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5

The code you show produces an error message: ! Missing $ inserted. when TeX finds _, because this character is legal only in math mode. The output from then on can not be relied unto. Fix errors as soon as they are raised when processing the file. Your input should be Let the training data \(X\) consist of \(x_{i\dots n}\) observations, where \(n\) is ...


4

First of all, your MWE doesn't work because you wrote \section{equation} ... \end{equation}. Latex does not recognise these tags to be paired, so change the first one to \begin{equation}. Delete the \begin{section} and \end{section} tags, they serve no purpose. If you want to start a chapter in your document (for the article class), then write ...


4

You are already using package amsmath and have therefore \tfrac, which puts the fraction in the math style \textstyle: \documentclass[10pt]{article} \usepackage{amsmath} \usepackage{amssymb} \usepackage{geometry} \geometry{a4paper, total={14.5cm, 23cm}} \newcommand*{\diff}{\mathop{}\!d} \begin{document} The amplitude $u_2 (x_2, y_2)$ at the back focal ...


3

I think a better solution would be to use the cuted package from the sttools bundle. It is dedicated to insert some material full-width in a twocolumn environment: \documentclass[journal]{IEEEtran} \usepackage{cite} \usepackage{graphicx} \usepackage{refstyle} \usepackage{amssymb} \usepackage{amsmath} \usepackage{cuted, nccmath} \usepackage{lipsum} ...


3

You can do \documentclass{article} \usepackage{bm} \showoutput \begin{document} $[ \vec{\nabla} \times \vec{v} ]$ $\bm{[} \vec{\nabla} \times \vec{v} \bm{]}$ \end{document} It does not work with \left, \right with the default cm fonts as there is no bold extension font (for large brackets) in that font set. However extended brackets are not needed ...


2

You want \intertext. \documentclass{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsthm} \usepackage{amsmath} \usepackage{manfnt} \begin{document} \noindent I want the comments to align with the main text. \begin{align*} \mathbb E X &= \int x F(dx) \\ \intertext{comments that align with the main text} &= \mu. \end{align*} ...


2

It is better to use the amsmath alignments than eqnarray but either way you get flush left equations by using \documentclass[12pt,fleqn]{article}


1

Here is a solution, patching flalign(*) from mathmath into a leftalign(*) environment, with one optional argument: the equation indent (default \parindent): \documentclass[11pt]{article} \usepackage[utf8]{inputenc} \usepackage[showframe, noheadfoot, nomarginpar]{geometry} \usepackage{mathtools} \makeatletter ...


1

You can, as documented in mathtools, thanks to a code by Sébastien Gouezel (§3.6.1 of the doc): \documentclass{article} \usepackage[utf8]{inputenc} \usepackage{mathtools} \usepackage{lmodern} \newcommand\MTkillspecial[1]{% helper macro \bgroup \catcode`\&=9 \let\\\relax% \scantokens{#1}% \egroup } \DeclarePairedDelimiter\brparen \lparen\rparen ...



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