We assume that the following assumptions are also satisfied: (H3) there exists a constant with such that (2.34).
If is Caratheodory, conditions (20), (30) and (40) of Theorem 4.2 are satisfied, condition (30) of Corollary 3.6 is also satisfied,, where are positive functions satisfying ; then (4.18) with (1.2), (1.3), and (1.4) has at least one solution.
If is Caratheodory, (4.45), (4.46) and conditions (20) and (30) of Theorem 4.2 are satisfied, condition (30) of Corollary 3.6 is also satisfied,, where are positive functions satisfying ; then (4.43) with (1.2), (1.3), and (1.8) has at least one solution when the parameter is small enough.
To summarize, we have proven that if either or both conditions [DilH2] and [DilH∞] are satisfied, then either or both of the following conditions are also satisfied: (i) (3.27) .
Conversely, if (3.3) holds, then (1) conditions (ii) are satisfied; (2) condition (i) is also satisfied but for w ≡ const or for p and p ¯ satisfying the condition p ≡ const, p ¯ ≡ const outside some large interval [ 0, 2 m 0 ], m 0 ∈ Z. .
I am also satisfied, on the basis of the evidence, that Alan's reputation for honesty and integrity in his work is fully justified," Mr Thompson said.
A good creamy Caesar salad ($7) also satisfied, but its "red chili croutons" turned out to be slices of toasted bread contributing no particular flavor.
"This is about principle, not about me," she told the Tagesspiegel newspaper in an interview, adding that her examiners were "tolerant but also satisfied" with her performance.
It's on you to create a meal from a menu of snack-size dishes which leaves you full but also satisfied, and there is no one else to blame if you order three of the crostini with the cheese that tastes like butter (it's stracchino) and then have to waddle off to the 1 train.
"I am also satisfied that, if you had any concerns about the approaches being made to you, you had an opportunity to mention them to the team captain or management, or if you were nervous of doing so, at least to your friends within the team.
