Sentence examples for hence given that from inspiring English sources

By Proposition 2.10, one root of the polynomial (p z)=z^{2}-c_{1}z-c_{0} ) is real and non-negative, λ say; hence given that (c_{0}geq0 ) then the other root must be real and non-positive, (-lambda' ) say, where (lambda'geq0 ).

But for every sequence ({s_{n}}_{ngeq0}subseteq S x^) ) convergent to (x^ ), it follows from Lemma 3.2 that the sequence ({Ts_{n}}_{ngeq0} ) is Cauchy; hence given that (x^in S x^)), then by Proposition 2.14 it follows that T is continuous at (x^ ) in (S x^) ) and consequently (Tx^=x^ ).

Hence, given that gross photosynthesis and carbon translocation were highly correlated (Pearson's correlation r2 = 0.98), coral photosynthesis can be measured as a reliable proxy for coral growth.

Hence, given that this is the best we can do in the face of a very effective lobbying campaign by the big global mining companies, I support the MRRT.

Hence, given that [UVY] is equivalent to [UιVιYι] by construction, the post-upgrading losses are lower than the pre-upgrading losses by the area [UιιUYYιι].

Hence, given that the same channels are reused among SBSs due to the scarce spectral resources, CCI constitutes an important restrictive factor for the network performance.

And if 'the organism descended from sperm s and egg e' indeed expresses an essence of Cicero, it must designate just Cicero in all possible worlds, and hence rigidly: so, given that the statement at issue is necessarily true, 'Cicero' must be rigid, too.

Hence Theorem 3.1 gives that also F upper supra-continuous.

Hence, given the fact that the 2-aminopyridine-3-carbonitriles were the only RECAP series that could be synthesized via a one-pot synthetic scheme [37, 76, 77], we have selected these for synthesis and subsequent validation as multi-target ligands.

5 Hence, given these constrains, a design that was appropriate for the current assessment and feasible for a large scale-public health programmes was adopted.

Hence, given the reasonable assumption that the negative value of adding extra lives with negative welfare does not decrease relatively to population size, a proportional expansion in the population size can turn a good population into a bad one a version of the so-called "Absurd Conclusion" (Parfit 1984).