Sentence examples for by using analytical formulas from inspiring English sources

From these numerical results, mathematical relations between design variables are drawn by using analytical formulas based on classical sandwich theory.

Standard error estimates are shown in parentheses and were obtained by using analytical formulas.

Correcting for underestimation of the type 1 error rate can be performed easily using analytical formulae or by analyzing the QQ plot [ 43], which would allow for a faster analysis than with the FASTA model.

In addition, the energy storage capacity of each sample is estimated using analytical formulae.

Figure 2 The BEP performance for the sharing DF scenario for different channels' conditions using analytical formula.

Each QTL variance and effect, and the total QTL variance were also estimated using analytical formulae.

§ p-value computed using analytical formula for secondary-structure-constrained 3D modeling in (Hajdin et al., 2010); it is not applicable to peripheral domains.

Finally, the minimum weight designs are presented by using the analytical formulae.

Fraction BR-3 containing PA (Rf 0.29) was dried using a rotary evaporator and weighed using analytical balance to obtain 0.767 g pure crystals of PA (96.6%) as confirmed by High Performance Liquid Chromatography (HPLC) and calculated by the following formula: % Purity = Peak Area of Panduratin A / Total Peak Area − Peak Area of Solvent.

As a result, the author expects that a designer is to be free to design more accurate springs by using the global analytical formulas presented in this study.

I have created the following drawings by using mathematical formulas.