## 3 Results and Discussion
### Kinetics Analysis of Oxidation  
Oxidation time measured in isothermal conditions (100-140 \({}^{\circ}\)C) enabled preparation of graphical dependence between the logarithm of the induction time (\(\tau\)) and the reciprocal temperature (in absolute scale) (Figure 4). Due to the fact that high R\({}^{2}\) coefficients were obtained (>0.99), the data from the equation describing the linear relationship were the starting point for calculating the kinetic parameters (Table 4). In Table 5, the oxidation parameters of amaranth and quinoa oil (obtained in this study) with the available references data on the oxidation of other vegetable oils were presented. Obtained values of activation energy were lower than values obtained by [PERSON] et al. [10] for linseed oil (93.14-94.53 kJ), [PERSON] et al. [44] for _Camelia sativa_ oil (87.63-93.61 kJ), and [PERSON] et al. [41] for hazelnut oil (89.06 kJ), olive oil (92.81 kJ), and rapeseed oil (92.68 kJ). Due to the high content of polyunsaturated fatty acids in the analyzed amaranth and quinoa oils, a small amount of energy was needed to initiate the oxidation reaction. According to [PERSON] et al. [45], high content of MUFA and SFA would increase the activation energy, whereas the high content of PUFA would decrease the activation energy value for lipid oxidation. Figure 4: Log PDSC induction time (\(\tau\)) versus reciprocal temperature for oxidation of amaranth (red line) and quinoa (blue line) oil. Taking into account the rate constant of the oxidation reaction, it can be observed that the reaction rate increased with increasing temperature, both for amaranth oil and quinoa oil. The k values obtained by other research [10; 41; 44] demonstrated the same pattern. This study had limitations. In the present study we did not analyze the oxidative stability by the Rancimat method in wide range of temperatures (only at 120 \({}^{\circ}\)C), as well as in total phenolic compounds. Interest in quinoa and amaranth has markedly increased, due to their significant amount of bioactive compounds, such as phenolic compounds, flavonoids and their glycosides, betanins, and carotenoids [46]. Total phenolic compounds were positively correlated with antioxidant activities of quinoa and amaranth seeds [46; 47]. Phytochemical nutrients in quinoa and amaranth may help restore the balance between oxidative stress and antioxidant defense. Diet supplemented with quinoa and amaranth seeds reduced oxidative stress in the plasma, heart, kidney, liver, spleen, lung, testis and pancreas of fructose administered rats [46]. [PERSON] et al. [48] reported that activity of superoxide dismutase (an enzyme that catalyzes the dissociation of the free radical in water and hydrogen peroxide) was increased when quinoa seeds were supplied to hypertension-induced rats. In addition, the free phenolic and PUFA fractions of cooked quinoa showed strong antioxidant ability based on Caco-2 cell-based antioxidant activity assay. In addition, the phenolics and unsaturated fatty acids exhibited protective effects on H\({}_{2}\)O\({}_{2}\)-induced Caco-2 cell oxidative injury [46]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Quinoa** & **Amaranth** \\ \hline \(a\) & 4.27 & 4.44 \\ \(b\) & 8.82 & 9.38 \\ \(\text{R}^{2}\) & 0.9919 & 0.9982 \\ \(\text{{E}a}\) (kJ/mol) & \(77.75\pm 3.24\) a  & 80.82 \(\pm\) 2.87 a  \\ \(Z\) (1/min) & \(1.44\times 10^{7}\) & \(5.13\times 10^{7}\) \\ \(k\) at 100 \({}^{\circ}\)C & \(1.89\times 10^{-4}\) & \(2.48\times 10^{-4}\) \\ \(k\) at 110 \({}^{\circ}\)C & \(3.63\times 10^{-4}\) & \(4.91\times 10^{-4}\) \\ \(k\) at 120 \({}^{\circ}\)C & \(6.76\times 10^{-4}\) & \(9.36\times 10^{-4}\) \\ \(k\) at 130 \({}^{\circ}\)C & \(1.22\times 10^{-3}\) & \(1.72\times 10^{-3}\) \\ \(k\) at 140 \({}^{\circ}\)C & \(2.14\times 10^{-3}\) & \(3.10\times 10^{-3}\) \\ \hline \hline \end{tabular} Data denoted by the same letter are not statistically different (\(\alpha=0.05\)).  
\end{table}