Sentence examples for supplementary assumption from inspiring English sources

Note that estimate (17) for the differential operator (A^{x}) defined by formula (4) can be proved without using coercive inequality (3) under supplementary assumption for σ.

Secondly, supplementary assumptions about Lipschitz continuity of the coefficients w.r.t.

For aspects not covered by the 3GPP recommendation (e.g., multi-hop relaying), supplementary assumptions are taken from [44].

Under some supplementary assumptions satisfied by our system, we can moreover show that there exists a stable periodic orbit [28].

For scenarios 2 4, we assumed frequency-dependent long-cycle transmission, and examined the sensitivity of our results to this assumption (Supplementary Table 1).

(Interested readers may wish to read the supplementary document Background Assumptions for Plantinga's Account).

Diagnostic tests indicated no violations of the model assumptions (Supplementary Material 3 5).

We clarified the assumption in Supplementary file 1. Start is triggered when phosphorylated Whi5, Whi5 p, reaches the threshold Whi5 p (G1)=Whi5 tot -Whi5 c.

For each participant, the slope of the mean activity across conditions was calculated by fitting a regression line to the mean beta value from each condition (assuming an equivalent interval between all conditions, for discussion of this assumption, see Supplementary Methods).

The results varied little by methodological assumption (see supplementary table S6), using estimates per 250 mL/day (median of 17 studies) rather than per serving/day; excluding studies with a high risk of potential bias or with relatively large within person dietary variability; and incorporating uncertainty of within person variability and precision of type 2 diabetes diagnosis.

Based upon the logic above, on the structure of Fig. 2 and subsequent to biologically realistic simplifying assumptions (see supplementary Text S1) we obtained the following system of equations.