Sentence examples for proved a result from inspiring English sources

Remarkably, Kato proved a result that, at least for self-adjoint contraction semigroups, always holds.

Cruz-Uribe and Wang [21], Proposition 5.4, have proved a result similar to the lemma.

Wittmann [21] proved a result in 1992 which finally allowed for λ n = 1 n + 2 in Hilbert spaces.

In 1980, Cycon [99] proved a result when there was an additional technical condition on (-Delta +V).

The asymptotic normality of the proposed test statistic under the null hypothesis is proved, a result which is different from the χ2 law for a model with a fixed variable number.

In fact, Zhang and Korhonen [19] also proved a result similar to Theorem C under the condition n ≥ 6. Obviously, it is an interesting question to reduce the number n.

Next, we prove a result concerning estimates near the boundary.

We first prove a result, which will be helpful to prove main result of this section.

We first prove a result for maps in one dimension and use it to prove the result for skew-products.

To prove a result on the existence of solutions for (13) we need some preliminary results.

First, we prove a result on symmetry of positive solutions of p-Laplacian ODEs.