## 4 Discussion
### Some Remarks to All the Elements  
For dynamic conditions, the equation in differential form, Equation (8), is commonly recognized as the starting point for consideration. If the approximate form of the solution of Equation (8), referred to by the authors as the Coats\(-\)Redfern equation (Equation (9)), interacts with this equation, it leads to Equation (13). This equation has an identical mathematical structure, independent of the heating rate and pre-exponential factor. The \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Equations/Table** & \(T_{0}\), K & \(T_{iso}\), K & \(T_{c}\), K & **Remarks** \\ \hline (65) & - & 914.29 & - & - \\ (66) & - & - & 1164.6 & - \\ (67) & 896.29 & - & - & - \\  & 876.3–990.6 & - & - & - \\  & (939.0) & & - & - \\ \cline{2-5}  & 879.05–991.37 & & - & - \\  & (939.88) & & & \(T_{iso}\) is only of \\ Figures A1–A4 & - & 949.5–1060.6 & - & correlation\(-\)statistical \\  & - & & & meaning \\ Figures A1–A4 & - & 1074.0–1298.4 & - & \(T_{iso}\) is higher for \\  & - & 1074.0–1298.4 & - & isocorressional method \\  & & & & (\(\alpha\) = const.) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Summary of temperatures determined for experimental data (\(T_{\text{eq}}=1172.4\) K [19]). consequences of analyzing the adoption of specific analytical forms of the integration constant open up new possibilities for comparison of the Arrhenius parameters obtained through different paths, including Vyazovkin's, discussed in detail in the book [31]. In contrast to isoconversion concepts, in this work one still stays with the classical variant (\(q=\text{const}\)) and for this possibility and for simulated \"in silico\" data the very important significance of the coordinate \([T_{0},\alpha_{0}]\) is presented, thanks to which Equation (25) reproduces the activation energy \(E\) and also the constant \(\ln A\cdot f(\alpha_{0})\). For many models, \(f(\alpha_{0})\) can be calculated or simply ignored. In relation to the proposal to determine the \"elbow\" point coordinate, based on the knowledge of higher order derivatives [38], the methodology has been simplified, which boils down to determining the isokinetic temperature from the constant in Equation (19) and calculating the initial transformation step from Equation (27) or (40). On the other hand, consideration of simulated data does not provide a basis to demonstrate the existence of the \(KCE\), which appears for experimental data. It is necessary not only to verify it statistically, but also using the \(CQF\) and K indicators via Equations (46)\(-\)(49) to give the isokinetic temperature a physicochemical sense. In the association of works [5; 20; 21; 43], the experimentally determined considered temperatures form a sequence, where \(T_{\alpha q}\) denotes the thermodynamically determined equilibrium temperature of the reaction (Equation (6)), sometimes also called the inversion temperature:  
\[T_{0}\leftrightarrow T_{iso}\leftrightarrow T_{c}\leq T_{eq} \tag{72}\]  
The current work proved that the temperatures \(T_{iso}\) and \(T_{c}\) are theoretically equal (compare Equations (44) and (62)), while the temperature sequence given in Equation (72) follows from many factors. These are: sample quality (mass, degree of purity, moisture content, crystalline/amorphous form, analysis conditions: isothermal/dynamic, heating rate, atmosphere, flow, reactor type) and workshop issues (variation of \(\alpha\), calculation techniques, distinguishing variants: \(q=\text{const},\ \alpha=\text{var}\ \text{or}\ q=\text{var},\ \alpha=\text{const}\)). In light of these considerations, the isokinetic temperature \(T_{iso}\) is of lesser reliability than the initial temperature \(T_{0}\) or even the compensation temperature \(T_{c}\), which is implicit in the kinetic relationship. As noted in [52], Equation (69) is derived from various sources, and Equation (68) is composed of correlation and point analysis-both equations involve the same reaction/process of thermal decomposition of calcite.