Sentence examples for using the formulae in from inspiring English sources

We used Mathematica to evaluate variances of invariant GRFs, using the formulae in the theorem of Cramer and Leadbetter's.

Asymptotic sampling variances for all ten formulations were calculated using the formulae in Table 1.

Standard errors for the SMR and the DRS CMF for the DAVROS data have been calculated using the formulae in the Appendix (see Additional file 1) and by a simple bootstrap taking 1000 samples with replacement from each centre, calculating the SMRs and DRS CMFs for each sample, and calculating their standard deviation from the average value in the bootstrap samples.

We will then compute sensitivity indices for (R_{0}) using the formula in (10).

Finally, we will compute the sensitivity indices for (V_{2}^), (L_{2}^), (I_{2}^) and (W_{2}^) using the formulas in Theorem 1.

To get the histogram we generate several realizations of i q [k] for q = 410 using the formula in (15).

It is also shown that the cracking torque can be predicted using the formulas in the ACI and AASHTO LRFD codes without any modification.

We will first compute the sensitivity indices for (T_{1}^), (T_{2}^) with respect to the parameters by using the formulas in Theorem 1.

It is obvious that problem (42) match the framework of the problem (5), thus the solution of (42) can be obtained by using the formulas in Section 2.2.

In Section 2, we obtain an expression of stationary equations of system (1.1) in spherical coordinates by using the formula in [14].

The efficiencies of DNA elongation, primer translocation, circularization, and DNA elongation were then calculated using the formulas in Fig. S3B.