Why does the Sun "shine brighter" some days?
Why is the sun brighter in Australia compared to parts of Asia?
Does a card that affects 'each' creature affect creatures that enter the battlefield after it resolves? A question about the higher-order Weyl variation for the geodesic distance I have a question in deriving Eqs. (3.6.15b) and (3.6.15c) in Polchinski's string theory vol I p. 105.   Given      $$\Delta (\sigma,\sigma') = \frac{ \alpha'}{2} \ln d^2 (\sigma, \sigma') \tag{3.6.6}$$   where $d(\sigma,\sigma')$ is the geodesic distance between points $\sigma$ and $\sigma'$.   It is said for the Weyl variation $\delta_W$,     $$\partial_a \delta_W \Delta(\sigma,\sigma')|_{\sigma'=\sigma}= \frac{ 1}{2} \alpha' \partial_a \delta \omega(\sigma) \tag{3.6.15a} $$   $$ \partial_a \partial_b' \delta_W \Delta(\sigma,\sigma')|_{\sigma'=\sigma}= \frac{ 1+ \gamma}{2} \alpha' \nabla_a \partial_b \delta \omega(\sigma) \tag{3.6.15b} $$   $$ \nabla_a \partial_b \delta_W \Delta(\sigma,\sigma')|_{\sigma'=\sigma}= - \frac{  \gamma}{2} \alpha' \nabla_a \partial_b \delta \omega(\sigma) \tag{3.6.15c} $$   Here $\gamma=-\frac{2}{3}$.   I know the reason for the factor of $1/2$ in the RHS of Eq. (3.6.15a) and I can derive it. But, putting $\nabla$ on LHS and RHS of Eq. (3.6.15a) will not lead to (3.6.15c). I guess it is because there is some higher-order terms in the geodesic distance where the treatment of (3.6.9)-(3.6.11) omitted. But I don't know how to get it. I tried $ds^2= g_{ab} dx^a dx^b= (\eta_{ab} + h_{ab})dx^a dx^b $ to separate the deviation of Minkowski metric, but I cannot get the factor $\gamma$   My question is, how to derive Eqs. (3.6.15b) and (3.6.15c) (especially there is a prime, $'$, namely $\partial'_b$ in the LHS of (3.6.15b) but not in the RHS) I'm curious of how illusions would affect spells or abilities that require a target to be looking at something. A good example of this would be Medusa's Petrifying Gaze which has the following effect:  Petrifying Gaze: When a creature that can see the medusa's eyes starts its turn within 30 feet of the medusa, the medusa can force it to make a DC 14 Constitution saving throw if the medusa isn't incapacitated and can see the creature. If the saving throw fails by 5 or more, the creature is instantly petrified. [...]  So if someone were to cast Minor Illusion to put a bag over Medusa's head, would other player/creatures who do not realize that the bag is an illusion be affected by the gaze if they were looking in the direction of it? Does the illusion block the effect? How do I test for an empty JavaScript object? Is there a reason why we gain ghost reputation on the meta of an SE website? Is there any reason behind the ghost reputation we gain on the meta of a Stack Exchange site? This reputation doesn't add up to anything, but it still shows me I have gained some. Is this supposed to make any sense? Is there a function to round a float in C or do I need to write my own?       float conver = 45.592346543;   I would like to round the actual value to one decimal place, conver = 45.6. Why only light nuclei are able to undergo nuclear fusion not heavy nuclei? Is it because of the binding energy or the binding energy per nuclei .  I am having trouble with this whole binding energy and nuclear fusion concept. Rewrite rules goes away Let $X(n)$ denote number of all permutations of $\left\{1,\ldots,n \right\}$ that have only cycles of even length. Let $Y(n)$ denote number of all permutations of the same set that have only cycles of odd length. Count $X(2n)-Y(2n)$.   I don't know even how to start. I counted this sum for $n=1,2,3$ and it seems that it is always equal to $0$, but it doesn't help with calculating it in general. I'm using the package braket for my physics notes, and this speeds things up a great deal but I'm constantly writing \ket{\psi} or \bra{\psi}, and because this specific pair of bra and ket appears so often, this gets repetitive and I would like a macro to speed this up.  However since the braket package works only in math mode, my attempt \newcommand{\ketp}{$\ket{\psi}}$ work when I'm writing in text mode, but when I'm writing in mathmode it breaks (unsurprisingly).  Is there any way I can get this command to work in both mathmode and textmode without having to define two different macros, one for each?    Thanks in advance for any help.  P.S. I'm certain this is a very simple question but I could find little to no explanation of this feature. After enabling hibernate grub menu appears on start-up with 30s timeout My system is not dual boot just single OS UBUNTU 16.04. Prior to making the following changes, the Grub screen would not appear at start-up (OK).  After following these steps from  to enable hibernate in the system menu:   Open terminal and enter;   sudo nano /etc/polkit-1/localauthority/50-local.d/com.ubuntu.enable-hibernate.pkla  add the lines into the empty file;  [Re-enable hibernate by default in upower] Identity=unix-user:* Action=org.freedesktop.upower.hibernate ResultActive=yes  [Re-enable hibernate by default in logind] Identity=unix-user:* Action=org.freedesktop.login1.hibernate;org.freedesktop.login1.handle-hibernate-key;org.freedesktop.login1;org.freedesktop.login1.hibernate-multiple-sessions;org.freedesktop.login1.hibernate-ignore-inhibit ResultActive=yes  ^X then Y to save (a filename was suggested and I accepted without taking note).  Reboot for the changes to take effect.   hibernate now works and appears in the menu (OK) but whenever I reboot I now get a Grub menu at start up with a full 30 second timeout (NOK). I tried playing around with the Grub menu timeout settings but still get the full 30 sec timeout.  How do I stop the Grub menu from appearing and reduce my boot time to what it was before I made these changes.   Current Grub settings;   GRUB_DEFAULT="0" GRUB_HIDDEN_TIMEOUT="0" GRUB_HIDDEN_TIMEOUT_QUIET="true" GRUB_TIMEOUT="1" GRUB_DISTRIBUTOR="`lsb_release -i -s 2&gt; /dev/null || echo Debian`" GRUB_CMDLINE_LINUX_DEFAULT="quiet splash" GRUB_CMDLINE_LINUX="" Intuition for groups This is quite a non-standard question, certainly for mathematics, though I believe it is no less important (for me and my peers, i.e. grads).  The course I am reading so far introduced us to Groups, rings, fields, etc. in the first year, progressing to characters, reps etc in the latter years.  However, even with representation theory I still don't feel like I have a good intuition.  How do you gain intuition in such an area. I know there will be a response of doing examples, but this doesn't really help - I've done lots already.  Am I doomed. All group homomorphism from $ \mathbb{Z} _m $ to $ \mathbb{Z}_n $  How could I find every group homomorphism? I can't figure out how to line up the symbols of an itemize environment in beamer with the left part of the main text. In other words, I would like to supress the left margin in beamer itemize lists.  It would be nice if the solution worked with any itemize label defined with  \setbeamertemplate{itemize item}[]   In order to make myself clearer, what beamer produces by default is something like:  Main text. Main text. Main text...    * Item 1    * Item 2    * Item 3    ....   and the desired result is   Main text. Main text. Main text... * Item 1 * Item 2 * Item 3 .... Is there a way to edit SVG files in Illustrator where you can specify a CSS class for each path?  I already know in Illustrator that if you give the layer name an actual name, Illustrator will use that name as the path's ID, which is fine if you don't plan on reusing the icon more than once on the same page.  My current workaround is to just use the IDs method, but then later convert the IDs to classes in my code editor, but it's pretty annoying to have to do every time I generate my SVG sprite.  If that's currently not possible in Illustrator, are there any other apps that will allow you to specify that? Or maybe a Grunt or Gulp package?  It looks like you might be able to do it with Inkscape with a , so I might look at that if there's no other good solutions out there. Why does the x86-64 / AMD64 System V ABI mandate a 16 byte stack alignment? How can I show a supremum of a set is also its limit point? It just seems like I can't wrap my head around this. For a set $A$ how can I show that the supremum of that set $\sup(A)$ is also a limit point of said set? Can I just set $$a=\sup(A)$$ $$b\le a \: \:  \forall \: b \in A$$ and then show that there's a point different from $a$ in any $\epsilon$-neighbourhood for any $\epsilon&gt;0$? Or should I use a completely different approach? I'm looking for an answer considering both technical limitations and user experience.   Does it need a reload from a technical standpoint? Is it possible to interrupt spellcasting? As  suggests, there seems to be a hole in the D&amp;D Basic rules.  Maybe.  The rules for readying an action state:     When the trigger occurs, you can either take your reaction right after the trigger finishes or ignore the trigger.   This seems to imply that it is impossible to interrupt a spell in 5e.  If you set your trigger to be "I attack the Wizard when he casts a spell", then you make the attack after the spell has been cast.  Does this mean that spells can no longer be interrupted in combat like they could be in previous editions? Is there a reason why we gain ghost reputation on the meta of an SE website?