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A contradiction with the definition of ρ.
Let, we have (2.10). in contradiction to the definition of.
This is a contradiction to the definition of (T^).
which is a contradiction to the definition of.
This causes a contradiction to the definition of "Pareto-optimality".
This is a contradiction with the definition of ρ.
This is a contradiction with the definition of ρ, too.
(4.5) This is a contradiction to the definition of λ̅.
This is a contradiction with the definition of a snap-back repeller.
This means that λ ∗ + δ ∈ Δ, which is a contradiction to the definition of λ ∗.
end{aligned} (3.12) From (3.11) and (3.12), we easily obtain (xi> xi), a contradiction with the definition of ξ.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com