Probability that no balls go in the right boxes
Number of permutations of $n$ elements where no number $i$ is in position $i$
How can I change the registered name in Windows 7 to my own? Inequality involving sides of a triangle How can one show that for triangles of sides $a,b,c$ that   $$\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b} &lt; 2$$  My proof is long winded, which is why I am posting the problem here.   Step 1: let $a=x+y$, $b=y+z$, $c=x+z$, and let $x+y+z=1$ to get   $\frac{1-x}{1+x}+\frac{1-y}{1+y}+\frac{1-z}{1+z}&lt;2$  Step 2: consider the function $f(x)=\frac{1-x}{1+x}$, and note that it is convex on the interval (0,1), so the minimum of   $\frac{1-x}{1+x}+\frac{1-y}{1+y}+\frac{1-z}{1+z}$  is reached when the function takes the extreme points. i.e. $x=y=0, z=1$.    But going back to the fact that this is a triangle, we note that $x=y=0 \implies a=0$ which is not possible, so the inequality is strict. Sum of $\sum \limits_{n=0}^{\infty} \frac{1}{(kn)!}$ Does a closed form exist for      $$\sum \limits_{n=0}^{\infty} \frac{1}{(kn)!}$$   in terms of $k$ and other functions? The best that I have been able to do is solve the case where $k=1$, since the sum is just the infinite series for $e$. I would guess that any closed form must involve the exponential function, but am at a loss to prove it. Do I need to activate the firewall? I only use Ubuntu for a home desktop use? I am a novice at Ubuntu (12.04).  I have it on my netbook which I use mainly for surfing the net, learning python and remote desktop into my work computer.    Do I need to enable a Firewall type software?  If so, what would you suggest, and what are sensible default suggestions? This is a  about Monitoring Software. Also Related:   I need to monitor my servers; what do I need to consider when deciding on a monitoring solution? Find Total number of ways out of N Number taking K numbers every M interval I have been stuck in a problem, that has thrown my brain out of the coding. This problem is at very high priority and I need the solution as early as possible. Problem is as :  There are exactly N advertising boards on the highway. Now a company want to advertise on some of these advertising boards(each advertising board costs some money) .  Company strategy is that, they want at least 'K' advertisement should be there among M consecutive advertising boards. But at the same time Company want to pay minimum for its advertisement .  Now, what is the total number of ways, different ways Company can advertise meeting its minimum cost strategy.  As for Example: N= 3, M = 2, K=1 ==> there is only one way for minimum cost, ie. 0C0 , where '0' denotes No company advertisement, and 'C' denotes company advertisement board.  Similarly, for N =4, M =2, K =1 ==> there is 3 possible ways, ie. C0C0, 0C0C, 0CC0.  Hope to get a reply from someone soon. Thanks. Is there a ".bashrc" equivalent file read by all shells? Is ~/.bashrc  the only place to specify user specific environment variables, aliases, modifications to PATH variable, etc?  I ask because it seems that ~/.bashrc seems to be bash-only, but other shells exist too… In Inno Setup is it possible to add conditional statements to what in the [Run] section gets executed? Alternatively is it possible to manually update the built in progress bar? Basically I have 2 MSIs included and using Inno Setup as a bootstrapper, and depending on user input one or both of the MSIs are to be installed.  I have something working using Exec statements in CurStepChanged but it doesn't update the progress bar as the files are extracted and it looks like the installer is stalled.  I guess the end result is I want some progress bar updates while the files are extracted to the temp folder.  The following is my current code:  procedure CurStepChanged(CurStep: TSetupStep); var     ResultCode: Integer; begin     if(CurStep = ssInstall) then begin         if(InstallServer) then begin             ExtractTemporaryFile('ServerSetup.msi');             Exec('msiexec',ExpandConstant('/i "{tmp}\ServerSetup.msi" /qb INSTALLDIR="{code:GetInstallPath}\Server\" ALLUSERS=2'),'', SW_SHOW, ewWaitUntilTerminated, ResultCode);         end;         if(InstallClient) then begin             ExtractTemporaryFile('ClientSetup.msi');             Exec('msiexec',ExpandConstant('/i "{tmp}\ClientSetup.msi" /qb INSTALLDIR="{code:GetInstallPath}\Client\" ALLUSERS=2'),'', SW_SHOW, ewWaitUntilTerminated, ResultCode);         end;     end; end; What should I opt for?   Option A) very well paid PhD, around €3000 per month at a respectable university or;  Option B) a non-paid PhD, where I have to pay €2000 per year at one of the top 10 universities of the world?  EDIT: Actually they are both UK universities, Option B  is ranked between the top 10 in the world in engineering and tech, and I do get a scholarship that pays 18000 pounds which covers the difference between international student tuition and EU tuition. In Option A, I will be doing research in a good university and will be working alongside giants in the industry. TikZ: remove margin, padding, border around nodes containing images Let $f: \mathbb{R} \to \mathbb{R}$ be continuous. Then $G = \{ (x, f(x) ) : x \in \mathbb{R} \} $ is a closed set.  My try: Suppose $(z_n) =  (x_n, f(x_n) ) $ is sequence in $G$ with limit $(x,y)$. We must show $(x,y) \in G$. Since $x_n \to x$ and since $f$ is continuous, then we must have that $f(x_n) \to f(x) $. Since limits are unique. Then $y = f(x) $. Is this enough to conlude that $(x,y) \in G $ ? Hence showing $G$ is closed ?  thanks How To: Execute command line in C#, get STD OUT results I have two directories that should contain the same files and have the same directory structure.  I think that something is missing in one of these directories.  Using the bash shell, is there a way to compare my directories and see if one of them is missing files that are present in the other? Combine or rebase an arbitrarily large number of commits What's the quickest Schengen consulate to issue a visa in London? In the movies, the pack of Uruk-Hai capture Merry and Pippin, and are bringing them back to Saruman as quickly as possible.  Why didn't they use Wargs to carry the Hobbits instead of packing them on their backs?    Or, better yet, why didn't the Nazgul fly down and take them on their Fell Beasts? I'm sure its a simple question and I suppose it was asked many times, but I just can't figure it out from other answers, sorry.  I use recent versions of PostgreSQL and MySQL. I have 2 tables:  CREATE TABLE authors (     id INT,     name VARCHAR )  CREATE TABLE posts (     id INT,     author_id INT,     text VARCHAR,     date DATE )   I need to select one most recent post for each author. Thanks!  UPDATE  Thanks, both links provide answers to my question with some exception. All the following queries give the same result (which one is the most efficient btw?) The issue is when there is more than one post from the same author with the same date. Then the returned result set contains all such posts. How should I modify these queries to return exactly one post per author?  SELECT p1.* FROM posts p1 LEFT JOIN posts p2 ON p1.author_id = p2.author_id AND p1.date &lt; p2.date WHERE p2.author_id IS NULL ORDER BY p1.author_id;  SELECT p1.*  FROM posts p1 INNER JOIN (   SELECT author_id, MAX(date) AS max_date   FROM posts   GROUP BY author_id) p2   ON p1.author_id = p2.author_id AND p1.date = p2.max_date ORDER BY p1.author_id;  SELECT * FROM posts p1 WHERE date = (SELECT MAX(p2.date)               FROM posts p2               WHERE p1.author_id = p2.author_id) ORDER BY author_id;  SELECT * FROM (     SELECT author_id, MAX(date) date     FROM posts GROUP BY author_id ) p1 INNER JOIN posts p2 USING (author_id, date) ORDER BY author_id; In a  question, an answerer says:  an empty bag is a bag with nothing inside it.  Makes sense, but I'm reading a textbook right now that says:  The empty set has only one subset (namely, itself).  Which seems odd to me. If a set is empty, why would it contain a subset? Regardless of whether or not the subset is also an empty set, the &quot;empty set&quot; still contains a subset, so how is it really &quot;empty&quot;? To go back to the empty bag analogy, it just sounds like my text book is saying:  an empty bag is a bag with nothing but an empty bag inside it.  Which doesn't make sense because then the bag isn't empty. I can't wrap my head around this concept. Outlier Detection on skewed Distributions Nvidia graphics card no longer works in Windows 10 (error: Code 43) but works in Ubuntu Currently, when I boot into Windows, one monitor stays black (undetected), and the other can only display 800x600 resolution.  When I look at Device Manager &gt; Display Adapters &gt; NVIDIA GeForce GTX 970 &gt; General &gt; Device Status, it says "Windows has stopped this device because it has reported problems. (Code 43)".  Details &gt; Problem Code says "00002b". Details &gt; Status says:  01802400 DN_HAS_PROBLEM DN_DISABLEABLE DN_NT_ENUMERATOR DN_NT_DRIVER   When I then click into the Events tab, it says "Device PCI\VEN_10DE&amp;DEV_13C2&amp;SUBSYS_29763842&amp;REV_A1\4&amp;25438c51&amp;0&amp;0008 requires further installation."  I have a EVGA Nvidia GeForce GTX 970 graphics card with the latest drivers (376.19 from 12/1/2016).  My Windows 10 Pro has the latest updates and is at Version 1607, OS Build 14393.576.  My ASRock Z170 Pro4 motherboard BIOS is also updated to the latest version (7.00 from 10/4/2016).  I have dual Acer monitors with 1920x1080 resolution.  I downloaded Ubuntu 16.04.1 LTS onto a bootable USB drive and booted into the Ubuntu operating system instead of Windows. Both monitors immediately worked at full 1920x1080 resolution. So the hardware seems functional! My remaining challenge is to figure out why my video card has stopped working within Windows.  What I Have Tried   I've tried using Display Driver Uninstaller from Guru3d in Safe Mode to delete all drivers and try to install fresh.   I've tried many different versions of the driver dating back more than 12 months. I've tried reseating the card. I've tried moving the card to a different slot. EVGA's phone support told me to reinstall windows (Windows &gt; Reset this PC &gt; Keep my files). Unfortunately, I followed their advice (and now don't have any of my programs), and I still get Code 43 with the EVGA Nvidia card.   What I Have NOT Tried   I would love to try installing this card onto a different Windows 10 computer to see what happens, but I don't have access to any other computers. If you live northeast of Atlanta, let me know. ;-)   I'd appreciate any other ideas you have!.