How can I install ubuntu-restricted-extras?
"Unable to locate package" while trying to install packages with APT
Let $G$ be a group, $H\subseteq G$ a subgroup and $a\in G$ an element of the group. Is it possible that $aHa^{-1} \subset H$, but $aHa^{-1} \neq H$?   If $H$ has finite index or finite order, this is not possible. If Eren Jaeger dies without transfering his titan powers, will both powers transfer to the same child? It's told in the story that if a titan shifter dies without transferring his power, this power will go to an eldian person who just was born. If Eren Jaeger dies without transferring his titan powers, will the attack titan and the founding titan go to different persons?  Note that his is not a duplicate of  as this is not about what happens when a titan shifter dies. But what happens if a titan shifter with 2 powers dies, which is not answered in the answer. I have a table to store StudentID, SubjectID, ObtainedMarks. Now I have to create a pivot table to show studentID and obtainedMarks in different subject. Number of subject may differ. I could generate pivot table for fixed subjectID like    SELECT * FROM (SELECT StudentID, SubjectID, ObtainedMarks from [Exam].[ObtainedMarkEntry]) as InvoiceResult PIVOT (     sum(ObtainedMarks) for [SubjectID] in  ([1],[2],[3],[4]) )as finalResult   This works but problem is 1,2,3 is not static it should come from same table   So I did something like   declare @minvalue int, @maxvalue int declare @myArray varchar(max) set @MyArray=''  select RowID=IDENTITY(int, 1,1), SubjectID into #tempSubject from [Exam].[ObtainedMarkEntry] select * from #tempSubject set @minvalue = (select min(RowID) from #tempSubject) set @maxvalue = (select max(RowID) from #tempSubject) while (@minvalue&lt;=@maxvalue) begin     declare @sid nvarchar(10)     set @sid=(select SubjectID from #tempSubject where RowID=@minvalue)     set @myArray= @myArray + '[' + @sid + '], '      set @minvalue= @minvalue+1 end set @myArray= SUBSTRING(@myArray,0,len(@myArray)) drop table #tempSubject  declare @q as nvarchar(max) SELECT * FROM (SELECT StudentID, SubjectID, ObtainedMarks  from [Exam].[ObtainedMarkEntry]) as InvoiceResult PIVOT (     sum(ObtainedMarks) for [SubjectID] in  (@myArray) )as finalResult   Now I am getting error at in(@myArray) can't I assign variable in this section. Problem with sudo apt update in Ubuntu 18.04: Post-Invoke-Success if /usr/bin/test -w /var/lib/command-not-found/ The terminal gave me these errors when updating the software with sudo apt update.    Hit:1 http://it.archive.ubuntu.com/ubuntu bionic InRelease Hit:2 http://it.archive.ubuntu.com/ubuntu bionic-updates InRelease                                                                                        Hit:3 http://it.archive.ubuntu.com/ubuntu bionic-backports InRelease                                                                                      Hit:4 http://security.ubuntu.com/ubuntu bionic-security InRelease                                      Hit:5 http://archive.canonical.com/ubuntu bionic InRelease                 Traceback (most recent call last):                       File "/usr/lib/cnf-update-db", line 8, in &lt;module&gt;     from CommandNotFound.db.creator import DbCreator ModuleNotFoundError: No module named 'CommandNotFound' Reading packages list... Done E: Problem executing scripts APT::Update::Post-Invoke-Success     'if /usr/bin/test -w /var/lib/command-not-found/ -a -e /usr/lib/cnf-update-db;       then /usr/lib/cnf-update-db &gt; /dev/null; fi'   E: Sub-process returned an error code     These are the results of sudo apt install --reinstall command-not-found  Reading package lists... Done  Building dependency tree         Reading state information... Done 0 upgraded, 0 newly installed, 1 reinstalled, 0 to remove and 0 not upgraded. Need to get 0 B/5.188 B of archives After this operation, 0 B of additional disk space will be used. (Reading the database ... 225797 files and directories currently installed.) Preparations for extracting ... / command-not-found_18.04.4_all.deb ... Extracting command-not-found (18.04.4) on (18.04.4) ... Configuring command-not-found (18.04.4) ... libdvd-pkg: Package libdvdcss2-1.4.2-1 was removed, stop processing...   When I tried the command sudo apt update again after reinstalling command-not-found, the results were the same as described in the first text block. Can I install Python 3.x and 2.x on the same Windows computer? Why is the derivative of a vector orthogonal to the vector itself? $R(t) \cdot R'(t) = 0$, which is what every source I can find tells me. Even though I understand the proof I don't understand the underlying concept. If $R(t)\cdot R'(t) = 0$, then $R'(t)$ is orthogonal to $R(t)$, right?   But you use the same derivative to find the tangent of a curve. Then somehow if you differentiate the tangent itself, you get the normal to the curve.  I really can't wrap my head around this. Could someone help me understand? Deduction of $\forall y \exists x (x=y)$ Give a deduction of $\forall y \exists x (x=y)$  My thinking is I can prove $\exists x(x=y)$ then use generalization theorem， which is equivalent to prove $\neg \forall x \neg (x=y)$ but I got stuck proving this... thanks in advance  Sorry that I did not specify what deduction system that I want to use here, it is the deduction sequence  where ai is either Axiom or original hypothesis or obtained from MP For which $f,g \in k[t]$, $k[f,g]$ is integrally closed? Let $f,g \in k[t]$, $k$ is a field of characteristic zero, $\deg(f)=n \geq 2$, $\deg(g)=m \geq 2$.     Is it possible to characterize all such $f$ and $g$ for which $k[f,g]$ is integrally closed in its field of fractions $k(f,g)$?   I do not mind to further assume that $k(f,g)=k(t)$ (but I do not want to assume that $k[f,g]=k[t]$, which makes my question trivial).  Thank you very much!  Edit: (i)  is relevant.  (ii) If also $k(f,g)=k(t)$, then being integrally closed is equivalent to $k[f,g]=k[t]$. Indeed: (a) If $k[f,g]=k[t]$ then $k[f,g]$ is integrally closed (since $k[t]$ is). (b) If $k[f,g]$ is integrally closed then, in particular, since $t \in k(t)=k(f,g)$ (= the field of fractions of $k[f,g]$) and obviously $t$ is integral over $k[f,g]$ (for example, $t$ is a root of $f(T)-f \in k[f,g][T]$) hence $t \in k[f,g]$, so $k[f,g]=k[t]$.  For example: $f(t)=t^2+1$, $g(t)=t^3-4t$. We have, $t= \frac{t(t^2-4)}{t^2+1-5}=\frac{g}{f-5}$, so $k(f,g)=k(t)$. By Abhyankar-Moh-Suzuki theorem, $k[f,g] \neq k[t]$, so $k[f,g]$ is not integrally closed. Similarly, for every $f,g$ such that $k(f,g)=k(t)$ and one of the degrees does not divides the other, then $k[f,g]$ is not integrally closed.  (iii) If also $k(f,g)=k(t)$ and $k$ is algebraically closed, then being integrally closed is equivalent to $H(t)=(f(t),g(t))$ is injective and $H'(t)=(f'(t),g'(t)) \neq (0,0)$ for every $t \in k$. Indeed, $k[f,g]=k[t]$ is equivalent to the new conditions (it is important that $k$ is algebraically closed!!).  Edit: What if we replace $k$ by an integral domain $D$ (which is a $k$-algebra)? See also  question. I have a Xonar DX (CMI8788 driver) 7.1 surround sound card installed on my Ubuntu 11.10 system.   I want to use the outputs of the card as 4 separate stereo outputs and I am struggling with ALSA to get it to work.  This is my asound.conf:  #/etc/asound.conf pcm_slave.eightchannels {         pcm "hw:0,0"            # or "hw:1,0" for the second card         channels 8 } pcm.stereo1 {         type plug         slave.pcm {                 type dshare                 ipc_key 87882222                 slave eightchannels                 bindings [ 2 3 ]         } } pcm.stereo2 {         type plug         slave.pcm {                 type dshare                 ipc_key 87882222                 slave eightchannels                 bindings [ 4 5 ]         } } pcm.stereo3 {         type plug         slave.pcm {                 type dshare                 ipc_key 87882222                 slave eightchannels                 bindings [ 6 7 ]         } } pcm.stereo4 {         type plug         slave.pcm {                 type dshare                 ipc_key 87882222                 slave eightchannels                 bindings [ 0 1 ]         } }   This is my aplay -l output:  $ aplay -l **** List of PLAYBACK Hardware Devices **** card 0: DX [Xonar DX], device 0: Multichannel [Multichannel]   Subdevices: 1/1   Subdevice #0: subdevice #0 card 0: DX [Xonar DX], device 1: Digital [Digital]   Subdevices: 1/1   Subdevice #0: subdevice #0 card 1: Intel [HDA Intel], device 0: ALC662 rev1 Analog [ALC662 rev1 Analog]   Subdevices: 1/1   Subdevice #0: subdevice #0 card 1: Intel [HDA Intel], device 1: ALC662 rev1 Digital [ALC662 rev1 Digital]   Subdevices: 1/1   Subdevice #0: subdevice #0   This is my aplay -L output:   The system seems to completely ignore my configuration. However, I am sure that the config is used, because when i insert a random string at the top, i get a parsing error.  Any help is greatly appreciated. steam fatal error "steam needs to be online to update, but was set to offline movies." I tried re-installing  it but it simply keeps giving me this error in a little window. When I close it, an identical error pops up some 3 seconds later without any new provocation. Why are some galaxies flat? What is the explanation for the flatness of some galaxies?   (If it's due to their rotation then why they are rotating, why some other galaxies are not flat etc., I would like to hear a nice and complete answer :) ) fleqn document class option, long text lines, and hyperref package When the fleqn option is used, the vertical spacing before an equation placed right after a "long" text line (exactly \linewidth I would say) is improperly set up. See below:    From the mathmode user guide, this could probably be fixed through the \topsep length. Is it the right way to proceed? The problem is reproduced by the code below:  \documentclass[12pt,fleqn]{book} \usepackage{amsmath} \usepackage{hyperref} \begin{document} \chapter{plo} \section{plo} eoiu oieu oeiuoe ueoi ueoi ueoiu eoiu oeu oe iupaêio umùaeoiuaem oeiu eoiu eoiu oeee. eoiu oieu oeiuoe ueoi ueoi ueoiu eoiu oeu oe iupaêio umùaeoiuaemm \begin{equation} \cos\pi=-1 \end{equation} eoiu oieu oeiuoe ueoi ueoi ueoiu eoiu oeu oe iupaêio umùaeoiuaem oeiu eoiu eoiu oeee. eoiu oieu oeiuoe ueoi ueoi ueoiu eoiu oeu oe iupaêio umùae \begin{equation} \cos\pi=-1 \end{equation} \end{document}   There is something wrong involving hyperref, amsmath, and fleqn. Removing one of those removes the problem. I am having trouble with the following problem.      Let $R$ be an integral domain, and let $a \in R$ be a non-zero element. Let $D = \{1, a, a^2, ...\}$. I need to show that $R_D \cong R[x]/(ax-1)$.    I just want a hint.  Basically, I've been looking for a surjective homomorphism from $R[x]$ to $R_D$, but everything I've tried has failed. I think the fact that $f(a)$ is a unit, where $f$ is our mapping, is relevant, but I'm not sure. Thanks Why does this not work with an imaginary exponent? Could someone please tell me why this exponentiation rule does not work when the exponent is imaginary?  The following seems to be true but is only true if $x$ is an integer.  $$e^{2\pi ix} = \left( e^{2\pi i} \right)^x = 1^x = 1$$ Can we continue to show the "Take a tour" banner after a user has created an account? What's the protocol for requesting a tag warning? On a particular site, RPG Stack Exchange, we've decided on our meta on a couple of tags that should have tag warnings, and on what those tag warnings should say. I am  on the site in question.  What should we do to get the tag warnings implemented? Do we do any/all of the following?:   start a [feature-request] on our meta for the tag warnings? raise a CM escalation? contact staff via the contact form? ping a staff member in the Teacher's Lounge? anything else? Nested Quantifiers true or false I have a concern with nested quantifiers.  I have: $$  \forall x \exists y \forall z(x^2-y+z=0) $$ such that $$ x,y,z \in \Bbb Z^+$$   My first question, can it be read like this:  $$  \forall x \forall z \exists y(x^2-y+z=0)  $$  The way I did it, is I started off with $x=1, z=1 $   $$ 2-y = 0 $$ $$ y =2 $$  Is this a good approach? Is there a way to stream Netflix content to my Ubuntu machine? For all $a, m, n \in \mathbb{Z}^+$,   $$\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$$ Hypothesis test for difference in medians among more than two samples Question  The test scores of three groups of people are saved as separate vectors in R.  set.seed(1) group1 &lt;- rnorm(100, mean = 75, sd = 10) group2 &lt;- rnorm(100, mean = 85, sd = 10) group3 &lt;- rnorm(100, mean = 95, sd = 10)   I want to know if there is a significant difference in the medians between these groups. I know that I could test group 1 versus group 2 using the Wilcoxon test, like so.  wilcox.test(group1, group2)   However, this compares only two groups at a time, and I would like to compare all three simultaneously. I would like a statistical test that yields a p value at the 0.05 significance level. Could someone please help?  Edit #1 - Mood's median test  Following user Hibernating's suggested answer, I tried Mood's median test.  median.test &lt;- function(x, y){     z &lt;- c(x, y)     g &lt;- rep(1:2, c(length(x), length(y)))     m &lt;- median(z)     fisher.test(z &lt; m, g)$p.value }  median.test(group1, group2)   However, this approach allows me to test for a significant difference between the medians of only two groups at a time. I am not sure of how to use it to compare the medians of all three simultaneously.  Edit #2 - Kruskal-Wallis test  User dmartin's suggested answer appears to be more or less what I need, and allows me to test all three groups simultaneously.  kruskal.test(list(group1, group2, group3))   Edit #3  User Greg Snow helpfully notes in his answer that the Kruskal-Wallis test is appropriate as long as it makes strict assumptions that make it also a test of means.