What spell was used to defeat this Death Eater?
How was this character killed without Avada Kedavra?
Why won't my villagers breed If $A,B,C$ are matrices I am thinking how to show that $$ A(B + C) = AB + AC$$  Is possible to show without sums like $\sum_i a_i, ..., \sum_j b_j$? It seems if I do the proof with many indexes then is tedious and I don't learn much from it. Please add Right To Left text support in Stack Exchange You know, some of us read right to left...  Certain sites like  and  have an obvious need for this, as Arabic and Hebrew are Right To Left (RTL) languages. Many answers on those sites cite the Torah and the Quran respectively. Directly quoting these sources properly requires RTL text. How do I make the Super key open the activities overview in Ubuntu 20.04 LTS? Can't we compute $\lim_{n \to \infty}\frac{1+ \cdots +n}{n^2}=\lim_{n\to\infty}\frac{1}{n^2}+\cdots +\lim_{n\to\infty}\frac{n}{n^2}=0$? I just learned the definition of limits, and I learned that if $\{a_n\}, \{b_n\} $ converges, then $$\lim_{n\to \infty} (a_n+b_n)=\lim_{n \to \infty} a_n+\lim_{n \to \infty}b_n$$ holds.  And my teacher said that $\lim_{n \to \infty}\frac{1+2+3+ \cdots +n}{n^2}=\lim_{n\to \infty}\frac{\frac{n(n+1)}{2}}{n^2}=\frac{1}{2}$.  But can't we compute like  $$\lim_{n \to \infty}\frac{1+2+3+ \cdots +n}{n^2}=\lim_{n\to\infty}\frac{1}{n^2}+\lim_{n\to\infty}\frac{2}{n^2}+\lim_{n\to\infty}\frac{3}{n^2}+\cdots +\lim_{n\to\infty}\frac{n}{n^2}=0+0+\cdots+0=0$$? Why does bright pure red/green/blue light look white if bright enough? I believe that white light is white because it contains every wavelength, as white by itself has no frequency by itself.  Can somebody explain why really bright pure red, green, or blue LEDs seem white to us and to cameras?  Also, can a bright light ever be pure(eg is it possible to emit a pure red/pure blue/pure green bright light only with wavelengths in the range of that light), or will the inherent brightness of a light force other wavelengths into the light? What method in the String class returns only the first N characters? Background Video is shown in Rendered mode but not when szene is rendered Compactness and Hausdorffness Is it possible to have a topological space having all compact subsets closed, but the space itselt is not Hausdorff?  I couldn't find any counterexample. I tried $\mathbb R$ with cofinite, point inclusion and point exclusion topologies, but these didn't work.  Any suggestion in this context will be helpful for me. 2/15/18 compiz update broke unity This  forced removal of unity and ubuntu-desktop on my 16.04 Ubuntu system.   The offending package that is missing, but unity needs, seems to be compiz-core-abiversion-20151010. It seems to be a , and I can't find it to download.    As it happens, I mostly use LXDE on this system, but I'd be very unhappy if I used Unity...  Since I do occasionally use the Unity desktop, is there a fix for this?  Edit: related questions are rolling in. Looks like a major quality escape          Edit 2: How to enlarge thickbox media library iframe? The iframe in thickbox media library is not big enough to display my custom tab. I tried to add "width=900&amp;height=600" at the end of the link that pointing to the library, but no luck. How can I modify the inframe size? Compiling LaTeX document empties .bbl file I'm trying out biblatex for the document I'm compiling, using the biber backend on my miktex distribution. Everything, including biber, should be up to date, assuming the MiKTeX repository currently holds the latest versions of everything.  This is what the biblatex documentation (p. 101) says about how often I have to run biber to update my .bbl file:     Whenever a reference to a work which has not been cited before is   added, this procedure must be repeated. This is also the case if the   last reference to a work which has been cited before is removed   because some citation labels may change in this case.   So if I make changes to my document (which is a very common activity in the process of writing a document), but leave the citations unchanged, I should not have to re-run biber before compiling the changes. However, every time I compile my document, regardless of the compiler or documentclass, the .bbl file is emptied. Consequently, the next time I compile the document without running biber, the bibliography is removed (seeing as the .bbl file contains nothing), and all my citations are broken. For this reason, I have to run biber before every time I compile the document, which largely counters the benefit of externalizing the bibliography in the first place.  How can I make the compilers stop overwriting my .bbl file and make everything behave as described in the biblatex manual?  Upon investigating the contents of the auxiliary files, I found that the .bbl file (after running biber, before compiling) begins with the following lines:  % $ biblatex auxiliary file $ % $ biblatex bbl format version 2.3 $   Does the biblatex version 2.8 still mark the .bbl files as version 2.3? If not, could this be the problem? And if so, why does my 2.8 version of biblatex (partly) behave as version 2.3?  Any help solving this problem would be much appreciated. How to track the number of tag wikis I edited? I want to see the number of tag wiki that I edited till now. Also I want to see which are accepted and which are rejected with the detail of all those tags. How can I know that? Also I want to know the progress for Research Assisstant badge. From Geneva airport to Lausanne station On September 4, I will be arriving in Geneva by airplane at approximately 11 AM. After that, I need to go to Lausanne. I have two questions:   Do I need to buy a train ticket online, or can I buy it directly at the station without any problems? (Problems such as: the trains are always full, it's not permitted to buy a ticket etc.) Moreover, are the tickets only for a specific train or it is like "you can board any train from Geneve to Lausanne with this ticket"? How do I get from the airport to the Geneva train station (as low a budget as possible, I guess walking is not an option though), and how much does it cost?   I'd appreciate answers from people who have been there, but if you're able to find an exhaustive link from any website that's okay too. Prove that the minimum number of cycles is $m-n+1$ The question I have is:   Prove that the minimum number of cycles is $m-n+1$ in a connected graph. Where one cycle is a path that starts that begins and ends at the same vertex. Where $m$ is edges and $n$ is the vertices.   I have no idea where to start. A few hints would be appreciated. Please do not provide me with the answer. Is it possible to remove "Show Desktop" from the Alt+Tab application switcher? When an account is deleted, the username in the user's posts and comments is changed to a generic user&lt;userID&gt;. But the username stays the same on close and delete notifications on posts the user had voted to close / delete1. I think it shouldn't, especially for users who used their real name as their username, if they chose to distance themselves from the site and remove their accounts, it makes sense that they wouldn't really want their name plastered on close and delete notifications.   A perhaps easy way to avoid the actual username remaining visible would be to change it to the generic user&lt;userID&gt; (or anything generic enough, like "anonymous") prior to deletion, and wait a bit for the generic username to propagate all over the site. If I'm not horribly misreading , this was part of the process in the old days.   This could be automated or added as a suggestion to the .  Glaring example can be seen , where the deleted user also posted a comment where their name is properly anonymized:        1 I've seen it on close notifications and self deleted answers. I'm not sure it happens on deleted questions, or deleted answers that aren't self deletions, and I don't have a way to verify it - other than stumbling on them accidentally Script to raise a single window to the front dpkg -V , What does the output mean? I ran DPKG Verify on all packges and got this output and I don't know what it means :  ??5?????? c /etc/lightdm/lightdm-gtk-greeter.conf ??5?????? c /etc/default/chromium-browser ??5??????   /usr/local/etc/no-ip2.conf ??5??????   /var/lib/dokuwiki/data/cache/_dummy ??5?????? c /etc/xdg/menus/mate-settings.menu ??5?????? c /etc/apache2/apache2.conf ??5?????? c /etc/apt/apt.conf.d/10periodic ??5?????? c /etc/sysctl.conf ??5??????   /var/lib/xine/xine.desktop ??5??????   /boot/vmlinuz-4.4.0-21-generic ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/cupshelpers.cpython-35.pyc ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/xmldriverprefs.cpython-35.pyc ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/config.cpython-35.pyc ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/openprinting.cpython-35.pyc ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/__init__.cpython-35.pyc ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/ppds.cpython-35.pyc ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/installdriver.cpython-35.pyc ??5?????? c /etc/xdg/autostart/mate-volume-control-applet.desktop ??5?????? c /etc/libvirt/qemu/networks/default.xml multiple Open Drain UART over long distance I have 9 microcontrollers  and I have connected the RX and TX lines of 8 of them in parallel. My configuration is in master-slave. The master microcontroller send data to one of the 8 RX lines but only one of them can respond at a time. The cable length is about 3 to 5 metres between each node.  I have two questions. My test was done with 2 slaves instead of 8. UART at 9600bps.  If I setup the TX lines of the slaves as Open Drain it works fine, but the signal doesn't have steep ramps. I thought this happens due to Pull-up resistors. And I also think that is going to be better with 8 slaves on the bus, right?  Why doesn't that topology work if the TX lines of the slaves are not Open Drain?  I managed to make it work by disabling the transmit of the UART in all of them except one, and it worked fine. I had two slaves, so I disabled the one and left the other. Also I noticed that the edges of the signal was sharper. Why are they sharper in that case?  Regarding resistors: The value of the resistors for both RX and TX lines are 2.7KΩ. However the Open Drain topology would parallel the internal pull-up resistors. According to the datasheet that resistor is about 20KΩ at minimum. So, using a 2.7KΩ in the output would give us a total resistance of 2.52KΩ (20+2.7)/9. And the Open Drain would make a voltage divider 2.52KΩ + 2.7KΩ (Schematic 2). Which means with 8 slaves and Open Drain topology the signal will not go lower than 1V which is the threshold of the low level. Is that correct?  Wouldn't it be better to disable all the internal pull up resistors and place two (let's say: 4.7KΩ) only at the master side?  Distance: What is the maximum baud rate for such distance? I'm a little worried about the signal integrity. The test was done with 9600bps but I didn't notice any significant difference in 4800bps. The distortion of the signal didn't have a difference.  Voltage values are 3.3V for the UART bus.  Schematic 1. (all resistors are 2.7KΩ)        &ndash; Schematic created using   Schematic 2. (U4, U5, U6, U7, and U8 are omitted for simplicity).          EDIT: Thank you all very much about your answers so far. I wanted to point out that this is a question about UART only. I am not looking for alternative solutions. I'm just trying to find some answers about the above implementation.  EDIT2: Thank you very much for your answers! I ended up modifying a little my schematic. I disabled the internal pullup resistors of the microcontrollers and I placed external ones at the master's board. Their value would be around 1 KOhm to 3 KOhm. I have to do some tests more to decide the final value. I also replaced all series resistors with 130 Ohm.   I tested 5 slaves over 20 metre cable (with pullup 3 KOhm and 130 Ohm series resistors) and it worked fine.   Would it be better to add open drain/open collector line drivers on every TX lines?