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Using the same, we can compute the corresponding prescient bound giving the point.
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Since the gap between the achievable rates and the bound given by (55) is bounded by bit/channel use when, the gap between the achievable rates and the bound given by (41) is also bounded by bit/channel use when and.
Next, we prove that as long as, this upper bound is always looser than the bound given by (38 - 39 38 - 39
Hence, it follows from Theorem 3.3 that the closed-loop system given by (4.17), (A.2), and (A.3) is globally ultimately bounded with respect to uniformly in with ultimate bound given by, where.
For comparison purposes, the distortion lower bound given by (44) and the distortion upper bound given by (45) are also included in the plot.
He says that during 14 months in army custody he was kept permanently blindfolded and bound, given electric shocks, hung upside down, half-drowned and then beaten unconscious.
So is the distortion bound given by (25).
The Hashin- Shtrikman (HS) lower bound gives good estimation results under this condition.
It seems that the lower bound given by Theorem 8.1 is very accurate.
The bound given by (4.13) and the estimate in (4.14) are best possible.
In that case, 70 80% of the bound given by the dynamic model are achievable.
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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