From 99baacb1f33acaea45b00e6661c29302b01562a6 Mon Sep 17 00:00:00 2001
From: ottjk <joshott16@gmail.com>
Date: Sun, 31 Dec 2023 15:01:25 -0500
Subject: sway and tex

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+% ****** Start of file apssamp.tex ******
+%
+%   This file is part of the APS files in the REVTeX 4.2 distribution.
+%   Version 4.2a of REVTeX, December 2014
+%
+%   Copyright (c) 2014 The American Physical Society.
+%
+%   See the REVTeX 4 README file for restrictions and more information.
+%
+% TeX'ing this file requires that you have AMS-LaTeX 2.0 installed
+% as well as the rest of the prerequisites for REVTeX 4.2
+%
+% See the REVTeX 4 README file
+% It also requires running BibTeX. The commands are as follows:
+%
+%  1)  latex apssamp.tex
+%  2)  bibtex apssamp
+%  3)  latex apssamp.tex
+%  4)  latex apssamp.tex
+%
+\documentclass[%
+ reprint,
+%superscriptaddress,
+%groupedaddress,
+%unsortedaddress,
+%runinaddress,
+%frontmatterverbose, 
+%preprint,
+%preprintnumbers,
+%nofootinbib,
+%nobibnotes,
+%bibnotes,
+ amsmath,amssymb,
+ aps,
+%pra,
+%prb,
+%rmp,
+%prstab,
+%prstper,
+%floatfix,
+]{revtex4-2}
+
+\usepackage{graphicx}% Include figure files
+\usepackage{dcolumn}% Align table columns on decimal point
+\usepackage{bm}% bold math
+%\usepackage{hyperref}% add hypertext capabilities
+%\usepackage[mathlines]{lineno}% Enable numbering of text and display math
+%\linenumbers\relax % Commence numbering lines
+
+%\usepackage[showframe,%Uncomment any one of the following lines to test 
+%%scale=0.7, marginratio={1:1, 2:3}, ignoreall,% default settings
+%%text={7in,10in},centering,
+%%margin=1.5in,
+%%total={6.5in,8.75in}, top=1.2in, left=0.9in, includefoot,
+%%height=10in,a5paper,hmargin={3cm,0.8in},
+%]{geometry}
+
+\begin{document}
+
+\preprint{APS/123-QED}
+
+\title{Manuscript Title:\\with Forced Linebreak}% Force line breaks with \\
+\thanks{A footnote to the article title}%
+
+\author{Ann Author}
+ \altaffiliation[Also at ]{Physics Department, XYZ University.}%Lines break automatically or can be forced with \\
+\author{Second Author}%
+ \email{Second.Author@institution.edu}
+\affiliation{%
+ Authors' institution and/or address\\
+ This line break forced with \textbackslash\textbackslash
+}%
+
+\collaboration{MUSO Collaboration}%\noaffiliation
+
+\author{Charlie Author}
+ \homepage{http://www.Second.institution.edu/~Charlie.Author}
+\affiliation{
+ Second institution and/or address\\
+ This line break forced% with \\
+}%
+\affiliation{
+ Third institution, the second for Charlie Author
+}%
+\author{Delta Author}
+\affiliation{%
+ Authors' institution and/or address\\
+ This line break forced with \textbackslash\textbackslash
+}%
+
+\collaboration{CLEO Collaboration}%\noaffiliation
+
+\date{\today}% It is always \today, today,
+             %  but any date may be explicitly specified
+
+\begin{abstract}
+An article usually includes an abstract, a concise summary of the work
+covered at length in the main body of the article. 
+\begin{description}
+\item[Usage]
+Secondary publications and information retrieval purposes.
+\item[Structure]
+You may use the \texttt{description} environment to structure your abstract;
+use the optional argument of the \verb+\item+ command to give the category of each item. 
+\end{description}
+\end{abstract}
+
+%\keywords{Suggested keywords}%Use showkeys class option if keyword
+                              %display desired
+\maketitle
+
+%\tableofcontents
+
+\section{\label{sec:level1}First-level heading:\protect\\ The line
+break was forced \lowercase{via} \textbackslash\textbackslash}
+
+This sample document demonstrates proper use of REV\TeX~4.2 (and
+\LaTeXe) in mansucripts prepared for submission to APS
+journals. Further information can be found in the REV\TeX~4.2
+documentation included in the distribution or available at
+\url{http://journals.aps.org/revtex/}.
+
+When commands are referred to in this example file, they are always
+shown with their required arguments, using normal \TeX{} format. In
+this format, \verb+#1+, \verb+#2+, etc. stand for required
+author-supplied arguments to commands. For example, in
+\verb+\section{#1}+ the \verb+#1+ stands for the title text of the
+author's section heading, and in \verb+\title{#1}+ the \verb+#1+
+stands for the title text of the paper.
+
+Line breaks in section headings at all levels can be introduced using
+\textbackslash\textbackslash. A blank input line tells \TeX\ that the
+paragraph has ended. Note that top-level section headings are
+automatically uppercased. If a specific letter or word should appear in
+lowercase instead, you must escape it using \verb+\lowercase{#1}+ as
+in the word ``via'' above.
+
+\subsection{\label{sec:level2}Second-level heading: Formatting}
+
+This file may be formatted in either the \texttt{preprint} or
+\texttt{reprint} style. \texttt{reprint} format mimics final journal output. 
+Either format may be used for submission purposes. \texttt{letter} sized paper should
+be used when submitting to APS journals.
+
+\subsubsection{Wide text (A level-3 head)}
+The \texttt{widetext} environment will make the text the width of the
+full page, as on page~\pageref{eq:wideeq}. (Note the use the
+\verb+\pageref{#1}+ command to refer to the page number.) 
+\paragraph{Note (Fourth-level head is run in)}
+The width-changing commands only take effect in two-column formatting. 
+There is no effect if text is in a single column.
+
+\subsection{\label{sec:citeref}Citations and References}
+A citation in text uses the command \verb+\cite{#1}+ or
+\verb+\onlinecite{#1}+ and refers to an entry in the bibliography. 
+An entry in the bibliography is a reference to another document.
+
+\subsubsection{Citations}
+Because REV\TeX\ uses the \verb+natbib+ package of Patrick Daly, 
+the entire repertoire of commands in that package are available for your document;
+see the \verb+natbib+ documentation for further details. Please note that
+REV\TeX\ requires version 8.31a or later of \verb+natbib+.
+
+\paragraph{Syntax}
+The argument of \verb+\cite+ may be a single \emph{key}, 
+or may consist of a comma-separated list of keys.
+The citation \emph{key} may contain 
+letters, numbers, the dash (-) character, or the period (.) character. 
+New with natbib 8.3 is an extension to the syntax that allows for 
+a star (*) form and two optional arguments on the citation key itself.
+The syntax of the \verb+\cite+ command is thus (informally stated)
+\begin{quotation}\flushleft\leftskip1em
+\verb+\cite+ \verb+{+ \emph{key} \verb+}+, or\\
+\verb+\cite+ \verb+{+ \emph{optarg+key} \verb+}+, or\\
+\verb+\cite+ \verb+{+ \emph{optarg+key} \verb+,+ \emph{optarg+key}\ldots \verb+}+,
+\end{quotation}\noindent
+where \emph{optarg+key} signifies 
+\begin{quotation}\flushleft\leftskip1em
+\emph{key}, or\\
+\texttt{*}\emph{key}, or\\
+\texttt{[}\emph{pre}\texttt{]}\emph{key}, or\\
+\texttt{[}\emph{pre}\texttt{]}\texttt{[}\emph{post}\texttt{]}\emph{key}, or even\\
+\texttt{*}\texttt{[}\emph{pre}\texttt{]}\texttt{[}\emph{post}\texttt{]}\emph{key}.
+\end{quotation}\noindent
+where \emph{pre} and \emph{post} is whatever text you wish to place 
+at the beginning and end, respectively, of the bibliographic reference
+(see Ref.~[\onlinecite{witten2001}] and the two under Ref.~[\onlinecite{feyn54}]).
+(Keep in mind that no automatic space or punctuation is applied.)
+It is highly recommended that you put the entire \emph{pre} or \emph{post} portion 
+within its own set of braces, for example: 
+\verb+\cite+ \verb+{+ \texttt{[} \verb+{+\emph{text}\verb+}+\texttt{]}\emph{key}\verb+}+.
+The extra set of braces will keep \LaTeX\ out of trouble if your \emph{text} contains the comma (,) character.
+
+The star (*) modifier to the \emph{key} signifies that the reference is to be 
+merged with the previous reference into a single bibliographic entry, 
+a common idiom in APS and AIP articles (see below, Ref.~[\onlinecite{epr}]). 
+When references are merged in this way, they are separated by a semicolon instead of 
+the period (full stop) that would otherwise appear.
+
+\paragraph{Eliding repeated information}
+When a reference is merged, some of its fields may be elided: for example, 
+when the author matches that of the previous reference, it is omitted. 
+If both author and journal match, both are omitted.
+If the journal matches, but the author does not, the journal is replaced by \emph{ibid.},
+as exemplified by Ref.~[\onlinecite{epr}]. 
+These rules embody common editorial practice in APS and AIP journals and will only
+be in effect if the markup features of the APS and AIP Bib\TeX\ styles is employed.
+
+\paragraph{The options of the cite command itself}
+Please note that optional arguments to the \emph{key} change the reference in the bibliography, 
+not the citation in the body of the document. 
+For the latter, use the optional arguments of the \verb+\cite+ command itself:
+\verb+\cite+ \texttt{*}\allowbreak
+\texttt{[}\emph{pre-cite}\texttt{]}\allowbreak
+\texttt{[}\emph{post-cite}\texttt{]}\allowbreak
+\verb+{+\emph{key-list}\verb+}+.
+
+\subsubsection{Example citations}
+By default, citations are numerical\cite{Beutler1994}.
+Author-year citations are used when the journal is RMP. 
+To give a textual citation, use \verb+\onlinecite{#1}+: 
+Refs.~\onlinecite{[][{, and references therein}]witten2001,Bire82}. 
+By default, the \texttt{natbib} package automatically sorts your citations into numerical order and ``compresses'' runs of three or more consecutive numerical citations.
+REV\TeX\ provides the ability to automatically change the punctuation when switching between journal styles that provide citations in square brackets and those that use a superscript style instead. This is done through the \texttt{citeautoscript} option. For instance, the journal style \texttt{prb} automatically invokes this option because \textit{Physical 
+Review B} uses superscript-style citations. The effect is to move the punctuation, which normally comes after a citation in square brackets, to its proper position before the superscript. 
+To illustrate, we cite several together 
+\cite{[See the explanation of time travel in ]feyn54,*[The classical relativistic treatment of ][ is a relative classic]epr,witten2001,Berman1983,Davies1998,Bire82}, 
+and once again in different order (Refs.~\cite{epr,feyn54,Bire82,Berman1983,witten2001,Davies1998}). 
+Note that the citations were both compressed and sorted. Futhermore, running this sample file under the \texttt{prb} option will move the punctuation to the correct place.
+
+When the \verb+prb+ class option is used, the \verb+\cite{#1}+ command
+displays the reference's number as a superscript rather than in
+square brackets. Note that the location of the \verb+\cite{#1}+
+command should be adjusted for the reference style: the superscript
+references in \verb+prb+ style must appear after punctuation;
+otherwise the reference must appear before any punctuation. This
+sample was written for the regular (non-\texttt{prb}) citation style.
+The command \verb+\onlinecite{#1}+ in the \texttt{prb} style also
+displays the reference on the baseline.
+
+\subsubsection{References}
+A reference in the bibliography is specified by a \verb+\bibitem{#1}+ command
+with the same argument as the \verb+\cite{#1}+ command.
+\verb+\bibitem{#1}+ commands may be crafted by hand or, preferably,
+generated by Bib\TeX. 
+REV\TeX~4.2 includes Bib\TeX\ style files
+\verb+apsrev4-2.bst+, \verb+apsrmp4-2.bst+ appropriate for
+\textit{Physical Review} and \textit{Reviews of Modern Physics},
+respectively.
+
+\subsubsection{Example references}
+This sample file employs the \verb+\bibliography+ command, 
+which formats the \texttt{\jobname .bbl} file
+and specifies which bibliographic databases are to be used by Bib\TeX\ 
+(one of these should be by arXiv convention \texttt{\jobname .bib}).
+Running Bib\TeX\ (via \texttt{bibtex \jobname}) 
+after the first pass of \LaTeX\ produces the file
+\texttt{\jobname .bbl} which contains the automatically formatted
+\verb+\bibitem+ commands (including extra markup information via
+\verb+\bibinfo+ and \verb+\bibfield+ commands). 
+If not using Bib\TeX, you will have to create the \verb+thebibiliography+ environment 
+and its \verb+\bibitem+ commands by hand.
+
+Numerous examples of the use of the APS bibliographic entry types appear in the bibliography of this sample document.
+You can refer to the \texttt{\jobname .bib} file, 
+and compare its information to the formatted bibliography itself.
+
+\subsection{Footnotes}%
+Footnotes, produced using the \verb+\footnote{#1}+ command, 
+usually integrated into the bibliography alongside the other entries.
+Numerical citation styles do this%
+\footnote{Automatically placing footnotes into the bibliography requires using BibTeX to compile the bibliography.};
+author-year citation styles place the footnote at the bottom of the text column.
+Note: due to the method used to place footnotes in the bibliography, 
+\emph{you must re-run Bib\TeX\ every time you change any of your document's footnotes}. 
+
+\section{Math and Equations}
+Inline math may be typeset using the \verb+$+ delimiters. Bold math
+symbols may be achieved using the \verb+bm+ package and the
+\verb+\bm{#1}+ command it supplies. For instance, a bold $\alpha$ can
+be typeset as \verb+$\bm{\alpha}$+ giving $\bm{\alpha}$. Fraktur and
+Blackboard (or open face or double struck) characters should be
+typeset using the \verb+\mathfrak{#1}+ and \verb+\mathbb{#1}+ commands
+respectively. Both are supplied by the \texttt{amssymb} package. For
+example, \verb+$\mathbb{R}$+ gives $\mathbb{R}$ and
+\verb+$\mathfrak{G}$+ gives $\mathfrak{G}$
+
+In \LaTeX\ there are many different ways to display equations, and a
+few preferred ways are noted below. Displayed math will center by
+default. Use the class option \verb+fleqn+ to flush equations left.
+
+Below we have numbered single-line equations; this is the most common
+type of equation in \textit{Physical Review}:
+\begin{eqnarray}
+\chi_+(p)\alt{\bf [}2|{\bf p}|(|{\bf p}|+p_z){\bf ]}^{-1/2}
+\left(
+\begin{array}{c}
+|{\bf p}|+p_z\\
+px+ip_y
+\end{array}\right)\;,
+\\
+\left\{%
+ \openone234567890abc123\alpha\beta\gamma\delta1234556\alpha\beta
+ \frac{1\sum^{a}_{b}}{A^2}%
+\right\}%
+\label{eq:one}.
+\end{eqnarray}
+Note the open one in Eq.~(\ref{eq:one}).
+
+Not all numbered equations will fit within a narrow column this
+way. The equation number will move down automatically if it cannot fit
+on the same line with a one-line equation:
+\begin{equation}
+\left\{
+ ab12345678abc123456abcdef\alpha\beta\gamma\delta1234556\alpha\beta
+ \frac{1\sum^{a}_{b}}{A^2}%
+\right\}.
+\end{equation}
+
+When the \verb+\label{#1}+ command is used [cf. input for
+Eq.~(\ref{eq:one})], the equation can be referred to in text without
+knowing the equation number that \TeX\ will assign to it. Just
+use \verb+\ref{#1}+, where \verb+#1+ is the same name that used in
+the \verb+\label{#1}+ command.
+
+Unnumbered single-line equations can be typeset
+using the \verb+\[+, \verb+\]+ format:
+\[g^+g^+ \rightarrow g^+g^+g^+g^+ \dots ~,~~q^+q^+\rightarrow
+q^+g^+g^+ \dots ~. \]
+
+
+\subsection{Multiline equations}
+
+Multiline equations are obtained by using the \verb+eqnarray+
+environment.  Use the \verb+\nonumber+ command at the end of each line
+to avoid assigning a number:
+\begin{eqnarray}
+{\cal M}=&&ig_Z^2(4E_1E_2)^{1/2}(l_i^2)^{-1}
+\delta_{\sigma_1,-\sigma_2}
+(g_{\sigma_2}^e)^2\chi_{-\sigma_2}(p_2)\nonumber\\
+&&\times
+[\epsilon_jl_i\epsilon_i]_{\sigma_1}\chi_{\sigma_1}(p_1),
+\end{eqnarray}
+\begin{eqnarray}
+\sum \vert M^{\text{viol}}_g \vert ^2&=&g^{2n-4}_S(Q^2)~N^{n-2}
+        (N^2-1)\nonumber \\
+ & &\times \left( \sum_{i<j}\right)
+  \sum_{\text{perm}}
+ \frac{1}{S_{12}}
+ \frac{1}{S_{12}}
+ \sum_\tau c^f_\tau~.
+\end{eqnarray}
+\textbf{Note:} Do not use \verb+\label{#1}+ on a line of a multiline
+equation if \verb+\nonumber+ is also used on that line. Incorrect
+cross-referencing will result. Notice the use \verb+\text{#1}+ for
+using a Roman font within a math environment.
+
+To set a multiline equation without \emph{any} equation
+numbers, use the \verb+\begin{eqnarray*}+,
+\verb+\end{eqnarray*}+ format:
+\begin{eqnarray*}
+\sum \vert M^{\text{viol}}_g \vert ^2&=&g^{2n-4}_S(Q^2)~N^{n-2}
+        (N^2-1)\\
+ & &\times \left( \sum_{i<j}\right)
+ \left(
+  \sum_{\text{perm}}\frac{1}{S_{12}S_{23}S_{n1}}
+ \right)
+ \frac{1}{S_{12}}~.
+\end{eqnarray*}
+
+To obtain numbers not normally produced by the automatic numbering,
+use the \verb+\tag{#1}+ command, where \verb+#1+ is the desired
+equation number. For example, to get an equation number of
+(\ref{eq:mynum}),
+\begin{equation}
+g^+g^+ \rightarrow g^+g^+g^+g^+ \dots ~,~~q^+q^+\rightarrow
+q^+g^+g^+ \dots ~. \tag{2.6$'$}\label{eq:mynum}
+\end{equation}
+
+\paragraph{A few notes on \texttt{tag}s} 
+\verb+\tag{#1}+ requires the \texttt{amsmath} package. 
+Place the \verb+\tag{#1}+ command before the \verb+\label{#1}+, if any. 
+The numbering produced by \verb+\tag{#1}+ \textit{does not affect} 
+the automatic numbering in REV\TeX; 
+therefore, the number must be known ahead of time, 
+and it must be manually adjusted if other equations are added. 
+\verb+\tag{#1}+ works with both single-line and multiline equations. 
+\verb+\tag{#1}+ should only be used in exceptional cases---%
+do not use it to number many equations in your paper. 
+Please note that this feature of the \texttt{amsmath} package
+is \emph{not} compatible with the \texttt{hyperref} (6.77u) package.
+
+Enclosing display math within
+\verb+\begin{subequations}+ and \verb+\end{subequations}+ will produce
+a set of equations that are labeled with letters, as shown in
+Eqs.~(\ref{subeq:1}) and (\ref{subeq:2}) below.
+You may include any number of single-line and multiline equations,
+although it is probably not a good idea to follow one display math
+directly after another.
+\begin{subequations}
+\label{eq:whole}
+\begin{eqnarray}
+{\cal M}=&&ig_Z^2(4E_1E_2)^{1/2}(l_i^2)^{-1}
+(g_{\sigma_2}^e)^2\chi_{-\sigma_2}(p_2)\nonumber\\
+&&\times
+[\epsilon_i]_{\sigma_1}\chi_{\sigma_1}(p_1).\label{subeq:2}
+\end{eqnarray}
+\begin{equation}
+\left\{
+ abc123456abcdef\alpha\beta\gamma\delta1234556\alpha\beta
+ \frac{1\sum^{a}_{b}}{A^2}
+\right\},\label{subeq:1}
+\end{equation}
+\end{subequations}
+Giving a \verb+\label{#1}+ command directly after the \verb+\begin{subequations}+, 
+allows you to reference all the equations in the \texttt{subequations} environment. 
+For example, the equations in the preceding subequations environment were
+Eqs.~(\ref{eq:whole}).
+
+\subsubsection{Wide equations}
+The equation that follows is set in a wide format, i.e., it spans the full page. 
+The wide format is reserved for long equations
+that cannot easily be set in a single column:
+\begin{widetext}
+\begin{equation}
+{\cal R}^{(\text{d})}=
+ g_{\sigma_2}^e
+ \left(
+   \frac{[\Gamma^Z(3,21)]_{\sigma_1}}{Q_{12}^2-M_W^2}
+  +\frac{[\Gamma^Z(13,2)]_{\sigma_1}}{Q_{13}^2-M_W^2}
+ \right)
+ + x_WQ_e
+ \left(
+   \frac{[\Gamma^\gamma(3,21)]_{\sigma_1}}{Q_{12}^2-M_W^2}
+  +\frac{[\Gamma^\gamma(13,2)]_{\sigma_1}}{Q_{13}^2-M_W^2}
+ \right)\;. 
+ \label{eq:wideeq}
+\end{equation}
+\end{widetext}
+This is typed to show how the output appears in wide format.
+(Incidentally, since there is no blank line between the \texttt{equation} environment above 
+and the start of this paragraph, this paragraph is not indented.)
+
+\section{Cross-referencing}
+REV\TeX{} will automatically number such things as
+sections, footnotes, equations, figure captions, and table captions. 
+In order to reference them in text, use the
+\verb+\label{#1}+ and \verb+\ref{#1}+ commands. 
+To reference a particular page, use the \verb+\pageref{#1}+ command.
+
+The \verb+\label{#1}+ should appear 
+within the section heading, 
+within the footnote text, 
+within the equation, or 
+within the table or figure caption. 
+The \verb+\ref{#1}+ command
+is used in text at the point where the reference is to be displayed.  
+Some examples: Section~\ref{sec:level1} on page~\pageref{sec:level1},
+Table~\ref{tab:table1},%
+\begin{table}[b]%The best place to locate the table environment is directly after its first reference in text
+\caption{\label{tab:table1}%
+A table that fits into a single column of a two-column layout. 
+Note that REV\TeX~4 adjusts the intercolumn spacing so that the table fills the
+entire width of the column. Table captions are numbered
+automatically. 
+This table illustrates left-, center-, decimal- and right-aligned columns,
+along with the use of the \texttt{ruledtabular} environment which sets the 
+Scotch (double) rules above and below the alignment, per APS style.
+}
+\begin{ruledtabular}
+\begin{tabular}{lcdr}
+\textrm{Left\footnote{Note a.}}&
+\textrm{Centered\footnote{Note b.}}&
+\multicolumn{1}{c}{\textrm{Decimal}}&
+\textrm{Right}\\
+\colrule
+1 & 2 & 3.001 & 4\\
+10 & 20 & 30 & 40\\
+100 & 200 & 300.0 & 400\\
+\end{tabular}
+\end{ruledtabular}
+\end{table}
+and Fig.~\ref{fig:epsart}.%
+\begin{figure}[b]
+\includegraphics{fig_1}% Here is how to import EPS art
+\caption{\label{fig:epsart} A figure caption. The figure captions are
+automatically numbered.}
+\end{figure}
+
+\section{Floats: Figures, Tables, Videos, etc.}
+Figures and tables are usually allowed to ``float'', which means that their
+placement is determined by \LaTeX, while the document is being typeset. 
+
+Use the \texttt{figure} environment for a figure, the \texttt{table} environment for a table.
+In each case, use the \verb+\caption+ command within to give the text of the
+figure or table caption along with the \verb+\label+ command to provide
+a key for referring to this figure or table.
+The typical content of a figure is an image of some kind; 
+that of a table is an alignment.%
+\begin{figure*}
+\includegraphics{fig_2}% Here is how to import EPS art
+\caption{\label{fig:wide}Use the figure* environment to get a wide
+figure that spans the page in \texttt{twocolumn} formatting.}
+\end{figure*}
+\begin{table*}
+\caption{\label{tab:table3}This is a wide table that spans the full page
+width in a two-column layout. It is formatted using the
+\texttt{table*} environment. It also demonstates the use of
+\textbackslash\texttt{multicolumn} in rows with entries that span
+more than one column.}
+\begin{ruledtabular}
+\begin{tabular}{ccccc}
+ &\multicolumn{2}{c}{$D_{4h}^1$}&\multicolumn{2}{c}{$D_{4h}^5$}\\
+ Ion&1st alternative&2nd alternative&lst alternative
+&2nd alternative\\ \hline
+ K&$(2e)+(2f)$&$(4i)$ &$(2c)+(2d)$&$(4f)$ \\
+ Mn&$(2g)$\footnote{The $z$ parameter of these positions is $z\sim\frac{1}{4}$.}
+ &$(a)+(b)+(c)+(d)$&$(4e)$&$(2a)+(2b)$\\
+ Cl&$(a)+(b)+(c)+(d)$&$(2g)$\footnotemark[1]
+ &$(4e)^{\text{a}}$\\
+ He&$(8r)^{\text{a}}$&$(4j)^{\text{a}}$&$(4g)^{\text{a}}$\\
+ Ag& &$(4k)^{\text{a}}$& &$(4h)^{\text{a}}$\\
+\end{tabular}
+\end{ruledtabular}
+\end{table*}
+
+Insert an image using either the \texttt{graphics} or
+\texttt{graphix} packages, which define the \verb+\includegraphics{#1}+ command.
+(The two packages differ in respect of the optional arguments 
+used to specify the orientation, scaling, and translation of the image.) 
+To create an alignment, use the \texttt{tabular} environment. 
+
+The best place to locate the \texttt{figure} or \texttt{table} environment
+is immediately following its first reference in text; this sample document
+illustrates this practice for Fig.~\ref{fig:epsart}, which
+shows a figure that is small enough to fit in a single column. 
+
+In exceptional cases, you will need to move the float earlier in the document, as was done
+with Table~\ref{tab:table3}: \LaTeX's float placement algorithms need to know
+about a full-page-width float earlier. 
+
+Fig.~\ref{fig:wide}
+has content that is too wide for a single column,
+so the \texttt{figure*} environment has been used.%
+\begin{table}[b]
+\caption{\label{tab:table4}%
+Numbers in columns Three--Five are aligned with the ``d'' column specifier 
+(requires the \texttt{dcolumn} package). 
+Non-numeric entries (those entries without a ``.'') in a ``d'' column are aligned on the decimal point. 
+Use the ``D'' specifier for more complex layouts. }
+\begin{ruledtabular}
+\begin{tabular}{ccddd}
+One&Two&
+\multicolumn{1}{c}{\textrm{Three}}&
+\multicolumn{1}{c}{\textrm{Four}}&
+\multicolumn{1}{c}{\textrm{Five}}\\
+%\mbox{Three}&\mbox{Four}&\mbox{Five}\\
+\hline
+one&two&\mbox{three}&\mbox{four}&\mbox{five}\\
+He&2& 2.77234 & 45672. & 0.69 \\
+C\footnote{Some tables require footnotes.}
+  &C\footnote{Some tables need more than one footnote.}
+  & 12537.64 & 37.66345 & 86.37 \\
+\end{tabular}
+\end{ruledtabular}
+\end{table}
+
+The content of a table is typically a \texttt{tabular} environment, 
+giving rows of type in aligned columns. 
+Column entries separated by \verb+&+'s, and 
+each row ends with \textbackslash\textbackslash. 
+The required argument for the \texttt{tabular} environment
+specifies how data are aligned in the columns. 
+For instance, entries may be centered, left-justified, right-justified, aligned on a decimal
+point. 
+Extra column-spacing may be be specified as well, 
+although REV\TeX~4 sets this spacing so that the columns fill the width of the
+table. Horizontal rules are typeset using the \verb+\hline+
+command. The doubled (or Scotch) rules that appear at the top and
+bottom of a table can be achieved enclosing the \texttt{tabular}
+environment within a \texttt{ruledtabular} environment. Rows whose
+columns span multiple columns can be typeset using the
+\verb+\multicolumn{#1}{#2}{#3}+ command (for example, see the first
+row of Table~\ref{tab:table3}).%
+
+Tables~\ref{tab:table1}, \ref{tab:table3}, \ref{tab:table4}, and \ref{tab:table2}%
+\begin{table}[b]
+\caption{\label{tab:table2}
+A table with numerous columns that still fits into a single column. 
+Here, several entries share the same footnote. 
+Inspect the \LaTeX\ input for this table to see exactly how it is done.}
+\begin{ruledtabular}
+\begin{tabular}{cccccccc}
+ &$r_c$ (\AA)&$r_0$ (\AA)&$\kappa r_0$&
+ &$r_c$ (\AA) &$r_0$ (\AA)&$\kappa r_0$\\
+\hline
+Cu& 0.800 & 14.10 & 2.550 &Sn\footnotemark[1]
+& 0.680 & 1.870 & 3.700 \\
+Ag& 0.990 & 15.90 & 2.710 &Pb\footnotemark[2]
+& 0.450 & 1.930 & 3.760 \\
+Au& 1.150 & 15.90 & 2.710 &Ca\footnotemark[3]
+& 0.750 & 2.170 & 3.560 \\
+Mg& 0.490 & 17.60 & 3.200 &Sr\footnotemark[4]
+& 0.900 & 2.370 & 3.720 \\
+Zn& 0.300 & 15.20 & 2.970 &Li\footnotemark[2]
+& 0.380 & 1.730 & 2.830 \\
+Cd& 0.530 & 17.10 & 3.160 &Na\footnotemark[5]
+& 0.760 & 2.110 & 3.120 \\
+Hg& 0.550 & 17.80 & 3.220 &K\footnotemark[5]
+&  1.120 & 2.620 & 3.480 \\
+Al& 0.230 & 15.80 & 3.240 &Rb\footnotemark[3]
+& 1.330 & 2.800 & 3.590 \\
+Ga& 0.310 & 16.70 & 3.330 &Cs\footnotemark[4]
+& 1.420 & 3.030 & 3.740 \\
+In& 0.460 & 18.40 & 3.500 &Ba\footnotemark[5]
+& 0.960 & 2.460 & 3.780 \\
+Tl& 0.480 & 18.90 & 3.550 & & & & \\
+\end{tabular}
+\end{ruledtabular}
+\footnotetext[1]{Here's the first, from Ref.~\onlinecite{feyn54}.}
+\footnotetext[2]{Here's the second.}
+\footnotetext[3]{Here's the third.}
+\footnotetext[4]{Here's the fourth.}
+\footnotetext[5]{And etc.}
+\end{table}
+show various effects.
+A table that fits in a single column employs the \texttt{table}
+environment. 
+Table~\ref{tab:table3} is a wide table, set with the \texttt{table*} environment. 
+Long tables may need to break across pages. 
+The most straightforward way to accomplish this is to specify
+the \verb+[H]+ float placement on the \texttt{table} or
+\texttt{table*} environment. 
+However, the \LaTeXe\ package \texttt{longtable} allows headers and footers to be specified for each page of the table. 
+A simple example of the use of \texttt{longtable} can be found
+in the file \texttt{summary.tex} that is included with the REV\TeX~4
+distribution.
+
+There are two methods for setting footnotes within a table (these
+footnotes will be displayed directly below the table rather than at
+the bottom of the page or in the bibliography). The easiest
+and preferred method is just to use the \verb+\footnote{#1}+
+command. This will automatically enumerate the footnotes with
+lowercase roman letters. However, it is sometimes necessary to have
+multiple entries in the table share the same footnote. In this case,
+there is no choice but to manually create the footnotes using
+\verb+\footnotemark[#1]+ and \verb+\footnotetext[#1]{#2}+.
+\texttt{\#1} is a numeric value. Each time the same value for
+\texttt{\#1} is used, the same mark is produced in the table. The
+\verb+\footnotetext[#1]{#2}+ commands are placed after the \texttt{tabular}
+environment. Examine the \LaTeX\ source and output for
+Tables~\ref{tab:table1} and \ref{tab:table2}
+for examples.
+
+Video~\ref{vid:PRSTPER.4.010101} 
+illustrates several features new with REV\TeX4.2,
+starting with the \texttt{video} environment, which is in the same category with
+\texttt{figure} and \texttt{table}.%
+\begin{video}
+\href{http://prst-per.aps.org/multimedia/PRSTPER/v4/i1/e010101/e010101_vid1a.mpg}{\includegraphics{vid_1a}}%
+ \quad
+\href{http://prst-per.aps.org/multimedia/PRSTPER/v4/i1/e010101/e010101_vid1b.mpg}{\includegraphics{vid_1b}}
+ \setfloatlink{http://link.aps.org/multimedia/PRSTPER/v4/i1/e010101}%
+ \caption{\label{vid:PRSTPER.4.010101}%
+  Students explain their initial idea about Newton's third law to a teaching assistant. 
+  Clip (a): same force.
+  Clip (b): move backwards.
+ }%
+\end{video}
+The \verb+\setfloatlink+ command causes the title of the video to be a hyperlink to the
+indicated URL; it may be used with any environment that takes the \verb+\caption+
+command.
+The \verb+\href+ command has the same significance as it does in the context of
+the \texttt{hyperref} package: the second argument is a piece of text to be 
+typeset in your document; the first is its hyperlink, a URL.
+
+\textit{Physical Review} style requires that the initial citation of
+figures or tables be in numerical order in text, so don't cite
+Fig.~\ref{fig:wide} until Fig.~\ref{fig:epsart} has been cited.
+
+\begin{acknowledgments}
+We wish to acknowledge the support of the author community in using
+REV\TeX{}, offering suggestions and encouragement, testing new versions,
+\dots.
+\end{acknowledgments}
+
+\appendix
+
+\section{Appendixes}
+
+To start the appendixes, use the \verb+\appendix+ command.
+This signals that all following section commands refer to appendixes
+instead of regular sections. Therefore, the \verb+\appendix+ command
+should be used only once---to setup the section commands to act as
+appendixes. Thereafter normal section commands are used. The heading
+for a section can be left empty. For example,
+\begin{verbatim}
+\appendix
+\section{}
+\end{verbatim}
+will produce an appendix heading that says ``APPENDIX A'' and
+\begin{verbatim}
+\appendix
+\section{Background}
+\end{verbatim}
+will produce an appendix heading that says ``APPENDIX A: BACKGROUND''
+(note that the colon is set automatically).
+
+If there is only one appendix, then the letter ``A'' should not
+appear. This is suppressed by using the star version of the appendix
+command (\verb+\appendix*+ in the place of \verb+\appendix+).
+
+\section{A little more on appendixes}
+
+Observe that this appendix was started by using
+\begin{verbatim}
+\section{A little more on appendixes}
+\end{verbatim}
+
+Note the equation number in an appendix:
+\begin{equation}
+E=mc^2.
+\end{equation}
+
+\subsection{\label{app:subsec}A subsection in an appendix}
+
+You can use a subsection or subsubsection in an appendix. Note the
+numbering: we are now in Appendix~\ref{app:subsec}.
+
+Note the equation numbers in this appendix, produced with the
+subequations environment:
+\begin{subequations}
+\begin{eqnarray}
+E&=&mc, \label{appa}
+\\
+E&=&mc^2, \label{appb}
+\\
+E&\agt& mc^3. \label{appc}
+\end{eqnarray}
+\end{subequations}
+They turn out to be Eqs.~(\ref{appa}), (\ref{appb}), and (\ref{appc}).
+
+% The \nocite command causes all entries in a bibliography to be printed out
+% whether or not they are actually referenced in the text. This is appropriate
+% for the sample file to show the different styles of references, but authors
+% most likely will not want to use it.
+\nocite{*}
+
+\bibliography{apssamp}% Produces the bibliography via BibTeX.
+
+\end{document}
+%
+% ****** End of file apssamp.tex ******
-- 
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