Sentence examples for a direct proofs for from inspiring English sources

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.

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.

Hence, it is a direct proof for a lower number of Cav1.4 channels at the plasma membrane.

A direct proof for this scenario may be impossible; however, if the mechanisms of cellular growth arrest at distant sites are better understood, indirect proof could come from therapeutic intervention by keeping the cells in check and thereby reducing metastasis.

We did not show a direct proof for regulation of SERCA via NFAT in vivo, but previously we [ 17] and others [ 1] could show that calcineurin NFAT is involved in SERCA upregulation.

Computational studies have also proposed that the inhibitory asynchronous release is able to change the postsynaptic gain for a relatively prolonged period after presynaptic activity has subsided (Volman et al. 2010), but a direct proof for this functional role has remained elusive.