Sentence examples for existing proofs from inspiring English sources

Existing proofs of this result all rely on uniform ellipticity or hypoellipticity assumptions on the diffusion.

Note that all existing proofs of Theorems 1 and 2 involve rather high level geometrical or analytical methods.

Given this state of affairs, it is not clear what can be concluded from existing proofs of correctness.

Moreover, we develop a proof of Theorem 1.1 which is an alternative proof of (1.1) for all positive real numbers a, b, and r ∈ [ 0, e ], which is distinct from the existing proofs given in [14, 29].

The question is ambiguous because it is not immediately clear whether Wodeham's intention is to show that there is only one God or if he intends to evaluate the relative degrees of evidence of the existing proofs of God's unicity or multiplicity.

Although it has been established with clear assumptions for geometric planners, the panorama of completeness results for kinodynamic planners is still incomplete, as most existing proofs rely on strong assumptions that are difficult, if not impossible, to verify on practical systems.

It is worth mentioning that our proof of the following theorem is very precise and it is interesting to compare it with the existing proof in the literature.

In addition to the results, we follow up a different and novel approach in proving this theorem compared with the existing proof for the rectangular window case where the Stieltjes transform m z) has the explicit inverse [15].

With the necessary proof of concept established in our previous work [ 19], the current work extends our existing proof to a full-fledged implementation of the score dissection idea, herewith, dissectHMMER (available at dissecthmmer.bii.a-star.edu.sg).sg

Although telephone interviews have been noted to be impersonal and not 'the gold standard' for collecting data related to sensitive topics, 59 the method has many advantages, without existing proof of inferiority.

The rare sightings gave me a strange feeling of both actually existing – look, proof in print!