Sentence examples for applying the expression from inspiring English sources

By applying the expression in (3.1) to (2.1), (2.2), (2.8) and (2.9), we obtain four integral formulas in Corollaries 3, 4, 5 and 6, respectively.

To solve this problem, the density is periodically re-initialized applying the expression ρ i = ∑ j m j W ij. Open image in new window (5).

end{aligned} Hence, applying the expression of (x t)) in Lemma 2.2 and taking suitable estimates, we obtain |b_{n+1}|_{0}leq K_{2}|b_{n}|_{0}^{2}, where (K_{2}) is a positive matrix.

After applying the expression threshold, 2126 probe sets pairs were retained.

It then uses a correction function that reverses the probe positional intensity decay d(x) after applying the expression level dependency of the hybridization mode (details are given in the Supplementary Material).

The relative error obtained in our simulations is always inferior to 1% and is monotone decreasing with K. Hence, applying the expressions in Eqs.

The minimum can be numerically determined as a function of the load and the real-time capacity parameters at every SS ( and the distribution of for ), by applying the expressions for the mean overall delay of the tagged -packet (22).

Hence, before applying the expressions for breeding value and heritable variation of [ 5] to estimates obtained from the methods proposed here, they need to be translated into average effects of alleles [ 15].

Hazel Blears and the singer Mika both applied the expression to themselves pre-emptively.

They applied the expression to a case where the signal does not average out within the cap, thus constructing aliased power spectra.

The aim of the present work is to apply the expression found to a geometrically nonlinear analysis of quasistatic, coplanar crack propagation in some heterogeneous medium.