Sentence examples for exists a weak from inspiring English sources

Then there exists a weak solution to Problem 1 in the sense of Definition 4.1.

Then by Lemma 2.3, there exists a weak solution for problem (3.2) satisfying, and (3.5).

We start observing that there exists a weak upper solution such that on and.

As we know that there exists a weak solution y to (2.2), due to (u= 1-kpartial_{x}^{2}+gamma_{2}partial_{x}^{2})^{-1}y), we know that there exists a weak solu= 1-kpartial_{x.

end{aligned} Since ({ x_{n} } ) is bounded, there exists a weak convergent subsequence ({ x_{n_{k}} } ) of ({ x_{n} } ).

The computed rank correlation is 0.1936 (P<0.0001), which indicates there exists a weak correlation between them.

However, we prove that there exists a weaker form of absorbing state, that we call Haar trace, for the free and the tensor convolutions.

The study results indicated that when the apparent cohesion was very large, or the friction between the wall and the footing was small, or there existed a weak interlayer in the wall, sliding failure was found to occur in geocell-reinforced retaining walls, similar to the failure mode of rigid retaining walls.

Suppose the contrary, then there exist a weak neighborhood N w of τ ( y ) and a subsequence { y n j } of { y n } such that τ ( y n j ) ∉ N w for all j ≥ 1. Naturally, ( y n j ) converges weakly to y.

We may deduce from this systematic review that there does exist a weak association between episodes of VTED and a long travel, but not by plane specifically.

If there already existed a weak binding site for the displaced tRNA on the ancestral peptidyl transferase (an ancestral E or exit site), the proto-mRNA may have remained bound to the anticodons of the two tRNAs long enough for the selection of a new (aminoacylated) tRNA for the now empty A site.