Sentence examples for approximation which has been from inspiring English sources

To overcome this limitation, the Taylor series expansion is used to simplify the phase terms in (26), with a sufficient precision of approximation which has been verified in [39].

The present paper proposes a simple model based on the point kinetics approximation, which has been set up deriving an alternative formulation of the time-dependent neutron transport equation.

To numerically model the holographic microscopic imaging of the nanoparticles and nanolenses, we first treat the nanoparticles and nanolenses using the thin-lens approximation, which has been shown to be equivalent to an FDTD simulation for similar objects, although here we model the materials using complex refractive indices to account for absorption and scattering.

Simulated data are commonly acknowledged to be approximations which have been generated based on previous data (e.g. [ 4]).

The high computational load of JLH comes from the fact that all parameters have to be estimated in one problem; the computational time in NONMEM and Monolix is reduced via various approximations, which have been developed over the years.

First, the approximation of is similar to the approximation of, which has been discussed previously.

By applying the theory of stochastic approximation [14], which has been used in many studies on wireless networks [15, 16], we will prove the main result of this paper, that is, the learning converges to a stationary point regardless of the initial strategies (Propositions 1 and 2).

It is possible that the inconsistency between the BF-based support for more highly partitioned models versus evidence for model overparameterization that we observed may be related to calculation of BFs based on harmonic mean approximations of marginal likelihoods, which has been shown previously [ 42, 43, 45].

The ASE is a discrete approximation of the Integrated Squared Error (ISE), which has been shown by Marron et al. [33] to lead asymptotically to the same level of smoothing as the ISE and mean integrated squared error (MISE).

The most common approximation method is the LNA which has been derived by van Kampen through the system size expansion of the Master equation.

Clearly, the modulus is meaningful to describe the approximation degree and the smoothness of, which has been widely used in the study of approximation on sphere.