How can I make the board render correctly (Sharelatex)?
How to use PSTricks in pdfLaTeX?
How does "curved space" explain gravitational attraction? They say that gravity is technically not a real force and that it's caused by objects traveling a straight path through curved space, and that space becomes curved by mass, giving the illusion of a force of gravity.  That makes perfect sense for planetary orbits, but a lot less sense for the expression of gravity that we are the most familiar with in our day-to-day lives: "what goes up must come down."  Imagine that I hold a ball in my hand, several feet off the ground, with my fingers curled around it, and my hand is above the ball.  Then I open my fingers, releasing my grip on it, being very careful to not impart any momentum to the ball from my hand as I do so.  An object at rest remains at rest unless acted upon by an outside force.  If the ball is not moving (relative to my inertial reference frame), it has no path to travel that's any different from the Earth's path through space.  It should remain at rest, hanging there in the air.  And yet it falls, demonstrating that an outside force (gravity) did indeed act upon it.  How does curved space explain this? Difference between processing.runalg() and general.runalg() In the discussion from a question I asked several days ago (), someone suggested that I use general.runalg() instead of processing.runalg() for running QGIS algorithms.    I've now used both, and haven't noticed a difference in either performance or syntax between them.  I'm just wondering what sort of differences there are between these two methods, and which one I should be using. Proof of Young's inequality The following problem is from Spivak's Calculus.  Suppose that $f$ is a continuous increasing function with $f(0)=0$. Prove that for $a,b \gt 0$ we have Young's inequality   $$ ab \le \int_0^af(x)dx+\int_0^bf^{-1}(x)dx$$, and that equality holds if and only if $b=f(a)$.  It is enough to consider the case $f(a) \gt b$, and show that the strict inequality occurs in this case.  I've tried proving this using the theorem  $$ \int_a^bf^{-1}=bf^{-1}(b)-af^{-1}(a)-\int_{f^{-1}(a)}^{f^{-1}(b)}f$$  but I got stuck along the way.   How may I show this rigorously using the definition or properties of integrals? Any hint, suggestions or solutions would be appreciated. Billing Information Required for App Updates I'm trying to update 3 apps on my iPad and 3 things happen that never usually happen.   It asks me to sign in. It asks for my billing information. My card gets denied.   Now I know my card still works fine so that isn't the problem. The same thing happens when I try to install previously downloaded apps (that cloud button) or install new free apps.  I have no outstanding payments (is it even possible to have outstanding payments with Apple?) so why is this happening?  In case it's needed, I'm using an iPad Air running the latest version. 16GB Harddrive and Wi-Fi only.  I should also make it clear that "None" isn't an option for payment. Ubuntu Won't Boot After Install on Samsung NP915S3G: error "All boot options are tried." So yesterday I went ahead and bought the Samsung NP915S3G (ATIV Book 9 Lite) and installed Tahr in hope that everything would go smoothly. For the most part it; everything necessary seems to work off the bat. Unfortunately when I restart it, nothing boots. I erased Windows so that's obviously not an option, but the computer seems pretty dead certain that there's nothing there to boot. I think this might have a lot to do with UEFI which is a field I have next to no experience with. There also seems to be a fat32 partition that consistently reappears when I delete it.   Any help is much appreciated, thanks. Changing default \citet font in biblatex I'm using biblatex to manage my citation in a natbib style :  \usepackage[style=alphabetic,maxnames=6,natbib=true]{biblatex}   However when I use the \citet command, the author's name is in a \textsc font, I would like to change this behavior so that the font used is the default one, but I could not find how to do this in biblatex's documentation. Convert HTML entities to Unicode and vice versa Plotting Population Regression Function with pgfplot I want the make the following population regression function with pgfplot.     My attempted code is  \documentclass[border=5mm]{standalone} \usepackage{pgfplots}   \begin{document}  \begin{tikzpicture}[ % Define Normal Probability Function declare function={             normal(\m,\s)=1/(2*\s*sqrt(pi))*exp(-(x-\m)^2/(2*\s^2));         }        ] \begin{axis}[     no markers   , domain=-3.2:3.2   , samples=100   , ymin=0   , axis lines*=left   , xlabel=     , every axis y label/.style={at=(current axis.above origin),anchor=south}   , every axis x label/.style={at=(current axis.right of origin),anchor=west}   , height=5cm   , width=12cm   , xtick=\empty   , ytick=\empty   , enlargelimits=false   , clip=false   , axis on top   , grid = major   , hide x axis   , hide y axis   ]    \addplot[cyan!50!black, rotate=-45] (x, {normal(0, 1)});  \end{axis}   \end{tikzpicture}  \end{document}     Any help to get this graph will be highly appreciated. Thanks What is the relation between electromagnetic wave and photon? At the end of this nice video (), she says that  is a chain reaction of electric and magnetic fields creating each other so the chain of wave moves forward.  I wonder where the  is in this explanation. What is the relation between electromagnetic wave and photon? How to hide Authoring information,Revision information,Publishing options tabs in create/edit node for any content type I am trying to hide Authoring information, Revision information, Publishing options tabs in create/edit node for any content type. I tried different modules with no luck. Please give me suggestions how to achieve this. Thanks a lot I am new to the netplan on Ubuntu 18.04, just discovered it exists today. I have an interface that I am trying to add to create a floating IP on google cloud. It is based on this example:   I tested the example, and it works, but now I try to do the same on ubuntu, and I don't know how to convert this:  cat &lt;&lt; EOF &gt;&gt; /etc/network/interfaces auto eth0:0 iface eth0:0 inet static     address 10.190.1.1     netmask 255.255.255.255 EOF   to netplan.  The output for ls /etc/netplan is '50-cloud-init.yaml'. and the output for cat /etc/netplan/*.yaml is:  network:     version: 2     ethernets:         ens4:             dhcp4: true             match:                 macaddress: 42:01:0a:8e:00:3e             set-name: ens4   my ifconfig:  # ifconfig  ens4 ens4: flags=4163&lt;UP,BROADCAST,RUNNING,MULTICAST&gt;  mtu 1460     inet 10.142.0.62  netmask 255.255.255.255  broadcast 0.0.0.0     inet6 fe80::4001:aff:fe8e:3e  prefixlen 64  scopeid 0x20&lt;link&gt;     ether 42:01:0a:8e:00:3e  txqueuelen 1000  (Ethernet)     RX packets 9430  bytes 1635180 (1.6 MB)     RX errors 0  dropped 0  overruns 0  frame 0     TX packets 13383  bytes 1513428 (1.5 MB)     TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0   What is the equivalent of what he said to put in the file, for netplan? Beginner here with an issue on a simple presentation using beamer  \documentclass{beamer}  \begin{document} \begin{frame}   \tau \epsilon \chi \end{frame} \end{document}   The above fails with the message "! Missing $ inserted." and waits for me to do something when converting to pdf. I have tried adding the instruction \usepackage[utf8]{inputenc} and also \usepackage[greek]{babel}. I have not seen references either to needing to use any other package. What is exactly I am missing? Because I'm still living like it's 2008, I run a website with a .in TLD. The website has nothing to do we India and does not target Indian users.  Unfortunately, when I go to Google Webmaster Tools I see that Google have locked my geotargeting status to India:    On the , Google state that:     Sites with country-coded top-level domains (such as .ie) are already associated with a geographic region, in this case Ireland. In this case, you won't be able to specify a geographic location.   This seems implausibly inflexible, so I want to know if there are any sneaky ways of removing auto-geotargeting, or changing it to a more appropriate region? sudo find / -name "*" | xargs grep -sn --color=auto "-j"   Above command returns below:  grep: invalid option -- 'j' Usage: grep [OPTION]... PATTERN [FILE]... Try `grep --help' for more information. ...   How do I search for string -j? When are stopovers permitted on Japan Railways (JR) trains? Regarding : in general, what are the rules governing stopovers for JR trains if one does not use a rail pass? A stopover means you have a ticket from stations A to B (say, Tokyo to Hiroshima) and you disembark and exit the ticket gates at an intermediate station (say, Kyoto).  (Spoiler alert: it's complicated.) "Economic" vs. "economical" I looked "$\divideontimes$" up on Google and now I know that it's Unicode U+22c7 but when would it be used?  I am guessing that $5 \divideontimes 5 = 25$ and $1$...? Accumulation Points for $S = \{(-1)^n + \frac1n \mid n \in \mathbb{N}\}$ I was recently asked to find the accumulation points of the set $$S = \{(-1)^n + \frac{1}{n} \mid n \in \mathbb{N}\}$$  I answered that the accumulation points are $\{-1,1\}$, because despite the fact that $\frac{1}{n}$ diverges, we can still use $\frac{1}{n}$ to find an element arbitrarily close to either $1$ or $-1$, i.e. to show that there is an element in an arbitrarily small neighborhood of $1$ or $-1$. (No proof was required for this question --- this is my intuition.)  Am I right at all? How to get the type of T from a member of a generic class or method Let's say I have a generic member in a class or method, like so: public class Foo&lt;T&gt; {     public List&lt;T&gt; Bar { get; set; }          public void Baz()     {         // get type of T     }    }  When I instantiate the class, the T becomes MyTypeObject1, so the class has a generic list property: List&lt;MyTypeObject1&gt;. The same applies to a generic method in a non-generic class: public class Foo {     public void Bar&lt;T&gt;()     {         var baz = new List&lt;T&gt;();                  // get type of T     } }  I would like to know what type of objects the list of my class contains. So what type of T does the list property called Bar or the local variable baz contain? I cannot do Bar[0].GetType(), because the list might contain zero elements. How can I do it? Abnormal behavior with iwlwifi driver: the device is shown as not working