Replacing colum with values from lookup table in R
How to do vlookup and fill down (like in Excel) in R?
Unbiased estimator for geometric distribution parameter p 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. Patching commands to remove surrounding whitespace I'm using the todonotes package to add little margin notes to my text, however writing  Hello\todo{test} World!   removes the interword space as is already pointed out in . So I tried  \pretocmd{\todo}{\@bsphack}{}{} \apptocmd{\todo}{\@esphack}{}{}   and this adds the interword space but simply outputs all parameters instead of passing them to \todo.  Full MWE:  \documentclass{article}  \usepackage{etoolbox} \usepackage{todonotes}  \makeatletter \pretocmd{\todo}{\@bsphack}{}{} \apptocmd{\todo}{\@esphack}{}{} \makeatother  \begin{document} Hello\todo{test} World! \end{document} I have to resit a calculus exam and for some reason set proofs were never my best friend...  Anyway, on a practice exam I encountered the following proof:  $$A\cap(B\cup C) = (A\cap B)\cup(A\cap C)$$  When I draw a Venn-diagram it seems quite obvious but I couldn't manage to write the proof down properly.  If someone could help me, that'd be great! How do I get the distinct/unique values in a column in Excel? If I have a column with values, and I want to find out what distinct values are in there (not how many - but the actual distinct values), how can I do that?  In SQL Server I would do something like   SELECT Distinct(MyColumn) FROM MyTable When I am at my desk and my laptop is in its docking station I want to ensure that it uses its wired connection and not my wireless network. I am hoping/guessing that the preference in connection is based on the order of the listed connections in the Network and Sharing Center. I could just switch the wireless off but I'd prefer to not have to go through the trouble. What is the difference between test set and validation set? I found this confusing when I use the neural network toolbox in Matlab. It divided the raw data set into three parts:   training set validation set test set   I notice in many training or learning algorithm, the data is often divided into 2 parts, the training set and the test set.  My questions are:   what is the difference between validation set and test set?  Is the validation set really specific to neural network? Or it is optional. To go further, is there a difference between validation and testing in context of machine learning? Error on Ubuntu boot up - "recovering journal" Trying to figure out what this means:    I got into the GRUB menu, chose Advanced Options, boot in recovery mode, login as root, and I did:  root@xps:~# sudo fsck -f / fsck from util-linux 2.27.1 e2fsck 1.42.13 (17-May-2015) /dev/nvme0n1p2 is mounted. e2fsck: Cannot continue, aborting.   Coincidentally, I am also seeing this fuzzy rainbow thing on the outside of desktop windows:    But now the machine won't even boot up at all. How do I recover the Facebook account password? I have forgotten my Facebook account password and also I have no access to the number which I use to log-in to Facebook account.   On this page (see the image below) they are asking for a government photo-ID to verify my account. The problem is that I don't have a driving license, voter ID card, passport etc. All I have is a school ID card but that hasn't worked for me. Is there any other way to recover my password? How to animate multiple lines I wonder what would be the best way of animating multiple 2 dimensional lines in blender.  Lets say I have lots of line, that are parallel and have some sort of rule, kind of like a PCB board with hundreds of circuits.  The starting frame would be when nothing is visible and during the animation the lines would slowly build up from nothing all the way to the end forming the finished lines.  I have a couple of ideas that might work, but all include heavy hand animation, like:   grease pencil animation, drawing them one by one, converting to curve, then build up modifier some dynamic paint hack   There maybe other more efficient methods that I don't know of and if so, please let me know. Fisher Information of a function of a parameter There are some .exe and .dll files belonging to some programs on my laptop which communicate with the internet without my permission (for self-update generally). I want to prevent those files one by one from accessing the internet. I don't want to install any external firewalls. I'm using Windows 7 Home Pro and if this can be done by Windows Firewall, it's OK. I took a look at Windows Firewall but couldn't find a setting to disable file access. Piping for loop output prevents local variable modification I'm trying to write a simple bash function that takes, as its arguments, a number of files and/or directories. It should:   Fully qualify the filenames. Sort them. Remove duplicates. Print all that actually exist. Return the number of non-existent files.   I have a script that almost does what I want, but falls down on the sorting. The return value of the script as it stands is correct, but the output is not (unsorted and duplicates). If I uncomment the | sort -u statement as indicated, the output is correct but the return value is always 0.  N.B. Simpler solutions to solve the problem are welcome but the question is really about why is this occurring in the code I have. That is, why does adding the pipe seemingly stop the script incrementing the variable r?  Here's the script:  function uniqfile {     local r=0       for arg in "$@"     do           readlink -e "$arg" || (( ++r ))      done #| sort -u    ## remove that comment      return $r } How to check if a string "StartsWith" another string? What is the formula for armor/magic resist reduction? As far as I can tell, it's something like this:  damage reduction = armor / (armor + 100)   Is this accurate? What's the easiest way to set up a LAMP stack? I set up a new VPS instance of Ubuntu and am wondering what the easiest way is to get up and running with a basic LAMP stack (i.e. which packages are required, which configuration options need to be tweaked, if any, etc.). How to troubleshoot unwanted white spaces smartly? If $11z^{10}+10iz^9+10iz-11 = 0$. Then possible value of $\mid z \mid,$ is If $11z^{10}+10iz^9+10iz-11 = 0$. Then possible value of $\mid z \mid,$ is  $\bf{My\; Try::}$ Given $11z^{10}+10iz^9+10iz-11 = 0\Rightarrow \displaystyle z^9 = \frac{11-10iz}{11z+10i}.$  Now Put $z = x+iy\;,$ we get $\displaystyle (x+iy)^9 = \frac{11-10i(x+iy)}{11(x+iy)+10i} = \frac{(11+10y)-10ix}{11x+i(10+11y)}$  Now i did not understand how can i solve it,  Help Required  Thanks I would like footnote numbering to continue over pages and chapters. In my document it's reset every chapter. I'm using the report documentclass. I am having trouble with the following sentence:      "The complexity and diversity of the new platforms is worrying us."   If "complexity" and "diversity" constitute two subjects, then the verb should presumably be "are"; however, the sentence feels more natural with "is". Is this correct? Is there a linguistic term for this occurrence?    The following questions address the general topic of compound subjects, but not specific cases like this:             And the following question seems to have somewhat inconclusive answers:         So this question is not really a duplicate of these three.