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Note that the operator K N has the following properties.
Note that the operator G 0 is odd.
Note that the operator has the following properties.
Note that the operator P : V ¯ → C ( [ 0, T ], R ) is continuous and completely continuous.
Note that the operator F : U ¯ → C ( [ 0, 1 ], R ) is continuous and completely continuous.
To begin, note that the operator (S Bto B) is continuous and completely continuous.
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Note that the operators L n a and ℓ k a are computable by construction.
Note that the operators f ˜ k were defined in Eq. (38).
Note that the operators L ( m 2 p − 1 m 2 p ) form a maximal abelian subalgebra which proves that the system algebra has rank d.
Similarly, by using the conditions of Theorem 3.2 [38], we note that the operators T and g are in fact strongly monotone.
end{aligned}Note that the operators (varepsilon (varphi _1)) and (mu (varphi _0)) increase the (mathbb {Z} -degree of (mathfrak {a}(V)) by one, while the operators (iota (v_1)) and (delta (v_0)) decrease it by one.
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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