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werpuc committed Jan 16, 2025
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8 changes: 4 additions & 4 deletions vignettes/workflow.Rmd
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Expand Up @@ -123,14 +123,14 @@ The number of unknown parameters is 6.
The two-component fitting function, is described as follows:

$$
D = n_a \cdot (1 - exp(-k_a \cdot t)) + n_b \cdot (1-exp(-k_b \cdot t))
D = n_1 \cdot (1 - exp(-k_1 \cdot t)) + n_2 \cdot (1-exp(-k_2 \cdot t))
$$

Where $a$ and $b$ are two of three exchange groups defined for the Zhang \& Smith equation. We perform three fitting processes (for each group combination) and select the best result comparing the $R^2$ value. That means we look for the fit using $k_1$ with $k_2$, $k_2$ with $k_3$, or $k_1$ with $k_3$ and select one as the answer.
Where $1$ and $2$ are two of three exchange groups defined for the Zhang \& Smith equation. We perform three fitting processes (for each group combination) and select the best result comparing the $R^2$ value. That means we look for the fit using $k_1$ with $k_2$, $k_2$ with $k_3$, or $k_1$ with $k_3$ and select one as the answer.

The initial value for $n_a$ and $n_b$ is 0.5. The initial values for $k$ are the same with analogical cases from the three-component equation (see section *x*).
The initial value for $n_1$ and $n_2$ is 0.5. The initial values for $k$ are the same with analogical cases from the three-component equation (see section *x*).

In this case, we assume that $n_a$ of hydrogen particles are undergoing the exchange with $k_a$ exchange rate, an $n_b$ with exchange rate $k_b$.
In this case, we assume that $n_1$ of hydrogen particles are undergoing the exchange with $k_1$ exchange rate, an $n_2$ with exchange rate $k_2$.

The number of unknown parameters is 4.

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