Ordering ratios
Ranking based on binomial data (example: website conversions)
Rewiring a switch controlled receptacle to a ceiling light How to redirect output to screen as well as a file? My aim is to log all output from a script into a directory that the script is going to create.  For example, I have:  ~/.abc.sh:  #! /bin/bash rails new myapp   When I run...  cd ~/code . ~/.abc.sh   ...that will create a new Rails app in directory ~/code/myapp.  When Rails is creating an app, it outputs a whole lot of text that I want to capture and store in a log file in the same directory the rails command newly created. I also want to display that text in the terminal as well.  How do I go about doing this? I need a non trivial  examples of group isomorphism that maps $G\to H$ such that   $G/H \cong G$. How to get reflections from 3D to show up on real images What is the order of the Crisis on Earth X episodes in the Arrowverse? Bionic - Group addition using usermod -aG doesn't take effect until the next reboot Convex function as supremum of countably many affine functions Let $f:\mathbb{R}^n\to \mathbb{R}$ be a convex function. It is well-known that (see e.g.~) that there exists a set $A$ such that  $$ f(x)=\sup_{a\in A}A(a)x+b(a), \quad \forall x\in \mathbb{R}^n, $$ where $A(a)\in\mathbb{R}^{n\times n}$ and $b(a)\in \mathbb{R}^n$.  I was wondering, is there any reference saying we can choose $A$ as a countable set? Tweaking AStar to find closest location to unreachable destination I've implemented AStar in Java and it works ok for an area with obstacles where the chosen destination is reachable.  However, when the destination is unreachable, the calculated "path" is in no way to the closest location (to the unreachable location) but is instead some random path.  Is there a feasible way to tweak AStar into finding the path to the closest location to an unreachable destination? Why catch Exceptions in Java, when you can catch Throwables? We recently had a problem with a Java server application where the application was throwing Errors which were not caught because Error is a separate subclass of Throwable and we were only catching Exceptions.  We solved the immediate problem by catching Throwables rather than Exceptions, but this got me thinking as to why you would ever want to catch Exceptions, rather than Throwables, because you would then miss the Errors.  So, why would you want to catch Exceptions, when you can catch Throwables? Chrome phishing warning on main How can I disable Amazon search results in the Dash? What is the Killing form of $\mathfrak{gl}_{m}$? Consider the Killing form of the Lie algebra $\mathfrak{gl}_{m}$. Then $\{e_{ij}\}$ is a basis for this Lie algebra where $e_{ij}$ is a matrix with 1 in the $i$th row, $j$th column and 0 everywhere else. Then every $A = (a_{ij}) \in \mathfrak{gl}_{m}$ can be written as $A = \sum_{i, j = 1}^{m}a_{ij}e_{ij}$. Since $[e_{ij}, e_{kl}] = \delta_{jk}e_{il}-\delta_{li}e_{kj}$, we have $ad(a)e_{ij} = \sum_{kl}(a_{ki}\delta_{lj} -a_{jl}\delta_{ki})e_{kl}$. From this we have $$ad(a)ad(b)e_{ij} = \sum_{k, r, s}(a_{rk}b_{ki}\delta_{sj} + a_{ks}b_{jk}\delta_{ri} - a_{ri}b_{jk}\delta_{sk} - a_{js}b_{ki}\delta_{rk})e_{rs}.$$ From this how can I see that the Killing form is $2m tr(ab) - 2tr(a)tr(b)$. I know that the Killing form is just the trace of the above centered equation, but I seem to be getting confused with all the indices. I know that there are questions asking like "intersection of a infinite collection of sets" and I can understand that the answer for that one is a null set, but I got a question here, in which all sets are finite and nonempty. Please take a look at the pic below.  It's a True/False question.  What I'm confused about is that the "infinity" sign in the interception. Since all sets are finite, does it mean that there are many sets in the chain are the same? (because the symbol used is for subsets not for proper subsets). Please give me some hints how I should think about this question.  Thank you What is the difference between 'git pull' and 'git fetch'? What are the differences between git pull and git fetch? Is diamagnetism a static or dynamic effect? When we put a diamagnetic material in the presence of an external magnetic field $\vec B_0$, the magnetic field inside the material decreases to $$\vec B=(1+\chi_m)\vec B_0,$$ where the magnetic susceptibility $\chi_m$ is a small negative number. I am assuming the material is linear and isotropic.  On the other hand the diamagnetism is explained in terms of Lenz law. When we change the magnetic flux of the external field over the material, atomic currents generate an induced magnetic field trying to restore the flux. But then the induced field could have any sign (in the appropriated direction), depending if we are increasing or decreasing the flux of the external field. It seems diamagnetism is a dynamic effect. How come the sign of $\chi_m$ is always negative? Moreover, the magnitude of $\chi_m$ should depend on how large is the variation of the flux but I do not see any suggestion of this when looking at tables of $\chi_m$. Generating list of manually installed packages and querying individual packages I'd like to get a list of packages installed manually by apt or aptitude and be able to find out whether a foobar package was installed manually or automatically. Is there any neat way of doing that from the command line? New passport and entrance Schengen I am from Brazil and travel a lot in Schengen countries. Under the rules of Schengen visa (3 months stay in a 6 months period). In my passport are the entrance and exit stamps, also to chec the days I stay in Schengen.  I need a new passport and will get this in Brazil. So in this new passport are NOT the stamps. Does this mean I start new with the Schengen visa rule? I seems like. The new passport is empty. Or do I miss something? It would be great because I am almost on my 90 days stay in the period of 180 days. Can I use an "if" clause without "then"? Are the following two sentences correct?     I want you to go to sleep.   and     I want you going to sleep.   If they are both correct, what's the difference? Confidence Interval for variance given one observation This is a problem from the "7th Kolmogorov Student Olympiad in Probability Theory":     Given one observation $X$ from a $\operatorname{Normal}(\mu,\sigma^2)$ distribution with both parameters unknown, give a confidence interval for $\sigma^2$ with a confidence level of at least 99%.   It seems to me that this should be impossible. I have the solution, but haven't read it yet. Any thoughts?  I'll post the solution in a couple days.  [Follow-up edit: Official solution posted below. Cardinal's solution is longer, but gives a better confidence interval. Thanks also to Max and Glen_b for their input.]