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Assume that is a sequence in satisfying and that is a sequences in satisfying.
The LPCD model states that, where is a sequences of i.i.d random variables uniformly distributed in a predefined interval.
for every, where is the duality mapping on, is a sequences in such that and for some, Then, converges strongly to.
where is the sequence generated by (1.23), is a sequences in and is a real sequence in satisfying the following conditions: (i).
More complex filters can be defined on so-called handoff patterns, that is a sequences of cell towers that a moving phone uses while engaged in one voice call, e.g. in [49] where only sequences of more than 5 cell towers are included.
We note that if { X k, F k : n ⪯ k ⪯ N } is strong adapted, when d = 1 then { X k − E ( X k | F k − 1 ∗ ), F k : n ≤ k ≤ N } is a sequences of martingale differences, but when d > 1 then { X k − E ( X k | F k − 1 ∗ ), F k : n ⪯ k ⪯ N } is not necessarily a field of martingale differences, because X k − E ( X k | F k − 1 ∗ ) may not be F k -measurable (see [9], Example 3.1).
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In other words, any list is a sequence, any vector is a sequence, and any string is a sequence.
There is a sequence, she said.
But life as prime minister is a sequence of shocks.
History is a sequence of causes and effects.
This is a sequence all pairs should discuss.
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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