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We argue that guaranteeing a certain amount of bandwidth is enough for QoS assurance, i.e., throughput, delay, jitter, and losses due to buffer overflow will be bounded as a consequence, as explained in [28].
This is the main reason why we maintain that guaranteeing enough bandwidth to empty all buffers during each cycle is enough to make sure that all other QoS metrics (throughput, delay, jitter, and losses due to buffer overflow) will also be bounded as a consequence.
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If ({z(n)}) is bounded, then, by Lemma 2, ({x_{1}(n)}) is bounded as well and, therefore, there exists a finite (lim_{ntoinfty}x_{1}(n)).
Thus, ({ x_{n} } subset X) converges to some (a in X) (Definition 2.3) and it is bounded as a result.
Then the Bergman projection P is bounded as a map from (L^{p} phi)) to (mathcal{F}^{p} phi)).
It is well known that (mathcal{F}) is bounded as a map from (L^{1}) to (L^{infty}) and also as a map from (L^{2}) to (L^{2}).
Then (mathcal{F}) is bounded as a map from E to F. We simply put (L^{1}=L^{1}(mathbb{R}^{n})) and (L^{infty}=L^{infty }(mathbb{R}^{n})).
Since T ( r, f ) − T 0 ( r, f ) is bounded as a function of r, we can replace T 0 ( r, f ) with T ( r, f ) in this paper.
Nover and Hájek (2004) rebut Jeffrey, arguing that even if all utility functions are bounded as a matter of contingent fact, unbounded utility functions are a conceptual possibility, and that they may be useful for developing idealized models of actual agents.
Procedure-related complications were bounded as an intraprocedural aneurysm perforation, thromboembolic complications, or any other complications associated with the endovascular procedure and recorded.
It means that the measured distances can be bounded as d i ( x, a i ) − ρ 1 i ≤ d ̂ i ≤ d i ( x, a i ) + ρ 2 i. (12).
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