Sentence examples for equation is justified from inspiring English sources

The use of the JKR equation is justified through an analysis of the shape of the fibril extremities (parabolic) as well as their diameter (∼200 nm).

Finally, the extended dual-site Langmuir equation is justified as a suitable macroscopic model for multi-component adsorption on heterogeneous porous media with parameters estimated from small-scale models.

(5) Extrapolation of half-lives to lower temperatures using the Arrhenius equation is justified for assessing exposure to industrial chemicals and biocidal products in a standard European environment as well as for comparing degradation of PPP in different European climate zones as long as the limitations of this approach are kept into consideration.

In this paper, the motivation for introducing HJB equations is justified with mathematical rigor, which is given by reference to the maximum likelihood approach to deriving the EKF.

In Additional File 1 we further show that noise terms are indeed sufficiently small that linearisation of the pathway equations is justified.

Furthermore, the equivalences of solutions and weak solutions for the aforementioned equations are justified.

The following equations are justified.

This limit is given by the next equation, which is justified in Subsection 2.1.

The minimum of the solution (Equation 12) is justified by the positive Hermitian characteristic of the covariance matrix Rnn,k.

In our case, the computation of the peak is performed on the discrete-time version of s p (t) given by Equation 6; such approximation is justified if the oversampling factor Q is sufficiently high.

This observation is justified by Equation 33 to 35; increasing the value of h will further increase the CW size beyond the optimum value and result in throughput degradation.