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Avoiding NullPointerException in Java Fetching all (javascript) global variables in a page CSS :after not adding content to certain elements Can a ring of positive characteristic have infinite number of elements? I have a question about the pattern "turn &lt;something&gt; on &lt;somebody&gt;" :     Then he allegedly turned the body-building equipment on his 44 year-old wife, identified by sources as Feng Liang, and his elderly mother-in-law, Feng Kun Zaehng,77, the sources said.     I understand the phrase "*turn the gun on &lt;somebody&gt;", am not sure about "turn the equipment on &lt;somebody&gt;".  Could the example be wrong? iOS StackExchange app doesn't handle non-ASCII correctly The iOS StackExchange app doesn't handle non-ASCII characters correctly, see city name in the screenshot below. Twin Paradox, calculating spacetime intervals from both perspectives I've very recently started to try to understand special relativity. I'm want to get a decent understanding of the twin paradox. I'll post what I've done so far and highlight what's gone wrong for me.  The situation is that Alice and Bob both begin at point $x_1$ in Alice's coordinate system $(x,t)$ (we have orientated the axis so that y and z will not matter). Bob then instantaneously moves off with velocity $v$ in the positive $x$ direction. Bob's coordinate system is now $(x',t')=(\gamma (x-vt), \gamma (t-v\frac{x}{c^2}))$. In Alice's coordinates, Bob reaches point $x_2$ after having moved distance $d$, then instantly turns around and travels back to Alice at $-v$. I want to show that Alice's space time interval $\Delta s_A^2$ is greater than Bob's $\Delta s_B^2$, as each path's space time interval is proportional to the proper time passed along that path.    According to Alice: $\Delta s_A^2=-c^2\Delta t^2 + \Delta x_A^2$ where $\Delta t=\dfrac{2d}{v}$ and $\Delta x_A=0$ as she didn't move, but the time elapsed is the time it took bob to travel the distance and then come back. Thus $\Delta s_A^2=-\dfrac{4c^2d^2}{v^2}$  Still according to Alice, Bob's $\Delta s_B^2=-c^2\Delta t^2+\Delta x_B^2$, where the change in time is the same, but now bob has moved distance $d$ twice, thus $\Delta x_B=2d$ ($\Delta x$ refers to total distance traveled rather than displacement which is 0 in this case). Now we have $\Delta s_B^2=-\dfrac{4c^2d^2}{v^2}+4d^2$.     The |size| of Bob's spacetime interval now definitely smaller than Alice's, and this would be all OK, except that when I do the calculations in Bob's frame, they don't agree. This is contradictory to the fact that $\Delta s^2$ is conserved under Lorentz transformations.    According to Bob: $\Delta {s'}_A^2=-c^2\Delta t'^2 + \Delta {x'}_A^2$ where $\Delta t'=\dfrac{2d'}{v}$. I'm not sure if I'm right in saying that $v$, the relative velocity of the two frames, is the only velocity upon which both Alice and Bob will agree on, other than the speed of light. Anyway, $d=\gamma d'$ as lengths contract by $\gamma$ i.e. $d'$ is smaller than $d$ by factor $\gamma$. Also, $\Delta {x'}_A=2d'$, so we have $\Delta {s'}_A^2=-\dfrac{4c^2d'^2}{v^2}+4d'^2=-\dfrac{4c^2d^2}{\gamma ^2 v^2}+\dfrac{4d^2}{\gamma ^2}=4d^2\dfrac{v^2-c^2}{\gamma^2 v^2}\neq \Delta s_A^2$  Although I haven't included them here, my calculations for $\Delta {s'}_B^2$ and $\Delta s_B^2$ agree. Sorry for the ultra-long post, but any help would we well appreciated! Connected compact covering space of torus is homeomorphic to $S^1\times S^1$ Are human bodies programmed to die? Following from this question: :  Is there any evidence that human bodies have systemic self-destruction built into their developmental program? I'm not talking about the cell death response, which I know is an important part of growth, development and cancer prevention.  I've read some things about telomere-shortening but don't know if this is a cause or an effect. Order of evaluation in C++ function parameters I find it very strange that $$ e^x \geq x^e \, \quad \forall x \in \mathbb{R}^+.$$   I have scratched my head for a long time, but could not find any logical reason. Can anybody explain what is the reason behind the above inequality? I know this is math community, but I'd appreciate a more intuitive explanation than a technical one. Passing list to viewparams variables in GeoServer SQL views? I have a sql view which take only one parameter, but this parameter is a list, and a need to know how can i pass this parameter in the url  Here is my sql view  SELECT * FROM shop WHERE id IN %list%   When I put the default value for %list% as (1, 2 ,3) as example, the layer preview works and show the shopa with the default ids,  but when I try this in the url  viewparams=list:(1,2,3)   does not work.   I already tried other things like   viewparams=list:"1,2,3"   but nothing works.  Does anyone know how to do this? Why are site stats graph for beta sites not available to public? Currently, on all beta sites, the current site stats is placed prominently on the front page, which is great for knowing how the site is currently doing.  However, it doesn't say anything about the trend of the numbers - whether the site is sailing or it is sinking compared to the last month. According to Madara Uchiha, our moderator on Anime &amp; Manga SE, . Disregarding data which are not already public, , I can't see any reason why we are not allowed access to graphical representation of public site statistics. In fact, there is already a third-party app that scraps the information from the home page and . Can we have a beautiful visualization on how our beta sites evolve over time, from pony to unicorn?   Images stolen borrowed from Bulbapedia How do I create a script file for terminal commands? Tag scores are not updated and the issue is getting worse How are "related" questions selected? What is $dx$ in integration? Is there a preinstalled or automatic firewall? Does Ubuntu come with a preinstalled or automatic firewall? If not, do I need one?   I've read some articles about the advantages of Linux over other operating systems about security (no need to have antivirus, ...) but would like to be sure. Is there anyway to restore the Blender default Cloth settings? Or is there anyway to find what the default settings are?  I didn't realize at the time that by changing the values I was overriding the default values.  Using Blender v2.76. Recursively list files with file names, folder names and permission