Add arrow to parametric plot
Adding arrows in curves
I am trying to pickle some mangoes the Indian way. I boiled the jar in hot water, dried it and then added the mixture of spices, salt and mangoes to the jars after the mixture had cooled. I made the mixture in a frying pan to try and remove as much water as I could. After it was cooled, I put it in the jar and heated some mustard oil till it just barely started smoking. I let that cool and poured it over the mango spice mixture.  For the first three days it was fine. On the fourth day, I opened it to test the taste and ended up adding more salt. Now, there seems to be gas forming in the jar. I've noticed it a few times now. When I open the jar, I hear a whooshing noise as air escapes. It's quite a lot, since I opened the container about 3 times in a 10 hour period and each time gas escaped. Has this pickle gone bad? Or is this something that's normal? What's the main difference between int.Parse() and Convert.ToInt32 I have a script that I need to execute on an NTFS partition. The script's permission is set to 600.  I attempted to modify the permissions by running chmod 755 script.sh, which doesn't report a failure or anything - but it also doesn't change the permissions on the file:  $ stat script.sh    File: `script.sh'   Size: 297070      Blocks: 584        IO Block: 4096   regular file Device: 811h/2065d  Inode: 35515       Links: 1 Access: (0600/-rw-------)  Uid: ( 1000/  xxxxxx)   Gid: ( 1000/  xxxxxx) Access: 2010-09-30 14:05:16.041621000 -0700 Modify: 2010-09-30 14:05:05.070157000 -0700 Change: 2010-09-30 14:05:05.070475000 -0700  $ chmod 755 script.sh $ stat script.sh    File: `script.sh'   Size: 297070      Blocks: 584        IO Block: 4096   regular file Device: 811h/2065d  Inode: 35515       Links: 1 Access: (0600/-rw-------)  Uid: ( 1000/  xxxxxx)   Gid: ( 1000/  xxxxxx) Access: 2010-09-30 14:05:16.041621000 -0700 Modify: 2010-09-30 14:05:05.070157000 -0700 Change: 2010-09-30 14:05:05.070475000 -0700   As you can see, it remains unchanged. When induction proofs need a choice function Reading the comment to  the user makes the argument that one can pick a dense subset of a separable vector spaces without relying the axiom of countable choices. Since the comment got a lot of up votes, I guess it's correct, but to me this seems very strange. My rule of thumb was/is the following: We can get by without a choice function if   There is a canonical choice at each iteration. The proof doesn't actually require the iteration process to terminate.   None of these seem to be satisfied in the present case, unless there is a canonical choice for the dense subset, or the set is dense at some finite iteration, so my question is:   When can I tell if an induction arguments relies on the existence of a countable choice function? How to Translate Content type name using i18n module? I am developing a multilingual site that supports English and Norsk bokmal. I have set English as my default language. I wanted to translate the contents and the other things in the site.  My real problem started when I found that I was unable to see the translation of the content type's name. I went to admin/config/regional/translate/translate and translated everything, but still my content type's name is not translated.  I have attached a screenshot of the translation page. Still I don't find a way to translate the content type's name. How can I print the table of contents multiple times in my document? Is it correct to say user accounts or users account when referring to the accounts any user has on a site like this one?  In general, in the case of a noun that is used as adjective for the noun that follows, is it better to use &lt;plural-noun&gt; &lt;singular-noun&gt; or &lt;singular-noun&gt; &lt;plural-noun&gt;? Show $d_{1}(x_{n},x)\rightarrow{0}$ if and only if $d_{2}(x_{n},x)\rightarrow{0}$. Let $X=(0,\infty)$. Define two metrics on $X$ by   $d_{1}(x,y)=|x-y|$ and   $d_{2}(x,y)=|x-y|+|\frac{1}{x}-\frac{1}{y}|$   for all $x, y \in{X}$.   Let $(x_{n})$ be a sequence in $X$ and $x\in{X}$.   Show  $d_{1}(x_{n},x)\rightarrow{0}$ if and only if $d_{2}(x_{n},x)\rightarrow{0}$.  Note: $d_{1}$ and $d_{2}$ are then said to be equivalent metrics on $X$.  Since $d_{1}$ and $d_{2}$ are equivalent metrics, will it be sufficient to show $c*d_{2}(x,y)\leq{d_{1}(x,y)}\leq{C*d_{2}(x,y)}$?  So far I have the following: $d_{1}(x,y)=|x-y|\leq{|x-y|+|\frac{1}{x}-\frac{1}{y}|}=d_{2}(x,y)$. Therefore, $d_{1}(x,y)\leq{C*d_{2}(x,y)}$ where $C=1$. Is there a $c$ that would satisfy the left-hand side of the inequality?  Any help would be appreciated. (this is not homework) How do filament LED bulbs work, looking very similar to incandescent bulbs? Filament LED bulbs use very narrow strips containing the LED, which look similar to filaments of an old incandescent bulb:  They look like a normal bulb with large "old-style" coal filaments, and are of about the same size and shape as the common standart E27 socket bulb.    There are two basic variants of these bulbs:     One "plain" as described, looking impressively similar to a classic bulb The other has a white coating on the glass, about 15mm wide next to the metal socket.   How are these filaments build? I could imagine the it's "pretty normal" LEDs, but lots of them, directly bonded to something? (There are references to COB)  How does the heat management work? Ii have seen speculations about filling the bulb with either helium or "some patented organic gas" - could that be enough for cooling?  How does the driver - which seems to be very small - work?  In the variant with white coating - hiding some components, I assume - is already not that much space, and in the plain variant, there seems to be almost no space for something nontrivial.  Below you see some bulbs of the white coating variant, switched on:   (Images with the permission of this )    Note how the LED filament bulbs are not so much similar to the tungsten filament bulbs recently being phased out - they are more resembling the long outdated carbon filament bulbs: How do I set a custom resolution? I tried to use xrandr to set 1680x1050 as a new mode to VGA output, but it says:  sudo xrandr --addmode VGA-0 1680 X Error of failed request:  BadMatch (invalid parameter attributes) Major opcode of failed request:  140 (RANDR) Minor opcode of failed request:  18 (RRAddOutputMode) Serial number of failed request:  35 Current serial number in output stream:  36 Prove by mathematical induction that $n^3 - n$ is divisible by $3$ for all natural number $n$ Anonymous questions and Avatars If $X^n$ is a diagonal matrix with distinct eigenvalues, then is $X$ also a diagonal matrix with distinct eigenvalues? What is the difference between old style and new style classes in Python? What is the difference between old style and new style classes in Python?  When should I use one or the other? How to change ubuntu install from legacy to uefi "Access is denied" JavaScript error when trying to access the document object of a programmatically-created  (IE-only) I want to create a scratch-card-like effect in new Unity UI's new Image tag.  I know it's possible with setPixels, but that's prohibitively expensive on mobile devices.  Something like this:    I'd like the user to be able to drag on any part of the image to "scratch off" the top layer and reveal the content underneath it.  How can I do this? I think the title is pretty self explanatory.   The question is how can I create an alias in a Windows cmd that will also work after I close and then reopen it. For example I would like an alias called ip to call the command ipconfig or an alias ls -l to call Dir.  My operating system is Windows 10, in case that makes a difference. Work the Spring There's a book that I read several years ago that I'd like to find.  However, I cannot remember enough about it to find it myself.  Neither the title nor author remain in my mind, nor any keyword or phrase that's unique enough for the Grand Google to nail for me.  Hence my desperate plea here.  In the book, there is an interstellar civilization composed of several power blocks.  The entire civilization did not fill the galaxy, but it did span several stellar systems.  Maybe 10s or 100s.  I seem to remember that one of the civilizations was a decentralized group referred to as the Brotherhood and they seemed to have been keen on preserving old learning and political ideals.  A derelict alien spacecraft from outside all of this had been discovered and at least two of the power blocks sent ships to recover it.  I don't recall if they knew at the time about the power the alien ship had, but they must have had some clue since there was some urgency in capturing this ship.  One of the ships sent to capture the Alien craft was commanded by somebody who was rather shaken up, to say the least.  He had had some big trauma in his past (like... the last ship he captained was annihilated with all hands.) so he was kinda bummed out about things and wasn't really putting his heart into getting this done.  He was assisted by the ship's AI who had a lot of soul-to-soul chats with the captain, and at one point almost relieved him of command because he was just not getting the job done.  I think the ship's name was Boaz.  These were the "good guys".  There was at least one other ship sent from the "bad guys."  The alien craft had some remarkable powers.  The interior volume was apparently infinite and the operators could see and manipulate anything in the universe.  There might have been some example given where all the rats somewhere were found and disposed of.  Whoever had control was tempted by the ole absolute power corrupts absolutely problem, but nobody but nobody could stop them because of their power.  They could eat and multiply within the ship and become real bad-asses.  But alas... (or hurray, depending upon which side you're one) everything fails eventually, and whoever controlled the ship would eventually succumb to some horrible end.  Whereupon the ship became derelict again until some other lucky race found it and repeated the cycle.  The ship had an AI that was real interested in taking the power for itself, but there was some mechanical, spring-loaded, mechanism outside of its control that needed to be worked in order to execute power.  The AI apparently never figured out how to "work the spring" and this made him crazy angry.  The ending is equally foggy for me.  I'm pretty sure the good guys got the ship.  They agonized over what to do with it.  Apparently it was indestructable and nobody wanted to taste the temptation of all that power.  In the end they dumped it on the surface of a neutron star.  There it sat forever more, probably with the crazy AI really pissed off about being there.  If you've read this book, you'll recognize it immediately from these clues.  I'm looking forward to finding out the name of this book.  Thanks! NSDictionary with ordered keys I have an NSDictionary (stored in a plist) that I'm basically using as an associative array (strings as keys and values).  I want to use the array of keys as part of my application, but I'd like them to be in a specific order (not really an order that I can write an algorithm to sort them into).  I could always store a separate array of the keys, but that seems kind of kludgey because I'd always have to update the keys of the dictionary as well as the values of the array, and make sure they always correspond.  Currently I just use [myDictionary allKeys], but obviously this returns them in an arbitrary, non-guaranteed order.  Is there a data structure in Objective-C that I'm missing?  Does anyone have any suggestions on how to more elegantly do this?