Is electric potential always differentiable?  If so, why?  If it isn't always, then what properties of a charge-distribution are required to make it differentiable?
Recently when skimming through my physics-text I encountered an interesting definition of Force $$F(x) = -\frac{\mathrm dU(x)}{\mathrm dx}$$  We were taught that some functions are continuous but not differentiable. So for the force to exist $U(x)$ has to be differentiable. So how can we prove that $U(x)$ is differentiable everywhere?
Can people PLEASE spell out their slang acronyms What are tag synonyms and merged tags? How do they work? How to get from Heathrow Airport to King's Cross, London? My wife and I will be arriving in London via Heathrow Airport (LHR) and are staying at a hotel near King's Cross station. So, we were wondering what the best (which means fastest but also easiest when carrying two large pieces of luggage and two carry-ons) way to get from LHR to King's Cross?  I gather that, with only one changeover, we can take the Tube. However, in the interest of other passengers, we thought it would be best to take a taxi, or maybe a bus?  Thoughts? I want to update my sources.list file with the fastest server from the command line in a fresh Ubuntu Server install. I know this is trivially easy with the GUI, but there doesn't seem to be a simple way to do it from from the command line? How to create a squiggle arrow with some text on it in TikZ? I need to define a new command to create a squiggle arrow with some text on it. Something similar to what \xrightarrow command produces but with wiggly arrows as in \rightsquigarrow. The length of the arrow should automatically be adjusted to fit the text above it and I do not know how to handle this part in TikZ. Any ideas would be much appreciated. When compiling a tex file including references (by Texstudio editor and Miktex distribution) using biblatex with bibtex backend and ieee style, the results of the displayed references in the output pdf is messed up at the "volume" and "issue number" entries as follows:   The volume label "vol." is missing (Ref. 1 &amp; 2 in the given example below). The numeric issue number "3" is missing (Ref. 1 in the given example). The issue number label "no." is displayed although NO input entry was being given (Ref. 2 in the given example).   If it helps, this behavior was noticed after the recent update of Miktex on March 11, 2017, including  package (ver. 1.2a 2017-03-02). As before which, everything was going fine!  So is this issue noticed by someone else? Is there any idea about the reason of such strange act by biblatex?  \documentclass{article} \usepackage{filecontents} \begin{filecontents}{reference.bib}     @article{author1,         author  = "George Green",         title   = "Basic latex",         year    = "2000",         journal = "Sharelatex Journal",         volume  = "10",         number  = "3",         pages   = "100--101"     }     @article{author2,         author  = "Carol White",         title   = "Basic studio",         year    = "2010",         journal = "Club Journal",         volume  = "20",         pages   = "200--201"     } \end{filecontents} \usepackage[backend=bibtex, style=ieee]{biblatex}  \addbibresource{reference.bib} \begin{document}     Hi there! \\     Ref 1 Green \cite{author1}. \\     Ref 2 White \cite{author2}.     \printbibliography  \end{document}   The output is as follows: How do I restore /usr/bin/env after overwriting it with start-tor-browser file I was installing Tor and wanted to access it directly from the terminal, so I was trying to copy start-tor-browser to /usr/bin. But by mistake, I have replaced the /usr/bin/env file with the start-tor-browser file. What should I do now?? What determines the number of comments that are displayed? I'm curious how it is decided how many comments to display before the "Show more comments" link. Sometimes I see a dozen comments on a question and no "Show more comments" link, in other occasions no comments are visible at all, only the link. How to use notify-send to notify users as root? #!/bin/bash export DISPLAY=:0 state=$(upower -i $(upower -e | grep BAT) | grep --color=never -E "state" ) stat=${state:25:32} batperct=$(upower -i $(upower -e | grep '/battery') | grep  -E "percentage:") bat=${batperct:24:26} intbat=$(echo $bat | cut -d'%' -f1) if [ "$intbat" -lt "15" -a "$stat" == "discharging" ]; then     notify-send 'battery low..! please plugin charger..... charge is only' "$intbat"     fi     The script runs fine when run as a normal user (bash script.sh). The desktop notification is displayed.  If I run it as root with sudo bash script.sh, the desktop notification is not displayed.  How can I use notify-send to notify users as root?  I am using Arch Linux. I am not sure what caused this error, but here is what the whole error says, and also this is sitting as a notification, and preventing me from updating any software using Update Manager - Please provide some assistance or tell me how to figure out what to do to fix it.  Could not calculate the upgrade  An unresolvable problem occurred while calculating the upgrade.  Please report this bug against the 'update-manager' package and include the following error message: 'E:Error, pkgProblemResolver::Resolve generated breaks, this may be caused by held packages.' Area51 proposals are being advertised now all over the network? Can a Filipino citizen with no Korean visa with a long layover in Seoul take the airport free city tour? I am a Filipino citizen traveling from Saipan to Manila via Seoul, with 13 hours layover.  Do I need a Korean visa to take the airport free city tour? If $a$ and $b$ commute and $\text{gcd}\left(\text{ord}(a),\text{ord}(b)\right)=1$, then $\text{ord}(ab)=\text{ord}(a)\text{ord}(b)$. Prove if $\operatorname{ord}(a)=m$, $\operatorname{ord}(b)=n$, and $\operatorname{gcd}(m,n)=1$, then $\operatorname{ord}(ab)=mn$.   I was reading this and was thinking how this proof would look like. I tried to do it and am not sure if this is correct. Here is what I did:  If $a$ and $b$ commute then $(ab)^{mn} = a^{mn} * b^{mn} = (a^m)^n * (b^n)^m = 1 * 1 = 1.$ So $ord(ab) | mn$.  Now, take $k = \operatorname{ord}(ab) = m^\prime * n^\prime$ where m' is relatively prime with $n$ and $n'$ is relatively prime with $m$. By the result above $m' | m$ and $n' | n$. Now we have $((ab)^k)^{m/m'} = 1$ since $(ab)^k=1$. But on the other hand, by the commutativity:  $$((ab)^k)^(m/m') =$$  $$((ab)^(m' * n'))^(m/m') =$$  $$ a^{n'm} * b^{n'm} = $$  $$(a^m)^{n'} * b^{n'm'}=$$  $$b^{n'm'} = 1$$  This implies that $n' * m'$ is divisible by $n$. But $m'$ is relatively prime with $n$, so we must have $n' = n.$ By symmetry, $m' = m$. So $ord(ab) = mn$.  Just to say this again, I want to prove if $a$ and $b$ commute and $m$ and $n$ are relatively prime then   $$ord(ab)=mn.$$   The comments are vague. I guess this must be the answer then and there probably is not another way to do this. Indicate How Trustworthy the UpVotes Are Why doesn't my ~/.bash_profile work? I'm using Linux Mint. My login shell (cat /etc/passwd | grep myUserName) is bash.  After I start my graphical desktop environment and run a terminal emulator from it, I can see that .bash_profile is not sourced (environment vars that are exported in it are unset). But if I log in from a text console (ctrl+alt+F1) or manually run bash -l from the terminal emulator, .bash_profile works fine.  Am I wrong when I think that .bash_profile should be sourced when X starts and all export'ed vars should be available in the terminal, running from X?  P.S. Placing everything in .bashrc and sourcing it from .bash_profile is not good idea (): environment stuff should be sourced only once. How is Dru-Zod/General Zod still alive after this character died? Openshift application url: example.rhcloud.com  Custom domain: example.com  I came across this  and added the redirection rule. However, I can not access example.rhcloud.com now. My custom domain is www.example.com.  To avoid duplicate content problems, I tried this redirection.   Here is my .htaccess file:  RewriteEngine on   # Uncomment the following lines to force HTTPS #RewriteCond %{HTTP:X-Forwarded-Proto} !https  #RewriteRule .* https://%{HTTP_HOST}%{REQUEST_URI} [R,L]   # WordPress Defaults RewriteBase / RewriteRule ^index\.php$ - [L] RewriteCond %{REQUEST_FILENAME} !-f RewriteCond %{REQUEST_FILENAME} !-d RewriteRule . /index.php [L]  # Redirect Https traffic to Http RewriteEngine on  RewriteCond %{SERVER_PORT} ^443$ [OR] RewriteCond %{HTTPS} on RewriteRule  ^(.*)$ http://%{HTTP_HOST}%{REQUEST_URI} [R=301,L]   # Redirect non-www to www RewriteEngine on  RewriteCond %{HTTP_HOST} !^www\. [NC] RewriteRule ^(.*)$ http://www.%{HTTP_HOST}/$1 [R=301,L]    # Redirect openshift rhcloud domain to custom domain RewriteEngine on  RewriteCond %{HTTP_HOST} ^example.rhcloud.com$ RewriteRule (.*)$ http://www.example.com/$1 [R=301,L]   Why is example.com not redirecting to ww.example.com? How do I fix this?  Also, I see that since I have https to http redirection and non www to www redirection, my blog has been loading slow. How can I reduce it to lesser number of rules?  Edit:  In chrome:   In Firefox:     The page isn't redirecting properly, Firefox has detected that the server is redirecting the request for this address in a way that will never complete.     This problem can sometimes be caused by disabling or refusing to accept cookies. Can I use Ctrl+Shift for changing languages? I can't set this hotkey for changing keyboard languages.  At this moment Alt+Shift switch languages, but I can't see this hotkey in keyboard hotkeys list or in   gsettings list-recursively  org.gnome.desktop.wm.keybindings | sort | more   output. Tool to manage and/or make available a list of my publications on the web? A subgroup of a cyclic group is cyclic - Understanding Proof I'm having some trouble understanding the proof of the following theorem  A subgroup of a cyclic group is cyclic  I will list each step of the proof in my textbook and indicate the places that I'm confused and hopefully somewhere out there can clear some things up for me.  Proof Let  G be a cyclic group generated by &quot;$a$&quot; and let H be a subgroup of G. If $H = {\{e\}}$, then $H \text{ = &lt;e&gt;}$ is cyclic. If $H \neq \space {\{e\}}$, then $a^n \in H$ for some $n \in \mathbb{Z}^{+}$. Let $m$ be the smallest integer in $\mathbb{Z}^{+}$ such that $a^m \in H$. We claim that $c = a^m$ generates H; that is, $$H \space = \space &lt;a^m&gt; \space = \space &lt;c&gt;.$$ We must show that every $b \in H$ is a power of c. Since $b \in H$ and $H \leq G$, we have $b = a^n$ for some $n$. Find $q$ and $r$ such that $$ n = mq + r \space \space \space \space for \space \space \space 0 \leq r &lt; m,$$  Alright this is the first part in the proof where I start to get confused. Where does the division algorithm come from and why are we using it? The proof continues as follows:  $$a^n = a^{mq + r} = (a^m)^q \cdot a^r,$$ so $$ a^r = (a^m)^{-q} \cdot a^n.$$ Now since $a^n \in H$, $a^m \in H$, and $H$ is a group, both $(a^m)^{-q}$ and $a^n$ are in $H$. Thus $$(a^m)^{-q} \cdot a^n \in H; \space \space \space \text{that is,} \space \space a^r \in H.$$  This is another point at which I’m a little confused. What exactly about $a^n$ and $a^m$ being elements of $H$ allows us to accept that $(a^m)^{-q}$ and $a^{n}$ are in $H$? The proof continues:  Since $m$ was the smallest positive integer such that $a^m \in H$ and $0$ $\leq r$ $&lt; m$, we must have $r = 0$. Thus $n = qm$ and $$b \space = \space a^n \space = \space (a^m)^q \space = \space c^q,$$ so b is a power of c.  This final step is confusing as well, but I think its just because of the previous parts I was confused about. Any help in understanding this proof would be greatly appreciated