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Did the date of Frodo's rescue out of the fire of Mordor have any particular meaning in The Lord of the Rings? Did the date of Frodo's rescue out of the fire of Mordor have any particular meaning in The Lord of the Rings?  We read in The Return of the King (Book 6 Chapter 4) that Gandalf states to Frodo and Sam:     The fourteenth of the New Year, or if you like, the eighth day of April in the Shire reckoning. But in Gondor the New Year will always now begin on the twenty-fifth of March when Sauron fell, and when you were brought out of the fire to the King.   Did Tolkien have any particular reason for choosing this date for Sauron's fall and Frodo's rescue out of the fire of Mordor, either allegorically or otherwise?  We are aware that Tolkien was not a fan of , but preferred the term applicability instead. On any SE post one can use the backtick symbol ("`") in order to mark some text as being a piece of code, or computer output. For example: void main().  Is there a way to make use of "`" the same way in a LaTeX document? How to edit command line in full screen editor in ZSH? Is there a word for someone who somewhat delights in their illnesses/medications? Cut part from video file from start position to end position with FFmpeg I have a video file of 30 minutes, but I want to extract a video from 00:09:23 to 00:25:33.   I can define the startposition with -ss, but I couldn't find one for the end position. Any help please? Simple question but I am confused.  What is the boundary of $S^2\times\mathbb{R}$? Is it just $S^2$?  What would be the general way to evaluate the boundary of a product manifold?  Thanks for the replies! I am working on a proof about Dedekind cuts on the positive rational numbers. I have been stuck for a while on the following point and would appreciate any help.  Given $x\in \mathbb{Q}^+$ such that $x^2&lt;2$, how to find $y\in \mathbb{Q}^+$ such $y&gt;x$ and $y^2&lt;2$? How can I add motion to a rigid body? I'm trying to create a bowling animation and I want the ball to hit the pins. I already added the Rigid Body physics to the objects but can't get the ball to move.  Obviously I could just add keyframes but   that seems to interfere with the Rigid Body physics it doesn't look too realistic.   Is there a way to add some kind of motion to the ball? How to configure Jaybird with hibernate Application is "Ready to Sale" but not reflected on iTunes Store I'm at a loss with “Dungeons and Dragons.” How does one play it, anyway? I'm no gamer at all, so this could be like a very silly, basic question for you guys. The thing is that I always read about "Dungeons and Dragons" game (not the video game, but the normal game to play with friends that are actually gathered together). And I would like to know how to play it.  I've read that it is a book (or several ones, which is more confusing for me to understand), but I've read somewhere that it can be played as a normal "table" game, with a board, and pieces, and somewhat weird dice (or sets of dice).  Is it like a normal game, where you pull the stuff out of a box and start to play?  I don't know if any of you watch the show "The Big Bang Theory", but I think they have played the game in a recent episode, and it looks just like a regular game.  I've Googled it for more information, but I haven't found anything as basic as I need, because I've never played a role game (except in a video game).  I just want to learn how to play, so I can get my friends into it to play it each time we get together. What test can I use to compare slopes from two or more regression models? I would like to test the difference in response of two variables to one predictor. Here is a minimal reproducible example.   library(nlme)  ## gls is used in the application; lm would suffice for this example m.set &lt;- gls(Sepal.Length ~ Petal.Width, data = iris,                 subset = Species == "setosa") m.vir &lt;- gls(Sepal.Length ~ Petal.Width, data = iris,                 subset = Species == "virginica") m.ver &lt;- gls(Sepal.Length ~ Petal.Width, data = iris,                 subset = Species == "versicolor")   I can see that the slope coefficients are different:  m.set$coefficients (Intercept) Petal.Width    4.7771775   0.9301727 m.vir$coefficients (Intercept) Petal.Width    5.2694172   0.6508306  m.ver$coefficients (Intercept) Petal.Width     4.044640    1.426365    I have three questions:   How can I test the difference between slopes? How can I test the difference between residual variances? What is a simple, effective way to present these comparisons?    A related question, , suggests re-running the model with a dummy variable to differentiate the slopes, are there options that would allow the use of independent data sets? Help + Noun + Gerund or Infinitive Help my sister peel oranges. Help my sister to peel oranges. Help my sister peeling oranges.  Help my sister with peeling oranges.   Which of the above is/are correct, and why are the others incorrect? SWR surname that in fact describes or applies to the human in question? There are (in real life) many amazing examples of this (Bill Gates, "gates" being the fundament of computers, Tiger "Woods", the greatest ever user of "woods" golf-clubs, etc) and it is a staple of fiction.  Is there a single-word for this, or a frequently-used term?  Note that in fictional usage, I observe there is literal "X", so, for example I just saw a children's movie where "Madame Work" was a taskmaster. However, authors often employ near-literal "X": for example, most of the minor character surnames in Harry Potter are 'kind of" "X".  So, is there an "X" for Bill "Gates", Tiger "Woods", an undertaken named Mr. Death, etc?  Sorry if this has been asked already, I couldn't find it.    Note - I've just found there's a "wikipedia" page claiming 'aptonym' or 'euonym' is sometimes used.  Wikipedia is often valueless, so I do not know if this is a meaningful claim. Whenever I click on software updater it says Failed to download repository information.  It's been saying this for the past few days now and I don't know why, my Internet connection is fine, I am able to manually download software.  Sometimes it crashes when I click okay, then attempts to look for updates again and gives me the same message.  Any ideas?  [EDIT] I just tried an answer posted where I reset where the downloads come from, but I was left with this message:  W:The repository 'http://ppa.launchpad.net/noobslab/noobslab-conky/ubuntu xenial Release' does not have a Release file.,  W:Data from such a repository can't be authenticated and is therefore potentially dangerous to use.,  W:See apt-secure(8) manpage for repository creation and user configuration details.,  W:https://content.runescape.com/downloads/ubuntu/dists/trusty/InRelease: Signature by key AAC9264309E4D717441DB9527373B12CE03BEB4B uses weak digest algorithm (SHA1),  E:Failed to fetch http://ppa.launchpad.net/noobslab/noobslab-conky/ubuntu/dists/xenial/main/binary-amd64/Packages  404  Not Found,  E:Some index files failed to download. They have been ignored, or old ones used instead. How do I repair a corrupted Firefox places.sqlite database? I had some problems with my RAM (bluescreen several times, Windows XP) and now are my Firefox databases damaged. Firefox is working, but my history is gone and it's reporting several inconsistencies and errors when executing pragma integrity_check on places.sqlite:     database disk image is malformed   Now the question, how do I repair SQLite-Databases? I came across following problem     Evaluate $$\int\frac{1}{1+x^6} \,dx$$   When I asked my teacher for hint he said first evaluate     $$\int\frac{1}{1+x^4} \,dx$$   I've tried to factorize $1+x^6$ as  $$1+x^6=(x^2 + 1)(x^4 - x^2 + 1)$$ and then writing  $$I=\int\frac{1}{1+x^6} \,dx=\int\frac{1}{(x^2 + 1)(x^4 - x^2 + 1)} \,dx=\int\frac{1+x^2-x^2}{(x^2 + 1)(x^4 - x^2 + 1)} \,dx$$ $$I=\int\frac{1}{x^4 - x^2 + 1} \,dx-\int\frac{x^2}{(x^2 + 1)(x^4 - x^2 + 1)} \,dx$$  However $$x^4-x^2+1=\left(x^2-\frac12\right)^2+\frac{3}{4}$$ But I can't see how it helps  I've also tried to reverse engineer the   And I need to have terms similar to $$\frac{x^2-1}{x^4-x^2+1} \quad , \quad \frac{1}{1+x^2} \quad , \quad \frac{1}{(x+c)^2+1}\quad , \quad \frac{1}{(x+c)^2+1}$$ in integrand, How can I transform my cute looking integrand into these huge terms?  Since in exams I will neither have access to WA nor time to reverse engineer the solution moreover it does not seem intuitive,is there any way to solve this problem with some nice tricks or maybe substitutions? Division by $0$ I came up some definitions I have sort of difficulty to distinguish. In parentheses are my questions.   $\dfrac {x}{0}$ is Impossible (  If it's impossible it can't have neither infinite solutions or even one. Nevertheless, both $1.$ and $2.$ are divided by zero, but only $2. $ has infinite solutions so as $1.$ has none solution, how and why ?) $\dfrac {0}{0}$ is Undefined and has infinite solutions. (How come one be Undefined and yet has infinite solutions ?) $\dfrac {0}{x}$ and $x \ne 0$, it's okay for me, no problem, but if someone else wants to add something about it, feel free to do it. When does a reaction happen if the trigger is movement? Background - I am doing my PhD in atmospheric physics/photobiology.  Here is a scenario:   The experiments are complete - the results are far better than expected  Successfully got the computer program to work properly and have developed another Papers are published Much of the thesis is drafted   The light at the end of the tunnel is most definitely no longer an oncoming train.  But, at this stage, you just don't feel like working on the thesis, you do other things like cleaning, reading, watching movies - procrastination gets worse, and worse despite the submission deadline coming closer.     The procrastination resulting in more apathy towards the project, despite being fully aware of how much work has been put into the project, how much has been achieved and how little, comparatively, needs to be done.  What strategies are there to overcome this academic-apathy, particularly in this late stage of the thesis?