How to add link (via php) to xmlsitemap
How can my module add xml sitemap entries?
Given an infinite number of monkeys and an infinite amount of time, would one of them write Hamlet? Of course, we've all heard the colloquialism "If a bunch of monkeys pound on a typewriter, eventually one of them will write Hamlet."  I have a (not very mathematically intelligent) friend who presented it as if it were a mathematical fact, which got me thinking... Is this really true?  Of course, I've learned that dealing with infinity can be tricky, but my intuition says that time is countably infinite while the number of works the monkeys could produce is uncountably infinite.  Therefore, it isn't necessarily given that the monkeys would write Hamlet.  Could someone who's better at this kind of math than me tell me if this is correct?  Or is there more to it than I'm thinking? I need to define a new command to create a squiggle arrow with some text on it. Something similar to what \xrightarrow command produces but with wiggly arrows as in \rightsquigarrow. The length of the arrow should automatically be adjusted to fit the text above it and I do not know how to handle this part in TikZ. Any ideas would be much appreciated. Putting a table next to a figure Minipage: 2 tables side by side isn't working I have the following code to layout two tables side by side:  \begin{minipage}{0.3\textwidth} \begin{tabular}{c | c | c | c | c | c | c} F &amp; D &amp; E &amp; G &amp; P &amp; A &amp; L\\ \hline C &amp; H &amp; I &amp; I &amp; U &amp; G &amp; F\\ \hline G &amp; Z &amp; G &amp; A &amp; F &amp; Z &amp; U\\ \hline F &amp; R &amp; \textbf{H} &amp; \textbf{A} &amp; \textbf{U} &amp; \textbf{S} &amp; Z\\ \hline R &amp; P &amp; L &amp; I &amp; N &amp; F &amp; H\\ \hline L &amp; U &amp; G &amp; I &amp; A &amp; C &amp; T\\ \hline A &amp; B &amp; D &amp; N &amp; E &amp; R &amp; Z\\ \end{tabular}  \end{minipage}  \begin{minipage}{0.3\textwidth} \begin{tabular}{c | c | c | c | c | c | c} F &amp; D &amp; E &amp; G &amp; P &amp; A &amp; L\\ \hline C &amp; H &amp; I &amp; I &amp; U &amp; G &amp; F\\ \hline G &amp; Z &amp; G &amp; A &amp; F &amp; Z &amp; U\\ \hline F &amp; R &amp; \textbf{H} &amp; \textbf{A} &amp; \textbf{U} &amp; \textbf{S} &amp; Z\\ \hline R &amp; P &amp; L &amp; I &amp; N &amp; F &amp; H\\ \hline L &amp; U &amp; G &amp; I &amp; A &amp; C &amp; T\\ \hline A &amp; B &amp; D &amp; N &amp; E &amp; R &amp; Z\\ \end{tabular}  \end{minipage}   But it doesn't work. The tables are one below the other. What am I doing wrong? Tikzpictures side by side X Windows special programs: do some of these still exist? Find all n such that $\phi(n) = n/2$ My idea for the solution is something like this:  Since $2 | n$, $n = 2^a p_1^{e1} p_2^{e2} \cdots p_t^{et}$ where $a \geq 1$.  Then, $n/2 = \phi(2^a) \phi(p_1^{e1}) \phi(p_2^{e2}) \cdots \phi(p_t^{et})$.  Looking at the case that $t = 0$,  $n/2 = \phi(2^a) = 2^{a-1}$, and therefore $n = 2^a$.  Otherwise, $n = 2^a \phi(p_1^{e1}) \phi(p_2^{e2}) \cdots \phi(p_t^{et}) = n = 2^a p_1^{e1} p_2^{e2} \cdots p_t^{et}$. Since $\phi(n) &lt; n$, this is a contradiction, and therefore, the only $n$'s that apply are the powers of 2.  Is this right? Also, we were asked to find $n$ such that $\phi(n) = n/3$. How would I go about that one? How to transfer between International T2 to Domestic 1B terminals in Mumbai? I will be arriving in Mumbai Terminal T2 on a Turkish Airlines international flight. I have a separately-purchased IndiGo ticket 5 hours later from Terminal 1B (Domestic). In the past I heard of a free bus to transfer.    Is that still the case and if not how do I get to Terminal 1B from Terminal 2? What is the difference between 32-bit and 64-bit Ubuntu? I've heard the 64-bit platform performs better and can detect more than 4GB of RAM. Also, while some apps haven't ported to 64-bit yet, ia32-libs lets a 64-bit machine run them.  If so, why not promote 64-bit over 32-bit? In Magic, at the start of the game, you draw 7 cards. How would you calculate the likelihood of drawing a specific card in your opening hand?  For example, let's say I have a 60 card deck, and I'm running 4 . What is the percent chance that I will have at least one Bird in my opening hand? Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$ Question 1: For $n \in \mathbb{N}$ explain why $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$   We must show that it is normal and separable.   $\mathbb{Q}(\zeta_n)/\mathbb{Q}$ is normal since it is a splitting field for $X^n-1 \in\mathbb{Q}[X]$ (I think... Is this correct?).  It is separable because it is of characteristic $0$  Question 2: $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$  Is this because the primitive nth root of unity $\zeta_n$ acts as a generator for a cyclic group? I am unable to fill out a decent proof on this.   Thanks for your help Trying to use "Difference" tool gives out "'QgsWKBTypes' is not defined" error I am trying to separate two overlapping vector layers and find out the difference in QGIS 2.18. I have tried finding difference with layers with points and also with buffers. Both of them give following error:  global name 'QgsWKBTypes' is not defined See log for more details   I have searched the web for this but can't seem to find a solution. Is it possible to use an Ubuntu Live CD and run GParted to partition a my HDD (including the partition that is usually mounted on a given system)? I'm encountering a problem with my HDD's partitions and can't resize it. I've described my problem and my system here: .  Now, from a more general perspective, I was thinking on whether it is possible to use an Ubuntu Live CD and use GParted in a live session to possibly go around that problem. Is that possible? I made a separate question as I'm interested in the possibility independently from my current problem.  You see, I only have one partition and that's mounted. When I use GParted through Ubuntu I don't get any error reports (unlike the case reported in the question linked above).  Thanks beforehand. I am calculating the class group of $\mathbb Q(\sqrt 6)$. My working is as follows:  The Minkowski bound is $\lambda(6)=\sqrt 6&lt;3$ so we only need to look at prime ideals of norm $2$. $2$ divides the discriminant, $24$, of $\mathbb Q(\sqrt 6)$, so $2$ ramifies, and so for any prime ideal $\mathfrak p$ of norm $2$, $\mathfrak p^2$ is principal. But $(2, \sqrt 6)^2=(2)$, so $\mathfrak p=(2, \sqrt 6)$ has norm $2$. If I can show $\mathfrak p$ is not principal, then I can conclude that $Cl(\mathbb Q(\sqrt 6))\cong C_2.$ But if there was an element of $\mathcal O_{\mathbb Q(\sqrt 6)}$ of norm 2, this would correspond to a solution of the diophantine equation $x^2-6y^2=2$. Clearly $x$ is even, so writing $x=2n$ we get $2n^2-3y^2=1$. Now reducing modulo $3$, we get $2n^2\equiv 1 \pmod 3$ which has no soultions. Hence $\mathfrak p$ is not principal and $Cl (\mathbb Q(\sqrt 6)) \cong C_2.$  However,  says that the class group is trivial. Where have I gone wrong? What am I misunderstanding? Is $(2, \sqrt 6)$ principal? I need to write a small program that can detect that it has been changed. Please give me a suggestion!  Thank you. Let's say I have a script that will be executed on various machines with root privileges, but I want to execute certain commands within that script without root.   Is that possible? Does there exist an $a_0$ such that the sequence $a_{n+1} = 2a_n + 1$ is prime for all $n \ge 0$? I believe I see that $a_n = 2^n(a_0+1) - 1$ but am somewhat uncertain where to proceed afterwards. I am a complete beginner at number theory and would appreciate it if someone could point me in the right direction--surely there is some obvious argument I am missing. Evaluating $\int_{-\infty}^{\infty}\frac{1}{(x^2+b^2)^2}dx$ As I finished programming the MCU in the Arduino Uno board to receive some RF Signal and drive relays, I moved it into a standalone board I made with Eagle. The circuit is pretty basic, the MCU receives data from a RF Receiver, processes it and then turns on/off some pins that drive 5V relays (through transistors, of course). When I test it on the Arduino Board, you can see that the LEDs toggle ON and OFF whenever I send the data through the RF Transmitter. You send once, it toggles ON, you send another time, it toggles OFF and so on. This works for all the 4 PINS that it has programmed. In my standalone board, each of these four pins are connected to transistors that drive 5V relays. The problem is that only one pin seems to activate, and then it won't even toggle OFF, like you send the data once and you can hear the relay's coil go ON, but then if you try to toggle it OFF it just won't, it's latched ON and I have to unplug and plug the USB cable again to reset it. The ATMEGA328P has a 16MHz crystal, two 22pF caps for the crystal, and a 10K resistor that goes from the Reset Pin to VCC. I'm not sure why the MCU behaves so weird in my board. There's also another VERY weird detail I didn't mention. If instead of using the RF Receiver, I connect the Data Output pin of the PIC that drives the RF Transmitter directly into the Receiver board, that one pin I mentioned that works is able to toggle OFF and ON again, but still, the other pins just don't work. I've tested it not only by hearing the relay's coil but also by using a multimeter. Any help would be really appreciated.  EDIT:  Here is the Eagle Schematic of the board:    It's true that I really didn't concern about the noise, but since it was quite a simple project I didn't think that noise was going to attack so violently, plus  I don't really know how to protect the circuit from inductive noise. Thank you for answering fast!  EDIT 2:  Okay so here goes more detail:    Real photos:      The soldering seems quite awkward but I probed all the traces to check for continuity.  I could make some extra holes to, for example, add a 100nF decoupling capacitor for the MCU and so, but if you think I should enhance the schematic and add a lot more components, then I'll gladly remake the board.   About the supply, right now (for debugging) I'm connecting the Arduino Uno to a Cellphone Charger (Notebook won't supply enough current for relays), and I'm connecting those red and black cables to the Arduino Uno. I'm using that Cheap 433MHZ RF Receiver so if the circuit is so vulnerable to noise as you say, it may also be getting fouled up by the noise. How to make all faces flip to the right/consistent direction? What's happening is that I have tried to flip the normals, inside and out, but there are always faces which have to be flipped!  Normals recalculated   Inside View    If I flip them again, all faces get flipped and end up horrible and, not working at all. So how can I make all of the faces flip to the right direction?