Changes between Version 138 and Version 139 of DatabaseBasedAnalysis/Spectrum


Ignore:
Timestamp:
12/05/19 14:28:55 (6 years ago)
Author:
tbretz
Comment:

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  • DatabaseBasedAnalysis/Spectrum

    v138 v139  
    8989
    9090
    91 N is the number of events in the energy interval \(E\in\Delta E=[E_\textrm{min};E_\textrm{max}]\) and the zenith angle interval \(\theta\in\Delta\theta=[\theta_\textrm{min};\theta_\textrm{max}]\)
    92 
    93 \[N_0^\textrm{tot} = \sum_{i=0...N}^{E\in\Delta E}\sum_{j=0...N}^{\theta\in\Delta\theta} \omega(E_i, \theta_j)\]
     91\(N\) is the number of produced events in the energy interval \(E\in\Delta E=[E_\textrm{min};E_\textrm{max}]\) and the zenith angle interval \(\theta\in\Delta\theta=[\theta_\textrm{min};\theta_\textrm{max}]\). The weightes number of events \(N'\) in that interval is then
     92
     93\[N'(\Delta E, \Delta\theta) = \sum_{i=0...N}^{E\in\Delta E}\sum_{j=0...N}^{\theta\in\Delta\theta} \omega(E_i, \theta_j)\]
    9494
    9595Since \(\omega(E, \theta) = \rho(E)\cdot \tau(\theta) \)
    9696
    97 \[N_0^\textrm{tot} = \sum_{i=0...N}^{E\in\Delta}\sum_{j=0...N}^{\theta\in\Delta\theta} \rho(E_i)\cdot\tau(\theta_j) = \sum_{i=0...N}^{E\in\Delta E}\rho(E_i)\cdot\sum_{j=0...N}^{\theta\in\Delta\theta} \tau(\theta_j)\]
     97\[N'(\Delta E, \Delta\theta) = \sum_{i=0...N}^{E\in\Delta}\sum_{j=0...N}^{\theta\in\Delta\theta} \rho(E_i)\cdot\tau(\theta_j) = \sum_{i=0...N}^{E\in\Delta E}\rho(E_i)\cdot\sum_{j=0...N}^{\theta\in\Delta\theta} \tau(\theta_j)\]
    9898
    9999