What's the difference between apt and apt-get
What is the difference between apt and apt-get?
How can be solved the equation $x^3+x-1=y^2$ in positive integers?    I know this equation defines an elliptic curve, but this seems to be a non-elementary way to solve this question. Is there a more elementary solution?   By the way I found three solutions: $(1,1), (2,3)$ and $(13,47)$. Is this related to the law group property of elliptic curves? Thanks for further answers. Random quadratic equation I would like to produce quadratic equation with integer coefficients.  Here's my code using pgfmath.  \documentclass{article} \usepackage{tikz} \pgfmathsetseed{\pdfuniformdeviate 10000000}  \begin{document} $\pgfmathdeclarerandomlist{signe}{{+}{-}}% \pgfmathrandomitem{\s}{signe}% \pgfmathparse{random(2)}% \pgfmathparse{ifthenelse(\pgfmathresult==1,"-"," ")}\pgfmathresult \pgfmathrandominteger{\a}{1}{6} \pgfmathparse{ifthenelse(\a==1," x^{2} ","\a x^{2}")}\pgfmathresult % coeff a \pgfmathdeclarerandomlist{lincoeff}{{}{2}{3}{4}{5}{6}} \pgfmathrandomitem{\b}{lincoeff}% \pgfmathrandomitem{\s'}{signe}% \pgfmathsetmacro{\e}{random(0,6)} \pgfmathparse{ifthenelse(\e==0," ", " \s' \b x ")}\pgfmathresult % coeff b \pgfmathrandominteger{\c}{0}{6} \pgfmathrandomitem{\s''}{signe}% \pgfmathparse{ifthenelse(\c==0,"","\s'' \c")}\pgfmathresult % coeff c =0$ \end{document}   It works but it seems to be not a good way, I had some pain with the x-coeficient and my solution looks complicated. I tried to use an ifthenelse inside an other ifthenelse but without success. Is there a better way ? I love admin-ajax.php. But I hate having to localize in order to point frontend scripts to it, and I wish there was an equivalent, easy-to-find file for themes. (It also just bothers me to see frontend requests go through "/wp-admin/". No practical reason, just looks ugly IMO.)  So I've simply copied admin-ajax.php to the root dir at "/ajax.php", adjusted the include paths and removed the WP_ADMIN constant definition. Seems to work like gangbusters (I can now just direct all my frontend AJAX requests to /ajax.php! And I can still use the normal wp_ajax hooks in my plugins!).  But is this safe? What might go wrong? Since this isn't built into core, I assume there's a good reason as to why not. But looking through the code, I can't see any immediate problems.   You're smart--tell me if this approach is crazy. Or if there's a simpler method that I'm overlooking. I'd like to do the equivalent of the following in LINQ, but I can't figure out how:  IEnumerable&lt;Item&gt; items = GetItems(); items.ForEach(i =&gt; i.DoStuff());   What is the real syntax? How do I run a sudo command in Emacs? What does $\lim\limits_{x \to \infty} f(x) = 1$ say about $\lim\limits_{x \to \infty} f'(x)$? Given that $f$ is differentiable, what does $\lim\limits_{x \to \infty} f(x) = 1$ say about $\lim\limits_{x \to \infty} f^\prime(x)$ ? Intuitively I feel that it's $0$.  I attempted to solve this by trying to evaluate $$\lim_{x \to \infty} \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} $$ by trying to interchange the limits after showing that $\frac{f(x + h) - f(x)}{h}$ converges uniformly as $x \to \infty$. But I couldn't proceed further.  Trying to work backwards, as a specific example, $f(x) = \arctan(x)$ came to my mind. It's derivative certainly goes to $0$ as $x \to \infty$. Doesn't this show that $\frac{f(x + h) - f(x)}{h}$ converges uniformly to $0$ as $x \to \infty$ ?  I'm totally confused! I would really appreciate if anyone told me what I am doing wrong. Enabling CORS in GeoServer (jetty)? I hope somebody has already figured this one out. I just installed Geoserver 2.9 on a vanilla Ubuntu 16.04 distro. The Geoserver 2.8 method of enabling CORS with the shanbe.hezoun class does no longer work with Jetty 9.2.13.  There are mentions that CORS support is already packaged with Jetty 9.2.13 in the jetty-servlets.jar.  The Jetty lib which is compiled with Geoserver contains a jetty-servlet-9.2.13.v20150730.jar in geoserver/lib but not jetty-servlets.9.2.13.v20150730.jar. Are these supposed to be the same jar with a different name?  It should be possible to enable CORS either in geoserver/etc/webdefault.xml or in geoserver/webapps/geoserver/WEB-INF/web.xml.  My understanding is that the webdefault.xml is applied first and the web.xml thereafter.  I have tried following filter in both xml. I haven't got as far as adding a filter mapping. Adding the filter alone will cause the Geoserver/Jetty service to not start proper.  &lt;filter&gt;     &lt;filter-name&gt;cross-origin&lt;/filter-name&gt;     &lt;filter-class&gt;org.eclipse.jetty.servlets.CrossOriginFilter&lt;/filter-class&gt; &lt;/filter&gt; So I had an exam today and one of the questions were: Give an example of a function $f$ which is nowhere continuous but $|f|$ should be continuous at all points. At first I had no idea how to do it then I came up with this, even though I know it's wrong:  $$f(x)= \begin {cases} \ \sqrt{x}&amp;\text{if }x &lt;0\\ \sqrt{-x}\ &amp;\text{if }x &gt; 0\\ \end {cases}$$  Like I said I know it's wrong..but can someone give me an example of this? Thanks. I have a large dictionary file with 300,000+ words in it and I'm trying to find all words with the vowels aeiou in that order and have only exactly 5 vowels. My current attempt does not seem to be working and for the life of me I don't understand why.  less mywords | grep -iE [^aeiou]*a[^aeiou]*e[^aeiou]*i[^aeiou]*o[^aeiou]*u[^aeiou]*   I think it get's all the words I'm looking for but there are a few words that pop up which I can not get rid of.  abstemiousnesses ultraserious   There are a few other but they are in the same vein. Curiously, even if I add something like [^u]* to the front ultraserious keeping popping back up! Any solution would be fine however I would like it restricted to grep as we've been told it can be done using only grep. Homeomorphism between the unit disc and the unit square I know that the function that describes the homeomorphism is: $f(x,y) =       \begin{cases}     \frac{x^{2}+y^{2}}{\max(|x|,|y|)}(x,y) &amp;\quad\text{if } (x,y)\ne  (0,0) \\       \text{} (0,0) &amp;\quad\text{if } (x,y) =  (0,0) \\       \end{cases}$  But it's impossible to me to show that $f(x,y)$ is an homeomorphism. Mostly i can't see the injectivity. Django model with 2 foreign keys from the same table Color gradient for bars in pgfplots I want that each bar in my diagram has a color gradient from black to white (from left to the right). However, for the following code, the gradient exists for the entire diagram such that the left bar is black, the middle one is gray, and the right one is white.   \documentclass{report}  \usepackage{pgfplots}   \begin{document}  \begin{tikzpicture}      \begin{axis}[ybar]          \addplot[left color=black,right color=white] coordinates {(1,2) (2,3) (3,4)};      \end{axis}  \end{tikzpicture}  \end{document} The event horizon of a black hole is where gravity is such that not even light can escape. This is also the point I understand that according to Einstein time dilation will be infinite for a far-away-observer.  If this is the case how can anything ever fall into a black hole.  In my thought experiment I am in a spaceship with a powerful telescope that can detect light at a wide range of wavelengths.  I have it focused on the black hole and watch as a large rock approaches the event horizon.  Am I correct in saying that from my far-away-position the rock would freeze outside the event horizon and would never pass it? If this is the case how can a black hole ever consume any material, let alone grow to millions of solar masses.  If I was able to train the telescope onto the black hole for millions of years would I still see the rock at the edge of the event horizon?  I am getting ready for the response of the object would slowly fade.  Why would it slowly fade and if it would how long would this fading take?  If it is going to red shift at some point would the red shifting not slow down to a standstill? This question has been bugging me for years!  OK - just an edit based on responses so far.  Again, please keep thinking from an observers point of view.  If observers see objects slowly fade and slowly disappear as they approach the event horizon would that mean that over time the event horizon would be "lumpy" with objects invisible, but not passed through?  We should be able to detect the "lumpiness" should we not through? The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition Do you ever center AND standardize variables in multiple regression? It seems as if standardization would automatically center variables...is this true? Have Blender on about 4 machines rendering animations. Just spotted on one of the machines its rendering something different from the actual scene that I have setup.    Top window shows a different set of layers objects to whats actually being rendered in the rendering window below.  In my scene contents, layers objects 1-5 are not visible, but these are the ones that look like they are being rendered.  The only thing I can assume is that perhaps it might be because I did not save the document before clicking render, but I would not have expected that behaviour (you dont need to save your word document before printing it).  Can anyone confirm why this is happening? I have 2 hard disks, on first I have installed win xp. I boot into xp and run setup of win7 and installed it on second hard disk. Now the problem is that win7 bootloader is installed on first harddisk, so if I remove the first harddisk, I cannot boot into win7.   How I can move / install bootloader of win7 on second hard disk? Does it make sense to Favourite a Question you created? Is this just a redundant act, or are there differences? Brightness changes while "Adaptive Brightness" is disabled in Windows 8.1/10 with Intel HD Graphics The brightness changes with the colors displayed on the screen on my Lenovo Thinkpads with Intel HD Graphics. Light colors make the screen brighter, dark make it darker. Same behavior in Windows 8.1 and 10.  The "adaptive brightness" feature in Windows is disabled. I saw her dance/dancing? I saw a flash of lightning strike/striking? I caught her steal/stealing?