Sentence examples for the key estimates from inspiring English sources

The key estimates are to obtain appropriate lower and upper bounds on the gas and liquid masses.

The following estimates are the key estimates in the proof of Theorem 1.1, which depends on the critical Sobolev inequality of logarithmic type (see Lemma 2.6).

We do not observe significant changes of the key estimates across specifications, net of the level effect of a larger share of population reporting "1" as the value of the dependent variable.

The PSM estimate corresponds closely to the key estimates from the probit models, suggesting that, at least in relation to the incidence of mismatch, selection bias is not an issue (Table 6).

The NHANES study also supported adjustment of models for a range of potential confounding factors, which in fact made relatively minor differences to the key estimates, suggesting that the associations are robust.

The key estimates used to identify optimal outgroups included, for each possible outgroup 1) the maximum likelihood (ML) distance to the Ecdysozoa, 2) the G + C content, 3) the content of G + C-rich codon encoded amino acids, and 4) the two indicators of GC strand asymmetry: GC skew and the skew index, an indicator of gene overall strand asymmetry.

Probably the key estimate was that on productivity.

The key estimate is employed to recover the primary data.

There are some minor errors here (e.g. the final expression in the third display on page 3 cannot be right since it is identically zero), but this writeup does recite the proof of the key estimate (3.5) on complete character sums starting from Weil's theorem (RH for curves over finite fields).

The next result shows the key estimate for the solution of (3.4).

The key estimate of interest is the effect through the variance, since this estimate tells if the degree of discrimination depends on perceived group differences in the variance of unobserved variables.