Explain this bash script: echo "${1##*.}"
How do ${0##*/} and ${0%/*} work?
Is the density operator a mathematical convenience or a 'fundamental' aspect of quantum mechanics? In quantum mechanics, one makes the distinction between mixed states and pure states.  A classic example of a mixed state is a beam of photons in which 50% have spin in the positive $z$-direction and 50% have spin in the positive $x$-direction.  Note that this is not the same as a beam of photons, 100% of which are in the state $$ \frac{1}{\sqrt{2}}[\lvert z,+\rangle + \lvert x,+\rangle]. $$ It seems, however, that at least in principle, we could describe this beam of particles as a single pure state in a 'very large' Hilbert space, namely the Hilbert space that is the tensor product of all the $\sim 10^{23}$ particles (I think that's the proper order of magnitude at least).  So then, is the density operator a mathematical convenience, or are there other aspects of quantum mechanics that truly require the density operator to be a 'fundamental' object of the theory?  (If what I mean by this is at all unclear, please let me know in the comments, and I will do my best to clarify.) How to get back to a site when viewing one of its questions When viewing a question on a site which I don't use (I never registered on it), I can't figure out how to get back to the list of questions of the site.  See this example  from the Stack Exchange Android app. Where should I click to see the list of questions? (I chose Mathematics Educators because it's the most recent site, it is very likely that most users don't have an account on this website)  Here is a random example:    When viewing a question, I don't know how to view the list of questions. This site can't be found in the sidebar since it's not in my Your Sites list. The top menu containing the site's title only opens the sidebar. Number or regions formed when $n$ points on a circle are joined The maximum number $R_{n}$ of regions formed when $n$ points on a circle are joined in pairs is $\frac{1}{24}\left(n^{4}-6n^{3}+23n^{2}-18n+24\right)$.  This is a fact that I have read in several essays on the dangers of jumping to conclusions in mathematics.  In your opinion, what's the quickest (and/or nicest) way to prove this formula?  Professor  explains somewhere an especially convincing way to tackle this pearl following an idea which a certain high schooler in one of his talks (lectures?) came up with; yet, I don't remember  where it was that I actually read this...  Let me thank you in advance for your insightful replies. Reviewing suggested edit of own post after completing 20 reviews I've completed 20 suggested edits reviews today. Then, I came across a  and I approved it.   Then, I had a doubt that whether the review count has incremented or not, oh! it's not incrementing. System works fine.  But, take a look at review page,     The edit was already reviewed by one reviewer and then I reviewed it. As I'm the Owner of the post it's enough to approve the edit. But, the review history doesn't show the detail that I had approved it. It's misleading that only one vote of a reviewer who is neither the community user nor the OP nor the moderator, is enough.  So, what should we do in this type of situation?  Is it correct to make OP to review the suggested edit after completing daily limit?  Should we need to display/hide the OP has approved the edit in the review history? Is there a list of Ubuntu versions with default corresponding Linux kernel versions somewhere?  I would specifically like to know the most recent version of Ubuntu that still used Linux Kernel 2.x. P-adic expansion construction addplot3[surf] creates lines instead of a surface I have been trying to create a surface plot but I am unable to get it to work. Any help would be greatly appreciated. I've tried using surf which only produces lines instead of a surface (Fig. 1). Note: Although I was originally able to produce output, thesurf plot no longer compiles: "Package tikz Error". I've tried compiling with both pdflatex and lualatex with -shell-escape flag.    Figure 1  I also tried to use the patch style plot. This produces gibberish (Fig. 2)    Figure 2  MWE:  \documentclass{article} \usepackage{pgfplots} \usepgfplotslibrary{external} \usepgfplotslibrary{patchplots} \tikzexternalize  \begin{document} \begin{figure}[t]   \centering    \tikzsetnextfilename{surface_plot}   \begin{tikzpicture}     \begin{axis} [       height=12cm,       width=15cm,       grid=major,       grid style={dotted},       colormap/jet,       mesh/ordering=x varies     ]       %\addplot3[patch,patch type=biquadratic,shader=faceted interp,patch refines=3] coordinates {       \addplot3[surf] coordinates {  (-6,-6,446.788)  (-5,-6,423.361)  (-4,-6,413.264)  (-3,-6,402.349)  (-2,-6,388.948)  (-1,-6,391.747)  (0,-6,386.874)  (1,-6,423.778)  (2,-6, 439.19)  (3,-6,449.074)  (4,-6,462.155)  (5,-6,484.399)  (6,-6,505.412) (-6,-5, 423.48)  (-5,-5,392.382)  (-4,-5,406.696)  (-3,-5,392.592)  (-2,-5,371.158)  (-1,-5,384.142)  (0,-5,394.666)  (1,-5,408.105)  (2,-5, 422.51)  (3,-5,420.173)  (4,-5,445.816)  (5,-5,464.731)  (6,-5,485.349) (-6,-4,402.646)  (-5,-4,371.879)  (-4,-4,376.239)  (-3,-4,396.874)  (-2,-4,382.761)  (-1,-4,386.665)  (0,-4,397.148)  (1,-4,410.875)  (2,-4,425.998)  (3,-4,385.143)  (4,-4,420.458)  (5,-4,438.432)  (6,-4,    458) (-6,-3,423.219)  (-5,-3,370.582)  (-4,-3,464.786)  (-3,-3,443.921)  (-2,-3,425.196)  (-1,-3,427.138)  (0,-3,438.002)  (1,-3, 453.97)  (2,-3,473.021)  (3,-3,418.583)  (4,-3,435.887)  (5,-3,414.993)  (6,-3,475.148) (-6,-2,401.995)  (-5,-2,385.612)  (-4,-2,438.956)  (-3,-2,418.583)  (-2,-2,400.093)  (-1,-2,400.773)  (0,-2, 410.58)  (1,-2,426.024)  (2,-2, 444.92)  (3,-2,397.131)  (4,-2,413.739)  (5,-2,431.741)  (6,-2,451.267) (-6,-1,382.978)  (-5,-1,335.274)  (-4,-1,416.598)  (-3,-1,396.718)  (-2,-1,378.348)  (-1,-1,377.455)  (0,-1,32.0089)  (1,-1,400.683)  (2,-1,419.918)  (3,-1,377.371)  (4,-1,393.286)  (5,-1,374.648)  (6,-1,429.077) (-6, 0,365.902)  (-5, 0,350.965)  (-4, 0,397.527)  (-3, 0, 378.36)  (-2, 0,360.454)  (-1, 0,358.447)  (0, 0,    363)  (1, 0,381.147)  (2, 0,401.177)  (3, 0,362.155)  (4, 0,378.174)  (5, 0,395.513)  (6, 0, 414.34) (-6, 1,372.511)  (-5, 1,326.945)  (-4, 1,407.215)  (-3, 1,388.646)  (-2, 1,371.945)  (-1, 1,371.003)  (0, 1,380.027)  (1, 1,396.414)  (2, 1,416.602)  (3, 1,374.897)  (4, 1,391.276)  (5, 1, 373.32)  (6, 1,428.284) (-6, 2,391.149)  (-5, 2,376.191)  (-4, 2,406.941)  (-3, 2,369.633)  (-2, 2,393.583)  (-1, 2,394.184)  (0, 2,404.263)  (1, 2,420.588)  (2, 2,  440.5)  (3, 2,416.631)  (4, 2,374.948)  (5, 2,391.855)  (6, 2,418.511) (-6, 3,375.967)  (-5, 3,361.698)  (-4, 3,357.421)  (-3, 3,368.273)  (-2, 3,377.106)  (-1, 3,378.664)  (0, 3,369.175)  (1, 3, 382.42)  (2, 3,397.821)  (3, 3,377.942)  (4, 3,384.944)  (5, 3,387.862)  (6, 3,424.429) (-6, 4,396.478)  (-5, 4,381.554)  (-4, 4,376.162)  (-3, 4,388.843)  (-2, 4,375.881)  (-1, 4,378.384)  (0, 4, 355.14)  (1, 4,403.654)  (2, 4,419.779)  (3, 4,398.599)  (4, 4,407.113)  (5, 4,426.715)  (6, 4,448.245) (-6, 5,409.364)  (-5, 5,380.492)  (-4, 5,387.843)  (-3, 5,360.034)  (-2, 5, 362.23)  (-1, 5,364.909)  (0, 5,358.321)  (1, 5,363.226)  (2, 5,379.325)  (3, 5,397.152)  (4, 5,410.086)  (5, 5,433.909)  (6, 5,460.548) (-6, 6, 423.99)  (-5, 6,408.967)  (-4, 6,400.475)  (-3, 6,372.922)  (-2, 6,371.116)  (-1, 6, 373.92)  (0, 6,384.778)  (1, 6,  398.8)  (2, 6, 415.62)  (3, 6,420.127)  (4, 6,436.064)  (5, 6,461.957)  (6, 6,491.123)        };     \end{axis}   \end{tikzpicture}      \end{figure} \end{document}   Thank you so much. How can I prevent my parents' divorce? I am a young teenager, younger than 16. (I do not want to give my age online)    My dad told me he wants a divorce, but I don't want my parents divorced. My dad says he can't stand my mom anymore.  My dad is older than 45 and my mom is older than 40.    If it happens, I would choose to stay with my mom. My dad can cook and drive, but my mom can't. There's a school bus in high school though.    What can I do to prevent this divorce? How to change radius/weight of curve bezier? try scaling, change radius, but its dont work Cleaning my Macbook Pro Retina leaves greasy 'streaks' across the screen Continuum between addition, multiplication and exponentiation? I noticed this  which attempts to find the shades of grey between a linear and log scale where results are between zero and one.  However, I was looking for the more general case where we find the continuum between the operators themselves - add, multiply, and exponentiation or even higher.  The function could be a hyperoperation$(n,x,y)$, where $x$ and $y$ are the numbers to operate on, and $n$ is allowed to be a non-integer number for the type of operator. So $n=1$ would be 'addition', $n=2$ would be multiplication, and $n=3$ would be exponentiation. But one would also have $n=2.5$ to be the shade of grey BETWEEN multiplication and exponentiation, or $n=3.5$ or $4$ for beyond exponentiation and tetration).  I want the formula to work with real numbers, not just integers. Any thoughts?  These related posts may also be of interest: Every time I insert the SD card from my camera into the card reader, I get this dialog:    Of course there is no need to scan it. Is there a way to disable it? Massive 404 attack with non existent URLs. How to prevent this? The problem is a whole load of 404 errors, as reported by Google Webmaster Tools, with pages and queries that have never been there. One of them is viewtopic.php, and I've also noticed a scary number of attempts to check if the site is a WordPress site (wp_admin) and for the cPanel login. I block TRACE already, and the server is equipped with some defense against scanning/hacking. However, this doesn't seem to stop. The referrer is, according to Google Webmaster, totally.me.  I have looked for a solution to stop this, because it isn't certainly good for the poor real actual users, let alone the SEO concerns.  I am using the Perishable Press mini black list (), a standard referrer blocker (for porn, herbal, casino sites), and even some software to protect the site (XSS blocking, SQL injection, etc). The server is using other measures as well, so one would assume that the site is safe (hopefully), but it isn't ending.  Does anybody else have the same problem, or am I the only one seeing this? Is it what I think, i.e., some sort of attack? Is there a way to fix it, or better, prevent this useless resource waste?  EDIT I've never used the question to thank for the answers, and hope this can be done. Thank you all for your insightful replies, which helped me to find my way out of this. I have followed everyone's suggestions and implemented the following:   a honeypot a script that listens to suspect urls in the 404 page and sends me an email with user agent/ip, while returning a standard 404 header a script that rewards legitimate users, in the same 404 custom page,  in case they end up clicking on one of those urls. In less than 24 hours I have been able to isolate some suspect IPs, all listed in Spamhaus. All the IPs logged so far belong to spam VPS hosting companies.   Thank you all again, I would have accepted all answers if I could. I have an equation contained inside \[...\], which automatically makes a \sum with sub- and superscripts turn big--so that the summation sign looks awkward inside parenthesis.  Any idea how to make the parenthesis completely enclose the whole summation?  \documentclass{article} \begin{document} We have: \[ \sum_{i=1}^n i = (\sum_{i=1}^{n-1} i) + n = \frac{(n-1)(n)}{2} + n = \frac{n(n+1)}{2} \] \end{document} How to edit files in a terminal with nano? Protecting game assets through archiving I'm writing a game in C++ (with OpenGL) and am getting quite far into development. Currently I'm loading the data directly from different directories.  (E.G. I load textures from a /Data/Textures/...png)  This is fine, but not preferable. Ideally I would like to protect these assets without too much of a performance hit. I looked at other games that I own, both Indie and AAA and found that the majority of them archive the data. However, I am unable to access these archives with programs like Winrar Archiver which implies that they have some level of protection.  I'm not particularly knowledgeable in the field of encryption and data storage, so I may be overlooking something obvious but I would like to know how exactly I could achieve something similar.  (I am aware that competent individuals are able to use the GPU to gain access to the data but that's not preventable) Intel HD Graphics 620: Does my display adapter support HDMI 2.0 necessary for a 4k display? I want to connect my laptop (Inspiron 15 5000 Series) to a 4k display. When I read online about this it seems that HDMI 2.0 is a necessaity to handle the large resolutions / refresh rates involved to get full benefits of a 4k display.  Use case: I'm not going to use this to play games. Most of my use-case is editing documents, emails, spreadsheets and some engineering drawings and video (watching not editing).   The goal behind going 4k is to boost productivity by having more things open at once to read side by side.   I looked into the Dell specs and they only mention an HDMI without going into the details of what type or whether it will support HDMI 2.0 / 4K TV.     How do I tell whether my Dell Inspiron Laptop (i7 7500 U processor) supports this?  I looked under the Display Adapters and can see that I have an "Intel HD Graphics 620"  listed.   Will this suffice to tell me if this display adapter will support HDMI 2.0 / 4k display?   Or should I be checking out some other settings?  Thanks! I recall a short lived TV show that I think was broadcast on the British TV channel ITV in the late 90s or early 2000s and it was about time travel. It was set in Britain in relatively modern times. The scene that really sticks in my head is when the protagonist goes to use their time travelling machine they go in to a room where the machine is and they close all the windows. The windows have latches on them and by closing the window it creates a circuit. By closing all the latches the circuit is complete and the machine is able to be activated. I don't know if it's much to go on, but it's been really bugging me for ages. Filling between two listplots Minecraft webpage links in chat?