From c44f2f9d679e76e48555c52c001f657619f3805d Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Tue, 11 Jan 2022 21:59:35 +0000 Subject: asmejour (11jan22) git-svn-id: svn://tug.org/texlive/trunk@61568 c570f23f-e606-0410-a88d-b1316a301751 --- Master/texmf-dist/doc/latex/asmejour/README.md | 11 +- .../doc/latex/asmejour/asmejour-sample.bib | 12 +- .../doc/latex/asmejour/asmejour-template.pdf | Bin 670642 -> 628626 bytes .../doc/latex/asmejour/asmejour-template.tex | 6 +- .../asmejour-wide-equation-examples.pdf | Bin 0 -> 2978593 bytes .../asmejour-wide-equation-examples.tex | 355 +++++++++++++++++++++ .../latex/asmejour/asmewide_example/asmewide.sty | 128 ++++++++ .../asmewide_example/tesseral-harmonic.pdf | Bin 0 -> 1237557 bytes .../asmejour/asmewide_example/zonal-harmonic2.pdf | Bin 0 -> 1221215 bytes Master/texmf-dist/tex/latex/asmejour/asmejour.cls | 12 +- 10 files changed, 511 insertions(+), 13 deletions(-) create mode 100644 Master/texmf-dist/doc/latex/asmejour/asmewide_example/asmejour-wide-equation-examples.pdf create mode 100644 Master/texmf-dist/doc/latex/asmejour/asmewide_example/asmejour-wide-equation-examples.tex create mode 100644 Master/texmf-dist/doc/latex/asmejour/asmewide_example/asmewide.sty create mode 100644 Master/texmf-dist/doc/latex/asmejour/asmewide_example/tesseral-harmonic.pdf create mode 100644 Master/texmf-dist/doc/latex/asmejour/asmewide_example/zonal-harmonic2.pdf (limited to 'Master') diff --git a/Master/texmf-dist/doc/latex/asmejour/README.md b/Master/texmf-dist/doc/latex/asmejour/README.md index 32376dd7cf9..54c16035c77 100644 --- a/Master/texmf-dist/doc/latex/asmejour/README.md +++ b/Master/texmf-dist/doc/latex/asmejour/README.md @@ -1,7 +1,7 @@ #asmejour: A template for ASME journal papers# - Version 1.17 dated 2021/12/26. + Version 1.18 dated 2022/01/10. ####Overview#### This class provides a template to format preprints in the style of journal papers published by the American Society of Mechanical Engineers. @@ -9,7 +9,7 @@ This work is not a publication of ASME. - Files in this distribution are: + Files in this distribution are: ``` README.md -- this file asmejour.cls -- the class file @@ -20,7 +20,9 @@ * sample-figure-1.pdf, sample-figure-2a.pdf, - sample-figure-2b.pdf -- figures for the example``` + sample-figure-2b.pdf -- figures for the example template + /asmewide_example -- directory includes asmewide.sty and examples of wide equations``` + The .tex and .cls files are commented and should be self-explanatory. @@ -64,6 +66,9 @@ --- ####Change log#### +v1.18 (2022/01/10) + - Introduce asmewide.sty, an experimental package for setting page-width equations in a two column format. A document with examples of use is included. + v1.17 (2021/12/26): - Add code to warn about obsolete LaTeX installations. TeX Live 2020 or later is recommended for the asmejour package. diff --git a/Master/texmf-dist/doc/latex/asmejour/asmejour-sample.bib b/Master/texmf-dist/doc/latex/asmejour/asmejour-sample.bib index 7f6e8d353d7..e51503369bd 100644 --- a/Master/texmf-dist/doc/latex/asmejour/asmejour-sample.bib +++ b/Master/texmf-dist/doc/latex/asmejour/asmejour-sample.bib @@ -1,6 +1,6 @@ %% Sample bibliography file for asmejour.bst and asmejour.cls %% -%% Revised: 22 December 2022 +%% Revised: 10 January 2022 %% Copyright John H. Lienhard, MIT %% Offered under the MIT license: https://ctan.org/license/mit @@ -276,6 +276,16 @@ urldate = {July 5, 2019}, } +@online{lienhard2022, + author = {Lienhard, V, John H.}, + title = {Wide Equations in {\texttt{asmejour.cls}}}, + version = {1.0}, + organization = {Comprehensive \TeX\ Archive Network}, + year = {2022}, + url = {https://www.ctan.org/pkg/asmejour}, + urldate = {January 10, 2022}, +} + @article{Lienhard2019c, author = {Lienhard, V, John H.}, year = {2019}, diff --git a/Master/texmf-dist/doc/latex/asmejour/asmejour-template.pdf b/Master/texmf-dist/doc/latex/asmejour/asmejour-template.pdf index fe57fe02e02..5c79214158f 100644 Binary files a/Master/texmf-dist/doc/latex/asmejour/asmejour-template.pdf and b/Master/texmf-dist/doc/latex/asmejour/asmejour-template.pdf differ diff --git a/Master/texmf-dist/doc/latex/asmejour/asmejour-template.tex b/Master/texmf-dist/doc/latex/asmejour/asmejour-template.tex index f1109b714b7..28cebec8e20 100644 --- a/Master/texmf-dist/doc/latex/asmejour/asmejour-template.tex +++ b/Master/texmf-dist/doc/latex/asmejour/asmejour-template.tex @@ -3,7 +3,7 @@ %% %% This file is asmejour-template.tex, a template to format papers in the style of ASME journal papers. %% -%% This file is version 1.17 dated 2021/12/26 +%% This file is version 1.18 dated 2022/01/10 %% %% Author: John H. Lienhard V %% Department of Mechanical Engineering @@ -73,7 +73,7 @@ %% %% LICENSE: %% -%% Copyright (c) 2021 John H. Lienhard +%% Copyright (c) 2022 John H. Lienhard %% %% Offered under the MIT license: https://ctan.org/license/mit %% @@ -344,7 +344,7 @@ such as \texttt{align}, \texttt{split}, or \texttt{multline}~\cite{amsmath}. The \end{multline} An example using \texttt{align} appears in Appendix~\ref{app:zetafunction}. -An alternative solution may be to set large equations into two-column-wide tables or figures. While a package exists for setting equations that span two columns (\texttt{widetext.sty}), that code is erratic in relation to floats and page breaks. +An alternative solution may be to set large equations into two-column-wide tables or figures. An experimental package for setting equations that span two columns, \texttt{asmewide.sty}, can be loaded as well, but that code may require hand-fitting around floats and page breaks. See the examples in~\cite{lienhard2022}. Math italics are used for Roman and lower-case Greek letters by default. If you want an upright letter in math, you can use the relevant math alphabet, e.g., \verb|\mathrm, \mathbf, \mathsf|: \begin{equation}\label{eqn:newton2} diff --git a/Master/texmf-dist/doc/latex/asmejour/asmewide_example/asmejour-wide-equation-examples.pdf b/Master/texmf-dist/doc/latex/asmejour/asmewide_example/asmejour-wide-equation-examples.pdf new file mode 100644 index 00000000000..5cd8ea6a865 Binary files /dev/null and b/Master/texmf-dist/doc/latex/asmejour/asmewide_example/asmejour-wide-equation-examples.pdf differ diff --git a/Master/texmf-dist/doc/latex/asmejour/asmewide_example/asmejour-wide-equation-examples.tex b/Master/texmf-dist/doc/latex/asmejour/asmewide_example/asmejour-wide-equation-examples.tex new file mode 100644 index 00000000000..1efd910acce --- /dev/null +++ b/Master/texmf-dist/doc/latex/asmejour/asmewide_example/asmejour-wide-equation-examples.tex @@ -0,0 +1,355 @@ +%% Examples of a widetext macro for setting wide equations in the asmejour class. +%% +%% Copyright (c) 2022 John H. Lienhard. Use under the MIT license: https://ctan.org/license/mit +%% +%% +%% USAGE: * \begin{widetext} ...wide material here... \end{widetext} +%% OPTIONAL ARGUMENTS: +%% * \begin{widetext[N] .. changes upper/lower separation of wide material from default 10pt to Npt +%% * \begin{widetext}[][tbn]: t = top line only; b = bottom line only; n = no lines. BOTH arguments are REQUIRED, even if first is left empty. +%% +%% The widetext environment can only appear once per page. It clashes with floats and footnotes, as discussed herein. +%% +%% NB: the strip environment from cuted is incompatible with the [lineno] option to asmejour! +%% +\documentclass[nocopyright,nolists,balance,pdf-a]{asmejour} + +%% This file's version and date are: + \def\AJwidetextversion{1.0} + \def\AJverdate{January 10, 2022} +% +\usepackage{asmewide} +\usepackage{lipsum}% Latin filler text +% +%%%% asmejour template inputs %%%% +\JourName{Applied Mechanics} +\date{Version~\AJwidetextversion. Revised \AJverdate} +% +\makeatletter + \definecolor{JAMBlue}{rgb}{0.090, 0.574, 0.637} % 23, 147, 163 - similar to JAM masthead color + \renewcommand\@ColorName{JAMBlue!80!white} +\makeatother +% +%%%% +% +\begin{filecontents}{asme-wide-equations.bib} +@online{lienhard2021, + author = {Lienhard, John H., V}, + title = {Preprint Template for {ASME} Journal Papers: \texttt{asmejour.cls}}, + organization = {Comprehensive \TeX\ Archive Network}, + version = {{\versionno}}, + year = {2021}, + url = {https://ctan.org/pkg/asmejour}, + urldate = {{\today}}, +} +@online{tolucsis1, + author = {Sigitas Tolu\v{s}is}, + year = {2021}, + title = {The \texttt{cuted} package}, + version = {2.0}, + organization = {Comprehensive \TeX\ Archive Network}, + url = {https://ctan.org/pkg/cuted}, + urldate = {Dec. 30, 2021}, +} +@online{tolucsis2, + author = {Sigitas Tolu\v{s}is}, + year = {2021}, + title = {The \texttt{sttools} collection}, + version = {3.0}, + organization = {Comprehensive \TeX\ Archive Network}, + url = {https://ctan.org/pkg/sttools}, + urldate = {Dec. 30, 2021}, +} +@book{stakgold, +author = {Ivar Stakgold}, +title = {Boundary Value Problems of Mathematical Physics}, +year = {1967}, +publisher = {Macmillan}, +address = {New York}, +} +\end{filecontents} +% +\hypersetup{% + pdfauthor={John H. Lienhard}, + pdftitle={Wide Equations in asmejour.cls}, + pdfkeywords={ASME journal paper, LaTeX template, wide equations, widetext}, + pdfsubject = {Examples of setting wide equations in the asmejour LaTeX template}, + pdfurl={https://ctan.org/pkg/asmejour}, + pdflicenseurl={https://ctan.org/pkg/asmejour}, +} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{document} + +\SetAuthorBlock{John H.\ Lienhard V}{% +Fellow of ASME \\ +Rohsenow Kendall Heat Transfer Laboratory, \\ +Department of Mechanical Engineering,\\ +Massachusetts Institute of Technology, \\ +Cambridge, MA 02139 USA \\ +email: lienhard@mit.edu +} + +\title{Wide Equations in asmejour.cls} +\keywords{ASME journal, paper, {\upshape\LaTeX} template, wide equations, asmejour} + +\begin{abstract} +This paper gives several examples of typesetting very wide equations with {\upshape\LaTeX} in the {\upshape\texttt{asmejour}} class~{\upshape\cite{lienhard2021}} using +{\upshape\texttt{asmewide.sty}}. The style defines is a version of the {\upshape\texttt{widetext}} enviroment built on the 2021 release of +{\upshape\texttt{cuted.sty}}~{\upshape\cite{tolucsis1}} from the +{\upshape\texttt{sttools}} bundle~{\upshape\cite{tolucsis2}}, which is available from CTAN, \href{http://ctan.org}{ctan.org}. +Significant hand-fitting around page breaks, floats, and footnotes is required to obtain good results. \textcolor{red}{Only the text +in \textbf{red} in this document meant to be read---the rest is simply filler to aid in layout.} +\end{abstract} + +\maketitle + +\section{Introduction} +\lipsum[1-3] +\section{Section} +\lipsum[4] + +%%%%%%%%%%%%%%%%% begin two column figure %%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{figure*}[t] +\begin{subfigure}[c]{0.495\textwidth} +\centering{\includegraphics{zonal-harmonic2.pdf}}% +\subcaption{\label{fig:zonal}} +\end{subfigure} +%%%%%%%% don't leave a break here +\begin{subfigure}[c]{0.495\textwidth} +\centering{\includegraphics{tesseral-harmonic.pdf}}% +\subcaption{\label{fig:tesseral}}% +\end{subfigure}% +\caption{A figure with two subfigures: (a) Zonal harmonic $n=1, m=0$, (b) Tesseral harmonic $n=2, m=3$. See Appendix~\ref{sec:sph-har}.\label{fig:1}} +\end{figure*} +%%%%%%%%%%%%%%%%%%% end two column figure %%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\lipsum[5-8] +\section{Section} +\lipsum[9-12] + +%%%%%%%%%%%%%%%%%%%% Example WT1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Single Wide Equation on the Page} + +\textcolor{red}{Equation~\eqref{eqn:WT1} is an equation with a matrix that is too large to fit into one column. A multiline math environment will not help because the equation cannot be broken into parts that each fit into a column.} + +\textcolor{red}{A two-column wide figure, Fig.~\ref{fig:1}, has floated from a previous page to the top of this page, but this figure does not interfere with the \texttt{widetext} environment (a single column figure would cause problems).} + +\begin{widetext} +\begin{equation}\label{eqn:WT1} +\mathbf{WT1:}\quad +\mathfrak{W}(\bm{\Phi})= \begin{Vmatrix} +\dfrac\varphi{(\varphi_1,\varepsilon_1)} & 0 & \hdotsfor{4} & 0 & \\[\jot] +\dfrac{\varphi k_{21}}{(\varphi_2,\varepsilon_1)} & \dfrac\varphi{(\varphi_2,\varepsilon_2)} & 0 & \hdotsfor{3} & 0 \\[\jot] +\dfrac{\varphi k_{31}}{(\varphi_3,\varepsilon_1)} &\dfrac{\varphi k_{32}}{(\varphi_3,\varepsilon_2)} & \dfrac\varphi{(\varphi_3,\varepsilon_3)}& 0 & \hdotsfor{2} & 0 \\[\jot] +\vdots & & & \smash{\rotatebox{15}{$\ddots$}} & & & \vdots \\[\jot] +\dfrac{\varphi k_{n-2\, 1}}{(\varphi_{n-2},\varepsilon_1)} & +\dfrac{\varphi k_{n-2\, 2}}{(\varphi_{n-2},\varepsilon_2)} &\hdotsfor{1} & \dfrac{\varphi k_{n-2\,n-3}}{(\varphi_{n-2},\varepsilon_{n-3})} & \dfrac\varphi{(\varphi_{n-2},\varepsilon_{n-2})}& 0& 0 \\[\jot] +\dfrac{\varphi k_{n-1\, 1}}{(\varphi_{n-1},\varepsilon_1)} & \dfrac{\varphi k_{n-1\, 2}}{(\varphi_{n-1},\varepsilon_2)} &\hdotsfor{2} & +\dfrac{\varphi k_{n-1\,n-2}}{(\varphi_{n-1},\varepsilon_{n-2})}& \dfrac{\varphi}{(\varphi_{n-1},\varepsilon_{n-1})} & 0 \\[\jot] +\dfrac{\varphi k_{n1}}{(\varphi_n,\varepsilon_1)} & \dfrac{\varphi k_{n2}}{(\varphi_n,\varepsilon_2)} & \hdotsfor{3} & +\dfrac{\varphi k_{n\,n-1}}{(\varphi_n,\varepsilon_{n-1})} & \dfrac{\varphi}{(\varphi_n,\varepsilon_n)} +\end{Vmatrix} +\end{equation} +\end{widetext} + +\lipsum[12-13] + +%%%%%%%%%%%%%%%%%%%% Examples WT2 & WT3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Two Wide Equations on the Page} + +\lipsum[14-16] + +\begin{widetext}% +\begin{equation}\mathbf{WT2:} +\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2] + -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy + \ne \frac{1}{\sqrt{\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2 + \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy}} +\end{equation} + +\textcolor{red}{In this case, we have a pair of wide equations on the same page. The \texttt{widetext} environment cannot be used twice on the same page! To resolve the conflict, we remain in single column mode between the two equations.} + +\textcolor{red}{This page also includes a single column float, Table~\ref{tab:2}. This float must come after the \texttt{widetext} environment. We use the \texttt{\textbackslash begin\{table\}[b]} option to force the table to the bottom of the column. The two column table, Table~\ref{tab:4}, floats to the top of the next page and creates no problems.} + +\begin{equation}\mathbf{WT3:} +\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2] + -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy + \ne \frac{1}{\sqrt{\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2 + \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy}} +\end{equation} +\end{widetext} +\lipsum[17] + +%%%%%%%%%%%%%%% begin single column table %%%%%%%%%%%%%%%%%%%%%% +\begin{table}[b] +\caption{Table with more complicated columns}\label{tab:2}% +\centering{% +\begin{tabular}{!{\hspace*{0.5cm}} >{\raggedright\hangindent=1em} p{3cm} d{3} @{\hspace*{1cm}} d{3} !{\hspace*{0.5cm}}} +\hline\hline +\rule{0pt}{10pt} Experiment & \multicolumn{1}{c@{\hspace*{1cm}}}{$u$ [m/s]} & \multicolumn{1}{c!{\hspace*{0.5cm}}}{$T$ [\textdegree C]} \\[1pt] +\hline +The first experiment we ran this morning & 124.3 & 68.3 \rule{0pt}{10pt} \\ +The second experiment we ran this morning & 82.50 & 103.46 \\ +Our competitor's data & 72.321 & 141.384 \\[1pt] +\hline\hline +\end{tabular} +} +\end{table} +%%%%%%%%%%%%%%%% end table %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%% begin two column table %%%%%%%%%%%%%%%%%%%%%%%%% +\begin{table*}[t] +\caption{A table spanning two columns}\label{tab:4}% +\centering{% +\begin{tabular*}{0.8\textwidth}{@{\hspace*{1.5em}}@{\extracolsep{\fill}}ccc!{\hspace*{3.em}}ccc@{\hspace*{1.5em}}} +\hline\hline +\multicolumn{1}{@{\hspace*{1.5em}}c}{$x$\rule{0pt}{11pt}} & +\multicolumn{1}{c}{$\textrm{erf}(x)$} & +\multicolumn{1}{c!{\hspace*{3.em}}}{$\textrm{erfc}(x)$} & +\multicolumn{1}{c}{$x$} & +\multicolumn{1}{c}{$\textrm{erf}(x)$} & +\multicolumn{1}{c@{\hspace*{1.5em}}}{$\textrm{erfc}(x)$} \\ \hline +0.00 & 0.00000 & 1.00000 & 1.10 & 0.88021 & 0.11980\rule{0pt}{11pt} \\ +0.05 & 0.05637 & 0.94363 & 1.20 & 0.91031 & 0.08969 \\ +0.10 & 0.11246 & 0.88754 & 1.30 & 0.93401 & 0.06599 \\ +0.15 & 0.16800 & 0.83200 & 1.40 & 0.95229 & 0.04771 \\ +0.20 & 0.22270 & 0.77730 & 1.50 & 0.96611 & 0.03389 \\ +0.30 & 0.32863 & 0.67137 & 1.60 & 0.97635 & 0.02365 \\ +0.40 & 0.42839 & 0.57161 & 1.70 & 0.98379 & 0.01621 \\ +0.50 & 0.52050 & 0.47950 & 1.80 & 0.98909 & 0.01091 \\ +0.60 & 0.60386 & 0.39614 & 1.82\makebox[0pt][l]{14} & 0.99000 & 0.01000 \\ +0.70 & 0.67780 & 0.32220 & 1.90 & 0.99279 & 0.00721 \\ +0.80 & 0.74210 & 0.25790 & 2.00 & 0.99532 & 0.00468 \\ +0.90 & 0.79691 & 0.20309 & 2.50 & 0.99959 & 0.00041 \\ +1.00 & 0.84270 & 0.15730 & 3.00 & 0.99998 & 0.00002 \\[2pt] +\hline\hline +\end{tabular*} +} +\end{table*} +%%%%%%%%%%%%%%%% end table %%%%%%%%%%%%%%%%%%% + +\lipsum[18-25] +\lipsum[27] + +%%%%%%%%%%%%%%%%%%%% Examples WT4 & WT5 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Wide Equation Pair Split Across Page Break and Followed by Wide Equation} + +\textcolor{red}{Note that the upper rule is cleared after the first use in a \texttt{widetext} environment. This means that it will not show up at the top of the next page.} + +\textcolor{red}{The \texttt{\textbackslash newpage} command may be used between the equations to force the second one onto the next page, e.g., try removing the source code line \texttt{\textbackslash lipsum[27]} with and without \texttt{\textbackslash newpage}.} + +\lipsum[26-28] + +\begin{widetext}[5]% reducing \stripsep from the default 10pt to 5pt with the option [5], to make more room below the equation number +\begin{equation}\mathbf{WT4:} +\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2] -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy + \ne \frac{1}{\sqrt{\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2 \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy}} +\end{equation} +%\newpage +\begin{equation}\mathbf{WT5:} +\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2] + -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy + \ne \frac{1}{\sqrt{\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2 + \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy}} +\end{equation} +\vskip 3pt % some extra space for cramped equation number + +\textcolor{red}{In this case, we again have a pair of wide equations on the same page, so we stay in single column mode +until both are done\footnotemark. The single column table, Table~\ref{tab:3}, is forced to the bottom of the page with the \texttt{[b]} option.} + +\lipsum[32-33] + +\begin{equation}\mathbf{WT6:} +\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2] + -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy + \ne \frac{1}{\sqrt{\int_a^b\biggl\{g^2\int_a^bf^2+f^2 + \int_a^b g^2-2fg\int_a^b fg\biggr\}\,dy}} +\end{equation} +\end{widetext} +\footnotetext{\textcolor{red}{The code from \texttt{cuted.sty} doesn't play well with footnotes, so we put a \texttt{\textbackslash footnotemark} command inside the wide environment and place a separate \texttt{\textbackslash footnotetext\{..\}} command outside the wide environment.}}% + +\lipsum[34-37] + +%%%%%%%%%%%%%%%%%%% begin linewidth table %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{table}[b] +\newcolumntype{C}{>{$}c<{$}} % math-mode version of "c" column type, from array package +\caption{\label{tab:3}Table at full column width with columns in math mode} +\centering{% +\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}CCCC@{\extracolsep{\fill}}} +\hline\hline +X_{z} & X_{c} & X_{c,m} & X_{c,2}\rule{0pt}{11pt}\\ + 3.92069 & 5.70943 & 6.32429 & 7.08757\\[2pt] +\varepsilon (T_1) & \varepsilon^i (T_1) & \varepsilon^i (T_m) & \alpha (T_1, T_2)\\ +0.7258 & 0.6237 & 0.6807 & 0.7964 \\[2pt] +q_\textrm{gray} & q_\textrm{int, $T_1$} & q_\textrm{int, $T_m$} & q_\textrm{exact}\\ +400.2 & 462.1 & 371.0 & 371.8 \\[1pt] +\hline\hline +\end{tabular*} +} +\end{table} +%%%%%%%%%%%%%%%%%%%% end linewidth table %%%%%%%%%%%%%%%%%%%%%%% + +\lipsum[40-54] + +\textcolor{red}{For eqn.~\eqref{eqn:WT7}, we drop the bottom line, keeping the top line and reducing the vertical space a bit: \texttt{\textbackslash begin\{widetext\}[8][t]}.} +\begin{widetext}[8][t] +\begin{equation}\label{eqn:WT7} +\mathbf{WT7:}\quad +\cfrac{1}{1+ \cfrac{1}{abcxyz+(ax^2-by^3+cz^4)(\alpha\chi^2-\beta\upsilon^3+\kappa\zeta^4)(ax^4-by^3+cz^2)(a^2x^2-by^3+c^2z^2)}} +\end{equation} +\end{widetext} + +\lipsum[50-63] + +\textcolor{red}{In this case, we drop the top line: \texttt{\textbackslash begin\{widetext\}[][b]}.} + +\vskip 80pt% <== an extra skip to push this widetext over the edge + +\begin{widetext}[][b] +\begin{equation}\label{eqn:WT8} +\mathbf{WT8:}\quad +\mathfrak{W}(\bm{\Phi})= \begin{Vmatrix} +\dfrac\varphi{(\varphi_1,\varepsilon_1)} & 0 & \hdotsfor{4} & 0 & \\[\jot] +\dfrac{\varphi k_{21}}{(\varphi_2,\varepsilon_1)} & \dfrac\varphi{(\varphi_2,\varepsilon_2)} & 0 & \hdotsfor{3} & 0 \\[\jot] +\dfrac{\varphi k_{31}}{(\varphi_3,\varepsilon_1)} &\dfrac{\varphi k_{32}}{(\varphi_3,\varepsilon_2)} & \dfrac\varphi{(\varphi_3,\varepsilon_3)}& 0 & \hdotsfor{2} & 0 \\[\jot] +\vdots & & & \smash{\rotatebox{15}{$\ddots$}} & & & \vdots \\[\jot] +\dfrac{\varphi k_{n-2\, 1}}{(\varphi_{n-2},\varepsilon_1)} & +\dfrac{\varphi k_{n-2\, 2}}{(\varphi_{n-2},\varepsilon_2)} &\hdotsfor{1} & \dfrac{\varphi k_{n-2\,n-3}}{(\varphi_{n-2},\varepsilon_{n-3})} & \dfrac\varphi{(\varphi_{n-2},\varepsilon_{n-2})}& 0& 0 \\[\jot] +\dfrac{\varphi k_{n-1\, 1}}{(\varphi_{n-1},\varepsilon_1)} & \dfrac{\varphi k_{n-1\, 2}}{(\varphi_{n-1},\varepsilon_2)} &\hdotsfor{2} & +\dfrac{\varphi k_{n-1\,n-2}}{(\varphi_{n-1},\varepsilon_{n-2})}& \dfrac{\varphi}{(\varphi_{n-1},\varepsilon_{n-1})} & 0 \\[\jot] +\dfrac{\varphi k_{n1}}{(\varphi_n,\varepsilon_1)} & \dfrac{\varphi k_{n2}}{(\varphi_n,\varepsilon_2)} & \hdotsfor{3} & +\dfrac{\varphi k_{n\,n-1}}{(\varphi_n,\varepsilon_{n-1})} & \dfrac{\varphi}{(\varphi_n,\varepsilon_n)} +\end{Vmatrix} +\end{equation} +\end{widetext} + +\lipsum[55-56] + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\appendix +\section{Spherical harmonics\label{sec:sph-har}} + +Without getting into the details, a regular function $f(\theta,\phi)$ on the surface of the unit sphere may be written +\begin{equation} +f(\theta,\phi) = \sum_{n=0}^\infty \sum_{m=-n}^n f_{m,n} Y_n^m(\theta,\phi) +\end{equation} +for $Y_n^m(\theta,\phi) = e^{i m\phi}P^{|m|}_n(\cos\theta)$, for $|m|