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The presence of outliers makes the evaluation of any least squares model parameters difficult, while the missing values influence the adequate identification of outliers.
The simulation results indicate that the one-way property of the proposed algorithm is remarkably high, and any least difference of the message or key will cause huge changes in the final hash value.
Lemma 4.1 Any least energy solution u of (AP) satisfies the estimate ∥ u ∥ p ≤ p k c ¯ p − 1. Proof Since u is a critical point in the minimax level c ≤ c ¯, by Lemma 3.3, we have ( p − 1 ) p k ∥ u ∥ p ≤ J ( u ) − 1 θ J ′ ( u ) u = c ≤ c ¯.
Any least with single-family houses we know what we own.
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Mr. McLamore does not really have any least-favorite spots along the line, except that for a while he really loathed the Utica Avenue station in Brooklyn, where a man would position himself at the front of the platform every day and launch a large wad of spit at the train's windshield.
In scenarios where there exists no BLUE node, any least-distant node which is minimum hops away from the sink is selected.
This can be attributed to the fact that, like in any least-squares adjustment, small changes of an a priori value always lead to the same estimated value of this parameter.
Finally, in scenarios (especially for higher values of k) where there exist fewer BLUE nodes, any least-distant neighbor which is minimal hops away from sink node is selected.
Sultans establish their power by making sure no one else has any — or at least any that is independent of the sultan himself.
I will never stop smoking weed again for any reason, at least any reason I can think of now.
Few succeed in going it alone in any field, least of all these.
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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