Sentence examples for a direct proof for from inspiring English sources

Recently, Zhou and his collaborators [7] give a direct proof for McKean's theorem [5].

This is a direct proof for less oxygen content for the upper layers of the thicker film.

We give a direct proof for the following useful lemma, which can also be deduced from Theorem 2.3.9 in [24].

Furthermore, the marked area highlighted the opened CNT tips, which provides a direct proof for the opening of the exposed CNTs by oxidative plasma.

Hereby we present a direct proof for the sake of completeness, adapting ideas from Kerr and Li in [40, Theorem 3.4, (vi) (Rightarrow ) (v)] to the setting of extended metric spaces (see also [40]).

Thus, a direct proof for PS exposure by Leishmania parasites is currently lacking.

In contrast with [23], we give a direct proofs for the continuity and compactness of F and G without using a continuity result on superposition operators.

She said: "The rape culture of India is a direct proof of complete disregard for women's & girls' rights and bodily integrity".

We can give a direct proof of exponential decay for M based on this expression and using simpler assumptions on p and K that, however, do not cover the case when p can have large variation and p ( s ) can vanish for s ≃ 0. It is a natural extension of the case when p is constant as covered in [12].

Although the current evidence of the role of anti-PLA2R antibodies in the pathogenesis of MN has enlightened our understanding of the disease, a transgenic animal model of MN is still needed for a direct proof of a pathogenic link between PLA2R ABs and MN.

We give a direct proof of the 'upper' Khintchine inequality for a noncommutative symmetric (quasi- Banach function space with nontrivial upper Boyd index.