Error on Swipe Refresh
What is a NullPointerException, and how do I fix it?
$ac\equiv bc \pmod{\!m}\!\!\iff\!\! a\equiv b \pmod{\!\!\frac{m}{(c,m)}}$ [Euclid's Lemma, congruence form] I came across this theorem:   For all integers a,b,c and m&gt;0, if d = GCD(c,m) then a*c ≡ b*c (mod m) iff a ≡ b (mod m/d).  The =&gt;proof states this:  a*c ≡ b*c (mod m) =&gt; m|(a-b)*c                    =&gt; m/d | (a-b)*c/d                   =&gt; m/d | (a-b)                   =&gt; a ≡ b (mod m/d)   I don't understand how to go from step 2 to step 3. The proof states that this is possible because m/d and c/d are coprime. To me this means GCD(m/d, c/d) = 1 but how does this cancel out the whole term? "State-of-the-art" and "technology" When using the serial console of my system I always end up with $COLUMNS=80 and $LINES=24.  While I can change these variables manually it is somewhat annoying to do this any time when the client side terminal window has been resized.  Usually I'm connecting to the console using screen /dev/mytty baudrate.  Changing the $TERM environment variable to "screen" or "xterm" does not help.  Will I need to call getty with some of those instead of vt100?  Needless to say that all of this works fine, when I connect to the same machine using ssh. The Chinese government has a really specific list of requirements for visa photos:    I had an old unused photo from last time I applied for a visa or passport, and compared it to the requirements (decided not to use it because it was damaged). It seemed to match most of the requirements, except that it seems that they want a photo which isn't square: The required width is less than the required height.  Assuming most drugstores are still providing square passport photos, the question becomes: Should I cut the photo to match the specified width?   What adds to the confusion is if you look at the  the box for the photo is nearly square, not the oblong shape in the requirements. And I have seen other advice that you need to make sure it fully fits the box.  Any advice about what to do here? Why is there a peeking duck in my profile pic? Evaluating a PDF to find an unkown constant Evaluate the PDF to find K  $1 = \int_0^{\infty} \frac{k}{(1+x)^4}$  using u substitution I got:  $u=1+x$ and $du= dx$  $\int_0^{\infty} \frac{k}{u^4} \to \frac{k}{\frac{-1}{3} u^3}$   Since $u^4 du = \frac{u^{-4+1}}{-4+1}=$ $\frac{u^{-3}}{-3}$  which evaluating gives:  $1=\frac{k}{\frac{-1}{3(1+x)^3}} \vert_0^{\infty} \to \frac{-3k}{(1+x)^3} \vert_0^{\infty} = 0 -3k$   and $k= \frac{-1}{3}$  somehow though they came up with $\frac{-k}{3} \frac{1}{(1+x)^3}$ after integrating $\int_0^{\infty} \frac{k}{(1+x)^3}$   Was my approach correct to use substitution? Where does my work go wrong? How do we know the universe is expanding, and not that its contents are shrinking? Is there a physical reason why not to think that instead of space expanding, all physical constants and parameters are shrinking (including of course the instruments we use to measure the constants) and space is static, or is it a case of Occam's razor? Adding user to a group - Why had to reboot? I was not able to access the VirtualBox shared folder, so I made the user part of the vboxsf group. But, still not able to access it. Rebooting the guest resolved the problem. Is it a bug? A reboot is not required to add a user to a group.   sudo usermod -a -G vboxsf praveensripati   There was similar query .  I am using 11.10 and don't remember seeing similar behavior in 11.04. I need to remove every line that has a value of 2 or less in the 8th field (column).   My data looks like this:  12-31   Airport 189 379 41  49.70946503 -124.91377258   2   2880    30.8 01-01   AlberniElementary   165 331 16  49.26100922 -124.80662537   4   5760    26.1 01-09   BamfieldMarine  161 323 23  48.83490372 -125.13572693   2   2875    27.4 01-10   BamfieldMarine  161 323 23  48.83490372 -125.13572693   3   3068    38.6   I understand that using awk I can strip off the values desired and print them to another file, and I understand that sed would edit the current file. In either case, I need to retain the original file.   Note: Please provide thorough explanations with your solutions. It is not suffice to just write the command, please annotate suggestions.   Further note: The data has a header line, so most likely solution will need to      awk 'FNR >1'   I suppose? Why the name 'Rogue One'? So far, is there any suggestion, or speculation as to the reason for the name 'Rogue One' for the next Star Wars film?   To me, the name seems very close to the Rogue Squadron, most known from Hoth (their leader Luke Skywalker), especially the number following Rogue like a callsign.   However as far as I know, they were formed after the first Death Star destruction. So why Rogue One? Energy-momentum tensor transformation Which statistical test to analyse? I am trying to find out how inflammatory markers change in response to a mechanical device change. I have daily readings for the 5 days before the event and for the 5 days after the event. I am expecting a rise in inflammatory markers in the pre readings followed by a fall after the device change. I also need to find out how the change differs in two subgroups (sample sizes of the subgroups are n=21 and n=88). The aim is to find out if the change is significant, to consider these markers as predictors of the device failing and hence needing to be changed.    I would like to know what test would be appropriate to analyse this. I need to keep things simple as I and the people reading the results are non-statisticians. Can apostrophe 's' be used with 'etc.'? What would be the associated wavelength of the particle if its velocity is zero? I have tried to map this simple object, but the uv mapping does not correspond to what i see in the textured object. It cuts the image a bit on top and a bit on the bottom of the faces. It does not fill the faces with the texture, even though i have mapped them correctly. Does anyone know what could be happening? Thanks in advance. Where did the age go on the network profile? Ever since the profile redo, the age was shown in the network profile, but not in the per-site profiles. So if someone wanted to see the age, they had to go to the network profile. However.. It's vanished! The field is still there in the profile editing, however. It doesn't appear as if this was implemented:   So... Where is it? How do I change JPanel inside a JFrame on the fly? To put it simple, there's a simple java swing app that consists of JFrame with some components in it. One of the components is a JPanel that is meant to be replaced by another JPanel on user action.  So, what's the correct way of doing such a thing? I've tried  panel = new CustomJPanelWithComponentsOnIt(); parentFrameJPanelBelongsTo.pack();   but this won't work. What would you suggest? Customise date-time format in Windows Is it possible to customize data (or date-time) format in Windows (I am using Windows&nbsp;XP)?  The current format which is followed by the OS [to show date-modified, etc.] is MM/DD/YYYY or M/D/YYYY, whereas I have been comfortable with DD/MM/YYYY or D/M/YYYY format. I am finding it hard to refer Date-modified [which I use often] of files and folders. How is the authenticity of Debian packages guaranteed? I would like to use pgfplots to create a figure where I plot curves that have a recursive formula. I tried a very simple case that uses the declare function command to see whether this is possible, and I can't compile (TeX capacity exceeded). Is it even possible to do this?  \documentclass{standalone}  \usepackage{pgfplots}  \begin{document}  \begin{tikzpicture}[   declare function={test(\p)=ifthenelse(\p&gt;1, test(\p-1), 0.5);}, ]     \begin{axis}[]     % use TeX as calculator:     \addplot [mark=none] {x};     \addplot [mark=none] {test(0)};     \end{axis} \end{tikzpicture}  \end{document}