Sentence examples for exactly therefore from inspiring English sources

However, due to the fact that the regularization parameter (stage index p) is an integer, the discrepancy principle defined by Equation (21) may not be satisfied exactly; therefore, we reformulate the definition to p o p t = arg min 1 ≤ p ≤ P p s.t.

Moreover, the hypotheses that have been raised in the literature are generally not specified exactly therefore we were left to make some arbitrary assumptions, e.g. to define what is exactly the behavior of an indolent cancer.

In our study population, the distinction between premenopausal and postmenopausal women could not be made exactly; therefore, it was assumed that women older than 50 years are representative for the group of postmenopausal women.

Because it solves the transport equation stochastically, complicated geometry may be modeled exactly and therefore heterogeneity even at the most detailed level does not challenge the method.

Further, in many cases, it is impossible to solve nonlinear equations exactly, and therefore there is a need for some approximate solution method.

It should be noted that in real-world environments, noise is never exactly isotropic; therefore, these evaluations must be considered with caution.

Repetitions of the CSP within the same sequence are not exactly identical; therefore, after an initial event of internal duplication, a differentiation of the CSP may have occurred.

In addition, the qualitative and quantitative composition of the products were heterogeneous and not exactly titrated, therefore reported perceptions could be also affected by different doses and ingredients of products.

In our cases, the carcinoma cells were positive for CK but not vimentin, so they were not exactly "rhabdoid cells"; therefore, we diagnosed them as salivary duct carcinoma cells with rhabdoid features.

The Book of Genesis is therefore exactly wrong.

"These three names are not exactly the same, therefore we believed that there was a need to clarify," he said.