Could there be a dark matter planet?
can we have a parallel earth made of dark matter?
RSA is not designed to be used on long blocks of plaintext like a block cipher, but I need to use it to send a large (encrypted) message.  How can I do this? Let $f$ be differentiable at $x=a$.   Prove that if $x_n \to a^+$ and $y_n \to a^-$ then:  $$\lim_{n\to \infty} \frac{f(x_n)-f(y_n)}{x_n-y_n}=f'(a).$$  Every option that I think about seems to my very trivial, so I believe that I am doing something wrong.  Both numerator and denominator approach zero as $n\to\infty$ as the case of the formal definition of derivative, but it isn't guaranteed that the limits are equal (“$\frac{0}{0}$”).   Any direction? Confusion with floating point numbers Interpreting Granger causality test's results I'm trying to educate myself on Granger Causality. I've read the posts on this site and several good articles online.  I also came across a very helpful tool, the , that allows you to enter your time series and calculate the Granger Stats.  Below, is the output from the sample data included on the site. I have also taken a crack at interpreting the results.   My Questions:     Is my interpretation directionally correct?   What key insights have I overlooked?   Also what is the meaning and interpretation of the CCF charts?  (I'm assuming CCF is cross correlation.)     Here are the results and plots that I have interpreted:  Summary of computational transaction Raw Input   view raw input (R code) Raw Output  view raw output of R engine Computing time  2 seconds R Server    'Herman Ole Andreas Wold' @ wold.wessa.net  Granger Causality Test: Y = f(X) Model   Res.DF  Diff. DF    F   p-value Complete model  356          Reduced model   357 -1  17.9144959720894    2.94360540545316e-05  Granger Causality Test: X = f(Y) Model   Res.DF  Diff. DF    F   p-value Complete model  356          Reduced model   357 -1  0.0929541667364279  0.760632773377753       My interpretation:    Test was based upon 357 data points and was performed with a lag value of 1 The p-value of 0.0000294 means I can reject the null hypothesis that x does not cause y for the Y = f(x). The p-value of .76 allows me to accept the null for X = f(Y) The fact that first hypothesis was rejected and second accepted is a good thing  I'm a little rusty on my F-test so I don't really have anything to say on this for now. I'm also not sure how to interpret the CCF graph.   I really appreciate it if any of you who are well versed with Granger-causality could let me know if I'm interpeting this correctly and also fill in some of the blanks.   Thanks for your help. How do I programmatically obtain the version in JBoss AS 5.1? I want to automatically split all lines in a QGIS layer at their vertices (). I've done a Google search and found , which is quite close but the workflow is complicated. Because I'll have to train my co-workers (who are unfamiliar with GIS) to use this tool, I want something as simple as a plugin or something that doesn't require GRASS. Since it's been a long time from 2010 - the time of , I wonder if there is any better way to achieve the same result? wp_customize_image_control default value I am trying to create a custom theme using Wordpress 3.4's customization options. I would like to create an option to change the theme's logo, but I would like to also display a default logo image.   I am using the following code in my function.php page:  $defaultbranding = "get_bloginfo('template_directory') . '/images/logo.png";      $wp_customize-&gt;add_setting( 'change_branding', array(         'default' =&gt; get_bloginfo('template_directory') . '/images/logo.png',     ) );      $wp_customize-&gt;add_control( new WP_Customize_Image_Control( $wp_customize, 'change_branding', array(         'label'   =&gt; 'Image Control',         'section' =&gt; 'theme_settings',         'settings'   =&gt; 'change_branding',     ) ) );   And in the theme's header.php page:  src='&lt;?php echo get_theme_mod( 'change_branding' , 'default' ) ?&gt;'   I would like the 'default' value on the front end to be:  get_bloginfo('template_directory') . '/images/logo.png'   Is there some way I can achieve this?  Thanks in advance for any help. This is my first question on here. I'm trying to numerically solve the Schrödinger equation for the  and find the energy eigenvalues and eigenfunctions but I am confused about how exactly this should be done.  I've solved some initial value problems in the past using iterative methods such as Runge–Kutta. I've read that  is the way to solve Schrödinger's equation but Wikipedia also describes it as an iterative method for initial value problems.  How do I use it to solve an eigenvalue problem?  This confuses me for the following reasons:   Wouldn't iteratively solving the DE require knowledge of the energy eigenvalues to use as input to the calculation? I don't know the eigenvalues yet; they're precisely what I'm trying to calculate. If I did that, wouldn't I simply get a unique solution, instead of a family of eigenfunctions and eigenvalues?    I've seen some mention of "tridiagonal matrices" being generated somehow, but am not sure what the elements of that matrix would be or how that applies to the problem. Leandro M. mentioned that "the discretization defines a finite dimensional (matrix) eigenvalue problem". This seems like the correct road I should be going down, but I haven't been able to find anything that explicitly explains this process or how the matrix is constructed. If this is the correct procedure, how is such a matrix constructed? File issues after importing Drupal site I recently tried to move my Drupal site to a new server using this page: . But now the style doesn't seem be loaded and more importantly I get this error on every page in the site (even on the frontpage):  Warning: file_put_contents(temporary://filef76T9k): failed to open stream: &quot;DrupalTemporaryStreamWrapper::stream_open&quot; call failed in file_unmanaged_save_data() (line 1900 of /Library/Server/Web/Data/Sites/Default/drupal/includes/file.inc). The file could not be created.  Any ideas what this could be about? Proof of uniform limit of Continuous Functions The uniform limit of Continuous Functions is continuous.   Proof Let $\varepsilon &gt; 0$. There exists $N$ in natural numbers such that $n&gt;N$ implies  $|f_n(x)-f(x)| &lt; \frac{\varepsilon}{3}$ for all $x$ in $S$. In particular $|f_{N+1}(x)-f(x)| &lt; \frac{\varepsilon}{3}$ for all $x$ in $S$. Since $f_{N+1}$ is continuous at $x_0$ there is a $\delta&gt;0$ such that, $x$ in $S$ and $|x-x_0| &lt; \delta$ imply $|f_{N+1}(x)-f_{N+1}(x_0)|&lt; \frac{\varepsilon}{3}$ Now we conclude $x$ in $S$ and $|x-x_0| &lt; \delta$ imply $|f(x)-f(x_0)|&lt; 3 \cdot \frac{\varepsilon}{3} = \varepsilon$.  Can someone explain what is happening here? I don't follow it all. Non-principal ideal in $K[x,y]$? How to retain HTML5 Attributes on Markup I have a page with certain html markup and element attributes as shown in the snippit below:  &lt;ul class="accordion" data-accordion=""&gt;  When I edit the page as a user with the WP Administrator Role the &lt;ul&gt; remains intact upon page update. Perfect.  Yet when a user with WP Editor Role edits the page, the ul tag saves as follows:  &lt;ul class="accordion"&gt;  Notice the data-accordion attribute is removed.  How can I get WordPress to retain markup tag attributes for users with the Editor role? Why does Calculate button remain gray in Group Stats Plugin for QGIS? In my case I failed to use  plugin (2.0.30) with QGIS 2.14.11 and 2.18.3 on windows64.  Tested on several datasets: points, polygons, and csv.- But I am not sure what I have missed.    I want to click on this Calculate button. Reverse (parse the output) of Arrays.toString(int[]) Is there in the JDK or Jakarta Commons (or anywhere else) a method that can parse the output of Arrays.toString, at least for integer arrays?  int[] i = fromString(Arrays.toString(new int[] { 1, 2, 3} ); Which graphic file formats are supported by browsers? Is there anything I can do about someone who has pointed their domain at my ip? This is kind of a weird request. For some reason whoever owns safeandbuy.com has pointed their domain at my IP address. The reason it's a problem is that I'm having all kinds of crawlers that are trying to crawl my site with that domain name.   Is there anything I can do about this? How do I save terminal output to a file? How do I save the output of a command to a file?  Is there a way without using any software? I would like to know how. Please require more reviewers on First Posts On the one hand, I see very few posts in the review queue when I visit.  On the other hand, I see a lot of pretty awful first posts sitting on the front page.  This leads me to suspect that robo-reviewers are blowing through the queue.  Given how empty the queue is, could you please increase the number of people who have to check in before a post leaves the queue?  Of course, some honey-pot solution to detect and disable the auto-clickers would be even better. Julian day of the year in Java Workaround for Android 4.4 not being able to write to SD cards?