How to set a default graphics card?
Is my mobile AMD card being used?
Determine whether or not a point lies within a rotated rectangle I tried to use xrandr to set 1680x1050 as a new mode to VGA output, but it says:  sudo xrandr --addmode VGA-0 1680 X Error of failed request:  BadMatch (invalid parameter attributes) Major opcode of failed request:  140 (RANDR) Minor opcode of failed request:  18 (RRAddOutputMode) Serial number of failed request:  35 Current serial number in output stream:  36 Timeline vote summary shows votes for the 24 hours following the timestamp, which is confusing The new timeline is pretty snazzy. But there's one thing I've noticed that's a bit jarring; the timestamp for vote summaries is always 0:00:00 on a particular day, and the summary covers the rest of that day. So you end up with a summary that always shows up earlier than the events that presumably triggered the votes that show up in it.  A simple solution is to have it display 23:59:59 instead, and sort accordingly. This way the summary comes in after the events it summarizes. Please add a reply button to messages in the pinned/starred section I've run into this a few times; I'll rejoin chat after being away for a while and notice something interesting in the starred section.  I'd like to reply directly to the message but there's no reply button.  Currently, the only ways to explicitly reply to one of those messages are either:-   find the message by scrolling up and looking for it, then click the reply button or; copy and paste the permalink, deleting all the way up to the fragment identifier and adding the colon at the start.   Please add a reply link, even if it just goes in the popup menu it's an improvement. What are the fault tolerances on the FDA food handling guidelines? Sometimes I have suggested that food that sat out a little longer than optimal may be safe to eat.    Granted, this is based on my experience, and I always qualify that it shouldn't be served to guests (and by extension, customers) and that one should determine their own tolerance to risk, but I want to know if there is information as to the methodology of the FDA guidelines.  Specifically, what is the contamination rate at n hours, and what are the initial conditions of the food and environment?  How much risk is there REALLY (in incidences per n-population and such) in a standard kitchen for food that has sat out 50%, 100%, 200%, etc. longer than recommended? How Do You Use An Image As The World Background? How do you set a default value for a MySQL Datetime column?  In SQL Server it's getdate(). What is the equivalant for MySQL? I'm using MySQL 5.x if that is a factor. Maximum value of $\sin A+\sin B+\sin C$? What is the maximum value of $\sin A+\sin B+\sin C$ in a triangle $ABC$. My book says its $3\sqrt3/2$ but I have no idea how to prove it.   I can see that if $A=B=C=\frac\pi3$ then I get $\sin A+\sin B+\sin C=\frac{3\sqrt3}2$. And also  maximum is attained for $a=b=c$. But this does not give me any idea for the proof.  Can anyone help? Learning special relativity and working with Minkowski diagrams for a while now i am still trying to get my head around some oddity.   From my understanding time can often be seen as the dependent variable in those diagrams, so why put it to the vertical axis? What confuses me even more is the apparent convention to denote a point in space time $(t,x)$ even though $x$ is on the horizontal and $t$ is on the vertical axis, so the usual notation would be to refer to that vector as $(x, t)$.  Are there mostly historical reasons or why is it beneficial to use this notation and to violate usual conventions? Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$ How can I create and extract zip archives from the command line? Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx$ I am trying to find a closed form for  $$\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx = 0.094561677526995723016 \cdots$$  It seems that the answer is $$\frac{\pi^2}{12}\left( 1-\sqrt{3}\right)+\log(2) \log \left(1+\sqrt{3} \right)$$  Mathematica is unable to give a closed form for the indefinite integral.  How can we prove this result? Please help me.  EDIT  Apart from this result, the following equalities are also known to exist: $$\begin{align*} \int_0^1 \frac{\log \left( 1+x^{4+\sqrt{15}}\right)}{1+x}\mathrm dx &amp;=\frac{\pi^2}{12} \left( 2-\sqrt{15}\right)+\log \left( \frac{1+\sqrt{5}}{2}\right)\log \left(2+\sqrt{3} \right) \\ &amp;\quad +\log(2)\log\left( \sqrt{3}+\sqrt{5}\right) \\ \int_0^1 \frac{\log \left( 1+x^{6+\sqrt{35}}\right)}{1+x}\mathrm dx &amp;= \frac{\pi^2}{12} \left( 3-\sqrt{35}\right)+\log \left(\frac{1+\sqrt{5}}{2} \right)\log \left(8+3\sqrt{7} \right) \\ &amp;\quad +\log(2) \log \left( \sqrt{5}+\sqrt{7}\right) \end{align*}$$  Please take a look . Errors in matrix equation? I'm getting errors in a matrix equation. When I compile it looks fine, but I'd like to fix them so I don't have to press return for every error at compile time. The code for the equation is:  \begin{equation*}  \begin{bmatrix} U(1,t)  &amp; \cdots &amp; U(n,t) \\  \vdots &amp; \ddots &amp; \vdots \\ O_{n1} &amp; \cdots &amp; O_{nn}  \end{bmatrix} \times \begin{bmatrix} W(1,1)  &amp; \cdots &amp; W(1,n) \\  \vdots &amp; \ddots &amp; \vdots \\  W(n,1) &amp; \cdots &amp; W(n,n)  \end{bmatrix} = \begin{bmatrix}  D(1,t)  &amp; \cdots &amp; D(n,t) \\ \vdots &amp; \ddots &amp; \vdots \\ I_{n1} &amp; \cdots &amp; I_{nn} \end{bmatrix}  \end{equation*}   The errors I'm getting are related to missing $'s inserted. Fixed Field of $\sigma, \tau$ Let $k$ be a field and let $K=k(x)$ be the rational function field in one variable over $k$. Let $\DeclareMathOperator{\aut}{Aut}\sigma, \tau \in \aut(K)$ s.t. $$\sigma\left(\frac {f(x)}{ g(x)}\right)=\frac {f(1/x)}{g(1/x)}\qquad \&amp;\qquad \tau\left(\frac {f(x)}{ g(x)}\right)=\frac {f(1-x)}{g(1-x)}.$$ Find the fixed field $F$ of $&lt;\sigma, \tau&gt;$. Determine $\DeclareMathOperator{\gal}{Gal}\gal(k/F)$. Find an $h \in F$ so that $F=k(h)$.   Now for the first automorphism $\sigma$, I think if I concentrate on $k[x]$ it will give me some idea. Now, if $f(x)=a_0+a_1x+a_2x^2+ \cdots + a_nx^n \in k[x]$ then if $x^n \sigma(f(x))=f(x)$ the case will be $a_i=a_{n-i}$ $\forall i=0(1)[n/2]$. So all the funtions in $K$ which will be fixed by $\sigma$ are of the form $\frac {f(x)}{ g(x)}$ where $f(x)=a_0+a_1x+a_2x^2+ \cdots + a_nx^n$ and $g(x)=b_0+b_1x+b_2x^2+ \cdots + b_nx^n$ such that $a_i=a_{n-i}$ $\forall i=0(1)[n/2]$ and $b_i=b_{n-i}$ $\forall i=0(1)[n/2]$.   Please check whether am I right or not?  And any ideas for the rest of the part? My QGIS project has two layers, one layer is retrieved by Google layer plugin which fetches the static Google map image whose CRS is +proj=merc +lon_0=0 +lat_ts=0 +x_0=0 +y_0=0 +a=6378137 +b=6378137 +units=m +no_defs and another vector layer is a postgis layer whose CRS is +proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs.  I digitalized some polygon features from Google Layers and added it to the vector layer. However, QGIS seems do not make the automatic CRS transformation. How can I change its projection?   Thanks Taking back turns, and forgotten privileges How to create a hole in a polygon in QGIS? I'm trying to use the tool "delete ring" in order to create a hole in a polygon. The geometry of the hole is another feature of the same shapefile   I cannot manage to delete the part of the polygone. Does someone have a tutorial or some explanation? What is the relationship between symmetry and degeneracy in quantum mechanics? Let me remind you about the following classical  examples in quantum mechanics.     Example 1. Bound states in 1-dim potential V(x).   Let $V(x)$ be a symmetric potential i.e.   $$V(x) = V(-x)$$   Let us introduce the parity operator $\hat\Pi$ in the following way:   $$\hat\Pi f(x) = f(-x).$$   It is obvious that    $$[\hat H,\hat\Pi] = 0.$$   Therefore, for any eigenfunction of $\hat H$ we have:   $$\hat H|\psi_E(x)\rangle = E|\psi_E(x)\rangle = E\hat\Pi|\psi_E(x)\rangle,$$   i.e. state $\hat\Pi|\psi_E(x)\rangle$ is eigenfunction with the same eigenvalue. Is $E$ a degenerate level? No, because of linear dependence of $|\psi\rangle$ and $\hat\Pi|\psi\rangle.$   Consider the second example.     Example 2. Bound states in 3-dim a potential $V(r)$. Where $V(r)$ possesses central symmetry, i.e. depends only on distance to center.   In that potential we can choose eigenfunction of     angular momentum $\hat L^2$ for basis    $$|l,m\rangle,$$   where $l$ is total angular momentum and $m$ - its projection on chosen axis (usually $z$). Because of isotropy eigenfunction with different $m$ but the same $l$ correspond to one energy level and linearly independent. Therefore, $E_l$ is a degenerate level.      My question is if there is some connection between symmetries and degeneracy of energy levels. Two cases are possible at the first sight:   Existence of symmetry $\Rightarrow$ Existence of degeneracy Existence of degeneracy $\Rightarrow$ Existence of symmetry     It seems like the first case is not always fulfilled as shown in the first example. I think case 1 may be fulfilled if there is continuous symmetry. I think the second case is always true. Counterexample: $G \times K \cong H \times K \implies G \cong H$ I am having a hard time finding a counterexample for the statement: $G \times K \cong H \times K \implies G \cong H$  I think this should be true for abelian, finite groups. But is this true in general? What would be a counterexample?  Any hints appreciated!  Thanks Function that returns the second argument of Reap