Changes between Version 142 and Version 143 of DatabaseBasedAnalysis/Spectrum

Timestamp:

12/05/19 14:41:09 (6 years ago)

Author:

tbretz

Comment:

--

DatabaseBasedAnalysis/Spectrum

@@ -89 +89 @@
 
 
-\(N(\Delta E, \Delta\theta)\) 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 weighted number of events \(N'(\Delta E, \Delta\theta)\) in that interval is then
-
-\[N'(\Delta E, \Delta\theta) = \sum_{i=0...N}^{E\in\Delta E}\sum_{j=0...N}^{\theta\in\Delta\theta} \omega(E_i, \theta_j)\]
+\(n(\delta E, \delta\theta)\) 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 weighted number of events \(n'(\delta E, \delta\theta)\) in that interval is then
+
+\[n'(\delta E, \delta\theta) = \sum_{i=0...n}^{E\in\delta E}\sum_{j=0...n}^{\theta\in\delta\theta} \omega(E_i, \theta_j)\]
 
 Since \(\omega(E, \theta) = \rho(E)\cdot \tau(\theta) \) with \(\rho(E)\) the spectral weight to adapt the spectral shape of the simulated spectrum to the real (measured) spectrum of the source and \(\tau(\theta)\) the weight to adapt to oberservation time versus zenith angle.
 
-\[N'(\Delta E, \Delta\theta) = \sum_{i=0...N}^{E\in\Delta}\sum_{j=0...N}^{\theta\in\Delta\theta} \rho(E_i)\cdot\tau(\theta_j) = \sum_{i=0...N}^{E\in\Delta E}\rho(E_i)\cdot\sum_{j=0...N}^{\theta\in\Delta\theta} \tau(\theta_j)\]
+\[n'(\delta E, \delta\theta) = \sum_{i=0...n}^{E\in\Delta}\sum_{j=0...N}^{\theta\in\Delta\theta} \rho(E_i)\cdot\tau(\theta_j) = \sum_{i=0...n}^{E\in\Delta E}\rho(E_i)\cdot\sum_{j=0...N}^{\theta\in\Delta\theta} \tau(\theta_j)\]
+
+The weighted number of produced events \(N'(\Delta E, \Delta\Theta)\) in the total energy interval \(E\in\Delta E=[E_\textrm{min};E_\textrm{max}]\) and the total zenith angle interval \(\theta\in\Delta\Theta=[\Theta_\textrm{min};\Theta_\textrm{max}]\) is then
+
+\[N'(\Delta E, \Delta\Theta) = \sum_{i=0...N}^{E\in\Delta}\sum_{j=0...N}^{\theta\in\Delta\Theta} \rho(E_i)\cdot\tau(\theta_j) = \sum_{i=0...N}^{E\in\Delta E}\rho(E_i)\cdot\sum_{j=0...N}^{\theta\in\Delta\Theta} \tau(\theta_j)\]
+
+with \(N\) being the total number of produced events;
+
+
+
+