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how many permutations of {1,2,...,9} How many permutations of {1,2,…,9} are there such that 1 does not immediately precede 2, 2 does not immediately precede 3, and so forth up to 8 not immediately preceding 9? One obvious example of such a permutation might be 987654321, but there are many others, such as 132465879 or 351724698. Galois group of irreducible cubic equation Adding coordinate system to layout in QGIS composer? I would like to know if there is a way to add a dynamic coordinate system field into a QGIS composer layout.  I can use an expression to add many items such as document name, file path, etc but I can;t seem to figure out how to add the coordinate system? This material is covered in detail in Dickson's "Linear Groups with an exposition of the Galois Field Theory", chapter XXII and Huppert's "Endliche Gruppen", chapter II, paragraph 8. Since I don't speak german and Dickson's treatment often requires deciphering, I was wondering if there is a "modern" account of this somewhere. Lots of new batteries (for mobile devices, MP3 players, etc) have connectors with 3 pins. I would like to know what is the purpose of this and how should I use these three pins?    They are usually marked as (+) plus, (-) minus, and T. Run TTY script every time I open a GUI terminal When I log in to a TTY I get the following nice text:  Ubuntu 16.04.03 LTS Log-in: username Password: Last log-in date/time Welcome to Ubuntu 16.04.03 LTS   * Documentation:  * Management:  * Support:  9 packages to update 4 updates are security updates   I would like the last 2 lines repeated every time I open a GUI terminal for all users in the adm group (but will settle for having the entire thing displayed each and every time I open a GUI Terminal for all users)  I tried the obvious:  fab-root@fab-ux-predator:~ $ cd /etc/update-motd.d/ fab-root@fab-ux-predator:/etc/update-motd.d $ ./90-updates-available  fab-root@fab-ux-predator:/etc/update-motd.d $ cat /var/lib/update-notifier/updates-available cat: /var/lib/update-notifier/updates-available: Permission denied fab-root@fab-ux-predator:/etc/update-motd.d $   What am I missing?  P.S. Obviously I can chmod o+r the file, but how future-proof would that be? Evaluation of $\displaystyle \int_{0}^{1}\frac{x\ln (x)}{\sqrt{1-x^2}}dx$   $\bf{My\; Try::}$ Let $\displaystyle I = \int_{0}^{1}\frac{x\ln x}{\sqrt{1-x^2}}dx\;,$ Put $x=\cos \phi\;,$ Then $dx = -\sin \phi d\phi$  and Changing Limit, We get  $$\displaystyle I = -\int_{\frac{\pi}{2}}^{0}\cos \phi \cdot \ln(\cos \phi )d\phi = \int_{0}^{\frac{\pi}{2}} \ln(\cos \phi)\cdot \cos \phi d\phi$$  Now Using Integration by parts, We get  $$\displaystyle I = \left[\ln(\cos \phi)\cdot \sin \phi\right]_{0}^{\frac{\pi}{2}}+\int_{0}^{\frac{\pi}{2}}\frac{\sin^2 \phi}{\cos \phi}d\phi$$  So $$\displaystyle I = \left[\ln(\cos \phi)\cdot \sin \phi\right]_{0}^{\frac{\pi}{2}}+\int_{0}^{\frac{\pi}{2}}\frac{(1-\cos^2 \phi)}{\cos \phi}d\phi$$  So $$\displaystyle I = \left[\ln(\cos \phi)\cdot \sin \phi\right]_{0}^{\frac{\pi}{2}}+\int_{0}^{\frac{\pi}{2}}\sec \phi d\phi-\int_{0}^{\frac{\pi}{2}}\cos \phi d\phi$$  So $$\displaystyle I = \left[\ln(\cos \phi)\cdot \sin \phi\right]_{0}^{\frac{\pi}{2}}+\left[\ln\left|\sec \phi+\tan \phi\right|\right]_{0}^{\frac{\pi}{2}}-\left[\sin \phi\right]_{0}^{\frac{\pi}{2}}$$  So $$\displaystyle I = \left[\ln(\cos \phi)\cdot \sin \phi\right]_{0}^{\frac{\pi}{2}}+\left[\ln\left|\sec \phi+\tan \phi\right|\right]_{0}^{\frac{\pi}{2}}-1$$  Now How can I solve after that, Help Required, Thanks What's a word/phrase for a player/seducer? I can't seem to remember this particular word/phrase. I'm almost certain it's a two-word phrase. It specifically refers to someone who is skilled with the ladies, ie, someone who knows the tricks of the trade.  Usage: - "Unless you're a X-Y, that's not going to work with her."  Edit :  I'm not looking for 'ladies man', 'casanova', 'womanizer' etc. This phrase refers to someone who's more of a pro and one who is serious about his business. Everybody knows :-) that in Windows plain text files lines are terminated with CR+LF, and in Unix&amp;Linux - with LF only. How can I quickly convert all my source code files from one format to another and back? Meta SE account is shown 3 times in accounts Earlier today I asked my first question on this site. So Meta SE was added to my accounts. But this account is shown three times:        One of them also has a badge while the other two don't.   The network profile doesn't show MSE at all:        Also I have got this long wierd user name and  I am not able to change it. In the edit- display name this long name is not there.My user name on other sites is shown there.   After all this happened Meta SE questions are not getting loaded in my SE app.    Edit: the issue of name is solved now. I changed the profile picture and saved changes and it worked. Something's been bugging me about SO for a while now, that is the inaccuracy of "length of time" strings.  The best example I can give at the moment is .  If you look at the length of time he's been registered, it says 1 year.  He joined the site September 2008, which is only 3 months off two years.  It's the same with answers - you can give an answer 50 seconds before anyone else, but at certain times page views will show both as "5 minutes ago" or whatever.  That's not quite as bad, but with answers being sorted "randomly by votes" by default you could lose out on votes or being marked as the correct answer to the slower answer even if they're both the same.  There's probably a better method amongst these, IMO:   "Vulgar fraction" unicode characters     Member for 1½ years   answered 5¼ minutes ago asked 3⅓ hours ago  Different units   Member for 21 months (at least it's better than "1 year") Answered 306 seconds ago (ugly, I know) Asked 64 minutes ago (also ugly)  Combining units   Member for 1 year 9 months (fits easily on the profile screen) Answered 5 minutes 6 seconds ago (probably too long) Asked 3 hours 20 minutes ago (also long)  Rounding up   I personally prefer option 1, unicode fraction characters.  "Member for 21 months" is pretty good too because it's easy to quickly work out.  "Asked 452 seconds" ago is horrible though.  EDIT: I'm completely aware of the timestamp hover because I am forced into using it so much. It's a great feature, but it's not really in your face so not everyone knows about it. I still think there's a better "glancing" solution than having to hover over the time string. Prove that $T$ is an orthogonal projection Let $T$ be a linear operator on a finite-dimensional inner product space $V$. Suppose that $T$ is a projection such that $\|T(x)\| \le \|x\|$ for $x \in V$. Prove that $T$ is an orthogonal projection.    I can't understand well. The definition of orthogonal operator is $\|T(x)\| = \|x\|$. But why that $\|T(x)\| \le \|x\|$ for $x \in V$ means orthogonal projection? The question asks to prove that -  $$\frac {\sin x} {\cos 3x} + \frac {\sin 3x} {\cos 9x} + \frac {\sin 9x} {\cos 27x}  = \frac 12 (\tan 27x - \tan x) $$  I tried combining the first two or the last two fractions on the L.H.S to allow me to use the double angle formula and get $\sin 6x$ or $\sin 18x$ but that did not help at all.   I'm pretty sure that if I express everything in terms of $x$, the answer will ultimately appear but I'm also certain that there must be another simpler way. Left and right subscript / superscript I am trying to put two subscripts at the left and right of a character. For example, something like:  _{t} p_{x}  where p is in the middle. How do you do this? What's the "Bad magic number" ImportError in python, and how do I fix it?  The only thing I can find online suggests this is caused by compiling a .py -> .pyc file and then trying to use it with the wrong version of python. In my case, however, the file seems to import fine some times but not others, and I'm not sure why.  The information python's providing in the traceback isn't particularly helpful (which is why I was asking here...), but here it is in case it helps:  Traceback (most recent call last):   File "run.py", line 7, in &lt;module&gt;     from Normalization import Normalizer I have the following image    that was created with this code:  \documentclass[varwidth=true, border=2pt]{standalone} \usepackage{tikz} \usepackage{tkz-euclide}  \begin{document} \usetkzobj{all} \begin{tikzpicture}     \tkzSetUpPoint[shape=circle,size=10,color=black,fill=black]     \tkzSetUpLine[line width=1]     \tkzDefPoints{0/0/A, 3/0/B', 2/2/C, 4/4/C'}     \tkzDefLine[parallel=through C](B',C') \tkzGetPoint{Phelper}     \tkzInterLL(A,B')(C,Phelper) \tkzGetPoint{B}     \tkzDrawLine[add=0 and 0.2](A,B')     \tkzDrawLine[add=0 and 0.2](A,C')     \tkzDrawSegment(B',C')      \node at ($(A)+(-0.1,-0.2)$)  {$A$};     \node at ($(B')+(0.2,-0.2)$)  {$B'$};     \node at ($(C')+(0,0.4)$)  {$C'$};     \node at ($(B)+(0.2,-0.2)$)  {$B$};     \node at ($(C)+(0.28,0.5)$)  {$C$};     \tkzDrawPolygon[ultra thick,color=blue,fill=blue!20](A,B',C')      \tkzDrawPolygon[line width=0.3pt,color=red,fill=red!20](A,B,C)      \tkzDrawPoints(A,B',C',B,C)     \tkzLabelSegment[below,red](A,B){$c$}     \tkzLabelSegment[left,red](A,C){$b$}     \tkzLabelSegment[right,red](B,C){$a$}     \tkzLabelSegment[below,blue,pos=0.8](A,B'){$c'$}     \tkzLabelSegment[left,blue,pos=0.8](A,C'){$b'$}     \tkzLabelSegment[right,blue](B',C'){$a'$} \end{tikzpicture} \end{document}   As you might notice, the space above C' is bigger than necessary. This is because of Phelper. I need Phelper for the construction, but it should not influence the image size in any way. I've tried to get Phelper closer to C, but that seems not to be possible.  How can I stop defined (but not visible) points from influencing image size?  Please note: I wrap code like this in a figure. So images like the one above are only a part of the whole document. So working with standalone does not solve my problem. How to request a random row in SQL? Pandas Merging 101 Slow math typing I have been using LaTeX for quite some time, but I find the math writing to be a bit frustrating. It seems to take me a relatively long time to code-write long math expressions, and sometimes it's hard to see where { start and end.  I am interested in writing as fast as possible.  Is code-typing each symbol really the fastest way? Is there any good program (in the spirit of Word's MathType) that enables producing math expressions by button clicking, that you recommend? I have gotten as far as to create the bootable usb, booting into that bootable usb and getting to the install options however i quit because I had some concerns.  I currently have a Samsung 850 evo 1tb that has win 10ninstalled. I want to dual boot with Ubuntu 18.04 by installing it on a brand new unformatted uninitialized Samsung 860bevo 250gb. Should i format the brand new ssd as a new volume in win 10 and then proceed with the Ubuntu install on this volume. What else should i do? Im a first time Ubuntu user and installer.  Any and all help is appreciated.