Why the name of picture can not to be removed?  This is my code:  &gt;     \begin{figure} &gt;       \centering &gt;       \includegraphics[scale=0.7]{One Step Multi Step.png}\\ &gt;       \caption{hehehe} &gt;     \end{figure}   and this is the result:   What is the problem? So, I can remove the "one step multi step.png".
I want to import graphics into my main input file using the macro \includegraphics. It does not work if the filename contains spaces.   also discusses this subject, but there is no solution there.  My compilation routine is latex->dvips->ps2pdf (because of PSTricks).
Is trace of regular representation in Lie group a delta function? My major is physics. I need to use some tools in group theory, but I am really  confused by the trace in compact infinite groups. The following is my question:  In discrete group theory, the irreducible representation of identity group element $e$ is always an identity matrix. So the trace of $e$ under  regular representation is the order of the group : $\chi(e) = |G|$. I hope to get  similar result for Lie group. For example, SO(2) has infinite number of irreducible representations, $D^{(m)}$, where $m=0,\pm 1, \pm 2,\cdots $. All of them are 1-dimensional $D^{(m)} = e^{im\phi}$. Here $\phi$ is the rotation angle. For element $R(\phi)$ in SO(2), the trace in $m$th irreducible representation should be  $\chi(R(\phi))=e^{im\phi}$, if we sum all these traces up, we get the trace in regular representation. So what is the trace of $e$ in the regular representation ? It seems to be infinite. Labeling Multiple Equations Per Row of a Table I am trying to create a table with two columns of independently labelled equations (1-6). Unfortunately, everything I have found so far either has not worked or would number them as sub-equations (1a, 1b, etc).  My current attempt is:  \documentclass{article} \usepackage{graphicx, verbatim, tabularx} \usepackage{amsfonts} \usepackage{amsmath, amssymb}  \newcommand{\grad}{\vec{\nabla}}       \newcommand{\prtl}[2]{\frac{\partial #1}{\partial #2}}  \newcommand{\curl}{\grad\times} \begin{document}  \begin{tabular}{p{5cm}p{5cm}}  $\curl\vec{E} = -i\omega\mu\vec{H}$ &amp;   $\curl\vec{H} = i\omega\mu\vec{E}$ \\  \begin{equation}  \label{eq:curlHx}   \prtl{E_z}{y} +\gamma E_y= -i\omega\mu H_x  \end{equation}  &amp;  \begin{equation}  \label{eq:curlEx}    \prtl{H_z}{y} +\gamma H_y= i\omega\mu E_x  \end{equation}\\  \begin{equation}  \label{eq:curlHy}    -\prtl{E_z}{x} -\gamma E_x= -i\omega\mu H_y  \end{equation}  &amp;  \begin{equation}  \label{eq:curlEy}    -\prtl{H_z}{x} -\gamma H_x= -i\omega\mu E_y  \end{equation}  \\  \begin{equation}  \label{eq:curlHz}   \prtl{E_y}{x}-\prtl{E_x}{y} = -i\omega\mu H_z  \end{equation}  &amp;  \begin{equation}  \label{eq:curlEz}    \prtl{H_y}{x}-\prtl{H_x}{y} = -i\omega\mu E_z  \end{equation}  \end{tabular}  \end{document}   Is there an environment other than tabular that would make this work? Tabularx came close (got the numbering correct), but the formatting/spacing was horrific. I'd like to modify the names used to typeset some of my document elements. For example, the caption of figure floats should change from "Figure" to "Fig.", and my \tableofcontents sectioning heading shouldn't read "Contents", but "Table of Contents". How can I do that?  \documentclass{article} % \usepackage[english]{babel} \begin{document} \tableofcontents \section{foo} \begin{figure}[h] \centering \rule{1cm}{1cm}% placeholder for graphic \caption{A figure} \end{figure} \end{document} Can ovulation and menstruation occur simultaneously? Is that possible that ovulation happens in the time of actual menstrual haemorrhage in human females - let say in a case that woman has 21 day cycle and her menstrual period is 7 days?   If yes, does it means that in this particular case the woman has lower chances to conceive? In order to solve  $$y''-2y'+y=te^t$$ I did:  $$y = (at+b)e^t\implies\\ y' = ate^t+ae^t+be^t\implies \\y''= ate^t+2ae^t+be^t$$  but when I put these in the differential equation I'm getting zeros eveywhere. Does somebody know what I'm doing wrong? The following is an old qualifying exam that I cannot solve:  Suppose $f$ is holomorphic on the punctured unit disk and $ \frac{f '}{f} $ has a simple pole at $0$.  Show that $f$ does not have an essential singularity at $0$. How do I bind a WPF DataGrid to a variable number of columns? My WPF application generates sets of data which may have a different number of columns each time.  Included in the output is a description of each column that will be used to apply formatting.  A simplified version of the output might be something like:  class Data {     IList&lt;ColumnDescription&gt; ColumnDescriptions { get; set; }     string[][] Rows { get; set; } }   This class is set as the DataContext on a WPF DataGrid but I actually create the columns programmatically:  for (int i = 0; i &lt; data.ColumnDescriptions.Count; i++) {     dataGrid.Columns.Add(new DataGridTextColumn     {         Header = data.ColumnDescriptions[i].Name,         Binding = new Binding(string.Format("[{0}]", i))     }); }   Is there any way to replace this code with data bindings in the XAML file instead? Not able to execute a .sh file: /bin/bash^M: bad interpreter I wanted to execute a shell script:  -rwxr-x--x 1 root root   17234 Jun  6 18:31 create_mgw_3shelf_6xIPNI1P.sh   I tried to do a standard procedure, but I got this error:  ./create_mgw_3shelf_6xIPNI1P.sh  localhost 389 -l /opt/fews/sessions/AMGWM19/log/2013-06-06-143637_CLA-0  DEBUG   cd/etc/opt/ldapfiles/ldif_in ; ./create_mgw_3shelf_6xIPNI1P.sh  localhost 389 -l /opt/fews/sessions/AMGWM19/log/2013-06-06-143637_CLA-0 **ERROR  sh: ./create_mgw_3shelf_6xIPNI1P.sh: /bin/bash^M: bad interpreter: No such file or directory**   What does it mean? I was doing this as the root user under the root group.  Does it mean that the file does not have the correct permission for the root user? Why is rendered viewport faster than rendering individual frames? When I'm using rendered viewport it initially takes a while before rendering starts, but once it does, I can freely move around and rendering a new view happens almost instantaneously. When on the other hand I'm rendering a movie, for each frame Blender takes a significant amount of time before rendering even starts, usually doing the following:  Synchronizing object, Updating images, Updating meshes, Updating Scene BVH, Packing BVH,  Why does it do this? And is it possible to disable this to increase movie rendering speed? Looking for a short story about an insect-like alien captured by humans on its own planet This poor creature is taken aboard the spaceship and the humans do not know that it is intelligent.  The alien can repeat what it hears, e,g, "pass the sugar".  It is able to escape at night and it communicates messages to its fellow aliens.  It directs that they turn up the heat of the atmosphere (somehow they can do this) so as to force the humans to leave.  The alien protagonist states that it will die w/ the humans or leave with them. Can Minecraft Pocket Edition play with a desktop Minecraft? Windows Media Player 12 shows wrong cover art when playing Workaround for Android 4.4 not being able to write to SD cards? This issue came up when I got different records counts for what I thought were identical queries one using a not in where constraint and the other a left join. The table in the not in constraint had one null value (bad data) which caused that query to return a count of 0 records. I sort of understand why but I could use some help fully grasping the concept.  To state it simply, why does query A return a result but B doesn't?  A: select 'true' where 3 in (1, 2, 3, null) B: select 'true' where 3 not in (1, 2, null)   This was on SQL Server 2005. I also found that calling set ansi_nulls off causes B to return a result. Does adding two linear equations will result in a line which will pass through an intersection of the linear equations? I was wondering why it is almost impossible to find a geometrical explanation of why adding two linear equations helps us to find a solution of a system of linear equations? Am I right that adding two linear equations will result in an equation of a line which will pass through a point where two linear equations intersect?  If it is right then I completely don't understand why such a crucial point in understanding how to solve systems of equations is never properly taught even at a university level. Looking for the title of a book about alien invasion, mining asteroids and using lasers to defend earth What I remember of this novel/series is that the main character creates solar laser satellites and mines asteroids to create more satellites to defend Earth from aliens. Later on, he uses the hollowed out asteroids as a base and eventually as an armored fortress to repulse the alien fleets. I last remember the main character attempting to hollow out more asteroids to defend and attack the aliens eventually. I am wondering whether there exists a function such that:  $$\lim_{x \rightarrow a}f(x)=\infty$$  at some point $a$ on the real axis but yet,  $$\int_{-\infty}^{+\infty}\left|f(x)\right|\ dx&lt;\infty$$  Does the fact that a function is unbounded imply that it has no finite integral? Proof: $\cos^p (\theta) \le \cos(p\theta)$ I came across this problem when I was at a book store inside of a book made to prepare Berkeley graduates to pass a mandatory exam. I wanted to buy the book, but, alas, I didn't have the money (forty bucks is a lot of money when you don't have a job). So I took my phone out and started taking as many pictures as I could. Unfortunately, I didn't take any pictures of the solutions!  Enough backstory. Time for math. The problem is as follows:  Prove that $\cos^p( \theta) \le \cos(p \theta)$ if $0\le\theta\le\frac\pi2$ and $0\le p\le 1$.  I tried using the series expansion for cosine, but that seemed to be a dead end. Then I tried using Euler's theorem, but I got stuck. Then I got distracted and started to think about other cosine identities. For example, $$\cos\left(\frac\theta2\right)=\pm\sqrt{\frac{1+\cos(\theta)}{2}}.$$ Then what is $\cos(\frac\theta3)$ equal to? I tried to figure it out then I realized that I needed to find the root of a cubic polynomial. Then I realized that I'm better at staying focused than finding the roots of cubic polynomials.  Anyways, a proof would be nice here. I really appreciate any hints or answers. I apologize for my digressions! What are the differences between struct and class in C++? List of all active modules used in a site