article talks about de-arrangement in permutation combination.     Funda 1: De-arrangement      If $n$ distinct items are arranged in a row, then the number of ways they can be rearranged such that none of them occupies its original position is,   $$n! \left(\frac{1}{0!} – \frac{1}{1!} + \frac{1}{2!} – \frac{1}{3!} + \cdots + (-1)^n \frac{1}{n!}\right).$$      Note: De-arrangement of 1 object is not possible.      $\mathrm{Dearr}(2) = 1$; $\mathrm{Dearr}(3) = 2$; $\mathrm{Dearr}(4) =12 – 4 + 1 = 9$; $\mathrm{Dearr}(5) = 60 – 20 + 5 – 1 = 44$.   I am not able to understand the logic behind the equation. I searched in the internet, but could not find any links to this particular topic.  Can anyone explain the logic behind this equation or point me to some link that does it ?
I understand the whole concept of Rencontres numbers but I can't understand how to prove this equation  $$D_{n,0}=\left[\frac{n!}{e}\right]$$  where $[\cdot]$ denotes the rounding function (i.e., $[x]$ is the integer nearest to $x$). This equation that I wrote comes from solving the following recursion, but I don't understand how exactly the author calculated this recursion.  $$\begin {align*}  D_{n+2,0} &amp; =(n+1)(D_{n+1,0}+D_{n,0}) \\ D_{0,0} &amp; = 1 \\ D_{1,0} &amp; = 0  \end {align*} $$
How to retrieve GET parameters from JavaScript How do I copy Team Fortress 2 to other computers? What is the difference between the Bash operators [[ vs [ vs ( vs ((? I am a little bit confused on what do these operators do differently when used in bash (brackets, double brackets, parenthesis and double parenthesis).  [[ , [ , ( , ((   I have seen people use them on if statements like this :  if [[condition]]  if [condition]  if ((condition))  if (condition) Say I have an embedded device which is only capable of doing HMAC-SHA1 transformations (that device is, in fact, a YubiKey).  Would it be secure to feed it like a block cipher in counter mode to get a random pad suitable as an stream cipher?  Of course, I'm talking about not repeating the counter value ever to encrypt data (so this construction would also need some random IV or treating the counter value as a nonce forever). Difference between a Structure and a Union Is there any good example to give the difference between a struct and a union? Basically I know that struct uses all the memory of its member and union uses the largest members memory space. Is there any other OS level difference? Dual monitors not working with an Nvidia card Even my main monitor is shown as unknown. I have tried setting up dual monitors using Nvidia settings with no joy however it does recognize that I have 2 monitors.  This was not an issue in 11.04. My problem with the Nvidia settings appears to be that my 2 monitors require different resolutions but even when I set them to a resolution that they both can handle, it is then only appearing in cloned mode. I really hope someone can help or I will have to roll back to 11.04.  Why won't Ubuntu 11.10 recognize that I have 2 Monitors?   Here is the contents of my xorg.conf:  # nvidia-settings: X configuration file generated by nvidia-settings # nvidia-settings:  version 280.13  (buildd@rothera)  Thu Aug 11 17:28:49 UTC 2011  Section "ServerLayout"     Identifier     "Layout0"     Screen      0  "Screen0" 0 0     InputDevice    "Keyboard0" "CoreKeyboard"     InputDevice    "Mouse0" "CorePointer"     Option         "Xinerama" "0" EndSection  Section "Files" EndSection  Section "InputDevice"     # generated from default     Identifier     "Mouse0"     Driver         "mouse"     Option         "Protocol" "auto"     Option         "Device" "/dev/psaux"     Option         "Emulate3Buttons" "no"     Option         "ZAxisMapping" "4 5" EndSection  Section "InputDevice"     # generated from default     Identifier     "Keyboard0"     Driver         "kbd" EndSection  Section "Monitor"     # HorizSync source: xconfig, VertRefresh source: xconfig     Identifier     "Monitor0"     VendorName     "Unknown"     ModelName      "CRT-0"     HorizSync       30.0 - 83.0     VertRefresh     50.0 - 76.0     Option         "DPMS" EndSection  Section "Device"     Identifier     "Device0"     Driver         "nvidia"     VendorName     "NVIDIA Corporation"     BoardName      "GeForce 7025 / nForce 630a" EndSection  Section "Screen"     Identifier     "Screen0"     Device         "Device0"     Monitor        "Monitor0"     DefaultDepth    24     Option         "TwinView" "1"     Option         "TwinViewXineramaInfoOrder" "CRT-0"     Option         "metamodes" "CRT: 1280x1024 +1024+0, DFP: 1024x768 +0+0"     SubSection     "Display"         Depth       24     EndSubSection EndSection"   ok I have tried disper -e. Problem is that Nvidia settings appear to be treating both monitors as the same one. so changing the settings to one has no effect, but change the other and it affects both screens identically.  Results of disper -l as follows:      carter@carter-desktop:~$ disper -l display DFP-0: HP vs17  resolutions: 320x240, 400x300, 416x312, 512x384, 576x432, 680x384, 640x480, 720x450, 640x512, 800x512, 840x525, 800x600, 960x540, 832x624, 960x600, 896x672, 1024x768, 1152x864, 1280x960, 1280x1024 display CRT-0: CRT-0  resolutions: 320x240, 400x300, 416x312, 512x384, 576x432, 680x384, 640x480, 720x450, 640x512, 800x512, 840x525, 800x600, 960x540, 832x624, 960x600, 896x672, 1024x768, 1152x864, 1360x768, 1280x960, 1440x900, 1280x1024, 1400x1050, 1600x1024, 1680x1050, 1600x1200, 1920x1080, 1920x1200, 1792x1344 carter@carter-desktop:~$ How to identify hardware performance bottleneck in laptop? Is there any tool that helps to determine the weakest link of my current laptop hardware specification? Any online guide to help me choose nice balanced configuration for the new laptop?    I need to find the answers:  a) which component should be invested to increase overall performance the most? CPU? GPU? RAM?  b) which component may decrease overall performance and work as a bottleneck for the specific configuration?    The question is general and regards both to validating the current hardware usage (and its possible bottlenecks) and estimating the performance (and avoiding possible issues) of specs I'm going to choose and buy.    P.S. For the specific laptop I need to replace, the following software will be in use:    Windows antivirus, firewall, dropbox service running in the background mail app + web browser with a dozen or so tabs open from time to time: libreoffice apps, movies, games (both online and installed). There are no compact minimal surfaces This is one of the exercises of 'Do Carmo' (Section 3.5, 12)     How do you prove that there are no compact (i.e., bounded and closed in $\mathbb{R}^3$) minimal surfaces?   Thanks! My adoptable storage is full. How can I move the data to a bigger MicroSD card? I've got a Moto G 2014 LTE running CM13. When I found out about the whole 'adopt SD card as internal storage' thing, I was quite excited, as the actual internal storage on this phone is tiny. I set up a 16gb micro SD, the biggest I had at the time, and have been using it with minimal problems.  Fast-forward to this day, and I now have a 64gb micro SD that I want to use instead of the 16gb one. However, I'm at a loss as to the best way to copy the data over onto the new one, or if it's even possible. The ideas I've got so far include:   Titanium Backup all [system] apps, factory reset, format new SD and then restore (should work, but a massive pain) NANDroid the SD card onto a USB OTG stick, then restore to the new one (pretty sure this is a bad idea and won't work, but...) Copy all the stuff onto my computer via my phone through a file manager of some sort (I have a linux/linux/windows triple boot, so file format isn't a problem), format the new SD into phone, and copy back (can't be that simple, can it? Hidden/inaccessible files?) Copy the files onto USB OTG with a root file explorer app, reformat the SD as portable, format the new one as adopted, and then copy them back (could work, except for the point below)  with the command adb shell sm set-force-adoptable true, use a root browser to copy all the data over from the old SD, format the old SD as external and remove it, and take the new SD and put it in the SD card slot (seems overly complicated, and also suffers the below pitfall)   The other thing that worries me is mount points: will the apps with externally-stored data know to look at the new SD card for it? Will I have to remount it in a specific location with the shell each boot (or use an init.d script perhaps)? I suppose that it can always be accessed through /sdcard or /storage/emulated/0, but I'm not 100% sure what goes on behind the scenes.  I've got recent NANDroid backups, so if anyone can eliminate the options that definitely won't work (or say which one[s] probably will), I can try them and report back in case someone stumbles across this question in the future.  EDIT: So, my phone further bit the dust and got to the point where it got into a pretty major bootloop. Ended up having to flash a whole new ROM. As such, I probably won't be able to test the full image/decryption/etc. method that I was originally planning. However, I will write up what I've discovered so far in case anyone wants to take up this particular method in the future:   Image the old SD with dd as follows: sudo dd if=/dev/mmcblk0 of=~/SDCardBackup.img, where /dev/mmcblk0 is the location of the sd card as obtainable through lsblk Restore the image you just made to the NEW sd card : sudo dd bs=4M if=~/SDCardBackup.img of=/dev/mmcblk0 (you may have to unmount it first) From here on in, I was following  (thanks @beeshyams!) tutorial, which explains the next steps way better than I ever could have done. The plan was to decrypt the storage and resize the main partition with gparted. I had no idea whether it would work or not, but I felt it was worth a try. However, when I came to run the actual decryption command using the key I'd extracted, I got an error (which I believe was my shoddy linux skills more than anything).   As I say, I have no idea if the above method would work or not even if everything did go to plan. Also, feel free to correct any of my commands above if I mis-typed them (I'm on Windows currently, so this is all from memory.) If this info helps anyone, then good. But until then,  should work fine.  Thanks, Jackdafish Is the .minecraft folder hidden on a Mac? I have a friend who is playing with me on a server we've created. Unfortunately, he is on a  Mac whereas I am on a Windows machine. I told him that I should be able to compile and send a .minecraft folder to him so that we can both play. Unfortunately, he can't find his .minecraft folder where it is supposed to be. Is it hidden and how can I unhide it? How can I change the default "ens33" network device to old "eth0" on Fedora 19? Another question I am struggling with:  Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be defined in a neighborhood of $a$ (except maybe $a$ itself) and suppose that, $\lim_{x \rightarrow a}\left(f(x)+\dfrac{1}{\left|f(x)\right|}\right)=0$. Find $\lim_{x \rightarrow a}f(x)$, and prove by definition, that this is indeed the limit.    Thank you all for your answers!!  But.. How can I prove by definition that this is indeed the limit? take $\epsilon&gt;0$, I have to show that there exists a $\delta&gt;0$ such that, $|x-a| \leq \delta$ implies $|f(x)+1| \leq \epsilon$. now, I do know that there exists an $\delta_1&gt;0$, such that $|f(x)+\frac{1}{|f(x)|}|&lt; \epsilon$.Or, $\frac{\epsilon}{k}$ for some constant $k$ But, how can I continue from there? Apex PMD: Problem: Validate CRUD permission before SOQL/DML operation Background   I am using the Apex PMD plugin for VS Code and it's giving me this problem:     Validate CRUD permission before SOQL/DML operation   For this line of code:  insert contentVersion;   Which is part of this method:  private void attachReport(Id recordId) {      ContentVersion contentVersion = new ContentVersion(         versionData = Blob.valueOf(buffer.toStr()),         title = 'Import Report',         pathOnClient =  StringUtils.format('/Import-Report-{0}.txt', DateTime.now().getTime()),         FirstPublishLocationId = recordId);      insert contentVersion; }   Questions    Why am I getting the problem? What should I do to not get the problem?     Reference Create backup iPhone with forgotten encryption password I'm trying to make a backup from my iPhone, however it's set to be password protected. I do not know the password, as I've never set one. I've tried all the passwords I know, which I've ever used to make sure I didn't set it.  I've also tried the default 0000 and 1234 codes.   I want to uncheck the encryption checkbox in iTunes, but it requires me to type a password. What else can I try?  I have no problems in removing all backups and start from the scratch somehow, however - I do not want to restore my phone as new and remove all those settings. What diagnostic plots (and perhaps formal tests) do you find most informative for regressions where the outcome is a count variable?  I'm especially interested in Poisson and negative binomial models, as well as zero-inflated and hurdle counterparts of each. Most of the sources I've found simply plot the residuals vs. fitted values without discussion of what these plots "should" look like.  Wisdom and references greatly appreciated. The back story on why I'm asking this, if it's relevant, is .  Related discussions: How to correctly add a path to PATH? I'm wondering where a new path has to be added to the PATH environment variable. I know this can be accomplished by editing .bashrc (for example), but it's not clear how to do this.  This way:  export PATH=~/opt/bin:$PATH   or this?    export PATH=$PATH:~/opt/bin Installing opencv I've downloaded opencv but unfortunately I've got no idea how to install it. All the pages I found online were only telling me how to download and install it directly from the console, not what to do when you already have it downloaded. Could anybody tell me what to do? Solve $f(x)f(2x^2) = f(2x^3+x)$ Pacman option to assume "yes" to every question? When installing software in debian systems we can put something like this:   sudo apt-get install -y chromium-browser  that way the installation occurs automatically, whitout asking to confirm installation [Y/n]. Can i do the same with pacman? I don't know which buttons I have to click or what key combination to type to calculate a cube root.