Formatting a line between a Figure and a caption
How to add coloured line before caption?
How to Flatten a Multidimensional Array? Say I have a code to draw a flow chart, I want now a arrow from node 3 to node 1, how can I do that?  1&lt;--| |   | 2   | |   | 3----   MWE  \documentclass[class=article,border=0pt]{standalone}  \usepackage{tikz} \usetikzlibrary{shapes,arrows}  % Define block styles \tikzset{     block/.style={rectangle, draw, line width=0.5mm, black, text width=5em, text centered,                   rounded corners, minimum height=2em},     line/.style={draw, -latex} }% &lt;- if you insist in using this in the document add this % here. \begin{document} \begin{tikzpicture}[node distance = 1cm, auto]     % Place nodes     \node [block] (BLOCK1) {a};     \node [block, below of=BLOCK1] (BLOCK2) {b};     \node [block, below of=BLOCK2, node distance=1cm] (BLOCK3) {c};     % Draw edges     \path [line] (BLOCK1) -- (BLOCK2);     \path [line] (BLOCK2) -- (BLOCK3); \end{tikzpicture} \end{document} Deriving the Lagrangian for a free particle I'm a newbie in physics. Sorry, if the following questions are dumb. I began reading &quot;Mechanics&quot; by Landau and Lifshitz recently and hit a few roadblocks right away.  Proving that a free particle moves with a constant velocity in an inertial frame of reference ($\S$3. Galileo's relativity principle). The proof begins with explaining that the Lagrangian must only depend on the speed of the particle ($v^2={\bf v}^2$): $$L=L(v^2).$$ Hence the Lagrance's equations will be $$\frac{d}{dt}\left(\frac{\partial L}{\partial {\bf v}}\right)=0,$$ so $$\frac{\partial L}{\partial {\bf v}}=\text{constant}.$$ And this is where the authors say   Since $\partial L/\partial \bf v$ is a function of the velocity only, it follows that $${\bf v}=\text{constant}.$$  Why so? I can put $L=\|{\bf v}\|=\sqrt{v^2_x+v^2_y+v^2_z}$. Then $$\frac{\partial L}{\partial {\bf v}}=\frac{2}{\sqrt{v^2_x+v^2_y+v^2_z}}\begin{pmatrix} v_x \\ v_y \\ v_z \end{pmatrix},$$ which will remain a constant vector $\begin{pmatrix} 2 \\ 0 \\ 0 \end{pmatrix}$ as the particle moves with an arbitrary non-constant positive $v_x$ and $v_y=v_z=0$. Where am I wrong here? If I am, how does one prove the quoted statement?  Proving that $L=\frac{m v^2}2$ ($\S$4. The Lagrangian for a free particle). The authors consider an inertial frame of reference $K$ moving with a velocity ${\bf\epsilon}$ relative to another frame of reference $K'$, so ${\bf v'=v+\epsilon}$. Here is what troubles me:   Since the equations of motion must have same form in every frame, the Lagrangian $L(v^2)$ must be converted by this transformation into a function $L'$ which differs from $L(v^2)$, if at all, only by the total time derivative of a function of coordinates and time (see the end of $\S$2).  First of all, what does same form mean? I think the equations should be the same, but if I'm right, why wouldn't the authors write so? Second, it was shown in $\S$2 that adding a total derivative will not change the equations. There was nothing about total derivatives of time and coordinates being the only functions, adding which does not change the equations (or their form, whatever it means). Where am I wrong now? If I'm not, how does one prove the quoted statement and why haven't the authors done it? Where did the pardon come from? In the  episode  (S04E08), Barristan Selmy is presented with a Royal Pardon supposedly signed by the late Robert Baratheon for Ser Jorah Morment by a lowly boy of Meereen.  However, it is a bit confusing to me as where this actually came from.  Is this the same pardon that Jorah had towards the beginning of the series while Robert was actually alive, or is this pardon one that Tywin actually forged and wrote in a previous episode (remember he asks Mace Tyrell for a quill after learning about Dany's recent actions and allies).  It being from Tywin makes sense but this point is brought up by Jorah and then defeated a sentence later as he himself states it is not a forged Pardon.    So which is it and why would Jorah say it is not a forged copy if it indeed is? Should my first trip be to the country which issued my Schengen Visa? In case, if I get a multiple-entry Schengen visa in one of the embassies in Ukraine, Kyiv - should my first trip be to the country which issued the visa?  Any there any requirements of this sort? Does this condition vary depending on embassy which issued the visa?  What are the possible consequences on not visiting that country first? Does it somehow depend on country where the embassy is (i.e. non-Schengen and not EU members)? How do I drop root privileges in shell scripts? The "--up" option in OpenVPN is normally used for routing etc. And so it is processed before OpenVPN drops root privileges to run as nobody. However, I am invoking shell scripts that need to run as an unprivileged user.  How do I do that? I have studied , especially polynomial's and tylerl's answers, but I do not understand how to implement. I am working in Centos 6.5, and suid is blocked, both as "chmod u+s" and as "setuid()".  There is an OpenVPN plugin ("openvpn-down-root.so") which enables scripts invoked by the "--down" option to run as root. There could be an equivalent, such as "openvpn-up-user.so", but I have not found it.  Edit0  Per Nikola Kotur's answer, I've installed . Although the chpst command works in terminal, in the up script it fails with "command not found". What works is "sudo chpst" plus setting the proper display and language. Please see  Given that, the up script needs these four lines:  LANG="en_US.UTF-8"; export LANG GDM_LANG="en_US.UTF-8"; export GDM_LANG DISPLAY=:0; export DISPLAY sudo chpst -u user -U user /home/user/unprivileged.sh &amp;   Edit1  Per 0xC0000022L's comment, I find that "sudo -u user" works as well as "sudo chpst -u user -U user":  LANG="en_US.UTF-8"; export LANG GDM_LANG="en_US.UTF-8"; export GDM_LANG DISPLAY=:0; export DISPLAY sudo -u user /home/user/unprivileged.sh &amp;   I'll study man sudoers and update if/when I get sudo alone to work. Correct formula for LED current-limiting resistor? "grey" vs "gray" are both common equally in use? Yesterday I wrote "gray" in the meaning of the color, but my friend corrected me and told me to write "grey". Today I checked in the  and I found that they are both correct for the same meaning. So, now I just have doubt which one of them is more common in use. Can a character in the middle of a move action alter his movement based on a change in his surroundings? For example:      A player (speed 6) moves two squares towards a human bandit (pg. 162 MM) becoming adjacent to him, then proceeds to move around him to the right, provoking an opportunity attack. The bandit hits with his basic melee attack (+4 vs. AC; 1d8+1 damage, and the human bandit shifts 1 square), shifting one square to the left immediately.    This free shift makes it so that the PC would no longer flank the bandit at the END of his move. Can the player adjust his remaining three squares of movement so that he can once again flank the now-shifted bandit, or does he have to stick with his earlier movement designation?  This question boils down to: Is movement counted as you go, or do you say, "I am moving to here, it is within my range, and on the way to my destination 'blah' happens?" Photoelectric Effect - Dependence of current on frequency We all know that the amount of current flowing b/w the plates is independent of the frequency. If I were to ask why doesn't it depend then you'd probably say that it depends on the number of electrons rather than the frequency or you might show me a current vs frequency graph.  But here is my theoretical argument. Electric current is defined as the amount of charge flowing through a point/space/wire per unit time. Let I be current due to photo electrons ejected by photons of some frequency. Now if I would increase the frequency, the kinetic energy of the ejected electron would increases, therefore it will move faster and therefore contribute more current (charge will through the same point many times per unit time) . Thereby, giving a net current greater than I.  What is wrong with my argument?  After thinking a lot, I came up with a possible reason. However fast the electrons may move, but when they hit the metal plate, they would lose their velocity and start moving in drift velocity. Now there is a problem with this argument. If this were to be true then I should expect to see a big chunk of extra electrons getting stuck at the anode.  If my reasoning was correct, then why can't I see a big charge buildup at the anode. I am trying to recall the name of a story I read when I was fairly young (maybe 20 years ago, but not sure how old the story is).    What I remember: A man acquires a set of creatures that he keeps in his house, I think in an aquarium.  They evolve over time, quickly, and think of him as their benevolent god. They build statues in his likeness.   Then, I believe some sort of accident happens, and the statues they build become a little less benevolent, which bothers him.  This pattern continues on with his cruelty increasing and their depiction of him becoming more cruel. Show that if $f: \mathbb{R} \to \mathbb{R}$ is a continuous injective map, then it is strictly monotonic.    Could someone give me a proof for this? I have the intuition for why it's true - I'm just having trouble expressing that intuition in a rigorous manner. Basically consider two points $x_1, x_2 \in \mathbb{R}$. By the problem statement, $f$ is continuous on $[x_1, \, x_2]$. WLOG, assume that $f$ is strictly increasing. It there exists a point where it is not increasing, then $f$ hits a value twice, and it's not injective. Two question on harmonic function Can the graph of a bounded function ever have an unbounded derivative? How can I block all traffic *except* Tor? Why and how is the  of a matrix in $M_3(\mathbb C)$ fully determined by its characteristic and minimal polynomials? And why does it fail for $n &gt;3$?   Thanks. Vectorization operator extract fields from bib bibliographic file I want to extract specific fields from a natbib/bibtex bibliographic file to construct a table similar to:  title ------------------------------------------------- authors ------------------------------------------------- journal, year, volume ------------------------------------------------- abstract -------------------------------------------------   is there a way to do this in latex?  Thanks Jorge I am wondering what sudo apt-get update does?  What does it update? How to change Function (Fn) Key behavior on wireless Logitech keyboard I do have a wireless Logitech K750 keyboard (silver Mac version) connected to a Lenovo ThinkPad (via the unifying USB receiver, together with a wireless Logitech mouse M705) and currently running Ubuntu 12.04.  By default the F-keys are mapped as multimedia/function keys, e.g. Play  /Pause. As I don't use them very often, I want the F-keys to behave like the "real" F-keys (F1-F12). How can I do that?  I know there is an option in the BIOS settings, but this only toggles the built-in keyboard of the notebook, not on my wireless keyboard.  I know there is a way to change this for the Apple wireless keyboard (), but there is no "parameters" directory in /sys/module/hid_logitech_dj/.  Any ideas? Or is there maybe a way to do this in a later Ubuntu version (13.04)?  UPDATE:  lsusb -d 046d: shows Bus 002 Device 005: ID 046d:c52b Logitech, Inc. Unifying Receiver  UPDATE 2: Thanks a lot for your help Lekensteyn. Finally  works just fine. In the "Known Issues" of Solaar it says that it does not work with the Nano Receiver. But I have one and it works just fine. Just don't forget to read the installation instructions and run the rules.d/install.sh script. It also recognized my M705 Mouse.