Sentence examples for additional operations are required from inspiring English sources

The exception is factivity, discussed next, for which no additional operations are required, though additional axioms are.

Besides those conversion steps, additional operations are required in order to facilitate further modeling efforts by researchers.

No additional operations were required.

No additional operations were required to achieve the surgical objective.

The procedure offers postural correction at the level of the pelvis, low morbidity and no additional operations were required to achieve the surgical objective.

After Resaca de la Palma, Mexican forces were cleared from the Texan side of the Rio Grande, but additional operations were required to force Mexico to agree to the border.

(3) Provide the prestressing sequence in such a way that no additional tensioning operations are required to correct creep and shrinkage effects in service.

Although it can be realized using the permutation matrix (mathbf {P}) as (mathbf {M}'=mathbf {P}^{mathrm{T}}mathbf {M}mathbf {P}), this implementation is not efficient because the memory traffic increases and additional arithmetic operations are required compared to the COO format.

Additional O(d u ) operations are required for computing the term for row 1 and the row i such that v i  =  x∗, and therefore the total number of operations for computing the term for all d u  entries in column j of H u, u ′ is O(d u ).

Thus NM2 operations are required.

Thus, aN operations are required.