Test statistics help needed
Help with null hypothesis
I have a dual screen setup on my laptop (using 12.04 LTS) using a HDMI connected display. Everything works fine, but everytime I connect/disconnect the cable I have to go to Sound preferences and change the sound output device manually.  Is there any way to change the sound output device on connect/disconnection of cable, so when I connect my display the sound output is set to HDMI and when I disconnect it the sound goes back to laptop speakers? How to avoid the wrinkle at the poles of the UV sphere? When I create a UV sphere and add the subdivision surface modifier, the following wrinkle appears.    How can I avoid it?  I've read the article  but there seems to be no clear solution.  UPDATE 1  I've used the word 'apply' in the first sentence of the initial version of this question. It's misleading since I want to preserve the modifier without 'applying' it. Rather, what I meant is 'adding' the modifier.  UPDATE 2  I followed josh sanfelici's solution, but still there is an artifact at the pole.  Here is the screen: (A rendered view with a sun lamp)    Maybe it's the limitation of the general-purpose subdivision modifier.  BTW, when the cast modifier is added after the subdivision modifier, the sphere becomes perfect (even for my original wrinkled sphere).  But since I want to edit the resulting sphere (for example, scaling X, Y, etc) while modifier is added but not applied, it's not usable. "Do you know where's Linda?" vs "Do you know where Linda is?" Correct the "about" page to reference the new "on hold" policy Suppose $G$ is a finer filter than $F$ in a topological space $X$.  Is the net base in $G$ a subnet of the net base in $F$?  I am using the definitions of General Topology of Willard:     Definition 12.15. If $(x_\lambda)$ is a net in $X$, the filter generated by the filter base $\mathscr C$ consisting of the sets $B_{\lambda_0}=\{x_\lambda; \lambda\ge\lambda_0\}$, $\lambda_0\in\Lambda$, is called the filter generated by $(x_\lambda)$.      Definition 12.16. If $\mathscr F$ is a filter on $X$, let $\Lambda_{\mathscr F}=\{(x,F); x\in F\in\mathscr F\}$.   Then $\Lambda_{\mathscr F}$ is directed by the relation $(x_1,F_1)\le(x_2,F_2)$ iff $F_2\subset F_1$, so the map   $P\colon \Lambda_{\mathscr F} \to X$ defined by $P(x,F)=x$ is a net in $X$. It is called the net based on $\mathscr F$.   The definition of subnet used in Willard is the second one from this post:   Thank you I found this interesting problem in :     Given a point $P$ in space, and given a piece of malleable material of constant density, how should you shape and place the material in order to create the largest possible gravitational field at $P$?   Any ideas? Upgrade Debian Jessie (8) to Buster (10) possible or need to go sequential in versions upgrades? Just started working with a Debian Jessie (8) in a production environnent. While presently deployed it is not seeing any heavy use yet. I was looking at the OS , and I was thinking about how convenient it would be to just upgrade it before is start seeing some more steady use in our environment and possibly making things more complicated with a later upgrade.  I was looking for a procedure to upgrade from Debian v.8 to v.10 but most documented  are sequential in order (e.g. 8 -> 9, or 9 -> 10).  My question: should I upgrade sequentially, or there is some proper documented way to skip a main version while upgrading? There's no need to  the  that have led to a lack of trust between  of  and . Suffice it to say that astoundingly they continue to assert that  and, instead of apologizing and reinstating Monica have demanded that she go through a process with no transparency, due process, or involvement from the community.   Has the time has come for Stack Exchange, Inc to spin off the community and all the data needed to keep the sites running to a separate non-profit, who would then in turn license the software from the company?  What's in it for the community?   The community can practice self determination for issues from as basic as the number of moderators they have to as fundamental as the policies they enforce. If the company development continues to be unresponsive to the community's needs, the community would be able to develop its own open source software that would meet its needs. They can find their own funding model instead of having ads imposed on them.   What's in it for the company?   Community actions will no longer reflect on the company. Interaction with the community as a customer may come more naturally to current leadership than the present paradigm. They don't have to worry about paying for the community's operating expenses. They can focus on doing one thing well. I found Sean Carroll's "A No Nonsense Introduction to General Relativity" (about page .  pdf ), a 24-page overview of the topic, very helpful for beginning study.  It all got me over the hump of learning the meaning of various terms associated with GR, most of which I had heard before without understanding.  It also outlined the most important examples.  Is there a similar document for quantum field theory, which presents the main equations, briefly describes the main ideas, and summarizes the most important applications and results so that the reader can feel the lay of the land before studying in depth? What I am asking here is to please remove the privilege to participate in Meta for MSE.  This privilege is literally useless. You can't really have a meta site for a meta site. There's no Meta.Meta.SE here or any other SE site out there: Meta.SE covers for every site in SE, including itself.     When users find out that you don't really get anything new, it's kinda sad for those people. There is no use for it except just to be there and fill up the space between the first and third privilege. Privileges should be shown only if you earn something new, and this privilege to participate in the meta isn't new because it's where you report problems in all of SE, including Meta.SE.    So please remove the privilege to participate in meta just for Meta.SE.    This is not a dupe as this is a feature-request to remove it, not support on why it is there. $\mathbb Z[i]/ \langle 1+2i \rangle \cong \mathbb Z_5$ I am trying to prove that $\mathbb Z[i]/ \langle 1+2i \rangle$ is isomorphic to  $\mathbb  Z_5$.   The only thing that came to my mind was trying to apply the first isomorphism theorem using an appropiate function. If I consider the euclidean function $N: Z[i] \setminus \{0 \}  \to  \mathbb N$ defined as $N(a+bi)=a^2+b^2$, then I can express any element $z$ in $\mathbb Z[i]$ as $z=(1+2i)q+r$ with $N(r)=1,2,3,4$ or $r=0$.   If I define $f:\mathbb Z[i] \to \mathbb  Z_5$ as $f(x=(1+2i)q_x+r_x)=\overline{r_x}$, then it is clear that $f(x)=0$ if and only if $x \in  \langle 1+2i \rangle$. The problem with this function is that it doesn't satisfy $f(x+y)=f(x)+f(y)$ and it is not surjective for if $r_x=f(x)=3 (5)$, then if $r_x=a+bi$, we have $a^2+b^2=3$, which is absurd.  I don't know what else to do, any suggestions would be appreciated. He has  yet to receive an appointment.   He is yet to receive an appointment.      Is there any difference in meaning? Is one more correct than the other? This is a follow up question to my previous question  Let $k$ be a field and $V \subseteq \Bbb{A}^n$ and $W \subseteq \Bbb{A}^m$ be algebraic sets. Then it should be true that $I(V \times W ) = I(V) + I(W)$ where by $I(V)$ here we mean the extension of $I(V)k[x_1,\ldots,x_{m+n}]$. Now I believe I have proven this (see the proof at the bottom of my question) but when I look at Martin's answer , it is instead claimed that we  actually have  $$I(V \times W )= \sqrt{I(V) + I(W)},$$  and for $I(V) + I(W)$ to be a radical ideal we need $k$ to be algebraically closed.           My question is: What's going on here? I believe my claim is true even without the assumption that $k$ is algebraically closed.           Here's a proof user Sanchez told me of, which I have simplified:       First it is clear that we always have $I(V) + I(W) \subseteq I(V \times W)$. For the reverse inclusion consider a polynomial $f \in I(V \times W)$. Then we can always write $$f = \sum_{i=1}^n f_ig_i$$ where $f_i \in k[x_1,\ldots,x_n]$ and $g_i \in k[x_{n+1},\ldots,x_{m+n}]$. Now take any $b' \in W$. If for all $i$ we have $g_i(b') = 0$ then since $b'$ is arbitrary, $g_i \in I(W)$ for all $i$. Then $f \in I(W) \subseteq I(V ) + I(w)$ and we are done. Otherwise suppose there exists $b \in W$  and $i$ such that $g_i(b) \neq 0$. Then wlog we may suppose that  $g_1(b) \neq 0$.   Next, $\sum f_ig_i(b) = 0 $ on all of $V$ by assumption of $f \in I(V \times W)$. So $\sum f_i g_i(b) = p$ for some $p \in I(V)$. Now write $$f_1 = \frac{ p - g_2(b) f_2 + \ldots g_n(b)f_n}{g_1(b)}.$$  Substituting this for $f_1$ in $\sum f_ig_i$, followed by taking things mod $I(V)$ we get an  expression with only $n-1$ terms $\mod{I(V)}$. Continuing this process we will finally get an expression with $0$ terms $\mod{I(V)}$ so that $f \in I(V)$. This shows $I(V \times W) \subseteq I(V) + I(W)$ which completes the proof. Further anonymize deleted accounts by changing the username in close/delete notices When an account is deleted, the username in the user's posts and comments is changed to a generic user&lt;userID&gt;. But the username stays the same on close and delete notifications on posts the user had voted to close / delete1. I think it shouldn't, especially for users who used their real name as their username, if they chose to distance themselves from the site and remove their accounts, it makes sense that they wouldn't really want their name plastered on close and delete notifications.   A perhaps easy way to avoid the actual username remaining visible would be to change it to the generic user&lt;userID&gt; (or anything generic enough, like "anonymous") prior to deletion, and wait a bit for the generic username to propagate all over the site. If I'm not horribly misreading , this was part of the process in the old days.   This could be automated or added as a suggestion to the .  Glaring example can be seen , where the deleted user also posted a comment where their name is properly anonymized:        1 I've seen it on close notifications and self deleted answers. I'm not sure it happens on deleted questions, or deleted answers that aren't self deletions, and I don't have a way to verify it - other than stumbling on them accidentally Is returning a pointer to a static local variable safe? I'm working with some code that widely uses the idiom of returning a pointer to a static local variable.  eg:  char* const GetString() {   static char sTest[5];   strcpy(sTest, "Test");   return sTest; }   Am I right in thinking that this is safe?  PS, I know that this would be a better way of doing the same thing:  char* const GetString() {   return "Test"; }   Edit: Apologies, the function signature should of course be:  const char* GetString(); I was told that the following does not work:     Employees having children will be granted a day off.   However, this sounds better:     Having children, those employees will be granted a day off.   What is wrong with the first clause? Suggested Edits Dashboard doesn't agree with Suggested Edits view I recall :    It was one that I knew could use a bit more spit and polish, but I didn't have the inclination or energy to edit it myself, so I skipped it.  I wander my way over to  (10K only), and look at the listing...    ...so, when did I approve this again? I skipped the question; that doesn't mean I gave my tacit approval, does it?  Seems like the dashboard needs to agree with the suggested edits view. How can I avoid SQL injection attacks in my ASP.NET application? I need to avoid being vulnerable to SQL injection in my ASP.NET application. How might I accomplish this? Three-columns text with figures of 2\columnwidth Looking for old book, SF, artificial world, different zones for different species that visitors "inhabit" I read this book at least ten years ago.  Any help identifying it would be appreciated.  Characters are teleported to an artificial world where each take over the mind of a different species.  I remember a moving sentient plant, a faun-like character, and a wasp-like character.  The planet is subdivided into different zones designed for each species.  One of the characters had long sharp fingernails with poison in them.  Thanks for any help, steve