\begin{document}$\gamma$\end{document}-ray bursts (GRBs) carry significant physical information. The electron density in the GRBs outflow is very large. In this study, we calculate the matter effect on neutrinos when they propagate through such a dense region. The average survival probability and the flavor ratio of neutrinos are determined. The ratio of resonant neutrino energy from different spherical shells provides the information of power index N for the power-law distribution of electrons in the hot fireball model. Electron density in the magnetic jet model is sufficiently lower than in the hot fireball model. The matter effect on neutrinos can be used to distinguish these two models. The coherent effect of strongly lensed PeV neutrinos is also discussed. The average survival probability of strongly-lensed electron neutrinos in the normal and inverted hierarchical cases are presented. The results show that this coherent effect can be used to determine the hierarchical mass of neutrinos."> Matter effects and coherent effect of neutrinos produced from <inline-formula><tex-math id="M34">\begin{document}${{\gamma}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/510195dd-41ce-4130-b9c5-f4b90780497d/CPC-2019-0166_M34.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/510195dd-41ce-4130-b9c5-f4b90780497d/CPC-2019-0166_M34.png"/></alternatives></inline-formula>-ray bursts -
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