1 sec pass for the person rode on light
What is time dilation really?
Proof of $\frac{(n-1)S^2}{\sigma^2} \sim \chi^2_{n-1}$ It's a standard result that given $X_1,\cdots ,X_n $ random sample from $N(\mu,\sigma^2)$, the random variable $$\frac{(n-1)S^2}{\sigma^2}$$ has a chi-square distribution with $(n-1)$ degrees of freedom, where $$S^2=\frac{1}{n-1}\sum^{n}_{i=1}(X_i-\bar{X})^2.$$ I would like help in proving the above result. Thanks. How to replace plain URLs with links? Which one is correct: '3 hour journey' or a '3-hour journey'? Which one of the following is correct (bold part)?      It took us quite a long time to get here. It was 3 hour journey.   or     It took us quite a long time to get here. It was a 3-hour journey. $a$ and $b$ are natural numbers and $p$ is a prime number. Prove that if $a^{p}-b^{p}$ is divisible by $p$, then it is also divisible by $p^{2}$.  My attempt: Based on Fermat's theorem $(a^{p}-a)$ and $(b^{p}-b)$ are divisible by p, therefore their difference is divisible by $p$. I.e. $(a^{p}-a)-(b^{p}-b)=(a^{p}-b^{p})-(a-b)$ is divisible by $p$. Since the left hand side of this equation is divisible by $p$, the right hand side also should be divisible by $p$. Based on the problem's assumption $(a^{p}-b^{p})$ is divisible by $p$ therefore we conclude $(a-b)$ must be divisible by $p$. Now We can factorize $(a^{p}-b^{p})$ $$(a^{p}-b^{p})=(a-b)(a^{p-1}+a^{p-2}b+....+b^{p-1})$$ we have to prove $(a^{p}-b^{p})$ is multiple of $p^2$ which means we have to show the right hand side should be multiple of $p^{2}$. But $(a-b)$ is multiple of p therefore we have to show  $(a^{p-1}+a^{p-2}b+\cdots+b^{p-1})$ is multiple of $p$ and I am stuck here. Any help would be appreciated. Number of solutions of $x_1+2x_2+\cdots+kx_k=n$? In my document, I will write something like this (using natbib, but that shouldn't matter too much):  \citet{reference} show that .....   which would render as     Jones et al (1990) show that....   (\citet in \natbib creates an 'author-list (year)' reference style)  Of course if {reference} was a single individual, I should have written  \cite{reference} shows that ....   rendering as     Jones (1990) shows that....   Since I'm lazy and can't take the extra 5 seconds to search the reference to see if it's a single author or not, is there conceivably an automated way to do pluralization ? Or some relatively simple macro that would look like   \IfRefIsPlural{reference}{show}{shows} How do I handle partially correct edits in the Suggested Edits review queue? Contradicting Instructions While going through the suggested edits review queue, one sometimes stumbles upon partially useful edits like . Trying to follow the instructions listed in the descriptions doesn't lead to a conclusive answer. Considering our example:   Approve edits that clearly improve the post ↳ No, not *clearly* Improve Edit when you can make additional improvements to the post ↳ I most definitively can Reject and Edit to replace an ineffective edit with your own substantive changes ↳ It is ineffective in the sense that it made the post worse overall (imho) Reject edits that fail to improve the post or that make it worse ↳ Like the last option: yes Skip if you are not sure and want to go to the next suggested edit ↳ Well, yes. But that is really why I am here, asking this question   Reasoning about the remaining Choices This leaves us with three choices: Improve Edit, Reject and Edit and Reject (the last one slightly modified):  Improve Edit  + Acknowledges that some things in the edit where correct - Learning effect for author might vanish, as the improvement might get overlooked - Can't leave a custom message for edit author (except in comments, which pollutes the thread) - Doesn't trigger the system which &quot;punishes&quot; users who repeatedly have their edits rejected - Rewards the edit author with reputation for a poor edit   Reject and Edit  + Clearly shows the author that there were problems with the edit - Still can't leave a custom message explaining the problems of the original post. - One has to partially redo parts of the edit that have just been rejected, which might feel unjust to the original editor   Reject with a custom note and come back immediately to make a good Edit  + Clearly shows the author that there were problems with the edit + Possibility to leave an explanation as to what was wrong with the edit - One still has to redo parts of the edit that has just been rejected - Seems to be a weird workaround for Reject and Edit   Something else?   Each of the three options come with their distinct advantages/disadvantages making it non trivial to decide which one to pick.  Or does the answer simply depend on the quality of the edit? Like:  Improve Edit for subjectively slightly positive edits Reject and Edit (Or Reject and Edit) for subjectively slightly negative edits What antivirus program can I use on Ubuntu? Are there any antivirus applications that work on Ubuntu 16.04? Thanks! Order of a element on a Symmetric Group LINQ to Entities does not recognize the method 'System.String Format(System.String, System.Object, System.Object)' I want to programmatically create a new column in an MS Access table.  I've tried many permutations of ALTER TABLE MyTable Add  MyField DECIMAL (9,4) NULL; and got:      Syntax Error in Field Definition   I can easily create a number field that goes to a Double type, but I want decimal.  I would very strongly prefer to do this in a single ALTER TABLE statement and not have to create a field and then alter it.   I am using Access 2003. Is there a way to detach matplotlib plots so that the computation can continue? After these instructions in the Python interpreter one gets a window with a plot:  from matplotlib.pyplot import * plot([1,2,3]) show() # other code   Unfortunately, I don't know how to continue to interactively explore the figure created by show() while the program does further calculations.  Is it possible at all? Sometimes calculations are long and it would help if they would proceed during examination of intermediate results. Creating files in C++ Best practice of when to load data into a ListBox How to parse hex values into a uint? When to use LinkedList over ArrayList in Java? I've always been one to simply use:  List&lt;String&gt; names = new ArrayList&lt;&gt;();   I use the interface as the type name for portability, so that when I ask questions such as these I can rework my code.    When should  be used over  and vice-versa? I'd like to run a game of , but I'm not sure how many dice I roll when the characters face various challenges. I'm under the impression that it's supposed to be the same number of dice the character uses, but that seems to make impossible tasks far too easy to perform. Is there a general rule saying how many dice the GM rolls against a character's attempt at a given task?  Should the GM's dice equal the character's dice, or should the GM's dice vary depending on the task's difficulty? Linux Debian codenames I've got a few, quite silly, non-technical questions about giving  to  releases.  Each Debian release has its unique codename, which is (so far) a characters' name from  movies by .  Here is list of all assigned codenames so far:   release 1.1 is  (Buzz Lightyear) - the spaceman, release 1.2 is  - the tyrannosaurus, release 1.3.x is  (Bo Peep) - the girl who took care of the sheep, release 2.0 is  - the piggy bank, release 2.1 is  (Slinky Dog) - the toy dog, release 2.2 is  - Mr. Potato, release 3.0 is  -  the cowboy, release 3.1 is  - the sergeant of the Green Plastic Army Men, release 4.0 is  - the toy blackboard (Etch-a-Sketch), release 5.0 is  - the toy binoculars, release 6.0 is  - the name for the three-eyed aliens, release 7.0 is  - the name of the rubber toy penguin with a red bow tie, release 8.0 is  - the name of the yodelling cowgirl, release 9.0 is  - a purple rubbery octopus toy at , release 10.0 is  - 's pet dachshund (currently ).   List of upcoming major Debian releases' codenames after :   release 11.0 is  - 's horse (currently ), release 12.0 is  - intelligent worm toy with a built-in flashlight.   There are also:   special codename  () which is symbolic link to codename which is currently unstable,  which is symbolic link to codename which is currently stable,  which is symbolic link to codename which is currently testing.   The list of Toy Story  is quite  but at some time, there will be no more characters' names to assign.  My questions are:   What codenames will be assigned if we run out of characters' names? Who decides what is codename of next release (please don't answer ambiguously like: 'community')? How many releases' names are planned ahead?   BTW: Interesting quote from :     The  of using Toy Story names was  by  who   was, at the time, the Debian Project Leader and was working also at   , the company that produced the movies.     by  (: ). How does one experimentally determine chirality, helicity, spin and angular momentum of a fundamental particle? I try to write a simple Markdown parser in JavaScript. Therefore I want to check for the [link content][link id] syntax. I use the following code:  data = data.replace( /\[(.*?)\][ ]*\[([0-9]+)\]/g, '&lt;a href="$2"&gt;$1&lt;/a&gt;' );   It works well, but now I want to do this with a RegExp object. So I set up the following bit of code:  var r = new RegExp( '\[(.*?)\][ ]*\[([0-9]+)\]', 'g' ); data = data.replace( r, '&lt;a href="$2"&gt;$1&lt;/a&gt;' );   But it doesn't work. It even says that my regular expression (which works since the first example does a good job) is invalid:     unmatched ) in regular expression   I think it must have to do with some RegExp-object peculiarities I am not aware of. What am I doing wrong and how can the problem be solved?