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Applying the relation (A14).
The amount of dust attenuation is then calculated by applying the relation of Buat et al. (2011a).
By applying the relation between the joint Gaussian distribution and its corresponding conditionals, we arrive to a suitable proposal density for the M-H algorithm given by (37).
By applying the relation between integer system's characteristic equation and fractional system's characteristic equation, some brief sufficient stability conditions are deserved.
Assuming Vegard's law to hold for In x Al1-xN and considering the biaxial strain in the layer, the indium composition can be determined by applying the relation.
The evaluation value f((S,s)) can be calculated, which is the original problem's optimal value, by iteratively applying the relation for j=n,n−1,…,1 with initial values f((n,s))=iv(s).
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Then for every word (w') obtained from w by applying the relations of (tilde{S}( MM _4)) we have (alpha _j(w')=alpha _j w)), (j=1,2,3,4), u(w) is obtained from (u(w_1)) by applying relations of (S( MM _2)).
We applied the relation between Mellin and Laplace transforms.
The simplest approach to apply the relation given in eq. 4.3 is the linear method.
Each point represents a specific data pair, which makes it possible to apply the relation while retaining the reliability of the input data.
Then we apply the relation The 95% CI for the difference of the means thereby is Suppose the paired two-sided t-test was used.
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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