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This did not strictly contradict Oppenheimer's results, but extended them to include the point of view of infalling observers.
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Then the sum of the first three terms in (2.20) is non-positive and the fourth term is strictly negative, which contradicts δ ( n ) = 0.
When Ty replied no to the question of whether he had ever touched a female client more than was strictly necessary, the polygraph contradicted him, and he lost all his winnings.
This contradicts the strictly increasing of f, then every C 0 solution of (1.4) is strictly decreasing.
Therefore, we construct a sequence ({R(t_{varepsilon}+nomega)}_{n}) that is strictly increasing, which is contradicts the assumption that the zero steady state is globally stable.
It is much more common and severe in females than in males (3-4 : 1) [ 4], which contradicts a strictly autosomal dominant transmission but follows multifactorial inheritance.
But, since V > C h − C l by assumption (1), the LHS of this inequality is strictly smaller than 1, contradicting γ ⩾ 1. □ Observation 3 (part b) For any β a and any γ, (h, l | h ) ≽ (h, h | h ) ⇒ (h, l | h ) ≻ (l, l | h ) ≽ (l, h | h ).
But, since V > C h − C l by assumption (1), the LHS of this inequality is strictly smaller than 1, contradicting γ ⩾ 1. □ First note that (l, l | h ) ≽ (l, h | h ) is equivalent to P l − C l − γ max { E β a (π c ) + P l, 0 } ⩾ P h − C l − γ max { E β a (π c ) + P h }.
Hence, x ( t ) is strictly increasing on J, which contradicts x ( 0 ) = x ( T ).
Then, it is easy to see that, which contradicts that is strictly star shaped, since we also have that.
Indeed, if this were not the case, then (W + wouldould be a member of Open image in new window with dimension strictly greater than (dim (W)), contradicting the definition of Open image in new window.
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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