Sentence examples for more direct proof from inspiring English sources

We give a substantially simpler and more direct proof in a precise manner, in comparison to Corollary 5.2 of [10].

In the optimal transportation case, we obtain a different and more direct proof of the improved global regularity result in [15].

To obtain a more direct proof, first-order reversal curves (FORC) measurements were further applied to detect the presence of magnetosomes (Pike et al. 1999; Roberts et al. 2000).

In this paper, we give a more direct proof of the results by Clair and Mokhtari-Sharghi [B. Clair, S. Mokhtari-Sharghi, Zeta functions of discrete groups acting on trees, J. Algebra 237 (2001) 591 620] on the zeta functions of periodic graphs.

The method developed in this section can in fact be generalized to arbitrary curves, leading to a more direct proof of the finiteness of (_nmathrm{Br}(K _V) for a suitable explicitly defined set (V) of discrete valuations of an arbitrary finitely generated field (K); details will be published elsewhere.

To provide a more direct proof of Top2b involvement in the protective effect of DRZ, we manipulated this enzyme's level.

Measurements of the cosmic microwave background put the theory firmly on the fringe of physics 30 years ago; still, scientists sought more direct proofs of the expansion of the cosmos.

More direct proofs were the studies on mice with different genetic background, which indicated that IL-10 was responsible, at least in part, for the high survival, which suggested that aberrant innate immune response contributed to SS2 diseases [ 40].

In this paper, we give a more direct and much simpler proof of this result.

It would be more elegant to have a direct proof and tighter bounds.

Different and more direct methods are used in the proofs without any complicated theoretical discussions.