Sentence examples for by calculating the characteristic from inspiring English sources

(47) Hence we can determine (langle S_{j}rangle) by calculating the characteristic polynomial of G.

If (b_{1}<1) and (c_{1}<1), then the boundary equilibrium (E_{0}) is globally asymptotically stable with respect to G. By calculating, the characteristic equation at the boundary equilibrium (E_{0}) is given by ((lambda +1)^{2}(lambda -b_{1}+1)(lambda -c _{1}+1)=0).

Additionally, the discrimination of predicting mortality between AKI and proteinuria or hematuria was assessed by calculating the receiver operating characteristic (ROC) curve and the area under the curve (AUC).

Additionally, we assessed the discrimination power of miRNA expression levels to classify normal and tumor samples by calculating the receiver operating characteristic (ROC) curves and the area under the curve (AUC).

By calculating the receiver operating characteristic curve, an ONSD value of 5.35 mm resulted as the optimal cut-off point with a sensitivity of 95.1% and a specificity of 96.2%.

To show the reliability and relative performance of the proposed model, we compared our implementation with several other state-of-the-art segmentation algorithms (Table 1), using a similar approach as in [ 38], by calculating the receiver operating characteristic (ROC) curves on simulated data.

The concentration of released carbon dioxide was determined by calculating the area of the characteristic carbon dioxide peak at 2350 cm−1 and found to be 0.3 ppm.

The capacity of the TT genotype for predicting incident IFG and diabetes was examined by calculating the receiver operating characteristics (ROC) curves and the area under the curve (AUC).

The graft content was determined with the 1H-NMR spectroscopy by calculating the relative area of the characteristic peaks of PCL and GMA.

Then, we evaluate the properties of each node from the resulting networks by calculating the cumulative distribution of characteristic parameters such as degree, clustering coefficient, etc.

Moreover, the dependence of robust stability on the fractional order perturbation is analyzed by calculating the order sensitivity of characteristic polynomials.