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Once we have ruled out Collingwood, Pujara and Prince there are plenty of candidates for the middle order and we will be omitting some exceptional players: Trott, Pietersen, Bell, Dravid and Laxman.
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Other regimes will be omitted as we cannot access detailed information about the processing.
end{aligned}Again, the symbol (q) will be omitted when we don't expect any confusion.
We note that the BS index will be omitted in this subsection for simplicity's sake.
First, we give some useful lemmas whose proofs will be omitted because they can be obtained by standard argument.
We start with the following simple lemma whose proof will be omitted since it can be proved by a similar argument as that in [[44], Lemma 15.5].
If we fail to obtained sufficient data, the trials with missing data will be omitted from the data synthesis.
We only prove the case where (the proof of the case where is similar and will be omitted).
We prove that when l- odd, k, s- even (the other cases are similar and will be omitted).
In this section, we will prove the existence part of Theorem 1 and the uniqueness is standard so it will be omitted.
We observe that the case of heteroclinic solutions from P − to P + is analogous, thus it will be omitted.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com