Sentence examples for approximations were used from inspiring English sources

Energies along the reaction pathways were calculated at the MP2, LMP2 and LCCSD T0) levels (the L in the acronyms indicates that local approximations were used, and T0 is an approximate triples correction [27]), including the effects of the atomic point charges of the MM atoms in the calculations.

Integrated nested Laplace approximations were used as a Bayesian inference tool.

In all cases, second-order finite-difference approximations were used for spatial discretizations.

It should be pointed out that purely toroidal core flow approximations were used in previous studies (e.g., Bloxham et al. 2002; Olsen and Mandea 2008).

The Zimm/Debye approximations were used in the Astra software (Wyatt Technology) to estimate molar mass.

We investigated the behavior of the resulting systems of equations empirically for different values of s, N, and p with α = β = 0. We found that the system began to oscillate when p < 1/ Ns for s > 0 when second-order approximations were used for either the mean only or the mean and the variance, but not when first-order approximations were used for both of these moments.

Usually finite difference approximations are used to evaluate derivatives.

Characteristics of the approximations are used as feature descriptors.

Spectral approximations are used for the spatial discretization.

In the analytical solution three different approximations are used.

Moment closure approximations are used to provide analytic approximations to non-linear stochastic population models.