% Version: 10.10.2013
% sample file for an ZAA article
\documentclass[finalsize,finaltitle,draft]{zaa}

% If we include pictures, we need
\usepackage{graphicx}

\begin{document}

% add linebreaks in the title with \\
\title{ZAA Journal Sample Title which is\\ Quite Long}

% running title
\runtitle{ZAA Journal Sample}

\author{Author One and Author Two}
\runauthor{A. One et al.}

\address{A. One: Department of Mathematics, University of XX, ZZ Kingdom 
\email{one.address@gmx.net}}
\address{A. Two: Department of Physics, ZZ University, Republic of X
\email{address2@zz-uni.rx}}

\dedication{Dedicated Author Three to her 100th birthday}

\abstract{%
We discuss how to use \LaTeX\ for publications in mathematics. Citations inside the abstract should be expanded as the result of Richter [SIAM J.~Appl.~Math. 41 (1981), 210--221].
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}

\keywords{\LaTeX, mathematics, science}

% there are two possibilities for Mathematics Subject classification: 
%\classification{00D00,11A11}
%or 

\primclass{00D00}
\secclasses{11D11, 22D22}

% these four lines will be added by the editor
\received{April 1, 2012}
\revised{January 31, 2013}
\logo{32}{2013}{3}{301}
%%\logox{32}{2013}{3}{301}{303}
\doi{3445}

\maketitle


% let's define a new macro
\newcommand{\abs}[1]{\lvert#1\rvert}


\section{Introduction}


\subsection{How to use \LaTeX}

Here, the use of some environments is demonstrated.
The following environments
are supplied: \texttt{
theorem, lemma, proposition, corollary,
definition, conjecture, example, remark, note,  \!case} and \texttt{proof}.

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bla bla blafasel bla bla blafasel bla bla
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\begin{lemma}\label{lem}
Let $f, g\in  A(X)$ and let $E$, $F$ be cozero
sets in $X$.
\begin{itemize}
\item[\rm 1.] If $f$ is $E$-regular and $F\subseteq E$, then $f$ is $F$-regular.
\item[\rm 2.] If $f$ is $E$-regular and $F$-regular, then $f$ is $E\cup
F$-regular.
\item[\rm 3.] If $f(x)\geq c>0$ for all $x\in E$, then $f$ is $E$-regular.
\end{itemize}
\end{lemma}

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blafasel bla bla blafasel bla bla blafasel bla bla blafasel bla bla blafasel

The following is an example \cite{sv,c1,m1,l1} of a proof.

\begin{proof}[Proof of Lemma~{\rm \ref{lem}}] Set $j(\nu)=\max(I\backslash a(\nu))-1$. Then we have
\[
\sum_{i\notin a(\nu)}t_i\sim t_{j(\nu)+1}
  =\prod^{j(\nu)}_{j=0}\,\frac{t_{j+1}}{t_j}\,.
\]
Hence we have
\begin{align}
\begin{split}
\prod_\nu\Biggl(\sum_{i\notin
  a(\nu)}t_i\Biggr)^{\!\abs{a(\nu-1)}-\abs{a(\nu)}}
&\sim\prod_\nu\prod^{j(\nu)}_{j=0}
  \left(\frac{t_{j+1}}{t_j}\right)^{\abs{a(\nu-1)}-\abs{a(\nu)}}\\
&=\prod_{j\geq 0}\left(\frac{t_{j+1}}{t_j}\right)^{
  \sum_{j(\nu)\geq j}(\abs{a(\nu-1)}-\abs{a(\nu)})}. \qed
\end{split}
\end{align}
\end{proof}

\begin{note}
This is an example of a `note'. The magnetization $M_0$ of the Ising
model is related to the local state probability $P(a):M_0=P(1)-P(-1)$. 
For fractions, the representation $\frac{a}{b}$ is preferred instead of $a/b$. 
\end{note}


\begin{definition}
This is an example of a `definition' environment.
For $f\in A(X)$, we define
\begin{equation}\label{eq1}
\mathcal{Z} (f)=\{E\in Z[X]: \text{$f$ is $E^c$-regular}\}.
\end{equation}
\end{definition}

\begin{remark}
This is an example of a `remark' environment.
For $f\in A(X)$, we define
\begin{equation}
\mathcal{Z} (f)=\{E\in Z[X]: \text{$f$ is $E^c$-regular}\}. \tag*{($\star$)}
\end{equation}
\end{remark}

\begin{example}
This is an example of an `example' environment.
For $f\in A(X)$, we define
\begin{equation}
\mathcal{Z} (f)=\{E\in Z[X]: \text{$f$ is $E^c$-regular}\}.
\end{equation}
\end{example}


\begin{theorem} \label{thm}
This is an example of a theorem with  long labels in a list of assertions:
\begin{litemize}{SPA3}
\item[{\rm (SPA1)}]
%%\beg{enumerate} \item[{\bf (A1)}]   
There exists a constant $k\in [0,1)$ such that
   $$
|G(\xi)-G(\eta)|\le k|\xi-\eta\|_\infty ,\quad \xi,\eta\in \mathbb{C}.
$$
\item[{\rm (SPA2)}] There exist constants $ l_1\in \mathbb{R}$ and $ l_2\ge 0$ such that
\begin{equation*}
\left.
\begin{aligned}
 2\big\langle G(\xi)-G(\eta),
b(\xi)-b(\eta)\big \rangle &\\
%%\quad& \\
+\|\sin(\xi)-\sin(\eta)\|_{HS}^2 
 &\le l_1\|\xi-\eta\|^2_\infty \\
\|\sin(\xi)-\sin(\eta)\|_{HS}^2
&\le l_2\|\xi-\eta\|_\infty^2,
\end{aligned}\right\}
\quad\xi,\eta\in \mathbb{C}.
%\end{split}
\end{equation*}
\item[{\rm (SPA3)}] There exists a constant  $l_3> 0$ such that $\|\sin(\xi)\|\le l_3$ for all $\xi\in \mathbb{C}.$
\end{litemize}
\end{theorem}

\begin{proof} bla bla blafasel bla bla blafasel bla bla.
\qed
\end{proof}


\begin{theorem}[Meik's Theorem]
This is an example of Theorem~{\rm \ref{thm}} with a parenthetical note in the
heading.
\end{theorem}

\begin{proposition}[{\cite[Proposition~1.3]{v1}}]
This is an example of referring to an equation \eqref{eq1} within an environment.
\end{proposition}

\subsection*{Acknowledgement}
We thank all our friends for not interfering.
 

\begin{thebibliography}{99}

% alphabetically sorted by author,
% chronologically for same authors

\bibitem{c1} Chicone,~C.~and Gerlach,~J.,
Identifiability of distributed parameters.
In: {\it Inverse and Ill-Posed Problems} (eds.: H.~W.~Engl et al.).
%%and W.~Groetsch).
Boston: Academic Press 1987, pp.~513 -- 521.

\bibitem{l1} Lecumberry,~M. and Rivi\`ere,~T., 
The rectifiability of shock waves for the solutions of genuinely non-linear scalar conservation laws in 1+1 D. 
Preprint 2002.

\bibitem{m1} Metivier,~G. and Zumbrun,~K., 
{\it Large Viscous Boundary Layers for Noncharacteristic Nonlinear Hyperbolic Problems}. 
Mem.~Amer.~Math.~Soc.  175  (2005),  No. 826. 

\bibitem{r1} Richter,~G.~R.,
An inverse problem for the steady state diffusion equation.
{\it SIAM J.~Appl.~Math.} 41 (1981), 210 -- 221.

\bibitem{sv}
Servadei,~R. and Valdinoci,~E., 
The Brezis-Nirenberg result for the fractional Laplacian 
(submitted to {\it Trans.~Amer.~Math.~Soc.}).


\bibitem{s1} 
Silvestre,~L., 
{\em Regularity of the obstacle problem for a fractional power of the Laplace operator}.
PhD Thesis, Univ. of Texas at Austin (2005)
(available at http://math.uchicago.edu/$\sim$luis/preprints/luisdissreadable.pdf).

\bibitem{v1} Va\u\i nikko,~G.,
Identification of filtration coefficient.
In: {\it Ill-posed Problems in Natural Sciences} (to appear).

\bibitem{v2} Va\u\i nikko,~G.~M. and Veretennikov,~A.~Yu.,
{\it Iteration Procedures in Ill-Posed Problems} (in Russian).
Moscow: Nauka 1986.

\bibitem{w1} 
Willem,~M., 
{\em Minimax Theorems.} 
Progr. Nonlinear Diff.~Equ.~Appl. 24. Boston: Birkh\"{a}user 1996.

\bibitem{y1} Yeh,~W.~W.-G., 
Review of parameter identification procedures in groundwater hydrology: the inverse problem.
{\it Water Resources Res.} 22 (1986)(2), 95 -- 108.

\end{thebibliography}


\end{document}

