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It is based on the following observation: if (F:mathbb R^drightarrow mathbb R) is convex, then the inequality begin{aligned} F y ge F x)+pcdot (y-x quad text{ for } text{ all } y-x quadbb R^d end{aligned}charactextzes (by definition) the vectors (pin partial F(x)) and, if (Fin C^1), it is only satisfied for (p=nabla F(x)).
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For instance, users are only satisfied if they get a certain bit rate.
"You're only satisfied if you're in first place playing good baseball," Wright said.
He's not the only satisfied customer.
We've built a jail for ourselves, first engineered by the lies of false prophets, reinforced by the hate we were taught to inflict on our own selves, and guarded by pain that is only satisfied with unresolved hurt.
In contrast, in a study of the NHSC, Pathman and colleagues found that participants rated their satisfaction level between "dissatisfied" and "neutral" for 7 of 15 "work issues" and "personal-life" issues and participants' satisfaction level exceeded "satisfied" for only one issue (" [c]aring for needy patients").
Our approach will, under certain conditions, provide dissipation inequalities which remain satisfied for all input-output pairs that the system can produce, though only having been derived from finitely many of them.
Notice that condition (H1) is satisfied, for example, if (B_{1}(cdot,gamma)) is continuous or if it has only downwards discontinuities.
*For those who were "indifferent" or "dissatisfied" the numbers were too small in either group to create meaningful CI's and between group differences were only found for those "satisfied" or "somewhat satisfied".
We prove that all the conditions of our main Theorem 11 are satisfied, only for x, y ∈ B ( x 0, r ) ¯. Now we prove that F − 1 is α-admissible.
Recently, Ran and Reurings [20] have initiated another important direction in generalizing the Banach contraction mapping principle by considering a partial ordering on the metric space ( X, d ) and by requiring that the contraction condition (1.1) is satisfied only for comparable elements, that is, we have d ( T x, T y ) ≤ a d ( x, y ), for all x, y ∈ X, with x ≥ y. (1.3).
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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