Expansion of the Universe (within galaxies)
Can the Hubble constant be measured locally?
Is this an instance of Priori Incantatem? During the climax of Fantastic Beasts and Where to Find Them, Tina briefly duels with Graves and their wands appear to lock with each other (see picture). I believe this also happens some other times in the later Harry Potter films other than Harry and Voldemort's duel in the graveyard during Goblet of Fire.    We know that this is definitely a case of Priori Incantatem for the graveyard duel in Goblet of Fire, as the wands are locked for a sufficient amount of time for past spells to begin showing themselves (significantly, showing the people Voldemort had murdered), but is this the case for the other instances of wands locking? If so, does that mean there are a lot more wands out there with shared cores, as it was my understanding this could only happen if that criteria was satisfied? I have the following code in my theme's archive.php:  &lt;?php the_archive_title( '&lt;h1 class="page-title"&gt;', '&lt;/h1&gt;' ); ?&gt;   This gives me titles like "Category: Russia", "Tag: America", "Author: John".  I would like to remove the "Category:", "Tag:" and "Author:" part and just display the category, tag and author names.  Does anyone know how to accomplish this?  Thank you. /ə/ in a stressed syllable? According to , the schwa /ə/ doesn't occur in stressed syllables. But , Oxford Advanced Learner's Dictionary and Longman Pronunciation Dictionary say otherwise: the word "because" has been variously transcribed as /bɪˈkəz/ or /bəˈkəz/. So in which source should I believe? Or is there any error in transcription going on here? Or is "because" the only exception? And are there others? Inverse of a matrix is expressible as a polynomial? Let $A$ be an $n \times n$ matrix. Prove that if A is invertible, then there exists a polynomial $p$, such that $A^{-1}=p(A)$  Thus far:  Let $W$ denote the $k$ dimensional A-cyclic subspace spanned by a vector $v$.  Then, $I_n=\sum_{i=0}^{k} a_{i}A^i$ for some scalar $a_i$.  What I want to do is multiply both sides by $A^{-1}$, so that way it just falls into my hands, but Im not sure that is 'legal'. Character Limit in HTML How do you impose a character limit on a text input in HTML? Greek pdf bookmarks I am puzzled with sections titled with Greek characters. They do appear in the pdf's Content list, though not correctly.  For example, in my thesis--written in English with LyX, based on the KOMA-script--I choose to include a translation of the summary in Greek (=Περίληψη). The "raw" code for the (unnumbered) chapter title reads: \addchap{\textgreek{Per\char208lhyh}}. In the final .pdf file (using pdflatex) the respective entry appears as Per208lhyh. Using the unicode option for the hyperref package does not fix the problem.  Update detail: the document (should) not only contain Chapter or Section titles in Greek, but normal text as well.  I have found some relevant references within tex.stackexchange and elsewhere (e.g., , the manual of the textgreek package, , ). However, I cannot extract a concrete answer.  How can Greek characters appear correctly as bookmarks in the .pdf's Content list?  Note, the information of this Q&amp;A applies to/under LyX as well. How to correct for small p-value due to very large sample size I am running into a problem where an independent variable, which should have no predictive power on the dependent variable based on domain knowledge, comes out with very small p-value because the sample size is very large(~100,000). If I only use &lt; 5000 data points, then the p-value becomes large enough to support the prior that the variable is insignificant. However, I don't think tweaking the sample size to get to the desired conclusion is a good practice. Is there any procedure to adjust for small p-value simply due to huge sample size? Joined pipelines Considering a routine such as this one:  alpha() { echo a b c |tr ' ' '\n'; }   which outputs a stream, I would like to take the output stream, transform it, and paste it with the original output stream.  If I take use upcasing as a sample transformation, I can achieve what I want with:  $ mkfifo p1 p2 $ alpha | tee p1 &gt;( tr a-z A-Z &gt; p2) &gt;/dev/null &amp; $ paste p1 p2 a       A b       B c       C   My question is, is there a better way to do this, preferably one not involving named pipes? How can I prove that     $$1^3+ 2^3 + \cdots + n^3 = \left(\frac{n(n+1)}{2}\right)^2$$    for all $n \in \mathbb{N}$? I am looking for a proof using mathematical induction.  Thanks How to use the Alt + Right click in edit mode in Linux Getting "System program problem detected" pops up regularly after upgrade This started to happen immediately after I had rebooted the first time after doing a system upgrade. It first starts with a dialogue that says "System program problem detected". Then when I try to hit 'report problem' not much happens. I am led through a dialogue that always ends up the problem cannot be solved.  I am aware this is not a lot of information, however I'm not sure which information I need to publish and how should I obtain it to debug this problem.  Here's a screenshot! Zero-pad digits in string I have tried as following:  1. Turn off: export DISPLAY=:0.0 &amp;&amp; xset dpms force off  2. Turn on: export DISPLAY=:0.0 &amp;&amp; xset -dpms   Which works but that is a temporary solution, which does not fix my problem yet. When i reboot system it start again and again the same auto turn off mode.   How can i now remotely using SSH turn it off forever?  IMPORTANT:  - KIOSK (ATM machine will use this option) - 24/7 advertising display/slides will use this   Optional Note: this guide i followed   , but permanent solution did not worked. How can I restart an app game from the beginning Are any of the USB ports on a Macbook Pro "always on" Always on USB ports will provide power to a device even when the laptop is shut down. Obviously this can be problematic for battery issues, but sometimes a user wants this capability all things considered.  Do the Macbook Pro offer this on any of the USB ports and if not is there any chance its wired and just has to be enabled? During Thor's interrogation, Agent Coulson exits the room and Loki enters and informs him that his father Odin had passed away and that he cannot undo his banishment. Not only does he communicate with Thor, but he goes to the area where Mjölnir is embedded in the rock and attempts to lift it, with SHIELD scientists and agents completely oblivious to his presence. Loki shows a similar ability when he converses with 'The Other' and when he manipulates Erik Selvig. Is this a part of Loki's illusion powers or another one of his abilities that has not been addressed? How was he able to visit Earth without using the Bifrost? How to launch a command on network connection/disconnection? I have a wifi connection that requires to authenticate using a web form once the wireless link is established. I know how to automate the authentication with a script that uses curl/.  But how can I ask Windows to call my script every time I connect to a particular network connection?  I would be also interested in receiving the name of the wireless profile or the ESSID on the command-line of my script. Virtualbox Kernel driver not installed I tried to use my Virtual Box and this is the error I received - (I just updated to the new Ubuntu also) and I am VERY new at this Linux OS.     Kernel driver not installed (rc=-1908)      The VirtualBox Linux kernel driver (vboxdrv) is either not loaded or   there is a permission problem with /dev/vboxdrv. Please reinstall the   kernel module by executing      '/etc/init.d/vboxdrv setup'      as root. Users of Ubuntu, Fedora or Mandriva should install the DKMS   package first. This package keeps track of Linux kernel changes and   recompiles the vboxdrv kernel module if necessary. Show $$\lim_{h \to \ 0} \frac{f(x + 2h) - 2f(x+h) + f(x)}{h^{2}} = f''(x)$$   Proof:  By definition:    $$f'(x) = \lim_{h \to \ 0} \frac{f(x + h) - f(x)}{h}$$  Using this idea it would imply:   $$1)\ \ f''(x) = \lim_{h \to \ 0} \frac{f'(x + h) - f'(x)}{h}$$  As such it is required that I find an expression for $f'(x+h)$. This is where I'm not sure if the step I took is legitimate.  An expression for $f'(x + h)$ is:  $$f'(x+h) =  \lim_{h \to \ 0} \frac{f(x + 2h) - f(x + h)}{h}$$  Combining this with the definition of $f'(x)$ and inserting it into 1) you arrive at: $$\lim_{h \to \ 0} \frac{f(x + 2h) - 2f(x+h) + f(x)}{h^{2}} = f''(x)$$   As required.    Concern: I feel a discomfort with this solution. Even though "mechanically" it worked out, if I am taking the limit as $h \rightarrow 0$ that would mean $x + 2h$ and $x + h$ both go to $x$. But I am attempting to use the idea that $x +2h$ goes to $x + h$. Perhaps it is a notation idea that I need to communicate better, but I feel it is larger than just that. Passing multidimensional arrays as function arguments in C In C can I pass a multidimensional array to a function as a single argument when I don't know what the dimensions of the array are going to be?  Besides, my multidimensional array may contain types other than strings.