I recently reread The Deathly Hallows, in which Hermione uses polyjuice potion to turn into Bellatrix Lestrange. I was wondering whether Hermione could have summoned Lord Voldemort by touching the Dark Mark. It is not the original mark after all.
I was just reading Harry Potter and the Deathly Hallows, and I was wondering, when Hermione Granger changed into Bellatrix Lestrange, she should've obtained the Dark Mark, temporarily.  Now, my question is: would the Dark Mark work if pressed?
How do I take the limit as $n$ goes to $\infty$ of $\frac{\sqrt{n}}{\log(n)}$? How do take this limit:  $$ \lim_{n\to\infty} \frac{\sqrt{n}}{\log(n)}$$  I have a feeling that it is infinity, but I'm not sure how to prove it. Should I use L'Hopitals Rule? I just bought a  game (Forza 4) for my Xbox 360 (bought in the US). When I tried to play the game, it wouldn't load because of region issue. Is there a legal way to solve this (no crack)? C# HttpWebRequest with XML Structured Data How to avoid the 'not properly formatted as code' alert Consider the following MWE:  \documentclass{article} \usepackage{pstricks} \begin{document} A \end{document}   It produces the error  Runaway argument? ] {pgffor.code.tex}  ! Paragraph ended before \ProvidesPackageRCS@i was complete. &lt;to be read again&gt;                     \par  l.11   How do I fix this? Adding a comment should not make me fail the review audit I just failed these   in First Post, I read the question and thought it seemed reasonable but the user was deleted so to be on the safe side I clicked add comment and I failed the audit.  I'm not sure why adding a comment would be considered a negative action, is the correct option to click No Action Needed or edit?  What was I supposed to do in this situation?  Adding a comment should not be a review audit fail. Is There a Natural Way to Extend Repeated Exponentiation Beyond Integers? This question has been in my mind since high school.  We can get multiplication of natural numbers by repeated addition; equivalently, if we define $f$ recursively by $f(1)=m$ and $f(n+1)=f(n)+m$, then $f(n) = m \times n$.  Likewise, we get exponentiation by repeated multiplication. If $g(1)=m$ and $g(n+1)=mg(n)$, then $g(n) = m^n$.  In my high school mind it was natural to imagine a new function defined by repeated exponentiation: $h(1)=m$ and $h(n+1)=m^{h(n)}$.  These definitions only make sense for $n$ a natural number, but of course there are standard very mathematically satisfying ways to define multiplication and exponentiation by any real number. My question is this:  Can the function $h$ defined above also be extended in a natural way to $\mathbb{R}^{&gt;0}$?  The question is in the spirit of seeking an extension of $f(n)=n!$ to $\mathbb{R}$ and arriving at $\Gamma(x)$.  Let me focus the question, and attempt to make precise what I mean by "in a natural way." Take $h(1)=2$ and $h(n+1)=2^{h(n)}$. $h$ is now defined on $\mathbb{N}$, and $h(2)=4$, $h(3)=16$, $h(4)=2^{16}=65,536$ etc. Is it possible to extend the domain of definition of $h$ to all positive reals in such a way that  a) The functional equation $h(x+1)=2^{h(x)}$ continues to be satisfied for all $x$ in the domain.  b) $h$ is $C^\infty$. (Analytic would be even better but this seems maybe too much to hope for?)  c) All $h$'s derivatives are monotone.  These requirements are my attempt to codify what would count as "natural." I am open to suggestions about what would be a better list of requirements.  If such a function exists, I would like to know how to construct it; if it doesn't, I would like to know why (i.e. outline of proof), and if relaxing some of the requirements (e.g. just the first derivative monotone) would make it possible.  (If the function exists, I am also interested in the questions, "is it unique?" "Could we add some natural requirements to make it unique?" But my main query is about existence.) Review Count - Fix It or Lose It Evaluation of $\sum_{k=0}^n{n\choose k}^2u^k$ I am trying to evaluate the finite sum \begin{equation} f(u)=\sum_{k=0}^n{n\choose k}^2u^k,\quad 0&lt;u\le1 \end{equation}  In an first attempt, I think of the generating function \begin{equation} (1+x)^n(u+x)^n = \sum_{k\ge0}{n\choose k}x^k\sum_{k\ge0}{n\choose k}u^kx^{n-k}=\cdots+x^n\sum_{k\ge0}{n\choose k}^2u^k+\cdots \end{equation}  which means that $f(u)$ is the coefficients of the term $x^n$.  Expanding $(1+x)^n(u+x)^n$ into $[1+(1+u)x+x^2]^n$, and using the multinomial expansion, I get an expression for the coefficient of $x^n$. However, such an expression is more complicated than $f(u)$. It seems I am making the problem even more difficult.  Can someone help me find the value of $f(u)$.  Thank you. How to extend the text under summation symbol without making extra space equirectangular rendering for Blender Internal? Can such frames/videos be rendered in Blender Internal as well? If not, how indirectly?  EDIT: The below solution is great as long as you can write your own Python script and only render solid objects. When you need things like particles/hair, it won't work as those won't be reflected. What kind of components are black blobs on a PCB? In low-cost mass-produced items I often run into black blobs of what looks like resin applied directly on top of something on the PCB. What are these things exactly? I suspect this is some kind of custom IC that is layed out directly on the PCB to save on the plastic  housing/connector pins. Is this correct? If so, what is this technique called?    This is a photograph of the inside of a cheap digital multimeter. The black blob is the only non-basic piece of circuitry present, along with an op-amp (top) and a single bipolar junction transistor. The equation $y^2 = x^3 + k$ for $k = (4n-1)^3 - 4m^2$, with $m, n \in \mathbb{N}$ and no prime number that p is congruent to 1 modulo 4 divids m, doesn't have any answer and its proof can be obtained by using quadratic reciprocity law.  Do you know answers of this equation for two or three different values of $k$? In addition, do you know any reference about that? Compact vs Mirrorless - why pick one over another? What would be a reason for one to pick the compact (whatever it'd be P&amp;S or something more advanced) over mirrorless compact system camera  ?  Right now market is quite confusing — we have huge market of tiny-sensor compacts, we have mirrorless that use sensors in a size of these from P&amp;S cameras (Nikon 1 being notable example), we have compacts with sensors bigger than most popular mirrorless system (Canon G1X vs m4/3), we have lot of APS-C sensor mirrorless which are matched by some of the compacts (Fuji X100 being most notable example, but even Leica has its X2),  and to make it even more confusing — Sony released RX1 with full frame sensor, beating crap out of every mirrorless on a market.  So what are your arguments to pick compact over a mirrorless?  Why are they better, what's the reason behind logic of companies like Fujifilm which at the same time offers P&amp;S and X-mount mirrorless using same sensor size? dpkg --configure -a  Setting up linux-image-3.13.0-35-generic (3.13.0-35.62) ... Running depmod. update-initramfs: deferring update (hook will be called later) The link /initrd.img is a dangling linkto /boot/initrd.img-3.13.0-35-generic vmlinuz(/boot/vmlinuz-3.13.0-35-generic ) points to /boot/vmlinuz-3.13.0-35-generic  (/boot/vmlinuz-3.13.0-35-generic) -- doing nothing at /var/lib/dpkg/info/linux-image-3.13.0-35-generic.postinst line 491. Examining /etc/kernel/postinst.d. run-parts: executing /etc/kernel/postinst.d/apt-auto-removal 3.13.0-35-generic /boot/vmlinuz-3.13.0-35-generic run-parts: executing /etc/kernel/postinst.d/initramfs-tools 3.13.0-35-generic /boot/vmlinuz-3.13.0-35-generic update-initramfs: Generating /boot/initrd.img-3.13.0-35-generic  gzip: stdout: No space left on device E: mkinitramfs failure cpio 141 gzip 1 update-initramfs: failed for /boot/initrd.img-3.13.0-35-generic with 1. run-parts: /etc/kernel/postinst.d/initramfs-tools exited with return code 1 Failed to process /etc/kernel/postinst.d at /var/lib/dpkg/info/linux-image-3.13.0-35-generic.postinst line 1025. dpkg: error processing package linux-image-3.13.0-35-generic (--configure):  subprocess installed post-installation script returned error exit status 2 dpkg: dependency problems prevent configuration of linux-image-extra-3.13.0-35-generic:  linux-image-extra-3.13.0-35-generic depends on linux-image-3.13.0-35-generic; however:   Package linux-image-3.13.0-35-generic is not configured yet.  dpkg: error processing package linux-image-extra-3.13.0-35-generic (--configure):  dependency problems - leaving unconfigured dpkg: dependency problems prevent configuration of linux-image-generic:  linux-image-generic depends on linux-image-3.13.0-35-generic; however:   Package linux-image-3.13.0-35-generic is not configured yet.  linux-image-generic depends on linux-image-extra-3.13.0-35-generic; however:   Package linux-image-extra-3.13.0-35-generic is not configured yet.  dpkg: error processing package linux-image-generic (--configure):  dependency problems - leaving unconfigured Errors were encountered while processing:  linux-image-3.13.0-35-generic  linux-image-extra-3.13.0-35-generic  linux-image-generic I have a simple page that has some iframe sections (to display RSS links). How can I apply the same CSS format from the main page to the page displayed in the iframe? Which livestock is the most efficient food source? Why can't Mathematica integrate this? Why aren't my turtles breeding? The 1st law of thermodynamics If a gas expands adiabatically will the work done be positive or negative?  I think it will be positive as $\delta W=p dV$ and we have a positive sign due to the work done by the gas is positive as it pushes to expand. But this site has the negative of the answer I obtain.   (See adiabatic processes section)