diff --git a/slides/images/fwhm.pdf b/slides/images/fwhm.pdf new file mode 100644 index 0000000..8ec5928 Binary files /dev/null and b/slides/images/fwhm.pdf differ diff --git a/slides/sections/2.md b/slides/sections/2.md index 6556c24..b432a74 100644 --- a/slides/sections/2.md +++ b/slides/sections/2.md @@ -55,14 +55,16 @@ ## Landau median - CDF computed by numerical integration -- QDF computed by numerical root-finding +- Mean computed by numerical root-finding +$$ + F(x) = \frac{1}{2} \thus m_L\ex = 1.3557804... +$$ \setbeamercovered{} \begin{center} - \begin{tikzpicture}[remember picture] - \node at (0,0) (here) {$m_L\ex = 1.3557804...$}; + \begin{tikzpicture}[overlay] \pause - \node [opacity=0.5, xscale=0.35, yscale=0.25 ] at (here) {\includegraphics{images/high.png}}; + \node [opacity=0.5, xscale=0.35, yscale=0.25 ] at (2.4,0.95) {\includegraphics{images/high.png}}; \end{tikzpicture} \end{center} @@ -83,7 +85,8 @@ \begin{tikzpicture}[remember picture] \node at (0,0) (here) {$\mu_L\ex = − 0.22278...$}; \pause - \node [opacity=0.5, xscale=0.32, yscale=0.25 ] at (here) {\includegraphics{images/high.png}}; + \node [opacity=0.5, xscale=0.32, yscale=0.25 ] at (here) + {\includegraphics{images/high.png}}; \end{tikzpicture} \end{center} @@ -92,27 +95,38 @@ ## Landau FWHM -We need to compute the maximum: +::::: {.columns} -$$ - L_{\text{max}} = L(\mu_L) -$$ -$$ - \text{FWHM} = w = x_+ - x_- \with L(x_{\pm}) = \frac{L_{\text{max}}}{2} -$$ +:::: {.column width=50%} + $$ + \text{FWHM} = w = x_+ - x_- + $$ + $$ + L(x_{\pm}) = \frac{L_{\text{max}}}{2} = \frac{L(\mu_L)}{2} + $$ -. . . + . . . -- Computed by numerical root finding (Brent) + \vspace{20pt} -\setbeamercovered{} + - Computed by numerical root finding (Brent) -\begin{center} - \begin{tikzpicture}[remember picture] - \node at (0,0) (here) {$w_L\ex = 4.018645...$}; - \pause - \node [opacity=0.5, xscale=0.32, yscale=0.25 ] at (here) {\includegraphics{images/high.png}}; - \end{tikzpicture} -\end{center} + \setbeamercovered{} -\setbeamercovered{transparent} + \begin{center} + \begin{tikzpicture}[remember picture] + \node at (-1,0) (here) {$w_L\ex = 4.018645...$}; + \pause + \node [opacity=0.5, xscale=0.65, yscale=0.5 ] at (here) + {\includegraphics{images/high.png}}; + \end{tikzpicture} + \end{center} + + \setbeamercovered{transparent} +:::: + +::: {.column width=50%} + ![](images/fwhm.pdf) +::: + +:::::