The diameter of observable universe is 93 billion light years but the age of universe is only estimated to be 14 billion years. So how does light have 46.5 billion years to travel from the boundary of observable universe to us? I mean if the radius is 46.5 billion light years then that should mean light took 46.4 billion years to go from there to here right?
I was reading through the Wikipedia article on  and came across the fact that the most distant Quasar is 29 Billion Light years. This is what the  exactly says      The highest redshift quasar known (as of June 2011[update]) is ULAS-J1120+0641, with a redshift of 7.085, which corresponds to a proper distance of approximately 29 billion light-years from Earth.   Now I come to understand that the  singularity is believed to be around 13.8 Billion years ago.  So how is this possible? Does the presence of such a quasar negate the Big Bang Theory?   I'm not a student of Physics and was reading this out of (whimsical) curiosity. Is there something I'm missing here or the "proper distance" mentioned in the fact is a concept that explains this?  Edit: My Bad! Here's how..  A simple google search led me to  which says the farthest quasar found is 12.9 billion LYs and not 29 billion. So in the end we have just proven that wikipedia needs more moderation.
How can I access a JavaScript object which has spaces in the object's key? Clarifications about Gstreamer I'm a bit confused about what Gstreamer does.   Does it come installed by default with Ubuntu ?  If so which version  is the default for 14.04?  Does it provide hardware accelerated video playback (decoding) ?   If so does it work with VA-API and VDPAU or is it an alternative to those?    Thanks for your help How to debug a Custom Timer Job in SharePoint 2010? Do you use "a" or "an" before acronyms / initialisms? I found a video on YouTube that shows someone using the command tasksel from the server's boot menu after a fresh install of Ubuntu Server. Simple enough it looked like, but when I go to the options I want to choose for installation it has no information on how to select them, and when I click Enter on one of them it takes me back to the command prompt.  So how do I make a selection of the items listed under tasksel?  I have tried Shift++ to add, but no luck. Anyone know?  I want to install Ubuntu Desktop, as Ubuntu GNOME GUI is not an option in the listing for Ubuntu 17.10 Server. Machine Learning - Where is the difference between one-class, binary-class and multinominal-class classification? Where is the difference between one-class, binary-class and multinominal-class classification?  If I like to classify text in lets say four classes and also want the system to be able to tell me that none of these classes matches the unknown/untrained test-data.   Couldn't I just use all the methods that I mentioned above to reach my goal? e.g. I could describe C1, C2, C3 and C4 as four different trainings-sets for binary-classification and use the trained models to label an unknow data-set ...  Just by saying, Training-Set for C1 contains class 1 (all good samples for C1) and class 0 (mix of all C2, C3 and C4 as bad samples for C1).  Is unlabeled-data C1 -> 1 or 0  Is unlabeled-data C2 -> 1 or 0 ... and so on ...  For multinominal classification I could just define a training-set containing all good sample data for C1, C2, C3 and C4 in one training-set and then use the one resulting model for classification ...  But where is the difference between this two methods? (except of that I have to use different algorithms)  And how would I define a training-set for the described problem of categorizing data in those four classes using one-class classfication (is that even possible)?  Excuse me if I'm completely wrong in my thinking. Would appreciate an answer that makes the methodology a little bit clearer to me =) I have a PDF that consists of several hundred pages of bilingual text. Since I need to use OCR on each language separately, I want to grab the even and odd pages and make two separate PDFs, using convert or ghostscript. The language I want to do first is on the odd-numbered pages. What convert or ghostscript command can I use to grab these and write them to a new file? Does $f(x) = f(2x)$ for all real $x$, imply that $f(x)$ is a constant function? If a Continuous function $f(x)$ satisfies $f(x) = f(2x)$, for all real $x$, then does $f(x)$ necessarily have to be constant function? If so, how do you prove it? If not any counter examples? What is the number of strings at size $n$ that is constructed from ${a,b,c,d}$ and there is an even num of $a$ I've been making a map for 1.10 and it's going great, but 1.11 shows great mobs to use for it. However, most things have channged in command syntax. For example, /kill @e[type=ArmorStand,r=6] is now /kill @e[type=Armor_Stand,r=6]  What about /testfor? I can't find a way to testfor a player to stand on a block and give them an effect.   What's is going on in this image is that a redstone clock is running into this command /testfor @a[1117,20,507,r=1] (if I was to stand on them cords the comparator would turn on and power that command block), but it only works in 1.10... from 1.11 snapshots, I've seen some errors of it, like it now needs to have {} at the beginning and end of it. (e.g. /testfor @a{[1117,20,507,r=1]})   It's still not working, though, so does anyone know how to get it to work? Tikz won't plot the function properly I tried to plot the following function but it didn't work:  y = 300 + 1000/x + 2.5x.  This is the document, but instead of the plot it only shows the axis.  \documentclass{article}  \usepackage{pgfplots}% This uses tikz \pgfplotsset{compat=newest}% use newest version  \pgfmathdeclarefunction{Function}{1}{%   \pgfmathparse{300 + 1000/x + 2.5}% }  \tikzset{My Line Style/.style={smooth, thick, samples=400}}  \begin{document} \begin{tikzpicture} \begin{axis}[     xmin=0.0,     xmax=250,     ymin=0,     ymax=50,     axis x line=bottom,     axis y line=left,      xlabel= $y$,     ylabel=Cost,      xtick={250},     xticklabels={250},         restrict x to domain=0:250,     ]        \addplot+[My Line Style, color=black, samples at={1,2,3,4,...,249,250}] (\x,{Function(\x)});   \end{axis}  \end{tikzpicture} \end{document} \documentclass{article} Is it possible to highlight text inside of a textarea using javascript? Either changing the background of just a portion of the text area or making a portion of the text selected? In thinking about Sturm-Liouville theory a bit I see I have no actual idea what is going on.  The first issue I have is that my book began with the statement that given  $$L[y] = a(x)y'' + b(x)y' + c(x)y = f(x)$$  the problem $L[y] \ = \ f$ can be re-cast in the form $L[y] \ = \ \lambda y$.  Now it could be a typo on their part but I see no justification for the way you can just do that!  More importantly though is the motivation for Sturm-Liouville theory in the first place. The story as I know it is as follows:  Given a linear second order ode   $$F(x,y,y',y'') = L[y] = a(x)y'' + b(x)y' + c(x)y = f(x)$$  it is an exact equation if it is derivable from a differential equation of one order lower, i.e.  $$F(x,y,y',y'') = \frac{d}{dx}g(x,y,y').$$  The equation is exact iff  $$a''(x) - b'(x) + c(x) = 0. $$  If $F$ is not exact it can be made exact on multiplication by a suitable integrating factor $\alpha(x)$.  This equation is exact iff  $$(\alpha(x)a(x))'' - (\alpha(x)b(x))' + \alpha(x)c(x) = 0 $$  If you expand this out you get the Adjoint operator  $$L^*[\alpha(x)] \ = \ (\alpha(x)a(x))'' \ - \ (\alpha(x)b(x))' \ + \ \alpha(x)c(x) \ = 0 $$  If you expand $L^*$ you see that we can satisfy $L \ = \ L^*$ if $a'(x) \ = \ b(x)$ &amp; $a''(x) \ = \ b'(x)$ which then turns $L[y]$ into something of the form  $$L[y] \ = \ \frac{d}{dx}[a(x)y'] \ + \ c(x)y \ = \ f(x).$$  Thus we seek an integratiing factor $\alpha(x)$ so that we can satisfy this &amp; the condition this will hold is that $\alpha(x) \ = \ \frac{1}{a(x)}e^{\int\frac{b(x)}{a(x)}dx}$  Then we're dealing with:  $$\frac{d}{dx}[\alpha(x)a(x)y'] \ + \ \alpha(x)c(x)y \ = \ \alpha(x)f(x)$$  But again, by what my book said they magically re-cast this problem as  $$\frac{d}{dx}[\alpha(x)a(x)y'] \ + \ \alpha(x)c(x)y \ = \ \lambda \alpha(x) y(x)$$  Then calling  $$\frac{d}{dx}[\alpha(x)a(x)y'] \ + \ ( \alpha(x)c(x)y \ - \ \lambda \alpha(x) )y(x) \ = \ 0$$  a Sturm-Liouville problem.  My question is, how can I make sense of everything I wrote above? How can I clean it up &amp; interpret it, like at one stage I thought we were turning our 2nd order ode into something so that it reduces to the derivative of a first order ode so we can easily find first integrals then the next moment we're pulling out eigenvalues &amp; finding full solutions - what's going on? I want to be able to look at $a(x)y'' \ + \ b(x)y' \ + \ c(x)y \ = \ f(x)$ &amp; know how &amp; why we're turning this into a Sturm-Liouville problem in a way that makes sense of exactness &amp; integrating factors, thanks for reading! I have an Android phone that connects with my computer via MTP. This works fine; I can see and transfer files with Nautilus. However, I often want to use the terminal to move large numbers of files, and I cannot seem to find the device anywhere in the filesystem tree. Nautilus reports the location as mtp://[usb:003,007]/, but it's not under /media or /mnt.  Does anyone know where it is? Binomial Distribution Problem - Airline Overbooking I have a program which spawns several child processes.  I want to know which files this program and its children are creating, deleting, and modifying.   inotifywait can tell me which files are being accessed, but cannot tell me which process is doing it. And I have to know where the files are being created in order to set up the monitor. auditctl will let me log which processes modify a file, but, again, I have to know where the files are in order to set up logging. lsof will tell me all of the files, but doesn't seem to be a good solution for real-time tracking.   Is there anything that will let me monitor a program's file manipulation without knowing a priori which files will be manipulated? How do I bake chocolate chip cookies like Subway? I want a chocolate chip cookie like the ones Subway has. Those cookies have a smooth top and chewy texture.  I have a recipe for 3/4 cup fat, 0.5 cup sugar 0,5 cup brown sugar, 3/4 cup flour, 1 egg, 2 tsp extract. I get a semi stiff dough, but also an airy cookie, not as dense like Subway. I use room temperature margarine.  I have tried to bake cookies with 2 eggs and with 1 egg, but they always come out wrinkly on top, not as stiff. Is it possible that using an egg and a yolk would work? (But wouldn't that waste a lot of whites if that's how they do it?)  I think as part of this I want a stiff dough, that'll leave the bowl clean, to minimize spread and keep the tops from getting wrinkly as stiffness will keep the the cookies from expanding and contracting. Is that true? If so, I'm afraid that if I add more flour to stiffen the dough will make the cookies cakey - is that the case? How would I avoid that? Select top 10 records for each category I want to return top 10 records from each section in one query. Can anyone help with how to do it?  Section is one of the columns in the table.  Database is SQL Server 2005. I want to return the top 10 by date entered.  Sections are business, local, and feature.  For one particular date I want only the top (10) business rows (most recent entry), the top (10) local rows, and the top (10) features. Can a black hole be explained by Newtonian gravity? In the simple explanation that a black hole appears when a big star collapses under missing internal pressure and huge gravity, I can't see  any need to invoke relativity. Is this correct? After upgrading to Firefox 57 Quantum many website have rendering issues, such as empty frames, missing text or fonts, etc. I use Kubuntu 16.04 64 bit.  So far, I've tried:   Restarting Firefox in safe mode Disabling "hardware acceleration"   Wiping out my profile Purging Firefox and reinstalling Running Firefox from a clean user account   But nothing helped so far.  Any tips on how to solve this are much appreciated