In the "Gotchas" section of the  it's mentioned that performance issues could occur with highly fragmented files (vm images and databases). The solution for this is to disable copy-on-write for those files.      For a Debian installation, in what system directories should we also disable copy-on-write (mounting them in a nodatacow subvolume)?   edit To reduce the broadness of the question, assume it's a server with full allocation image VMs (log server, file server, for example). Also, operations like btrfs add/remove missing causes a lot of logging to occur in the host machine.  My question is, besides disabling copy-on-write for those "write active" VMs, is disabling it on the /var/log directory enough or are there other system directories/files that I could also do this from the start (like all of /var and /tmp as Stephen Harris suggested)? Or is it just a matter of starting somewhere, checking regularly for fragmented files and performance issues, and disabling the copy-on-write when needed?
The  recommends that images have Copy-On-Write disabled on the directory when using btfs.  I do see that it would be a good idea if you had a lot of file read/writes.   question explores this idea.  I know that VMWare will grow into different files and will write snapshots out which could be problematic when using Copy-On-Write.  For QEMU the file is left open for the VMs existance so there is a potential problem in the write after the VM is shutdown, but I would see slow I/O after a VM is shutdown not being an issue.  What pitfalls would I be avoiding by performing this step for QEMU.    Additionally: I have assumed that the image is raw for this question.  Is there a possible stability issue as qcow2 already has copy-on write.
I want to justificate following equation:  $$\sum_{k=0}^n \frac{(-1)^k}{k!(n-k)!}\frac{1}{2k+1} = \frac{2^n}{(2n+1)!!}$$  I calculated the both sides for $n$ from 1 to 10 and it was true. How the mathematical induction can be applied to this equation? Or is there other way to justificate it? Why are mutable structs “evil”? Following the discussions here on SO I already read several times the remark that mutable structs are “evil” (like in the answer to this ).  What's the actual problem with mutability and structs in C#? Suppose $f$ is an isometric (i.e., distance preserving) function on $\mathbb{E}^2$ such that $f(0,0) = (0,0)$.  Then I want to show that $f$ is necessarily linear.  Now $f$ is linear iff $f$ is both additive and homogenous.  The following is an attempted proof for the homogeneity of f (missing the last step); still more, I have no idea how to argue for the additivity of $f$.  Any ideas?  Let $x \in \mathbb{E}^2$ and $\alpha \in \mathbb{R}$   We know that $\forall x \in \mathbb{E}^2$, $\Vert x - 0 \Vert = \Vert f(x) - f(0)\Vert = \Vert f(x) - 0 \Vert$ so that $\Vert x\Vert = \Vert f(x)\Vert$.  From this we immediately have the following facts:  $\Vert x \Vert = \Vert f(x) \Vert$  $\Vert \alpha x \Vert = \Vert f(\alpha x) \Vert$  We can then argue that since $\Vert \alpha x\Vert = |\alpha| \Vert x \Vert = |\alpha| \Vert f(x) \Vert = \Vert \alpha f(x) \Vert$, we also have that $\Vert f(\alpha x) \Vert = \Vert \alpha f(x)\Vert$.  Finally, we have that  $\Vert \alpha x - x \Vert = \Vert \alpha f(x) - f(x) \Vert$   iff $ \Vert (\alpha - 1)x \Vert = \Vert (\alpha - 1) f(x) \Vert$   iff $|\alpha - 1| \Vert x \Vert = |\alpha - 1| \Vert f(x) \Vert$  Since the last of these statements is in fact true, we now have $\Vert \alpha x - x \Vert = \Vert \alpha f(x) - f(x) \Vert$ as desired.  Now at this point it seems like I have all of the facts required to assert that $f(\alpha x) = \alpha f(x)$, but I can't figure out how to formally state why without illegally appealing to visual intuition.  Any ideas? Is it worth encrypting email addresses in the database? I've heard that Lubuntu consumes less resources than Ubuntu. Is it because of the fact that Lubuntu uses different desktop environment and window manager?  If so, would it be equivalent to install lubuntu-desktop on top of Ubuntu rather than doing a fresh install? I have a Python script which takes as input a list of integers, which I need to work with four integers at a time.  Unfortunately, I don't have control of the input, or I'd have it passed in as a list of four-element tuples.  Currently, I'm iterating over it this way: for i in range(0, len(ints), 4):     # dummy op for example code     foo += ints[i] * ints[i + 1] + ints[i + 2] * ints[i + 3]  It looks a lot like &quot;C-think&quot;, though, which makes me suspect there's a more pythonic way of dealing with this situation.  The list is discarded after iterating, so it needn't be preserved.  Perhaps something like this would be better? while ints:     foo += ints[0] * ints[1] + ints[2] * ints[3]     ints[0:4] = []  Still doesn't quite &quot;feel&quot; right, though.  :-/ Related question: Let $P$ denote the quotient space obtained by the action of $\mathbb{Z}\backslash2\mathbb{Z}$ by the antipodal map $z\mapsto\frac{1}{z}$ on the riemann sphere $\hat{\mathbb{C}}$ (identified here with $\mathbb{C}\cup\left\{\infty\right\}$). I identify $P$ with the set:  $\left\{ z\in\mathbb{C}:\left|z\right|&lt;1\right\} \cup\left\{ e^{it}:0\leq t\leq\pi\right\} $   that is to say, I use elements of the above set as the representatives for the equivalence classes in $P$. I am looking for formula for a function $f:P\times P\rightarrow[0,\infty)$ such that $f$ is a metric on $P$. Specifically, I would like a formula for $f$ that I can evaluate by plugging in representative elements in the above set (or something like that, more or less).  Thanks in advance.  Edit: forgive me for sounding desperate, but I cannot make due with an explanation of how to obtain such a formula. I want the formula.   An analogy for you if I have yet to make myself clear: suppose I was asking for the area of a square with side length $s$. The answers I have received so far for my question are akin to saying "multiply $s$ by itself" or "use the area formula for a square". The answer I am looking for is akin to saying "$s^{2}$". I need the formula. And please, no expressions with differentials, nor matrices, or any of that. I need to know how to compute the metric by using the complex numbers in the indicated set that I have identified with $P$. I've seen a couple other questions with this error message but it seemed that the host and ip in question were ones the OP knew. These two are unrelated to my server.  Where and why is postfix generating this error?     Jul 24 17:42:14 email postfix/smtpd[32277]: warning: hostname kimtake.respectedopinion.com does not resolve to address 62.210.28.114   Jul 24 17:42:14 email postfix/smtpd[32277]: connect from unknown[62.210.28.114]   Jul 24 17:42:14 email postfix/smtpd[32277]: disconnect from unknown[62.210.28.114] Prove that 10101...10101 is NOT a prime. So basically we have a number $10101...10101$ that contains $2016$ zeros and can be written as$ \sum _{ k=0 }^{ 2016 }{ 100^{ k } }$ . I want to prove that this number is not a prime without using anything besides a piece of paper and a pen. I'm stuck on this for quite a few days now. New profile pages are out - bugs and feedback master list Update:  Thanks for all the feedback and bug reports! I am locking this thread so people don't keep answering it when we no longer monitor it.  If you see a bug or want to raise a feature request, please do so in the usual manner, as a new question.    Some of you may have noticed that  the  and  pages that we have been talking about for a while now on .  Most? Well, yes, the new design is dependent on a SE network-wide update (a new base css framework) that the design team have been working on. This is an ongoing effort and we will be launching the new pages as sites are moved to the new design.  You've all been hugely helpful already - much of what we love most in here came from  and  you gave us on Meta.     But it's possible that it's not quite perfect yet. If you find any bugs and have any feedback to give, please post these as answers to this post.  Just post one issue per answer - that would help us focus on specific items one at a time. Ok, see the word "conscious" has the IPA /ˈkɑːnʃəs/ in the   However, when you listen clearly, you will feel like it should be /ˈkɑːntʃəs/ not /ˈkɑːnʃəs/.  So it should read /tʃ/ rather than /ʃ/.  In some other dictionaries, which use different transcription systems, they give the entry "ˈkän(t)-shəs" , for example in the . Here we see it with a /t/.  So, should the IPA for the word "conscious" be /ˈkɑːnʃəs/ or /ˈkɑːntʃəs/? I bought a new MacBook Air and was able to connect to the internet at first but now it won't connect.  I have other devices as well as other computers on wifi but my Mac won't connect.  When I try and click on the wifi, it tells me that it can't be joined.  How can I troubleshoot? I need to extrude a circular shape from a surface that's basically just a grid of quads. What's the best practice to do this without screwing up the topology too much?  I basically want to have a circular face I can extrude, in order to have a cylinder like protuberance on the object, something like this: Why didn't Dumbledore prevent the prosecution of Sirius Black? Dumbledore performed the Fidelius charm on the Potters, so he knew who the Secret-Keeper was1. That implies he knew not Sirius but Wormtail betrayed the Potters. Why didn't he prevent Sirius's conviction and suspect the explosion killing twelve Muggles was caused by Wormtail (and that Sirius cornered Wormtail instead of the other way around)?   1: Though in  it is said Dumbledore didn't know. I find it hard to believe the person casting the Fidelius charm doesn't know who the Secret-Keeper is. Do film industries outside India use intervals/Intermission? A hidden process, what it is? [root@datacenteronline ~]# ssh root@192.168.1.172 Last login: Wed Apr 17 09:55:45 2013 from 192.168.1.187 [root@localhost ~]# ls /proc/ | grep 2266 [root@localhost ~]# cd /proc/2266 [root@localhost 2266]# ls attr             cpuset   limits      net            root       statm autogroup        cwd      loginuid    numa_maps      sched      status auxv             environ  maps        oom_adj        schedstat  syscall cgroup           exe      mem         oom_score      sessionid  task clear_refs       fd       mountinfo   oom_score_adj  smaps      wchan cmdline          fdinfo   mounts      pagemap        stack coredump_filter  io       mountstats  personality    stat [root@localhost 2266]# ls -al /proc/2266 total 0 dr-xr-xr-x   7 apache apache 0 Apr 17 09:45 . dr-xr-xr-x 266 root   root   0 Apr 17 09:11 .. dr-xr-xr-x   2 apache apache 0 Apr 17 09:45 attr -rw-r--r--   1 root   root   0 Apr 17 09:45 autogroup -r--------   1 root   root   0 Apr 17 09:45 auxv -r--r--r--   1 root   root   0 Apr 17 09:45 cgroup --w-------   1 root   root   0 Apr 17 09:45 clear_refs -r--r--r--   1 root   root   0 Apr 17 09:45 cmdline -rw-r--r--   1 root   root   0 Apr 17 09:45 coredump_filter -r--r--r--   1 root   root   0 Apr 17 09:45 cpuset lrwxrwxrwx   1 root   root   0 Apr 17 09:45 cwd -&gt; / -r--------   1 root   root   0 Apr 17 09:45 environ lrwxrwxrwx   1 root   root   0 Apr 17 09:45 exe -&gt; /usr/local/apache2/bin/httpd dr-x------   2 root   root   0 Apr 17 09:45 fd dr-x------   2 root   root   0 Apr 17 09:45 fdinfo -r--------   1 root   root   0 Apr 17 09:45 io -rw-------   1 root   root   0 Apr 17 09:45 limits -rw-r--r--   1 root   root   0 Apr 17 09:45 loginuid -r--r--r--   1 root   root   0 Apr 17 09:45 maps -rw-------   1 root   root   0 Apr 17 09:45 mem -r--r--r--   1 root   root   0 Apr 17 09:45 mountinfo -r--r--r--   1 root   root   0 Apr 17 09:45 mounts -r--------   1 root   root   0 Apr 17 09:45 mountstats dr-xr-xr-x   6 apache apache 0 Apr 17 09:45 net -r--r--r--   1 root   root   0 Apr 17 09:45 numa_maps -rw-r--r--   1 root   root   0 Apr 17 09:45 oom_adj -r--r--r--   1 root   root   0 Apr 17 09:45 oom_score -rw-r--r--   1 root   root   0 Apr 17 09:45 oom_score_adj -r--r--r--   1 root   root   0 Apr 17 09:45 pagemap -r--r--r--   1 root   root   0 Apr 17 09:45 personality lrwxrwxrwx   1 root   root   0 Apr 17 09:45 root -&gt; / -rw-r--r--   1 root   root   0 Apr 17 09:45 sched -r--r--r--   1 root   root   0 Apr 17 09:45 schedstat -r--r--r--   1 root   root   0 Apr 17 09:45 sessionid -r--r--r--   1 root   root   0 Apr 17 09:45 smaps -r--r--r--   1 root   root   0 Apr 17 09:45 stack -r--r--r--   1 root   root   0 Apr 17 09:45 stat -r--r--r--   1 root   root   0 Apr 17 09:45 statm -r--r--r--   1 root   root   0 Apr 17 09:45 status -r--r--r--   1 root   root   0 Apr 17 09:45 syscall dr-xr-xr-x  29 apache apache 0 Apr 17 09:45 task -r--r--r--   1 root   root   0 Apr 17 09:45 wchan   Cound anyone tell me what it is? Following discussion , what constitutes a weapon damage die?  Is it any damage die dealt by the weapon? For example, consider a  longsword.     While the sword is ablaze, it deals an extra 2d6 fire damage to any target it hits.   What are the weapon damage dice? Just the 1d8 from the longsword? Or do the 2d6 Fire damage also count? I'm a bit annoyed with the typesetting of citations that biblatex deems "ambiguous". In the following example, I have two papers with the same first author, but a different second author in two different years. When citing in the main text, the second author is included before "et al", since biblatex deems these references to be ambiguous. However, the references were published in different years, so I cannot see why these are ambiguous. Is it possible to get these citations referenced using only the first author?  MWE  \documentclass{article}  \usepackage{filecontents} \usepackage[hyperref,style=authoryear,natbib=true,maxbibnames=10,maxcitenames=2,useeditor=false,url=false,useprefix,giveninits=false]{biblatex} \addbibresource{ref.bib}  \begin{filecontents}{jobname.bib} @book{author_book, title = {Book's title}, author = {Author, Some and Better, Some and Cetter, Some}, location = {The City}, publisher = {Publisher}, date = {2005}, } @book{author_book2, title = {Book's title}, author = {Author, Some and Getter, Some and Cetter, Some}, location = {The City}, publisher = {Publisher}, date = {2006}, } \end{filecontents}  \bibliography{jobname} % \bibliography{ref}  \begin{document} Hello world \citet{author_book} \citet{author_book2} \printbibliography \end{document} Quotient ring of a localization of a ring Let $A$ be a commutative ring. Let $P$ be a prime ideal of $A$. Let $I$ be an ideal of $A$ such that $I \subset P$. Let $\bar A = A/I$. Let $\bar P = P/I$. Is $\bar A_{\bar P}$ isomorphic to $A_P/IA_P$? Filling HTML  dropdown list in JSP with values fetched from database in Servlet