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A subsequence of a given sequence is any sequence all of whose entries appear in the original sequence and in the same manner of succession.



in mathematics, the sequence

xn1, xn2,…., xnk

derived from the given sequence x1, x2,…, xn with observation of the order, that is, provided that n1 <n2 < … <nk….

References in periodicals archive ?
The homogenized equation has a unique solution in [H.sup.2.sub.0] ([OMEGA]), so every subsequence of ([u.sub.n]) converges to the same limit u and this implies that the entire sequence ([u.sub.n]) converges to u.
(1) If y and z are limit points of ([x.sub.n]), then there exist subsequences [mathematical expression not reproducible].
(b) [P'.sub.i] holds for some boundedly spaced subsequence [mathematical expression not reproducible] of {[T.sup.n]}
Moreover, the DTW algorithm-based approach provides the advantage of searching all matched subsequences automatically from a long sequence.
If {[[??].sub.n]} is a sequence in a bounded soft closed set S, then there exists a subsequence [mathematical expression not reproducible] of {[[??].sub.n]} converging to some [??] [member of] S.
Section 3 introduces our approach for completing large missing subsequences in low/uncorrelated multivariate time series.
Assume, up to a subsequence, that [mathematical expression not reproducible].
Setting [v.sup.[k]] = [u.sup.[k]] / [parallel] [u.sup.[k]] [parallel] and arguing as in the proof of Claim 1, we conclude that, possibly passing to a subsequence,
We utilize LSTM network itself without additional model to complete subsequence selection.
The traditionally LCS method measures the similarity by calculating the length of the longest common subsequence. Given two strings [S.sub.1] and [S.sub.2] with length I and J respectively, [S.sub.1](i) and [S.sub.2](j) are the [] member of the string [S.sub.1] and the [] member of [S.sub.2] respectively, and L(i, j) represents the value of the LCS matrix at the location of (i, j).
A traversal sequence S' is said to be a subsequence of sequence S if it is a subset of S.