Changes between Version 143 and Version 144 of DatabaseBasedAnalysis/Spectrum

Timestamp:

12/05/19 14:42:14 (6 years ago)

Author:

tbretz

Comment:

--

DatabaseBasedAnalysis/Spectrum

@@ -95 +95 @@
 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
@@ -101 +101 @@
 \[N'(\Delta E, \Delta\Theta) = \sum_{i=0...N}^{E\in\Delta}\sum_{j=0...N}^{\theta\in\Delta\Theta} \rho(E_i)\cdot\tau(\theta_j) = \sum_{i=0...N}^{E\in\Delta E}\rho(E_i)\cdot\sum_{j=0...N}^{\theta\in\Delta\Theta} \tau(\theta_j)\]
 
-with \(N\) being the total number of produced events;
+with \(N(\Delta E, \Delta\Theta\) being the total number of produced events.