Upper bound on error function
Proving $1-\exp(-4x^2/ \pi) \ge \text{erf}(x)^2$
Broken URL for data.stackexchange.com help page When using data.stackexchange.com I fail to remember if as [post link] is the correct alias to get the url for the post. Luckily the site has an  link. Unfortunately it is now broken. Can this be fixed? Activity has leaked window com.android.internal.policy.impl.PhoneWindow$DecorView@44f72ff0 that was originally added here How do I remove duplicate "Open With" context menu items in Finder.app? For whatever reason, the "Open With" context menu in Finder is always listing every app four times (exactly).     I've read about (and tried) rebuilding the Launch Services database to restore the context menu to its initial state, but nothing seems to work. I've also used Onyx.app to clear user and system caches, but I'm still left with four repetitions of each app under the "Open With" service. I have restarted the system a few times just to be sure it was not some temporary corruption of the list.  I'm running OS X 10.6.6 on a 2011 17" MacBook Pro with a fresh install of OS X (i.e. I didn't use Migration Assistant.app or a Time Machine backup). I did, however, sync all my preferences and other files using MobileMe like I always do, so I imagine it's feasible that a preference file somewhere is causing problems? I didn't notice whether this was happening before or after my MobileMe sync.  How can I fix this so one app shows? facl ignoring the "x" permission but only on files Force NTFS permissions inheritance for newly created files Is there an official Marvel Cinematic Universe viewing order? Disable or prevent multitouch in Activity Often called "He-Who-Must-Not-Be-Named" and "You know who", was it common knowledge at the Ministry of Magic that Voldemort was the same person as Tom Riddle? Prove that $ a $ divides $1^{a^{n}} + 2^{a^{n}} + ... + (a-1)^{a^{n}}$? Tikz: shading region bounded by several curves I know that my effort below can be improved upon considerably.  In particular, there must be a way of shading the region in a single scope, as opposed to subdividing as I have done (thus necessitating a hidden gray boundary).  Neither am I fond of sample points, but this is where my research has led me.  Your constructive criticism is appreciated.    \documentclass{article} \usepackage{tikz} \begin{document}  \begin{tikzpicture} %graph \draw[draw=gray!50!white,fill=gray!50!white]      plot[smooth,samples=100,domain=0:1] (\x,{0}) --      plot[smooth,samples=100,domain=1:0] (\x,{1}); \draw[fill=gray!50!white] plot[smooth,samples=100,domain=1:2.71828] (\x,{ln(\x)}) --      plot[smooth,samples=100,domain=2.71828:1] (\x,{1}); \draw[domain=0:4] plot (\x,{1}); \draw[samples=100,domain=.25:4] plot (\x,{ln(\x)}) node[above left]{$y=\ln x$}; %coordinate grid \draw (-.5,0)--(4.5,0) node[right]{$x$}; \draw (0,-1.5)--(0,2.5) node[above]{$y$}; \foreach \x in {1,2,3,4}     \draw (\x,2pt)--(\x,-2pt) node[below] {$\x$}; \foreach \y/\ytext in {1,2}     \draw (2pt,\y)--(-2pt,\y) node[left] {$\y$};     %labels  \node at (.75,.5) {$\mathcal{D}$}; \end{tikzpicture}  \end{document} What is the difference between 32-bit and 64-bit Ubuntu? I've heard the 64-bit platform performs better and can detect more than 4GB of RAM. Also, while some apps haven't ported to 64-bit yet, ia32-libs lets a 64-bit machine run them.  If so, why not promote 64-bit over 32-bit? Show that every group of prime order is cyclic Show that every group of prime order is cyclic.   I was given this problem for homework and I am not sure where to start. I know a solution using Lagrange's theorem, but we have not proven Lagrange's theorem yet, actually our teacher hasn't even mentioned it, so I am guessing there must be another solution. The only thing I could think of was showing that a group of prime order $p$ is isomorphic to $\mathbb{Z}/p\mathbb{Z}$. Would this work?    Any guidance would be appreciated. How long can cooked food be safely stored at room/warm temperature? 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? How to sort a list of objects based on an attribute of the objects? I've got a list of Python objects that I'd like to sort by an attribute of the objects themselves.  The list looks like:  &gt;&gt;&gt; ut [&lt;Tag: 128&gt;, &lt;Tag: 2008&gt;, &lt;Tag: &lt;&gt;, &lt;Tag: actionscript&gt;, &lt;Tag: addresses&gt;,  &lt;Tag: aes&gt;, &lt;Tag: ajax&gt; ...]   Each object has a count:  &gt;&gt;&gt; ut[1].count 1L   I need to sort the list by number of counts descending.  I've seen several methods for this, but I'm looking for best practice in Python. Can I enter Croatia with single entry visa Schengen? How can I reject all changes in a Linq to SQL's DataContext? On Linq to SQL's DataContext I am able to call SubmitChanges() to submit all changes.  What I want is to somehow reject all changes in the datacontext and rollback all changes (preferable without going to the database).  Is this possible? Why is sudoers NOPASSWD option not working? The command history between sessions is not getting saved. I'm using guake and the history for the session is working fine. I noticed that .bash_history had some commands I executed in sudo -s mode and tried the same again and all the commands while in the session got saved so I tried: chmod 777 .bash_history  Now the old commands appear at the start of a session but no new commands are getting saved. Anyone on the Android Jelly Bean OS and not able to buy Apps/Books through wallet? I have just bought the Samsung GalaxyNote 800 and am facing this issue.   The error is (RPC:S-7:AEC-0).   What is the solution?