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#LyX 2.3 created this file. For more info see http://www.lyx.org/
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docs/notes.lyx  view on Meta::CPAN

, 
\begin_inset Formula $w$
\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{eqnarray*}
E_{0} & = & P-fw\\
i_{min} & = & \left\lfloor \frac{R_{min}-E_{0}}{w}\right\rfloor \\
i_{max} & = & \left\lceil \frac{R_{max}-E_{0}}{w}\right\rceil \\
n & = & i_{max}-i_{min}+1
\end{eqnarray*}

\end_inset


\end_layout

\begin_layout Subsection
Aligned bins, Fixed 
\begin_inset Formula $n$
\end_inset

, variable 
\begin_inset Formula $w$
\end_inset


\end_layout

\begin_layout Standard
Given: 
\begin_inset Formula $\Delta$
\end_inset

, 
\begin_inset Formula $P$
\end_inset

, 
\begin_inset Formula $R_{max}$
\end_inset

, 
\begin_inset Formula $R_{min}$
\end_inset

, 
\begin_inset Formula $n$
\end_inset

.
\end_layout

\begin_layout Standard
Wanted: minimum 
\begin_inset Formula $w\ni w\geq\frac{R_{min}-R_{max}}{n}$
\end_inset

 
\end_layout

\begin_layout Standard
Because Eqs.
\begin_inset space ~
\end_inset


\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Emin-General"
plural "false"
caps "false"
noprefix "false"

\end_inset

 and 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Emax-General"
plural "false"
caps "false"
noprefix "false"

\end_inset

 are painful to solve, let's see if we can figure things out another way.
\end_layout

\begin_layout Standard
Once we have a bin width such that bin edges 
\begin_inset Formula $\left[E_{min},E_{max}\right]$
\end_inset

 cover our data range, 
\begin_inset Formula $\left[R_{min},R_{max}\right]$
\end_inset

, attending to alignment with the fiducial point 
\begin_inset Formula $P$
\end_inset

 is a simple translation of the bins.
 
\begin_inset Formula $P$
\end_inset

's position relative to its containing bin is given by 
\begin_inset Formula $fw$
\end_inset

, so it's a periodic condition (it doesn't matter 
\emph on
which
\emph default
 bin it's in) and the maximum we need to translate is exactly one bin.