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How do you compute the earth's radius at a given geodetic latitude? R's lmer cheat sheet There's a lot of discussion going on on this forum about the proper way to specify various hierarchical models using lmer.  I thought it would be great to have all the information in one place. A couple of questions to start:   How to specify multiple levels, where one group is nested within the other: is it (1|group1:group2) or (1+group1|group2)? What's the difference between (~1 + ....) and (1 | ...) and (0 | ...) etc.? How to specify group-level interactions? Is an irrational number times a rational number always irrational?  If the rational number is zero, then the result will be rational. So can we conclude that in general, we can't decide, and it depends on the rational number? Windows 10 won't accept Firefox as the default browser How can I format to show text inside ""? I've posted a lot to StackOverflow, and I've noticed something kind of irritating with the formatting in writing questions and comments. If I need to put something inside a &lt; and a >, without spaces in the middle (like right there), it will think it's code and not show up, like this   (obviously it won't come up what I wrote there, or else this wouldn't be an issue, but if you open up the question to edit you can see what's written there.)  If I want it to show up, right now I have to add an extra set of brackets inside of the originals with a junk variable, like right &lt;here> (again, open in edit window to see).  This is really annoying when trying to show variables like lists that require those brackets, and I feel like the junk variables could confuse people looking at the edits. Is there a way to get around this formatting? Thanks! Run command whenever someone joins a Minecraft server Is there any way to run a command automatically when a player joins the server? I need to do this without the use of a Bukkit plugin. I think it's possible with MCP but I want to know how! Limit values of struct member How do I watch a file for changes? I have a log file being written by another process which I want to watch for changes. Each time a change occurs I'd like to read the new data in to do some processing on it.  What's the best way to do this? I was hoping there'd be some sort of hook from the PyWin32 library. I've found the win32file.FindNextChangeNotification function but have no idea how to ask it to watch a specific file.  If anyone's done anything like this I'd be really grateful to hear how...  [Edit] I should have mentioned that I was after a solution that doesn't require polling.  [Edit] Curses! It seems this doesn't work over a mapped network drive. I'm guessing windows doesn't 'hear' any updates to the file the way it does on a local disk. Script to remove certain span elements from an HTML file In many languages, including English, the most important verbs are irregular. Examples include:   to be  to do  to get  to go  to have  to make   The same applies (roughly) to many other languages I know about (Dutch, German, French, Spanish, Swedish) and presumably to many other languages too.  Is there any reason why these everyday verbs tend to be irregular? I have two Ubuntu Software Centers, one can be opened, another one can't Simplifying adjacent polygons using QGIS Simplify Geometries tool Gradient and Swiftest Ascent I want to understand intuitively why it is that the gradient gives the direction of steepest ascent. (I will consider the case of $f:\mathbb{R}^2\to\mathbb{R}$)  The standard proof is to note that the directional derivative is $$D_vf=v\cdot \nabla f=|\nabla f|\,\cos\theta$$ which is maximized at $\theta=0$. This is a good verification, but it doesn't really help me understand the result. Is the expression      All women who are mothers of daughters are here.   correct? I mean every woman who has at least one daughter is here. What's the keyboard shortcut for keyboard layout switch in Mojave? Shift + Control + Space doesn't seem to work anymore. Search for singleton tags on questions How prove that $q \geq b+d$ for $ad-bc = 1$ and $\frac{a}{b} > \frac{p}{q} > \frac{c}{d}$? Let $a,b,c,d,p$, and $q$ be natural numbers such that $ad-bc = 1$ and $\frac{a}{b} &gt; \frac{p}{q} &gt; \frac{c}{d}$.  How prove that  $q \geq b+d$? Send mail without MFMailComposeViewController From Wikipedia: Fermi was known for his ability to make good approximate calculations with little or no actual data, hence the name. One example is his estimate of the strength of the atomic bomb detonated at the Trinity test, based on the distance travelled by pieces of paper dropped from his hand during the blast. Fermi's estimate of 10 kilotons of TNT was remarkably close to the now-accepted value of around 20 kilotons, a difference of less than one order of magnitude.  I have not been able to find any references explaining how he made this calculation. Please provide a reference or an example calculation.  See also: How can I have  for Ubuntu?