PDF here: http://to.ly/5tVs

 \documentclass[twocolumn]{article}


  \title{Hello World!}
  \author{phoeagon}
  \date{\today}

\usepackage[version=3]{mhchem}
%chemistry environment
\usepackage{amsmath}
\usepackage{amssymb}
% math symbols & environments
\usepackage{footnpag} %re-count the footnotes per page
\usepackage{abstract}
%one-col abstract for 2-columned
\usepackage{fix2col} 
%fix the title on the top of the page when 2-columned
\usepackage{vector}


\begin{document}

\newcommand{\lgvec}[1]{\stackrel\longrightarrow{\smash{#1}\vphantom{i}\,}}
\newcommand{\bfvec}[1]{\mbox{\boldmath$#1$}}


\maketitle

%\tableofcontents
\begin{abstract}
%\twocolumn[\begin{onecolabstract}
\textit {this is a test.}
%\end{onecolabstract}]
\end{abstract}

\section{Hp6}
``Dumbledore says people finds it far easier to forgive others
 for being wrong than being right,''said Hermione.\cite{hp6}\\

\section{Pascal's Triangle}
\begin{center}
1\\
1 1\\
1 2 1\\
1 3 3 1\\
1 4 6 4 1\\
1 5 10 10 5 1\\
\end{center}

\section{What a shame!}
I can't see what's wrong on here! the only chance I have is to save it and see if a PDF is generated.\\
{\textit{//oh, I see the log up there!}}\\
Turns out Chinese is not supported at all! {Quite normal, no fonts?}

\section{the sorting of [adj]}
This is a nice long new black British plastic pen.

\section{Neil Armstrong}
This is one step for man{\footnote {Later researches found that there ought 
to be an `a'.}}, one giant leap for mankind.

\section{Newton}
It's said that Issac Newton was born on Christmas Day, Dec 25. It was a time when calendars were changing.\\
Newton founded the famous {\emph{Newton's laws for motions}}\cite{newph}.

\section{C++}
\begin{verbatim}
int getfather(int nd){
   return pa[nd]==nd?nd:pa[nd]=father(pa[nd]);
}
\end{verbatim}

\section {Formulas}
Calculating the root of $ax^2+bx+c=0$ : \\
$x=\frac{-b\pm{}\sqrt{b^2-4ac}}{2\cdot{}a}$\\
$x_1+x_2=-\frac{b}{a}$\\
$x_1x_2=\frac{c}{a}$\\
$E=mc^2$\\
\begin{displaymath}
Q_T=W=\frac{m}{M}RT\int_{V_1}^{V_2}\frac{1}{V}\mathrm{d}V=\frac{m}{M}RT\ln{}\frac{V_2}{V_1}
\end{displaymath}
\begin{displaymath}
\Delta{}S=S_2-S_1=k\ln{}\frac{\Omega_2}{\Omega_1}=k\ln{}n^N=k\ln{}\left(\frac{V_2}{V_1}\right)^n
\end{displaymath}
\begin{displaymath}
F=ma=\frac{mv^2}{R}=m\omega^2R=m\frac{4\pi{}^2R}{T^2}
\end{displaymath}
\begin{displaymath}
F=\frac{\Delta\phi}{\Delta{}t}=\frac{B\Delta{}S}{\Delta{}t}=\frac{Bl\Delta{}s}{\Delta{}t}=Blv
\end{displaymath}
\\
\ce{HCl + NaOH -> NaCl + H2O }\\
\ce{ CuO + CO ->[\text{$\Delta$}] Cu + CO2}\\
\ce{OH- + H+ -> H2O }\\
\ce{CH2=CH2 ->[\text{[H$^+$][MnO$_4^-$]}] CO2}
\\

$\vec a\cdot\vec b=|\vec a||\vec b|\cos\theta $\\
$\overrightarrow{AB}$\\
$|\vec a\times \vec b|=|\vec a||\vec b|\sin\theta$\\
$\lgvec{AB}$\\
$\bfvec{a}$\\
%$\textbf{fds}$
\begin{displaymath}
\cos\theta=\frac{\vec{a}\cdot\vec{b}}{|\vec{a}|\cdot|\vec{b}|}
\end{displaymath}
\\
$\vec{\alpha}=(a,b,c)$, $\vec{\beta}=(x,y,z)$,\\
$\vec{\alpha}\cdot\vec{\beta}=ax+by+cz$
\\
\begin{displaymath}
\begin{aligned}
\vec{\alpha}\times\vec{\beta}&=
\left|
\begin{matrix}
\vec{i}&\vec{j}&\vec{k}\\
a&b&c\\
x&y&z\\
\end{matrix}
\right| = \left|
\begin{matrix}
b & c\\
y & z
\end{matrix}\right|
\vec{i}-\left|
\begin{matrix}
a & c\\
x & z
\end{matrix}\right|\vec{j}+\left|
\begin{matrix}
a&b\\
x&y
\end{matrix}\right|\vec{k}\\
&=(bz-cy,cx-az,ay-bx)
\end{aligned}
\end{displaymath}
\\
$
\left\{
\begin{aligned}
a_1x+b_1y+c_1z=&d_1\\
a_2x+b_2y+c_2z=&d_2\\
a_3x+b_3y+c_3z=&d_3
\end{aligned}
\right.\Rightarrow$\\
let $D=
\left|
\begin{matrix}
a_1&b_1&c_1\\
a_2&b_2&c_2\\
a_3&b_3&c_3
\end{matrix}
\right|
$,
$D_1=
\left|
\begin{matrix}
d_1&b_1&c_1\\
d_2&b_2&c_2\\
d_3&b_3&c_3
\end{matrix}
\right|
$,
$D_2=
\left|
\begin{matrix}
a_1&d_1&c_1\\
a_2&d_2&c_2\\
a_3&d_3&c_3
\end{matrix}
\right|
$,
$D_3=
\left|
\begin{matrix}
a_1&b_1&d_1\\
a_2&b_2&d_2\\
a_3&b_3&d_3
\end{matrix}
\right|
$,\\
then \begin{displaymath}
x=\frac{D_1}{D},\quad y=\frac{D_2}{D},\quad z=\frac{D_3}{D}.
\end{displaymath}\footnote{Cramer's Rule}\\
$\therefore$ $\because$\\



\begin{thebibliography}{99}
\bibitem{hp6}
J.K.Rowling, {\em Harry Potter and the Half Blood Prince}, Chapter Five, {\textit{the Excess of Phlegm}}.

\bibitem{newph}
Issac Newton, {\textit{the Mathematical Principle of Natural Philosophy}}.
\end{thebibliography}

\end{document}