How to prove this for a self-complementary graph?
Proof that any self-complementary graph has to have $4k$ or $4k+1$ vertex, for some $k \in \mathbb N$
When a person lifts a book while standing on the earth's surface. Why is his force considered external to the book-earth system? Isn't his force internal like the case of the forces that cause the exploson of a bomb. I think the forces the person exerts on both the book and the earth are internal since they are equal but opposite therefore resulting in the position of the centre of mass of the system being maintained and if i'm right is the mechanical energy of the system constant?  Am i wrong? Please correct me. How to increase the signal power of a wi-fi card? I use an atheros card that requires ath9k driver. Are there any tools that can be used to increase the signal power of the wi-fi card? What documents to show if I'm a US citizen with no US passport to re-enter the US? Suppose I am a naturalized citizen of the US, but also a citizen of another country, "XYZ". I then boarded a plane and left the US to another country (maybe not necessarily to XYZ), without first getting a US passport, but using my old, but valid XYZ passport.   In this case what would be the best documents to have for me to gain entry back into the US as a US Citizen without a passport?  Would I need to contact the US Embassy for help in order to be able return?  If the airline does let me aboard to return to the US, even without the US passport, what are the best documents could I show at the border to prove I am a US citizen but that I just don't have a passport, for whatever reason? First off I did try the power options setting and it's on 'Never' but that did nothing. The drive still spins down after 15-20 seconds of not being used. I need it to spin all the time because it's more efficient with my way of using it. Also listening to music from that drive is absolutely destroying the drive making it spin up and down all the time causing immense wear and tear. Any ideas on how to stop it from spinning down? Please don't suggest bat files that keep creating editing a file.  &nbsp;  Oh and here is the model of the drive: wdc wd10jpvx-22jc3t0 and my OS is Windows 10 64 bit. Why is the Java plugin (JRE) disabled in Chrome? Why is the Java plugin (JRE) is disabled in Chrome? It is some security concern?  From official Java website:     Chrome no longer supports NPAPI (technology required for Java applets)   The Java plug-in for web browsers relies on the cross platform plugin architecture NPAPI,   which has been supported by all major web browsers for over a decade.   Google's Chrome version 45 (scheduled for release in September 2015) drops support   for NPAPI,   impacting plugins for Silverlight, Java, Facebook Video   and other similar NPAPI based plugins.   But anyone knows why? How it could be dangerous for Chrome user with latest version of Java JRE installed? Let $F$ be a field and $f: \mathbb{Z} \to F$ be a ring epimorphism. Remember window locations when docked and undocked I find this beyond frustrating.  I have two extra screens on my laptop at work. I take my laptop and go home, with no extra screens connected. I come back, dock the laptop, and the windows need to be rearranged again.  Is there a way to get windows (or a utility) to keep track of the overall screen configuration (#, size, resolution), and remember where windows were placed, so when the screen configuration matches again, it puts applications BACK where they were? Create JSON using apex Show that $\sum_{n=1}^{\infty}(n^{3}\sin\left(\frac{1}{n}\right)-n^{2}+\frac{1}{6})$ converges Let $t\in \mathbb R$. Prove that $\displaystyle{\sum_{n=1}^{\infty}n^{3}\sin\left(\frac{1}{n}\right)-n^{2}+t}$ converges iff $t=\frac{1}{6}$.  While the $(\Rightarrow)$ direction was fairly easy (as $a_n$ should converge to $0$, forcing $t=\frac{1}{6}$), i'm facing some hard time trying to prove the second direction, that is $\displaystyle{\sum_{n=1}^{\infty}(n^{3}\sin\left(\frac{1}{n}\right)-n^{2}+\frac{1}{6})}$ converges. I did notice that $a_n=a_{-n}$ and tried to write this series as a Leibnitz series, but had no luck since the sequence doesn't decrease. I also tried to prove absolute convergence but then again, no luck. Thanks. How to write a Hello World application in Java? Story where people inject "books" in the back of their necks? I read this story in middle school or high school and I cannot for the life of me remember the name of it. I think it started off in a small clan of people, there was a young boy who had just come of age and he had some kind of gift that related to the books? Also I think the injecting was illegal, because I vaguely remember the boy encountering an old man who had a bunch of books that he had to keep hidden. There was also a city and he met a girl there that was Special some how. I may just be merging memories but I think at some point the boy and girl went to an underground city?  Does anyone know what I'm talking about? factorization of a^n+1? I'm trying to prove that $a^n+1$ can only be prime if $n$ is a power of $2$. Is there a general factorization of $a^n+1$? the root of $N$th transpose matrix For $n=3,$ $L$ matrix is as below:  $$ \left[\begin{matrix} 1&amp;0&amp;0\\ -1&amp;1&amp;0\\ -0.5&amp;-0.5&amp;1\\ \end{matrix}\right] $$  for $n=4$ we have:  $$ \left[\begin{matrix} 1&amp;0&amp;0&amp;0\\ -1&amp;1&amp;0&amp;0\\ -0.5&amp;-0.5&amp;1&amp;0\\ -1/3&amp;-1/3&amp;-1/3&amp;1 \end{matrix} \right] $$  and for $N$th we have: $$ \left[ \begin{matrix} 1&amp;0&amp;0&amp;0&amp;\cdots&amp;0&amp;0\\ -1&amp;1&amp;0&amp;0&amp;\cdots&amp;0&amp;0\\ -0.5&amp;-0.5&amp;1&amp;0&amp;\cdots&amp;0&amp;0\\ \vdots&amp;\vdots&amp;\vdots&amp;\vdots&amp; &amp; \vdots&amp;\vdots\\ -1/(N-2)&amp;-1/(N-2)&amp;-1/(N-2)&amp;-1/(N-2)&amp;\cdots&amp;1&amp;0\\ -1/(N-1)&amp;-1/(N-1)&amp;-1/(N-1)&amp;-1/(N-1)&amp;\cdots&amp;-1/(N-1)&amp;1 \end{matrix} \right] $$  How to get the roots (eigenvalues) of the $N$th order of the $L+L^T$ matrix? is there a specific logic between the roots of this matrix? Why does water pouring from a glass sometimes travel down the side of the glass? If you have a glass of water, say, three quarters full and you pour it at an angle of say, $45^{\circ}$ with respect to the the table, the water comes out of the glass and goes directly down towards the floor.  However, when the glass is more full, or even three quarters full and the 'angle of pouring' is far less with respect the table, when the water comes out of the glass, rather than going straight down it kind of stays stuck to the glass and travels down the outside of it.  Why does this happen? (I'm sure many of you have observed it yourself by accident and ended up making a mess). Testing whether two regression coefficients are significantly different (in R ideally) If this is a duplicate question, please point to the right way, but the similar questions I've found here haven't been sufficiently similar. Suppose I estimate the model $$Y=\alpha + \beta X + u$$  and find that $\beta&gt;0$. However, it turns out that $X=X_1+X_2$, and I suspect $\partial Y/\partial X_1 \ne \partial Y / \partial X_2$, and in particular, that $\partial Y/\partial X_1 &gt; \partial Y / \partial X_2$. So I estimate the model $$Y=\alpha + \beta_1 X_1 + \beta_2 X_2 +u$$and find significant evidence for $\beta_1,\beta_2&gt;0$. How can I then test whether $\beta_1&gt; \beta_2$? I considered running another regression $$Y=\alpha +\gamma(X_1 - X_2) + u$$ And testing whether $\gamma&gt;0$. Is this the best way?  Also, I need to generalize the answer to many variables, i.e. suppose we have $$Y=\alpha + \beta^1 X^1 + \beta ^2 X^2 + \dots + \beta^nX^n + u$$ where for each $j=1,\dots,n$, $X^j=X_1^j+X_2^j$, and I would like to test for each $j$ whether $\partial Y/\partial X_1^j \ne \partial Y / \partial X_2^j$.  By the way, I am primarily working in R. What is the connection between special and general relativity? What is the connection between  and ? As I understand general relativity does not need the assumption on speed of light constant. It is about the relation between mass and spacetime and gravity. Can general relativity be valid without special relativity? What if the LHC doesn't see SUSY? A question in four parts.   What are the main problems which supersymmetry purports to solve?  What would constitute lack of evidence for SUSY at the proposed LHC energy scales (e.g. certain predicted superpartners are not in fact observed)?  Are there alternative theoretical approaches which would address the SUSY problem set and which would still be credible in such an LHC no-SUSY-scenario? Where would LHC-disconfirmation of SUSY leave String Theory?   I would like to think that these four points could be taken together as one question. Omitting article “the” in front of plural nouns I'm helping someone learn English (second language), and I'm having trouble explaining when to use the and when not to. For example:     Students learn better when teachers are passionate about teaching.   versus     The students learn better when the teachers are passionate about teaching.   There's a subtle difference. The first one is a general statement, whereas the second might imply a study where a group of students learned better than another.  Is the difference simply that, general v. specific? Can you add a separate discussion site? Sometimes you just want to let out some steam, and troll about some technology or software. You are not looking for any answers, but for users with similar experiences and interesting stories. So why not create a separate discussion site (trolling.stackoverflow.com?), where you could ask questions like "why do you hate technology X" or "What are the stupidest bugs you encountered in X"? How do I open PDF in Adobe Reader DC without locking the file from being updated by pdflatex? I don't know if this is possible on Adobe Reader DC on Windows, but asking in case someone has managed to do it.   When I am working on a large document in LaTeX (I use TexStudio) I sometimes like to keep a second copy of my PDF on a second screen so that I can easily refer to what I wrote before, while on my main screen I would have TexStudio with its preview window, which is typically automatically in sync with my current editing location.  On Ubuntu (which uses evince as its default PDF viewer) I used to do it quite nicely. It also seems to watch the PDF file for updates, and keeps in sync of any new versions of the PDF file and reloads it (staying on the same page) when I re-run pdflatex from TexStudio.  At the moment I am working on a Windows machine, and I am trying to recreate the same workflow. I would really like to open a second viewer on my second screen so that I can navigate easily to previous chapters without losing my current position in TexStudio's preview window (which will anyway go back to the current editing location when I run pdflatex).  The only problem however is that when I open the PDF in Adobe Reader DC to put it on the second screen and then I try to recompile the PDF I get the error "I can't write to file". I presume that for some stupid reason Adobe Reader DC maintains some write lock on the file, probably keeping it open while the PDF is visible on screen.  Is there a way to disable this stupid file-locking behaviour from Adobe Reader DC?  UPDATE  After some valuable comments, a workaround is possible using a different viewer. One could either use  or  (the default PDF viewer on Ubuntu, but also available for Windows). They are not so feature rich, and maybe do not look so nice, but in this case do the job.  A similar question was posted  for reference.