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Here u denotes a reference approximation of the solution of (1), calculated using the same scheme up to a precision of 10−5.
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However, from a practical perspective, experiments indicate that the difference in fault probabilities in the second cache obtained by comparing the independent reference model approximation and the actual miss stream is not large, although measurable.
Smaller number of misalignments: aligners match sequences to a reference using approximation which is done by allowing up to a small number of allowed base mismatches (abm).
The modal analysis solution is of interest not only as a reference for approximations but also for practical applications, because the aspect of computing time becomes more and more unimportant (the 3D-plots presented below for the sound field were evaluated with modal analysis in about 6 s).
The paper of Mursaleen et al. [11] is one of the latest references on approximation by q-analogue.
Until now, in many references, viscosity approximation methods still are used and studied, which formally generates the sequence { x n } by the recursive formula: x n + 1 = α n f ( x n ) + ( 1 − α n ) S x n, where f is a contraction and α n ⊂ ( 0, 1 ) is a slowly vanishing sequence.
A 500 m observation distance on either side of the aircraft was achieved by having observers look in the area from 45 degrees down towards the plane, and also marked using tape on the windows for reference; these approximations were calibrated against markings on the ground using a marked football field in Cancun as a guide.
We calculated the evolutionary distance between every pair of species in the proximal promoter, in the enhancer region and in the fifth intron (the last for reference, as an approximation to the neutral rate of substitution).
In references, several different approximation schemes are proposed, such as the Grünwald-Letnikov scheme, (L_{1}) approximation.
Other approaches based on Hermite polynomials expansion were also introduced by [1 3] and were extended in several directions recently, see [25] and all the references on the approximation of transition densities therein.
In [6] and references therein, the approximation J[ρ0] ≈ CJ[∫ρ06/5d r1]5/3 is also discussed (see some more remarks in ' Some numerical illustration' section and Appendix 4) which, similar to Equation 5 as mentioned, allows numerical integration for GTO and STO basis sets as well, while J[ρ0] is traditionally evaluated effectively and analytically with GTO basis sets.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com