De-arrangement in permutation and combination
I have a problem understanding the proof of Rencontres numbers (Derangements)
Problem with sudo apt get update: The repository cdrom... does not have a Release file Every time I try update (using sudo apt-get update) my Ubuntu I get this problem:  W: The repository 'cdrom://Ubuntu 16.04 LTS _Xenial Xerus_ - Release amd64 (20160420.1) xenial Release' does not have a Release file. N: Data from such a repository can't be authenticated and is therefore potentially dangerous to use. N: See apt-secure(8) manpage for repository creation and user configuration details. W: The repository 'ppa.launchpad.net/kirillshkrogalev/ffmpeg-next/ubuntu xenial Release' does not have a Release file. N: Data from such a repository can't be authenticated and is therefore potentially dangerous to use. N: See apt-secure(8) manpage for repository creation and user configuration details. E: Failed to fetch cdrom://Ubuntu 16.04 LTS _Xenial Xerus_ - Release amd64 (20160420.1)/dists/xenial/main/binary-amd64/Packages  Please use apt-cdrom to make this CD-ROM recognized by APT. apt-get update cannot be used to add new CD-ROMs E: Failed to fetch cdrom://Ubuntu 16.04 LTS _Xenial Xerus_ - Release amd64 (20160420.1)/dists/xenial/main/binary-i386/Packages  Please use apt-cdrom to make this CD-ROM recognized by APT. apt-get update cannot be used to add new CD-ROMs E: Failed to fetch ppa.launchpad.net/kirillshkrogalev/ffmpeg-next/ubuntu/dists/xenial/main/binary-amd64/Packages  404  Not Found E: Failed to fetch ppa.launchpad.net/kirillshkrogalev/ffmpeg-next/ubuntu/dists/xenial/main/binary-i386/Packages  404  Not Found E: Some index files failed to download. They have been ignored, or old ones used instead.   How can I fix it? I use Ubuntu 16.04 LTS Getting full JS autocompletion under Sublime Text If I have the following enum:  public enum ReturnValue{     Success = 0,     FailReason1 = 1,     FailReason2 = 2     //Etc... }   Can I avoid casting when I return, like this:  public static int main(string[] args){     return (int)ReturnValue.Success; }   If not, why isn't an enum value treated as an int by default? How to install tzdata on a ubuntu docker image? I have the following line in the Dockerfile.  RUN apt-get install -y tzdata   When I run it, it asks for my input. After I provided my input, it hung there. Does anybody know how to solve this problem?  Step 25/25 : RUN apt-get install -y tzdata  ---&gt; Running in ee47a1beff84 Reading package lists... Building dependency tree... Reading state information... The following NEW packages will be installed:   tzdata 0 upgraded, 1 newly installed, 0 to remove and 0 not upgraded. Need to get 189 kB of archives. After this operation, 3104 kB of additional disk space will be used. Get:1 http://archive.ubuntu.com/ubuntu bionic-updates/main amd64 tzdata all 2018i-0ubuntu0.18.04 [189 kB] debconf: unable to initialize frontend: Dialog debconf: (TERM is not set, so the dialog frontend is not usable.) debconf: falling back to frontend: Readline debconf: unable to initialize frontend: Readline debconf: (This frontend requires a controlling tty.) debconf: falling back to frontend: Teletype dpkg-preconfigure: unable to re-open stdin:  Fetched 189 kB in 1s (219 kB/s) Selecting previously unselected package tzdata. (Reading database ... 25194 files and directories currently installed.) Preparing to unpack .../tzdata_2018i-0ubuntu0.18.04_all.deb ... Unpacking tzdata (2018i-0ubuntu0.18.04) ... Setting up tzdata (2018i-0ubuntu0.18.04) ... debconf: unable to initialize frontend: Dialog debconf: (TERM is not set, so the dialog frontend is not usable.) debconf: falling back to frontend: Readline Configuring tzdata ------------------  Please select the geographic area in which you live. Subsequent configuration questions will narrow this down by presenting a list of cities, representing the time zones in which they are located.    1. Africa      4. Australia  7. Atlantic  10. Pacific  13. Etc   2. America     5. Arctic     8. Europe    11. SystemV   3. Antarctica  6. Asia       9. Indian    12. US Geographic area: `` I want to find an example of a homomorphism $f:G\to H$ such that $A$ is a normal subgroup of $G,$ but $f(A)$ is not so in $H.$  I know that if $f$ was onto $f(A )$ must be normal , but otherwise i want to find an example! "FTL" Communication with Quantum Entanglement? Can quantum entanglement make sending a message, whether audio, video, or even Morse code, instantaneous between two points (faster than it could travel normally at the speed of light)?  Let me first be clear, my question is not whether a message can travel faster than light. I simply mean whether a message can be generated here and then a copy of that message heard over there sooner than the message would normally be received.  Say a large number of entangled pairs are generated. One half the particles are given to Jack and the opposite ones to Sally. Jack then hops on a ship and travels 8 months to Mars. Sally then manipulates her particles in the form of a message. Do the corresponding opposite particles get manipulated simultaneously so that Jack receives the message instantly instead of the 16 light-minutes for a classically transmitted message? Is it possible to embed a scrollable frame inside a PDF? (This is an end-of-year crazy question)   Is it possible to embed a (scrollable) frame or a PDF inside a PDF? If so, how to do it in (pdf)LaTeX?  This is something pretty common in HTML (see for example ). Here it is a webpage with PDF frames   Here it is a fake screenshot so you get the idea.  Portable and non-portable (e.g. only-Acrobat) answers are welcomed.     Example of a down arrow below a frame. The up arrow can be on top of the frame and the triangles point up. How to change color of the text in TextView on hover like in css? How to show hyperlink in LWC toast Is a Schengen visa/transit visa required for a transit flight through two Schengen airports? I am travelling form Delhi (DEL) to San Francisco (SFO), I have to make a connection flight in Vienna that would take me to Frankfurt (FRA). My flight to SFO is from FRA, I have one ticket for entire journey and the flights are operated by Lufthansa or its subsidiaries.  Do I need a transit visa? My flight arrives at Vienna international airport and leaves from the same, and for second leg it arrives at Frankfurt international airport.  I asked this question as an addendum to my  but was advised to make a new post.  I hold Indian passport and valid US visa. Is there a way to use Dvorak keyboard layout, but with command keys mapped to qwerty? How do I prompt for Yes/No/Cancel input in a Linux shell script? In what kind of rings a divisor of a product is a product of divisors? In a , if $a|bc$, then $a$ can be written as $a = a_1a_2$ so that $a_1|b$ and $a_2|c$.  Is this property of a commutative ring strictly weaker than the property of being a UFD?  If so, does it have a name, or is it equivalent to some other well-known property? Blank image when I render Use masks as part of materials in cycles Is there any performance reason to declare method parameters final in Java?  As in:  public void foo(int bar) { ... }   Versus:  public void foo(final int bar) { ... }   Assuming that bar is only read and never modified in foo(). Proof on showing if F(x,y,z)=0 then product of partial derivatives (evaluated at an assigned coordinate) is -1 The task is as follows:     Given: $$F(x,y,z) = 0$$    Goal:  Show    $\frac{\partial  z}{\partial y}|_x \frac{\partial  y}{\partial x}|_z \frac{\partial x}{\partial z} |_y = -1$   Here is my work so far:  (1) Differentiate with respect to y, I get:  $0 + F_2 + F_3  \frac{\partial z}{\partial y} = 0$  So $ F_3  \frac{\partial z}{\partial y} = - F_2$  (2) Differentiate with respect to x, I get:  $F_1 + F_2 \frac{\partial y}{\partial x}  + 0 = 0$  So $ F_2  \frac{\partial y}{\partial x} = - F_1$  (3) Differentiate with respect to z, I get:  $F_1  \frac{\partial x}{\partial z}    + 0  + F_3 = 0$  So $ F_1  \frac{\partial x}{\partial z} = - F_3$  (4) After some manipulations with the $F_i$, I get to the conclusion that $\frac{\partial z}{\partial y}* \frac{\partial y}{\partial x} * \frac{\partial x}{\partial z}  = -1$, so when evaluated with x, z, y respectively, conclusion is still true  My questions are:  (1) Is my proof correct?  (2) For example, when I differentiate with respect to y, I "let" $F_1$ be 0 and find partials for other coordinates.    I had a hard time trying to explain to my friend on the reason(s) why I can do such "let be 0" thing.  Although I think if I can't do that, then there is no way that I can reach the conclusion, but I somehow feel confused about the fact too.  Since my book is doing it that way, my understanding is that I can do such "let be 0" thing based on the independece of x with respect to y, when I differentiate with respect to y.  But is my thought ok?  Would someone please help me on this question? Thank you very much ^_^ We completed development on our dev environment and I copied the files over from the dev server to the production server through FTP.   Then through back up and migrade module, I made a back up of the SQL database. I created a new database through Plesk with the same name, username and password. I then imported the SQL database into the new server through phpmyadmin. I go to the URL and get the Site Maintenance message (which is correct, I placed the site in maintenance mode before copying the files over) but cannot navigate to any sub pages. Generally I can add /user or /admin to the end of the url and get the login screen. However all I get are 404 errors. How to make git mark a deleted and a new file as a file move? What do the .eh_frame and .eh_frame_hdr sections store, exactly?