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Let (underline {k}) be the maximal element of Λ f.
Otherwise, let (underline {k}^{prime }) be the maximal element of (Lambda _{X}^{prime }).
Let (underline {k} = (k_{1},ldots,k_{n})) be the maximal element of Λ.
Let (underline {k}) be the maximal element of Λ X and (Lambda _{X}^{prime }) be as in section 3.4.1.
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Now let ([c_1], ldots, [c_n]) be the maximal elements of (C/{sim }), and pick a vertex (v_i) in each cycle (c_i).
In particular, under the usual pointwise ordering of functions, is the maximal element of.
Obviously, (mathcal{P}^prec B), which is a contradiction since (mathcal{P}^) is the maximal element of (mathscr{P}).
The set Δ, as well as its subsets, can be partially ordered by the usual pointwise order: in this order, H0 is the maximal element in Δ+.
The set Δ, as well as its subsets, can partially be ordered by the usual pointwise order; in this order, ε0 is the maximal element in Δ+.
Then, if (T x):=Ax+Psi(x)) is an M-function, the unique solution of problem (1.2) is the maximal element of (underline{mathcal{S}}) (see, e.g., [12]).
The set Δ, as well as its subsets, can be partially ordered by the usual pointwise order: in this order, ε 0 is the maximal element in Δ +.
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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