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Moreover, from Fig. 7 a, b, it can be apperceived that the proposed mixture approximation precisely fits the empirical PDF and the tail of the empirical data with respect to those of the HTR-LM1, HTR-LM2, and HTR-FLOM mixture approximation models for ultrasound images taken from the pancreas and breast mass, respectively.
It is not surprising this parameter is underestimated when scattering increases, as the hypothesis of a single scattering regime may not be reasonable anymore, while first-order approximation precisely does not take into consideration multi-scattering regimes.
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He himself had previously said as much, and it also didn't make sense that a man who had reportedly wanted to avoid the invasiveness and turmoil of a presidential campaign would then opt for an approximation of precisely that in the Number 2 instead of the Number 1 slot.
As illustrated in this figure, the proposed mixture approximation fits more precisely the empirical HTR obtained from the samples, while sample size is small and the statistics of distribution is impulsive.
This approximation scheme computes precisely the effect on the mean and covariance of a normal distribution by the third order and below terms of the Taylor expansion of the non-linear function, while presence of fourth order or higher terms in the Taylor expansion introduce error [70].
More precisely, the approximation 1/ i = ln N + CE + N-1/2 - N-2/12 has an error less then 10-6 for N > 10.
Similar to the classical case, the lower bound for the admissible speeds of a function f of type A can be reconstructed starting from a sequence of increasing approximations of type B. Precisely, we have the following proposition.
Modern soil classification started with the publication of the 7th Approximation of the USDA Soil Taxonomy, where precisely defined and quantified soil properties as such, or in combination, were used to define "diagnostic soil horizons".
The 3D elastic wave equations can be used to simulate the physics of waves traveling through the Earth more precisely than acoustic approximations.
A 2016 paper the two published together in Linear and Multilinear Algebra ("On the Maximal Error of Spectral Approximation of Graph Bisection") evaluates how precisely such work can be performed.
By this algorithm, not only can the bulk physical quantities be evaluated more precisely but also an approximation to the boundary thermodynamic quantities can be obtained.
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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