Could these hypothetical very long distance properties of light offer alternatives to an expanding universe or a finite number of galaxies?
Other explanation for cosmological redshift?
My employer didn't send me W-2 for December 2015. In fact, he told me that I wasn't on payroll for the two months(Dec/Jan) I worked for them so I am not sure whether he will be able to generate W-2 for me or not. I am wondering should I call IRS and inform them about the same, and probably they will call the employer? Or should I report my December 2015 earnings as Miscellaneous and report to IRS while filing taxes? Or what other options do I have? I am a non resident alien on F-1 Visa. My employer also has not paid me full salary as promised, which I am discussing with him.  Also, I got paid by check in January month for my December payment, so I am wondering does this apply for 2015 tax filing as I got paid in January 2016? The  spell says:     The spell captures some of the incoming energy, lessening its effect on you and storing it for your next melee attack. You have resistance to the triggering damage type until the start of your next turn. Also, the fist time you hit with a melee attack on your next turn, the target takes an extra 1d6 damage of the triggering type, and the spell ends.   The  cantrip says:     Lightning springs from your hand to deliver a shock to a creature you try to touch. Make a melee spell attack against the target. You have advantage on the attack roll if the target is wearing armor made of metal. On a hit, the target takes 1d8 lightning damage, and it can’t take reactions until the start of its next turn.   If I absorb fire damage with absorb elements, would I be able to add an extra 1d6 fire damage to my next shocking grasp attack? Calculate a running total in MySQL I have this MySQL query:  SELECT DAYOFYEAR(`date`)  AS d, COUNT(*)  FROM  `orders`  WHERE  `hasPaid` &gt; 0 GROUP  BY d ORDER  BY d   Which returns something like this:  d  | COUNT(*) | 20 |  5       | 21 |  7       | 22 | 12       | 23 |  4       |   What I'd really like is another column on the end to show the running total:  d  | COUNT(*) | ??? | 20 |  5       |   5 | 21 |  7       |  12 | 22 | 12       |  24 | 23 |  4       |  28 |   Is this possible? Earlier this year, I read a huge (1000+ pg) novel about a cloistered group of monks that sort of worshiped math. The story involved alternate dimensions or time travel or something. A big thing in the book was coordinates, containing data like for speed or something as an alternate axis. There were several rings of the monastery.   At some point the main character was called out of his monastery to never return. I'm hoping to figure out the name so I can discuss it with my book club. Nobody owner (99 99) in FTP caused by php functions? How to change background and maintain realistic effect? I have like 30 different photos to process like this, but I want to know key things to maintain realistic photo by changing it's background, or maybe just modify background so it would be more pleasing to eye.(If you know tutorial related to my problem, please do provide it to me)  Here is the photo:   Here is my step 2:   Here is background:   Here is the result:   As you can see, it isn't any close to realistic feel. I fooled around with levels, but all I got was this and still it doesn't feels right.  First try:   Second try:   Update  Different background: lstlisting - line number gaps Is it possible to add non-number characters on the left of a code block?  Specifically, I want to add ... to correspond with some source code (see image).    I am currently using commands to stop / start the line numbers. Here is the code:  \documentclass[12pt]{article}  \usepackage[a4paper, margin = 20mm, top = 30mm, bottom = 25mm]{geometry} \usepackage{xcolor, soul} \usepackage{listings}  \definecolor{codebackground}{rgb}{0.95, 0.95, 0.92}  \lstset {     frame            = tb, % hrule above and below     keepspaces       = true,     columns          = flexible,     basicstyle       = {\normalsize\ttfamily},     escapeinside     = {(*@}{@*)}, % for escaping     backgroundcolor  = \color{codebackground},     showstringspaces = false,     language         = C,     keywordstyle     = \color{blue},     stringstyle      = \color{red},     commentstyle     = \color{teal},     numbers          = left, % {none, left, right}     firstnumber      = 1,     numberstyle      = \scriptsize\color{black},     numbersep        = 5pt }  \let\origthelstnumber\thelstnumber \makeatletter % for stopping line numbers \newcommand*\stopnumber {     \lst@AddToHook{OnNewLine}     {         \let\thelstnumber\relax         \advance\c@lstnumber-\@ne\relax     } } % for starting line numbers \newcommand*\startnumber[1] {     \setcounter{lstnumber}{\numexpr#1-1\relax}     \lst@AddToHook{OnNewLine}     {         \let\thelstnumber\origthelstnumber         \refstepcounter{lstnumber}     } } \makeatother  \begin{document} \begin{lstlisting}[firstnumber = 456] int third_function(const int c) {     /* error checking */     if(c &lt; 0)     {         return;     } (*@ \stopnumber @*)      ...     (*@ \startnumber{512} @*)     /* other stuff */     int d = 4;     char* word = "third function"; (*@ \stopnumber @*)      ...     (*@ \startnumber{678} @*)     return (c * d); } \end{lstlisting} \end{document} Prove that $\left(1+\dfrac{1}{1^3}\right)\left(1+\dfrac{1}{2^3}\right)\cdots\left(1+\dfrac{1}{n^3}\right)&lt;3$   for all positive integers $n$   This problem is copied from Math Olympiad Treasures by Titu Andreescu and Bogdan Enescu.They start by stating that induction wouldn't directly work here since the right hand side stays constant while the left increases.They get rid of this problem by strengthening the hypothesis.$$\left(1+\dfrac{1}{1^3}\right)\left(1+\dfrac{1}{2^3}\right)\cdots\left(1+\dfrac{1}{n^3}\right)\le3-\dfrac{1}{n}$$ and then proceed by induction.  The problem is that I can't find a motivation for the above change.I mean,we could have subtracted a lot of things from the RHS but what should nudge us to try $\dfrac{1}{n}$?The rest of the proof is quite standard,but I can't see how I am supposed to have thought of it.Is it just experience?Or is it a standard technique?A little guidance and motivation will be appreciated. Display current layout (language code/country flag) in keyboard indicator Just upgraded from 10.04 to 10.10, and the keyboard indicator applet no longer displays the two-letter country code for the active layout.  This is terrible. Is this the default behaviour? Anyone using two layouts can't tell which language they're in.  I can't seem to find the setting for this, it used to be in the preferences for keyboard layout.  Update 1: In case this wasn't obvious - I have two keyboard layouts - English and Hebrew. I just upgraded form 10.04, where the country code (USA/IL) was displayed, overlaid on the flag.  Now all I get is a vague keyboard icon, and can't find the settings for this.  Update 2: this seems to be a , and is now back in Maverick How can I protect my save data from casual hacking? What options are there for saving game data in a secure manner? I'm interested in solutions specifically tailored for C++.   I'm looking for something that is fast and easy to use. I'm only concerned about storing simple information such as   Which levels are and are not unlocked The user's score for each level   I'm curious again to know what's out there to use, any good libraries to use that give me nice, secure game data files that the average player can't mess with.   I just found  here which looks very nice, but it would be great to get some opinions on potential other libraries/options out there. Add the ability to add "top questions" to Careers 2.0 Profile Allow me to add my own "top questions" too! I know, I know, the site should be more heavily weighted to answering, but sometimes, how and what people ask is important too! For example I recently asked  which I think is a fairly good question. Clearly I'm going to avoid questions where I've asked something very simple, but I know of a user or two who are implementing their own C standard libraries and the depth of those questions is important/ought to be on show.  Of course, the argument I can just look at their profile holds, but that awesome q/a might have been from a year or so ago in which case finding it is difficult. Exponential of the differential operator I am not sure whether this question is even well-posed. But today I learnt that $e^Df(x) = f(x+1)$ where $D$ is differential operator and  $$e^D \triangleq \sum_{i=0}^{\infty} \frac{D^i}{i!}.$$  (ref. )  So I was curious as to whether the differential equation  $$\frac{df(t)}{dt} = e^Df(t) = f(t+1)$$  has any solutions apart from $f = 0$? Was Stack Exchange named after Experts Exchange? Was Stack Exchange named after Experts Exchange, or is the former using the word "Exchange" a coincidence? How would I use Takeown to take ownership of all folders on one drive? It is given that $X,Y \overset{\text{i.i.d.}}{\sim} N(0,1)$  Show that $\frac{XY}{\sqrt{X^2+Y^2}},\frac{X^2-Y^2}{2\sqrt{X^2+Y^2}} \overset{\text{i.i.d.}}{\sim} N(0,\frac{1}{4})$  I was thinking of making polar transformations $X=r \cos \theta, Y=r \sin \theta$  Then I am getting stuck at ranges of $\theta$ Is there a systematic way of solving cubic equations? In my text book, to solve cubic equations, I need to    find by trial &amp; error what $f(a)$ will make the equation 0. The factor will be $(x-a)$ then the other factor will be $Ax^2+Bx+C$ then I can solve using compare coefficient   But for te first part, is there any other way apart from trail &amp; error? Or is there some technique to guess the factor of an equation?   The question I am currently doing happens to be $2x^3+3x+4=9$   UPDATE:  $2x^3+3x+4=9$ should be $2x^3+3x+4=9x^2$   UPDATE 2  So I am going to try substituting   $x=\pm{1}, \pm\frac{1}{2}, \pm{2}, \pm{4}$  When $x=-\frac{1}{2}$, one of the provided answers,   $2(−0.5)^3−9(−0.5)^2+3(−0.5)+4=-18.75\neq 0$   did I make a mistake? The ship flying away from Rey in her flashback of being left on Jakku looks like one of the ships in the group that takes her away when she is captured.  If so, and it is a First Order ship that dropped her off, this is an interesting Easter egg. Are you allowed to stack Divine Smite and Eldritch Smite on the same attack? How do I tell if ACR will work with my camera and how do I get the correct version for Photoshop? What's the associated matrix of this linear operator? Let $V$ be a complex vector space of dimension $n$ with a scalar product, and let $u$ be an unitary vector in $V$. Let $H_u: V \to V$ be defined as  $$H_u(v) = v - 2 \langle v,u \rangle u$$  for all $v \in V$. I need to find the characteristic polynomial of this linear operator, but the only way to find it that I know of is using the associated matrix of the operator.  I don't know how to find this matrix because I don't know how to deal with the scalar product. Is there some other way to find the characteristic polynomial? If not, how can I find the associated matrix of this linear operator?  Thanks in advance.