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which is admissibly homotopic (in ) to the linear vector field defined by with (4.11).
Clearly, is admissibly homotopic to in.
which is admissibly homotopic (in ) to the tangent vector field, given by.
Observe also that is zero, because is admissibly homotopic in to the never-vanishing vector field given by.
Then, there exists a local tangent vector field on which is admissibly homotopic to in and such that is a nondegenerate pair.
Instead of defining a maximum admissible debt ratio, some tax jurisdictions limit the fraction of net earnings to be admissibly spent on interest.
"Small" is generously defined.
Nothing is really defined.
Unfortunately, deservingness is not defined.
Furthermore, how is attendance defined?
"The problem is sharply defined.
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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