Is it possible for a planet to be made entirely of water (even it's core)?
Could there be a body of water the size of a planet?
Does it give higher quality to shoot in low-res mode in-camera, or to downsize high-res photos later? Suppose you want to store your photos at some lower resolution, let's say about ~1 MB large.  You own a camera able to make photos at 5 MPix and more.  And, you want to have the maximum quality at the smaller size.  Would it be better to make a photo at highest resolution and then resize it with PC software (with a good filter of course), or to directly set the camera to make photos at 2 MPix only? How did the Swooping Evil Venom infused rain affect the magical community? Which function (s) is(are) the k-th derivative of itself? As I attempted to solve for a function that is the $k$-th derivative of itself where $k$ is some natural number, and generalise the result, I realised it gets very hard to prove anything. For $k= 1$, apart from trivial corner cases, it's the exponential function with any constant multiplied.  For $k=2$, along with the exponential function and it's reciprocal, it works for their sum along with any mixture by constants multiplied...  For any $k$, I guessed it should be of the form $e^{x w}$ where w is the $k$-th root of unity. And we can add all these $k$ terms for each root with constants multiplied.  While it is easy to verify it's satisfying the condition, it is beyond my scope to prove this is the only family of functions that satisfy it.  I am hoping for some interesting math at work here, and want to know if this is an already established fact. Also, how do I prove anything here? Good methods for density plots of non-negative variables in R? plot(density(rexp(100))   Obviously all density to the left of zero represents bias.  I'm looking to summarize some data for non-statisticians, and I want to avoid questions about why non-negative data has density to the left of zero.  The plots are for randomization checking; I want to show the distributions of variables by treatment and control groups. The distributions are often exponential-ish.  Histograms are tricky for various reasons.    A quick google search gives me work by statisticians on non-negative kernels, e.g.:  .    But has any of it been implemented in R?  Of implemented methods, are any of them "best" in some way for descriptive statistics?  EDIT:  even if the from command can solve my current problem, it'd be nice to know whether anyone has implemented kernels based on literature on non-negative density estimation Use LaTeX to simulate old typewriter written texts This question led to a new package:      I'm giving my students an old exam and barely remembered to change the date at the top. A colleague and I joked about how long we could reuse the same exam, and it made me wonder if I could use LaTeX to create an exam that looked like it was written in 1963 on a typewriter.  Here's what I'd like to see:   Typewriter font even in math mode. (Several ways to accomplish this; is there a "best" way?) Slight inconsistencies in the printing of each letter. I attempt this below adapting code taken from . Each word has a random vertical shift, though I'd like to see it reduced to each letter having its own vertical shift. Other typewriter-like irregularities would be great. It would be great if math-mode delimeters \left(, \right}, etc., can be created in a piece-meal fashion as they did in days of old. Fraction bars, tops of square-root symbols -- any horizontal line, really -- is made up of a series of en-dashes that don't quite match up.   Here is what I've come up with so far:  \documentclass[10pt]{article}% This is a document class providing more font size options \usepackage{graphicx} \usepackage{ifthen} \usepackage[textwidth=7.5in,textheight=9.5in]{geometry} \pagestyle{empty}  % thanks to Bruno Le Floch: https://tex.stackexchange.com/q/9331/4012 % and in his comments to https://tex.stackexchange.com/a/29458/4012 \usepackage[first=-1,last=1]{lcg}% you can play around with these values \makeatletter \newcommand{\globalrand}{\rand\global\cr@nd\cr@nd} \makeatother  \newcommand{\randomvshift}[1]{\globalrand\raisebox{\value{rand}pt}{#1}}  %%% thanks to Martin Scharrer: https://tex.stackexchange.com/q/11598/4012 \makeatletter \def\typewriter#1{%     \@typewriter#1 \@empty } \def\@typewriter#1 #2{%    \randomvshift{#1}\space    \ifx #2\@empty\else     \expandafter\@typewriter    \fi    #2% } \makeatother \begin{document}\tt  \typewriter{Math 101 Fall 1963}  \begin{enumerate} \item   \typewriter{$\frac{\texttt{d}}{\texttt{dx}}\texttt{(x)}^2$}  \item \typewriter{State the Fundamental Theorem of Calculus.}  \end{enumerate}  \end{document} The photon sphere is a spherical region in space where photons are forced to travel in an orbit at $r = \frac{3GM}{c^{2}}$.   Is it possible to detect these spheres?  What happens if I fall through it? What happens to a photon that tangentially hits the event horizon, wouldn't this also lead to a photon orbiting the black hole? EDIT Since neutron stars also might have a , do we know neutron stars that should have such a sphere? E: Could not get lock /var/lib/dpkg/lock-frontend - open (11: Resource temporarily unavailable) The question  only deals with flights in the US sourced from the  . Is there some similar source for EU, Asia etc? Delete all lines in Notepad++ except lines containing a word I need? Disabling middle mouse button Solution check: Let $f_n$ be fibonacci numbers. Prove: $\sum_{k=0}^{n-1} \binom{n+k}{2k+1} = f_{2n-1}$ and $\sum_{k=0}^n \binom{n+k}{2k} = f_{2n}$ Is there an official Marvel Cinematic Universe viewing order? I'm planning on re-watching the currently-released 5 Marvel films prior to seeing The Avengers.  Have Marvel released any sort of official viewing order?  Captain America: The First Avenger seems like the hardest one for me to place in order with the rest.  It takes place prior to the other films, but has the greatest number of references to the other films.  So should it be watched first, or last?  The rest of them are relatively clear, as they're chronological in the order they're released, with the possible exception of The Incredible Hulk and Iron Man 2 happening at the same time. How do I recover my Google account (or Gmail) password or username? I have forgotten the password or username for my Google account, or I'm unable to access my account for other reasons.  How can I recover my account?  (This Q&amp;A is meant as a general description for all Google and Gmail username/password questions. See: ) I recently found a formula to help find a sequence given a generating function:  $(\frac{1}{1-x})^k=\sum_{n=0}^{\infty}\binom{n+k-1}{n}x^n, k \in \mathbb{N}$  I just wondered if there was a known proof for this, or if anyone knows of a way to prove it. Show "Insufficient Privileges" directly when clicking 'Edit' (override), not on 'Save' If a user clicks 'Edit' on an opportunity which he isn't allowed to edit, the "Insufficient Privileges" page directly appears. This is good. If a user clicks 'Edit' on a custom object (which has an edit override that points to a visualforce page), he first sees the form without problems, and the "Insufficient Privileges" page only appears when he tries to save it. This behaviour is misleading for the users, because they think they can manipulate the data and put effort into it, and only afterwards they realize that this wasn't possible after all.  An idea was to check at page load if the user has edit permissions and otherwise redirect him to the "Insufficient Privileges" page.  Might there be another way? Thanks! Is there a way to exclude other particle systems from the effects of a Wind effect? I have a scene with a number of particle systems. I'd like to have a separate wind effect for my main scene and another for an extra: an emitter + wind-effect to blow leaves into my scene. I can't find any way to exclude, so here I am. At the very worst, I can just render the main scene and then render the wind effect and composite it, but I figured I'd check first. Why didn't Harry die in the dark forest? Getting new files to inherit group permissions on Linux I am having a problem with permissions on a Linux server. I am used to BSD. When a directory is owned by a group the user who owns it isn't in such as www-data, files created in it will be owned by that group. This is important because I want files to be readable by the webserver (which I will not run as root) but so a user can still put new files in the directory. I can't put the users in www-data because then they can read every other users websites.   I want the webserver to read all websites, I want users to be able to change their own.  The permissions are set like this on the folders at the moment....  drwxr-x--- 3 john www-data 4096 Feb 17 21:27 john   It is standard behavior on BSD for permissions to work this way. How do I get Linux to do this? How many maximum CPUs does Ubuntu support by default? I'm an Egyptian citizen, who holds Schengen visa and stay permit in Italy. Can I go to UK for some days with my stay permit and Schengen visa?