Sentence examples for convergent by from inspiring English sources

Since is convergent by the assumption.

Therefore, since is complete metric space, if, then (3.5). is absolutely and uniformly convergent by Weirstrass's M-test theorem.

Now, let us see that the series is convergent: by using, it follows that there exist and sufficiently large such that (2.5).

Observe that the series is absolutely convergent by using the ratio test and hence the series in (17) is absolutely convergent.

Thus (operatorname{crit} H={ z^,z^):z^=(x^,y^)inoperatorname{crit} L}), and hence (Omegasubsetoperatorname{crit} H). (iii) Notice that ({L(x_{k},y_{k})}) is convergent by Lemma 3.5 ii).

It is worth noting that the products in (4.1) and (4.2) are convergent, by Lemma 4.1, since sum_{k=0}^{infty}biglVert A bigl(h^{k}(t bigr bigrVert q^{k} bigl(t 1-q -omega bigr) is convergent 1-q -omega

If, in addition, x ∈ l ∞ 2, then x is said to be boundedly P-convergent to L. We shall denote the space of all bounded convergent double sequences (or, boundedly P-convergent) by  c ∞ 2. Let S ⊆ N × N and let ϵ > 0 be given.

Construct validity was assessed by discriminant validity and convergent validity by Pearson's correlation.

Motifs shared among nonhomologous genes may have arisen independently by convergent evolution or by domain shuffling, and suggest a biochemical feature of general importance.

This grouping could be explained either by convergent evolution, or by the fact that all eight CD94L genes derive from a common ancestor.

It is also obvious, as Aristotle claims, that every convergent series by addition is identical with some convergent series by division.