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Figure 1 Numerical evaluation of equation ( 15 ).
(56) Figure 3 shows the numerical evaluation of equation (56).
Figure 1 shows the numerical evaluation of equation (40).
Figure 4 Numerical evaluation of equation ( 44 ) in Atangana-Baleanu-Caputo sense.
Figure 3 Numerical evaluation of equation ( 38 ) in Caputo-Fabrizio sense.
First of all, the evaluation of Equation 13 requires an implementation of v -1(c), which is not straightforward.
Similar(45)
Moreover, the evaluation of Equations 32 and 33 is relatively easy since computing s i,j and q i,j required in A 0 and B 0 can be achieved via [7]: s i, j = S i, j 1 - γ j S i, j, q i, j = Q i, j 1 - γ j S i, j, g i, j = G i + γ j Q i, j 2 1 - γ j S i, j (34).
To enable a thorough exploration of the search space, the optimization runs were restarted after 100,000 evaluations of equation (6) using the best parameters currently available as starting values in the following iteration.
At the point on the frequency axis where the DFT amplitude becomes maximum (i.e., the integral frequency when the frame length is 1 s), the evaluation function of Equation 2 is minimized at the initial phase determined by DFT. Figure 3 Distribution of the cost function.
The figure also shows that the formulated optimum (CW^{text {opt}}_{text {wu}}) (Equation 22) is almost 20% higher than the actual (CW^{text {opt}}_{text {wu}}) (for k=1) based on brute force evaluations of Equations 3, 7, and 14.
To anticipate and mitigate struvite buildup, solubility models have been developed that employ equilibria software for the evaluation of equilibrium equations.
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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