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The phrase "denoted with the same" is not correct in standard written English
It may be intended to express that something is represented or indicated by the same term or symbol. Example: "The variables in the equation are denoted with the same letter to indicate their equivalence."
Exact(2)
(With this convention, the group action and the induced action are denoted with the same symbol).
Suppose, by contradiction, that c* < c 0. Consider the harmonic extensions (denoted with the same notations) on Ω of g i 's and of g and introduce.
Similar(58)
We denote with the same letter H its self-adjoint extension.
Instead, we trained the chimpanzees on specific associations between arbitrary pairs (denoted here with the same numeric index), involving arbitrary associative dependencies.
Each QL is configured with the packets denoted by the same QL index, where the QL with QL index 1 and each of the other QLs are BL and EL, respectively.
The frames each of which is configured with the packets denoted by the same frame index can be coded by using the temporal prediction of the hierarchical-B structure in order to improve the coding efficiency and to enable the temporal scalability[12].
In the RadA-AMP-PNP 61 right-handed filament, the guanidinium group of R0 forms salt bridges with the carboxyl groups of two glutamate residues: Glu96 (denoted "E1") of the same protomer and Glu157 (denoted "E2") of the neighboring protomer.
Another key finding was that patients with pathological T1 ESCC denoted the same tendency.
For a cube (Qsubsetmathbb{R}^{n}), we use (l(Q)) to denote the side-length (l(Q)) and cQ to denote the cube with the same center as Q but with side-length (cl(Q)).
For we use to denote the cube with the same center as, but with sidelength of.
We use to denote the ball with the same center as and with,.
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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