The minimum of $F(u)=\int_0^1 |u'(x)-u(x)| dx$
Show $\inf_f\int_0^1|f'(x)-f(x)|dx=1/e$ for continuously differentiable functions with $f(0)=0$, $f(1)=1$.
What do you call the feeling you get when you're satisfied to the point of nausea? So you're craving something, say a particular chocolate or sex with one very attractive person that you desire. Take the sexual encounter one for example. You sleep with the person so many times until you are fulfilled. But it gets somewhat "nauseating" to enjoy that thing again (the sex or the chocolate) because you've overindulged earlier.   Now what is that feeling called, the feeling of being overly "satisfied" or "quenched" to the point of nausea?  I wouldn't say what I'm looking for is satisfaction or quench. Is there a more specific term?  Example sentence:     "I've been eating T-bone steak all day yesterday. I had leftovers today, but I couldn't eat them - I'm just so ____ towards (or from) steak right now." What does ` (backquote/backtick) mean in commands? I came across the following command:  sudo chown `id -u` /somedir   and I wonder: what is the meaning of the ` symbol. I noticed for instance that while the command above works well, the one below does not:  sudo chown 'id -u' /somedir Best way to implement keyboard shortcuts in a Windows Forms application? I'm looking for a best way to implement common Windows keyboard shortcuts (for example Ctrl+F, Ctrl+N) in my  application in C#.  The application has a main form which hosts many child forms (one at a time). When a user hits Ctrl+F, I'd like to show a custom search form. The search form would depend on the current open child form in the application.  I was thinking of using something like this in the ChildForm_KeyDown event:     if (e.KeyCode == Keys.F &amp;&amp; Control.ModifierKeys == Keys.Control)         // Show search form   But this doesn't work. The event doesn't even fire when you press a key. What is the solution? Trigger Task Scheduler in Windows 7 when computer wakes up from sleep/hibernate I don't want task scheduler or whatever to wake the computer, but when I open the laptop back up and the machine wakes I'd like that to be the trigger that task scheduler or something uses to run an app. Lost email settings and no icon for Mail I've lost my Settings → Mail, Contacts, and Calendars on my iPhone 5.  No icon for Mail and no Mail settings.  How do I get it back? Run as a different user on a shortcut How do I run as a different user on a shortcut in Windows 7?   On Windows XP, I had the ability to mark a shortcut as being run by a different user, so that every time I ran it it would prompt me for a username/password. This let me have two shortcuts for things like , one for my normal account and one for my domain administrator account which has access to production servers.  I can get to the 'Run as different user' option with Shift + right-click, but I can't see an option anywhere that would let me mark the shortcut as doing this every time. In simple terms, what is the purpose of flush() in ostream Number of possible combinations of x numbers that sum to y I want to find out the number of possible combinations of $x$ numbers that sum to $y$. For example, I want to calculate all combination of 5 numbers, which their sum equals to 10.  An asymptotic approixmation is also useful. This question seems to be very close to number partitioning, with the difference that a number can be 0. See:    All possible partitions for sum 10 and 3 positions that can be zero, are 63 possiblities: (numbers shown as 3 digits)  019 028 037 046 055 064 073 082 091 109 118 127 136 145 154 163 172 181 190 208 217 226 235 244 253 262 271 280 307 316 325 334 343 352 361 370 406 415 424 433 442 451 460 505 514 523 532 541 550 604 613 622 631 640 703 712 721 730 802 811 820 901 910 Quotient ring of Gaussian integers $\mathbb{Z}[i]/(a+bi)$ when $a$ and $b$ are NOT coprime The isomorphism $\mathbb{Z}[i]/(a+bi) \cong \Bbb Z/(a^2+b^2)\Bbb Z$ is , when the integers $a$ and $b$ are coprime. But what happens when they are not coprime, say $(a,b)=d&gt;1$?      — For instance if $p$ is prime (which is not coprime with $0$) then $$\mathbb{Z}[i]/(p) \cong \mathbb{F}_p[X]/(X^2+1) \cong \begin{cases} \mathbb{F}_{p^2} &amp;\text{if } p \equiv 3 \pmod 4\\ \mathbb{F}_{p} \times \mathbb{F}_{p} &amp;\text{if } p \equiv 1 \pmod 4 \end{cases}$$ (because $-1$ is a square mod $p$ iff $(-1)^{(p-1)/2}=1$).  — More generally, if $n=p_1^{r_1} \cdots p_m^{r_m} \in \Bbb N$, then  each pair of integers $p_j^{r_j}$ are coprime, so that by CRT we get $$\mathbb{Z}[i]/(n) \cong \mathbb{Z}[i]/(p_1^{r_1}) \times \cdots \times \mathbb{Z}[i]/(p_m^{r_m})$$  I was not sure how to find the structure of $\mathbb{Z}[i]/(p^{r}) \cong (\Bbb Z/p^r \Bbb Z)[X] \,/\, (X^2+1)$ when $p$ is prime and $r&gt;1$.  — Even more generally, in order to determine the structure of $\mathbb{Z}[i]/(a+bi)$ with $a+bi=d(x+iy)$ and $(x,y)=1$, we could try to use the CRT, provided that $d$ is coprime with $x+iy$ in $\Bbb Z[i]$. But this is not always true: for $d=13$ and $x+iy=2+3i$, we can't find Gauss integers $u$ and $v$ such that $du + (x+iy)v=1$, because this would mean that $(2+3i)[(2-3i)u+v]=1$, i.e. $2+3i$ is a unit in $\Bbb Z[i]$ which is not because its norm is $13 \neq ±1$.  — I was not able to go further. I recall that my general question is to known what $\mathbb{Z}[i]/(a+bi)$ is isomorphic to, when $a$ and $b$ are integers which are not coprime (for instance $a=p^r,b=0$ or $d=(a,b) = a^2+b^2&gt;1$).  Thank you for your help! Multiplying by a $1\times 1$ matrix? For matrix multiplication to work, you have to multiply an $m \times n$ matrix by an $n \times p$ matrix, so we have $$\bigg(m \times n\bigg)\bigg(   n\times p \bigg).$$  But what about a $1 \times 1$ matrix? Is this just a scalar? But every matrix can be mulitplied by a scalar; so do $1 \times 1$ matrices break the rule? Denoting the end of example/remark What is the etiquette to denote the end of an example or remark? For proofs, it's the QED symbol (white box). I know it's not necessary for everyone, but I would like to use it to break up the text a little. What should I use? A circle or filled box or what? Can a continuous function from the reals to the reals assume each value an even number of times? Mathematical notation around the world What are the differences in mathematical notation around the world? I know that in some other countries they write 1,2 meaning 1.2, but what else can be confusing in an academic environment (when people are doing math on a board or on paper). What happens if a person can't die of a heart attack? A question about causality and Quantum Field Theory from improper Lorentz transformation How do I draw text at an angle using python's PIL? Using Python I want to be able to draw text at different angles using PIL.  For example, imagine you were drawing the number around the face of a clock.  The number 3 would appear as expected whereas 12 would we drawn rotated counter-clockwise 90 degrees.  Therefore, I need to be able to draw many different strings at many different angles. About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$ How do I list the default installed packages? I am developing an offline installer for all versions of Ubuntu, and I need Ubuntu's default installed packages list. Is there a way to get this information from any server (web server)? Any script to fetch any Ubuntu version's default installed packages list.  I will give the Ubuntu version, and the script will fetch the packages list.  Note: I need at least a server address. I can write a script for this. Embedding $S_n$ into $A_{n+2}$ Where's my Vox Populi badge? Possible Duplicate:          I was a very good boy yesterday, voting 40 times (and getting the message that told me to wait until the next day before voting again) on a good mix of questions and answers. But I didn't receive the Vox Populi badge for it. What gives?