Sentence examples for use the diagonal method from inspiring English sources

Since is bounded for all and, we can use the diagonal method to get a subsequence of such that converges for each as.

If you use the diagonal method, switching sides is not necessary.

Robust standard errors are therefore calculated using the (diagonal) method suggested by White (1980).

His main idea is to find a minimizing Cerami sequence for Φ outside (mathcal{M}) by using the diagonal method; see Lemma 3.10.

It relies on finding a minimizing Cerami sequence for variational functional related to (1.1) outside the Nehari manifold by using the diagonal method (see Lemma 2.8).

Since the sequence ( x n ( i ) ) i = 1 ∞ is bounded for each i ∈ N, by using the diagonal method, we can find a subsequence ( x n l ) of ( x n ) such that ( x n l ( k ) ) converges for each k ∈ N. Therefore, there is an increasing sequence t m with sep ( ( x n l m ) l > t m ) ≥ ε.

By using the diagonal method, we see that for each j ∈ N we can find a subsequence ( x n l ) of ( x n ) such that ( x n l ( i ) ) converges for each i ∈ N. Therefore, for any j ∈ N there exists an increasing sequence ( t j ) such that sep ( ( x n l j ) l > t j ) ≥ ε.

Since for each i ∈ N, ( x n ( i ) ) i = 1 ∞ is bounded, by using the diagonal method, we can find a subsequence ( x n j ) of ( x n ) such that ( x n j ( i ) ) converges for each i ∈ N with 1 ≤ i ≤ l.

Let and with for Take There exists such that Let Since for each is bounded, by using the diagonal method, we have that for each, we can find a subsequence of such that converges for all with Since is Cauchy sequence for all there exists such that (4.7).

By using the diagonal method, we can find a subsequence ( x n r ) of ( x n ) for each N ∈ N such that ( x n r ( k ) ) converges for each k ∈ N with 1 ≤ k ≤ N, since ( x n ( k ) ) k = 1 ∞ is bounded for each k ∈ N. Therefore, there is t N ∈ N for each N ∈ N such that sep ( ( x n N ) r > t N ) ≥ ε.

Use the same diagonal method.