a point on the line is uniquely determined by its position among the rationals.
Consequently, is uniquely determined by.
Note that (n) is uniquely determined by (M).
We note that such a matrix is uniquely determined by.
Therefore, in Step 2 is uniquely determined by.
In this case c is uniquely determined by y.
Hence λ (if exists) is uniquely determined by ρ.
The maximal sectorial operator A is uniquely determined by condition (i).
Hence the length (|J_{1}|=eta_{1}-xi_{1}) is uniquely determined by the parameter τ.
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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