I am trying to draw a filled triangle where one of the edges is curved.  When I do the "obvious" thing, I find that the curved edge overshoots the vertices at either end.  Here is a minimal working example.  \documentclass{article} \usepackage{tikz} \begin{document} \begin{tikzpicture}   \coordinate [label=left:{$a$}] (a) at (5, -2);   \coordinate [label=right:{$b$}] (b) at (9, -3);   \coordinate [label=right:{$c$}] (c) at (9,0);   \filldraw [line width=2pt, color=green!70!black, fill=green!15!white] (b) -- (a) to [out=20,in=250] (c) -- (b);   \foreach \point in {a,b,c}   \filldraw [color=green!70!black,fill=green!70!black] (\point) circle     (1.5pt); \end{tikzpicture} \end{document}     As you can see in the figure, the edge overshoots the vertices at (a) and (c).  Thanks in advance!
While drawing a simple 3D (fake 3D in fact) cube, I realized that the corners end up with unwanted extensions of the line. I understand this is related to the width of the lines themselves, but how can I remove them? An alternative solution of drawing the desired figure is also welcomed.  Example:  \documentclass{article} \usepackage{tikz}   \begin{document} \begin{tikzpicture}  \draw[draw=black,fill=gray!20] (0,0) --(4.8,0)-- (4.8,5)--(0, 5)--cycle; \draw[draw=black,fill=gray!20] (4.8,5) -- (4.9,4.8)--(4.9,-0.1)--(4.8,0)--cycle; \draw[draw=black,fill=gray!20] (0,0) -- (0.1,-0.1)--(4.9,-0.1)--(4.8,0)--cycle; \draw[dashed,draw=black] (4.8,5) -- (4.9,4.8)--(0.1,4.8)--(0.,5)--cycle; \draw[dashed,draw=black] (0.1,-0.1)--(0.1,4.8)--(0.,5)--(0,0)--cycle; \end{tikzpicture} \end{document}
I have a laptop which I hook up to an external display when I'm at home. I also connected an external keyboard and mouse which makes it more comfortable for me.  I have noticed that pressing caps lock on the external keyboard does not light up the capslock indicator of the laptop keyboard (and vice versa).  When googling, I came across the setleds function, but when I type it into a console all I get is this:  KDGKBLED: Inappropriate ioctl for device Error reading current flags setting. Maybe you are not on the console?   Any idea if I can get this working? How to make a sound once a process is complete? I have started a long process through a terminal. Is it possible to make the Ubuntu terminal make a sound once the process is complete? This way, I don’t need to keep checking, but will instead be notified through a sound. What are the options for managing multiple Ubuntu installations together and keeping them in same state Recently I got in charge of managing 2 computer labs (currently 35 workstations, could double in a month or two) in university with total control over software stack as long as I install a bunch of commonly used scientific software (Mathematica and friends).  I plan to use Ubuntu for various reasons.   Installing Ubuntu and managing updates etc by hand is certainly an option, But I want to know if there is a more efficient way to do this stuff in and a more "Don't Repeat Yourself" manner?  Tasks   Ubuntu installation Installation (duplication) of same software stack and configuration over each workstation Keeping them updated Linearlayout order is reversed on some devices TikZ: remove margin, padding, border around nodes containing images I have ran into some issues when it went down to install Steam on Debian. The console as well as Apper comes up with missing dependencies  and the package isn't going to install. Apache: Scammers point dozens of domain names at my dedicated IP. How to prevent this? For the sake of discussion, pretend that I have an Apache webserver which serves a website at www.example.org. This domain name resolves to the public IP address at 192.168.1.100 (pretend this is a public IP).  The discussion at  demonstrates that anyone can point their domain at my IP. Apache won't prevent this by default, but an administrator can deal with these one at a time through use of a blacklist.  However, it's becoming more common for scammers to register dozens of domains (or more) for use in a scam. I'm concerned about the following possible attack:   A scammer registers hundreds of domain names, and points them at my dedicated IP address. The scammer directs search engines at their scam domains, thus using my content to increase their standing in the search engines. Later, the scammer moves their domain names to point to their own servers which host a scam/porn, or a competing business, etc. thereby reaping the benefits of their standing in the search engines. Some of these domains might be used to in  as well. Profit!!   I believe I have seen scammers using this trick in the past, involving dozens of domains. We didn't realize the scam implications at the time, and assumed these were misconfigured domains.  Is there a term for this nefarious SEO trick? SEO masquerading? DNS Diversion?  How could I prevent this using Apache? I'm considering a "whitelist" fix based on using a default VirtualHosts, ServerNames &amp; ServerAliases so that Apache only responds to requests where these white-listed ServerNames appear in the "Host: " header. Everything else would be rejected (or redirected to a particular page). However, I am unsure if this is the best approach.  For example, I've configured the domain  to point at the IP for Serverfault.com. You can see the results here:  . Why does python 2.5.2 have the following behavior  &gt;&gt;&gt;[2].extend([]) == [2] False  &gt;&gt;&gt; [2].extend([]) == None True  $ python --version Python 2.5.2   I assume I'm not understanding something here, but intuitively I'd think that [2].extend([]) should yield [2] What should be the intuition when working with compactness? I have a question that may be regarded by many as duplicate since there's a  one at MathOverflow. The point is that I think I'm not really getting the idea on compactness. I mean, in $\mathbb{R}^n$ the compact sets are those that are closed and bounded, however the guy who answered this question and had his answer accepted says that compactness is some analogue of finiteness. That's the first problem: In my intuitive view of finiteness, only boundedness would suffice to say that a certain subset of $\mathbb{R}^n$ is in some sense &quot;finite&quot;. On the other hand there's the other definition of compactness (in terms of covers) which is the one I really need to work with and I cannot see how that definition implies this intuition on finiteness. Also, I feel it's pretty strange the covers people use when they want to deal with compact sets. To prove a set is compact I know they must show that for every open cover there's a finite subcover; the problem is that I can't see intuitively how one could show this for every cover. Also when trying to disprove compactness the books I've read start presenting strange covers that I would have never thought about. I think my real problem is that I didn't yet get the intuition on compactness. So, what intuition should we have about compact sets in general and how should we really put this definition to use? Can someone provide some reference that shows how to understand the process of proving (and disproving) compactness? For reasons both complex and confusing, I would like to caption a longtable without incrementing the table counter in the process.  I want to have two consecutive longtable environments to be captioned with identical table numbers; i.e. one longtable captioned "Table x.y: Data Set (Part A)" and one captioned "Table x.y: Data Set (Part B)", with x.y being identical for both tables.  Apparently however, even \caption*{} command bumps table. I am a bit at a loss here.  Note: I know that the xtab package would enable me to have one long table with switches of headers and captions mid-table. However I got a (different) problem with that package, akin to  but sadly not solved by egreg's answer there; so this question should be considered longtable-only as xtab, supertabular etc. don't float my boat right now. :-( I want to kill all running processes of a particular user from either a shell script or native code on a Linux system.  Do I have to read the /proc directory and look for these?  Any ideas? Is there a dynamic mapping of the pids under UIDs in Linux? Isn't this in the proc?  If not, then where is this list maintained? Should I read from it? Also where is the static list of all UIDs in the system so I can validate this this user exists and then proceed to kill all processes running under it? I extracted simple example:  require 'pp' x = 1..3 pp x.map do |i| {:value =&gt; i, :double =&gt; (i*2)} end pp x.map { |i| {:value =&gt; i, :double =&gt; (i*2)} }  pp(x.map do |i| {:value =&gt; i, :double =&gt; (i*2)} end) pp(x.map { |i| {:value =&gt; i, :double =&gt; (i*2)} })   I am wondering why first pp produces:  [1, 2, 3]   While all the oders are giving:  [{:value=&gt;1, :double=&gt;2}, {:value=&gt;2, :double=&gt;4}, {:value=&gt;3, :double=&gt;6}]   I assume it has something to do with operator precedence. Where can I find good explanation? I was putting the following in /etc/sysctl.conf in Ubuntu 16.04 and ipv6 was disabled.  net.ipv6.conf.all.disable_ipv6 = 1 net.ipv6.conf.default.disable_ipv6 = 1 net.ipv6.conf.lo.disable_ipv6 = 1   In Ubuntu 18.04 I have to add the following to grub.  GRUB_CMDLINE_LINUX_DEFAULT="ipv6.disable=1"   Just wanted to have confirmation whether this is the new way in Ubuntu 18.04 to disable IPv6. Checking integrity of my server data Difference between standard error and standard deviation I'm struggling to understand the difference between the standard error and the standard deviation. How are they different and why do you need to measure the standard error? Levels or First Differences, VECM or VAR for Ultimate Impulse Response Functions? My final goal is to generate Impulse Response Functions in R.  I have variables that are non stationary when I set k = 5 in a Unit Root test, and they are cointegrated which to my understanding prompts the use of the VECM, from which the Vec2Var argument is used to then generate IRFs. However, my response functions from this methodology do not decay over time and mostly do not revert to the zero line.  Furthermore, I noticed that when I input first differenced variables into the VECM as opposed to level data above, response function do revert to the zero line. Therefore my first question is: 1) is it appropriate to use differenced variables in a VECM model?  Secondly, as an alternative I am considering restricting the number of lags used in the Unit Root tests so that the variables are not all non-stationary; in this case 2) would the use of VECM be void and the VAR with first differences be a more appropriate model? Again, using differenced data is giving me better response functions that revert to zero in the long run. However, 3) is it ok to use the VAR for stationary/non-stationary data in levels where these variables are still cointegrated?  Also, I am using growth rate variables, 4) should I still long transform all variables and use logs in all tests?  Thank you for the help! How can be solved the equation $x^3+x-1=y^2$ in positive integers?    I know this equation defines an elliptic curve, but this seems to be a non-elementary way to solve this question. Is there a more elementary solution?   By the way I found three solutions: $(1,1), (2,3)$ and $(13,47)$. Is this related to the law group property of elliptic curves? Thanks for further answers. Geometric intuition for the tensor product of vector spaces Can I bind a (large) block of addresses to an interface? I know that the ip tool lets you bind multiple addresses to an interface (eg, ). Right now, though, I'm trying to build something on top of IPv6, and it would be really useful to have an entire block of addresses (say, a /64) available, so that programs could pick any address from the range and bind to that. Needless to say, attaching every IP from this range to an interface would take a while.  Does Linux support binding a whole block of addresses to an interface? In Ubuntu 20.04, on the desktop, there is a number of actions I wish I could do, such as, by order of importance :  use keyboard shortcuts such as select all, copy / paste. use drag &amp; drop with icons deactivate the &quot;mouse over&quot; highlight, and restrict the clicking area to only the icon, not the surrounding square  To put it simply, I'd like to have the exact same features as offered by the desktop of Ubuntu 18.04 (probably related to a specific version of GNOME, and not Ubuntu itself). Am I missing something obvious here? I actually see no reason why those actions are removed or deactivated on the desktop, since they all work in any Nautilus window.