We also generalize Theorem 1.3 utilizing Ćirić-type contraction in two directions wherein (sigma in mathbb {S}) is utilized rather than the constant (tau.) In doing so, we obtain a slightly sharpened form of Theorem 1.1.
This supports one of the main findings of the paper: that broad, regularly collected input and output measures (some measure of life expectancy, early age mortality, total education, and per capita healthcare spending) should be utilized, rather than specific measures that are collected sporadically.
Moreover, for every (x_0in X), the Picard sequence ({f^nx_0}) converges to x. f is continuous, The proof is omitted as it is very similar to that of [18, Theorem 2.4] and [3, Theorem 2.2] where the completeness of the whole space is utilized rather than the completeness of the orbit of f.
For the metabolism of hexoses, Entner-Doudoroff (ED) pathway is utilized rather than the EMP pathway [ 31, 32].
The composition of both bottom ashes and fly ashes were determined and it is most likely that both could be utilized rather than being land-filled.
Second, the scoring system of codominant markers was utilized rather than the single dose dominant markers previously used by Okada et al. (2010) and Missaoui et al. (2005).
A propensity approach to natural selection, in which "expected fitness" is utilized rather than "fitness," can save natural selection from tautology.
The remaining solid fraction was assessed as a fuel for conversion by combustion yielding thermal energy and inorganic ashes with the prospective of being utilized rather than being land-filled.
The model showed the ability to recapture parameterizations with small numbers of data points, although more data points were required to reject alternative null parameterizations with nonfunctionalization when AIC was utilized rather than simply likelihoods.
WQS C2 was utilized rather than WQS C0 or C1 because samples from the earlier cycles of selection did not include enough individuals for reliable estimates of allele frequencies.
