How can I invert a mathematical operator about an imaginary vertical axis that runs through the symbol's center? Specifically, consider the symbol \prec, which resembles the less-than symbol &lt;. I'd like to create an analogous version that is to the greater-than symbol &gt; as \prec is to &lt;. How can I do so?  I'm looking for an answer that I will be able to easily modify to various symbols other than \prec. In particular, besides \prec I'm currently interested in inverting the symbols \preceq as well as the following custom-made symbol:  \newcommand{\pprec}{\mathbin{{\prec}\mspace{-5mu}{\prec}}}   that is to \ll as \prec is to &lt;.
I know what my symbol or character looks like, but I don't know what the command is or which math alphabet it came from. How do I go about finding this out?
Does anybody know how to easily undo a git rebase?  The only way that comes to mind is to go at it manually:   git checkout the commit parent to both of the branches  then create a temp branch from there cherry-pick all commits by hand replace the branch in which I rebased by the manually-created branch   In my current situation this is gonna work because I can easily spot commits from both branches (one was my stuff, the other was my colleague's stuff).  However my approach strikes me as suboptimal and error-prone (let's say I had just rebased with 2 of my own branches).  Any ideas?  Clarification: I'm talking about a rebase during which a bunch of commits were replayed. Not only one. Story about criminal being "adjusted" which stops a man's commute I'm trying to remember the name of a story, I think the author was Larry Niven, but it might possibly be from Heinlein's "Future History" series (but a check of the stories included in the Future History indicates it's not in there), about a man whose commute is stopped because a criminal has to be 'adjusted'.  In this case, the criminal was a hit-and-run driver who left his victim untreated on the roadside, and was sentenced to suffer in the same manner. So his leg was carefully broken and he was left, untreated and in pain, on the side of the road in the same place for an hour. All the time ambulances were standing by, and every effort was made to ensure that the criminal did not suffer unduly - but that he did suffer, in a manner as close to the suffering he inflicted on his victim. Change the location of saved screenshot when screenshot taken by printscreen button in GNOME 3 How to create a meta-package that automatically installs other packages? I'd like to be able to create a package that doesnt contain any code or programs itself, but instead installs other packages that exist in the repositories onto a computer, sort of how the ubuntu-restricted-extras package does? Distance between surfaces Black hole "no hair" theorem The  (or conjecture), suggests that black holes can be entirely described by their mass, angular momentum and charge. All other details of the BH formation are lost.  Is there a simple way of understanding why you would be able to tell the difference between a BH made from protons and one made from electrons, but not between one made from matter rather than anti-matter?  i.e. What is special about charge, and why aren't lepton number, baryon number, strangeness etc, also black hole properties? Linux ACL behaviour: settings the mask changes 'ls' output, but not actual permissions It might be the time of night, but this is puzzling me. Picture the following.  [root@node1 acltest]# getfacl foo/ # file: foo # owner: root # group: testuser user::rwx group::r-x other::---  [root@node1 acltest]# ls -la . total 24 drwxr-xr-x  3 root root     4096 Feb  9 21:53 . drwxr-xr-x 25 root root     4096 Feb  9 21:54 .. drwxr-x---  2 root testuser 4096 Feb  9 21:53 foo [root@node1 acltest]# setfacl -m m::rwx foo [root@node1 acltest]# getfacl foo/ # file: foo # owner: root # group: testuser user::rwx group::r-x mask::rwx other::---  [root@node1 acltest]# ls -la . total 24 drwxr-xr-x   3 root root     4096 Feb  9 21:53 . drwxr-xr-x  25 root root     4096 Feb  9 21:54 .. drwxrwx---+  2 root testuser 4096 Feb  9 21:53 foo [root@node1 acltest]# su - testuser [testuser@node1 ~]$ cd /acltest/foo/ [testuser@node1 foo]$ ls -la . total 16 drwxrwx---+ 2 root testuser 4096 Feb  9 21:53 . drwxr-xr-x  3 root root     4096 Feb  9 21:53 .. [testuser@node1 foo]$ touch bar touch: cannot touch `bar': Permission denied   In words: I create a directory foo, with mode 0750, root as owner and testuser as the group. (testuser is the private group of testuser, but that doesn't matter.)  The getfacl command correctly shows no ACL's on this directory and there is not mask yet. The mask will be set accordingly to the group permissions if I would add a named group or user now.  If I explicitly set the mask to rwx now, the group permissions as shown by ls change too. I know it happens the other way around (the mask changes when the group permissions change), but this seems puzzling.  The more puzzling because the getfacl output does not show the group permissions as rwx but - as said - ls does.  Which one is right? Apparently, the output of getfacl is right, because testuser cannot write to foo. As expected, by the way, because I did not grant the testuser group any permissions to do so.  It goes on. I cannot allow the testuser group write permissions on foo by just using chmod. I have to explicitly set an ACL using setfacl -m g:testuser:rwx foo to allow testuser to finally touch foo/bar.   Can someone explain the rationale behind the difference in the outputs of getfacl and ls? I know it can be tricky to have normal permissions go together with ACL's, but this seems plain wrong. (Though I expect to be missing something glaringly obvious ;))  I have already seen Indefinite articles used with plural nouns: It was AN amazing TWO DAYS The indefinite article a(n), derives from the old English word an meaning "one". Generally this word only occurs in determiner function before noun phrases which are singular. However, there seem to be some cases where this determiner occurs before plural noun phrases. I say that, but actually these noun phrase seem so bizarre to me, in terms of their structure, that I'm not sure they're definitely noun phrases at all. Here are some examples:   a full three months before we left an amazing two days an awkward ten minutes   Ignoring the article here for a moment, these noun phrases are odd because the adjective is occurring before the numeral. We would normally expect to see:   three full months two amazing days ten awkward minutes   Even given the oddness of the word order in the original phrases, I can see no reason why the normally singular indefinite article is licensed here.   Can anybody give an account of the syntactic structure of these phrases, and/or explain why the semantically singular article is able to be used with such phrases - even if they compulsorily trigger plural verb agreement?  Here is an example of one of these instances which seems to demand a plural verb:   An amazing two million people attend every year. *An amazing two million people attends every year. (ungrammatical) Why is there no chat in the footer on Stack Overflow like on other sites? Difference of Gamma random variables Holomorphic function has at most countably zeros Let $f$ be holomorphic in a domain $U$, then $f$ has at most countably zeros.  How can I prove this statement? I have seen it in Sheng Gong  explicitly, but without any indications. When hyperref is loaded I receive the following error:     TeX capacity exceeded, sorry [input stack size=5000].   However, when I remove hyperref package it compiles successfully. I traced it back and found that \maketitle causes the error but don't know how to fix it. Is there any way to use hyperref in my setup.   Code:       %!TEX TS-program = xelatex     \documentclass[journal,transmag,]{IEEEtran}      \usepackage[hyphens]{url}     \usepackage{hyperref}      \usepackage{xunicode}      \usepackage{fontspec}      \usepackage{polyglossia}     \setmainlanguage{english}     \setotherlanguage{arabic}     \newfontfamily\arabicfont[Script = Arabic]{Amiri} % Replace 'Simplified Arabic' with a font from your system       \begin{document}     \title{A Very Nice Title}      \author{\IEEEauthorblockN{             John Doe\IEEEauthorrefmark{1}}%,~\IEEEmembership{Member,~IEEE}         \IEEEauthorblockA{\IEEEauthorrefmark{1}My address}         % &lt;-this % stops an unwanted space         \thanks{Manuscript received mm dd, 20xx; revised mm dd, 20xx.               }     }      % The paper headers     \markboth{headers...}%     {Shell \MakeLowercase{\textit{et al.}}: Bare Demo of IEEEtran.cls for IEEE Transactions on Magnetics Journals}      \IEEEtitleabstractindextext{%         \begin{abstract}My Abstract.\end{abstract}          % Note that keywords are not normally used for peerreview papers.         \begin{IEEEkeywords}             Key 1, Key 2     \end{IEEEkeywords}}      \maketitle       \IEEEdisplaynontitleabstractindextext     % \IEEEdisplaynontitleabstractindextext has no effect when using     \IEEEpeerreviewmaketitle       \section{Introduction}     English Text      \begin{Arabic}      السَلَامُ عَلَيكُمْ     \end{Arabic}       \end{document} File changed listener in Java I'd like to be notified when a file has been changed in the file system. I have found nothing but a thread that polls the lastModified File property and clearly this solution is not optimal. I've recently been learning about differential equations, and my teacher has been giving some particularly difficult examples out for those of us who finish early. He gave us the following differential equation: $$x=y\frac{dy}{dx}-\left(\frac{dy}{dx}\right)^{2}$$ With the hint "Differentiate with respect to $y$, then let $\frac{dy}{dx}=p$". I've solved it after the lesson and would like someone to check whether or not I've done so correctly.    Following the hint, $$\frac{dx}{dy}=\frac{1}{p}=p+y\frac{dp}{dy}-2p\frac{dp}{dy}$$ Which rearranges to $$p-\frac{1}{p}+y\frac{dp}{dy}=2p\frac{dp}{dy}$$ Multiplying through by $\frac{dy}{dp}$, $$\left(p-\frac{1}{p}\right)\frac{dy}{dp}+y=2p$$ Rearranging into the form $\frac{dy}{dp}+f(p)y=g(p)$, and writing $p-\frac{1}{p}=\frac{p^{2}-1}{p}$ $$\frac{dy}{dp}+\frac{p}{p^{2}-1}y=\frac{2p^{2}}{p^{2}-1}$$ Our integrating factor is $$e^{\int\frac{p}{p^{2}-1}dp}=e^{\frac{1}{2}\ln(p^{2}-1)}=\sqrt{p^{2}-1}$$ So we have $$\sqrt{p^{2}-1}\frac{dy}{dp}+\frac{p}{\sqrt{p^{2}-1}}y=\frac{2p^{2}}{\sqrt{p^{2}-1}}$$ The left hand side is, by design, $\frac{d}{dp}(y\sqrt{p^{2}-1})$, and the right hand side can be integrated as follows: $$\int \frac{2p^{2}}{\sqrt{p^{2}-1}}dp=\int\frac{2(p^{2}-1)+2}{\sqrt{p^{2}-1}}dp=\int 2\sqrt{p^{2}-1}dp+\int \frac{2}{\sqrt{p^{2}-1}} dp$$ These can both be solved using the substitution $p=\cosh(u)$, and gives $$y\sqrt{p^{2}-1}=p\sqrt{p^{2}+1}-\cosh^{-1}(p)+\alpha$$ Where $\alpha$ is an arbitrary constant. Dividing, we finally have $$y=p+\frac{\cosh^{-1}(p)+\alpha}{\sqrt{p^{2}-1}}$$  Here I was stuck for a long time, until I realised that we also have the equation we began with: $x=py-p^{2}$, which we can solve as a quadratic in $p$ to also get $$p=\frac{y\pm \sqrt{y^{2}-4x}}{2} \implies p^{2}=\frac{y^{2}+y^{2}-4x \pm 2y\sqrt{y^{2}-4x}}{4}$$  Thus, $$y=\frac{y\pm \sqrt{y^{2}-4x}}{2}+\frac{\cosh^{-1}\left(\frac{y\pm \sqrt{y^{2}-4x}}{2}\right)+\alpha}{\sqrt{\frac{y^{2}-2x \pm y\sqrt{y^{2}-4x}}{2}-1}}$$  This is as good as I can do - we have a relation between $y$ and $x$ - am I done? Is this the correct answer? Is there an easier way?     Thank you for your time.    Following the suggestion by @Valentin $$\frac{dy}{dp}=1+\frac{\frac{1}{\sqrt{p^{2}-1}}\sqrt{p^{2}-1}-p\frac{\cosh^{-1}(p)+\alpha}{\sqrt{p^{2}-1}}}{p^{2}-1}=1+p\frac{1-\frac{\cosh^{-1}(p)+\alpha}{\sqrt{p^{2}-1}}}{p^{2}-1}$$ Hence, $$dx=\frac{dy}{p}=dp\left(\frac{1}{p}+\frac{1-\frac{\cosh^{-1}(p)+\alpha}{\sqrt{p^{2}-1}}}{p^{2}-1}\right)$$ Is the matrix diagonalizable for all values of t? iPad won't turn on after a complete battery drain My iPad mini retina is out of warranty,  I forgot to plug in my iPad after the critical battery warning and it went some minutes following the warning. I was not worried because same thing had happened a few times before and iPad was perfectly okay after charging it. However, this time I remember seeing a flash of blue screen immediately after it went black. Then, I plugged it in an waited for a while and tried starting it. Ever since, it fails to start hanging on the apple logo with white background screen.   I tried to connect to my Mac but nothing showed up in iTunes. I am worried now. Can I troubleshoot this or is it broken and needing repair? Prove that $\lim_{n\to\infty}a_n\le \lim_{n\to\infty}b_n$ Why is surface charge distribution uniform for a conducting sphere? Can't it be arbitrary? If the charge $q_1$ has to repel the charge $q_2$, the electric field has to go inside the conductor which contradicts the fact that electric field inside conductors is zero. Then why do the charges distribute themselves in a particular manner? Why can't they be distributed over a small place on the conductor? Textbook approach to modeling non-proportional hazards in the Cox model In Cox models with time varying coefficients, the effect of covariates on the hazard is allowed to change through time. In cases where a coefficient has a linear relationship with time, I am aware of at least two text books ( and an Appendix to ) that advocate for the following model, first in R code:  coxph(Surv(time, death) ~ disease + disease:time)   And now in mathematical notation:  $$ h(t|X) = h_0(t) \exp(\beta_1X + \beta_2X_T) $$ Where $h(t|X)$ is the instantaneous hazard rate at time $t$ given covariates $X$; $h_0(t)$ is the baseline hazard rate; and $T$ is the censoring or event times. $\beta_1$ represents the log hazard ratio for individuals with $T=0$ (which is sort of nonsensical since you can't have $T=0$ in the data), while $\beta_2$ is harder to interpret... $\beta_2$ shows how the log hazard ratio depends on censoring/event times, but that is circular because event times are also the response variable (this point is made in Terry Therneau’s vignette “”).  According to Therneau's vignette, to correctly specify a time varying coefficient, you need to use the following model, first in R code:  coxph(Surv(time, death) ~ disease + tt(disease), tt=function(x,t,...){x*t})   And now in mathematical notation: $$ h(t|X) = h_0(t) \exp(\beta_1X + \beta_2X_T) $$  The difference is that the time interaction is with $t$ in the model rather than with the event times $T$ in the data. The resulting parameters are easy to interpret: they are the intercept and slope of the linear relationship between the log hazard ratio of $X$ and time. This approach seems like the proper way to model a time varying effect.  Can anyone justify or advocate for the first approach to modeling non-proportional hazards in the Cox model? If it is really incorrect (as I suspect it is), what are the practical consequences of using this approach? On Latin.SE, I am getting a 404 error when clicking any of the three "history" links on the .  That is, this:        Gives this:        All three editable sections have a revision history with two revisions or more, and all three give an error.  The actual links are , , and .