%
%  This is an example LaTeX file. The percent sign is used to mark the
% start of a comment.
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%  - Michael Weeks, January, 2003
%
\documentclass{article}
\usepackage[dvips]{graphics}
\begin{document}
  \title{My Example LaTeX Paper}
  \author{Michael Weeks}
  \maketitle

\textheight 7.62in
% The above command controls the height of the text

\begin{abstract}
This is the abstract. You can use this file to start your own LaTeX file,
and just delete the stuff you do not need. \LaTeX  is a lot like working
with HTML: you can specify where text effects begin, and where they end.
\end{abstract}

\section{Introduction}\label{sec:intro}
Here is the introduction.
Since there is no blank line between these first 3 sentences, they are 
treated as one paragraph. 
Here is a vertical space (of 0.3 inches):
\vspace{.3in}

And here is a \hspace{.3in}horizontal space (of 0.3 inches).

A blank line means that the last paragraph is over, and it is time to start
a new one.

You can have text in {\it italics} font, or in {\bf bold} font,
\underline{underlined}, and even $\overline{overlined}$.


Citing a reference: This is a book about VLSI \cite{Weste93}.
Also, the references contain a good conference paper \cite{LiY88},
and a good journal article \cite{BiS92}.

What if you want to include a figure? 
Here is an example, figure~\ref{fig:phasor1}, that is saved in 
encapsulated postscript format.

\begin{figure}[!htb]
  \centering
    \scalebox{.4}{\includegraphics{phasor1.eps}}
  \caption{A complex number can be shown as a point or a vector}
  \label{fig:phasor1}
\end{figure}


Skip a lot of space  \bigskip  vertically.

\section{Here is some Math}\label{sec:math}
This is different from the previous section, section~\ref{sec:intro}.
This section gives some examples of Math.

Using superscript:  2$^{n}$

Using subscript: x$_{0}$

If you use a character, but LaTeX complains about it, try putting a 
back-slash before it. For example, 
f = x\^{}y  uses the carat character. 
If you want to end a line, use 2 back-slashes.
If you want the backslash character $\backslash$ in your document,
this can be done, too.

Here's an equation:

\[ M^\bot = \{ f \in V' : f(m) = 0 \mbox{ for all } m \in M \}.\]

Here's d2u/dx2 : (use the dollar sign before and after math stuff)

$ \frac{d^2 u}{dx^2} $

Here's another equation:

\[ \lim_{x \to 0} \frac{3x^2 +7x^3}{x^2 +5x^4} = 3.\]

Here's a summation:
\[ \sum_{k=1}^n k^2 = \frac{1}{2} n (n+1).\] 

and an integral:
\[ \int_a^b f(x)\,dx.\]

Here are some Greek letters:
$ \Delta \Psi \Phi $
and some lower case ones:
$ \delta \psi \phi \omega \pi \sigma \mu $.

For more info, see


http://www.maths.tcd.ie/\~{}dwilkins/LaTeXPrimer/


% Now here is the reference section.

\begin{thebibliography}{99}

  % Book
  \bibitem{Weste93} Neil H. E. Weste and Kamran Eshraghian, {\it Principles
  of CMOS VLSI Design}, 2nd ed. Reading, MA: Addison-Wesley, 1993.

  %Example of a Conference Paper
  \bibitem{LiY88} R. A. Lincoln and K. Yao, ``Efficient Systolic Kalman
  Filtering Design by Dependence Graph Mapping,'' in {\it VLSI Signal
  Processing, III}, IEEE Press, R. W. Brodersen and H. S. Moscovitz Eds.,
  1988, pp.~396--410.

  % Example of a Journal Paper
  \bibitem{BiS92} C. H. Bischof and G. M. Shroff, ``On Updating Signal
  Subspaces,'' {\it IEEE Trans. on Signal Processing}, vol.~40, no.~1,
  pp.~96--105, Jan. 1992.

\end{thebibliography}
\end{document}
