Getting used to projective coordinates, need help describing (2) objects geometrically I'm trying to get an intuition for what things look like in projective coordinates. There are two curves that I have to work a problem with, but I'm not sure how to visualize them. They are  $V(u^2 X + v^2 Y + uvZ) \subset \mathbb{P}^2 \times \mathbb{P}^1 $  $V(u^2 X^2 + v^2 Y^2 + uvZ^2) \subset \mathbb{P}^2 \times \mathbb{P}^1$  where $[u : v]$ are the projective coordinates of $\mathbb{P}^1$ and $[X : Y : Z]$ are the projective coordinates of $\mathbb{P}^2$. Is there any way to describe these objects geometrically?
Description of varieties in $\mathbb{P}^2\times \mathbb{P}^1$ If $[x:y]$ are coordinates of $\mathbb{P}^1$ and $[X:Y:Z]$ are coordinates of $\mathbb{P}^2$, what do the following varieties look like?   $V(x^2X+y^2Y+xyZ)\subset \mathbb{P}^2\times \mathbb{P}^1$ $V(x^2X^2+y^2Y^2+xyZ^2)\subset \mathbb{P}^2\times \mathbb{P}^1$   As of now, I don't quite know how to visualize these varieties. A detailed geometric picture would be especially welcome.
Uninstall apps locked by phone vendor I'm using a Samsung I9000 and I have some annoying apps that came pre installed by the phone vendor, like a music store, a custom web browser and other memory leaking apps.  Those crappy apps can't be uninstalled neither by Manage applications tool, nor by editing the apps tiles in the front menu.  I guess I have to be a root user or something to get rid of those apps, but I don't know how. Defragmenting an SSD drive is a bad idea and Windows 7 is (should be?) smart enough not to schedule defragmentation on such drives.  However, I've opened up Disk Defragmenter on my system and found, to my surprise, that my SSD has indeed been defragmented... recently!  Then I checked the disks selected for the scheduled defrag (I have one SSD and one normal disk), and there the list correctly shows only the non-SSD drive.   MSDN forum post seems to suggest that, at least on Windows 8, defragmenting an SSD drive will just cause the TRIM command to be sent to the drive, but there's no word on what actually happens if you try to defrag an SSD drive on Windows 7 (aside from the fact that it shouldn't happen automatically).  What happens in Windows 7 if one chooses to defrag and SSD? What could possibly have been the reason my SSD drive got been defragmented?  EDIT:  I just remembered - I've moved some folders (Users and ProgramData) from my SSD drive to my normal drive using junctions.  question suggests that this shouldn't have any effects at all on the defragmentation process, but could it have an effect on the "last run" in Disk Defragmenter? I have asked more than 100 questions on SO. The problem with asking so many questions is that it's sometimes very hard to navigate to the question I want.  Is there any way to improve the interface further? Is it ok to leave a slow cooker unattended? I am  with the Google login for Pokemon Go. Is there any way, be it contacting support or through Trainer Club, to either link my Google account to a new Trainer Club account or transfer my account to a Trainer Club account?  It seems like a better idea to have a Trainer Club account, so if there are Google login problems it won't matter.  Does anyone know if something like this is possible? How do I get a Cron like scheduler in Python? I'm looking for a library in Python which will provide at and cron like functionality.  I'd quite like have a pure Python solution, rather than relying on tools installed on the box; this way I run on machines with no cron.  For those unfamiliar with cron: you can schedule tasks based upon an expression like:    0 2 * * 7 /usr/bin/run-backup # run the backups at 0200 on Every Sunday  0 9-17/2 * * 1-5 /usr/bin/purge-temps # run the purge temps command, every 2 hours between 9am and 5pm on Mondays to Fridays.   The cron time expression syntax is less important, but I would like to have something with this sort of flexibility.   If there isn't something that does this for me out-the-box, any suggestions for the building blocks to make something like this would be gratefully received.  Edit I'm not interested in launching processes, just "jobs" also written in Python - python functions. By necessity I think this would be a different thread, but not in a different process.  To this end, I'm looking for the expressivity of the cron time expression, but in Python.   Cron has been around for years, but I'm trying to be as portable as possible. I cannot rely on its presence. What does "yield break;" do in C#? I have seen this syntax in MSDN: , but I don't know what it does.  Does anyone know? Cause of black artifacts in render? Notify us when one of our posts is edited Your summary page shows "N Edits to your posts" for the selected time period but you really have to be looking for it.  Could we add edits to the notification feed? You could put the reason for the edit (entered--or not--when the editor changes it) and just a link to the post. I have the formula $x! + y! = z!$ and I'm looking for positive integers that make it true. Upon  inspection it seems that x = y = 1 and z = 2 is the only solution. The problem is how to show it.   From the definition of the factorial function we know $x! = x(x-1)(x-2)...(2)(1)$  So we can do something like this:  $$ [x(x-1)(x-2)...(2)(1)] + [y(y-1)(y-2)...(2)(1)] = [z(z-1)(z-2)...(2)(1)]$$   we can then factor all of the common terms out on the LHS.  $$ [...(2)(1)][x(x-1)(x-2)... + y(y-1)(y-2)...] = [z(z-1)(z-2)...(2)(1)]$$ and divide the common terms out of the right hand side  $$[x(x-1)(x-2)...] + [y(y-1)(y-2)...] = [z(z-1)(z-2)...]$$  I'm stuck on how to proceed and how to make a clearer argument that there is only the one solution (if indeed there is only the one solution).   If anybody can provide a hint as to how to proceed I would appreciate it. Select current element in jQuery Quickly create a large file on a Linux system How can I quickly create a large file on a Linux () system?   will do the job, but reading from /dev/zero and writing to the drive can take a long time when you need a file several hundreds of GBs in size for testing... If you need to do that repeatedly, the time really adds up.  I don't care about the contents of the file, I just want it to be created quickly. How can this be done?  Using a sparse file won't work for this. I need the file to be allocated disk space. Areas versus volumes of revolution: why does the area require approximation by a cone? Suppose we rotate the graph of $y = f(x)$ about the $x$-axis from $a$ to $b$.  Then (using the disk method) the volume is $$\int_a^b \pi f(x)^2 dx$$ since we approximate a little piece as a cylinder.  However, if we want to find the surface area, then we approximate it as part of a cone and the formula is $$\int_a^b 2\pi f(x)\sqrt{1+f'(x)^2} dx.$$  But if approximated it by a circle with thickness $dx$ we would get $$\int_a^b 2\pi f(x) dx.$$  So my question is how come for volume we can make the cruder approximation of a disk but for surface area we can't. Baked beans still firm after soaking and hours of cooking Question Prove that for every integer k≥1, exists a self-complementary graph with 4k vertices half of which are of degree 2k-1 and the other half of degree 2k.  My approach So, I think the easiest way to prove what is asked is by induction. I can prove the base case for k=1, but as far as the inductive step is concerned, I cannot seem to reach a conclusion as to why if the statement holds for n, then it holds for n+1.  Any help would be appreciated. 0:root@SERVER:/root # echo "something" | sed -e 's/^/\t/g' tsomething 0:root@SERVER:/root #    AIX/ksh .. why doesn't it works? I just want to put a "tab" before every line! How would I go about creating a 3D MMORPG Mouse Look? How would I go about creating a 3D MMORPG Mouse Look? I have created a 3D Space Rpg that is almost finished with success so far. However, I didn't have a clue, how I would attempt to make a Mouse Look method where if a user right clickes and then holds the right mouse button and moves it around the camera moves around with the mouse. The camera can not move away from your character/ship, it should act as if the character/ship is it's origin and that it rotates all around the origin.  I don't mind coding this with python either. Advice is welcome! Prove inequality $n<3^n$ using mathematical induction Prove that $n&lt;3^n$ where $n \in \mathbb N$,  when $ n=1 $, I have proved it's true. And assumed when $n = p$ , $p&lt;3^p$ is true. Can any body help me in showing that it is true for $n =p+1$ An example of a lattice that's not totally ordered Geometric intuition behind gradient, divergence and curl