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(i) We can apply Theorem 3.
Since dist i min > b j - i, we can have disti > bj-i.
(ii) Similar to the proof of (i), we can get (ii) immediately.
For part (i), we can use Lemma 27 and Lemma 25 to see that.
From Lemma 2.1(i), we can see that S satisfies Assumption (A).
By assertion (i) we can further get that (|u_{n}|_{v}>r).
By a similar proof to case (i), we can easily obtain the conclusion of case (ii).
Similar(4)
After phase-I, we can separate the moving items from all the items.
On the other hand, with a fixed energy arrival distribution {h i }, we can find the influence of the utility function on the optimality of greedy policy.
With the help of the transformed sequence { x i * }, we can deduce the following conclusion.
By letting i → ∞, we can conclude that ∥ t ( z ) − z ∥ ≤ 0, that is z ∈ Fix ( t ).
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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