Sentence examples for approximated by applying from inspiring English sources

The corresponding rates of spatial exponential decay are approximated by applying statistical perturbation methods.

In practice, the covariance matrices are a priori approximated by applying the best available knowledge and tuned empirically in the application.

AE behavior is dependent on the degree of damage, and could be approximated by applying the AE rate-process analysis and damage mechanics.

Local site effects were approximated by applying the popular Nakamura technique [32, 33] which is based on the horizontal to vertical spectral ratio (HVSR) of ambient noise recordings at a site, using a three-component seismograph.

It is shown that in the low frequency region the wavenumbers may be approximated by applying so-called equivalent plate theory, in which the built-up plating is represented by an equivalent orthotropic plate.

Therefore when the number of channels M → ∞, the cdf of 1 M ∑ i = 1 M z i can still be approximated (by applying Theorem 3, Chap. VIII.4 in[27]) by a Gaussian cdf with mean and variance given by μ = 1 M ∑ i = 1 M E [ z i ], σ 2 = 1 M 2 ∑ i = 1 M Var [ z i ]. (43).

Based on our assumption, fixed above, the target distribution can be approximated iteratively by applying Eq. 1: begin{aligned} &pleft(mathbf{X}_{k+1}|mathbf{Z}_{0:k+1}right)= &C.pleft(mathbf{Z}_{k+1}|mathbf{X}_{k+1}right)int_{mathbf{X}_{k}}pleft(mathbf{X}_{k+1}|mathbf{X}_{k}right) pleft(mathbf{X}_{k}|mathbf{Z}_{0 k}right dmathbf{X}_{k} end{aligned} (1).

Water-level responses to pumping in hydrogeologically complex systems can be approximated well by applying multiple Theis models to a single pumping schedule.

The thermal data was approximated by functions and applied as material data to an analysis by finite element method (FEM).

The same model is also used to derive a linear approximate model by applying suitable system identification techniques.

For this purpose, we first of all develop an approximate controllability theory for the unperturbed linear system ((1.1) with (mathbf{f}equiv0 )), and then attempt to analyze the perturbed system (1.1) for its approximate controllability by applying the afore-developed linear theory.