Prove that orbits are conic sections
Derivation of Kepler's laws
Every retraction is a quotient map? I have to proof that every retraction is a quotient map.. I have no idea where to start or what to use! A retraction $r:X \rightarrow A$  is a continuous map s.t. $r(a)=a$ for every $a\in A$. If I have a legendary creature out, and I make a copy of it (such as by enchanting it with  or making a ), do I get enters-the-battlefield effects from the creature before I have to sacrifice it to the legend rule? The characteristic and minimal polynomial of a companion matrix of a monic polynomial $f \in \mathbb F\left[x\right]$ in $1$ variable $x$ over a field $\mathbb F$ plays an important role in understanding the structure of finite dimensional $\mathbb F[x]$-modules.  It is an important fact that the characteristic polynomial and the minimal polynomial of $C(f)$ are both equal to $f$. This can be seen quite easily by induction on the degree of $f$.  Does anyone know a different proof of this fact? I would love to see a graph theoretic proof or a non inductive algebraic proof, but I would be happy with anything that makes it seem like more than a coincidence! Evaluating limit (iterated sine function) The limit is   $$\lim_{x\rightarrow0} \frac{x-\sin_n(x)}{x^3},$$  where $\sin_n(x)$ is the $\sin(x)$ function composed with itself $n$ times:  $$\sin_n(x) = \sin(\sin(\dots \sin(x)))$$  For $n=1$ the limit is $\frac{1}{6}$, $n=2$, the limit is $\frac{1}{3}$ and so on.  Can we define a recurrent relation upon that given hypothesis? Also, how do I involve $n$ into calculation, because the final limit will depend on it?  Any suggestions on how to tackle this?  Thank you! jQuery/JavaScript: accessing contents of an iframe I would like to manipulate the HTML inside an iframe using jQuery.  I thought I'd be able to do this by setting the context of the jQuery function to be the document of the iframe, something like:  $(function(){ //document ready     $('some selector', frames['nameOfMyIframe'].document).doStuff() });   However this doesn't seem to work. A bit of inspection shows me that the variables in frames['nameOfMyIframe'] are undefined unless I wait a while for the iframe to load. However, when the iframe loads the variables are not accessible (I get permission denied-type errors).  Does anyone know of a work-around to this? Highest quality website screenshot? I have created a  that i would like to add to my portfolio, but i'm having a hard time getting high quality screenshots of the full site. I tried to save the website as PDF, but that was full of errors, other online services cant recreate the images and so on. I've also just tried to take regular screenshots on the mac at put it all together, but it really lost a lot of quality when i scaled it down.  Any good ideas? :) What do (lambda) function closures capture? I really enjoying using control+r to recursively search my command history. I've found a few good options I like to use with it: # ignore duplicate commands, ignore commands starting with a space export HISTCONTROL=erasedups:ignorespace  # keep the last 5000 entries export HISTSIZE=5000  # append to the history instead of overwriting (good for multiple connections) shopt -s histappend  The only problem for me is that erasedups only erases sequential duplicates - so that with this string of commands: ls cd ~ ls  The ls command will actually be recorded twice. I've thought about periodically running w/ cron: cat .bash_history | sort | uniq &gt; temp.txt mv temp.txt .bash_history  This would achieve removing the duplicates, but unfortunately the order would not be preserved. If I don't sort the file first I don't believe uniq can work properly. How can I remove duplicates in my .bash_history, preserving order? Extra Credit: Are there any problems with overwriting the .bash_history file via a script? For example, if you remove an apache log file I think you need to send a nohup / reset signal with kill to have it flush it's connection to the file. If that is the case with the .bash_history file, perhaps I could somehow use ps to check and make sure there are no connected sessions before the filtering script is run? Dubai (UAE) visa requirements when staying in the airport for a French citizen? Python module for converting PDF to text Is there any python module to convert PDF files into text? I tried  found in Activestate which uses pypdf but the text generated had no space between and was of no use. Applying for a Schengen Visa without itinerary I am currently residing in Ireland with work authorization permit. In the next few months I am planning for a trip to few schengen countries. I have not yet decided my itinerary. Is there any Schengen country embassy which can process a tourist Schengen visa for 90 days? I am trying to capitalize Western Canada or western Canada properly and am wanting a definition for when the "ern" is added as a suffix to a locational distinction of a proper noun.  I believe the capitalization is related to the suffix and am grouping two questions.  After researching on the internet I have found a trend that areas of discrete area become capitalized along with their proper noun   East New York West Hollywood East London (Britain) East Los Angeles   Some locations have "ern" added to their locational modifier.    Web Examples (from government sites):   eastern Canada ( Western Canada ()   All the examples listed contain discrete areas.  The "ern" suffix is used for larger areas, but I am unable to determine when an area becomes large enough. When I wanted to download Ubuntu 12.10 from ubuntu.com, I was asked to make a donation. However, there is only a PayPal option to make the payment. But I don't use PayPal. Is there any other option to make the payment? Why can't I run two mysqli queries? The second one fails urlEvent is undefined How do I change a user name in Windows 7? Parsing DD MM YY HH MM SS columns from TXT file using Python's pandas How to use unicode characters in Windows command line? On Chrome on Android, code blocks on the mobile site have no syntax highlighting, are not a monospaced font, and words are wrapped.  Mobile site on mobile browser:    Desktop site on mobile browser:    Inline code has the same issue, it isn't a monospaced font.  It has been this way for as long as I can remember. Wouldn't be surprised if this is a dupe. How to divide two 64-bit numbers in Linux Kernel? Some code that rounds up the division to demonstrate (C-syntax):  #define SINT64 long long int #define SINT32 long int  SINT64 divRound(SINT64 dividend, SINT64 divisor) {   SINT32 quotient1 = dividend / divisor;    SINT32 modResult = dividend % divisor;   SINT32 multResult = modResult * 2;   SINT32 quotient2 = multResult / divisor;    SINT64 result = quotient1 + quotient2;    return ( result ); }   Now, if this were User-space we probably wouldn't even notice that our compiler is generating code for those operators (e.g. divdi3() for division). Chances are we link with libgcc without even knowing it. The problem is that Kernel-space is different (e.g. no libgcc). What to do?  Crawl Google for a while, notice that pretty much everyone addresses the unsigned variant:  #define UINT64 long long int #define UINT32 long int  UINT64 divRound(UINT64 dividend, UINT64 divisor) {   UINT32 quotient1 = dividend / divisor;    UINT32 modResult = dividend % divisor;   UINT32 multResult = modResult * 2;   UINT32 quotient2 = multResult / divisor;    UINT64 result = quotient1 + quotient2;    return ( result ); }   I know how to fix this one: Override udivdi3() and umoddi3() with do_div() from asm/div64.h. Done right? Wrong. Signed is not the same as unsigned, sdivdi3() does not simply call udivdi3(), they are separate functions for a reason.  Have you solved this problem? Do you know of a library that will help me do this? I'm really stuck so whatever you might see here that I just don't right now would be really helpful.  Thanks, Chad