Take the square $[0,1]^2$ and divide it up with $n$ random lines. We can choose our random lines by choosing one point randomly on one of the four sides and then choosing another point randomly lines and also what is the probability that no region is greater than $0.5$?  If anyone has any cases or any ideas, or especially a full solution I'd be very grateful.   Thanks!
Take the square $[0,1]^2$ we take $n$ random lines through the square. You can choose random lines by choosing a point on one of the sides of the squares and randomly choosing a different point on any of the other three sides and then drawing a line connecting them.   What is the probability that after $n$ of these random lines the largest region is greater than or equal to $0.5$?  Any tips or cases help, thanks.
Export objects to separate files in Illustrator From :     Importantly, the DDH assumption does not hold in the multiplicative group $\mathbb {Z} _{p}^{*}$, where $p$ is prime. This is because given $g^{a}$ and $g^{b}$, one can efficiently compute the Legendre symbol of $g^{ab}$, giving a successful method to distinguish $g^{ab}$ from a random group element.   The only way I can think of to distinguish $g^c$ from $g^{ab}$ is:    If $\left(\frac{g}{p}\right)=-1$, then $\left(\frac{g^{ab}}{p}\right) = 1$ if and only if $a$ or $b$ is even (which is $3/4$ of the times). So if $\left(\frac{g^c}{p}\right) =-1$, probably $g^c\neq g^{ab}$. Nothing is certain.   How'd do you compute $\left(\frac{g^{ab}}{p}\right)$ given $g^a$ and $g^b$? Social network login or not? I am developing a niche social networking iPhone app of my own.   I was wondering if it would be best to allow the user to connect to social networks such as Facebook and Twitter to login to my app (and of course an eMail/Password fallback) or just go with regular eMail and Password login.  Any thoughts would be appreciated! :) What is currently the best way to get a favicon to display in all browsers that support Favicons? Texture packing algorithm What is a good texture packing algorithm?  Technically,  is , so a heuristic is what I'm really after. Prove that $U_{pq}$ is not cyclic if $p$ and $q$ are distinct odd primes.   I am a self taught person. I just learned this and tried this on my own and came up with this.  $x \equiv 1 \pmod{p}$ and $x \equiv -1 \pmod{q}$ has a solution $[a]_{pq}$, since $p$ and $q$ are relatively prime. Because $q$ is an odd prime, $[-1]_{pq}$ is not a solution, so $[a]_{pq}\neq [-1]_{pq}$. But $a^2 \equiv 1 \pmod{p}$ and $a^2 \equiv 1 \pmod{q}$, so $a^2 \equiv 1\pmod{pq}$ since $p$ and $q$ are relatively prime, and thus $[a]_{pq}$ has order 2.  Can someone please tell me if this proof this correct? Please help with proof as I learned it just now as a self taught person. I made a map with annotations in QGIS 3.0.  This is how it looks like in the layout view:    If I print the map as PDF, one would expect to get the PDF to be WYSIWYG, right? However, it looks like this (it's about half the size):    Is there a way to influence the the scaling of the Annoations? I already tried to play with the Scale and Magnifier in the map view. I also tried to change the Scale in the map item.   The strange thing is, I believe it worked a few days ago. But today I installed QGIS 3.0 on a new PC and it showed the same behaviour... Raster generalization - buffers in rasters, expand pixels? Is it possible to create buffers for pixels of raster files? Actually I need to expand the pixels classified as 1 (in white in the figure) with a spatial range of 1 or 2 pixels, in order to perform some generalization.  I'm using QGIS, is this possible with gdal or something? Hypernym for "audiobook", "podcast", "speech", etc.? I am looking for a short and concise term (preferably one word) that can be used as a hypernym for essentially everything that contains (audio) speech (e.g. audiobooks, podcasts, recorded news bulletins, recorded performances of comedians,..).  Does such a term exist? I've thought about 'speech', but that seems to be more adequate for e.g. political speeches, and not so much for audio books and the like. But maybe I'm wrong. Why does thermal radiation only occur at infrared and visible frequencies? The resources that I've checked out seem to say thermal radiation only occurs in the infrared and visible spectrum. For example my heat transfer textbook and the Wikipedia page on .  In my mind thermal radiation is just energy emitted as a result of internal collisions from temperature. So, since temperature can range from 0K to huge numbers, I would think you would have a similar range of emitted energies. So then thermal radiation could occur throughout the whole of the electromagnetic spectrum. Searching a virtual printer, that sends emails I need a software, that emulates a printer, converts the printed documents to PDF/TIFF and send it via eMail to a specified address (for windows).  The virtual printer / PDF conversion is possible with a lot of PDF-converters. But I need a software, which is also able to directly mail me these PDFs. It's always the same mailaddress, and I have an SMTP server.  Any suggestions? How do you start Windows 10 in safe mode? How to partition for Windows/Ubuntu dual boot on same SSD I have a 500GB SSD in which i would like to have both Windows and Ubuntu. My plan is to have something similar to this: Windows 8.1 and ubuntu 14.04 Uefi boot   an efi partition (created by windows installer) which will have Grub as bootloader 150GB ntfs for Windows 15GB ext4 for Ubuntu (root) 35GB ext4 for Ubuntu (home) ~8-16GB swap for Ubuntu (I have 16GB RAM) ~284-292GB ntfs for Data shared for both Windows and Ubuntu   My current setup is   200GB ntfs Windows 300GB ntfs for Data   I plan to shrink both the Windows and the data partiton in order to achieve my desired plan.  My questions:   Does the order of partitions matter? Does it matter if the ubuntu partitions are not at the end/beggining of the drive? Does the swap partition behaves better if its the last/first partition? Can I use the shared NTFS Data partition between windows and ubuntu without encountering problems? Do I have enough space for my ubuntu /home partition (thinking that I'll have access to the ntfs shared partition)?   Edit: Laptop, Asus N56jr, i7, 16Gb Ram, SSD samsung 850 evo 500gb  Windows 8.1 and Ubuntu 14.04 macOS Mojave won't install updates past 10.14.1 due to requirement for APFS formatting I have a MBP 2012 I upgraded from High Sierra to Mojave after it came out as GA. I don't recall if I was asked about upgrading to APFS when Id id that, but at this time the main volume is Mac OS Extended (Journaled).  My current About This Mac...version is Mojave 10.14.1 (18B75). Now, when updates are advertised from the App Store, I'm unable to upgrade because 10.14.3 is required.  No OS updates show in the App Store, and when I searched for the updaters (10.14.2 Combo, etc), I can't install because the installer reports "macOS 10.14.2 Update can't be installed on this disk. This Mac can only install macOS on APFS-formatted drives."  I tried the search results recommending to boot in Recovery Mode and use Disk Utility, but APFS is not available as a type.  I have good backups and I can reformat the boot volume if I need to, but I have not done this before. Should I get a 10.14.3 installer to do this and boot from an external drive? The only guies and message boards I've found just keep saying to install 10.14.3 (I can't) or convert the disk in Recovery Mode (APFS is not available as an option.)  Any known-good ways to get my 10.14.1 upgraded so I can keep getting App Store updates? How do I find peaks in a dataset? If I have a data set that produces a graph such as the following, how would I algorithmically determine the x-values of the peaks shown (in this case three of them): I am trying to make a snowball that triggers a command when it hits a player in 1.15, but I don't know how to do that. When I do execute at @e[type=snowball] run gamemode spectator @a[distance=..2] it only runs the command if it goes right next to them. Asymptotic of a sum involving binomial coefficients Is a memory leak created if a MemoryStream in .NET is not closed? I have the following code:  MemoryStream foo(){     MemoryStream ms = new MemoryStream();     // write stuff to ms     return ms; }  void bar(){     MemoryStream ms2 = foo();     // do stuff with ms2     return; }   Is there any chance that the MemoryStream that I've allocated will somehow fail to be disposed of later?    I've got a peer review insisting that I manually close this, and I can't find the information to tell if he has a valid point or not. What is the mass density distribution of an electron? Desktop link to Eclipse I was tring to install eclipse on ubuntu. What I did: I unzipped the tar archive of eclipse. I tried to start eclipse from the command line - like this - ./eclipse. It works. But then I tried to create a desktop icon with: gnome-desktop-item-edit ~/Desktop --create-new. In a new icon I showed the path to the eclipse executable which I could launch from the command line. But then eclipse does not start stating:  A Java Runtime Environment (JRE) or Java Development Kit (JDK) must be available in order to run Eclipse. No Java virtual machine was found after searching the following locations: /home/artem/eclipse/jre/bin/java java in your current PATH   The same message appears if I try to launch eclipse by double-clicking its original launcher. So it starts from the terminal but not from the desktop (it does not start when double-clicked) And also I get a message in the terminal (at some stage it appeared):  (gnome-desktop-item-edit:8998): Gtk-WARNING **: Attempting to store changes into `/root/.local/share/recently-used.xbel', but failed: Failed to create file '/root/.local/share/recently-used.xbel.DSV8LW': No such file or directory   I am using Ubuntu 12.04 x32 and eclipse Juno.  PS. PATH variable points at jdk/bin and JAVA_HOME - to the jdk folder PSS. I actually set the environment variables through .bashrc file(JAVA_HOME and PATH)