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Hence, the variation of the parameters can be defined the same as in the previous part.
Proof For each x ∈ X, let Λ ( x ) be defined the same as in Theorem 3.1.
Let G t, s) be defined the same as that in Lemma 3.2, then the following properties hold.
Let H = ℝ and the self-mapping T of be defined the same as in Example 2.18.
Let H = ℝ and let the self-mapping T of H be defined the same as in Example 2.17.
Transitioning gender isn't something Isis takes lightly, but it's also something that can't be defined the same way for every person.
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The order and degree of partial differential equations are defined the same as for ordinary differential equations.
If the proposer requests a constraint, the groups for calculating the constraint values are defined the same as for slew tax calculations.
And these figures fail to show the problem's real extent since the poverty level is defined the same throughout the continental United States: $20,650 for a family of four.
A strict definition is less important than ensuring that the backscale for the source dataset and its associated background dataset are defined the same, because only the ratio of source and background backscale is used in analyses.
The target is defined the same as for atomic policies.
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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