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The neutrino oscillation parameters are taken from the analysis of various neutrino ex- periments [17, 18], except for θ$_{13}$ [19], as 

and 

<img src='content_image/343963.jpg'>

<img src='content_image/343964.jpg'>

We calculate the neutrino survival probabilities for both normal (Δ m 2 13 > 0) and inverted (Δ m 2 13 < 0) mass hierarchies for four cases of sin $^{2}$2 θ$_{13}$ value: sin $^{2}$2 θ$_{13}$ = 10 − $^{2}$, 10 − $^{3}$, 10 − 4 and 10 − $^{5}$. 

The energy spectra of the neutrinos passed through the exploding supernova, φ SN ν ( E$_{ν}$ ), are obtained from the spectra of the neutrino emitted from the neutrino sphere, φ org ν ( E$_{ν}$ ), multiplied by the survival probability in accordance with the following equation, 

<img src='content_image/343965.jpg'>

where φ$_{ν}$$_{x}$ ≡ 1 $_{4}$( φ$_{ν}$$_{µ}$ + φ$_{ν}$$_{τ}$ + φ$_{¯}$ ν$_{µ}$ + φ$_{¯}$ $_{ν$_{τ}$}$), and P and ¯ P are survival probabilities of ν$_{e}$ and ¯ ν$_{e}$ , respectively. 

Neutrinos change largely their flavors at resonances of neutrino oscillations. There are two resonances for supernova neutrinos (e.g., [24]). The resonance points of higher and lower electron number densities correspond to H-resonance and L-resonance, respectively. The electron number density at the resonance point is written as 

<img src='content_image/343966.jpg'>

where Δ m 2 and θ correspond to | Δ m 2 13 | and θ$_{13}$ at H-resonance and to Δ m 2 12 and θ$_{12}$ at L-resonance, respectively. The flavor change at a resonance strongly depends on adiabaticity of the resonance. When the resonance is adiabatic, large flavor change occurs. The neutrino adiabaticity is estimated by γ , 

<img src='content_image/343967.jpg'>

