Given the definition of a Matrix Lie Group as a subgroup of $GL(n,\mathbb{C})$ such that for every sequence $A_n$ its limit $A$ is either in the subgroup or it is not invertible, what are the known examples for which the limit $A$ is invertible but is not contained in the subgroup, hence subgroups of $GL(n,\mathbb{C})$ that are not matrix Lie groups?
Let $G$ be a matrix Lie group and let $H$ be a Lie subgroup of $G$. My understanding is that all $g \in G$ are matrices, since $G$ is a subgroup of the general linear group. Then aren’t all elements $h \in H$ matrices, since $h \in G$?  From what I can gather $H$ is a matrix Lie group if $H$ is a closed subset of $G$. But if $H$ is not a closed subset of $G$, why is it not a matrix Lie group? Is the reasoning in the first paragraph wrong?
Lead in ice block This is a strange question I would like to have some explanation accompanied with:  We have an ice block, with in it a lead block. This entire block is put into a glass of water, resulting in a rise of water level until the edge of the glass. The block stays floating on the surface. What will happen with the water level when the ice melts?  The answer is that it will drop, but how is this even true?? My thoughts are: - block floats on water, so rho(block) &lt; rho(water) - Archimedes law, the Fg of block = Fg of water pushed away. - Since a smaller volume of water has equal mass (and so Fg) to block, and ice is less dense than water, when it melts, no mass is lost, so it will take in less space??? Please help me with this point of thinking. What do I if I used "Reset All" or "Erase All Content and Settings" on a jailbroken iOS Device? I recently received an iOS device and it was jailbroken. When I wanted to unjailbreak it, I used "Erase All Content and Settings." The loading screen came on and it has not changed. After rebooting the device, it is now stuck at the Apple logo. What should I do? How to pass Unicode characters as JSP/Servlet request.getParameter? I'm looking for a way to access raster layers in an Esri File-GeoDatabase without using ArcObjects or ArcPy, specifically I would like to access the raster layers with GDAL. I understand that the GDAL FileGDB and OpenFileGDB give access to vector datasets within File-GeoDatabases, and that ESRI's own FileGDB C++ API does not support raster access.   Is anyone out there aware of any open source solutions? I have a requirement to implement an "Unsaved Changes" prompt in an ASP .Net application.  If a user modifies controls on a web form, and attempts to navigate away before saving, a prompt should appear warning them that they have unsaved changes, and give them the option to cancel and stay on the current page.  The prompt should not display if the user hasn't touched any of the controls.  Ideally I'd like to implement this in JavaScript, but before I go down the path of rolling my own code, are there any existing frameworks or recommended design patterns for achieving this?  Ideally I'd like something that can easily be reused across multiple pages with minimal changes. Our GM won't let us affect the story; the more I play the less fun I have. What do I do? I was wondering if anyone could give me some advice or anything on a GM situation.   My current GM is running a campaign and it is very video game/anime like. It started out super fun and the deeper we get the less fun I have. The reason is, it feels like GM is telling us a story but we cannot interact or change anything during his, "cut scenes". No matter what any player does he just says, "No it didn't work," or, "Yeah you do that. See if you roll a 20." We also can't damage any boss he has until we reach the point in the story that he has planned, so our interactions we have with villains don't matter.  I feel like he is making us sit there and listen to an anime he has come up with in his head. Since the players can't change or react to the key situations. I find my self sitting there thinking, why would I react, it doesn't matter.  It's not just me either. Another player feels the same way. I am going to talk to my other fellow players soon about it and see how they feel.  Side note: the GM as a person is very defensive and I am afraid to confront him about it because I know he will throw a fit. We have also caught him straight lying about abilities and stats on his own PC in other campaigns, and he doesn't take to kindly when you call him out.  He is new to GMing. This is only the second game I have played with him as a GM. The first one had one session the he just never wrote more for.  Is there anything I can do to maybe get him to more lenient with his story? I really enjoy the story for the most part and if he would just let our characters do things and give us a chance at stopping his villians or letting us change the story based on our actions, everything would be cool. Unable to run any GRASS 7 algorithms in QGIS 2.18.10 on Windows 7(64) Is there a better way to do optional function parameters in JavaScript? I've always handled optional parameters in JavaScript like this:  function myFunc(requiredArg, optionalArg){   optionalArg = optionalArg || 'defaultValue';    // Do stuff }   Is there a better way to do it?  Are there any cases where using || like that is going to fail? I don't know how to integrate $\displaystyle \int\frac{1}{x^{4}+1}\mathrm dx$. Do I have to use trigonometric substitution? Calculate a running total in MySQL I have this MySQL query:  SELECT DAYOFYEAR(`date`)  AS d, COUNT(*)  FROM  `orders`  WHERE  `hasPaid` &gt; 0 GROUP  BY d ORDER  BY d   Which returns something like this:  d  | COUNT(*) | 20 |  5       | 21 |  7       | 22 | 12       | 23 |  4       |   What I'd really like is another column on the end to show the running total:  d  | COUNT(*) | ??? | 20 |  5       |   5 | 21 |  7       |  12 | 22 | 12       |  24 | 23 |  4       |  28 |   Is this possible? I installed Ubuntu 17.10. Now I am having trouble with gksu:  $ gksu -dg synaptic No ask_pass set, using default! xauth: /tmp/libgksu-HgUjgQ/.Xauthority STARTUP_ID: gksu/synaptic/8760-0-alex-XPS-15-9530_TIME4974977 cmd[0]: /usr/bin/sudo cmd[1]: -H cmd[2]: -S cmd[3]: -p cmd[4]: GNOME_SUDO_PASS cmd[5]: -u cmd[6]: root cmd[7]: -- cmd[8]: synaptic buffer: -GNOME_SUDO_PASS- brute force GNOME_SUDO_PASS ended... Yeah, we're in... 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And yet, every time I ask such a question, someone gives such an answer anyway, or an outright XY-type, i.e. frame-challenge answer – where in fact the framing of the question is exactly how I want it, and I don’t want it challenged. Since I have already said in the question body that such an answer would be inaqeduate, when I get one, I downvote it. I believe it’s only appropriate, but it tends not to be received very well – I get insulting comments and downvotes in retaliation. I realise that a proper answer would be much harder to come up with than an ‘obvious’ inadequate answer. I suspect that often a real answer should be negative: ‘there is no way to do that’ or ‘there is no way to answer that for sure’. Nevertheless, if that is the right answer, this is the one I want posted – I don’t want the Internet polluted with more tumbleweed of what is already well-known (and may even be subtly wrong), and I don’t want to give ‘A for effort’ upvotes. What is the most appropriate way to act in such a situation?  0 I am also reminded of when Gary Bernhardt  while trying to avoid reflexive ‘don’t use eval’ replies. Of course, expecting nuance from Twitter of all places is silly, but that’s beside the point. How to change/rewrite the lost password url? I used iThemes Security (formerly Better WP Security) hide back-end functionality to change the login url to /signin however clicking the lost password link /wp-login.php?action=lostpassword now generate a 404  Manually going to /signin?action=lostpassword works.  I came across the following code below which is suppose to make the change to however after some testing it doesn't seem to work  //******************************************************* //Function to change to lost password url //******************************************************** add_filter('site_url',  'wplogin_filter', 10, 3); function wplogin_filter( $url, $path, $orig_scheme ){     $old  = array( "/(wp-login\.php)/");     $new  = array( "signin/"); //this can be change to login or whatever or may remain there     return preg_replace( $old, $new, $url, 1); }   add to .htaccess  RewriteRule ^signin$ wp-login.php   How can i modify the above code in order to change the url for the lost password? How to automaticaly enter sudo's grace period upon login \documentclass{minimal} \usepackage{tikz} \begin{document} \pgfmathparse{random(-5,5)} \pgfmathresult \end{document}   Works, but I have a .0.0 that not supposed to be here. What do the plus and minus signs mean in Objective-C next to a method? I'm printing a tradeshow flyer and was wondering what type of paper I should print it on. I don't want anything glossy so I'm trying to decide on the following:   100# text weight matte 80# cover 80# matte   What is the difference between the types above? And how can I make a decision? I have an object with two solidify modifiers added, but the modifiers are not visible in the view pane. How can I see the applied modifiers. This is in Blender 2.91 In a Feistel cipher structure, what exactly does the "round function $F$" do? In a Feistel cipher structure, what exactly does the "round function $F$" do to the right half of the data, before taking XOR of the output with the left half of the data? How do I "decompile" Java class files? What program can I use to decompile a class file? Will I actually get Java code, or is it just JVM assembly code?  On Java performance questions on this site I often see responses from people who have "decompiled" the Java class file to see how the compiler optimizes certain things.