An old sci-fi story about an Earth ship orbiting Jupiter
Looking for title of sci fi short story about attempts to colonise planet (Venus?). Scientist and his dog are main characters
The successive difference of powers of integers leads to factorial of that power. Here's the formula:     $$\sum_{r=0}^{n}\binom{n}{r}(-1)^r(n-r)^n=n!$$   Can anyone give a proof of this result?  Note: The original question was to prove the more general     $$\sum_{r=0}^{n}\binom{n}{r}(-1)^r(l-r)^n=n!$$   for an integer $l$, which some of the answers address. How to prevent alt-f1 from selecting Dash Let $y$ be a differentiable function on $\mathbb{R}$. If  $$\lim_{x\rightarrow \infty}(y(x)+y'(x))=0$$ Then how does one show that $$\lim_{x\rightarrow \infty}y(x)=0$$ I'd appreciate some help on this problem. Thanks a lot. Strange Recurrence: What is it asymptotic to? So I have the following recurrence relation for the growth rate of an algorithm:  $T(n)$ = time taken by algorithm to solve problem of size n:  $$T(n) = T(n-1) + T(\lceil(n/2)\rceil)$$  Clearly this does not obey any polynomial law but now my question is what does it obey?  I merely want an asymptotic equivalence.  My guess is subexponential since this is faster than polynomial but clearly slower than any exponential form.  What though is the question.... Why is a stock that pays a dividend preferrable to one that doesn't? I understand that a dividend is a way for a company to return money to shareholders. But I'm not quite understanding why it is preferable to capital appreciation and putting the money to work increasing the earnings and revenue of the company. I get that people who buy stocks to get income from dividends, but the decrease in the price of a stock that correlates directly to the amount of the dividend seems to me like it's a zero-sum game.  Part of me thinks that I just fall into the Warren Buffet camp of thought that the money can be spent more wisely in house. But the other part feels like the desire for a dividend is to reinvest and add shares at a lower price (the price the stock goes to ex-dividend).   What am I missing here? How to make child collide How to install program to all user accounts in Windows? I have several accounts on my home PC. I want to install a program for all user accounts, not just the one I used to perform the installation. How do I go about doing this?  I installed a program from an admin account, but it doesn't show up in the other local accounts.  I was not able to find any documentation on how to do this.  I have Windows 8.1, if that matters. What is syntax highlighting and how does it work? how to solve $\int_{-\infty}^\infty e^{-x^2-x{\tau}} \cdot x\ dx$? Crop jpeg into circular tikz node \documentclass[demo]{article} \usepackage{graphicx} \usepackage{tikz} \begin{document} \begin{tikzpicture} \node[circle,draw,inner sep=2cm]{\includegraphics{myimage.jpg}}; \end{tikzpicture} \end{document}   How do I modify the above code so that the included image is adapted to the circle shape and cropped of the exceeding parts?  I want to specify a shape (a circle) and then include an image respecting the given dimension and cropped. Searching by user id in Android app only shows questions, no answers I have a Samsung Galaxy S3. Android version 4.3  I downloaded the official StackExchange app today. I am not able to view post related to android tag from my profile. I tried refreshing also  Snap     Edit:  However i am able to see one post for the relevant from the drop down list    Edit 2:  I tried what Steven V suggested. However it's the same.    I tried for a different user its the same. Previous questions confirmed that Hex can last through multiple encounters (assuming my warlock's concentration doesn't get broken by a club to the head or the like) and at higher levels even through a short rest.   My question is how targeting Hex works when trying to keep it up for extended periods of time.   Can I just cast it on nothing and keep it up until a valid target presents itself or is an initial valid target required?   Then later, does changing the target of the Hex require that the original target is brought to 0 HP?   Once the initial target dies does the spell stay active even if I don't immediately choose a new target?  My suspicion from reading the spell is that it needs an initial target, but then from that point on I can just keep it up after that target dies until it either expires or a new target presents itself. Is this correct? If a company is bought by another company, does my stock rollover to the new company when it is combined with the new parent company? Test model coefficient (regression slope) against some value In R, when I have a (generalized) linear model (lm, glm, gls, glmm, ...), how can I test the coefficient (regression slope) against any other value than 0? In the summary of the model, t-test results of the coefficient are automatically reported, but only for comparison with 0. I want to compare it with another value.  I know I can use a trick with reparametrizing y ~ x as y - T*x ~ x, where T is the tested value, and run this reparametrized model, but I seek simpler solution, that would possibly work on the original model. Securing SSH server against bruteforcing I have a little SVN server, old dell optiplex running debian. I don't have that high demands on my server, because its just a little SVN server... but do want it to be secure.  I just renewed my server to a newer and better optiplex, and started looking a bit into the old server. I took it down after experiencing problems. When I check the logs, its full of brute-force attempts and somehow someone has succeeded to enter my machine. This person created some extra volume called "knarkgosse" with two dirs "root" and "swap1" or something.  Don't really know why and what they do, but sure do want to prevent this from happening again. I find this a bit strange though because I change my password ever few months or so, and the passwords are always random letters and numbers put together... not easy to brute-force.  I know I can prevent root from logging in, and use sudoers... and change the SSH port, but what more can I do?  So I have a few questions:   How can I prevent logging in for 5 minutes after X amount of incorrect tries. Or slow tries down after each incorrect try? Is there some kind of central blacklist which a server can connect to? A blacklist that keeps track of IP addresses that are "unsafe" and should never be granted access? What more can I do to apply safety to my server?   Like I said earlier, I am running Debian 5 with Apache (www-data user problem?), svn, mysql, php, phpmyadmin, hudson. It is on a home network with port forwarding on 80, 443, 8080, 8180, 23 and 22. Proof of lack of pure prime producing polynomials. I recently encountered this following proposition:  For every polynomial, there is some positive integer for which it is composite.  What is the most elementary proof of this? Can .exe and .msi files (Windows software) be installed in Ubuntu? Can I play Minecraft Java if I only buy the Windows 10 version I do not own Minecraft outside my PS4, I know I can't play either Windows 10 or Java with that purchase. However, my primary computer is Linux and only supports the Java edition, and its past the deadline to get a redeem code for Windows 10 edition if I purchase the Java Edition.    Can I purchase the Windows 10 edition and use that purchase to login and play on the Java edition? Loading OpenStreetMap data in QGIS? Is it possible to import comments into a chat room without the link appearing? Question: For an answer on a stack exchange site with say 8 comments, how can I / is it possible to import the comments into a chat room? Background: I was helping with a  and made several comments before I saw the link to auto-import comments into a chat room.  This was awesome by the way!! Note that the person who asked the question left a link to the chat room in a comment. I wanted to make a similar chat room  because I edited an answer which wasn't mine and added a paragraph.  I wanted to chat with the answer's author @JonHopkins to say, 'hey feel free to remove my edit -- just wanted to add my $0.02' -- especially as the stack exchange engines said not to add an additional answer.  HOWEVER, there was no link to auto-import the comments -- probably because I hadn't previously left one, but I'm not sure. So I ask here, Stack Exchange Gurus, could a static link be added to auto-import a series of comments into a chat session?