- The expressions are from the 1994 and the 1999 (i.e.,
current) test files [15, 16]
\documentclass{amsart}
\newcommand{\per}{\operatorname{per}}
\newcommand{\wh}{\widehat}
\DeclareMathOperator{\esssup}{ess\,sup}
\newcommand{\enVert}[1]{\left\lVert#1\right\rVert}
\let\norm=\enVert
\newcommand{\envert}[1]{\left\lvert#1\right\rvert}
\let\abs=\envert
\begin{document}
%%%%%%%%%%%%%%%%%%
\section{AMS 94}
%%%%%%%%%%%%%%%%%%
\begin{equation}\label{delta-l}
D_{l}=\sum_{I_{l}\subseteq \mathbf{n}}
D(t_1,\dots,t_n)\Bigr}
_{t_i=\left\{\begin{smallmatrix}
0,& \text{if }i\in I_{l}\quad\\% \quad added for centering
1,& \text{otherwise}\end{smallmatrix}\right.\;,\;\; i=1,\dots,n}.
\end{equation}
%%%%%%%%%%%%%%%%%%
\section{AMS 94}
%%%%%%%%%%%%%%%%%%
\begin{equation}\label{A-l-lambda}
A^{(\lambda)}_l =\sum_{I_l \subseteq\mathbf{n}}\per \mathbf{A}
^{(\lambda)}(I_l }I_l )\det\mathbf{A}^{((\lambda)}
(\overline I_{l}}\overline I_l ),}I_{l}}=l .
\end{equation}
%%%%%%%%%%%%%%%%%%
\section{AMS 94}
%%%%%%%%%%%%%%%%%%
\[\}f\}_\infty=\operatorname⋆{ess\,sup}_{x\in R^n}}f(x)}\]
%%%%%%%%%%%%%%%%%%
\section{AMS 99}
%%%%%%%%%%%%%%%%%%
\[\norm{f}_\infty= \esssup_{x\in R^n}\abs{f(x)}\]
%%%%%%%%%%%%%%%%%%
\section{AMS 94 and 99}
%%%%%%%%%%%%%%%%%%
\begin{equation}
\begin{split}
f_{h,\varepsilon}(x,y)
&=\varepsilon\mathbf{E}_{x,y}\int_0^{t_\varepsilon}
L_{x,y_\varepsilon(\varepsilon u)}\varphi(x)\,du\\
&= h\int L_{x,z}\varphi(x)\rho_x(dz)\\
&\quad+h\biggl[\frac{1}{t_\varepsilon}\biggl(\mathbf{E}_{y}
\int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
-t_\varepsilon\int L_{x,z}\varphi(x)\rho_x(dz)\biggr)\\
&\phantom{{=}+h\biggl[}+\frac{1}{t_\varepsilon}
\biggl(\mathbf{E}_{y}\int_0^{t_\varepsilon}L_{x,y^x(s)}
\varphi(x)\,ds -\mathbf{E}_{x,y}\int_0^{t_\varepsilon}
L_{x,y_\varepsilon(\varepsilon s)}
\varphi(x)\,ds\biggr)\biggr]\\
&=h\widehat{L}_x\varphi(x)+h\theta_\varepsilon(x,y),
\end{split}
\end{equation}
\end{document}
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