Sentence examples for obvious modifications of from inspiring English sources

Hence, the proof of (b) only consists of obvious modifications of the proof of (a).

(b) All inequalities above hold in the reverse direction in this case, and the proof follows by just doing obvious modifications of the proof of (a).

Certain parameters may be different for each experiment, but the treatment of these local parameters and the different experiments requires only obvious modifications of the described procedures and therefore only the single-experiment design n exp = 1 is discussed in the following for sake of clarity.

When the boundary is not connected, the system of boundary conditions may be replaced by a collection of such systems, one for each connected component of Theorems 1.1 and 1.2 remain of course true in that setting, with the obvious modification of the target space in (1.3).

Then (as proved in [3]), Theorem 1.1 holds (once again, the LS condition amounts to proper ellipticity plus complementing condition and proper ellipticity is equivalent to ellipticity if and ) and it is straightforward to check that the proof of Theorem 1.2 carries over to this case if If so, Corollary 2.1 is also valid, with a similar proof and an obvious modification of the function spaces.

In addition, no obvious modification of actin fibers was observed in the TDI chondrocytes using phalloidin and actetylated alpha-tubulin staining.

If one is not willing to declare as an effect any p-value above α, the obvious modification of SGoF is simply given by Nα = min(K−bα+1, K. Clearly, FWER control at the α level remains true when this correction is applied.

Recurrence (2) is the obvious modification of the recurrence presented in (Jiang et al., 1995) for global alignments and node similarities.

A trial will be considered successful if the full plantar surface of the foot contacts the force platform in between the pylons of the force platform at the prescribed running speed without obvious modification of gait.

Our results suggest that the available algorithms, while potentially helpful in identifying splicing modulators especially when they are located in weakly defined exons, do not always correspond to an obvious modification of the splicing pattern.

However, we did not observe any obvious modification of the E2F1-dsRNA phenotypes (data not shown), indicating that these particular Su z 2 point mutations are insufficient to modify these phenotypes.