Sentence examples for sequence with a limit from inspiring English sources

Also, is a Cauchy sequence with a limit in which is a fixed point of.

But { S 2 n x } n ∈ N 0 is a Cauchy sequence with a limit z = S 2 z in A (respectively, with a limit y = S 2 y in B) if x ∈ A (respectively, if x ∈ B ) such that D = ∥ S z − z ∥ = d ( z, S z ) (Proposition 3.2, [14]).

But T 2 n x n ∈ N 0 is a Cauchy sequence with a limit z = T2z in A (respectively, with a limit y = T2y in B) if x ∈ A (respectively, if x ∈ B) such that D = ||Tz-z|| = d z,Tz) (Proposition 3.2 [14]).

In the same way, T 2 n x n ∈ N 0 is a Cauchy sequence with a limit T2y = y ∈ B which is a best approximation point in B of T A ∪ B → A ∪B if x ∈ B since B is convex and (X,|| ||) is strictly convex.

which is a contradiction and z = S 2 z is the best proximity point in A of S : A ∪ B → A ∪ B. In the same way, { S 2 n x } n ∈ N 0 is a Cauchy sequence with a limit S 2 y = y ∈ B which is the best proximity point in B of S : A ∪ B → A ∪ B if x ∈ B since B is convex and ( X, ∥ ∥ ) is strictly convex.

Then, ∃ lim n → ∞ d T n + 1 q + ∑ ℓ = i m j ℓ + j x i, T n q + ∑ ℓ = i m j ℓ x i = 0 and T n q + ∑ ℓ = i m j ℓ + j x i n ∈ N 0 is a Cauchy sequence with a limit in the closed and convex Ai+m+1∈ X for any j ∈ j m + 1 - 1 ¯, ∀x i ∈ A i and i ∈ p ̄.

Raw reads were trimmed for removal of low-quality sequences (with a limit of 0.05) and for ambiguous nucleotides.

To obtain high-quality transcriptome sequence data, raw reads were trimmed via the removal of low-quality sequences (with a limit of 0.05) and based on ambiguous nucleotides.

A single run with all the sequences (with a limit of 20 motifs and a minimum width of six sites) yielded motifs with e-values ranging from 4.3e-279 4.3e-27927.

Secondly, the genotypic data analysed were generated by population sequencing with a limit of sensitivity of approximately 15 to 25%. 31 32 Our estimates of the prevalence of transmitted HIV drug resistance may therefore be biased downwards.

Let be a strongly convergent sequence in with a limit and a sequence in defined by for each, where is a convergent sequence in with a limit.