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The results show that the accuracy of the developed method can be considered suitable because the average percentage error, in comparison with the exact model, is in the order of 4% for the first approximation and 5% for the second approximation.
In Section 4, we will observe that to solve the first system approximation, we need to solve a system of non-linear equations, whereas for the second approximation, we only need to solve a system of linear equations (which is much simpler and more efficient to solve).
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Figure 4 shows the surface of the exact solution (43) in (a) and the surface of the second approximation (34) for (alpha=0.7) and (beta=0.5) in (b) at (a=1), (b=1) and (c=1).
In this paper, we give some of the first approximation algorithms for it.
Therefore, for system performance evaluation, we propose to use the second approximation especially for systems with large number of channels (e.g., in realistic wireless systems).
In Figure 2 we show the absolute error between the exact solution (2) and the second approximation (16) for different values of b.
In Figure 1, we show the surface of the exact solution (2) and the second approximation (16) for (alpha=0.7) in (b) at (a=1, b=0.01) and (c=1).
For the first approximation of the solution of the non-linear mathematical model, the averaging method, based on the small parameter theory, is used.
This indicates that either the autofluorescence intensity index of the tissue or the Photofrin-induced fluorescence may provide a good parameter for the "first approximation" characterization of the tissue.
Using TPFPD correlations for normal gravity to reduced gravity and microgravity may be acceptable for the first approximation, but correlations intended for microgravity and reduced gravity are needed and more experiments are desired to obtain more data with high accuracy.
Breccias formation for the first approximation was considered as a homogeneous layer, which resulted in a relatively poor fit over the low gravity values.
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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