Is it cold inside a black hole?
Can there be temperature inside of a massive Black Hole?
How to sum data.frame column values? Coloring a black and white PDF graphic I have a graphic in PDF format (originally converted from an SVG) that is monochromatic (black on white). Is it possible using TikZ or PSTricks but not (Illustrator or Inkscape) to include this image in a different color?  Example:    While it lasts (there seems to be no long term way to host a pdf), you can .  Edit: Simple was perhaps a bit of a misnomer - the pdfs are cropped and monochromatic, but to intricate to redraw on my own. The above example is a character from a font (which I can recolor), but it gives a good example of what shapes I am talking about. I've just recently started playing D&amp;D 4e through the Red Box, and I am confused about how to fill in the power cards.  So, take Nimbus of Holy Shielding for instance. I understand the Target and Hit components as well as the effect, but my question is about the Attack component. It reads:     Attack: Wisdom vs Will.   Does the mean whatever my Wisdom score is, without the modifier, is compared to the Will score of the enemy? Would I then not even have to roll a d20 to see if it works? How do I copy a file in Python?  I couldn't find anything under . In Star Trek canon, what's the range of operation of Transporters? By "range of operation" of the transporter, I mean "distance up to which it could transport" or "distance from which it could transport something to its own location". The range of operation would have increased with time without a doubt but I want to know the average range at any period. It'll be better if you provide full stats of all times. Is Ubuntu an open source software? Is Ubuntu an open source software (OSS)? What happens when a caster targets an object that looks like a creature with a spell that targets only creatures? There are many spells which explicitly target creatures:     Choose one creature within range   The target creature is normally supposed to make a saving throw in this case.  What happens when the caster chooses a creature, that is actually an object? For instance, a scarecrow, a mannequin, an illusion, or a corpse.  Examples:   An evil mage is hiding in the bushes. He casts an illusion of himself on the road, using the Silent Image spell. A PC sorcerer walks down the road, sees the illusion and casts Magic Missile on it. A cleric is standing near a pile of dead bodies. He has suspicions that a few corpses are actually undead creatures. He casts Sacred Flame on every corpse, see which if them succeed, hence, reveals the undead. A wizard casts Acid Splash on a mannequin, trying to damage it with acid.   Possible outcomes I can think of are:   The caster cannot even try to cast the spell, regardless of their information about what the target actually is. The caster tries to cast the spell, the casting fails, not expending the spell slot. The caster casts the spell, it expends the spell slot, then fails. The caster casts the spell, but it hits the original and not the illusion. The caster casts the spell, it flies to the target illusion but deals no damage to it (passes through it).   References in the rules and Sage advice  I was trying to investigate, but it didn't make things clearer:    has an answer, that Magic Missile won't hit. It says nothing about if it can be targeted at all, it leaves it up to the DM. Magic Missile automatically finds the original, even when the caster targets an illusion. At least . Now . This supports the counter-intuitive option 4.   on the other hand   , if there were no perceivable effects (let's say you can try to cast the Command spell on an illusion). That assumes that casters can waste their spells on illusion, which means they at least can target it. This supports options 3 and 5. Transparency/Masking : See through an Outer Sphere and see Inner Sphere in true colours Summary  I want to be able to look through an outer sphere - BlueSphere, and see another sphere inside - RedSphere  This is the target goal I'm trying to get to:    Issues  Here is what I have tried, and the problems I'm having:  1)  If I set the spheres transparency alpha values to 0.75    - then the inner RedSphere does not take on its "true" colour and shows as blue instead of red.    2)  If I set the spheres transparency alpha to lower values of 0.5   the spheres lose their crispness which I don't want and the inner RedSphere still does not take on its "true" colour   { can't paste a 3rd sample - need more reputation points }   Background  I am animating two spheres, one inside the other, superimposed about a common origin.   At the start:   the outer BlueSphere is at full radius the inner RedSphere is at zero radius  As time progresses:   the outer BlueSphere shrinks the inner RedSphere expands    So what happens is the expanding inner RedSphere "bursts through" the contracting outer BlueSphere.  So the effect I am looking for is to see the RedSphere appearing as Red as it expands inside the BlueSphere.  Thinking/Logic  So I figure that transparency is not the way to go.  The transparency settings are behaving correctly - as one would expect, in a "real world" situation - the inner sphere (Red) takes on the colour of the outer sphere (Blue) seeing as we are looking through a (transparent) Blue material.  Any ideas on what approach to take ?  It's almost as if I should be "removing" the part of the BlueSphere that the RedSphere "occupies" so that we see the RedSphere directly without any BlueSphere between us and the RedSphere.  Some sort of masking ??  Advice, comments, suggestions welcome. Thanks.  [requested edit]  Using internal render.  [ My End Solution - Thanks for the guidance ]  Right, so here is the way I got to my final result:  1) I created python drivers for each sphere   I used the frame_current scene property for input Passed that to a scripted expression which used sin() as the scaling factor Used some if / elif conditionals against frame_current to make the spheres visible only when I needed them   2) I created 3 layers   On Layer-1 - background   I put RedSphere AND BlueSphere with drivers driver_Outer_RedSphere() &amp; driver_Outer_BlueSphere() limiting the display of each sphere to show only where each radius > halfway  On Layer-2 - foreground-1   I put RedSphere ONLY with driver driver_Inner_RedSphere() limiting the display of RedSphere to show only where its radius &lt;= halfway  On Layer-3 - foreground-2   I put BlueSphere ONLY with driver driver_Inner_BlueSphere() limiting the display of BlueSphere to show only where its radius &lt;= halfway    3) I rendered each layer to .PNG sequence [RGBA] (alpha channel for transparency)   Render Layer-1 - background   background : [sky]  Render Layer-2 - foreground-1   background : [transparent]  Render Layer-3 - foreground-2   background : [transparent]    4) I brought all 3 sequences into the Video Sequence Editor   Strip-1 - background   blend [cross] opacity [1.00]  Strip-2 - foreground-1   blend [alpha-over] opacity [0.50]  Strip-3 - foreground-2   blend [alpha-over] opacity [0.50]    5) Rendered the 3 layer final sequence to H.264  So the "aha moment" struck me right at the end when I was in the Video Sequence Editor:   "Don't try to make the Outer Spheres transparent, and see through to the Inner Spheres" "Instead overlay the Inner Spheres over the Outer Spheres, and limit the opacity of the Inner Sphere overlay"     So now I see my Inner Spheres in their true colours, but the colours are muted due to the .75 opacity - and hence it gives the visual impression that the Inner Spheres are in fact inside the Outer Spheres.  Thanks all for the input - it got me going in the right direction. Why is the top bar not changed on Stack Exchange, Area 51 and Ask Ubuntu? Irreducibility check for polynomials not satisfying Eisenstein Criterion. My Question is to check Irreducibility for polynomials not satisfying Eisenstein Criterion.  As an Illustration, to check whether $x^{p-1}+.....+x+1$ for p a prime is irreducible or not, we replaced $x$ by $x+1$ and by using Eisenstein's Criterion for the resulting polynomial we conclude that resulting polynomial is irreducible and so is the original polynomial.  In general, for a given irreducible polynomial $f(x)$ with coefficients in a known U.F.D, is there some element $a$ such that we can apply Eisenstein's criterion to $f(x+a)$?  I am sure there would be no general structure for this but I expect there to be at least some special cases.   Any Reference/suggestion would be appreciated.  Thank You. I understand if you travelling in or to the US, you can lock your luggage using the TSA Luggage Lock. (Immigration is still able to open your luggage using their own special keys)  How about Europe? Especially Heathrow + Charles de Gaulle?    If the TSA Lock is not acceptable in Europe, are there any other alternative precautions I could use instead?  (FYI, information about the ) How to copy symbolic links? Can the milky way actually be photographed ? I know the image is manipulated, and is probably a composite, but how do you capture such contrast in the milky way? Is an equitorially mounted scope required? Any advice or pointers are welcome, thanks.  I'm heading out towards much less light polluted areas middle of next week and I want to try some nighttime sky captures with my 7D.  Additional info: I just found  on wikipedia that says: 54s, tripod mounted 5D, 16mm lens, f/2.8, ISO800. What else do I need to be aware of? My 7D is only an APS-C and the widest lens I have is 19mm. I'm thinking that might not be wide enough to capture an interesting shot? How to derive variance-covariance matrix of coefficients in linear regression I am reading a book on linear regression and have some trouble understanding the variance-covariance matrix of $\mathbf{b}$:    The diagonal items are easy enough, but the off-diagonal ones are a bit more difficult, what puzzles me is that  $$ \sigma(b_0, b_1) = E(b_0 b_1) - E(b_0)E(b_1) = E(b_0 b_1) - \beta_0 \beta_1 $$  but there is no trace of $\beta_0$ and $\beta_1$ here. Groups of order $pq$ without using Sylow theorems If $|G| = pq$,  $p,q$ primes, $p \gt q, q \nmid p-1 $, then how do I prove $G$ is cyclic without using Sylow's theorems? If anonymity is so important, why is it not universal? A frequent argument brought up in support of voting anonymity is that it can lead to potential grudges. Certainly the review system is of the same nature.  I cannot wrap my mind around the fact that voting is anonymous and reviewing is not. Either both should be public--and this would be fine since public reviewing has been successful--or both should be anonymous--and I assume this would be the desired option since this community holds anonymity so dear.  One could say that voting rates the posts, the actual meat of the site, while reviewing is based on clarifying the purpose of the site and cleaning it up.   answer makes the point that the community can trust that votes are a good measure of quality for the very reason that they do not know who cast them; the mentality that a high-ranking member may have supported something could blur the line between "science" and "politics/religion."  Reviewing, then, can be seen as a judgment of specific members rather than quality of edit/questions, which seems to fall precisely under the "politics/religion" umbrella--the review system is much more vulnerable to grudges due to this.  So let's discuss the differences and the implications of these disjointed anonymity policies. IBM Slack links broken Last digits, numbers Can anyone please help me?  1) Find the last digit of $7^{12345}$   2) Find the last 2 digits of $3^{3^{2014}}$.  Attempt: 1)  By just setting the powers of $7$ we have $7^1 = 7$, $7^2=49$, $7^3=343$, $7^4 = 2401$, $7^5 = 16807$, $7^6 = 117649$, $\dots$  After the power of $4$, the last digits will repeat. Then by noticing the pattern the digits will end in $7,9,3$ and $1$.  Then we can divide the exponent $(12345)$ by $4$ since this is the cycle that makes it repeat. Then $12345 : 4$ has remainder $1$. So $7^1 = 7$ is the unit digit to $7^{12345}$.   So the last digit is $7$.   I know how to do it like this, the problem does not state how to find the last digit, but I know it has something do do with Euler's theorem.  for part $2$) I don't know how to start. Can anyone please help me?   Thank you for the help. In , I used quotes to demark specific terms, but after I posted the question, I wondered if I'm doing it right.  Usually, when quoting something a person says, the quotation mark goes after the comma or period, like so:     "This is my opinion," she said.   However, I sometimes use quotes not to represent something said by anyone, but instead for delineating a set term or phrase to make it clear that those words go together and none of them should be mistaken for a part of the rest of the sentence. Like this:     Should I say "stand up", "standup", or "stand-up"?   This looks weird to me:     Should I say "stand up," "standup," or "stand-up"?   ... but maybe I'm wrong about the rules.  Is it correct to use quotes in this way? And if so, are the quotes positioned correctly relative to the other punctuation marks?  Are there other alternatives for delineating terms without the use of quotes? Is there a subtle difference between "somebody" and "someone", "anybody" and "anyone"? Are there any subtle differences between "somebody" and "someone", or can they be used completely interchangeably? Similarly, can you imagine a situation in which you would prefer "anybody" to "anyone" or vice versa?