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Considering the region of validity of diffusion approximation only the part above the approximate mean free scattering path is presented for comparison.
For weak fluid structure interaction, the first order approximation only predicts the existence of the main inner resonance.
Because the heat effects associated with adsorption are comparatively large, the assumption of isothermal behavior is a valid approximation only when uptake rates are relatively slow.
Because the heat effects associated with adsorption are comparatively large, the assumption of isothermal behaviour is a valid approximation only when uptake rates are relatively slow.
The Ekberg, Kabo and Andersson calculation is shown to be a good approximation only for nearly circular contacts, high Poisson's ratio and high Dang Van constant.
The results show that, for a first order approximation, only the lower frequencies and first mode shape are significantly affected by the cubic non-linearity.
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Perceptrons also have the capability of universal approximation but only RBFs possess the ability of optimum approximation.
Then, aiming at reducing the complexity of nonlinear approximations, only two least-square-support-vector-machine-based (LS-SVM-based) approximators with two design parameters are required through norm form transformation of the original system.
More realistic band gaps from meta-generalized gradient approximations: Only in a generalized Kohn-Sham scheme.
In perturbative approximations, only the mean and variance of the mixing-ratio distribution are used.
(The focus on high level 'Big-O' approximations only seems fitting for this piece).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com