First we compare the performance of CFO estimation using CAZAC sequences with the following two sequences which also have good autocorrelation properties: (1) IEEE 802.11n short training field [3], (2) sequences [22]. .
Consider the following two sequences: vartheta_{n}=mathcal{F} vartheta_{n-1}), quad n=1,2,3,ldots, (3.12) and upsilon_{n}=mathcal{F} vartheta_{n-1},quad n=1,2,3,ldots.
Then, for each t ∈ N, define recursively the following two sequences of sets M i (t ) = ⋃ k ∈ M i (t − 1 ) B k, M j, i (t ) = ⋃ k ∈ M j, i (t − 1 ) B k ∖ { j }.
Consider the following three sequences, as a simple example.
We also interpret the following nine sequences (2.76– 2.60 m b.s. in Fig. 6) as deposits of overwash events (EWE III XI) affecting the interior of Saliña Tam due to the partial destruction of the barrier during EWE II.
If {y n } is not a Cauchy sequence, then there exist ε>0 and two sequences {m k } and {n k } of positive integers such that the following four sequences tend to ε when k→∞: d ( y m k, y n k ), d ( y m k, y n k + 1 ), d ( y m k − 1, y n k ), d ( y m k − 1, y n k + 1 ).
If { y 2 n } is not a Cauchy sequence in ( X, p ), then there exist ε > 0 and two sequences { m k } and { n ( k ) } of positive integers such that n ( k ) > m ( k ) > k and the following four sequences tend to ε when k → ∞ : (3.2).
Then there exist ε > 0 and two sequences { m k } and { n k } of positive integers such that n k > m k > k and the following four sequences tend to ε as k → ∞ : d ( y m k, y n k ), d ( y m k, y n k + 1 ), d ( y m k - 1, y n k ), d ( y m k - 1, y n k + 1 ).
Then there exist ϵ > 0 and two sequences { m k } and { n k } of positive integers such that n k > m k > k and the following four sequences d ( x m k, x n k ), d ( x m k, x n k + 1 ), d ( x m k − 1, x n k ), d ( x m k − 1, x n k + 1 ) (2.2). tend to ϵ as k → ∞.
If { x 2 n } is not a Cauchy sequence, then there exist ε > 0 and two sequences { m k } and { n k } of positive integers such that the following four sequences converge to ε when k → + ∞ : { d ( x 2 m k, x 2 n k ) }, { d ( x 2 m k, x 2 n k + 1 ) }, { d ( x 2 m k − 1, x 2 n k ) }, { d ( x 2 m k − 1, x 2 n k + 1 ) }. (6).
If { x 2 n } is not a Cauchy sequence, then there exist ε > 0 and two sequences { m k } and { n k } of positive integers such that m k > n k > k and the following four sequences tend to ε when k → + ∞ : { p ( x 2 m k, x 2 n k ) }, { p ( x 2 m k, x 2 n k + 1 ) }, { p ( x 2 m k − 1, x 2 n k ) }, { p ( x 2 m k − 1, x 2 n k + 1 ) }.
