Sentence examples for make the further assumption from inspiring English sources

In order to be able to derive our bounds we make the further assumption that there exists a β > 0 such that: ∥ τ − β ∥ L 2 ( Ω 2, R p × p ) < ∞.

If we are willing make the further assumption that it only takes one bijection to one such instance of the power set of ω to render the power set itself "absolutely" countable, then we can understand the Skolemite's strong claim about absolute countability.

There were eminent scientists, notably Ostwald (1904) and Duhem (2002), who, whilst accepting that the phenomena were indicative of some underlying structure, refused to make the further assumption that the formulae with their structures referred to arrangements of atoms at all.

We now make the further assumption that the dimensionless rate of complex formation (λ1) is small.

As above, we need to make the further assumption that the system is initially at steady state, that is: (14) The formulas required for the computation of p t) are derived in Section S4 of the Additional file 1.

The phenotype distribution of the progeny is q 1 (z ) = ∫ ℝ p 1 (y ) f (z | y ) d y (9)We now make the further assumption that (1) the environment and genotype are independent random variables, so that f (z | y ) = f (z − y ) and therefore the variances are additive: σ P 2 = σ A 2 + σ E 2 and (2) environment effects are of zero mean (∫ x x f (x ) d x = 0 ) and symmetric (f(− x) = f(x)).

We used the Wilcoxon signed rank test, which makes the assumption that the individual O3-induced responses are symmetrically distributed, and the paired t-test, which makes the further assumption that the responses are normally distributed (Fisher and Belle 1993).

If one then makes the further, natural assumption that the active intellect participates in ordinary human cognition, then Aristotle would clearly be committed to a version of divine illumination.

In the first of these, as remarked above, he reformulated AC in terms of transversals; in the second (1908a) he made explicit the further assumptions needed to carry through his proof of the well-ordering theorem.

This was of a US-based study of men, and so the further assumption was made that the estimated relationship also applied to women.

Therefore, the further assumption was made that an unmethylated marker in a primary tumour has a higher probability to be methylated in a clonally related second tumour than a methylated marker becoming unmethylated.