## 3 Results and Discussion
### Tocopherols  
Tocopherols play a considerable role in human physiology, protecting cells from the potentially damaging effects of oxygen. In foods, they primarily safeguard fats and certain natural colorants from the detrimental effects of oxygen. Scientific studies demonstrated that \(\gamma\)-tocopherol possesses a distinctive antioxidant and anti-inflammatory capacity in the prevention of disease [49]. Moreover, alpha-tocopherol fulfills a multitude of functions beyond its antioxidant properties. In addition to acting as an antioxidant by binding to lipid peroxyl radicals, it also exhibits pro-oxidant, cell signaling, and gene regulatory functions [50]. Walnuts are a rich source of tocopherols, predominantly gamma-tocopherol, with lesser quantities of delta- and alpha-tocopherol [44].  
Figures 2 and 3 show the change in the amount of tocopherols. It can be observed that the largest amount of gamma-tocopherol is found in the samples, between 60.6-75.8% at the beginning of storage, and between 65.9-80.7% at the end of storage. This is followed by alpha-tocopherol with an amount between 21.6-35.4%, which was between 14.4-29.1% in the eighth month of storage. The smallest amount of delta-tocopherol occurs in the samples in amounts between 2.2-3.9% and 3.8-5.0% at the end of storage. The total amount of tocopherols measured at the beginning of storage was between 1135-1630 ug/g, while at the end of storage it was 779-866 ug/g. The rate of decrease during storage was between 50.2-76.3%, the highest rate in the case of the one containing nitrogen. [PERSON] et al. [39] measured similar vitamin E contents in Polish varieties. According to [PERSON] and [PERSON] [44], vitamin E content decreased at the end of the experiment, alpha-tocopherol content decreased by 26.6-39.9%, the gamma-tocopherol content by 27.0-35.5%, while the delta-tocopherol by 20.8-31.5% in the case of walnut samples stored for six months in a normal air composition and packed in nitrogen gas.  
Figure 2: Tocopherol content of the MPP and PP packaging samples during storage (ug/g). MPP (metallized polypropylene), PP (polyppropylene), A–E– (air without edible coating), A–E+ (air, with edible coating), N–E- (nitrogen without edible coating).  
It can be concluded that the ratio of different tocopherols was almost constant during storage. For each sample, it can be said that the vitamin E content was the highest after two months of storage; however, in the case of the samples treated with the coating (E+), the amount of tocopherols was significantly lower (\(p<0.01\)) only for the eighth month. In the case of MPP packaging with a nitrogen atmosphere (MPP-N), the amount of tocopherols fluctuates, showing an increasing and then decreasing trend. In the case of MPP and PLA uncoated atmospheric packaging (MPP-A-E- and PLA-A-E-), the values gradually decrease after an initial increasing trend, the largest between six and eight months. In the case of MPP and PLA coated atmospheric packaging (MPP-A-E+ and PLA-A-E+), on the other hand, the values initially stagnate and then also decrease significantly between the sixth and eighth months (every two months the difference between the values are not significant, but between the sixth and eighth months the difference is significant for all combinations). A more detailed statistical analysis can be seen in the Tables S1-S3 with regard to alpha-, gamma-, and delta-tocopherol content.  
[PERSON] et al. [51] monitored the tocopherol content of walnut oil samples at 60 \({}^{\circ}\)C for 60 days. During this period, alternating increasing and decreasing trends were observed for each tocopherol component. At the end of storage, the amount of all tocopherols decreased.