Sentence examples for using the facts that from inspiring English sources

From (3.7) and using the facts that and are nonnegative, and (3.8).

There are well known ways to qualify analog systems using the facts that: (1) they are built from standard modules with known properties; (2) design documents are available and described in a well understood language; (3) the performance of the component is constrained by physics; and (4) physics models exist to predict the performance.

Using the facts that for each and we have (2.6).

By (5.20), using the facts that and, and by employing (5.6), we have (5.5) as required.

The proof follows by applying Theorem 13 and using the facts that (f^{sigma}(t)=f(t)) and (h_{2} t, s)=frac{ t-s)^{2}}{2}) (from the first item of Definition 11 for the case (k=frac{ t-s

Using the facts that the state of stress is not uniform across an element and that the deformation gradient is a spatially continuous (and possibly non-differentiable) tensor, the proposed model uses a continuously modified deformation gradient to capture the location and orientation of wrinkles more precisely.

With this substitution, and using the fact that is an even function of and, (23) becomes.

"We use the facts that are the most persuasive," said Suzii Paynter, executive director of the advocacy group.

where, and we have applied (7) and used the facts that is zero-mean and for.

Not long after, using the fact that his mother was English, he came to England.

Using the fact that (4.8).