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It is easy to see the following relation between the least period and a period of a periodic sequence.
In contrast, a periodic sequence such as LSLLSLLSLLSLLSL... has a fundamental unit (LSL) that is precisely repeated at equal intervals.
Let be an a.a.p. periodic sequence.
That is coexistence of a positive periodic sequence solution and its anti-sign periodic sequence solution.
Furthermore, the limit sequence is also an almost periodic sequence.
Because x ∈ S, then x is an asymptotically periodic sequence.
Similar(10)
By Theorem 3.1, there exists a positive ten-periodic sequence solution of (4.1) and a negative ten-periodic sequence solution.
During the quasi-periodic sequence, mode-locking occurs each time the two frequencies are locally commensurate.
We have (mathfrak{G } = G_omega ) when (omega ) is the (3 -periodic sequence (012012012cdots ).
In particular, an asymptotically 1-periodic sequence is a convergent sequence and conversely.
In fact, the asymptotically 2-periodic sequence x ( n ) = ( − 1 ) n + ( − 1 ) n 1 n. is such a solution.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com