Being born to James and Lily, how can Harry be called a half-blood?  It is said that admission in Hogwarts is given to children of Muggles when they show magical talents as a child, and Lily was no exception to this. This makes Lily a witch, so why is Harry half-blooded?
Harry is a half-blood and Ginny is a pure-blood, so what does that make his children? I've been told it means they are pure-bloods but I can't be sure. What do you think?
Boarding a train in India at another station I have booked a ticket on a train from Mumbai to Chennai and boarding at Pune. Since my schedules have changed, I will be in Mumbai on that day. Can I board the same train in Mumbai in my own ticket and claim the seat/berth? Prove or the disprove the existence of a limit of integrals Let $A \subset \mathbb{R}^2$ be the annulus defined, in polar coordinates, as  $$ A = \{ (r, \theta) \in [0, \infty) \times [0, 2\pi) : 2 \leq r \leq 3 \} \, .$$ Let $F: A \to A$, $F:(r, \theta) \mapsto (r, r \theta \text{ (mod } 2\pi))$. Let $g : A \to \mathbb{R}$ be a continuous function. Discuss the existence of the limit $$ \lim_{n \to \infty} \int_A g \circ F^{(n)}(x) \, \text{d}x \, ,$$ where $F^{(n)} = F \circ F \circ \dots \circ F$ denotes the composition of $F$ with itself $n$ times.  I cannot find a way to attack this problem. Here's what I tried: if $g \circ F^{(n)}$ converged, I think we could take the limit under the integral sign. So I tried to show the convergence of $F^{(n)}$. If it converged, then the limit function must send every point to a fixed point of $F$. So I determined the fixed points of $F$. But I don't think $F^{(n)}$ converges. Maximum weight an average bicycle can carry? A few years ago, I've bought  (see edit) bike. At that time I was around 90 kgs and I didn't have any problems.  Today I'm around 120 kgs and I was considering (among other things) starting cycling again. Is this bike "good" enough to carry me? What should I expect? Any tips?  EDIT! Apparently, Drag have renamed some of their bikes in the last few years, so the above information is a bit wrong.  seems to be my bike. At first I didn't recognize much difference, but this one has suspension on the front which mine also has. Does this change anything What is the difference between Halt and Shutdown commands? What is the difference between the halt and shutdown commands? This is about that old chestnut, $\newcommand{\d}{\mathrm{d}} \int \sin^2 x\,\d x$.   OK, I know that ordinarily you're supposed to use the identity $\sin^2 x = (1 - \cos 2x)/2$ and integrating that is easy. But just for the heck of it, I tried using the $u$-$v$ substitution method (otherwise known as integration by parts).  $$ \int \sin^2 x\,\d x = \int \sin x \sin x\,\d x $$  We can say $u=\sin x$ and $\d u=\cos x\,\d x$ while $\d v = \sin x\,\d x$ and $v = -\cos x$. When we put it all together:   $$\int \sin^2 x\,\d x = u v - \int v\,\d u = -\sin x \cos x - \int -\cos^2 x\,\d x$$  and doing the same routine with $\cos^2 x$ we get $u = \cos x$, $\d u = -\sin x\,\d x$, $\d v = \cos x\,\d x $ and $v = -\sin x$, leading to:  $$\begin{align}   \int \sin^2 x\,\d x = uv - \int v\,\d u     &amp;= -\sin x \cos x - (-\cos x \sin x - \int -\sin^2 x\,\d x) \\     &amp;= -\sin x \cos x + \sin x \cos x - \int \sin^2 x\,\d x \end{align}$$  which eventually works out to  $$2\int \sin^2 x\,\d x = 0$$  So I wanted to get an idea why this didn't work. Maybe it's higher math and the why will be beyond me (I would think that might be the case), or maybe it's one of those proofs that looks absurdly simple when shown that I am just unaware of. How to merge vertices in Blender? I am attempting to create my first 3D character just for practice. Being one of my first 3d models I going through the learning curve needless to say. In doing so I find myself creating many extra vertices. Where we will say 10 vertices on a rounded shape are spaced out on the equator and on the other north pole end of the edges they are very close. The close end could all be one vertex. Is it possible to say merge all points to one point and delete the rest? With biblatex, the author can be replaced by a dash (or “idem”) in the bibliography. Is it possible to have this replacement also if there are multiple authors, and the first of these multiple authors is the same as the author of the book listed before? (It is somewhat difficult to describe, see the attached example instead, where “Buchautor, Hans-Wilhelm” should be replaced in book3 as well.)   I assume that it should be possible by customising \DeclareNameFormat, but I don’t know how.  Minimal example:  \documentclass{scrartcl} \usepackage[T1]{fontenc} \usepackage[latin1]{inputenc} \usepackage[english]{babel} \usepackage{csquotes} \usepackage{filecontents} \begin{filecontents}{\jobname.bib} @BOOK{book1,   author = {Buchautor, Hans-Wilhelm},   title = {Irgendein Buch},   location = {Buch am Wald},   date = {2000} } @BOOK{book2,   author = {Buchautor, Hans-Wilhelm},   title = {Ein anderes Buch},   location = {Berlin},   date = {2001} } @BOOK{book3,   author = {Buchautor, Hans-Wilhelm and Zweitautor, Zoran},   title = {Noch ein Buch},   location = {London and New York},   date = {2010} } \end{filecontents}  \usepackage[ style=authortitle, backend=bibtex8 ]{biblatex} \bibliography{\jobname}  \renewcommand*{\bibnamedash}{%   \bibstring[\mkbibbold]{idem\thefield{gender}}}  \begin{document} \nocite{*}  \printbibliography \end{document}   Edit 15/02/2011 17:14   I should have added that there was a feature request for biber which pointed back to biblatex. See .  Edit 21/06/2011 9:26  Is this somehow possible now with biblatex 1.4/1.5? I played a bit with uniquename/uniquelist, but I could not get it to work. Electron flow and electric potential In the physics tutorial topic on current electricity it defines the positive terminal as the high potential terminal and the negative as the low potential. When talking about positive test charges this analogy makes sense, the charge moves from the +ve to the -ve where it loses potential till it has to be "topped" up by the cell.   What confuses me when they begin talking electrons. Using this analogy would mean that the electrons move from the -ve to the +ve but this means it would work against the electric field so the potential energy increases till it reaches the +ve terminal.   My question is how does this analogy, if it does, change to accommodate electrons? Does the electric field reverse so the -ve terminal is the high potential and the +ve the low potential? Characterization convex function. What is the difference between a synchronized method and synchronized block in Java? Hardware issue on iMac, flashing question mark I have an iMac 2008/2009 issue and recently the computer would not boot and I would get a flashing question mark. Ran through all the usual steps, try boot in safe mode, flash RAM,  try single user for fdisk, put in OS disk and boot from CD, etc... No dice.   Replaced the hard drive and put the OS disc in the system, press and hold option. (holding C didn't work) I can see the OS disk but when I click on it the system will act like it is going to run and then freeze. The best I got was the OS X disc that changed the screen to dark grey and told be the system had to restart.  Purchased a usb mount for an external hard drive. Was able to mount the old hard drive to a laptop and run disk utility. Everything checked out.  At this point I am pretty sure it isn't the hard drive.   Any other hard ware items this can point too? My iMAC can also "see" the hard drive (and the recovery partition) when connected via the USB and I hold "option" on start up. But it crashes when trying to boot from either.  I am going to take out and re-install the RAM for giggles but I am not sure what else to do.   Ideas are welcome. I'm using Ubuntu 11.10.  The python 2.7.2 provided has a bug that has been corrected in the latest 2.7.2 sources from the python repository.  What is the recommended way to replace the ubuntu provided python with the python from source? Or put another way, how do I "update" the ubuntu-provided one?  Ideally, I would just be able to create new .deb(s) that "update" the python2.7/python2.7-dev provided by Ubuntu. How to integrate $\int x^2 \sin^2(x)dx$ I don't know how to integrate $\int x^2\sin^2(x)\,\mathrm dx$. I know that I should do it by parts, where I have  $$ u=x^2\quad  v'=\sin^2x \\  u'=2x \quad v={-\sin x\cos x+x\over 2}$$  and now I have  $$ \int x^2\sin^2(x)\,\mathrm dx = {-\sin x\cos x+x\over 2} x^2 - \int 2x{-\sin x\cos x+x\over 2}\,\mathrm dx\\ ={-\sin x\cos x+x\over 2} x^2 - \int x(-\sin x\cos x+x)\,\mathrm dx\\  $$  so I have to calculate $$ \int x(-\sin x\cos x+x)\,\mathrm dx=-\int x\sin x\cos x\,\mathrm dx+\int x^2\,\mathrm dx$$  I know that $\int x^2\,\mathrm dx = {1 \over 3}x^3+C$ but I don't know what should I do with $$\int x\sin x\cos x \,\mathrm dx$$ Should i use parts again or what? Please help. I think it's well established that for the basic premise in the Back to the Future Trilogy to work, we have a system of alternate timelines.  If this is the case though, then why would Marty in Back to the Future (the original) begin to fade?  Logically, there would simply be no Marty in the alternate timeline created when Marty travels back to 1955 for the first time; why should this affect the original Marty from the original timeline? Can we calculate the standard error of prediction just based on simple linear regression output? The standard error of prediction in simple linear regression is $\hat\sigma\sqrt{1/n+(x_j-\bar{x})^2/\Sigma{(x_i-\bar{x})^2}}$.  My question is to calculate the standard error of prediction for $pop=1029$ just based on the following regression output. I can get all except $\bar{x}$. And I also know how to calculate the approximate standard error of prediction based on the standard errors of intercept and coefficient of $pop$, ignoring their correlation. Cite_key instead of a number, what is going on? I have the following problem: I correctly obtain a numbered bibliography at the end but along the text the cite_key appear instead of a number. How to fix this problem?   \documentclass[11pt]{book}  \usepackage[]{biblatex} \begin{document} %some text  ... \cite{ABKM2015}... %some text  \begin{thebibliography}{99} \bibitem{ABKM2015} Arroja, F. and Bartolo, N. and Karmakar P. and Matarrese, S. (2015). \newblock The Two Faces of Mimetic Horndeski Gravity             \newblock {\em ArXiV}, 1506.08575 (2015). \end{thebibliography} \end{document}   After compiling I get ... [ABKM2015] ... while I want for example  [1]. More options when flagging for migration I think there should be more Stack Exchange networks available when flagging a question to be migrated. For example I'd think that the following question:    ...would be a better fit on unix.stackexchange.com instead of Stack Overflow. But without the option to mark it so, I feel hesitant to mark it. Is there any way to recover unsaved notepad++ docs? Why can't a Federation Starship's transporter history be used to bring someone back to life? This works perfectly:  $ inotifywait --event create ~/foo Setting up watches. Watches established. /home/ron/foo/ CREATE bar   However, this just sits there when directory tun0 is created under /sys/devices/virtual/net.  $ inotifywait --event create /sys/devices/virtual/net Setting up watches. Watches established.   Since those folders are world readable, I'd expect inotifywait to work.  So, what am I doing wrong?  Thanks