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How to make a standalone document with one equation?
I'm running Fedora 25 and I need to take a few particular screen captures so I've read that shutter is a great tool for that. Sadly I am unable to use it for some reason. Whenever I try to take a screenshot this is the result: Failed to resolve version for org.apache.maven.archetypes For every generation of Excel I can remember (including 2010, which I'm using now), Excel's "Auto Size Row" features sometimes fails to actually auto size a row when the cell contains wrapped text. When it works properly, all the text is revealed and there is no additional space below the last line of text. When it fails, it adds extra space below the text. To make matters worse, what you see is not always what you get, i.e., text that appeared okay on screen gets cut off when it's printed. You also get different sizing depending on whether you are zoomed in/out or at actual size.  Simple test case:  Why is there a one-line gap after the text in cell A1 but not in A2?  (To reproduce: set width of column A to 17.14 (125 pixels), text wrap on, and cell alignment top.)  (I double-checked that I applied Auto Fit Row Height to both rows. Zoom level is 100%.)    Is there any known remedy for this without resorting to manually adjusting the row heights (which is not practical for more than a handful of rows)? How to dynamically load directive into page Open local folder from link Enumerate non-isomorphic graphs on n vertices In the following the graphs are assumed to be undirected and simple.  1.Enumerate the number of non-isomorphic graphs on $n$ vetrices where $n$ is fixed.  Here are some ideas I had:  The number of labeled graphs is $ 2^{\frac{n(n-1)}{2}} $.  So it is enough to find the number unlabeled graphs on $n$ vertices.I have no idea for this.  2.Enumerate the number of non-isomorphic graphs on $n$ vertices and $m$ edges where $n,m$ are fixed.   Can we find a closed formula for each of this?  Any help?   Thank you! Express partial derivatives of second order (and the Laplacian) in polar coordinates $z=f(x,y)$ where $x=rcosθ$ and $y=rsinθ$  Find $ \frac{\partial z}{\partial x}$ and $ \frac{\partial^2 z}{\partial x^2}$  I'm having big troubles with using chain rule, in particularly the second derivative. Spent 2 hours on this already. What I have...  $ \frac{\partial z}{\partial x}=\frac{\partial r}{\partial x}\frac{\partial z}{\partial r}+\frac{\partial z}{\partial θ}\frac{\partial θ}{\partial x}$. So I'm guessing that $\frac{\partial z}{\partial r}$ and $\frac{\partial z}{\partial θ}$ are unkown? And I will need to use them to differentiate again. Any help is really welcome. This is simply only part of a bigger question.   Full Question: How to prove $\lim\limits_{n \to \infty} (1+\frac1n)^n = e$? When is it correct to use the "-wise" suffix? Proving the determinant of a tridiagonal matrix with $-1, 2, -1$ on diagonal. Let $A_n$ denote an $n \times n$ tridiagonal matrix.  $$A_n=\begin{pmatrix}2 &amp; -1 &amp; &amp; &amp; 0 \\ -1 &amp; 2 &amp; -1 &amp; &amp; \\ &amp; \ddots &amp; \ddots &amp; \ddots &amp; \\ &amp; &amp; -1 &amp; 2 &amp; -1 \\ 0 &amp; &amp; &amp; -1 &amp; 2 \end{pmatrix} \quad\text{for }n \ge 2$$  Set $D_n = \det(A_n)$  Prove that $D_n = 2D_{n-1} - D_{n-2}$ for $n \ge 4$. I have two internet connection from two different ISP. ADSL on eth0 and 4G on wlan0. Is there any way that if one ISP fails, the other take over automatically without a physical router and by Host OS (Ubuntu 18.04)? Word for a person who continually tries to teach you when it's not necessary I've experienced this way too many times, and the best example I can give is a person who treats you like you have no idea how to do X and who keeps teaching you how to do it. I feel handicapped. Take for example how to play a card game. You know how to play the game because you've played it 5 times. However, there is a person always insists on explaining the game to you - like you are always new to the game - when you don't actually need any help and you just want to think for yourself. Another example situation is doing a repetitive task which you already have experience with, and yet the person continually tries to 'teach' you when you don't need help/already know how to do it. It almost makes you mad because you really don't need help. As an example which recently happened to me:  &quot;Hey, do you remember how to start the wood chipper?&quot; &quot;Yes I do&quot; &quot;Okay, well, let me show you one more time&quot;  Again, is there a term for someone who does this? pgAdmin 4: How to establish a connection through an SSH tunnel/interface in Windows I installed the latest pgAdmin 4 (v2.1) but I found out that (), for the moment, the only way to establish a connection through an SSH tunneling is using another outside process, an  says:  I setup a tunnel as follows: ssh -f dpage(at)hostname(dot)enterprisedb(dot)com -L 5999: hostname.enterprisedb.com:5432 -N  (...) I was running on Mac, but the same procedure should work on Linux. On Windows, there's a tunnelling app in Putty iirc, but I don't know how to use it offhand.  I have found a simple . The connection is established but it seems, when I try to connect through pgAdmin it fails or is refused (using 127.0.0.1:3306 or 127.0.0.1:5432 as the tunnel's destination). Why? Copy and set-mark in Bash as in Emacs? I would like to be able to copy and paste text in the command line in Bash using the same keyboard bindings that Emacs uses by default (i.e. using C-space for set-mark, M-w to copy text, C-y, M-y to paste it, etc.).  The  says that Bash comes with some of these key bindings set up by default.   For example, yanking (C-y) works by default on my terminal. However, I can't get the set-mark and copy commands to work, and they don't seem to be bound to any keys by default.  Usually, the way a user can define her own key bindings is to add them to .inputrc. So I looked and found the following bash functions in the documentation that I presume can help me define the Emacs-like behavior that I want (i.e. set-mark with C-space and copy with M-w).  copy-region-as-kill ()      Copy the text in the region to the   kill buffer, so it can be yanked right   away. By default, this command is   unbound.   and    set-mark (C-@)      Set the mark to the point. If a   numeric argument is supplied, the mark   is set to that position.   If I understand correctly, the above means that copy-region-as-kill is not bound to any keyboard sequence by default, while set-mark is bound to C-@ by default.   I tried C-@ on my terminal, but I don't think it runs set-mark because I don't see any text highlighted when I move my cursor. In any case, I tried adding  keyboard bindings (M-w and C-) to the functions  copy-region-as-kill and set-mark above in my .inputrc and then reloading it with C-x C-r, but this didn't work. I know that my other entries in .inputrc work because I have other user-defined keybindings defined in it.  Is there anything I am doing wrong? Am I missing anything? How can I produce a 'ring (or wheel) chart' like that on page 88 of the PGF manual? I really like the 'ring chart' or 'wheel chart' given as an example on page 88 of the PGF manual. It is like a pie chart, but with a label in the centre. Unfortunately, the manual doesn't give the source for that chart. Does anyone have an example? Thanks. Why is the Sun approximated as a black body at ~ 5800 K? Apparently spectral solar radiation is approximated by a black body at 5800 K. The spectral black body distribution (Planck distribution) is shown below (from Incropera, Fundamentals of Heat and Mass Transfer), with different temperatures including solar radiation at 5800 K.     The heat flux on an Earth surface perpendicular to sun rays (i.e., the solar constant), is roughly 1.36 kilowatts per square meter. Is this simply the integral of the above distribution? Why is the sun approximated as a black body at 5800 K? Does this mean that the surface of the sun which is emitting radiation has a temperature of 5800 K? That seems kind of low. Is solar radiation approximated as a black body at 5800 K only on Earth, or is it the same everywhere? Why don't atmospheric effects and scattering change measurements of the solar spectrum on Earth?   EDIT:  The solar constant is approximated by considering the Stefan-Boltzmann law (i.e., the integration of the spectral solar emission), the size of the sun, and the distance from the sun to Earth. A good derivation is shown here: How to validate an email address in JavaScript If $f(x)=x-\int^{\frac{\pi}{2}}_0f(x)\sin(x)dx$ find the explicit function for $f(x)$ in its simplest form Assume that $Y_0,\ldots , Y_n$ are independent random variables with the following identical distribution: $Y_i=1$ with propability $p$ and $Y_i=0$ with propability $1-p$. Also set $S_0=0$ and $S_n=Y_0+\ldots + Y_n$.  It's quite trivial that $(Y_n)_{n\geq 0}$ is a Markov chain, and I managed to show that $(X_n)=(S_n)_{n\geq 0}$ is also a Markov chain, by showing that  $\mathbb{P}(X_{n+1}=i_{n+1}\,|\,X_0=i_0,\ldots,X_n=i_n)=\mathbb{P}(X_{n+1}-X_n=i_{n+1}-X_n\,|\,X_0=i_0,\ldots,X_n=i_n)=\mathbb{P}(Y_{n+1}=i_{n+1}-X_n\,|\,X_0=i_0,\ldots,X_n=i_n)=\mathbb{P}(Y_{n+1}=i_{n+1}-i_n)=\mathbb{P}(Y_{n+1}+i_n=i_{n+1})=\mathbb{P}(X_{n+1}=i_{n+1}\,|\,X_n=i_n)$  However I am now running into the problem that I have to find whether or not $(X_n)=(S_0+\ldots + S_n)_{n\geq 0}$ is a Markov chain. I suspect that it isn't, but i'm having trouble finding a counterexample. I also need to find if $(X_n)=(S_n, S_0+\ldots+S_n)$ is a Markov chain, but I think this actually might be one, since $X_n$ gives "more information" (so to speak) to $X_(n+1)$. Again, having trouble actually proving that.  I appreciate any help, tips etc you can give me. Combining  with allowframebreaks in beamer