I want to update a table by merging the categories separated by comma wherever we have a duplicate IDs for instance:  ID            Category 802              A 802              k            803              x              804              y 804              z  So here is the desired results that I would like to see after the update is run: ID            Category 802              A, k 803              x              804              y, z   Thanks
Consider a database table holding names, with three rows:  Peter Paul Mary   Is there an easy way to turn this into a single string of Peter, Paul, Mary?
If a drive doesn't know about partitions and files systems why moving a file from one partition to another takes relatively long time, unlike the instantaneous move on the same partition? Is that file system inefficiency? In this case, NTFS. It seems like the file is being copied and then original is erased, instead of removing the entry about that file in one partition and making it in another? Relating the Color of meat to doneness I want to know more about how to correlate the color of meat to its level of doneness. How do I recognize how cooked my meat is based solely on color? Unable to modify files/folders in NTFS partition How should I add users non-interactively? I have a set of users I need to add to a new system as part of a BASH script that preps my server. How can I non-interactively add the user, create their home directory, set the group, and enter a default password?  For example, if I needed to add the following users, how would I go about that?  user: node password: spoon group: ultraMegaPermissions  user:serve password: spoot group: sortaNotMega  user:watcher password: spoogle group: notMega When does a locational distinction change its suffix and capitialization in a proper name? Integrate $e^{ax}\sin(bx)?$ Is there a general formula for finding the primitive of $$e^{ax}\sin(bx)?$$  I've done this manually with $a=9$ and $b=4$ using Euler's formulas. But it takes a bit of time. Is there a pattern here? Editing the "Self-Learner" Badge Description Stemming from  the text for "Self-Learner" badge is pretty easy to get confused by.  Current Text     Answered your own question with score of 3 or more    Issue  The person in the above question was confused as they thought they needed to answer their own question, and that the question had to have a score of 3 or more. What it actually means is that they have to answer their own question, and the answer needs to have a score of three or more. The way it is phrased is ambiguous, so why not make it clear?  Suggestion  Edit the text as follows:     Provide an answer with a score of 3 or more to your own question   No more confusion. Finding determinant of matrix without expanding How prove this equation $\alpha=\aleph_{0}\alpha$ Question:     let $\alpha$ be a infinite cardinal , show that:   $$\alpha=\aleph_{0}\alpha$$   where $\aleph_{0}$ is the cardinality of the natural numbers is denoted aleph-null   this equation is from a book,and I can't prove it,and the author say this is important equation,and can't prove it.Thank you for you help Ball to Ball Collision - Detection and Handling With the help of the Stack Overflow community I've written a pretty basic-but fun physics simulator.    You click and drag the mouse to launch a ball.  It will bounce around and eventually stop on the "floor".  My next big feature I want to add in is ball to ball collision.  The ball's movement is broken up into a x and y speed vector.  I have gravity (small reduction of the y vector each step), I have friction (small reduction of both vectors each collision with a wall). The balls honestly move around in a surprisingly realistic way.  I guess my question has two parts:   What is the best method to detect ball to ball collision? Do I just have an O(n^2) loop that iterates over each ball and checks every other ball to see if it's radius overlaps? What equations do I use to handle the ball to ball collisions? Physics 101 How does it effect the two balls speed x/y vectors?  What is the resulting direction the two balls head off in?  How do I apply this to each ball?     Handling the collision detection of the "walls" and the resulting vector changes were easy but I see more complications with ball-ball collisions.  With walls I simply had to take the negative of the appropriate x or y vector and off it would go in the correct direction.  With balls I don't think it is that way.  Some quick clarifications: for simplicity I'm ok with a perfectly elastic collision for now, also all my balls have the same mass right now, but I might change that in the future.    Edit: Resources I have found useful  2d Ball physics with vectors:  2d Ball collision detection example:     Success!  I have the ball collision detection and response working great!  Relevant code:  Collision Detection:  for (int i = 0; i &lt; ballCount; i++)   {       for (int j = i + 1; j &lt; ballCount; j++)       {           if (balls[i].colliding(balls[j]))           {             balls[i].resolveCollision(balls[j]);         }     } }   This will check for collisions between every ball but skip redundant checks (if you have to check if ball 1 collides with ball 2 then you don't need to check if ball 2 collides with ball 1.  Also, it skips checking for collisions with itself).  Then, in my ball class I have my colliding() and resolveCollision() methods:  public boolean colliding(Ball ball) {     float xd = position.getX() - ball.position.getX();     float yd = position.getY() - ball.position.getY();      float sumRadius = getRadius() + ball.getRadius();     float sqrRadius = sumRadius * sumRadius;      float distSqr = (xd * xd) + (yd * yd);      if (distSqr &lt;= sqrRadius)     {         return true;     }      return false; }  public void resolveCollision(Ball ball) {     // get the mtd     Vector2d delta = (position.subtract(ball.position));     float d = delta.getLength();     // minimum translation distance to push balls apart after intersecting     Vector2d mtd = delta.multiply(((getRadius() + ball.getRadius())-d)/d);        // resolve intersection --     // inverse mass quantities     float im1 = 1 / getMass();      float im2 = 1 / ball.getMass();      // push-pull them apart based off their mass     position = position.add(mtd.multiply(im1 / (im1 + im2)));     ball.position = ball.position.subtract(mtd.multiply(im2 / (im1 + im2)));      // impact speed     Vector2d v = (this.velocity.subtract(ball.velocity));     float vn = v.dot(mtd.normalize());      // sphere intersecting but moving away from each other already     if (vn &gt; 0.0f) return;      // collision impulse     float i = (-(1.0f + Constants.restitution) * vn) / (im1 + im2);     Vector2d impulse = mtd.normalize().multiply(i);      // change in momentum     this.velocity = this.velocity.add(impulse.multiply(im1));     ball.velocity = ball.velocity.subtract(impulse.multiply(im2));  }   Source Code:     If anyone has some suggestions for how to improve this basic physics simulator let me know!  One thing I have yet to add is angular momentum so the balls will roll more realistically.  Any other suggestions?  Leave a comment! Hi everyone I'm attempting to install spotify, I've been running linux for less than 24 hours so please cut me some slack if this seems trivial. Here is a link to the webpage  and the example script.         Add this line to your list of repositories by editing your /etc/apt/sources.list    deb http://repository.spotify.com stable non-free    If you want to verify the downloaded packages, you will need to add our public key  sudo apt-key adv --keyserver hkp://keyserver.ubuntu.com:80 --recv-keys 94558F59    Run apt-get update  sudo apt-get update    Install spotify!      sudo apt-get install spotify-client      would someone be nice enough to walk me through this? I'm not even sure where to start. Does a percentage quantity take singular or plural verb agreement? Does a percentage require a singular or plural verb, for example, do we say ten percent "go" or "goes"? How do I create a deb package for a single python script? I have a single python script that I want to distribute as a deb package. It is a  which shows local date in Unity panel. I did follow  but I could not create a deb package because it fails.   Can someone give me a step-by-step instruction on what I should do? As far as I know this script depends on python-appindicator.   NOTE: I do not want any links to Debian/Ubuntu packaging instructions. I have seen most of them. I don't find them beginner friendly. The layman's question. Is there a maximum temperature that can be reached by air on Earth due to global warming? For example, one that would prevent living organisms from functioning? I read somewhere that with the increase of the sun's brightness by 10%, the average temperature on our planet will be 47 C. This, however, only for about 600 million years. Would global warming enable reaching such a high average temperature? Let $R$ be a commutative ring with unit, $I$ an ideal of $R$ and consider the following three constructions.   The  $R_I$ of $R$ at $I$ (i.e. the localization of $R$ at the multiplicative system $R\setminus I$) gives a morphism $$ f_1:\operatorname{Spec}(R_I)\to \operatorname{Spec}(R)=:X $$ The  $\widehat{R}_I$ of $R$ at $I$ gives a morphism $$ f_2:\operatorname{Spec}(\widehat{R}_I)\to X $$ For the special case $I=(a)$, the localization $R_a$ (i.e. the localization of $R$ at the multiplicative system $\{1,a,a^2,\ldots\}$) gives a morphism $$ f_3:\operatorname{Spec}(R_a)\to X $$   My question is:     What is the geometric meaning of all three constructions and how are they related?   This is what I ''know'' already or describes at least the style of answer I would appreciate. As remarked in the comments, $I$ has to be a prime ideal.   $R\to R_I$ is injective iff $R\setminus I$ contains no zero divisors which is the case if $I$ is a prime ideal. The scheme $\operatorname{Spec}(R_I)$ is the intersection of all the neightbourhoods of $I$ in $X$. This is a little contra-intuitive for me since the last statement sounds like ''$f_1$ is injective'' but the $\operatorname{Spec}$-operator should turn 'injective'' and ''surjective'' around somehow (I know this is literally not true but I only want to get a feeling like ''is contained'', ''is bigger'', ''is smaller'', etc.). $\operatorname{Spec}(R_a)$ is somehow the opposite of $\operatorname{Spec}(R_{(a)})$ (= the intersection of all the neightbourhoods of $(a)$ in $X$) because $\operatorname{Spec}(R_a)$ seems to be something like the union of all the open sets of $X$ not containing the point $(a)$. $R\to\widehat{R}_I$ is injective iff $\cap I^n=(0)$ and this holds very often (e.g. for $R$ noetherian and either an integral domain or a local ring). Hence (this is probably false intuition as remarked before), $f_2$ should be something like a ''projection'' (from something ''big'' into something ''small''). But what is geometrically the difference between localization and completion. I don't have a geometric idea of completion at all.   As remarked by Qiaochu Yuan in the comments below, one should not think of $\operatorname{Spec}$ as injective-surjective switching. How restrict page for users logged? I have a website with login page that works normal. The problem is that once logged in, the user still has access to the login page form to enter, which should not happen.  I would like to know a wordpres plugin that redirects this user to another page when they access it after login. Java is one of my programming languages of choice.  I always run into the problem though of distributing my application to end-users.  Giving a user a JAR is not always as user friendly as I would like and using Java WebStart requires that I maintain a web server.  What's the best way to distribute a Java application?  What if the Java application needs to install artifacts to the user's computer?  Are there any good Java installation/packaging systems out there? What can $E=mc^2$ do? In the famous equation , the variables stand for:     $E$ is energy, $m$ is mass, and $c$ is the speed of light (in vacuum).   And I understand the equation fairly but limited in knowing in its effects/outputs in reality, honestly.   Some example? Could anybody please give me some sort of examples in real world which are done by this equation? The choice of measurement basis on one half of an entangled state affects the other half. Can this be used to communicate faster than light? It is often stated, particularly in popular physics articles and videos, that if one measures a particle A that is entangled with some other particle B, then this measurement will immediately affect the state of the entangled partner.  For example, if Alice and Bob share an entangled pair of electrons and Alice measures her spin in the $x$ direction, then Bob's spin will also end up spinning in that direction, and similarly if she measures in the $z$ direction. Moreover, the effect will be instantaneous, regardless of the spatial distance between the two particles, which seems at odds with special relativity.  Can I use a scheme like this to communicate faster than light? How to find users by name I have a whole bunch of people I would love to follow or at least check out on Stack Overflow. I know them from places like Github as well as personal friends. However I am having a really hard time finding them even though I know e.g. their Gmail address and that they use OpenID via Gmail to login and their full name.   How come this is so painful? Note that I don't want to have to fuzz around with the data explorer just to find a friend of mine on Stack Overflow. What am I missing? Is it just not there or just not working properly?