Sentence examples for formulas are shown from inspiring English sources

Results of the synthesis, calculated according to above formulas, are shown in Table 4.

The flame reaction of reaction solution further confirms the de-intercalation of Na+, and the reaction formulas are shown (Additional file 1: Figure S1).

Using substitute borehole wall stress distribution equations of arithmetic coordinate in the cylindrical coordinates' version can now be obtained, and the formulas are shown as shown in Eq. 11.

These two coefficients are defined as E = frac{{S_{(ABC + CDA)} }}{{S_{(OBE + ODF)} }} (21) h_{e} = frac{1}{2pi } times frac{{S_{(ABC + CDA)} }}{{S_{(OBE + ODF)} }} (22 Meanings of the parameters in above formulas are shown in Fig. 16.

By multiple regression analyses, bi-quadratic relationships between the rupture values, the strain energy density and the measured fracture density in the Chang 71 and 72 members of different episodes have been built and the empirical formulas are shown in Table 3.

The structural formulas are shown in Figure S2 in the Supporting Information.

The effectiveness of the proposed formulas is shown in our numerical studies.  .

A comparison of the curves obtained by simulations and by the analytical formulas is shown in Figs. 12 and 13.

Moreover, the 3D maps of the potential on the ground are reported in Fig. 4. Excellent agrement between the numerical results and the predictions through analytical formulas is shown in each of the examined case.

The use of second derivatives was first suggested in [ 24] and later studied in detail in [ 25], [ 26] and [ 27], and the resulting formulas were shown to have good stability properties.

The average difference for all the subjects between the IOL power calculated with our procedure and different regression based formulas is shown in Fig. 4a, together with the average absolute difference (Fig. 4b), in order to consider sign compensations.