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then 
\begin_inset Formula $E_{0}$
\end_inset

 may be determined from Eq.
\begin_inset space ~
\end_inset


\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Ratio-En"
plural "false"
caps "false"
noprefix "false"

\end_inset

, which in any case provides the remaining bin edges.
\end_layout

\begin_layout Subsection
\begin_inset Formula $\left[R,E_{max}\right]$
\end_inset

, 
\begin_inset Formula $w$
\end_inset

, 
\begin_inset Formula $r$
\end_inset


\end_layout

\begin_layout Standard
Similar to the last section, just note that 
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{eqnarray*}
E_{max} & \equiv & \begin{cases}
E_{0} & w<0\\
E_{n} & w>0
\end{cases}
\end{eqnarray*}

\end_inset


\end_layout

\begin_layout Subsection
\begin_inset Formula $E_{0}$
\end_inset

, 
\begin_inset Formula $[R_{min},R_{max}],$
\end_inset


\begin_inset Formula $w$
\end_inset

, 
\begin_inset Formula $r$
\end_inset


\end_layout

\begin_layout Standard
If 
\begin_inset Formula $E_{0}$
\end_inset

is not at one of the grid extrema, 
\begin_inset Formula $i_{min}$
\end_inset

 and 
\begin_inset Formula $i_{max}$
\end_inset

 can be determined from Eq.
\begin_inset space ~
\end_inset


\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Ratio-n-from-range"
plural "false"
caps "false"
noprefix "false"

\end_inset

, with 
\begin_inset Formula 
\begin{eqnarray*}
i_{min} & = & n(R_{min}-E_{0})-1\\
i_{max} & = & n(R_{max}-E_{0})
\end{eqnarray*}

\end_inset


\end_layout

\end_body
\end_document