Sentence examples for equation is demonstrated from inspiring English sources

Finally, the reliability and rationality of the proposed equation is demonstrated through examples.

The transfer function J (n) = mσ a (n)/F (n) relating input to response acceleration of a single oscillator can be expressed as in Eq. (4) whereas the validity of this equation is demonstrated in Eq. (5).

The means and linear regression equation are demonstrated in Table  3 and Fig.  2.

32 In contrast, free testosterone (calculated according to the Vermeulen equation) was demonstrated to be an independent predictor of BMD and fractures in elderly men 33 and a positive predictor of cortical bone size in young men at the age of peak bone mass.

Moreover, the role semi-inner products play when establishing various likelihood equations is demonstrated.

The accuracy of the derived analytical equations is demonstrated via simulations implemented with the designed graphical user interface program and experimental works.

The proposed topology with simple design equations is demonstrated with the input and output frequencies of 0.9/1.8 GHz and less than 3.2 dB insertion losses.

The suitability of the scheme for discretisation of the compressible Navier Stokes equations is demonstrated by computing inviscid and viscous eigensolutions of compressible Couette flow.

The accuracy of the resulting constitutive equations is demonstrated on uniaxial, equibiaxial and pure shear experimental data provided in the literature.

The accuracy of the derived constitutive equations is demonstrated by using uniaxial, equibiaxial, pure shear, and plane strain experimental data provided in the literature.

The robustness of the developed algorithm in solving multiple coupled equations is demonstrated by solving a nonlinear model of a fixed-bed reactor in which both exothermic and endothermic reactions occur in the gas phase.