I noticed that when I throw salt into a cooking pot and then mix, the salt collects in the center. As salt is denser than water, I would have expected it to go towards the border of the pot, and not in the middle. What is going on exactly there?
At xmas, I had a cup of tea with some debris at the bottom from the leaves.  With less than an inch of tea left, I'd shake the cup to get a little vortex going, then stop shaking and watch it spin.  At first, the particles were dispersed fairly evenly throughout the liquid, but as time went on (and the vortex slowed, although I don't know if it's relevant) the particles would collect in the middle, until, by the time the liquid appeared to almost no longer be turning, all the little bits were collected in this nice neat pile in the center.  What's the physical explanation of the accumulation of particles in the middle?  My guess is that it's something to do with a larger radius costing the particles more work through friction...
Every time I try to create a table using MySQL Workbench 6.3 CE it adds "broken" comments at the end of the script.  Example:  I am trying to create a table called "user". This is what the table should look like:   However when I click the apply button, the script generates incorrectly:  CREATE TABLE `user` (   `userid` INT NOT NULL AUTO_INCREMENT COMMENT '',   `record_status` INT NOT NULL DEFAULT 1 COMMENT '',   `createdby` VARCHAR(75) NOT NULL COMMENT '',   `createddate` DATETIME NOT NULL COMMENT '',   `updatedby` VARCHAR(75) NULL COMMENT '',   `updateddate` DATETIME NULL COMMENT '',   `username` INT NOT NULL COMMENT '',   `password` VARCHAR(75) NULL COMMENT '',   `firstname` VARCHAR(75) NULL COMMENT '',   `lastname` VARCHAR(75) NULL COMMENT '',   `email` VARCHAR(75) NULL COMMENT '',   `facebook_userid` VARCHAR(75) NULL COMMENT '',   `email_verified` VARCHAR(75) NULL COMMENT '',   PRIMARY KEY (`userid`, `username`)  COMMENT '');   The comment in this line should not be there, so the code should be:   PRIMARY KEY (`userid`, `username`));   and the code executes when I paste it into an editor and remove this comment. However I create massive databases daily. (Each with +- 15 tables). I can't keep doing this for each table as it is time consuming.  How can I disable this feature that adds the comments to the script? I don't need them in my databases Tangent lines to ellipse from external point I was wondering what the cardinality of the set of all real sequences is. A random search through this site says that it is equal to the cardinality of the real numbers. This is very surprising to me, since the cardinality of all rational sequences is the same as the cardinality of reals, and it seemed fairly intuitive to me that if cardinality of a set $A$ is strictly greater than the cardinality of the set $B$, then cardinality of $A^{\mathbb{N}}$ should be strictly greater than cardinality of $B^{\mathbb{N}}$. It turns out to be false.  Some technical answers have appeared in this forum elsewhere but I do not understand them. As I am not an expert in this topic, could some one explain me in simple terms why this is happening?  Also is the cardinality of all functions from reals to reals also the same as the cardinality of reals? Proving $\sum_{k=0}^n\binom{2n}{2k} = 2^{2n-1}$ I'm undergraduate student of mathematics.  I need to prove: $$\sum_{k=0}^{n} \binom{2n}{2k}= 2^{2n-1}$$ Can you please help me Do lenses have focal planes or focal spheres/ellipsoids? I'm printing a tradeshow flyer and was wondering what type of paper I should print it on. I don't want anything glossy so I'm trying to decide on the following:   100# text weight matte 80# cover 80# matte   What is the difference between the types above? And how can I make a decision? What did the public at large know about the assassination attempt on Palpatine and how he survived it? Why can't I paste § into a Minecraft command? Can someone remind me of the name of the author, the name of the hero and the name of the series if any? Adventure Sci-Fi books, short by today's epic standards ( = about same length as Heinlein's shorter youth books), probably published late 50s?, early 60s? by Bantam? or Del Rey? I think at least 30, possibly more than 40 books in the series. Not comic books. The author is not a well-known writer. At least, I don't remember seeing the name on any other books, ever.   Subject: a man who can move and respond to threats extremely fast learns about a secret potion that allows a person to change bodies with someone else and thus control them. A powerful organization does not want the secret to be known, because they use the potion to control politicians on many planets. The organization's goons are people who had surgeries to remove their emotions, and function like organic computers. They can communicate over interstellar distances and follow and murder anyone who learns the secret. I remember the following detail about the potion: there are two nearly identical molecules that have to be assembled in a certain sequence. Two of the components had to be switched around and that determined who would be dominant and who would be controlled during the mind switch / body swap.   Every book finds the hero on another planet with new adventures, and usually taking another deep-sleep-passage to another world, fleeing his pursuers. The background story about the secret potion is dished out little by little in each book.  One book in the series starts like this: hero is on very hot planet, diving for valuable marine life, catches a deadly fungus disease and is rescued last moment in exchange for his catch...  One of the themes that returns often is that the hero is an excellent knife fighter.  Of course he's a womanizer. In the second (or close to 2nd) book in the series, he's involved with a woman who rules a planet.  To travel to another world, he usually takes the cheapest dead-sleep passage, and there's always a 10-25% risk you won't wake up from that. I would like to know how to make this effect of merged circle selection. Here are images to illustrate:     Basically I'm looking for this effect:    How the merge effect of the circles can be achieved ? I didn't found any explanation concerning this effect. I know that to project those texture I can develop a decal system but I don't know how to create the merging effect.  If possible, I'm looking for purely shaders solution. Can I run OSX applications? I was setting up up android-studio referring to . While installing oracle-java7-installer, this error is displayed:  sudo apt-get install oracle-java7-installer [sudo] password for cyan:  Reading package lists... Done Building dependency tree        Reading state information... Done oracle-java7-installer is already the newest version (7u80+7u60arm-0~webupd8~1). The following package was automatically installed and is no longer required:   snap-confine Use 'sudo apt autoremove' to remove it. 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 1 not fully installed or removed. After this operation, 0 B of additional disk space will be used. Do you want to continue? [Y/n] y Setting up oracle-java7-installer (7u80+7u60arm-0~webupd8~1) ... Downloading Oracle Java 7... --2017-11-27 08:40:47--  http://download.oracle.com/otn-pub/java/jdk/7u80-b15/jdk-7u80-linux-x64.tar.gz Resolving download.oracle.com (download.oracle.com)... 223.223.158.138, 223.223.158.136 Connecting to download.oracle.com (download.oracle.com)|223.223.158.138|:80... connected. HTTP request sent, awaiting response... 302 Moved Temporarily Location: https://edelivery.oracle.com/otn-pub/java/jdk/7u80-b15/jdk-7u80-linux-x64.tar.gz [following] --2017-11-27 08:40:47--  https://edelivery.oracle.com/otn-pub/java/jdk/7u80-b15/jdk-7u80-linux-x64.tar.gz Resolving edelivery.oracle.com (edelivery.oracle.com)... 23.58.58.93, 2600:140f:7:18e::2d3e, 2600:140f:7:18d::2d3e Connecting to edelivery.oracle.com (edelivery.oracle.com)|23.58.58.93|:443... connected. HTTP request sent, awaiting response... 302 Moved Temporarily Location: http://download.oracle.com/otn-pub/java/jdk/7u80-b15/jdk-7u80-linux-x64.tar.gz?AuthParam=1511752368_824528560c20825821ecbcac8f4e9be9 [following] --2017-11-27 08:40:48--  http://download.oracle.com/otn-pub/java/jdk/7u80-b15/jdk-7u80-linux-x64.tar.gz?AuthParam=1511752368_824528560c20825821ecbcac8f4e9be9 Connecting to download.oracle.com (download.oracle.com)|223.223.158.138|:80... connected. HTTP request sent, awaiting response... 404 Not Found 2017-11-27 08:40:50 ERROR 404: Not Found.  download failed Oracle JDK 7 is NOT installed. dpkg: error processing package oracle-java7-installer (--configure):  subprocess installed post-installation script returned error exit status 1 Errors were encountered while processing:  oracle-java7-installer E: Sub-process /usr/bin/dpkg returned an error code (1)   How do I fix this error? I did a fresh installation of Ubuntu 16.04. If $\sum a_n b_n <\infty$ for all $(b_n)\in \ell^2$ then $(a_n) \in \ell^2$ I'm trying to prove the following:     If $(a_n)$ is a sequence of positive numbers such that $\sum_{n=1}^\infty a_n b_n&lt;\infty$ for all sequences of positive numbers $(b_n)$ such that $\sum_{n=1}^\infty b_n^2&lt;\infty$, then $\sum_{n=1}^\infty a_n^2 &lt;\infty$.   The context here is functional analysis homework, in the subject of Hilbert spaces.  Here's what I've thought:  Let $f=(a_n)&gt;0$. Then the problem reads: if $\int f\overline{g}&lt;\infty$ for all $g&gt;0,g\in \ell^2$, then $f\in \ell^2$. This brings the problem into the realm of $\ell^p$ spaces.  I know the inner product is defined only in $\ell^2$, but it's sort of like saying: if $\langle f,g\rangle &lt;\infty$ for all $g&gt;0,g\in \ell^2$ then $f\in \ell^2$.  I read this as: "to check a positive sequence is in $\ell^2$, just check its inner product with any positive sequence in $\ell^2$ is finite, then you're done", which I find nice, but I can't prove it :P  From there, I don't know what else to do. I thought of Hölder's inequality which in this context states: $$\sum_{n=1}^\infty a_nb_n \leq \left( \sum_{n=1}^\infty a_n^2 \right)^{1/2} \left( \sum_{n=1}^\infty b_n^2 \right)^{1/2}$$  but it's not useful here. Prove the equality of circle's areas Through a random point inside the circle, we draw $4$ lines with $45$ degrees between each other. Prove, that the total area of odd pieces, equals total area of even pieces.    I suppose there is a solution using integrals, but maybe there is geometric solution as well. Accessing Reduce from DSolve Given a subset $A$ of $\mathbb{R}^{n}$, a point $x \in \mathbb{R}^{n}$ is said to be in the boundary of A if and only if for every open rectangle $B\subseteq\mathbb{R}^{n}$ with $x\in B$, $B$ contains both a point of $A$ and a point of $\mathbb{R}^{n}\setminus A$.  My question is from Spivak's Calculus on Manifolds: Construct a set $A \subseteq [0,1]\times [0,1]$ such that $A$ contains at most one point on each horizontal and vertical line but has boundary equal to $[0,1]\times[0,1]$. Windows 2008 R2 Standard server - how to disable RC4 I have just used www.ssllabs.com and ran a few tests - my server is capped to a B grade because my server accepts RC4     This server accepts the RC4 cipher, which is weak. Grade capped to B.   I've researched and found that to disable RC4 I need to add 3 keys, and set their enabled dword to 0  and   I have done this for RC4 40/128, RC 56/128 and RC4 64/128  I then restarted my server. When the server was up again, I verified the Registry Changes were done, and they are - all 3 exist and all 3 have their enabled value set to 0.  I return to ssllabs, clear the cache, re-run the test and it returns the same result (capped to B due to RC4 being enabled).   At this stage, I'm not sure what this means - if SSLLabs showing incorrect results (I'm going to assume not), have I disabled RC 4.  How can I tell if I have successfully disabled RC4  Edit  I also saw the KB about this  so trying now... I've done the same registry changes but, when I try to download the 64 bit version for W2008 R2 Standard, it fails to install with error message     The update is not applicable to your computer accounting for LED resistance Complex numbers - Exponential numbers - Proof Let $z$ be a complex number, and let $n$ be a positive integer such that $z^n = (z + 1)^n = 1$. Prove that $n$ is divisible by 6.  For this problem I am stumped...how should I begin? Also there's a hint for it:  From $z^n = 1$, prove that $|z| = 1$. What does the equation $(z + 1)^n = 1$ tell you? What do the resulting equations tell you about $z$?  Could someone give me a hint on where to begin? thanks in advance This Community Wiki question is designed to be the "canonical question" for questions asking how to upgrade one's device to a new Android version.   I want to get a newer version of the OS for my Android device. How can I do that?  See also: