Sentence examples for assumptions are essential from inspiring English sources

But for these good things to happen, four assumptions are essential.

We will see that these assumptions are essential for the local feasibility of the continuation methods.

Two assumptions are essential for the emergence of externalities in the models of Acemoglu and Pischke (1999a, b) and Stevens (19941996).

Only two rather generic assumptions are essential: i) a spatially infinite universe such as any (island) universe in MWO; the multiverse, while integral to eternal inflation, is not actually required for my argument, ii) the finiteness of the number of macroscopic histories in any finite region of spacetime.

Bringing together scholars and students with different perspectives who challenge each other's base assumptions is essential to inquiry and discovery.

This assumption is essential for validity of Lemma 6 and Proposition 7, so it cannot be relaxed.

Since the validity of the NI margin is related to the interpretation of the NI trials, clear reporting of the method of NI margin determination and the constancy assumption is essential for every NI trial publication.

This assumption is essential for the G × E interaction to be valid.

For phylogenetic inference in the context of very dirty data, non-clocklike methods are more robust and should be preferred unless the clock assumption is essential (for example, in phylogenetic dating).

While the assumption is essential to interpret the PPI network as an ordered layout of interacting molecules, it does not exclude the possibility that different copies of the same protein might engage in different PPI.

Evaluation of the proportional hazards assumption is essential since its violation raises questions regarding the validity of Cox model results which, if unrecognized, could result in the publication of erroneous scientific findings.