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Exact(59)
Then there exists a (xin M) such that (x=Ax+Bx).
Then there exists (xin M) such that (x=Ax+Bx) provided (alpha+beta<1).
From ((H_{3})), there exists a positive constant M such that (Vert xVert ne M).
In view of ((S_{4})), there exists positive M such that (Vert x Vert neq M).
There exists Q ∈ M such that.
There is an m such that (xin V_m).
Then, there exists z ∈ M such that z = Az + Bz.
Then there exists (zin M) such that (z=Az + Bz).
If G acts effectively on M such that.
Fix m such that (3 leq m < v).
Similar(1)
Find m ^ such that f (m ) is minimized subject to G E m ≤ s 1.
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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