摘要：
Arithmetic operations taught in elementary schools are continuous in the high level topological point of view. This signifies that there is literally no clear boundary between simple and complex, low ... 阅读全文
$$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Self-defined math definitions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Math symbol commands
\newcommand{\intd}{\,{\rm d}} % Symbol 'd' used in integration, such as 'dx'
\newcommand{\diff}{{\rm d}} % Symbol 'd' used in differentiation
\newcommand{\Diff}{{\rm D}} % Symbol 'D' used in differentiation
\newcommand{\pdiff}{\partial} % Partial derivative
\newcommand{DD}[2]{\frac{\diff}{\diff #2}\left( #1 \right)}
\newcommand{Dd}[2]{\frac{\diff #1}{\diff #2}}
\newcommand{PD}[2]{\frac{\pdiff}{\pdiff #2}\left( #1 \right)}
\newcommand{Pd}[2]{\frac{\pdiff #1}{\pdiff #2}}
\newcommand{\rme}{{\rm e}} % Exponential e
\newcommand{\rmi}{{\rm i}} % Imaginary unit i
\newcommand{\rmj}{{\rm j}} % Imaginary unit j
\newcommand{\vect}[1]{\boldsymbol{#1}} % Vector typeset in bold and italic
\newcommand{\phs}[1]{\dot{#1}} % Scalar phasor
\newcommand{\phsvect}[1]{\boldsymbol{\dot{#1}}} % Vector phasor
\newcommand{\normvect}{\vect{n}} % Normal vector: n
\newcommand{\dform}[1]{\overset{\rightharpoonup}{\boldsymbol{#1}}} % Vector for differential form
\newcommand{\cochain}[1]{\overset{\rightharpoonup}{#1}} % Vector for cochain
\newcommand{\bigabs}[1]{\bigg\lvert#1\bigg\rvert} % Absolute value (single big vertical bar)
\newcommand{\Abs}[1]{\big\lvert#1\big\rvert} % Absolute value (single big vertical bar)
\newcommand{\abs}[1]{\lvert#1\rvert} % Absolute value (single vertical bar)
\newcommand{\bignorm}[1]{\bigg\lVert#1\bigg\rVert} % Norm (double big vertical bar)
\newcommand{\Norm}[1]{\big\lVert#1\big\rVert} % Norm (double big vertical bar)
\newcommand{\norm}[1]{\lVert#1\rVert} % Norm (double vertical bar)
\newcommand{\ouset}[3]{\overset{#3}{\underset{#2}{#1}}} % over and under set
% Super/subscript for column index of a matrix, which is used in tensor analysis.
\newcommand{\cscript}[1]{\;\; #1}
% Star symbol used as prefix in front of a paragraph with no indent
\newcommand{\prefstar}{\noindent$\ast$ }
% Big vertical line restricting the function.
% Example: $u(x)\restrict_{\Omega_0}$
\newcommand{\restrict}{\big\vert}
% Math operators which are typeset in Roman font
\DeclareMathOperator{\sgn}{sgn} % Sign function
\DeclareMathOperator{\erf}{erf} % Error function
\DeclareMathOperator{\Bd}{Bd} % Boundary of a set, used in topology
\DeclareMathOperator{\Int}{Int} % Interior of a set, used in topology
\DeclareMathOperator{\rank}{rank} % Rank of a matrix
\DeclareMathOperator{\divergence}{div} % Curl
\DeclareMathOperator{\curl}{curl} % Curl
\DeclareMathOperator{\grad}{grad} % Gradient
\DeclareMathOperator{\tr}{tr} % Trace
\DeclareMathOperator{\span}{span} % Span
$$