Complex matrices with null trace
If $\mathrm{Tr}(A)=0$ then $T=R^{-1}AR$ has all entries on its main diagonal equal to $0$
Site blocked by content filter I run a large and high trafficked WordPress powered platform. One of my editors informed me that our site is blocked at his workspace as a "games site". They use WebCat to filter the traffic.  The issue here is that our platform is not a gaming site, although it does have a games category that covers news. And that is a very minor part of the site.  My question is, what can I do to unblock the site? How does WebCat work? Do they use a universal database to filter the traffic (meaning that the site is blocked on all workspace with WebCat) etc. Obviously they need to improve their filtering algorithm. Is there a way to see the history of questions protected by me or another user? Having a record of all actions taken on a site, as is provided by the &quot;activity&quot; and &quot;votes&quot; tabs of our profile, comes in handy very often. Perhaps the most common case is being able to find a question I've interacted with in the past, to see if anything has changed about it. This applies to questions a user has protected as much as anything else. Users are theoretically encouraged to unprotect questions when it's no longer necessary, as emphasized , but in practice they often do not. In many cases it's hard to blame them: unless they specifically marked it as a favourite, the site doesn't keep any record of the question to allow them to find it again. We should help users more easily review their own protections in the future.    For personal review, the votes tab is adequate, but there may also be value in displaying this publicly in the activity tab. There may be users with a history of repeatedly protecting questions over-eagerly. It would be useful to be able to review other users' protection histories to see if this is the case. Even if this is not available to regular users, it may be helpful to moderators, unless their user activity views already allow them to filter down to see this. The "Satellite Paradox": Twin paradox in orbiting satellites I want to simply eliminate the effect of acceleration, which is the cornerstone in resolving the traditional twin paradox, through the following thought experiment: Assume twins $A$ &amp; $B$ are located in the same orbital height, far away from the surface of a massive planet, on a long concrete column at rest WRT the planet. A rapid explosion that happens between the twins makes them orbit the earth with a high velocity, say, $0.6 \ c$, in the same orbital path but in different directions. According to relativity, since the orbiting satellites are completely inertial frames, each twin attributes a variable time dilation to the other one, and each twin expects the other one to be younger. Nonetheless, these twins are automatically reunited after traveling half of the orbit's circumference without being affected by additional accelerations. Which twin is younger in this case? Indeed, If each twin sees the other's clock as running slow all along the way, how can the clocks agree when they meet? For this configuration:  The acceleration due to the explosion does not affect the twins' clock rates since it occurs abruptly in the same place on the column where the twins are located back-to-back. The clocks have been synchronized just before the explosion.  The traditional gamma factor, attributed to one twin from the viewpoint of the other, is variable because the resultant velocity of one twin complying with the relativistic velocity addition is a variable measured from the viewpoint of the other one. However, whether or not the corresponding time dilation is varying, each twin anticipates the other one to be younger. There is no breaking of symmetry!  The $g$-field of the planet has nothing to do with orbiting satellites since they are inertial, and thus GR corrections are not inserted. (Remember the GPS settings!) Significance contradiction in linear regression: significant t-test for a coefficient vs non-significant overall F-statistic I'm fitting a multiple linear regression model between 4 categorical variables (with 4 levels each) and a numerical output. My dataset has 43 observations.  Regression gives me the following $p$-values from the $t$-test for every slope coefficient: $.15, .67, .27, .02$. Thus, the coefficient for the 4th predictor is significant at $\alpha = .05$ confidence level.  On the other hand, the regression gives me a $p$-value from an overall $F$-test of the null hypothesis that all my slope coefficients are equal to zero. For my dataset, this $p$-value is $.11$.  My question: how should I interpret these results? Which $p$-value should I use and why? Is the coefficient for the 4th variable significantly different from $0$ at the $\alpha = .05$ confidence level?  I've seen a related question, , but there was an opposite situation: high $t$-test $p$-values and low $F$-test $p$-value. Honestly, I don't quite understand why we would need an $F$-test in addition to a $t$-test to see if linear regression coefficients are significantly different from zero. Is it true that $0.999999999\ldots=1$? I'm told by smart people that $$0.999999999\ldots=1$$ and I believe them, but is there a proof that explains why this is? How do I automate a key press in AppleScript? How can I chain implicits in Scala? Addition with NULL values Problem regarding radius of convergence of $\sum n!x^{n^2}$. $$\sum_{n=0}^\infty n!x^{n^2}$$   Can anyone tell me what will be the radius of convergence for this power series. According to me it is $0$.   If you can please show me how to go about it if I am wrong. Windows 8 upgrade Recovery Disk I have upgraded to Windows 8 from Win 7. I want to create a recovery disk for Windows 8, just in case something goes wrong. I didn't find the option of creating it from the control panel.  How do I create a Recovery CD/DVD? I want to executed command from file (which is script) in current shell in terminal.  Example: I have file ch_dir contains following:  #!/bin/bash cd /usr   Now if I execute file usually as following then it executes commands in different shell:  pandya@pandya-desktop:~$ ./ch_dir pandya@pandya-desktop:~$   Here cd /user is executed in different shell.  But I want to execute in Current shell. How do I do that?  Note: Here cd is only used to explain. Question's aim is to execute any command in current shell "really not" vs "not really" If someone says "David is not really a leader", it means something like: the speaker believes that David isn't the kind of person you would think of as a without-doubt a real leader; but the speaker isn't necessarily saying that David is definitely a very poor leader.  If someone says "David is really not a leader", it means that the speaker thinks that David is definitely a very poor leader.  What analysis (grammatical, dictionary, etc?) can help me understand how this difference in meaning is created? Minimum requirements of Ubuntu 20.10 Does anyone know what are the minimum requirements to install Ubuntu 20.10? What would be better practice when giving a function the original variable to work with:  unsigned long x = 4;  void func1(unsigned long&amp; val) {      val = 5;             } func1(x);   or:  void func2(unsigned long* val) {      *val = 5; } func2(&amp;x);   IOW: Is there any reason to pick one over another? I am not a administrator and I would like to find the administrator password. I would not like to reset it however. Is there anyway to find and not reset the administrator password? Cite_key instead of a number, what is going on? I have the following problem: I correctly obtain a numbered bibliography at the end but along the text the cite_key appear instead of a number. How to fix this problem?   \documentclass[11pt]{book}  \usepackage[]{biblatex} \begin{document} %some text  ... \cite{ABKM2015}... %some text  \begin{thebibliography}{99} \bibitem{ABKM2015} Arroja, F. and Bartolo, N. and Karmakar P. and Matarrese, S. (2015). \newblock The Two Faces of Mimetic Horndeski Gravity             \newblock {\em ArXiV}, 1506.08575 (2015). \end{thebibliography} \end{document}   After compiling I get ... [ABKM2015] ... while I want for example  [1]. How do I create this crease effect on glass? Find all solutions to $x^2\equiv 1\pmod {91},\ 91 = 7\cdot 13$ I split this into $x^2\equiv 1\pmod {7}$ and $x^2\equiv 1\pmod {13}$.  For $x^2\equiv 1\pmod {7}$, i did: $$ (\pm1 )^2\equiv 1\pmod{7}$$ $$(\pm2 )^2\equiv 4\pmod{7}$$ $$(\pm3 )^2\equiv 2\pmod{7}$$ Which shows that the solutions to $x^2\equiv 1\pmod {7}$ are $\pm1$.  For $x^2\equiv 1\pmod {13}$, i did: $$ (\pm1 )^2\equiv 1\pmod{13}$$ $$(\pm2 )^2\equiv 4\pmod{13}$$ $$(\pm3 )^2\equiv 9\pmod{13}$$ $$ (\pm4 )^2\equiv 3\pmod{13}$$ $$(\pm5 )^2\equiv {-1}\pmod{13}$$ $$(\pm6 )^2\equiv 10\pmod{13}$$Which shows that the solutions to $x^2\equiv 1\pmod {13}$ are $\pm1$.  Thus, I concluded that the solutions to $x^2\equiv 1\pmod {91}$ must be $\pm1$. I thought that $\pm1$ were the only solutions, but apparently I am incorrect! How do I go about finding the other solutions to this congruence? What does the dot mean How to get Ubuntu download for a Mac?