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For all bounds except R m, composite bounds were better than the corresponding local bounds and a better local bound always led to a better composite bound.
We are bound, always, to the shape of our era.
Therefore, the upper bound always takes a configuration (morphology) where the continuous phase is made of the higher-conductivity material.
The upper bound always holds if ϕ has compact support and the lower bound is equivalent to begin{aligned} bigl(hat{phi}(xi+2pi k bigr)_{k inmathbb{Z}}neqmathbf{0}, end{aligned} (6) for all (xiinmathbb{R}), where 0 denotes the zero sequence.
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This indicates that Haemers' bound is always sharp for connected graphs ((n leq m leq2n-3)).
In the simulations, this computable bound is always reasonably large, which makes the tightness result valuable.
This indicates that Haemers' bound is always sharp for connected graphs ((m leq2n-3)) othan treestrees.
Since the bound is always verified for every, the upper bound can be computed by substituting in (16) by the standard deviation of the per-channel multiplication error.
The small discrepancy between theory and simulation is mainly due to the use of the union bound, which always overestimates the true error rate.
Theorem 2.14 implies that if m ( G ) ≤ 2 n ( G ) − 3, Haemers' bound is always sharp for connected graphs other than trees.
The parties were always bound to Bork, just as they were always bound to feud bitterly about emotive subjects such as abortion.Rather, what seems to be happening is a tug-of-war over where exactly the bipartisan centre stands.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com