How can electrons spin if they have no volume?
What is spin as it relates to subatomic particles?
Solve the recurrence $T(n) = 2T(n-1) + n$ Zip using Oracle Stored Procedure Google page title not matching html  tag How to send variable to an inline shell-script? $n &gt; 2$ and $n$ is a prime number then $n$ is odd.  Prove by contradiction assume $n$ is even then there is some $k\in\Bbb N, n = 2k$ then $n &gt;2, 2k &gt; 2 , k &gt; 1$  Is this  a sufficient proof? How do you forcefully remove apps in Windows 10? How can I remove apps that Windows doesn't seem to allow to be uninstalled, like Xbox and Groove Music? Why does every server I try say it can't connect? I just re-purchased Minecraft (because my old profile stopped working so I bought it) after not playing it for a couple of months. I've added a bunch of servers, but almost every one says "can not connect."  I know its not because the server is not 1.7.2, because I checked that they'd update. It will say "server can't connect" after a long time. I don't know if its me or the servers.  My server screen looks like this (notice the one at the bottom – it's still loading!): Can Objective C determine the caller object reference at runtime (reflection)? Script-r Symbol The near-ubiquitous undergraduate reference on electrodynamics, "Introduction to Electrodynamics" by David Griffiths make extensive use of a script-r symbol, defined to be \vector{\scriptr} \equiv \vector{r} - \vector{r}^{\prime} and looks like:    Although the question of how to produce such a symbol in LaTeX is quite a common one I am yet to find a satisfactory solution.  The closest I've found is from the physymb package and uses the Calligra fonts:    Sadly, there is not a bold variant of this character and it is far more cursive than I would like.  I am hence wondering if there are any better facsimiles. Suppose you have 2 circles that intersect each other in such a way that each circle passes through the other's center. What is the area between the circle(or common area) i.e. area between the centres of the circles? I'm new to ArcGIS 10 and am trying to do a really simple field calculator equation and it is not working. I'm just trying to find the percentage of a certain demographic trait by doing:  [asian]/[total]*100   It is populating about 10% of the column correctly and then I get an error:     There was a failure during processing, check the Geoprocessing Results   window for details   Obviously my syntax is not incorrect or else it wouldn't start populating the field correctly.   Does anyone have any idea why this is happening? In the calculus of variations, particularly Lagrangian mechanics, people often say we vary the position and the velocity independently. But velocity is the derivative of position, so how can you treat them as independent variables? How may I reference the script tag that loaded the currently-executing script? How can I reference the script element that loaded the javascript that is currently running?  Here's the situation. I have a "master" script being loaded high in the page, first thing under the HEAD tag.  &lt;!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"  "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"&gt; &lt;html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"&gt; &lt;head&gt; &lt;script type="text/javascript" src="scripts.js"&gt;&lt;/script&gt;   There is a script in "scripts.js" which needs to be able to do on-demand loading of other scripts. The normal method doesn't quite work for me because I need to add new scripts without referencing the HEAD tag, because the HEAD element hasn't finished rendering:  document.getElementsByTagName('head')[0].appendChild(v);   What I want to do is reference the script element that loaded the current script so that I can then append my new dynamically loaded script tags into the DOM after it.  &lt;script type="text/javascript" src="scripts.js"&gt;&lt;/script&gt; loaded by scripts.js--&gt;&lt;script type="text/javascript" src="new_script1.js"&gt;&lt;/script&gt; loaded by scripts.js --&gt;&lt;script type="text/javascript" src="new_script2.js"&gt;&lt;/script&gt; Which movie/TV show has an evil cyborg harvesting eyes from androids in a hidden town? I watched it maybe more than 8 to 12 years ago, but as far as I remember there was this place where androids (or maybe they were cyborgs) lived. (I think it was more like a hidden town). This guy finds them by accident (or at least I remember it that way) and tries to help them. I don't remember seeing any aliens or spaceships or anything like that. It was live-action, and I think US-based.  So, what I remember:   The bad guy is a human who has one red flashy robotic eye (not like terminators, it looks like a square eye patch above one of his eyes that functions like a second eye), he is collecting eyes from these androids/cyborgs. He also kills some of these androids/cyborgs but not all of them, some of them he just collects their eyes and doesn't kill (or get to kill). There was this woman who was a sexbot or something, she tried to give pleasure to the bad guy at some point, yet the bad guy added one of her eyes to his collection instead, but didn't/wasn't able to kill her. Towards the end she says something like "I used to give pleasure, now I only want to give pain" The human guy who found them tried to help them defend themselves from the bad guys, but they were in bad shape, many of them needed repair. To repair some of them, they needed spare parts they didn't seem to have, but one of the android/cyborg dudes said something like "we don't really bury our dead" and he brought a box of spare parts (or maybe android/cyborg body parts), they used these parts to repair some of the androids/cyborgs. There was this android/cyborg guy who was an assassin or something, but lost his fingers or hands, they couldn't find any hands compatible to his, but he said something like "I can still feel my trigger finger, just attach the weapons to my hands".   I remember it as a great movie/tv show, but I can't find anything about it. Can someone help me?  Please and thank you in advance... Linear Discriminant Analysis for $p=1$ I'm studying 'Introduction to Statistical Learning' by James, Witten, Hastie, Tibshirani.   In page 139, of their book, they began by introducing Bayes' Theorem $p_k(X)=P(Y=k|X=x) = \dfrac{\pi_kf_k(x)}{\sum_{l=1}^k \pi_l f_l(x)}$. $\pi$ is not mathematical constant, but denotes the prior probability. Nothing is strange in this equation.   The book claims that it wants to obtain an estimate for $f_k(x)$ that it can plug into the equation given above. To estimate $f_k(x)$, it assumes that is normal. In the one dimensional setting, $f_k(x)=\dfrac{1}{\sqrt{2\pi}\sigma}\exp(-\dfrac{1}{2\sigma^2}(x-\mu_k)^2)$, where $\mu_k$ and $\sigma^2_k$ are the mean and variance for the $k$th class. It is assumed that $\sigma^2_1 = \sigma^2_2 = \cdots = \sigma^2_K$. (I began to get confused from the last statement.)   Plugging $f_k$ into $p_x$, you have this quite messy equation (1) :   $$p_x(k)=\dfrac{\pi_k \frac{1}{\sqrt{2\pi}\sigma}\exp(-\frac{1}{2\sigma^2}(x-\mu_k)^2)}{\sum_{l=1}^K \pi_l \frac{1}{\sqrt{2\pi}\sigma}\exp(-\frac{1}{2\sigma^2}(x-\mu_l)^2)}. $$  Again, no surprises here since it is just substitution.     The Bayes' Classifier involves assigning an observation to the class for which equation (1) is the largest. Taking the log of Equation (1) and rearranging terms, it is not hard to show that this is equivalent to assigning the observation to the class for which the following is the largest:  $$\delta_k(x)=x \cdot \dfrac{\mu_k}{\sigma^2} - \dfrac{\mu_k^2}{2\sigma^2} + \log(\pi_k) $$  Question: I do not understand where this came from, and what it means. I tried doing the log of equation and it doesn't become this. Are we taking the derivative somewhere here, since this is the largest observation? align vs equation Speeding up a NOT IN subquery Good evening,  I'm currently up to try to improve the performance of some of my queries. As far as I know, statements like "IN" or "NOT IN" are even faster with a large amount of values if a subquery on an indexed field without conditions is used.  SELECT * FROM table1 WHERE field1 NOT IN (SELECT index_field FROM table2)   When it comes to use conditions at table2, the query becomes realy slow on a large amount of data.  SELECT * FROM table1 WHERE     field1 NOT IN (         SELECT             index_field         FROM table2         WHERE             user_id = '2'     )   I was thinking about using LEFT Join but when I need to to the filtering for the user_id, it also becomes slow.  How may I solve this problem? Currently, I've no clue about that.  The original query looked sth. like this  SELECT     i.* FROM stream_item si LEFT JOIN user__publisher_item ui     ON ui.user_id = 2     &amp;&amp; ui.item_id = si.item_id INNER JOIN item i     ON i.id = si.item_id WHERE      si.stream_id IN (5,7,8,9,19,24,29,42,43,44)     &amp;&amp; ui.id IS NULL || (         ui.`read` = 0 || ui.saved = 1     ) GROUP BY     si.item_id ORDER BY     si.`found` DESC LIMIT 0,10     id      select_type     table   type        possible_keys                                                                           key                 key_len     ref                 rows        Extra 1       SIMPLE          si      index       PRIMARY,stream_2_item,stream_id_found                                                   stream_2_item       4           \N                  663236      Using temporary; Using filesort 1       SIMPLE          ui      eq_ref      user_id_item_id,user_2_item,user_id_read_saved_hidden,user_id_saved,user_id_hidden      user_id_item_id     8           const,si.item_id    1           Using where 1       SIMPLE          i       eq_ref      PRIMARY                                                                                 PRIMARY             4           si.item_id          1      I have a table which represents the n:m relationship between stream and items. An unique item can be accessible via multiple streams. Based upon this i have a state-table for user dependent states of an item. Currently, the user-state-entry will only be generated, if the item was read or saved the first tim. Otherwise, there is no entry in the user_item table. In the beginning, this query was fine but now, it takes a lot of time. Even if I leave out the "INNER JOIN" it takes 7 seconds on the current tables with around 500k rows each.  The table-structure in the background is as follows:   stream stream_item //n:m relation between stream and items item //unique items stream_group //user-defined groups of multiple streams stream_group_streams //_n:m relation between stream_groups and streams_ user user_item //state-table that holds the user-dependent states of an item - if there is no state, no row exists for an item   I already asked this question at  but added my 2 Edits with further information to late so that I haven't got an answer anymore. When should I use "when" and "while"? But you can't find anything while you're crying.   But you can't find anything when you're crying.   I'll tell you about it while Frank saddles the horse.   I'll tell you about it when Frank saddles the horse.     When should I use when, and when while? Are these sentences correct? function a () {     return "foo"; }  a.b = function () {     return "bar"; }  function c () { }; c.prototype = a;  var d = new c(); d.b(); // returns "bar" d(); // throws exception, d is not a function   Is there some way for d to be a function, and yet still inherit properties from a? Gravitational waves and time Two questions.  It is said that time can only go slower in gravity fields and if you move faster.  I have heard that when a gravitational wave pass earth then the space/time vibrate and time change for an instance.  But a wave is often with a top and a valley.  They have now atomic clocks that might be able to detect time variations, placed in satellites around the sun and "quantum entangled". "Using Atomic Clocks to Detect Gravitational Waves"   So what if we could compare time ticks between clocks in space at "absolute frame of reference" where time has its maximum universal speed as time in deep space between Galaxy Filaments.  Will we only detect that time ticks slower for an instance when the gravational wave pass?  1. Or will we detect that time tick slower AND faster than normal time also, as compared to zero gravity time and no movement time in "absolute frame of reference"?  2. Can time go let's say 10 times faster by theory/mathematics, by a extreme theoretical gravitational wave, than time in "absolute frame of reference time"?