Sentence examples for requires additionally from inspiring English sources

The presence of the maximum of the unknown function requires additionally some new comparison results, existence results as well as a new algorithm for constructing successive approximations to the exact unknown solution.

Similarly, our edge covering results can in principle be derived from the Asynchronous Computability Theorem [25] that requires additionally the continuous map to preserve identifiers of participants (because edge covering is not colorless).

Establishing similar bounds for V k ( ext ) ( s, t, ω ) requires the assumption that A ≤ i k ( ext ) ( t ) ≤ B, but obtaining tighter bounds requires additionally the knowledge of the sign of A C k + E L τ L, k and of B C k + E L τ L, k.

When ξ and η are summable, requiring additionally equality of their infinite series obtains the same conclusion, extending a theorem by Arveson and Kadison.

The structural elucidation of dimeric oxidation products of PTD is more challenging than analyzing PPD derivatives, since a determination of the ring positions of the methyl groups is required additionally.

The DBA-DR approach gives much insight into the behavior of components and their safety and shows critical design details, safety critical points, and cases where authorities require (additionally) a DBA-DR investigation.

We require additionally a m b m + 1 > 0 and a 0 b 0 > 0. Let moreover for two arbitrary but fixed j, k ∈ Z the sets J j + : = ( q j + 1, q j ), J k − : = ( − q k, − q k + 1 ) (61).

Dropping the three markers with the most extreme allele frequencies and recalculating Long's test yields a non-significant result for all ponds except Toro, which required additionally dropping the mtDNA marker to achieve adequate goodness-of-fit (P > 0.05) to the neutral admixture model (Table 2).

Unaligned reads were then trimmed to remove low-quality bases (requiring additionally that the remaining read fragment be at least half the original read length.

For this compile service we need a MATLAB license with all required toolboxes and additionally the MATLAB compiler toolbox.

The constitution additionally required new members to submit to a two-hour vetting visit at their home by a pair of BNP officials, a clause Collins ruled could be seen as intimidating for non-white applicants.