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sec-2: rewrite FWHM notes and add the relative image

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Giù Marcer 2020-06-12 22:16:25 +02:00 committed by rnhmjoj
parent 7ea2151aac
commit c39e0190aa
2 changed files with 37 additions and 23 deletions
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slides/sections/2.md
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@ -55,14 +55,16 @@
## Landau median ## Landau median
- CDF computed by numerical integration - 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{} \setbeamercovered{}
\begin{center} \begin{center}
\begin{tikzpicture}[remember picture] \begin{tikzpicture}[overlay]
\node at (0,0) (here) {$m_L\ex = 1.3557804...$};
\pause \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{tikzpicture}
\end{center} \end{center}
@ -83,7 +85,8 @@
\begin{tikzpicture}[remember picture] \begin{tikzpicture}[remember picture]
\node at (0,0) (here) {$\mu_L\ex = − 0.22278...$}; \node at (0,0) (here) {$\mu_L\ex = − 0.22278...$};
\pause \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{tikzpicture}
\end{center} \end{center}
@ -92,27 +95,38 @@
## Landau FWHM ## Landau FWHM
We need to compute the maximum: ::::: {.columns}
$$ :::: {.column width=50%}
L_{\text{max}} = L(\mu_L) $$
$$ \text{FWHM} = w = x_+ - x_-
$$ $$
\text{FWHM} = w = x_+ - x_- \with L(x_{\pm}) = \frac{L_{\text{max}}}{2} $$
$$ L(x_{\pm}) = \frac{L_{\text{max}}}{2} = \frac{L(\mu_L)}{2}
$$
. . . . . .
- Computed by numerical root finding (Brent) \vspace{20pt}
\setbeamercovered{} - Computed by numerical root finding (Brent)
\begin{center} \setbeamercovered{}
\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{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)
:::
:::::