Why aren't electrons positively charged?
Why is the charge naming convention wrong?
Restore console session after remote desktop disconnects? Why this :$\sum\limits_{n=1}^\infty\frac1{n\sin n}$ is not harmonic series and is convergent? I'm confused how this series :$$\displaystyle \sum_{n=1}^\infty\frac1{n\sin n}$$ is a convergent series as wolfram show  and it's not harmonic series in the same time .  My question here is:  Why this :$$\displaystyle \sum_{n=1}^\infty\frac1{n\sin n}$$ is not harmonic series and is convergent ? Is it possible to automatically "add" \left and \right commands in front of all brackets? The source code should be left intact, but LaTeX should interpret every pair of brackets as if they were preceded by such commands. This is because adding \left and \right commands is time consuming and makes source code longer and less readable. I considered defining new commands such as \lb and \rb for \left( and \right), but it doesn't seem very elegant to me: what if I also want to add square brackets for example?  Any ideas? Thanks. Ignore folders/files when Directory.GetFiles() is denied access How did the writers not notice that the mailbox of Leela's parents says "Turanga," and not "Leela"?  Turanga Leela is Leela's proper name, with Leela being her surname, so shouldn't it follow that her folks would be the same? Center of a free product Let $A$ and $B$ be two groups and let $G=A*B$ be their free product. Suppose both $A$ and $B$ are nontrivial. I want now to prove that $G$ is infinite and that $Z(G)$ is trivial.  I think I can prove that $G$ is infinite using this argument: two reduced words of $A*B$ are equal if and only if they have the same length and the ith letter of the first word is the same as the ith letter of the second one. Hence one can find a reduced word of $G$ of length arbitrarily big (since we are sure it won't be equal to a shorter word). Do you think it works? Has anyone another suggestion?  On the other hand, I don't really have a clue for the second part except trying to analyze a long list of cases of reduced words and prove for each one that the only element with which they commute is the identity. Does anyone have a smarter idea?  Thanks in advance! Investment options for f1 visa students in USA What is the best way to include R code in the Latex paragraph I am a newbie in Latex. I have two simple questions regarding including R code in Latex.  Q1: For a block of R code, I use 'listings' package, as follows.  \documentclass[12pt]{report} \usepackage{listings} \begin{document} \begin{lstlisting}[language=R] &gt; dpareto(4, 2, 3) [1] 0.09375 &gt; dpareto(4, -2, 3) [1] NaN &gt; dpareto(seq(-1, 4, 1), 2, 3) [1] 0.0000000 0.0000000 0.0000000 0.0000000 0.2962963 0.0937500 \end{lstlisting} \end{document}   I feel it's not professional. What is the best way to present the block of R code?  Q2: For code pieces in the paragraph, for example I wish to include a R function, or variable, or package name in my Latex context, what is the best way to do that? What is the difference of 3 object declarations of javascript I have a  for my phone, powered via a micro-usb port. The markings on it indicate that it will accept the typical 5V that nearly every USB port provides, or it will accept 9V for "fast charge".  I was under the impression that USB standards allowed for no more than 5V. My research shows that  has several profiles (up to 20V), and Revision 2.0 Version 1.2 includes a 9V profile.  Now I'm wondering: How can voltages above the usual 5V be provided without worry of damaging an expensive phone when connecting them directly (no wireless pad)? If things are running at different voltages, wouldn't that cause an issue?  In this example, 9V is used for fast charging, but could that 9V be sent to my phone? Do phones have a safeguard for this? The USB standard allows for up to 20V. That's a lot when expecting only 5V. Some "dumb" devices are powered directly off of USB, like cheap LEDs and fans that have no IC. Surely they would blow upon 20V!  I'm guessing there is data exchanged between the power source and the peripheral, ultimately telling the power source whether or not it's okay to provide more than 5V. Some USB charging cables don't have data pins though, which can allow for faster charging. In this case, it seems that not having data pins would be a restriction. Maybe the power source would have to default to 5V?. Unfortunately I cannot find an explicit protocol/explanation of how the different potentials are managed. Direct Link to a Comment The increase in the character limit of comments has led them to become as important as the questions and answers that spawn them. On several occasions (especially on meta) I've found reason to want to link to a comment directly. I'd imagine something as simple as making the date / time stamp an anchored link which mimics the behavior of the question link. How did Rita know she lost the power? Insert missing dates within table I have a table with a column for ID, Date and Frequency of occurrence for that particular date and ID.  ID    date          Frequency 1     2014-05-18      5 1     2014-05-19      4 1     2014-05-20      25 2     2014-05-20      7 3     2014-05-18      4 3     2014-05-20      1 4     2014-05-18      6   I'm looking to insert the dates for each ID that aren't currently there (assuming that the date ranges from 2014-05-18 to 2014-05-20) and add a value of 0 in Frequency for those.  For example, you can see that  ID 1 has an observation for all three dates;  ID 2 is missing 2014-05-18 and 2014-05-19;   ID 3 is missing 2014-05-19;   ID 4 is missing 2014-05-19 and 2014-05-20.  Therefore, the output should look like this  ID    date          Frequency 1     2014-05-18      5 1     2014-05-19      4 1     2014-05-20      25 2     2014-05-18      0 2     2014-05-19      0 2     2014-05-20      7 3     2014-05-18      4 3     2014-05-19      0 3     2014-05-20      1 4     2014-05-18      6 4     2014-05-19      0 4     2014-05-20      0   I've attempted the following from . However, that will only add dates with 0 Frequency that aren't present throughout the entire table instead of on an ID level.   DECLARE @s DATE = '20140518', @e DATE = '20140520';  SELECT c.date, Frequency = COALESCE(a.Frequency,0) FROM dbo.Calendar AS c LEFT OUTER JOIN dbo.table AS a ON c.date = s.[date] WHERE c.d &gt;= @s AND c.d &lt; DATEADD(DAY, 1, @e); Explode string into array with no empty elements? PHP's explode function returns an array of strings split on some provided substring. It will return empty strings when there are leading, trailing, or consecutive delimiters, like this: var_dump(explode('/', '1/2//3/')); array(5) {   [0]=&gt;   string(1) &quot;1&quot;   [1]=&gt;   string(1) &quot;2&quot;   [2]=&gt;   string(0) &quot;&quot;   [3]=&gt;   string(1) &quot;3&quot;   [4]=&gt;   string(0) &quot;&quot; }  Is there some different function or option or anything that would return everything except the empty strings? var_dump(different_explode('/', '1/2//3/')); array(3) {   [0]=&gt;   string(1) &quot;1&quot;   [1]=&gt;   string(1) &quot;2&quot;   [2]=&gt;   string(1) &quot;3&quot; } can any one tell me how to write long equation in multline i tried with coding below but some errors of \right and \left appear \begin{multline*} \displaystyle \left \| f  \right \|_{M\dot{K}^{\alpha(\cdot),q}_{p(\cdot), \lambda}(\mathbb{R}^{n})} \approx \max \left\{ \sup_{L\leqslant0,L\in  \mathbb{Z}}2^{-L\lambda}\left ( \sum_{k=-\infty}^{L}2^{k\alpha(0)q}\left \|  f\chi_{k} \right \|^{q}_{L^{p(\cdot)}} \right )^{1/q},\\\sup_{L&gt;0,L\in \mathbb{Z}}\left[ 2^{-L\lambda}\left ( \sum_{k=-\infty}^{-1}2^{k\alpha(0)q} \left \| f\chi_{k} \right \|^{q}_{L^{p(\cdot)}} \right )^{1/q}\\ +2^{-L\lambda}\left ( \sum_{k=0}^{L}2^{k\alpha(\infty)q}\left \|  f\chi_{k} \right \|^{q}_{L^{p(\cdot)}} \right )^{1/q}\right] \right\}  \end{multline*} are two consecutive numbers relatively prime? I have a question.  I have been given this proof: "For any $n$ in the integers where $n&gt;2$, show there are at least $2$ elements in $U(n)$ that satisfy $x^2=1$."  I have gone through and actually proved this, (that the numbers are $1$ and $n-1$) but i didn't' know how to prove that $n-1$ is in fact in the set $U(n)$. Is it because two consecutive numbers are always relatively prime? I run Windows XP and the wallpaper I used to have got lost. I have backups of the system itself, so if I knew where to look, I could find a copy of the old wallpaper.  I have some idea of the original filename (searching now), and I recall it saves it as a bitmap, but an exact location would be helpful.  It was a photo/JPEG that used to be on the filesystem, and I don't have backups, so the Firefox, and Internet Explorer wallpaper locations are unlikely. I checked %SYSTEMROOT%\system32 as well - so I'm assuming it's somewhere else. I really enjoying using control+r to recursively search my command history. I've found a few good options I like to use with it: # ignore duplicate commands, ignore commands starting with a space export HISTCONTROL=erasedups:ignorespace  # keep the last 5000 entries export HISTSIZE=5000  # append to the history instead of overwriting (good for multiple connections) shopt -s histappend  The only problem for me is that erasedups only erases sequential duplicates - so that with this string of commands: ls cd ~ ls  The ls command will actually be recorded twice. I've thought about periodically running w/ cron: cat .bash_history | sort | uniq &gt; temp.txt mv temp.txt .bash_history  This would achieve removing the duplicates, but unfortunately the order would not be preserved. If I don't sort the file first I don't believe uniq can work properly. How can I remove duplicates in my .bash_history, preserving order? Extra Credit: Are there any problems with overwriting the .bash_history file via a script? For example, if you remove an apache log file I think you need to send a nohup / reset signal with kill to have it flush it's connection to the file. If that is the case with the .bash_history file, perhaps I could somehow use ps to check and make sure there are no connected sessions before the filtering script is run? "No such file or directory" when trying to remove a file, but the file exists? Pandas Merging 101