Exact(10)
Clearly, there holds the relation for all (see [27]).
Then if and only if it holds the relation: (2.3).
As we all know if and only if there holds the relation (2.3).
Given and, then if and only if there holds the relation (16).
Clearly, there holds the relation J φ ( x ) = φ ( ∥ x ∥ ) ∥ x ∥ J ( x ) for all x ≠ 0 (see [2]).
Then (z=P_{K}x) if and only if there holds the relation langle x-z,y-zrangleleq0 quadtextit{for all } yin K. (See [17]).
Similar(50)
Given x ∈ H and z ∈ C. Then z = P C x if and only if there holds the relations: x - z, y - z ≤ 0, ∀ y ∈ C. (2.1).
It is easy to check that one holds the relations ° g AB = e A A ¯ e B B ¯ ° g ¯ A B ¯ Open image in new window.
The value of p is determined so as to hold the relation of (0 le alpha le 1).
This assumption set the clearness index, k T, to 1 and held the relation between the beam and sky-diffuse components of insolation in Equation 17 constant.
The Court remarked that the Senecas were "in a state of pupilage, and hold the relation to the Government as a ward to his guardian".
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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