How to locally decrease the distance between an equation and its numerical label

Question

I've faced with a situation like below in IEEEconf 2-column template:

\documentclass[letterpaper, 10pt, conference]{IEEEconf}

\usepackage{graphicx}
\usepackage{mathptmx}
\usepackage{amsmath}
\usepackage{amssymb}

\title{My Title*}

\author{Guy$^{1}$
\thanks{*This work was not supported by any organization}% <-this % stops a space
\thanks{$^{1}$Guy is with Hell, {\tt\small guy@hell.edu}}%
}

\begin{document}

\maketitle
\thispagestyle{empty}
\pagestyle{empty}

\begin{abstract}

ABSTRACT

\end{abstract}

\section{INTRODUCTION}

\noindent\begin{minipage}{.5\linewidth}
\begin{equation}
  \begin{cases}
    \theta_{i}^{h^{-}} = \frac{\displaystyle 2(i-1)\pi}{\displaystyle m_{c}^{\hat{x}}}\\
    \theta_{i}^{h^{+}} = \frac{\displaystyle 2i\pi}{\displaystyle m_{c}^{\hat{x}}}\\
\end{cases}
\end{equation}
\end{minipage}%
\begin{minipage}{.5\linewidth}
\begin{equation}
    \begin{cases}
    \theta_{j}^{v^{-}} = \frac{\displaystyle 2(j-1)\pi}{\displaystyle m_{c}^{\hat{v}}}\\
    \theta_{j}^{v^{+}} = \frac{\displaystyle 2j\pi}{\displaystyle m_{c}^{\hat{v}}}\\
\end{cases}
\end{equation}
\end{minipage}

\end{document}

I'm gonna decrease the distance between right equation with its label (i.e. (3)), such that everything will be placed in a straight line.

What is the best approach to do that?

Update 1: result of @Zarko's code:

Answer 1

The equation number has a minimum distance from the equation, but there's a slick trick in exercise 19.8 of the TeXbook.

\documentclass[letterpaper, 10pt, conference]{IEEEconf}  % Comment this line out if you need a4paper

\usepackage{graphicx} % for pdf, bitmapped graphics files
\usepackage{mathptmx} % assumes new font selection scheme installed
\usepackage{amsmath} % assumes amsmath package installed
\usepackage{amssymb}  % assumes amsmath package installed
\usepackage{amsthm}
\usepackage{lipsum}

\renewcommand{\qedsymbol}{$\blacksquare$}

\newtheorem{thm}{Theorem}[section]
\newtheorem{lem}[thm]{Lemma}
\newtheorem{prop}[thm]{Proposition}
\newtheorem{cor}{Corollary}
\newtheorem{conj}{Conjecture}[section]
\theoremstyle{definition}
\newtheorem{defn}{Definition}[section]
\newtheorem{exmp}{Example}[section]
\newtheorem{rem}{Remark}

\title{My Title*}

\author{Guy$^{1}$
\thanks{*This work was not supported by any organization}% <-this % stops a space
\thanks{$^{1}$Guy is with Hell, {\tt\small guy@hell.edu}}%
}

\begin{document}

\maketitle

\lipsum[2]\nopagebreak
\noindent
\begin{minipage}{.45\linewidth}
\begin{equation}
  \begin{cases}
    \theta_{i}^{h^{-}} = \dfrac{ 2(i-1)\pi}{ m_{c}^{\hat{x}}}\\
    \theta_{i}^{h^{+}} = \dfrac{ 2i\pi}{ m_{c}^{\hat{x}}}\\
\end{cases}
\hspace{10000pt minus 1fil}
\end{equation}
\end{minipage}\hspace{.1\linewidth plus 4pt}%
\begin{minipage}{.45\linewidth}
\begin{equation}
    \begin{cases}
    \theta_{j}^{v^{-}} = \dfrac{ 2(j-1)\pi}{ m_{c}^{\hat{v}}}\\
    \theta_{j}^{v^{+}} = \dfrac{ 2j\pi}{ m_{c}^{\hat{v}}}\\
\end{cases}
\hspace{10000pt minus 1fil}
\end{equation}
\end{minipage}\nopagebreak\vspace{\belowdisplayskip}%
\lipsum[3]

\end{document}

I have used lipsum to emulate some text before and after the equations. Note how to get the same spacing as for a normal equation environment, with no breaks before and after.

The trick is inserting a large glob of horizontal glue, which can be shrinked as much as possible:

\hspace{10000pt minus 1fil}

I have also reduced the width of the minipages, to avoid the left equation number to be too near to the part on the right.

Note also \dfrac, rather than all those \displaystyle tokens.

Answer 2

Edit: Since the question was misleading, the first answer version was accommodate to one column document. Of course meanwhile, after editing of question, appears other answers ...

Reduce width of minipages and push them apart with \hfill and reduce space between equation and equation number by \hspace{-1em}:

\documentclass{article}
\usepackage{mathtools}

\begin{document}

  \noindent$|$\hrulefill\ column width\ \hrulefill$|$

\noindent\begin{minipage}{.48\linewidth} % <-- reduced minipage width
\begin{equation}
  \begin{cases}
\theta_{i}^{h^{-}} = \frac{\displaystyle 2(i-1)\pi}{\displaystyle m_{c}^{\hat{x}}}\\
\theta_{i}^{h^{+}} = \frac{\displaystyle 2i\pi}{\displaystyle m_{c}^{\hat{x}}}
    \end{cases}\hspace{-1em}% <-- added to reduce distance to eq. numbering apart
\end{equation}
\end{minipage}\hfill % <-- added to push minipages appart
\begin{minipage}{.48\linewidth} % <-- reduced minipage width
\begin{equation}
    \begin{cases}
\theta_{j}^{v^{-}} = \frac{\displaystyle 2(j-1)\pi}{\displaystyle m_{c}^{\hat{v}}}\\
\theta_{j}^{v^{+}} = \frac{\displaystyle 2j\pi}{\displaystyle m_{c}^{\hat{v}}}
\end{cases}\hspace{-1em}% <-- added to reduce distance to eq. numbering
\end{equation}
\end{minipage}
\end{document}

Answer 3

Add some negative space

\begin{equation}
  \hspace{-2em}
  \begin{cases}
    ...
  \end{cases}
  \hspace{-2em}
\end{equation}

\documentclass[letterpaper, 10pt, conference]{IEEEconf}

\usepackage{graphicx}
\usepackage{mathptmx}
\usepackage{amsmath}
\usepackage{amssymb}

\title{My Title*}

\author{Guy$^{1}$
\thanks{*This work was not supported by any organization}% <-this % stops a space
\thanks{$^{1}$Guy is with Hell, {\tt\small guy@hell.edu}}%
}

\begin{document}

\maketitle
\thispagestyle{empty}
\pagestyle{empty}

\begin{abstract}

ABSTRACT

\end{abstract}

\section{INTRODUCTION}

\noindent\begin{minipage}{.5\linewidth}
\begin{equation}
  \hspace{-2em}
  \begin{cases}
    \theta_{i}^{h^{-}} = \frac{\displaystyle 2(i-1)\pi}{\displaystyle m_{c}^{\hat{x}}}\\
    \theta_{i}^{h^{+}} = \frac{\displaystyle 2i\pi}{\displaystyle m_{c}^{\hat{x}}}
  \end{cases}
  \hspace{-2em}
\end{equation}
\end{minipage}%
\begin{minipage}{.5\linewidth}
\begin{equation}
  \hspace{-2em}
  \begin{cases}
    \theta_{j}^{v^{-}} = \frac{\displaystyle 2(j-1)\pi}{\displaystyle m_{c}^{\hat{v}}}\\
    \theta_{j}^{v^{+}} = \frac{\displaystyle 2j\pi}{\displaystyle m_{c}^{\hat{v}}}
  \end{cases}
  \hspace{-2em}
\end{equation}
\end{minipage}

\end{document}

Answer 4

(Updated the answer to employ the Times Roman newtxtext and newtxmath font packages instead of the somewhat obsolescent mathptmx package.)

By using the fairly recent newtxtext and newtxmath Times Roman font package instead of mathptmx, enough space is saved to let you use significantly narrower minipage environments -- providing more separation between the minipage environments

To simplify the code in the equations, the answer sets up a custom macro, called \ddfrac, which automatically typesets the numerator and denominator material in display style.

For extra legibility, you may also want to use (a) dcases environments instead of cases environments and (b) a few \mathstrut directives to increase the space between the fraction lines and the material in the respective denominators.

\documentclass[letterpaper,conference,twocolumn]{IEEEconf}
\usepackage{newtxtext,newtxmath}% not "mathptmx"
\usepackage{mathtools,amssymb}
\newcommand\ddfrac[2]{\dfrac{\displaystyle #1}{\displaystyle #2}} % handy shortcut macro
\newcommand\Tstrut{\smash[b]{\mathstrut}} % "top strut"
\begin{document}
\hrule %  just to illustrate width of text block
\section{INTRODUCTION}

\noindent
\begin{minipage}{.45\columnwidth}
\begin{equation}
  \begin{dcases}
    \theta_{i}^{h^{-}} = \ddfrac{2(i-1)\pi}{m_{c}^{\Tstrut\hat{x}}}\\
    \theta_{i}^{h^{+}} = \ddfrac{2i\pi}{m_{c}^{\Tstrut\hat{x}}}\\
\end{dcases}
\end{equation}
\end{minipage}\hfill
\begin{minipage}{.45\columnwidth}
\begin{equation}
    \begin{dcases}
    \theta_{j}^{v^{-}} = \ddfrac{2(j-1)\pi}{m_{c}^{\Tstrut\hat{v}}}\\
    \theta_{j}^{v^{+}} = \ddfrac{2j\pi}{m_{c}^{\Tstrut\hat{v}}}\\
\end{dcases}
\end{equation}
\end{minipage}

\end{document}