Sentence examples for assume a sequence from inspiring English sources

(a) Assume a sequence ({x_{n}}) in X converges to some (ain X).

For all x, y ∈ E, there holds the inequality Φ ( ∥ x + y ∥ ) ≤ Φ ( ∥ x ∥ ) + 〈 y, J φ ( x + y ) 〉. Assume a sequence { x n } in E is weakly convergent to a point x.

Assume a sequence {x n } in E is weakly convergent to a point x, then there holds the equality lim sup n → ∞ Φ x n - y = lim sup n → ∞ Φ x n - x + Φ y - x, x, y ∈ E. Lemma 2.2.

Lemma 2.5 Assume that E has a weakly continuous duality map J φ with gauge φ. (i) For all x, y ∈ E, there holds the inequality Φ ( ∥ x + y ∥ ) ≤ Φ ( ∥ x ∥ ) + 〈 y, J φ ( x + y ) 〉.   (ii) Assume a sequence { x n } in E is weakly convergent to a point x.

Assume that E has a weakly continuous duality map J φ with gauge φ, (i) For all x, y ∈ E, there holds the inequality Φ x + y ≤ Φ x + y, J φ ( x + y ).   (ii) Assume a sequence {x n } in E is weakly convergent to a point x, then there holds the equality lim sup n → ∞ Φ x n - y = lim sup n → ∞ Φ x n - x + Φ y - x, x, y ∈ E.  .

Since we did not want to assume a sequence length for off-target cross-reaction, we chose to estimate the percentage identity over several lengths, i.e., over 25, 50, 100, 200 or 300 nucleotides.

Assuming a sequence length of 1000 bp, we compute Chen Stein error bounds for the cooperativity P-values.

These stochastic error margins are determined by assuming a sequence length of 500 bp in the first-order approximations given in (14) and (15), where σ is given by scaling σ (ΔK2P) by the slope A of the linear interpolation.

Both assume a linear sequence from supply of research to utilization by policy makers.

The phylogenetic shadowing principle is used to assume a multiple sequence alignment can be obtained from closely related species [ 28].

The wgsim (Li et al., 2009) read simulator was used to sample reads from the modified source sequence assuming a 1% sequencing error rate under different insert size, coverage and read length assumptions (Table 1).