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I would like to obtain a better expression of this

$$
Au(\cdot)=\nabla_{(\cdot)}\left{\frac{\cdot}{|\cdot|^{3}}\,1_{B(0,r)}(\cdot)\right}.
$$

where $\cdot$ refer to a variable $x$. More precisely, I want to place the $\cdot$ just in the middle in the \frac command and adjust properly the size of the parenthesis in all $(\cdot)$.

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To obtain curly braces, you need to type \{ and \} rather than { and }. The latter are "special-function" characters in TeX, as they are used to start and end "groups" (chunks of code, if you will). The characters need to be "escaped" with a backslash, ``, in order to generate curly braces. –  Mico Dec 13 '13 at 11:27
    
It is not clear what you wish. For me the expression looks nice. Do you want a smaller parenthesis.? –  Sigur Dec 13 '13 at 11:36
    
I already used ${\small (}$ and ${\small )}$. I think it is much better. –  SAKLY Dec 13 '13 at 11:43

2 Answers 2

up vote 3 down vote accepted

I usually define a \blank command for signposts in math expressions:

\newcommand{\blank}{{-}}

(the additional braces makes the symbol behave like a letter and not an operation symbol). You can adapt it to your liking:

\newcommand{\blank}{{\,\cdot\,}}

because some space should be added, in this case.

Here's the example

\documentclass{article}
\usepackage{amsmath}
\newcommand{\blank}{{\,\cdot\,}}

\begin{document}
\[
\mathit{Au}(\blank)=
  \nabla_{(\blank)}
  \left\{ \frac{\blank}{\lvert\blank\rvert^{3}}\,
  1_{B(0,r)}(\blank) \right\}.
\]
\[
\mathit{Au}(\blank)=
  \nabla_{(\blank)}
  \left\{ \frac{\blank\hphantom{^{3}}}{\lvert\blank\rvert^{3}}\,
  1_{B(0,r)}(\blank) \right\}.
\]
\end{document}

In the second version, the dot is moved left by adding a phantom; I'm not sure it's really wanted.

enter image description here

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When you write that "I want to place the \cdot just in the middle in the \frac command", I assume you're referring to the expression in the denominator. (The \cdot in the numerator is already centered.) Centering the denominator term on the \cdot part may be achieved, e.g., by creating a "phantom" superscript term to the left of the first vertical bar. In the code below, I've further replaced \left{ and \right} with \left\{ and \right\} in order to generate auto-sized curly braces.

enter image description here

\documentclass{article}
\begin{document}
\[
Au(\cdot)=\nabla_{(\cdot)} \left\{ \frac{\cdot}{\phantom{{}^{3}}|\cdot|^{3}}\,
    1_{B(0,r)}(\cdot) \right\}.
\]
\end{document}

Incidentally, use of the $$ displaymath switch is heavily deprecated in LaTeX. (See the discussion at Why is \[ \] preferable to $$ ... $$? for an in-depth examination of this issue.) In LaTeX documents, it's much better to use \[ and \] to initiate and terminate displaymath mode, as is done in the example code above.

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That's exactly what I want. Thank you. –  SAKLY Dec 13 '13 at 11:45

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