Is there a good summary of theorems to apply when deciding if a polynomial in $\mathbb{Q}[X]$ is irreducible, specifically one with positive integer coefficients?
Given a polynomial over a field, what are the methods to see it is irreducible? Only two comes to my mind now. First is Eisenstein criterion. Another is that if a polynomial is irreducible mod p then it is irreducible. Are there any others?
How does the radius of a pipe affect the rate of flow of fluid? Poiseuille's law states that the rate of flow of water is proportionate to $r^4$ where $r$ is the radius of the pipe. I don't see why.  Intuitively I would expect rate of flow of fluid to vary with $r^2$ as the volume of a cylinder varies with $r^2$ for a constant length. The volume that flows past a point is equal to rate of flow fluid, and thus it should vary with $r^2$.  I cannot understand the mathematical proof completely. Is there an intuitive explanation for this? A Putnam Integral $\int_2^4 \frac{\sqrt{\ln(9-x)}\,dx}{\sqrt{\ln(9-x)} + \sqrt{\ln(x+3)}}.$ This is a Putnam Problem that I have been trying to solve (on and off) for two years, but I have failed. I am in Calculus BC. This problem comes from the book "Calculus Eighth Edition by Larson, Hostetler, and Edwards". This problem is at the end of the first section of the chapter 8 exercises. Here's the problem:  Evaluate $$\int_2^4 \frac{\sqrt{\ln(9-x)}\,dx}{\sqrt{\ln(9-x)} + \sqrt{\ln(x+3)}}.$$  Please. Any help is very much appreciated. So are solutions. Thank you!  Edit: I like the solution given, but I was interested to see if there is any other way of doing the problem? I'm excited to see the results. I'm trying to install a Matlab R2011a launcher for Unity in Ubuntu 12.04. I've tried  (although I know it's for 11.10 and mentions that even 11.10 is an unsupported OS for Matlab R2011a) but without any satisfactory solution.  This is my launcher file, /usr/share/applications/matlab.desktop:  #!/usr/bin/env xdg-open [Desktop Entry] Type=Application Icon=/usr/share/icons/matlab.png Name=MATLAB R2011a Comment=Start MATLAB - The Language of Technical Computing Exec=matlab -desktop Categories=Development;   I open the dash panel and search for "matlab". This launcher is found among applications. I click it, and Matlab's splash screen shows up, but when it disappears the program doesn't start. (I've verified with htop that no matlab-processes are running in the background either.)  If I add  Terminal=true   to the launcher file, the program starts OK, and opens a terminal as well as Matlab. However, both the terminal and Matlab itself show up in the Launcher area, with the Matlab icon, so it looks like I have two Matlab instances running when really it's only one. (Actually, they show up as two different programs, and not just two instances of the same - the icons are independent, not grouped together.)  This is definitely not optimal. I had hoped to create a launcher I can lock to the launcher area, and then that same icon will be the icon for the active Matlab instance when the program is running.  How do I create a launcher for Matlab that works as expected?  Update: I was apparently a bit unclear on my symptoms, I'll try to clarify a little. I've also tried some suggestions from the answers, and further investigated what happens. My current setup (a launcher file with Terminal=true and Exec=matlab -desktop -nosplash &amp;) renders the following behavior:   I open Dash by pressing the Windows key on my laptop, and search for "matlab". It finds the launcher named "MATLAB R2011a". I click it. A terminal window opens, using the icon I referred to in the launcher file. Almost immediately, MATLAB's splash screen also opens, using the same icon (and thus being grouped with the terminal window in the launcher). The splash screen disappears and, so does one of the icons in the launcher. The MATLAB desktop environment opens, using a different version of the icon which is displayed next to the icon for the terminal window (not grouped with it).   I can lock the terminal window's icon to the launcher and successfully start MATLAB by clicking it, but it doesn't feel optimal that I start the program with one icon, and switch to it with another. I've also tried the following:   Exec without the ampersand &amp; in the launcher command, but it didn't make a difference. Executing matlab -nosplash manually from a terminal still shows the splash screen. (What, then, does the nosplash option really do?) Can I view a list of my "great comments", perhaps in my profile? I'm a little surprised no one asked this yet, but why isn't it possible to show your comments in descending order of "great comment" votes it has received? You can do this with upvotes on questions and answers, and since I think comments are the third major activity on SO, I'd like to view them. Even if you couldn't order them, it should at least show the number of votes on the activity#comments page of your profile... I have an internet connection that I'd like to be enabled only during the day. With multiple household internet devices, this would need to be something disabled at the level of the router.  I don't believe the router offers this sort of functionality, but I'm reasonably familiar with setting up web servers and the like, and I'm wondering if I can set up some sort of proxy server on the internet that the router must go through and have that proxy only active at certain times of day.  It's a bit vague I know, but is something like this even possible?  If not, are there other solutions to the problem? How does the eye perform the equivalent of white balance? Possible Duplicate:          How does the eye perform the equivalent of white balance? Why is the camera not able to replicate it? I'm using Microsoft Word 2010 and I worked in a word-2003 compatible document (.doc). After hours of working, I selected a half of text and did Ctrl+X to copy it into another document. Surprising, after closing the current document and opening a new one and pressing Ctrl+V, nothing happened. After closing original document, ms word asked me if I want to save the clipboard buffer and I pressed No, as I didn't knew that MS Word has it's own clipboard.  Is there a way to recover that text that was "cutten" from original document and never "pasted" to the new one? The PC was not rebooted so i guess all my temp files are here. This question is in response to . The original post mentioned that they wish to retract their paper from a "fake" journal. I don't know what a fake journal is but better safe than sorry so I want to make sure what defines a fake journal. In the comments, other people also mentioned "shady" journals and "predatory" journals. This is the first time I encounter these descriptions so I would like to know more about what they entail. I would be interested in hearing about your experience with such journals as well, if any. Checking if a key exists in a JavaScript object? mongodb $exists always returning 0 What is the strict aliasing rule? I have recently started using blender and one of the models I'm working on has dark shadows along edges. I started this model from scratch. I can't remember them being there when I first started the model, but I had trouble joining areas together and think I've pressed something I shouldn't have. However, there are so many options I'm not sure what I did.  Here is an image of what I mean   The one on the left has the shadow. As a test I started a new model, which is on the right in the image, and as you can see it doesn't have any shadows.  Also, occluded vertices partially show through the model. Occlusion doesn't work properly.   In orthogonal view small darkened triangles appear along the the edges.    I don't really want to start the model again from scratch so any ideas on how to remove this shadow would be great. Thanks. Is there a word for colloquial forms of address? For example, "dude," "man," "buddy," "pal," etc, when used to stand in for someone's name.  "Hey, pal, how's it going?"  Is there a word for terms like these?  Or is "colloquialism" as close as we can get? Smaug first appeared in TA 2770 as a mature Fire-drake. I'm not sure if there are canonical sources which say his age or maturity, but he must have been quite large and quite old at the time in order to destroy the city of Dale and capture Erebor.  Since it is safe to assume that Smaug would have been attacking towns and stealing all of the gold and jewels he could get his claws on for most of his life, then he must have amassed a huge fortune prior to taking residence at Erebor. How did he transport his existing horde to Erebor? It seems unlikely that he would have simply abandoned all of his treasure that he had previously accumulated.  EDIT: It has been established that Smaug was not a mature drake at the time of his appearance. However, he may have already had a small horde (compared to Erebor). I have been racking my brain to understand the solutions of constrained stars and bars problems like:  $a+b+c+d = 19$;  $a,b,c,d \in \{0,1,2,3,4,5,6,7\}$  Finding the total number of solutions is really simple $\dbinom{22}{3}$.   What to do after that? I want to understand the entire procedure step by step.   Please do not mark it as a duplicate of .  Reasons:   The accepted answer's trick doesn't always work.   Another person (the answer with two upvotes) has just listed out the binomial coefficients and I can't even remotely understand what he has tried to do.   The second answer isn't my cup of tea. Proving two entire functions are constant. Let $f$ and $g$ be entire functions such that $f^n+g^n=1$, where $n\geq 3$ is an integer. Prove that $f$ and $g$ are constant.  I suppose I should somehow prove that either $f$ or $g$ is bounded so that I can apply Liouville's Theorem, but I don't see how. I tried setting the derivative of the left hand side equal to zero and work with that but that did not seem to work. It seems that Mac OS X 10.6.1 Snow Leopard has a tendency to leave some windows off-screen at times, especially when I disconnect an external monitor from my MacBook. How can I move the window back on-screen when it's not possible to grab the title bar and drag it back onto the screen?   recommends adjusting your screen resolution downward to have off-screen windows "snap back into view" and then adjust your screen resolution back to its original setting. In OS X 10.4 Tiger, I had a script that brought all off-screen windows back on-screen, but in my upgrades to Leopard and now Snow Leopard, I don't seem to have that script.  Any better solutions out there? When do we still need the table and figure environments when we don't want the enclosed objects to float? The LaTeX Wikibook :     Please understand: you do not have to use floating tables. It only   looks more professional. If you want to place your tables where they   lie in your source code, do not use table at all! This is a very   common misunderstanding among newcomers.   LaTeX works with an intricate , but I often prefer immediate placement with the H placement specifier (enabled by the float package).  My understanding is that captions and table/figure numbering require the table/figure environments. Is this really so, or are there ways around that? What other reasons are there for using table/figure if we know that we don't want a particular object to float? There are many visa applicants who are working as an unregistered freelancer (photographer, construction contractor, fashion designer, journalist etc ). Some of these freelancers make really handsome monthly income and don't really need to work as a full time employee. Most of them receive variable amount of payments (cash, cheques, demand drafts etc) When it comes to filling a visa application form (USA, UK, Schengen etc), there is always an employment section in all visa form, eg for Schengen visa employment form :    This is a very important factor to make an application really strong.  Questions:   1 Unregistered freelancers can just simply write their profession? what documents to produce along with the application?  2 Bank statements with variable methods of payments could convince the visa officer that these are all legitimate payments? App Store asks for old Apple ID when installing updates I got a MacBook that a colleague of mine had used previously. It runs OS X 10.10.2. I created a new administrator account for myself and turned off the "admin" flag on the old account.  I also entered my iCloud / Apple ID account, so that it syncs my calendars and contacts correctly, and even in the App Store, I am signed in with my correct account.  But when I try to install pending software updates (that is, OS X system updates!), the window that pops up has the the e-mail address of my colleague filled in and greyed out—and I can't change it.     Note that I'm signed in with a different (correct) account in the App Store. When I go to Featured and click Account on the right, it has my correct e-mail address filled in:    How do I make the App Store "forget" the old Apple ID?  I  where it just says "it's not possible", and that apps are glued to the original account the Mac was set up with, but that doesn't make a lot of sense, especially in a company where laptops may be handed over from one person to another.