This is calculated from equations (1), using the above assumptions about mortality, growth and reproductive success.

Ostensibly objective textual scholarship adopted editorial policies which for many years worked to ensure the above assumptions could be confirmed.

From this and the above additional assumptions, predictions of deflections and failure strength are made.

The improbability of all the above assumptions obtaining casts doubt on the Tiebout proposition.

If the above assumption does not hold, then the wall heat transfer coefficient can be calculated using the following expression:

Under the above assumptions, the homeotopy groups for are defined to be:

From a mathematically rigorous point of view, care must be taken with the above assumptions.

The above assumptions resolve the relations between mixture fraction f and all the mass fractions.

James cautions that available scientific evidence stands against the above assumptions and conclusions.

Opponents of administrative detention challenge the above assumptions.