diff --git a/manual/docs/html/slsDetectors-FAQ/footnode.html b/manual/docs/html/slsDetectors-FAQ/footnode.html index 9d4a88914..77dff6a43 100644 --- a/manual/docs/html/slsDetectors-FAQ/footnode.html +++ b/manual/docs/html/slsDetectors-FAQ/footnode.html @@ -18,15 +18,13 @@ original version by: Nikos Drakos, CBLU, University of Leeds - -
. diff --git a/manual/docs/html/slsDetectors-FAQ/images.tex b/manual/docs/html/slsDetectors-FAQ/images.tex index 267e7c444..88c0f0113 100644 --- a/manual/docs/html/slsDetectors-FAQ/images.tex +++ b/manual/docs/html/slsDetectors-FAQ/images.tex @@ -229,54 +229,65 @@ % !!! IMAGES START HERE !!! {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7641}% +\lthtmlinlinemathA{tex2html_wrap_inline7639}% $ \chi ^2$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} \stepcounter{chapter} +\stepcounter{chapter} +\stepcounter{section} +\stepcounter{section} \stepcounter{section} \stepcounter{section} {\newpage\clearpage -\lthtmlpictureA{tex2html_wrap7721}% +\lthtmlpictureA{tex2html_wrap7723}% \includegraphics[width=\textwidth]{multi_detector}% \lthtmlpictureZ \lthtmlcheckvsize\clearpage} \stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{section} \stepcounter{section} {\newpage\clearpage -\lthtmlpictureA{tex2html_wrap7727}% +\lthtmlpictureA{tex2html_wrap7731}% \includegraphics[width=\textwidth]{data_receiver}% \lthtmlpictureZ \lthtmlcheckvsize\clearpage} +\stepcounter{section} \stepcounter{section} \stepcounter{subsection} \stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{section} +\stepcounter{section} \stepcounter{section} \stepcounter{section} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7737}% +\lthtmlinlinemathA{tex2html_wrap_inline7746}% $ d$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} +\stepcounter{section} \stepcounter{section} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7740}% +\lthtmlinlinemathA{tex2html_wrap_inline7750}% $ \Updownarrow$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7742}% +\lthtmlinlinemathA{tex2html_wrap_inline7752}% $ \Rightarrow$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmldisplayA{displaymath7744}% +\lthtmldisplayA{displaymath7754}% \begin{displaymath}\textrm{\textbf{MEASUREMENTS}} \\ \left\Updownarrow \, \begin{array}{l} \\ @@ -350,27 +361,28 @@ $ \Rightarrow$% \lthtmldisplayZ \lthtmlcheckvsize\clearpage} +\stepcounter{section} \stepcounter{section} {\newpage\clearpage -\lthtmlpictureA{tex2html_wrap7767}% +\lthtmlpictureA{tex2html_wrap7778}% \includegraphics[width=\textwidth]{images/normal_acquisition.eps}% \lthtmlpictureZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlpictureA{tex2html_wrap7771}% +\lthtmlpictureA{tex2html_wrap7782}% \includegraphics[width=\textwidth]{images/gated_acquisition.eps}% \lthtmlpictureZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlpictureA{tex2html_wrap7775}% +\lthtmlpictureA{tex2html_wrap7786}% \includegraphics[width=\textwidth]{images/trigger_acquisition.eps}% \lthtmlpictureZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlpictureA{tex2html_wrap7779}% +\lthtmlpictureA{tex2html_wrap7790}% \includegraphics[width=\textwidth]{images/ro_trigger_acquisition.eps}% \lthtmlpictureZ \lthtmlcheckvsize\clearpage} @@ -378,606 +390,643 @@ $ \Rightarrow$% \stepcounter{section} \stepcounter{section} \stepcounter{section} +\stepcounter{section} +\stepcounter{section} +\stepcounter{section} +\stepcounter{subsection} \stepcounter{subsection} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7790}% +\lthtmlinlinemathA{tex2html_wrap_inline7805}% $ (108602\&0xFFFFFFFE)>>1 = 54301$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7792}% +\lthtmlinlinemathA{tex2html_wrap_inline7807}% $ (108602\&0x1) =0$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} \stepcounter{subsection} \stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{chapter} \stepcounter{chapter} \stepcounter{section} +\stepcounter{section} +\stepcounter{subsection} \stepcounter{subsection} {\newpage\clearpage -\lthtmlpictureA{tex2html_wrap7801}% +\lthtmlpictureA{tex2html_wrap7821}% \includegraphics[width=\textwidth]{images/effiSiHardXRays2}% \lthtmlpictureZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7803}% +\lthtmlinlinemathA{tex2html_wrap_inline7823}% $ \mu$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlpictureA{tex2html_wrap7807}% +\lthtmlpictureA{tex2html_wrap7827}% \includegraphics[width=\textwidth]{images/effiThinkBackplanes}% \lthtmlpictureZ \lthtmlcheckvsize\clearpage} +\stepcounter{subsection} \stepcounter{subsection} {\newpage\clearpage -\lthtmlpictureA{tex2html_wrap7812}% +\lthtmlpictureA{tex2html_wrap7833}% \includegraphics[width=\textwidth]{images/settings}% \lthtmlpictureZ \lthtmlcheckvsize\clearpage} \stepcounter{section} +\stepcounter{section} +\stepcounter{chapter} \stepcounter{chapter} \stepcounter{section} +\stepcounter{section} +\stepcounter{subsection} \stepcounter{subsection} \stepcounter{section} +\stepcounter{section} {\newpage\clearpage -\lthtmlpictureA{tex2html_wrap7822}% +\lthtmlpictureA{tex2html_wrap7848}% \includegraphics[width=\textwidth]{images/thr_scan_expl}% \lthtmlpictureZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlpictureA{tex2html_wrap7826}% +\lthtmlpictureA{tex2html_wrap7852}% \includegraphics[width=\textwidth]{images/thr_scan_fluo}% \lthtmlpictureZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7831}% +\lthtmlinlinemathA{tex2html_wrap_inline7857}% $ E_0$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7835}% +\lthtmlinlinemathA{tex2html_wrap_inline7861}% $ E_t=E_0/2$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7839}% +\lthtmlinlinemathA{tex2html_wrap_inline7865}% $ E_f$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7843}% +\lthtmlinlinemathA{tex2html_wrap_inline7869}% $ E_t$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7857}% +\lthtmlinlinemathA{tex2html_wrap_inline7883}% $ E_fE_f+3$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7863}% +\lthtmlinlinemathA{tex2html_wrap_inline7889}% $ E_t 4$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlpictureA{tex2html_wrap7886}% +\lthtmlpictureA{tex2html_wrap7912}% \includegraphics[width=\textwidth]{images/sample_with_fluorescence}% \lthtmlpictureZ \lthtmlcheckvsize\clearpage} \stepcounter{section} +\stepcounter{section} +\stepcounter{subsection} \stepcounter{subsection} {\newpage\clearpage -\lthtmlpictureA{tex2html_wrap7892}% +\lthtmlpictureA{tex2html_wrap7920}% \includegraphics[width=\textwidth]{images/bad_ff_col}% \lthtmlpictureZ \lthtmlcheckvsize\clearpage} +\stepcounter{subsection} \stepcounter{subsection} {\newpage\clearpage -\lthtmlpictureA{tex2html_wrap7897}% +\lthtmlpictureA{tex2html_wrap7926}% \includegraphics[width=\textwidth]{images/FFSetup}% \lthtmlpictureZ \lthtmlcheckvsize\clearpage} \stepcounter{section} +\stepcounter{section} +\stepcounter{subsection} \stepcounter{subsection} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7904}% +\lthtmlinlinemathA{tex2html_wrap_inline7935}% $ Vthreshold=7$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7906}% +\lthtmlinlinemathA{tex2html_wrap_inline7937}% $ Counts=500$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7908}% +\lthtmlinlinemathA{tex2html_wrap_inline7939}% $ Resolution=4$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7910}% +\lthtmlinlinemathA{tex2html_wrap_inline7941}% $ \pm$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlpictureA{tex2html_wrap7911}% +\lthtmlpictureA{tex2html_wrap7942}% \includegraphics[width=\textwidth]{images/noise_thresholdscanuntrimmed}% \lthtmlpictureZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlpictureA{tex2html_wrap7915}% +\lthtmlpictureA{tex2html_wrap7946}% \includegraphics[width=\textwidth]{images/trimbitdistribution}% \lthtmlpictureZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlpictureA{tex2html_wrap7919}% +\lthtmlpictureA{tex2html_wrap7950}% \includegraphics[width=\textwidth]{images/trimbitplot}% \lthtmlpictureZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlpictureA{tex2html_wrap7923}% +\lthtmlpictureA{tex2html_wrap7954}% \includegraphics[width=\textwidth]{images/noise_thresholdscantrimmed}% \lthtmlpictureZ \lthtmlcheckvsize\clearpage} \stepcounter{section} +\stepcounter{section} +\stepcounter{subsection} \stepcounter{subsection} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7932}% +\lthtmlinlinemathA{tex2html_wrap_inline7965}% $ \cdot$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} \stepcounter{section} \stepcounter{section} +\stepcounter{section} +\stepcounter{section} +\stepcounter{subsection} \stepcounter{subsection} \stepcounter{chapter} +\stepcounter{chapter} +\stepcounter{section} +\stepcounter{section} +\stepcounter{section} +\stepcounter{section} \stepcounter{section} \stepcounter{section} \stepcounter{section} \stepcounter{section} \stepcounter{chapter} +\stepcounter{chapter} +\stepcounter{section} \stepcounter{section} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7946}% +\lthtmlinlinemathA{tex2html_wrap_inline7989}% $ \alpha_{jm}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7948}% +\lthtmlinlinemathA{tex2html_wrap_inline7991}% $ R_m$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7950}% +\lthtmlinlinemathA{tex2html_wrap_inline7993}% $ \Phi_m$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7952}% +\lthtmlinlinemathA{tex2html_wrap_inline7995}% $ D_m$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7954}% +\lthtmlinlinemathA{tex2html_wrap_inline7997}% $ c_m$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7956}% +\lthtmlinlinemathA{tex2html_wrap_inline7999}% $ o_m$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline7958}% +\lthtmlinlinemathA{tex2html_wrap_inline8001}% $ k_m$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay7960}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8003}% $\displaystyle \alpha_{jm}=\Phi_m-{\ensuremath{\left({{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{180}}}}{{\ensuremath{\displaystyle{\pi}}}}}}}}\right)}}\arctan{\ensuremath{\left({{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{D_m-pj}}}}{{\ensuremath{\displaystyle{R_m}}}}}}}}\right)}}$% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay7962}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8005}% $\displaystyle \alpha_{jm}=o_m+{\ensuremath{\left({{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{180}}}}{{\ensuremath{\displaystyle{\pi}}}}}}}}\right)}}c_mk_m+{\ensuremath{\left({{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{180}}}}{{\ensuremath{\displaystyle{\pi}}}}}}}}\right)}}\arctan{\ensuremath{\left[{{\ensuremath{\left({j-c_m}\right)}}k_m}\right]}}$% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay7965}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8008}% $\displaystyle c_m$% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay7967}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8010}% $\displaystyle =$% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay7969}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8012}% $\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{D_m}}}}{{\ensuremath{\displaystyle{p}}}}}}};$% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay7971}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8014}% $\displaystyle k_m$% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay7975}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8018}% $\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{p}}}}{{\ensuremath{\displaystyle{R_m}}}}}}};$% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay7977}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8020}% $\displaystyle o_m$% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay7981}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8024}% $\displaystyle \Phi_m-{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{180}}}}{{\ensuremath{\displaystyle{\pi}}}}}}}{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{D_m}}}}{{\ensuremath{\displaystyle{R_m}}}}}}}.$% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay7984}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8027}% $\displaystyle \Phi_m$% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay7988}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8031}% $\displaystyle o_m+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{180}}}}{{\ensuremath{\displaystyle{\pi}}}}}}}c_mk_m;$% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay7990}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8033}% $\displaystyle R_m$% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay7994}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8037}% $\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{p}}}}{{\ensuremath{\displaystyle{k_m}}}}}}};$% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay7996}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8039}% $\displaystyle D_m$% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8000}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8043}% $\displaystyle c_m p.$% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} \stepcounter{section} +\stepcounter{section} +\stepcounter{subsection} \stepcounter{subsection} \stepcounter{subsubsection} +\stepcounter{subsubsection} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8005}% +\lthtmlinlinemathA{tex2html_wrap_inline8051}% $ {\ensuremath{{2\theta}}}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8007}% +\lthtmlinlinemathA{tex2html_wrap_inline8053}% $ 2\theta$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} +\stepcounter{subsubsection} \stepcounter{subsubsection} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8010}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8057}% $\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{d}{}\, }}\bf {\sigma}}}}}{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{d}{}\, }}\Omega}}}}}}} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8012}% +\lthtmlinlinemathA{tex2html_wrap_inline8059}% $ \Omega$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8014}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8061}% $\displaystyle {I_0}\Delta t \Delta\Omega{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{d}{}\, }}\bf {\sigma}}}}}{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{d}{}\, }}\Omega}}}}}}} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8016}% +\lthtmlinlinemathA{tex2html_wrap_inline8063}% $ \Delta t$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8018}% +\lthtmlinlinemathA{tex2html_wrap_inline8065}% $ \Delta\Omega$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8020}% +\lthtmlinlinemathA{tex2html_wrap_inline8067}% $ I_0$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8024}% +\lthtmlinlinemathA{tex2html_wrap_inline8071}% $ \Delta\Omega\propto \Delta {\ensuremath{{2\theta}}}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} +\stepcounter{subsection} \stepcounter{subsection} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8035}% +\lthtmlinlinemathA{tex2html_wrap_inline8083}% $ P$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8037}% +\lthtmlinlinemathA{tex2html_wrap_inline8085}% $ k$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8039}% +\lthtmlinlinemathA{tex2html_wrap_inline8087}% $ k=1,\ldots,P$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8041}% +\lthtmlinlinemathA{tex2html_wrap_inline8089}% $ N_k$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8043}% +\lthtmlinlinemathA{tex2html_wrap_inline8091}% $ 2\theta\equiv{\ensuremath{{2\theta}}}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8045}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8093}% $\displaystyle b_{k,j}={\ensuremath{\left[{{\ensuremath{{2\theta}}}_{k,j}^{-},{\ensuremath{{2\theta}}}_{k,j}^{+}}\right]}},\qquad j=1,\ldots,N_k $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8047}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8095}% $\displaystyle \hat{b}_{k,j}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{{2\theta}}}_{k,j}^{+}+{\ensuremath{{2\theta}}}_{k,j}^{-}}}}}{{\ensuremath{\displaystyle{2}}}}}}} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8049}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8097}% $\displaystyle {\ensuremath{\left|{b_{k,j}}\right|}}={\ensuremath{{2\theta}}}_{k,j}^{+}-{\ensuremath{{2\theta}}}_{k,j}^{-} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8051}% +\lthtmlinlinemathA{tex2html_wrap_inline8099}% $ C_{k,j}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8053}% +\lthtmlinlinemathA{tex2html_wrap_inline8101}% $ e_{k,j}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8055}% +\lthtmlinlinemathA{tex2html_wrap_inline8103}% $ m_{k,j}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8057}% +\lthtmlinlinemathA{tex2html_wrap_inline8105}% $ b_{k,j}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8059}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8107}% $\displaystyle I_{k,j}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{e_{k,j}}}}}{{\ensuremath{\displaystyle{m_{k,j}}}}}}}}{\ensuremath{\left({C_{k,j}+\min{\ensuremath{\left({1,C_{k,j}}\right)}}}\right)}} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8061}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8109}% $\displaystyle \sigma_{I_{k,j}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{e_{k,j}}}}}{{\ensuremath{\displaystyle{m_{k,j}}}}}}}}\sqrt{{\ensuremath{\left({C_{k,j}+1}\right)}}} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8063}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8111}% $\displaystyle r_{k,j}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{I_{k,j}}}}}{{\ensuremath{\displaystyle{{\ensuremath{\left|{b_{k,j}}\right|}}}}}}}}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{e_{k,j}}}}}{{\ensuremath{\displaystyle{m_{k,j}{\ensuremath{\left|{b_{k,j}}\right|}}}}}}}}}{\ensuremath{\left({C_{k,j}+\min{\ensuremath{\left({1,C_{k,j}}\right)}}}\right)}} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8065}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8113}% $\displaystyle \sigma_{r_{k,j}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\sigma_{I_{k,j}}}}}}{{\ensuremath{\displaystyle{{\ensuremath{\left|{b_{k,j}}\right|}}}}}}}}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{e_{k,j}}}}}{{\ensuremath{\displaystyle{{\ensuremath{\left|{b_{k,j}}\right|}}m_{k,j}}}}}}}}\sqrt{{\ensuremath{\left({C_{k,j}+1}\right)}}} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8067}% +\lthtmlinlinemathA{tex2html_wrap_inline8115}% $ M$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8069}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8117}% $\displaystyle B_\ell=[{\ensuremath{{2\theta}}}_0+(\ell-1)B, {\ensuremath{{2\theta}}}_0+\ell B],\qquad \ell=1,\ldots,M $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8071}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8119}% $\displaystyle {\ensuremath{\left|{B_\ell}\right|}}=B$% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8073}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8121}% $\displaystyle \hat{B}_\ell={\ensuremath{{2\theta}}}_0+(\ell-1/2)B,$% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8075}% +\lthtmlinlinemathA{tex2html_wrap_inline8123}% $ {\ensuremath{{2\theta}}}_0$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8077}% +\lthtmlinlinemathA{tex2html_wrap_inline8125}% $ {\ensuremath{{2\theta}}}_{max}={\ensuremath{{2\theta}}}_0+MB$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8079}% +\lthtmlinlinemathA{tex2html_wrap_inline8127}% $ \ell$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8081}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8129}% $\displaystyle b_{k,j}$% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8082}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8130}% $\displaystyle \qquad {\ensuremath{\left|{ b_{k,j}\cap B_\ell }\right|}} > 0. $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8085}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8133}% $\displaystyle \qquad \hat{b}_{k,j}\in B_\ell . $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8089}% +\lthtmlinlinemathA{tex2html_wrap_inline8137}% $ B_\ell$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8091}% +\lthtmlinlinemathA{tex2html_wrap_inline8139}% $ N_E$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8093}% +\lthtmlinlinemathA{tex2html_wrap_inline8141}% $ O_n$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8095}% +\lthtmlinlinemathA{tex2html_wrap_inline8143}% $ O$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8097}% +\lthtmlinlinemathA{tex2html_wrap_inline8145}% $ \sigma_{O_n}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8099}% +\lthtmlinlinemathA{tex2html_wrap_inline8147}% $ \nu_n$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8101}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8149}% $\displaystyle \langle O\rangle ={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{ \mathop{\sum}_{n=1}^{N_E}\nu_n O_n\sigma_{O_n}^{-2} @@ -990,20 +1039,20 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8103}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8151}% $\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\left|{ b_{k,j}\cap B_\ell }\right|}}}}}}{{\ensuremath{\displaystyle{B}}}}}}} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8105}% +\lthtmlinlinemathA{tex2html_wrap_inline8153}% $ k,j$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8109}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8157}% $\displaystyle X_\ell=\mathop{\sum_{k,j}}_{ {\ensuremath{\left|{ b_{k,j}\cap B_\ell }\right|}} > 0} {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\left|{ b_{k,j}\cap B_\ell }\right|}}}}}}{{\ensuremath{\displaystyle{B}}}}}}}\ r_{k,j}\ {\ensuremath{\left({\sigma_{r_{k,j}}}\right)}}^{-2} $% @@ -1011,7 +1060,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8111}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8159}% $\displaystyle Y_\ell=\mathop{\sum_{k,j}}_{ {\ensuremath{\left|{ b_{k,j}\cap B_\ell }\right|}} > 0} {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\left|{ b_{k,j}\cap B_\ell }\right|}}}}}}{{\ensuremath{\displaystyle{B}}}}}}}\ {\ensuremath{\left({\sigma_{r_{k,j}}}\right)}}^{-2} $% @@ -1019,45 +1068,45 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8113}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8161}% $\displaystyle R_\ell={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{X_\ell}}}}{{\ensuremath{\displaystyle{Y_\ell}}}}}}}; $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8115}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8163}% $\displaystyle \sigma_{R_\ell}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{\sqrt{Y_\ell}}}}}}}}. $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8117}% +\lthtmlinlinemathA{tex2html_wrap_inline8165}% $ R_\ell$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8119}% +\lthtmlinlinemathA{tex2html_wrap_inline8167}% $ \sigma_{R_\ell}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8121}% +\lthtmlinlinemathA{tex2html_wrap_inline8169}% $ B$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8123}% +\lthtmlinlinemathA{tex2html_wrap_inline8171}% $ K$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8127}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8175}% $\displaystyle \mathop{\sum}_{\ell=1}^M{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{KR_\ell}}}}{{\ensuremath{\displaystyle{K^2\sigma_{R_\ell}^2}}}}}}}= {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{K}}}}}}} \mathop{\sum}_{\ell=1}^M{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{R_\ell}}}}{{\ensuremath{\displaystyle{\sigma_{R_\ell}^2}}}}}}}=M @@ -1066,7 +1115,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8131}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8179}% $\displaystyle K={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{ 1 }}}}{{\ensuremath{\displaystyle{ @@ -1077,33 +1126,34 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8133}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8181}% $\displaystyle \hat{B}_\ell, \quad KR_\ell, \quad K\sigma_{R_\ell} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} +\stepcounter{subsubsection} \stepcounter{subsubsection} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8144}% +\lthtmlinlinemathA{tex2html_wrap_inline8193}% $ X_\ell=0$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8146}% +\lthtmlinlinemathA{tex2html_wrap_inline8195}% $ Y_\ell=0$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8148}% +\lthtmlinlinemathA{tex2html_wrap_inline8197}% $ b$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8152}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8201}% $\displaystyle X_\ell={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\left|{ b\cap B_\ell }\right|}}}}}}{{\ensuremath{\displaystyle{B}}}}}}}\ {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{e(C+1)}}}}{{\ensuremath{\displaystyle{m|b|}}}}}}}\ {\ensuremath{\left({ @@ -1115,7 +1165,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8154}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8203}% $\displaystyle Y_\ell={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\left|{ b\cap B_\ell }\right|}}}}}}{{\ensuremath{\displaystyle{B}}}}}}}\ {\ensuremath{\left({ {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{|b|m}}}}{{\ensuremath{\displaystyle{e\sqrt{C+1}}}}}}}} @@ -1126,14 +1176,14 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8156}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8205}% $\displaystyle R_\ell={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{X_\ell}}}}{{\ensuremath{\displaystyle{Y_\ell}}}}}}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{e(C+1)}}}}{{\ensuremath{\displaystyle{m|b|}}}}}}} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8160}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8209}% $\displaystyle \sigma_{R_\ell}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{\sqrt{Y_\ell}}}}}}}}= \sqrt{{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{B}}}}{{\ensuremath{\displaystyle{{\ensuremath{\left|{ b\cap B_\ell }\right|}}}}}}}}}} {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{e\sqrt{(C+1)}}}}}{{\ensuremath{\displaystyle{|b|m}}}}}}} @@ -1142,46 +1192,48 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8164}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8213}% $\displaystyle \sqrt{{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{B}}}}{{\ensuremath{\displaystyle{{\ensuremath{\left|{ b\cap B_\ell }\right|}}}}}}}}}} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} +\stepcounter{subsection} \stepcounter{subsection} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8167}% +\lthtmlinlinemathA{tex2html_wrap_inline8217}% $ \hat{b}_{j,k}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8169}% +\lthtmlinlinemathA{tex2html_wrap_inline8219}% $ \hat{B}_\ell$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} +\stepcounter{subsection} \stepcounter{subsection} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8172}% +\lthtmlinlinemathA{tex2html_wrap_inline8223}% $ C_0$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8176}% +\lthtmlinlinemathA{tex2html_wrap_inline8227}% $ \sqrt{C_0}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8178}% +\lthtmlinlinemathA{tex2html_wrap_inline8229}% $ n$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8180}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8231}% $\displaystyle P(n)={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{C_0^n{\ensuremath{\mathrm{e}}}^{-C_0} }}}}{{\ensuremath{\displaystyle{ n!}}}}}}} @@ -1190,7 +1242,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8182}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8233}% $\displaystyle \mathop{\sum}_{n=0}^{+\infty} P(n)=1\ ; $% @@ -1198,7 +1250,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8184}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8235}% $\displaystyle \langle n\rangle=\mathop{\sum}_{n=0}^{+\infty} nP(n)=C_0\ ; $% @@ -1206,7 +1258,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8186}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8237}% $\displaystyle \langle n^2\rangle=\mathop{\sum}_{n=0}^{+\infty} n^2 P(n)=C_0^2+C_0\ ; $% @@ -1214,14 +1266,14 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8188}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8239}% $\displaystyle \sigma_{C_0}=\sqrt{\langle n^2\rangle-\langle n\rangle^2}=\sqrt{C_0} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8192}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8243}% $\displaystyle \chi^2 = \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}} {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\left({F_j-O_j}\right)}}^2 }}}}{{\ensuremath{\displaystyle{ @@ -1232,25 +1284,25 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8194}% +\lthtmlinlinemathA{tex2html_wrap_inline8245}% $ O_j$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8196}% +\lthtmlinlinemathA{tex2html_wrap_inline8247}% $ F_j$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8198}% +\lthtmlinlinemathA{tex2html_wrap_inline8249}% $ \sigma_j$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8200}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8251}% $\displaystyle \chi_{(0)}^2 = \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}} {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\left({F_j-C_j}\right)}}^2 }}}}{{\ensuremath{\displaystyle{ @@ -1261,7 +1313,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8202}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8253}% $\displaystyle \chi_{(1)}^2 = \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}} {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\left({F_j-{\ensuremath{\left({C_j+\min{\ensuremath{\left({1,C_j}\right)}}}\right)}}}\right)}}^2 }}}}{{\ensuremath{\displaystyle{ @@ -1272,27 +1324,29 @@ $% \lthtmlcheckvsize\clearpage} \stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsubsection} \stepcounter{subsubsection} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8208}% +\lthtmlinlinemathA{tex2html_wrap_inline8261}% $ N_{\mathrm{obs}}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8210}% +\lthtmlinlinemathA{tex2html_wrap_inline8263}% $ C_j,\quad j=1\ldots N_{\mathrm{obs}}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8212}% +\lthtmlinlinemathA{tex2html_wrap_inline8265}% $ x$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8216}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8269}% $\displaystyle x=\langle x\rangle={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{ N_{\mathrm{obs}}}}}}}}} \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}C_j\ . $% @@ -1300,7 +1354,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8218}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8271}% $\displaystyle \sigma_x=\sqrt{\langle x^2\rangle-\langle x\rangle^2}=\sqrt{ {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{ N_{\mathrm{obs}}}}}}}}} \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}C_j^2-{\ensuremath{\left({ @@ -1313,28 +1367,29 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8220}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8273}% $\displaystyle \sigma_x={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{ N_{\mathrm{obs}}}}}}}}}\sqrt{ \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}C_j } =\sqrt{{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\langle x\rangle}}}}{{\ensuremath{\displaystyle{N_{\mathrm{obs}}}}}}}}}} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} +\stepcounter{subsubsection} \stepcounter{subsubsection} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8223}% +\lthtmlinlinemathA{tex2html_wrap_inline8277}% $ C_j=0$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8225}% +\lthtmlinlinemathA{tex2html_wrap_inline8279}% $ N_{\mathrm{obs}}^*$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8227}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8281}% $\displaystyle x=\langle x\rangle^*={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{ N_{\mathrm{obs}}^*}}}}}}} \mathop{\sum}_ {\stackrel{1\leqslant j\leqslant N_{\mathrm{obs}}}{{C_j>0}}} C_j={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{ N_{\mathrm{obs}}^*}}}}}}} @@ -1344,7 +1399,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8229}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8283}% $\displaystyle \sigma_{x^*}= {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{N_{\mathrm{obs}}}}}}{{\ensuremath{\displaystyle{N_{\mathrm{obs}}^*}}}}}}}\sigma_x = \sqrt{{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{N_{\mathrm{obs}}}}}}{{\ensuremath{\displaystyle{N_{\mathrm{obs}}^*}}}}}}}} \sqrt{{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\langle x\rangle}}}}{{\ensuremath{\displaystyle{N_{\mathrm{obs}}^*}}}}}}}}=\sqrt{{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\langle x\rangle^*}}}}{{\ensuremath{\displaystyle{N_{\mathrm{obs}}^*}}}}}}}} $% @@ -1352,14 +1407,15 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8231}% +\lthtmlinlinemathA{tex2html_wrap_inline8285}% $ C_j$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} +\stepcounter{subsubsection} \stepcounter{subsubsection} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8238}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8295}% $\displaystyle \chi^2 = \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}} {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\left({x-O_j}\right)}}^2 }}}}{{\ensuremath{\displaystyle{ @@ -1370,7 +1426,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8240}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8297}% $\displaystyle x= \langle x \rangle_{\!\mathrm{w}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{ \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}} {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{O_j @@ -1389,7 +1445,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8244}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8301}% $\displaystyle \sigma_{\langle x \rangle_{\!\mathrm{w}}} = {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{ 1 }}}}{{\ensuremath{\displaystyle{\sqrt{ @@ -1404,7 +1460,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8246}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8303}% $\displaystyle \mathsf{GoF}= \sqrt{ {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{ @@ -1435,27 +1491,28 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8248}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8305}% $\displaystyle {\sigma}_{\langle x \rangle_{\!\mathrm{w}}}^{\mathrm{corrected}} = \mathsf{GoF}\ \sigma_{\langle x \rangle_{\!\mathrm{w}}} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} +\stepcounter{subsubsection} \stepcounter{subsubsection} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8251}% +\lthtmlinlinemathA{tex2html_wrap_inline8309}% $ O_j=C_j$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8253}% +\lthtmlinlinemathA{tex2html_wrap_inline8311}% $ \sigma_j^2=C_j$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8255}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8313}% $\displaystyle \langle x \rangle_{\!\mathrm{w(1)}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{ {N_{\mathrm{obs}}} }}}}{{\ensuremath{\displaystyle{ @@ -1470,7 +1527,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8263}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8321}% $\displaystyle \sigma_{\langle x \rangle_{\!\mathrm{w(1)}}} = {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{ 1 }}}}{{\ensuremath{\displaystyle{\sqrt{ @@ -1487,7 +1544,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8265}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8323}% $\displaystyle \mathsf{GoF}_{(1)}= \sqrt{ {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{ @@ -1517,33 +1574,34 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8267}% +\lthtmlinlinemathA{tex2html_wrap_inline8325}% $ \langle x\rangle^*$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8269}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8327}% $\displaystyle {\sigma}_{\langle x \rangle_{\!\mathrm{w(1)}}}^{\mathrm{corrected}} = \mathsf{GoF}_{(1)}\ \sigma_{\langle x \rangle_{\!\mathrm{w(1)}}} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} +\stepcounter{subsubsection} \stepcounter{subsubsection} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8272}% +\lthtmlinlinemathA{tex2html_wrap_inline8331}% $ O_j=C_j+\min{\ensuremath{\left({1,C_j}\right)}}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8274}% +\lthtmlinlinemathA{tex2html_wrap_inline8333}% $ \sigma_j^2=C_j+1$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8276}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8335}% $\displaystyle \langle x \rangle_{\!\mathrm{w(2)}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{ {N_{\mathrm{obs}}^*} }}}}{{\ensuremath{\displaystyle{ @@ -1558,7 +1616,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8278}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8337}% $\displaystyle \sigma_{\langle x \rangle_{\!\mathrm{w(2)}}} = {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{ 1 }}}}{{\ensuremath{\displaystyle{\sqrt{ @@ -1575,7 +1633,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8280}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8339}% $\displaystyle \mathsf{GoF}_{(2)}= \sqrt{ {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{ @@ -1605,66 +1663,68 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8284}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8343}% $\displaystyle {\sigma}_{\langle x \rangle_{\!\mathrm{w(2)}}}^{\mathrm{corrected}} = \mathsf{GoF}_{(2)}\ \sigma_{\langle x \rangle_{\!\mathrm{w(2)}}} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} +\stepcounter{subsubsection} \stepcounter{subsubsection} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8291}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8351}% $\displaystyle \epsilon_x = {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\sigma_x}}}}{{\ensuremath{\displaystyle{x}}}}}}} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8295}% +\lthtmlinlinemathA{tex2html_wrap_inline8355}% $ O(\epsilon_x^2)$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8299}% +\lthtmlinlinemathA{tex2html_wrap_inline8359}% $ \propto\epsilon_x$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8303}% +\lthtmlinlinemathA{tex2html_wrap_inline8363}% $ O(\epsilon_x^3)$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} +\stepcounter{subsubsection} \stepcounter{subsubsection} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8306}% +\lthtmlinlinemathA{tex2html_wrap_inline8367}% $ N_{\mathrm{obs}}=2$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8308}% +\lthtmlinlinemathA{tex2html_wrap_inline8369}% $ C_1$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8310}% +\lthtmlinlinemathA{tex2html_wrap_inline8371}% $ C_2$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8312}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8373}% $\displaystyle \langle x \rangle={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{C_1+C_2}}}}{{\ensuremath{\displaystyle{2}}}}}}}; \qquad \sigma_x={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\sqrt{C_1+C_2}}}}}{{\ensuremath{\displaystyle{2}}}}}}} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8314}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8375}% $\displaystyle \langle x \rangle_{\mathrm{w(2)}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{2(C_1+1)(C_2+1)}}}}{{\ensuremath{\displaystyle{C_1+C_2+2}}}}}}}; \qquad \sigma_{\langle x \rangle_{\mathrm{w(2)}}}=\sqrt{{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{(C_1+1)(C_2+1)}}}}{{\ensuremath{\displaystyle{C_1+C_2+2}}}}}}}} $% @@ -1672,19 +1732,19 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8316}% +\lthtmlinlinemathA{tex2html_wrap_inline8377}% $ C_1,C_2$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8318}% +\lthtmlinlinemathA{tex2html_wrap_inline8379}% $ \lambda$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8320}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8381}% $\displaystyle E{\ensuremath{\left({\langle x \rangle}\right)}} = \mathop{\sum}_{m,n=0}^{+\infty} {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{n+m}}}}{{\ensuremath{\displaystyle{2}}}}}}}P(n)P(m)=\mathop{\sum}_{m=0}^{+\infty} {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{m}}}}{{\ensuremath{\displaystyle{2}}}}}}}{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\lambda^m{\ensuremath{\mathrm{e}}}^{-\lambda}}}}}{{\ensuremath{\displaystyle{m!}}}}}}} @@ -1696,7 +1756,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8322}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8383}% $\displaystyle E{\ensuremath{\left({\sigma_x^2}\right)}} = \mathop{\sum}_{m,n=0}^{+\infty} {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{n+m}}}}{{\ensuremath{\displaystyle{4}}}}}}}P(n)P(m)={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{ \lambda}}}}{{\ensuremath{\displaystyle{2}}}}}}};\qquad E{\ensuremath{\left({\sigma_x}\right)}} =\sqrt{{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\lambda}}}}{{\ensuremath{\displaystyle{2}}}}}}}} @@ -1705,14 +1765,14 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8324}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8385}% $\displaystyle \langle x \rangle_{\mathrm{w(2)}}=\langle x \rangle + 1 -{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{(C_1-C_2)^2}}}}{{\ensuremath{\displaystyle{4(\langle x \rangle+1)}}}}}}} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8326}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8387}% $\displaystyle E{\ensuremath{\left({{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{(C_1-C_2)^2}}}}{{\ensuremath{\displaystyle{4(\langle x \rangle+1)}}}}}}}}\right)}} = \mathop{\sum}_{m,n=0}^{+\infty} {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{(n-m)^2}}}}{{\ensuremath{\displaystyle{2(n+m+2) }}}}}}}P(n)P(m)={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{e}}}^{-2\lambda}}}}}{{\ensuremath{\displaystyle{2}}}}}}} @@ -1723,31 +1783,31 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8328}% +\lthtmlinlinemathA{tex2html_wrap_inline8389}% $ s=n+m$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8330}% +\lthtmlinlinemathA{tex2html_wrap_inline8391}% $ s=0\ldots +\infty$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8332}% +\lthtmlinlinemathA{tex2html_wrap_inline8393}% $ n-m=s-2k$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8334}% +\lthtmlinlinemathA{tex2html_wrap_inline8395}% $ k=0\ldots s$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8336}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8397}% $\displaystyle E{\ensuremath{\left({{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{(C_1-C_2)^2}}}}{{\ensuremath{\displaystyle{4(\langle x \rangle+1)}}}}}}}}\right)}} = {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{e}}}^{-2\lambda}}}}}{{\ensuremath{\displaystyle{2}}}}}}} \mathop{\sum}_{s=0}^{+\infty} @@ -1760,7 +1820,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8338}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8399}% $\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{E{\ensuremath{\left({\langle x \rangle_{\mathrm{w(2)}}-\langle x \rangle}\right)}}}}}}{{\ensuremath{\displaystyle{E{\ensuremath{\left({\langle x \rangle}\right)}}}}}}}}}= {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{2\lambda}}}}}}}+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{2\lambda^2}}}}}}}-{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1-{\ensuremath{\mathrm{e}}}^{-2\lambda}}}}}{{\ensuremath{\displaystyle{4\lambda^3}}}}}}} $% @@ -1768,13 +1828,13 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8340}% +\lthtmlinlinemathA{tex2html_wrap_inline8401}% $ \langle x \rangle$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8342}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8403}% $\displaystyle \epsilon = {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\sigma_x}}}}{{\ensuremath{\displaystyle{\langle x \rangle}}}}}}} = {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\lambda^{1/2}}}}}{{\ensuremath{\displaystyle{\sqrt{2} \lambda}}}}}}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{\sqrt{2\lambda}}}}}}}} $% @@ -1782,145 +1842,147 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8344}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8405}% $\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{E{\ensuremath{\left({\langle x \rangle_{\mathrm{w(2)}}-\langle x \rangle}\right)}}}}}}{{\ensuremath{\displaystyle{E{\ensuremath{\left({\langle x \rangle}\right)}}}}}}}}}= O(\epsilon^2) $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} +\stepcounter{subsubsection} \stepcounter{subsubsection} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8349}% +\lthtmlinlinemathA{tex2html_wrap_inline8411}% $ \lambda=1,10,100,\ldots,1000000$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8353}% +\lthtmlinlinemathA{tex2html_wrap_inline8415}% $ N=10^8$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8359}% +\lthtmlinlinemathA{tex2html_wrap_inline8421}% $ \xi_\lambda=\sqrt{\lambda/N}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8361}% +\lthtmlinlinemathA{tex2html_wrap_inline8423}% $ \epsilon_\lambda=\sqrt{\lambda/N}/\lambda=1/\sqrt{N\lambda}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8363}% +\lthtmlinlinemathA{tex2html_wrap_inline8425}% $ E_\lambda$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8367}% +\lthtmlinlinemathA{tex2html_wrap_inline8429}% $ e_\lambda=E_\lambda/\lambda$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8369}% +\lthtmlinlinemathA{tex2html_wrap_inline8431}% $ e_\lambda/\epsilon_\lambda$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8371}% +\lthtmlinlinemathA{tex2html_wrap_inline8433}% $ \lambda =$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8373}% +\lthtmlinlinemathA{tex2html_wrap_inline8435}% $ \xi_\lambda = $% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8375}% +\lthtmlinlinemathA{tex2html_wrap_inline8437}% $ \epsilon_\lambda$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8377}% +\lthtmlinlinemathA{tex2html_wrap_inline8439}% $ {\langle x \rangle_{\!\mathrm{w(1)}}}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8379}% +\lthtmlinlinemathA{tex2html_wrap_inline8441}% $ {\langle x \rangle_{\!\mathrm{w(2)}}}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8387}% +\lthtmlinlinemathA{tex2html_wrap_inline8449}% $ e_\lambda$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8731}% +\lthtmlinlinemathA{tex2html_wrap_inline8793}% $ {\langle x \rangle_{\!\mathrm{w(1)}}}\ :$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8735}% +\lthtmlinlinemathA{tex2html_wrap_inline8797}% $ {\langle x \rangle^*}\ $% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8737}% +\lthtmlinlinemathA{tex2html_wrap_inline8799}% $ \lambda<100$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8739}% +\lthtmlinlinemathA{tex2html_wrap_inline8801}% $ {\langle x \rangle}\ $% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} +\stepcounter{subsection} \stepcounter{subsection} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8764}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8827}% $\displaystyle X_0=\eta_0 C_0 $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8766}% +\lthtmlinlinemathA{tex2html_wrap_inline8829}% $ \eta_0$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8768}% +\lthtmlinlinemathA{tex2html_wrap_inline8831}% $ X$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8770}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8833}% $\displaystyle P'(X)=P(X/\eta_0)=P(n)\qquad\Biggl|\Biggr.\qquad \frac{X}{\eta_0}\equiv n\in\mathbb{Z} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8774}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8837}% $\displaystyle \langle X\rangle=\mathop{\sum}_{n=0}^{+\infty} \eta_0 nP(n)=\eta_0 C_0=X_0\ ; $% @@ -1928,7 +1990,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8776}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8839}% $\displaystyle \langle X^2\rangle=\mathop{\sum}_{n=0}^{+\infty} \eta_0^2 n^2 P(n)=\eta_0^2(C_0^2+C_0)=X_0^2+\eta_0 X_0\ ; $% @@ -1936,33 +1998,33 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8778}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8841}% $\displaystyle \sigma_X=\sqrt{\langle X^2\rangle-\langle X\rangle^2}=\sqrt{\eta_0 X_0}=\eta_0\sqrt{C_0}=\sqrt{\eta_0}\sqrt{X_0} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8780}% +\lthtmlinlinemathA{tex2html_wrap_inline8843}% $ \sigma_X=\sqrt{\langle X\rangle}=\sqrt{X_0}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8782}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8845}% $\displaystyle \sigma_X=\sqrt{\eta_0}\sqrt{X_0}=\eta_0\sqrt{C_0}=\eta_0\sigma_{C_0} $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline8786}% +\lthtmlinlinemathA{tex2html_wrap_inline8849}% $ \sigma_{\eta_0}$% \lthtmlinlinemathZ \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8788}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8851}% $\displaystyle \widehat{P}(\eta)={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{ {\ensuremath{\mathrm{e}}}^{ -\frac{1}{2} @@ -1978,7 +2040,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8790}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8853}% $\displaystyle \int_{-\infty}^{+\infty}{\ensuremath{\mathrm{d}{\eta}\, }}\mathop{\sum}_{n=0}^{+\infty} P(n)\widehat{P}(\eta)=1\ ; $% @@ -1986,7 +2048,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8792}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8855}% $\displaystyle \langle X\rangle=\int_{-\infty}^{+\infty}{\ensuremath{\mathrm{d}{\eta}\, }}\mathop{\sum}_{n=0}^{+\infty} \widehat{P}(\eta)\eta nP(n)= \mathop{\sum}_{n=0}^{+\infty} @@ -1999,7 +2061,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8794}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8857}% $\displaystyle \langle X^2\rangle=\int_{-\infty}^{+\infty}{\ensuremath{\mathrm{d}{\eta}\, }}\mathop{\sum}_{n=0}^{+\infty} \widehat{P}(\eta)\eta^2 n^2 P(n)= \int_{-\infty}^{+\infty}{\ensuremath{\mathrm{d}{\eta}\, }}\widehat{P}(\eta)\eta^2 @@ -2012,7 +2074,7 @@ $% \lthtmlcheckvsize\clearpage} {\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay8796}% +\lthtmlinlinemathA{tex2html_wrap_indisplay8859}% $\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\sigma_X}}}}{{\ensuremath{\displaystyle{\langle X\rangle}}}}}}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\sqrt{\langle X^2\rangle-\langle X\rangle^2}}}}}{{\ensuremath{\displaystyle{\langle X\rangle}}}}}}} ={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\sqrt{ \eta_0^2 C_0+\sigma_{\eta_0}^2C_0^2+\sigma_{\eta_0}^2 C_0 @@ -2028,6 +2090,7 @@ $% \lthtmlindisplaymathZ \lthtmlcheckvsize\clearpage} +\stepcounter{section} \stepcounter{section} \end{document} diff --git a/manual/docs/html/slsDetectors-FAQ/index.html b/manual/docs/html/slsDetectors-FAQ/index.html index 3cc00c9b6..a46af170e 100644 --- a/manual/docs/html/slsDetectors-FAQ/index.html +++ b/manual/docs/html/slsDetectors-FAQ/index.html @@ -20,31 +20,9 @@ Frequently Asked Questions"> - - - - -
-
- -
-
- Next: Contents - Contents -
-
-@@ -53,198 +31,11 @@ Frequently Asked Questions"> Frequently Asked Questions
Anna Bergamaschi
-Date: February 9, 2018
+Date: February 22, 2018
- - --
- -- Contents -
- SLS Detectors Software -
-
-- Which programs can I use to control my detector? -
- How can I control many detectors in parallel or independently? -
-
-- Examples -
- How can I configure the data receiver? -
- What are settings and calibration files for? - -
- How should a configuration file look like? -
- What is the meaning of the file name? -
- Which is the sequence of the acquisition flow? -
- How can I synchronize my detector with the experiment? -
- How can several controllers be synchronized? -
- How can the detector movement and position and I0 readout be customized for my beamline? -
- In which data format are written the data? - -
-- General questions about detectors - -
-- Single photon counting detectors -
-
-- Which detector settings should I choose? -
-
-- MYTHEN -
- How do I chose the comparator threshold? -
- How does the flat field correction work? - -
- What happens when I trim the detector? -
-
-- MYTHEN -
- In what consists the energy calibration of the detector? -
-
-- MYTHEN -
- Why should I change the dynamic range of the counters? -
- When should I enable rate correction - -
-- Charge Integrating detectors - -
-- Angular conversion -
-
-- How is the channel number coverted into angle? -
- How are different positions merged together? - -
- Why can't I properly merge different positions? -
-- About this document ... -
- -Thattil Dhanya -2018-02-09 -