Sentence examples for and hence required from inspiring English sources

Second, models differ as a result of the objectives of model development, and hence required scale and degree of detail and comprehensiveness.

This is somewhat misleading since Halpern considered only an instance of Halpern iterations in which the reference point was set to 0 and hence required a closed ball around 0 to be contained in the domain C of the self-mapping T. In the paper, Halpern examined these iterations in the setting of Hilbert spaces.

His original 1990s contract specified one-year deadlines for his previous literary works, but Martin only realized later that his new books were longer and hence required more writing time.

The density higher than 100 K at times led to pronounced cell death because of cell overgrowth and hence required frequent medium replenishment.

Considering that both the morphological reorganization and the positional shift noted here have preferred directions, they may be predetermining the migration direction and hence, required for electrically-guided cell migration.

The spruce material was rather toxic itself and hence required no sodium azide addition.

However, after achieving the required performances, coefficients of the designed beamformers are of very high precision and hence require significant efforts in order to preserve the performance and trade off the computational efficiency.

The bank's hard line has exposed a fracture between Europe's large and small countries, which have divergent growth rates and hence require different monetary policies.

differ in subject matter and hence require different procedures to check the truth or falsity of their premises.

A programme that sought to save a species rather than individuals would allow each infected wolf to pass the disease on to more than one healthy animal and hence require fewer vaccinations.

Generally, the damage estimation is an ill-posed inverse problem, and hence requires regularization.