Why massless particles have less number of possible polarisations than massive ones?
Polarization vectors of massive and massless particles
How do I change how executable files are handled by the file manager? When I double click on text files, nautilus asks me what I would like to do with them. I find this to be intrusive, as I just want them to open.  How can I fix this?  Note: This question is a "canonical" question on the subject; edit if needed. Note 2: Text files can be HTML, CSS, TXT, and more. Integral change that I don't understand If $f(t)$ is a Probability density function of a positive RV.  $\int_0^\infty\int_x^{\infty}f(t)dtdx$ Using fubini theorem should become $\int_0^\infty\int_0^{t}f(t)dxdt$  But why? Surely the answer is very simple but I don't see it. Fubini theorem allows the change of the order of integration. So it should become $\int_0^\infty\int_x^{\infty}f(t)dxdt$  but then I don't understand what meaning could have $\int_x^{\infty}dx$ If I did  \setcounter{chapter}{-1} \chapter{Introduction}   then I get Chapter 0 Introduction. I just want the word Introduction, and I want it also in the contents when I use   \tableofcontents   How can I do that? How to modify a specified commit? Is there a PPA with the latest version of LibreOffice? There was recently another release of , but it is  a pain to have to manually go to their website and download the packages every time there is a new release. Is there a PPA that always has the latest version of LibreOffice? What does "had had" mean? How does this differ from "had"? For example, what is the difference between the following two sentences:     I had a bad day      I had had a bad day What is CUPS server and how to share a printer (Locally or over a network) The title tells you all, except that it's about sharing printers.   How do I connect to a shared printer on the network through CUPS or terminal? Homomorphism between free groups Let $F_a$ be the group which is freely generated by $a$ elements. How to show that there is a homomorphism from $F_a$ onto $F_b$ if and only if $b\le a$?  I was thinking one possibility is if $F_a$ generated freely by $\{x_1, \dots , x_a\}$ and $F_b$ generated freely by $\{y_1, \dots , y_b\}$ then consider map which says $\phi(x_i)=y_i$ for $1\le i \le b$ and $y_1$ otherwise. I do not know if this works or even how to proceed. How to show this fact? How to describe a guy who is popular with girls? Perhaps I should make it clear:  - He naturally attracts girls.  - He doesn't chase girls and have no intention for any relationship.  - You just see him often together with girls. How to download, modify, build and install a Debian source package? If I want to make minor changes to the source code of a Debian package, how do I go about downloading, incrementing the package version, building the (modified) source, and installing it on my computer? Algorithm to return all combinations of k elements from n Why does kworker cpu usage get so high? I recently installed Ubuntu 12.04 on my Samsung laptop alongside Windows 7. Whenever I use Ubuntu (even when its idle) kworker uses almost 90% of one of 8-cores. Even though it doesn't really affect my usage, it bugs me and I am afraid of that it might harm my processor. I even tried installing another Linux distro (Linux Mint), and kworker caused the same problem. So I don't know what to do. I would really appreciate your  help. How can I echo a newline in a batch file? How can you you insert a newline from your batch file output?  I want to do something like:  echo hello\nworld   Which would output:  hello world What is Ubuntu's status on the Meltdown and Spectre vulnerabilities? Any questions relating to status updates, or asking if anything is going to be patched for these vulnerabilities should be closed as duplicates of this question.    are in the news right now and sound pretty severe. I don't see any security updates from Ubuntu that cover these vulnerabilities.  What is Ubuntu doing about these vulnerabilities, and what should Ubuntu users be doing?  These are CVE-2017-5753, CVE-2017-5715 and CVE-2017-5754. Examples and Counterexamples of Relations which Satisfy Certain Properties Recurrence relation for number of ternary strings that contain two consecutive zeros The question is: Find a recurrence relation for number of ternary strings of length n that contain two consecutive zeros.    I know for ternary strings with length one, there are 0. For a length of 2, there is just 1 (00), and for a length of 3, there are 5 (000,001,002,100,200).    I did a similar problem, finding a relation for the number of bit strings of length n with two consecutive zeros: $$a_n = a_{n-1} + a_{n-2} + 2^{n-2}$$    Since you can add "1" to the end of all the $a_{n-1}$ strings, "10" to all the $a_{n-2}$ strings, and "00" any string of size $n-2$.    For the ternary string problem, I'm pretty sure you would replace the $2^{n-2}$ with $3^{n-2}$, but confused about the other terms of the relation. My guess is that it would have the coefficient $2$ in front of the other terms, since you can add either $1$ or $2$ to the end of $a_{n-1}$ and either $01$ or $02$ at the end of $a_{n-1}$.    So I believe the answer for the relation is: $$a_n = 2a_{n-1} + 2a_{n-2} + 3^{n-2}$$    How does that look? I checked the Wikipedia article and some interviews, and haven't found any specific answer.  What specifically does the "awakening" of the Force in the title refer to?  Was the Force somehow asleep or dormant? (which would, since it Binds The Galaxy Together, explain the Inflationary cosmological models).  Or that there were no active Force users since Vader and Sidious offed every Jedi and then each other? We know Luke's still around.  Or something else?  Canon or word-of-god answers only, please. Earlier today, I was talking with my friend about some "cool" infinite series and the value they converge to like the Basel problem, Madhava-Leibniz formula for $\pi/4, \log 2$ and similar alternating series etc.  One series that popped into our discussion was $\sum\limits_{n=1}^{\infty} \frac{1}{n^n}$.  Proving the convergence of this series is trivial but finding the value to which converges has defied me so far. Mathematica says this series converges to $\approx 1.29129$.  I tried Googling about this series and found very little information about this series (which is actually surprising since the series looks cool enough to arise in some context).  We were joking that it should have something to do with $\pi,e,\phi,\gamma$ or at the least it must be a transcendental number :-).  My questions are:   What does this series converge to? Does this series arise in any context and are there interesting trivia to be known about this series?   I am actually slightly puzzled that I have not been able to find much about this series on the Internet. (At least my Google search did not yield any interesting results). Ant-Man, shrinking, and weight Determining ethnicity according to ancestry? My sister, cousins, and other relatives speculate that my mom's grandmother was Jewish (for various reasons). I've heard people say at times things like, for example, "I'm 50% German" or "I'm 25% Swedish." This has to do with their ancestry. But, how exactly is this calculated? Say for example that my mother's paternal grandmother was indeed 100% Jewish, what would that make me and my siblings, and how is it calculated?